**Evaluation of Regression Analysis and Neural Networks to Predict Total Suspended Solids in Water Bodies from Unmanned Aerial Vehicle Images**

**Tainá T. Guimarães 1, Maurício R. Veronez 2,3,4,\*, Emilie C. Koste 2, Eniuce M. Souza 2,3, Diego Brum 2,3, Luiz Gonzaga Jr. 2,3 and Frederico F. Mauad <sup>1</sup>**


Received: 14 March 2019; Accepted: 22 April 2019; Published: 5 May 2019

**Abstract:** The concentration of suspended solids in water is one of the quality parameters that can be recovered using remote sensing data. This paper investigates the data obtained using a sensor coupled to an unmanned aerial vehicle (UAV) in order to estimate the concentration of suspended solids in a lake in southern Brazil based on the relation of spectral images and limnological data. The water samples underwent laboratory analysis to determine the concentration of total suspended solids (TSS). The images obtained using the UAV were orthorectified and georeferenced so that the values referring to the near, green, and blue infrared channels were collected at each sampling point to relate with the laboratory data. The prediction of the TSS concentration was performed using regression analysis and artificial neural networks. The obtained results were important for two main reasons. First, although regression methods have been used in remote sensing applications, they may not be adequate to capture the linear and/or non-linear relationships of interest. Second, results show that the integration of UAV in the mapping of water bodies together with the application of neural networks in the data analysis is a promising approach to predict TSS as well as their temporal and spatial variations.

**Keywords:** suspended solids; unmanned aerial vehicle; spectral imaging; artificial neural networks

### **1. Introduction**

The typical methodology for investigating water quality involves collecting water samples directly from various locations and laboratory analyses. While this method may result in accurate assessments of water body quality with limited areas, it is time consuming and expensive, and difficult to apply in large areas. Moreover, because the results are punctual, they do not necessarily reflect the quality of the whole site [1,2].

Alternative measures for in situ monitoring of water quality in lakes, dikes, and reservoirs can be obtained by means of remote sensing techniques. Such an application is only possible due to the presence of optically active components in the water. These substances can be identified via sensor systems in that their presence in a water body results in different absorption and backscattering patterns of the incident light, which are characteristic of each component. Among the parameters of water quality, suspended inorganic sediments, organic chlorophyll-a, and dissolved organic material are the main agents of absorption and scattering of electromagnetic radiation in a water body [3,4].

It should be noted that these components are directly related with the quality of the aquatic ecosystem and its surroundings. For example, total suspended solids (TSS), which represents the total amount of inorganic or organic particles drifting or floating in water [5], may be related to water pollution since these can serve as a transporting and storage agent of various pollutants, as well as erosive processes in a river basin (resulting in silting of major rivers and reservoirs) [4]. TSS concentration is often related to total primary production, heavy-metal and micro-pollutant flows, and in many turbid regions, is directly linked to sediment transport problems and the light available for primary production [6].

An indirect measurement of TSS in water bodies via remote sensing can compensate for deficiencies in manual water quality monitoring by being fast, allowing for continuous monitoring of large areas [2,7,8]. Most of the studies published on the TSS prediction from remote sensing involve the use of spectral data retrieved from satellite images. Because of its medium spatial resolution (30 m), in the studies of remote water sensing, one the most common satellites are Landsat, such as found in Qun et al. [2], Kong et al. [8], Din et al. [9], and Amanollahi et al. [10]. Song et al. [6] tested the images for medium spatial resolution IRS-P6 (Indian Remote Sensing Satellite) as well. Besides these, Wang et al. [7], Breuning et al. [11], and Moridnejad et al. [12] used MODIS (Moderate Resolution Imaging Spectroradiometer) satellite images and Campbell et al. [3] of the MERIS (Medium Resolution Imaging Spectrometer), with these having low spatial resolutions (250 and 300 m, respectively) and limited to large areas of water.

Thus, although remote sensing serves as a powerful technique for monitoring environmental and seasonal changes, and its ability to remotely monitor water resources has increased in recent decades because of the improved quality and availability of satellite imagery data [13], the analysis of small water bodies may not be adequate due to the medium image resolution of the most usual commercial satellites [1]. In this case, the use of aerial images obtained by unmanned aerial vehicle (UAVs) for monitoring small bodies of water has presented good results and becomes promising for producing greater detail due to high spatial resolution and the possibility of constant monitoring [14,15].

Although some applications of UAVs for water quality parameters monitoring, such as chlorophyll-a [1,15–17], organic matter [18], and suspended solids [1,18–20], have been demonstrated in the literature, there are still few studies focused on this application. For suspended solids monitoring, for example, Veronez et al. [18] and Saénz et al. [19] used regression analyses between TSS values measured in the laboratory and the UAV responses in the visible and near infrared (NIR) regions to generate their prediction models. Saenz et al. [19] explored relations between individual bands and combinations between them (as NIR-red, for example), and Veronez et al. [18] chose to relate to vegetation indexes such as normalized difference vegetation index (NDVI) and normalized difference water index (NDWI). Although both mentioned studies have shown positive results, the modeling of these parameters in complex environments is not always possible through regression analysis.

Therefore, cognizant of the limitations that techniques such as regression analysis has, the need for research and improvement of inland waters monitoring techniques integrated with the facilities provided by the technologies developed and available in the market can be seen. Among these modern techniques that can provide the support for the monitoring of waters via remote sensing is the artificial intelligence with the use of neural networks.

Approaches involving neural networks are promising in the area of remote sensing and the development of water quality models because they can be more sensitive and robust than other traditional regression techniques, with the ability to capture both linear and non-linear relationships between the involved parameters [8,12,13,21]. However, results presented in the literature on artificial neural networks (ANN) approaches in water bodies use mainly satellite imagery of low [12] to medium [8,13,21] spatial resolution.

No papers were found that included the application of artificial neural networks to the analysis of high spatial resolution images obtained using UAVs, and therefore, this study intends to fill this gap. The aim of this article was to use remote sensing technologies to evaluate water quality, identifying an

alternative method for monitoring and quantifying the concentration of suspended solids in water, through the correlation between UAV images and limnological data using regression analysis (RA) and artificial neural networks (ANN). Furthermore, this study aims to contribute to the development of temporal and spatial water quality monitoring techniques through modern remote sensing tools and artificial intelligence.

The manuscript is structured as follows: Section 2 contains the information about the field site, the acquisition of the data, and its subsequent analyses; in Section 3, we present and discuss the results of the research on the concentration of TSS, regression models, and ANN; and finally, Section 4 presents our conclusions regarding the study, with indications of its importance and its continuity.

### **2. Materials and Methods**

The method that we are proposing can be structured according to the following steps: GNSS (Global Navigation Satellite System) data acquisition, water sampling and laboratory analysis, overflight with the UAV and processing of the images, extraction of values from images UAV, regression analysis, and training and testing of the ANN. The flowchart of the proposed method is depicted in Figure 1 and detailed in the following subsections.

**Figure 1.** Flowchart of the proposed method.

### *2.1. Field Site*

The adopted study site was the lake on the Unisinos University campus, located in the state of Rio Grande do Sul, southern Brazil (Figure 2). The lake is artificial, has an area of approximately 0.025 km2 and maximum depth of 4 m. Although small, it is located at the lowest altitude of the campus, and because it is formed from rainwater drainage collected at the university, it contains several inorganic and organic compounds found in the form of suspended solids or organic matter from rainwater runoff [18].

The lake and its surroundings also function as an ecosystem for several species of animals, such as ducks, geese, and several other birds, as well as a great diversity of fish. Because it is a university campus, the area has several buildings, paved areas, and a large circulation of people and cars. However, the campus also has several vegetated areas, mainly around the lake, as can be seen in Figure 2.

**Figure 2.** Location of the study site.

Studies addressing the applicability of remote sensing in the monitoring of water bodies have already been developed in this area. Guimarães et al. [17] used spectral data collected in the field and UAV images to model the chlorophyll-a concentration in the environment. Veronez et al. [18], based on UAV images, applied neural networks to estimate Landsat 8 OLI satellite bands and correlated this with data on suspended solids and dissolved organic matter.

Studies including the characterization of this lake, the behavior of the limnological variables, and their relationships with the remote sensing variables are important as they serve as pilot studies to be applied in larger water bodies.

### *2.2. Data Acquisition*

We performed two field samplings in March 2016 and 2017 during the transition period between the seasons of summer and fall. The collections were carried out in a single day and we ensured that the climatic conditions of both days were similar. The average temperatures were between 22 and 24 ◦C, winds with a speed of 0.4 ms−<sup>1</sup> (southeast direction), and without the occurrence of precipitation events on the days of the collections.

On the same days, the UAV overflew the area and in situ collection of water samples occurred such that the two pieces of information could be compared as being representative of the same conditions of the lake. Besides, possible temporal variations from one year to another can be evaluated for the collected data and compared to the predicted one from the analyzed RA and ANN methods.

We selected 21 sample points, as shown in Figure 3, that were spatially distributed over the lake such that surface water samples (up to 0.5 m) were collected for the laboratory determination of suspended solids using the gravimetric method described in the Standard Methods for the Examination of Water and Wastewater [22].

**Figure 3.** Sample points used in the survey.

The UAV used to take the images was the SenseFly, Swinglet CAM model (SenseFly Parrot Group, Cheseaux-sur-Lausanne, Switzerland). It was coupled to a Canon ELPH 110HS (Canon U.S.A., Inc., New York, NY, United States) camera with a 16-megapixel resolution and was factory-modified to capture the NIR band instead of the red band. Thus, mapping was in three distinct channels, namely: near infrared (NIR), green (G), and blue (B).

As well as the sampling points for water collection, in the field we also established and tracked six ground control points (GCPs), through the GNSS (Global Navigation Satellite System), based on the RTK (real time kinematic) method, located in the area of coverage of the flight such that later their positions were used in the georeferencing of the images obtained.

The images obtained using the UAV were processed using the PIX4D software, version 2.1 (Pix4D S.A., Lausanne, Switzerland), in which the images were orthorectified and georeferenced, where we adopted the SIRGAS 2000 (Geocentric Reference System for the Americas) as the reference system, in the UTM (Universal Transverse Mercator) −22S projection zone. We generated orthophotos with a pixel size of 5 cm × 5 cm.

### *2.3. Data Analysis*

In order to perform analysis between the data collected of the water quality and those obtained via remote sensing, we plotted the sample points where samples were collected in the orthophotos generated by the overfly with the UAV and extracted the values of the pixels concerning each point for the NIR, G, and B channels. We emphasize that among the collected values of the two years (n = 42), four were disregarded because the points were located in a shaded area of the image. Thus, a sample of 38 points was considered for the analysis.

We used this data to predict the suspended solids concentration in Lake Unisinos using linear and non-linear regression analysis (RA) and artificial intelligence through an artificial neural network (ANN). The aim of this step was to identify a model to quantify the concentrations of suspended solids present in the water using the information obtained through remote sensing. We evaluated their performances using the following statistical metrics: coefficient of determination (R2) and root mean square error (RMSE).

Linear and non-linear regression models were investigated. The considered non-linear functions were exponential, logarithmic, quadratic, and power (range from −1 to 1). Knowing that different concentrations of suspended solids present different responses for each wavelength, to predict TSS in RA models, we considered as independent variables each channel individually (NIR, G, and B) and the operations of bands (sum, subtraction, and ratios) to highlight the spectral characteristics of the compounds [6–8,13,21]. Thus, besides the simple regressions with the covariates included individually, multiple regressions were considered with two or more independent variables combined, taking care to avoid dependence among the covariates.

Considering the sample size of this experiment, all 38 observations were used for RA modeling because the probabilistic assumptions of this class of models. After adjustment, the usual residual verifications related to the distribution (Gaussian), independence, and homoscedasticity were checked. If the estimated model was adequate, a cross-validation step could be performed where one observation at a time was left out of the adjustment for comparison or a sample part was reserved when the sample size was large.

In the TSS prediction from the ANN, which is a distribution-free method, the neural network modeling considered two processing steps, the first being the training of the network, and the second being its subsequent testing with a data set different from the first stage. In this study, we used 80% of the data collected for ANN training and 20% for testing, which were randomly defined [23].

As the objective of the method was to create an ANN capable of recovering the concentration of suspended solids in the water from the bands of the modified Canon sensor incorporated into a UAV, we considered the normalized values of the NIR, G, and B channels as inputs to ANN, and the TSS concentration as an output at the same sampling point. We used a network of feed-forward backpropagation, with this being commonly used in remote sensing studies [8,10,21].

During the training phase, several tests were carried out in order to obtain the best ANN topology applicable to this study, choosing the network that provided the highest correlation coefficient and the lowest mean square error during training and testing. We tested different numbers of neurons (from 5 to 20) in one single hidden layer, as well as three activation functions (sigmoid, tangent, and linear), and the number of training cycles.

### **3. Results and Discussion**

The results of the laboratory analyses were satisfactory for the research and compatible with prior knowledge of the water quality in the study area and analysis of the spatial behavior of these parameters, which would later be compared with the UAV images. Table 1 shows the descriptive statistics of the total suspended solids (TSS) analyzed in this research for March 2016 and 2017.



We observed from the analysis of the data presented in Table 1 that the characteristics of the study lake were not the same between the two collections. This was also confirmed from the Wilcoxon test at

a 95% confidence level. There was a decrease in the concentration of suspended solids from 2016 to 2017, which can be seen in the averages, medians, maximum, and minimum values of Table 1.

This difference in TSS concentration, although small, can be justified because although it did not rain on the days of sampling in 2016 and 2017, there were rainfall events in the week before the collection of 2016 (85 mm according to the experimental climatological station located at Unisinos University), which did not occur in 2017. Allen et al. [24] point out that in impermeable urban areas, the flow of rainwater in the soil causes the collection of the pollutants and sediments from these surfaces, which are transported to the nearest waterways. As the lake receives the drainage of rainwater from the university campus, it is expected that in rainy periods, various compounds will be carried into it, increasing the concentration of suspended solids, for example.

As initial cartographic products, obtained via overflying with the UAV in 2016 and 2017, and by processing the images, we have the orthophotos of the area, as shown in Figure 4.

**Figure 4.** Orthophotos generated by the overfly with UAV in March 2016 and 2017.

The simple and multiple linear and non-linear RA described in the previous section were evaluated; however, most of the results were unsatisfactory. Table 2 shows the best results that we obtained in these analyses. Although not shown, residual analyses were performed to check the error assumptions.



According to Table 2, the best adjustments of the simple regression analyses were for the NIR and G/NIR variables, agreeing with Song et al. [6] and Amanollahi et al. [10], although both studies obtained better results than ours (0.7 for Amanollahi et al. [10] and above 0.9 for Song et al. [6]). Also, a combination of B and G/NIR was the best result for the multiple linear regressions.

Although the regression models in Table 2 showed statistical significance, the low R<sup>2</sup> values indicate that the RA models were not ideal for TSS recovery in the study area. This result can be explained by the optical complexity of the study waters such that the relations between the bands of the collected images and the concentration of TSS could not be explained by traditional regression techniques.

To improve the accuracy of TSS predictions, ANN can be effective. Kong et al. [8] emphasize that ANN models establish different weights for each input in the network and thus take full advantage of the characteristics of TSS included in the different bands.

We performed several trainings of neural networks with different topologies. In Table 3, the results include a coefficient of determination (R2) greater than 0.5 in the training step and their respective topologies, activation functions, number of epochs, and time of training are presented.


**Table 3.** Results of the ANN training for R2 > 0.5.

<sup>a</sup> with "input (3)-neurons-output (1)". <sup>b</sup> Hidden layer/output layer. <sup>c</sup> Where the computer used had the following configuration: processor—Intel® Core ™ i3-4005U CPU @ 1.70 GHz <sup>×</sup>4, memory—4GB DDR3 1600MHz RAM.

According to Table 3, the topology in which we obtained the smallest RMSE and the highest determination coefficient was 3-7-1, with the tangent function as the activation function, and with 300 training cycles. Thus, the ANN adopted was a feed-forward backpropagation type, with three input layers (NIR, G, and B), seven neurons in a single hidden layer, and one output (TSS). As usual, the training processing time depended on the number of epochs and was not a problem in our experiment because of the reduced sample size.

The results that we found in the training and testing steps for this best ANN are presented in Table 4. The graph presented in Figure 5 demonstrates the comparison between the data measured in the laboratory and those estimated through ANN.

The ANN training stage resulted in an R2 of 0.84 and RMSE of 1.33, while during testing, these values were 0.57 and 2.97, respectively. As shown in Table 4 and Figure 5, considering all the data collected in this study as inputs to the ANN, the R2 was 0.75 and the RMSE was 1.81.

As expected, the results showed a significant improvement in the prediction of suspended solids data in the study area through the use of ANN in place of the simple and multiple linear and non-linear investigated RA.


**Table 4.** Results of the ANN.

**Figure 5.** Comparison between TSS measurements and estimated values from the ANN model in training (black) and testing (red) set using March 2016 (circular shape) and 2017 (triangular shape) samplings.

Although several studies show good results using regression methods to predict TSS [2,7,11,15–19], others, such as Song et al. [6], Amanollahi et al. [10], Moridnejad et al. [12], and Wu et al. [25], compared the two methodologies (RA and ANN) and obtained results indicating better quality in the prediction of the data through an ANN, signaling the capacity of the neural networks to model more complex and non-linear relations between the parameters. Only Kong et al. [8] reported that an ANN did not present better results than regression methods for TSS predictions in their area of study.

Din et al. [9] used statistical correlation analysis only as a support for choosing the ideal bands of the Landsat 8 OLI satellite for an ANN input. Then, the authors decided to include also the bands of the short-wave infrared (SWIR-1 and SWIR-2) as inputs, which is not common in papers about ANN for predicting water quality parameters since only visible and near infrared regions are exploited [6,8,10,12,13,21,25,26].

Although the aforementioned approaches from the literature are similar to our paper for comparing RA and ANN for the prediction of TSS, we point out that our results differ and are highlighted by the high spatial resolution of the UAV images used in comparison to low or medium spatial resolutions of the satellite images of other studies. Thus, our method allows for giving more geographically accurate TSS predictions because of the small pixel size of the UAV images (5 cm in comparison to 30 m for Landsat, for example) and generating high quality and resolution TSS monitoring maps.

Finally, the ANN model was used to predict the TSS concentration for the whole lake using the NIR, G, and B variables for the 2016 and 2017 UAV images. Thus, the generated TSS maps for Lake Unisinos are shown in Figure 6.

While analyzing Figure 6, we noticed the highest concentrations of suspended solids in the 2016 sampling compared to the 2017 one, a situation that was already indicated in Table 1. Besides, the used data set presented a significant statistical difference between the two years, where the spatial distribution also became evident in Figure 6. The highest concentrations of TSS in 2016 were in the lower central region of the lake, whereas in 2017, they were near the lower-right margin. A large part is found in the center of the lake for 2017 with the minimum TSS values. This difference in spatial distribution, mainly showing as a large TSS concentration in 2016, is consistent with the in situ collected water samples and is also explained by the rain that occurred in the previous week of the field collection in 2016. Figure 6 also shows that TSS concentrations were in the same range (9.33 to 23.75 mg/L) for both years. In this sense, to verify if the statistical characteristics of the prediction, data remain close to the observed ones, where Figure 7 shows the box plot of TSS concentrations for both observed and predicted values in March 2016 and 2017.

**Figure 6.** Maps of predicted TSS based on the ANN model for March, 2016 and 2017.

**Figure 7.** Box plot of TSS concentrations for observed and predicted values in 2016 and 2017.

From Figure 7, we can see the similarity between the observed and predicted distributions, even though this was not a large sample. From the Wilcoxon test, which is adequate for asymmetric distributions, the null hypothesis of equal medians was not rejected at a 5% significance level (*p*-value = 0.74). From the same test, the statistically significant difference between the years already seen for the observed TSS values was maintained for the predicted TSS (*p*-value = 0.0007). The observed average that was 16.27 and 13.65 (Table 1) became 15.72 and 12.51 for the predicted TSS in March 2016

and 2017. The variance coefficient also remained similar, 17.51% and 22.56%, which are close to 19.77% and 23.65% presented in Table 1.

Although the results of this study confirm the viability of the prediction of the concentration of TSS from remote sensing data and ANN, we emphasize that because it is a new methodology and that is still under development it has some limitations that should be considered.

For example, since each water body has its own characteristics (hydraulic, physical, chemical, and biological), which are related to its surroundings and the region's climate, the proposed model in this study was trained relative to these conditions of the study area. Thus, it is necessary to develop regional models adapted to the area of interest of the study. Other authors like Kong et al. [8] and Chen et al. [26] also point out the absence of a standard model for different regions.

In relation to temporal variation, we point out that the field samplings were carried out in March of the two years and therefore the seasonal variation of TSS (not considered in this study) may indicate that a single model trained with data from only one season is not sufficient to predict other values throughout the year. Another factor that stands out is that besides the seasonal variation of TSS, other changes can occur in the natural environments over the years. Once the environmental characteristics are modified, it is not possible to affirm the capability of the trained neural network to predict data in the long term at this time. Thus, the monitoring of TSS from remote sensing does not rule out laboratory analyses from time to time. For instance, if the predictions exhibit unexpected behavior, such as a growth trend, new TSS and spectral data may be collected to check if it is a real change in the TSS or the neural network needs to be updated for current conditions.

Finally, although studies as this serve as pilot studies to be applied in larger water bodies, we emphasize that adaptations need to be made for this to occur because when flying with a UAV in lakes and dams because large homogeneous areas makes it difficult to generate orthophotos and products generated from the Structure for Motion (SfM) technique. One of the ways to minimize this problem would be to perform high altitude flights, facilitating the identification of homologous points in the images for generating the orthophoto, but which would result in a loss in resolution of the images.

The presented limitations indicate that this research needs to be continued. Nevertheless, what we have demonstrated in this article should instigate replications of this method in other water bodies such that more involved communities benefit from our positive results. This can be done through area flyovers with UAVs with RGB and NIR cameras, correct processing of acquired images, reliable data collection of water quality, and the establishment of an ANN with the ideal parameters for the prediction of interest, which can be TSS as in this study, or for example, chlorophyll-a or organic matter.

The prediction of TSS in water bodies from images acquired using a UAV and processed via an ANN should benefit managers, professionals, and researchers linked to the management and control of water resources by presenting a method for the dynamic and spatial monitoring of water quality problems, such as the presence of suspended solids.

### **4. Conclusions**

The use of UAVs in the mapping of water quality is shown to be a promising tool because it alleviates issues found in the usual in situ monitoring, such as the insufficiency of data, high time and money costs, and modeling via remote orbital sensing, such as the low spectral and temporal resolutions. Through analysis of the response that the sensor on board the UAV collected in the regions of visible and near infrared, it was possible to model the concentration of optically active compounds, such as suspended solids, and generate maps that allowed for their temporal monitoring and spatial analysis at the study site.

We emphasize the applicability of the use of artificial intelligence through artificial neural networks to meet the need for modeling suspended solids in complex aquatic environments, where more simplistic analyses, such as the regression models presented in this study, may not be sufficient. The use of an ANN instead of RA significantly improved the quality of the results from the generated models, where R<sup>2</sup> values rose from 0.20 (RA) to 0.75 (ANN).

However, although the model presented could accurately predict suspended solids concentrations compatible with the statistical features of the in situ observed values, its use was limited only to the study area where the ANN was trained and calibrated, and possible adaptations to it are required for use in other environments.

The presented results are important for two main reasons. First, although regression methods have been used in remote sensing applications, they may not be adequate for capturing the linear and/or non-linear relationships of interest. Second, they show that the use of UAVs in the mapping of water bodies together with the application of neural networks in the analysis of the results obtained is a promising approach and has the potential to assist in monitoring the quality of these environments. Thus, we intend to continue monitoring the total suspended solids concentrations in Lake Unisinos by performing new overflights with a UAV in the region and simulating the data collected with the neural network.

We also emphasize the need to continue the research in order to improve the generated model, as well as to consider the interference of other optically active compounds, such as chlorophyll and organic matter, in the spectral response of water, and consequently, in the neural network generated.

**Author Contributions:** T.T.G., E.C.K., and D.B. were responsible for collecting and processing the images obtained from the UAV. T.T.G. and E.C.K. were responsible for water collection and for the laboratorial analysis. T.T.G., M.R.V., and L.G.J. implemented the artificial neural network. T.T.G., E.M.S., D.B., and L.G.J. were responsible for analyzing the data. T.T.G., M.R.V., and E.M.S. wrote the paper. M.R.V. and F.F.M. reviewed the paper. All the authors have read and approved the paper final version.

**Acknowledgments:** M.R.V. and F.F.M. thank the Brazilian Council for Scientific and Technological Development (CNPq) for the research grant. T.T.G. thanks DS/CAPES for the financial support of the MSc scholarship. D.B. thanks CAPES for the financial support of the MSc scholarship.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

*Review*

## **Reducing Groundwater Contamination from On-Site Sanitation in Peri-Urban Sub-Saharan Africa: Reviewing Transition Management Attributes towards Implementation of Water Safety Plans**

### **Felix R. B. Twinomucunguzi 1,\*, Philip M. Nyenje 1, Robinah N. Kulabako 1, Swaib Semiyaga 1, Jan Willem Foppen <sup>2</sup> and Frank Kansiime <sup>3</sup>**


Received: 15 April 2020; Accepted: 19 May 2020; Published: 21 May 2020

**Abstract:** High urbanization in Sub-Saharan Africa (SSA) has resulted in increased peri-urban groundwater contamination by on-site sanitation. The World Health Organization introduced Water Safety Plans (WSP) towards the elimination of contamination risks to water supply systems; however, their application to peri-urban groundwater sources has been limited. Focusing on Uganda, Ghana, and Tanzania, this paper reviews limitations of the existing water regime in addressing peri-urban groundwater contamination through WSPs and normative attributes of Transition Management (TM) towards a sustainable solution. Microbial and nutrient contamination remain prevalent hazards in peri-urban SSA, arising from on-site sanitation within a water regime following Integrated Water Resources Management (IWRM) principles. Limitations to implementation of WSPs for peri-urban groundwater protection include policy diversity, with low focus on groundwater; institutional incoherence; highly techno-centric management tools; and limited regard for socio-cultural and urban-poor aspects. In contrast, TM postulates a prescriptive approach promoted by community-led frontrunners, with flexible and multi-domain actors, experimenting through socio-technical tools towards a shared vision. Thus, a unified risk-based management framework, harnessing attributes of TM and IWRM, is proposed towards improved WSP implementation. The framework could assist peri-urban communities and policymakers in formulating sustainable strategies to reduce groundwater contamination, thereby contributing to improved access to safe water.

**Keywords:** contamination; integrated water resources management; groundwater; pollution; Sub-Saharan Africa; transition management; water safety plan

### **1. Introduction**

Groundwater contamination by human activities is a growing global concern in light of increasing population, urbanization, industrialization, and agriculture [1,2]. Over one-third of the global water use is derived from groundwater, which is under increasing stress from anthropogenic contamination and diminishing resource quantities due to over-extraction and climate change effects [2]. On-site sanitation practices for disposal of human excreta and greywater are major contributors to groundwater contamination, especially in peri-urban areas where settlement patterns are dense [3,4]. On-site sanitation facilities, mainly pit latrines and septic tanks, remain the primary form of improved

sanitation in rural and peri-urban areas in most of the developing world, including Sub-Saharan Africa (SSA); South, East, and Central Asia; Southern and Middle America, and Oceania [4–6]. While such facilities have promoted access to improved sanitation to the peri-urban communities, their increased number, and usually poor construction and maintenance, results in increased groundwater contamination [4,7–13]. Groundwater contamination by on-site sanitation systems in SSA is, thus, a significant hindrance to providing access to safe water to vulnerable populations [7–9]. Indeed, SSA lags behind other regions of the world in the struggle to meeting sustainable development goal (SDG) number 6 on universal access to safe water and sanitation [5,14].

Sub-Saharan Africa continues to register unprecedented urbanization, mainly occurring in peri-urban areas, which have low access to safe water and sanitation [10–12]. Groundwater, drawn mainly from boreholes, shallow wells, and springs, is the predominant source of water for domestic consumption, small scale industry, and irrigation to the majority of peri-urban residents in SSA due to its relatively low cost of abstraction and high availability [3,7,9]. Despite this high reliance on groundwater, on-site sanitary practices have increased contamination, leading to severe human health and ecological consequences [12,15–17]. For instance, Murphy et al. [18] reported that over 60% of groundwater sources tested in Kampala (Uganda) were positive for *Escherichia coli* (*E. coli*), which is commonly attributed to fecal contamination, during a typhoid outbreak in 2015, which affected more than 10,000 people. The scale and nature of the contamination and associated risks increase in complexity with a growing population.

The failure to address groundwater resource challenges, such as the increasing stress of groundwater resources due to contamination by on-site sanitation in peri-urban areas, can be attributed to limitations in the groundwater management (governance) framework [12,19,20]. Vardy et al. [20] described groundwater governance to include elements of institutional setting; availability and access to information and science; robustness of civil society; and economic and regulatory frameworks. Generally, groundwater governance has evolved within the overall realm of water governance, dating back to the Helsinki Rules on the use of waters of international rivers in 1966 [19]. Globally, there have been several groundwater governance approaches, depending upon the geographical scale (local, regional, or transboundary). These have included approaches based on 1) international water law and political ecology perspectives, especially in transboundary aquifer governance [19,21–23]; institutionalism, including management of "common pool resources" through polycentric approaches advanced by Elinor Ostrom and associates [24–26]; economic and market regulation perspectives [20,27]; and socio-ecological approaches [19,28]. Generally, the current water governance framework in SSA is mainly influenced by Integrated Water Resources Management (IWRM) principles, adopted after the International Conference on Water and Environment (Dublin) and the United Nations Conference on Environment and Development (Rio de Janeiro), both in 1992 [29]. However, despite the high importance of groundwater resources, it has always received less profiling within the overall water governance frameworks [19,22,30–32].

Many countries in SSA embraced IWRM as a multi-stakeholder framework towards addressing water resources challenges, including contamination [33–35]. IWRM is defined as 'a process which promotes the coordinated development and management of water, land and related resources, in order to maximize the resultant economic and social welfare in an equitable manner without compromising the sustainability of vital ecosystems' [29]. IWRM introduced improved integrated policies, and improved participatory and gender-responsive approach, which have provided an enabling environment for implementing water resources improvement initiatives. However, implementation of IWRM in SSA has faced several challenges, including; (1) a high level of diversity (ambiguity), leading to complexity and limited action to address specific societal challenges [30,33–36]; (2) contested institutional framework based on catchment-based structures [32,37–40]; (3) ineffective stakeholder participation and cooperation frameworks [30,37]; (4) undefined monitoring framework for assessing results [33,39]; (5) ineffective cost recovery mechanisms [35]; and (6) limited resources to implement the ambitious targets of IWRM approaches [40]. These IWRM experiences have influenced the adoption and implementation of water resources management initiatives within the water sector in SSA [40].

In 2004, the World Health Organization (WHO) introduced Water Safety Plans (WSPs) as an instrument for identification, prevention, and management of contamination risks to water supply systems, which has been adopted in SSA as well [41–43]. The WSP approach is based on the principles and steps of the "Multiple-Barrier" concept for prevention of contamination to water sources and the "Hazard Analysis and Critical Control Points (HACCP)" concept, adopted from food safety management systems [44]. The WSPs are intended to ensure continuous provision of safe water, free from any contamination, for all levels and types of community water supply systems [41,44]. WSPs have been implemented, mainly by water utilities, in all regions of the world, voluntarily or by regulation [42,45]. Uganda was among the first countries in SSA to implement WSPs for prevention of pollution to public water supplies [45]. Ghana and Tanzania have also recently adopted implementation of WSPs for protection of public water supplies [42]. Although WSPs have mainly been implemented for conventional urban water supply systems, with complex infrastructure, there have also been efforts to apply them for improvement of the safety of basic water supply infrastructure in rural and peri-urban areas [46]. However, like other management instruments, adoption and implementation of WSPs is greatly influenced by the existing water governance regime [47–51]. The influence of the existing water regime (IWRM) towards the implementation of WSPs for addressing peri-urban groundwater contamination, in particular, has not been comprehensively documented. An analysis of the challenges to the existing framework in implementing WSPs to address the growing challenge of peri-urban groundwater contamination would identify the gaps, which can be addressed by emerging management concepts.

Transition Management (TM) is an emerging management framework, within the context of sustainability science, which has been explored in various developing and developed countries to address complex socio-technical sustainability challenges [52–54]. TM is described as a 'prescriptive and descriptive, complex-based governance framework towards long-term social change through small steps basing on searching, learning and experimenting' [52]. TM has evolved in the past two decades in the realm of sustainability science, attempting to provide solutions to societal complex and persistent problems [52,53]. Groundwater contamination by on-site sanitation in peri-urban SSA is certainly one such challenge, which could benefit from developments of the emerging field of TM. TM acknowledges that societal problems are getting more complex with increased pressures like population growth, climate change, and technological advancement, and traditional management approaches are ill-equipped for this complexity [55]. Since 2015, a project has been implemented by the research team, T-group, focusing on adapting TM approach towards improved peri-urban groundwater management in Uganda, Ghana, and Tanzania [56,57].

Through a critical review, this paper aims to highlight the existing water regime challenges towards implementing WSPs for protecting peri-urban groundwater against contamination by on-site sanitation and explore normative attributes of TM towards a sustainable solution. The paper first illustrates the complex socio-technical system influencing peri-urban groundwater contamination arising from on-site sanitation in peri-urban SSA and then reviews the challenges of IWRM framework and the normative attributes of TM framework towards improved risk management. Using the Entity-Relationship Diagramming (ERD) technique, complementary attributes of IWRM and TM are demonstrated in a proposed risk-based management framework for reducing peri-urban groundwater contamination by on-site sanitation through WSPs for small communities. This framework could be a sound tool for comprehensive assessment and formulation of strategies to improve adoption and implementation WSPs targeted at reducing peri-urban groundwater contamination in SSA.

### **2. Methodology**

The literature survey was conducted in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines [58]. Relevant documentation (both published and unpublished) were searched, with no date restrictions, from Google Scholar, Google, Scopus, Water Safety Portal, and Web of Science. Titles of all retrieved documents were reviewed to remove any duplications followed by an analysis of abstracts for eligibility. Eligible documents included those that contained information on groundwater contamination/pollution, on-site sanitation, water contamination risk management, water safety plans, integrated water resources management, groundwater management/governance, aquifer management, and transition management. The full-text analysis was only undertaken for the documents with implication to SSA context, with particular focus on Ghana, Uganda, and Tanzania. Relevant subject articles and documents from WHO and other sources pertinent to WSP and groundwater contamination by on-site sanitation were also included in the review. The documents reviewed also provided additional sources, which were assessed for eligibility. The review was conducted between January 2019 to May 2020. Figure 1 shows the flow diagram for the literature review.

**Figure 1.** PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) flow diagram for the literature survey.

From the comprehensive review, the governance factors influencing implementation of WSPs for reducing peri-urban groundwater contamination in SSA were analyzed and represented using Entity-Relationship Diagramming technique (ERD). ERD can be used to visually display qualitative data on system entities, their relationships, and attributes [59]. Content validation of the proposed framework was achieved through expert opinion and stakeholder consultation at a stakeholder workshop held in Entebbe (Uganda), in February 2020. The workshop was attended by 37 participants drawn from government institutions, private sector, and research institutions. Iterative improvements were made to the final version presented.

### **3. Understanding the Complex Socio-Technical System Influencing Groundwater Contamination by On-Site Sanitation in Peri-Urban SSA**

On-site sanitation, through pit latrines and septic tanks, is the predominant sanitation system used in peri-urban areas for disposal of human waste in most of SSA, and the developing world, particularly in Asia, Middle America, and Oceania [3–8]. In the developed world, including Europe and North America, on-site facilities, mainly in the form of decentralized treatment options, are mostly used in the rural setting [60,61]. While on-site systems have contributed to the increased access to improved sanitation in peri-urban areas, they have been reported to be a source of contamination hazards to groundwater, which is used by many peri-urban dwellers [1–10,12,15–18,60,61]. Table 1 summarizes recently documented cases of peri-urban groundwater chemical and microbial contamination from on-site sanitation in the three focus countries of Uganda, Tanzania, and Ghana.


**Table 1.** Recently documented cases of urban groundwater contamination by on-site sanitation in Uganda, Tanzania, and Ghana.

<sup>1</sup> Data covering the period of 2010–2020.

From Table 1, it can be noted that *E. coli*, fecal coliforms, and salmonella are widely studied in peri-urban groundwater matrices in SSA. Due to increased access to modern analytical methods in SSA, previously un-detected microbial groundwater contaminants like viruses are also increasingly being analyzed and reported [70]. Chemical contamination has also been well documented, arising from on-site sanitation facilities, especially with respect to nitrate contamination (Table 1). High nutrient (nitrate and phosphorous) and microbial groundwater contamination by on-site sanitation are also widely reported in countries of other regions of the world, including India [4], France [60], and Sweden [61]. Shivendra and Ramaraju [4] reported microbial contamination in the majority of wells sampled from Kanakapura town (India), with nitrate concentration of up to 45.9 mg/L, which is comparable to the Table 1 data. In the developed world setting, there is growing concern over emerging organic and inorganic contaminants, including pharmaceutical and personal care products, which could be attributed to on-site sanitation systems [17,71]. However, there is still limited information on occurrence, distribution, and ecological effects of emerging contaminants in peri-urban groundwater in the SSA context, which could also potentially be attributed to on-site sanitation practices [17,71–73].

The WHO introduced WSPs as a management tool towards identification, reduction, and prevention of such hazards (Table 1) in a water supply system, from catchment to consumer [41]. Rickert et al. [44] provided a simplified WSP process for small communities encompassing six steps from assembling a WSP team, describing the community water supply system, hazard assessment, deriving improvement plans, monitoring, and finally reviewing the WSP process (Figure 2). The process acknowledges consideration of societal and technical factors across the entire catchment, which may affect the quality of a water supply system. The process, thus, attempts to integrate comprehensive technical and socio-institutional aspects influencing risks to water supply stems. A socio-technical

approach to resolving groundwater resources challenges has gained prominence due to the complexity of interactions [74,75].

**Figure 2.** Tasks to develop a Water Safety Plan (WSP) for small communities (adapted from World Health Organization (WHO) [44]).

These socio-technical regime factors, thus, significantly influence the adoption and implementation of technologies, processes, and management tools, such as WSPs. Socio-technical regime factors can be summarized into five dimensions of (1) policy and regulation, (2) institutions, (3) science and technology, (4) user and market dynamics, and (5) socio-cultural considerations [76–78]. Addressing a complex system, therefore, requires careful consideration of both technical and socio-institutional factors influencing the challenge. The WSP process has been implemented in Uganda, Ghana, and Tanzania within the last decades [42,50,51], with varying levels of enabling and inhibiting regime factors, as reviewed in the next section. In assessing a given socio-technical system, it is important to understand the system boundaries or geographical scale [79]. This review focuses on small community groundwater-based supplies in peri-urban areas, which may be part of larger aquifer systems.

### **4. Challenges of IWRM and Attributes of TM in Implementing WSPs to Reduce Peri-Urban Groundwater Contamination by On-Site Sanitation in SSA**

Like many countries in SSA, the existing water regime in Ghana, Uganda, and Tanzania generally follows the principles of IWRM [34,37,38]. IWRM promotes a multi-stakeholder approach to water resources management through a framework of creating an enabling environment, developing management instruments, and defining institutional roles for action [29]. IWRM promotes integrated management of water and land resources through four principles, namely; (1) fresh water is a finite and vulnerable resource, essential to sustain life, development, and the environment; (2) water development and management should be based on a participatory approach, involving users, planners, and policymakers, at all levels; (3) women play a central part in the provision, management, and safeguarding of water; and (4) water has an economic value in all its competing uses and should be recognized as an economic good [29]. These principles have been adopted in the policy and regulation framework, institutional set-up, and influence practices within the water sector in most of SSA. While the explicit implementation of WSPs in SSA is still growing [42,51], there is extensive

documentation on implementation of the constituent tasks of the WSP process (Figure 2), influenced by the IWRM regime.

Transition Management, on the other hand, is still unexplored in the context of SSA, despite promising attributes at addressing persistent societal challenges [56,57]. TM has been explored, especially in the global north, in addressing sustainability problems in the transport, energy, water, and environment sectors, among others [56,80,81]. Rotmans and Loorbach [55] summarized eight principles of TM as; (1) creating space for niche developments; (2) empowering the niches; (3) focus on frontrunners; (4) guided variation and selection (system flexibility); (5) radical change in incremental steps; (6) learning by doing and doing by learning; (7) multi-domain approach; and (8) anticipation and adaptation. Transition Management, in practice, is usually implemented through concepts of Transition Management Cycle (TMC), Multi-Level Perspective (MLP), Multi-Phase Perspective (MPP), and Multi-Pattern Approach (MPA), among others [82–84]. The normative attributes of these TM approaches towards re-enforcing the principles and application of IWRM in implementing WSPs for reducing groundwater contamination in peri-urban areas in SSA, are further discussed.

### *4.1. Policy and Regulation*

Ghana enacted the Water Resources Commission Act in 1996, which was the first legislation to embrace IWRM principles of managing water resources through a multidisciplinary and participatory approach [34]. Uganda developed the Water Action Plan in the period 1993–1995, basing on IWRM principles, culminating into the Water Policy of 1999 [85]. Adoption of IWRM principles in Tanzanian legislation can also be dated to as early as 1991, with the first river basin organization (Pangani River Basin Office, Moshi), and later entrenched in the Water Resources Management Act 2009 and the Water Supply and Sanitation Act 2009 [86]. The improved policy and legislation recognized holistic management of activities within a catchment and the interlinkages with the hydrological cycle, including groundwater, within overall sector objectives and documentation. This improved the appreciation of effects of human activities in the catchment on the quality of groundwater, and thus provided a holistic approach for groundwater contamination risk analysis, assessment, and management. This improved policy framework, thus, provided an enabling environment for the introduction of WSPs. Due to this holistic policy framework, Uganda was one of the first countries to adopt WSPs in SSA, undertaken in Kampala in 2005, which resulted in the national framework and guidelines for water source protection in 2013 [47,51]. In Ghana, the first WSPs were implemented in 2014, leading to the national drinking water quality management framework in 2016 [42]. In Tanzania, the first WSPs were undertaken in Dar es Salaam in 2014, and development of national guidelines is still underway [42].

However, in an attempt to include multiple stakeholders and multiple sectors towards water and land resources management, IWRM policies are conceptually diverse, without clear boundaries nor guidance to address specific societal challenges [32,33,87,88]. As a result, groundwater-specific issues have not been adequately addressed in policy and strategic sector direction [32]. Komakech and de Bont [89] pointed out that while the water management policies in Tanzania refer to groundwater protection, anthropogenic contamination of groundwater in urban areas continues unregulated, as depicted in Table 1. Within the maze of many issues affecting water resources management, it is therefore difficult to have sufficient scope analysis for the problem of peri-urban groundwater contamination, thus insufficient risk management strategies. Several pilot interventions on WSP implementation have been undertaken in Uganda, Ghana, and Tanzania, however, they are not specific to groundwater, despite the wide use of groundwater by the peri-urban majority, albeit, a low-income population [42,51,82]. Low funding for WSPs is also a manifestation of low prioritization to water safety, which is even more severe for the groundwater resources [90].

Transition Management approach is a prescriptive, stepwise, approach usually intended for a particular societal persistent (wicked) problem [91]. Loorbach [52] described the Transition Management Cycle to transition society from an undesirable state to a desired equilibrium state through; (a) establishing a transition arena, (b) establishing a transition agenda, (c) experimenting, and (d) monitoring and evaluating progress. Considering the extensive use of groundwater in peri-urban areas, the persistent hazards identified (Table 1) constitute a societal challenge that deserves particular attention. Through a TMC, the problem can be critically analyzed through its historical perspectives, identifying the critical formal and informal stakeholders and thereby addressing all socio-technical aspects. Through incremental steps and effective monitoring, the process is adapted until sustainability on this particular issue is achieved. The Multi-Phase Perspective (MPP) is a tool proposed under TM approaches for monitoring a transition process through stages of pre-development, take-off, acceleration, and finally stabilization, but aiming to avoid undesired scenarios of system lock-in, backlash, or system break down [92]. It is not clear to what extent WSPs have contributed to the elimination of contamination to public water supply systems in SSA, due to limited audits and follow-up processes [47,50]. Specific WSPs for sustainable protection of the groundwater resources against contamination by on-site sanitation in peri-urban areas could also be formulated, and implemented through small incremental steps until sustainability is attained by reduced contamination levels.

The need for prescriptive, flexible policy and regulation arrangements to groundwater management can be drawn from hydropolitics experiences in transboundary aquifer management in the Disi and Guarani aquifers, among others [22,23]. In an effort to address water scarcity in Jordan, a co-operation agreement was negotiated, with several geopolitical tradeoffs, between Jordan and Saudi Arabia for exploitation of the Disi aquifer to supply drinking water to the Jordanian capital, Aman, and other towns [23]. The co-operation agreement between Argentina, Uruguay, Paraguay, and Brazil towards improved management of the shared Guarani aquifer, reached after a decade of negotiations, also shows the benefits of policy specificity to handle a particular problem [22]. These examples from transboundary groundwater management show that specific and flexible policy and regulation instruments are required to address particular groundwater challenges. Thus, specific policies and regulations, within the local hydropilitics of the urban/peri-urban areas, could be helpful towards improved adoption and implementation of WSPs for reducing groundwater contamination.

### *4.2. Institutions*

The IWRM principle of subsidiarity, management of the water resources at the lowest level, has been mainly constructed around catchment/basin organizations. Uganda, Tanzania, and Ghana have all made progress towards operationalizing of the catchment-based institutions, with varying degrees of success [40,85,86]. However, the adequacy of catchment/ basin organizations for groundwater management has been severely contested [37,38,40]. Foster and Ait-Kadi [32] argued that for effective groundwater management, the hydrogeological delineation would serve better than river/lake basin delineation. The effectiveness and coordination between various institutions and governance entities, including town authorities, has not been well addressed [37,93]. Effectiveness of the basin organizations in Uganda, Ghana, and Tanzania is as well in infancy stages, trying to establish legitimacy in the already existing institutional framework [37,40,85]. 'Top-down' centralized planning and control of resources has also remained prevalent in all the countries reviewed, leaving the created basin institutions deprived of technical and financial resources to make meaningful contributions to issues affecting peri-urban areas [37,89,94]. This institutional conundrum, therefore, has resulted in failure to address groundwater contamination challenges in peri-urban areas, among other challenges.

Implementation of WSPs has not been shielded from these institutional challenges. The WSPs developed in Uganda have mainly been undertaken within the National Water and Sewerage Corporation (NWSC), with minimal involvement of external stakeholders in the process [51,95–97]. In Ghana, the implementation of a WSP for a small-town water supply system (Assin Fosu), not operated by the national utility company, showed limited capacity of the local government and community beneficiaries to participate in a formal WSP process effectively [98]. Adoption and implementation of an effective WSP process for community water supplies in a peri-urban area requires a diverse section of actors, owing to the complex interlinkages required to make a sustainable societal change [99]. In Tanzania, Herslund and Mguni [100] argued that the water utility in Dar es Salaam

city, the Dar es Salaam Water and Sewerage Corporation (DAWASCO), had done little to improve sanitation in low-income areas, despite high levels of contamination of the groundwater used by the peri-urban communities. This is evidenced by the microbial and nutrient contamination reviewed in Table 1, with a similar situation in urban centers in Uganda and Ghana. From all the cases, there is an institutional vacuum to supporting peri-urban communities in implementing WSPs for water supply options, which are usually off the conventional water supply network.

From TM concepts, the multi-domain principle encourages multiple pathways through both 'top-down' and 'bottom-up' approaches towards realizing an intended societal goal, as advanced by the Multi-Pattern Approach (MPA) [94,99]. The MPA advances a systematic analytic framework for review of different interrelated processes (patterns) aimed at achieving a desired societal goal by a different configuration of structures, cultures, and processes [84,99]. A specific system and its goal must first be defined, and then the relevant stakeholders and actors identified. In this regard, the societal goal is universal access to safe water (SDG 6). Through this approach, the tensions between different agencies in the water management initiatives can be minimized by exploring the most feasible and practical institutional constellation (formal and informal) for achieving the desired goal. De Haan and Rotmans [99] described that transitions could occur along three patterns of empowerment (bottom-up), re-constellation (top-down), or adaptation (internally induced change). Thus, this may include a co-existence of 'bottom-up' approaches aimed at improving community water sources in un-served low-income areas, while advances are also being explored by the existing regime (through public water utilities) for universal network coverage.

The concept of frontrunners can also be helpful to identify individuals from any pertinent organization, with commitment and capacity to contribute to the WSP process. This would ensure diversity of representatives in the process and thus improved community ownership of the processes. This approach is also supported by the attribute of guided variation and selection, which advocates for system flexibility, to devise alternative system configurations where a problem persists. De Haan and Rogers [84] documented several socio-institutional constellations that have been explored to address water management challenges in Melbourne (Australia), emphasizing the need for system flexibility to emerging challenges. Such a flexible institutional configuration, which may involve formal and informal agents towards a particular objective, is also supported by the growing literature on polycentric governance approaches [24–26]. Polycentric structures include multiple, interdependent autonomous agents (formal and informal), with a defined conflict resolution mechanism, working towards a common goal [25,26]. It is argued that polycentric governance approaches offer advantages of a context-specific institutional fit, enhanced system adaptability to emerging challenges, eliminate redundant actors, and improve local participation and accountability [26]. There is therefore sufficient theoretical grounding for an alternative institutional configuration to support community level initiatives for implementation of WSPs to protect their groundwater sources, with collaboration with the local governments and utilities providing water and sanitation services.

### *4.3. Science and Technology*

Through IWRM, research has also been supported to develop and promote groundwater quality management instruments and processes in SSA such as groundwater quality/risk mapping, modelling, and protection/zoning [8,15,94,101]. However, extensive risk analysis for emerging organic and inorganic contamination from on-site sanitation is still limited [71,72]. Aquifer vulnerability assessments have been conducted, mainly through DRASTIC approach (representing parameters of depth, net recharge, aquifer media, soil media, topography, impact of vadose zone and hydraulic conductivity), as a step in the risk management process [15]. Risk assessment tools, mainly Quantitative Microbial Risk Assessment, have also been explored in SSA [67]. However, most of the management instruments/tools developed under the IWRM regime are still techno-centric, being water-sector specific, with limited integration with socio-institutional parameters [1,101,102]. Management instruments that

integrate the socio-institutional aspects and hydrogeological assessments are limited, which complicates holistic decision making.

Water professionals have mainly been responsible for the WSP processes in Uganda, Tanzania, and Ghana, where the process tends to focus on the water treatment processes [95,97,98]. For instance, Howard et al. [95] noted that the WSPs should be based on health-based targets and independent surveillance conducted to ensure water safety by the health sector, but in practice, the WSP processes are usually implemented by the water sector. The limited capacity of local governments in participating in the WSPs process in Ghana could also be reviewed as a process left to the water sector [98]. Integration of traditional and non-traditional approaches, from various sectors and actors, could result in new, improved socio-technical approaches [103,104].

Transition Management concepts stem from complex systems theory trying to represent the complex relations between nature, science, society, and technology [55]. Complexity theory contends that such systems tend to be non-linear, continually evolving with changes in the environment and adapt to new situations. It is, thus, usually impossible to generalize or predict system behaviors [99]. Practical experimentation and learning from each experiment to adapt the system to an improved configuration is one of the prime attributes of TM. Peri-urban communities are usually served by groundwater supplies which are off the primary water supply network, thus not included in municipal physical models. Implementation of WSPs for such communities would be implemented in an experimental approach, learning lessons from incremental steps, which can be assimilated by the regime upon demonstrated successes. Such experimentation can be led by any relevant stakeholder, especially in the domain neglected by the primary grid, such as peri-urban areas. This variable approach could result in novel approaches, which could be adopted by the water regime. In analyzing requirements for a transition to sustainable urban wastewater management principles in Stellenbosch Municipality (South Africa), Malisa et al. [103] recommend for adoption of both traditional sources and alternatives such as rainwater harvesting, aquifer storage, and stormwater and wastewater reuse.

### *4.4. User and Market Dynamics*

It is also argued that stakeholder participation under IWRM has been largely focused to institutional and high-level stakeholders, with limited active involvement of lower-level community stakeholders (usually economically vulnerable) in decision making processes [37,87,105]. Stakeholder participation has been promoted through Multi-Stakeholder Platforms (MSPs), in the form of Catchment Management Committees, which are decision making bodies (voluntary or statutory) comprising different stakeholders aimed at interdependence in solving water resources management problems [106,107]. Stakeholders in groundwater should encompass all entities (institutional, individual, association), whose actions directly or indirectly affect groundwater, with or without there consciousness [107]. However, it is noted that individual households are vital sources of peri-urban groundwater contamination, and thus their involvement in key decision-making is crucial to the resolution of the problem. Water User Associations in Uganda were an attempt to involve the communities at the lowest level, but these structures were not supported to grow and remained inactive, especially in urban areas [85]. In Tanzania, Pantaleo et al. [12] showed that despite the high level of microbial contamination in shallow wells in Babati town, the local community was not aware of the contamination, nor the potential risks. The involvement of individual households or local communities in WSP process in SSA has equally been limited [43,51].

The Multi-Level Perspective (MLP) has gained prominence in structuring transition processes at different levels of influence, structured as landscape, regime, and niche levels [82,83]. The landscape level encompasses the external environment, which puts pressure on the regime processes to create space for niche innovations to emerge towards the desired sustainability [82]. In this regard, international commitment to the attainment of SDGs can be regarded as one of the vital landscape pressures influencing national processes to develop innovations at all levels towards the attainment of SDG targets. Such innovations may include implementation of WSPs to improve community water sources in peri-urban areas, which have previously been abandoned by the urban water utilities. The national processes (socio-technical regime) need to allow for protected spaces (niches) for various innovations to incubate, which can be assimilated by the regime upon successful demonstration [83]. Creating space for niches and empowering them significantly improves community participation at the lowest level of society, as emphasized by the TM approach. Niches are created at the local level, with the participation of willing individuals. Frontrunners, as well, could be derived from the community, which offers an opportunity for individual participation in vision creation and decision making. Poustie et al. [80] shared experiences in designing a transition experiment for leapfrogging to sustainable urban water management in the city of Port Vila through niche experiments. Through a TM process, it was analyzed that unsustainability of the urban water infrastructure in Port Vila was as a result of the focus on technical and institutional capacities, with limited stakeholder networks and collaborations. Participation in a new vision creation and transition pathways analysis was achieved through a transition arena composed of community members, state actors, and private sector actors. Individual households could, therefore, through such an approach, be engaged to champion sustainability transition towards improved on-site sanitation facilities to reduce the risk of peri-urban groundwater contamination.

Implementation of the IWRM economic principle (polluter-pays-principle) also remains to be effective in SSA and almost non-existent for peri-urban groundwater context, which is affected by communities with limited economic capacity to pay. Groundwater management strategies should take into consideration the socio-economic position of the community [20,27]. Even in the conventional utility networks, raising resources for WSPs is a cross-cutting challenge [47,51,96]. Komakech and de Bont [89] attested to the inability of peri-urban communities in Tanzania to pay for such services. The principle would essentially imply that individual households owning the on-site sanitation facilities would meet the costs of implementing the WSP. While the principle may be applicable to industrial discharges, it is impractical to implement for community-level sources, such as unlined pit latrines and illicit municipal waste dumping by impoverished communities. Through the system flexibility principle of TM approach, "polluter-pays-principle" in the context of peri-urban groundwater management can be assessed depending upon the community characteristics such as willingness and ability to pay for such services; the level of existing public sanitation infrastructure in the area and settlement (housing) patterns. An alternative framework for compensating polluting activities could be assessed and recommended for the peri-urban areas depending upon the economic vulnerability of the population. An example of promoting resource recovery approaches to a circular economy in the Dutch wastewater system transition demonstrates a policy shift from "polluter-pays-principle" [108]. In this regard, a WSP process that advocates for resource recovery from the on-site products would be recommended. The recovered products could then be marketed for nutrient recovery in agricultural production and energy recovery, which benefits the society [6,61], in comparison to requesting the community to pay for the pollution. The economic principle of IWRM has found limited application to groundwater, especially in low-income communities, thus, system flexibility is required to find alternative remedies.

### *4.5. Socio-Cultural Considerations*

Under IWRM, adequate consideration of socio-cultural aspects in the prevention of groundwater contamination in peri-urban areas in SSA has been rather limited [105,109]. Yeleliere et al. [110] highlighted the immense challenges of implementing integrated water resources policies in regulating peri-urban groundwater pollution in Ghana due to a disconnect with the customary practices in the region, which regulated equitable access to water resources and prevented community contamination of water resources. Such customary practices (like customary rights over water and gender customs in water utilization) are usually addressed by informal stakeholders such as traditional leaders, community elders, and unregistered well drillers (and diggers), who are unregulated by the regime, yet influential to a certain extent considering their high numbers in the SSA context [105,109]. Mapunda et al. [111] estimated that over 68% of the population from 20 cities in Tanzania is covered by informal providers, mainly from unregulated groundwater sources, which are not part of the city public water infrastructure. Such informal services are, thus, operated through social-cultural arrangements for water pricing, pollution control, operational schedules, and protection against vandalism. Culture (socio and institutional) issues have found limited space in the WSP processes to date [112]. Van Koppen et al. [86] argued that the implementation of IWRM in Tanzania removed the customary rights to water enshrined in previous arrangements. Consideration of socio-cultural factors in the implementation of WSPs in SSA has equally been limited, primarily focused on the technical factors [112].

Creating space for niches and empowering the niches to develop at the community level, as advocated by TM approaches, provides for an opportunity to incorporate and address socio-cultural issues, particular to the society [57]. These may include customary rights and practices to water and sanitation, and customary land ownership, which may influence groundwater protection zoning and community mobilization towards water source protection [57,105]. In assessing strategies for developing the transformative capacity of the urban water management sector in the city of Melbourne (Australia), Brodnik and Rebekha [113] emphasized the inclusion of organizational and socio-cultural factors in the transition process. Geels [82] also stressed the relevance of niche level innovations in achieving a transition process, usually emanating from the community, well grounded in the societal socio-cultural practices. Mukherji and Shah [28] also present strong arguments for active involvement of community users in groundwater management, drawing on experiences from India, Pakistan, Bangladesh, China, Spain, and Mexico, which have intensive use of groundwater.

However, the TM approach is also faced with unresolved socio-institutional challenges, including limited regard of "politics, power, and conflicts" in achieving democratic participation and ensuring equal and influential participation of weaker members of society in transition processes [56,114]. Other noted challenges include uncertainty in the framing of regimes and system boundaries, low legitimacy of frontrunners, concern for individual perspectives, and inadequate capacity for steering and monitoring societal changes [56]. Considering the complexity of the problems addressed in TM, the development of appropriate management instruments is a work-in-progress [84]. Globally, there are also still limited empirical prescriptive interventions by TM. In view of these limitations, TM alone, as well, may not be the "silver bullet" to addressing the complex dynamic challenge of peri-urban groundwater contamination in SSA. A complementary approach harnessing attributes of both IWRM and TM could offer complementarity towards improved uptake and implementation of WSPs for peri-urban groundwater management.

### **5. Proposal for a Risk-Based Management Framework towards Reducing Peri-Urban Groundwater Contamination by On-Site Sanitation in SSA**

Remedies to complex problems need an interdisciplinary and multifaceted approach [33]. While several studies have advocated for alternative approaches to IWRM [33,39,88], in light of the achievements and gains realized in the global efforts in the implementation of IWRM, others have argued for the strengthening of the concept with attributes of emerging frameworks in order to address emerging challenges [30,38,40]. From the achievements of IWRM in Uganda, Tanzania, and Ghana, this review advocates for strengthening of IWRM towards addressing the challenge of peri-urban groundwater contamination by on-site sanitation. From the analysis of attributes of IWRM and TM, a unified risk-based management framework is proposed towards improved adoption and implementation of WSPs for reducing groundwater contamination from peri-urban areas in SSA (Figure 3).

The socio-technical regime factors that influence groundwater contamination in peri-urban areas in SSA are presented in Figure 3, described with a simplified Entity-Relationship Diagramming (ERD) approach. These factors must be taken into consideration when designing the WSP process for protecting peri-urban groundwater sources against contamination from on-site sanitation. The tenets of natural resources sustainability are hinged on the balance between economic efficiency, social equity and environmental (ecological) sustainability, as advocated by IWRM. TM approach emphasizes a

prescriptive approach, which should target a particular persistent societal problem. The proposed framework is, thus, envisioned to contributed to reduce peri-urban groundwater contamination by on-site sanitation. The attributes of this vision are hinged on the sustainability tenets of ecological sustainability, social equity, and economic efficiency. Simultaneous maximization of the three attributes, as suggested by IWRM, has not been practical, leading to ambiguity in actions [33,36]. Giordano and Shah [88] advocated for context-specific approaches in consideration of the attributes. In this context, considering the social-economic marginalization of peri-urban communities, it can be argued that the proposed framework maximizes social equity, while taking into reasonable consideration the economic and ecological attributes. The focus on social equity is also in accordance with the transformative principle of the SDGs of "leave no one behind" [5].

**Figure 3.** Proposed risk-based management framework for reducing groundwater contamination by on-site sanitation peri-urban Sub-Saharan Africa (SSA) (Adapted from [29,44,52,82]).

The WSP process is in line with the WHO process for small communities [44]. The WSP team may represent the frontrunners, according to TM approach, who follow the process through. The team should be composed of stakeholders from diverse background, different sections of the community, institutions, and leaders, with willingness and ability to participate in the process [56]. In describing the water supply system, both technical and socio-institutional factors affecting community water supply need to be critically analyzed. The Catchment Management Committees, developed under IWRM approaches, have been critiqued for the limited representation of vulnerable community members, power imbalances in decision making, and high cost of operationalizing the committees [106]. The MLP perspective offers a structured approach in analyzing the system components at landscape, regime, and niche levels, ensuring effective representation from all levels. The niche level initiatives at community level, to some extent, address representation and power imbalances. Improved socio-technical management processes and instruments should be used to comprehensively identify and assess hazards, hazardous events, risks, and existing control measures. Experimental measures should be explored, including radical steps, which may not be in the main system configuration, but demonstrated to improve water safety of the peri-urban communities. The process and activities should be monitored, along the MPP approach, with a focus on the sustainability goal [83]. All aspects of the WSP process are continually reviewed and adapted to emerging situations and the process is repeated continuously to achieve sustainable reduction of groundwater contamination from on-site sanitation. Throughout the WSP

process, communication and feedback to and from all stakeholders is emphasized, while continually adapting tools, processes, and focus to emerging hazards and events. This continuous influence and adapting of processes are reflected in the bi-directional influence arrows between the various entities in Figure 3.

As postulated by IWRM, the process is influenced by a framework of 'enabling environment', 'management instruments', and 'institutional roles' [29]. Using concepts of TM approach, these elements are re-enforced for practical analysis and formulation of strategies for reducing groundwater contamination in peri-urban areas by on-site sanitation. In the enabling environment, the MLP differentiates between the socio-technical landscape and socio-technical regime to influence transitions towards sustainability. The landscape pressures, including international development agenda (SDGs), multinational development agencies, and international political/trade treaties are avenues for influencing regimes towards the sustainable achievement of groundwater quality. IWRM has been strong at mobilizing the international agenda towards holistic management of water resources [30,36]. The socio-technical regime, comprised of national level policies, structures, political dynamics, user preferences, national development, and cultures, can be rallied towards the support of groundwater protection initiatives. While the external environment influences the contamination risk management process, emerging innovations should equally impact the external environment for improved adaptation of the entire system. This provides for the possibility of upscaling promising niche level experiments to be adopted by the system regime and subsequently, the landscape level. This also ensures continuous adaptation of the landscape and regime forces towards emerging situations.

An array of stakeholders from both formal (under regulation by the regime) and informal (unregulated by the regime) settings, derived from the individual level, the national level, and the international level, are required for driving the transition towards the reduction of peri-urban groundwater contamination by on-site sanitation in SSA. This polycentric arrangement would enable a resilient and accountable institutional framework to support the particular challenges faced by peri-urban communities in managing groundwater resources. Management boundaries need to be specified between different stakeholders to avoid scenarios of inaction and conflicts. While IWRM advocates for catchment-based boundary systems, TM advocates for flexibility in setting the boundary of assessment, depending upon a given challenge. The peri-urban areas could be assessed as a specific sub-system, with particular socio-economic characteristics, within the overall urban water supply system. TM advocates for an approach that starts at the lowest community level, within the existing societal arrangements for change action. The informal arrangements with the community need to be given due consideration for any management arrangements proposed for implementation of the WSP.

Appropriate socio-technical management instruments are required to manage the entire process, stakeholders, and the environment towards realization of the sustainability objective. Prediction and modelling tools and techniques developed under IWRM could be strengthened, which could be used to study the overall system, including the technical and socio-institutional aspects and the complex interactions towards achieving the desired sustainability goal. Such management tools may include laboratory analysis techniques, problem analysis tools, pathways analysis tools such as back-casting, and vulnerability assessment tools. The process of tools development is continuous with knowledge advancement. Experimentation with various processes and adaptation of the WSP process to emerging issues from the peri-urban communities is an integral part of the process.

### **6. Conclusions**

Groundwater is a vital resource for most of the population in low-income peri-urban areas in SSA. However, the resource is threatened by increasing contamination arising from on-site sanitation facilities, in light of a growing population. From the review of literature, it is evident that microbial and chemical contamination is prevalent and well documented in SSA. The WHO introduced WSPs to assist communities to manage such contamination by managing the technical and socio processes from catchments to the water user. However, adoption and implementation of the WSPs have been met with several successes and challenges influenced by the existing management framework (regime), which is aligned to the IWRM principles [36,37,85].

IWRM introduced improved holistic water resource management policies, improved public participation, improved management tools, and gender-sensitive approaches, which provided an enabling environment for the adoption of WSPs, which were multi-stakeholder by design [44]. However, implementation of IWRM has had a low focus on groundwater-specific problems and implemented through an incoherent institutional framework based on catchment management structures within already existing governance structures. The practicality of such structures to address groundwater-specific issues has been severely questioned [34,37]. The management instruments developed under IWRM have also, to date, remained techno-centric, with limited integration of socio-technical factors. There has also been limited regard for socio-cultural aspects and the economically vulnerable society segments, reflected in low financing of WSPs initiatives [51,98]. These limitations have affected the adoption and implementation of WSPs for groundwater interventions in peri-urban areas in SSA. The WSPs have been mainly implemented by urban water utilities for the conventional piped water supplies, with no consideration to community sources within the peri-urban areas.

TM advances normative strengths of long-term planning for societal transformation and implementation of the plan through incremental short-term measures, which has shown promise at addressing such complex adaptive systems. It provides a prescriptive approach, which targets a particular societal concern and works towards a shared vision, guided by frontrunners, which addresses the challenge of system diversity. TM processes are also multi-domain and flexible to institutional and actor dynamics, with emphasis on community-level (niche) initiatives [82]. These attributes can eliminate institutional tensions, ensure incorporation of community vulnerable persons, and integration of socio-cultural elements in a transition process towards the elimination of groundwater contamination. The process is improved through learning by doing and doing by learning, through a multi-domain approach, further adapting the system in light of increased pressures like increased urbanization and climate change. The normative strengths proposed by TM are consistent with emerging approaches in polycentric governance approaches, postulated to improve system adaptability to emerging challenges and accountability for results to the local population in attainment of set goals.

Based on the normative strengths of IWRM and TM, a unified risk-based management framework is advanced by this review towards the improved adoption and implementation of WSPs for reducing peri-urban groundwater contamination from on-site sanitation in SSA. The framework strengthens the vision of the WSP process, illuminates the enabling environment along landscape and regime aspects while refining the WSP process at the community level for incremental steps towards sustainability. Socio-technical management instruments are identified, which could be strengthened and applied in improved WSP implementation. The stakeholders, coordinated by a specific team of frontrunners, are also structured into formal and informal stakeholders towards improved WSP process implementation to emphasize community-level interventions. Experimentation of the proposed framework is recommended for empirical validation, which could then be adopted towards the improved implementation of WSPs for reducing groundwater contamination by on-site sanitation in peri-urban SSA, in the effort towards attaining sustainable development goal number 6 for universal access to safe water.

Key research gaps identified by the review include; the need for a further understanding of emerging contaminants in peri-urban groundwater, in light of increased urbanization, which have not been addressed by the WSP processes. There is also need for further assessment of the context and regional specific socio-institutional factors influencing adoption and implementation of WSPs in addressing the persistent challenge of groundwater contamination by on-site sanitation in SSA, such as cultures, power imbalances, societal practices, which differ between various socio-technical settings. While the integration of TM and IWRM approaches for improved implementation of WSPs is recommended, tensions between attributes of the approaches may also arise, which need further study through experimentation. There are also limited management instruments that incorporate analysis of socio-technical aspects of groundwater contamination, in the light of emerging challenges.

**Author Contributions:** Conceptualization, F.K., R.N.K., J.W.F., and F.R.B.T.; methodology, F.R.B.T.; software, F.R.B.T. and S.S.; validation, P.M.N., S.S., and F.R.B.T.; formal analysis, F.R.B.T. and F.K.; investigation, F.R.B.T.; resources, R.N.K. and J.W.F.; data curation, F.R.B.T.; writing—original draft preparation, F.R.B.T.; writing—review and editing, F.R.B.T., P.M.N., and S.S.; visualization, P.M.N.; supervision, R.N.K. and F.K.; project administration, R.N.K.; funding acquisition, J.W.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the UK Department for International Development (DFID), the Economic and Social Research Council (ESRC), and the Natural and Environment Research Council (NERC) under the UPGro Programme, grant number NE/M008045/1. The APC was funded by T-Group project under the UPGro Programme.

**Acknowledgments:** The authors are also grateful to Maryam Nastar for her critical input to the paper and Ismail Bukenya for his support in production of figures. We are also grateful to the two anonymous reviewers for their critical comments, which have significantly improved the quality of this paper.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Review* **Rivers' Temporal Sustainability through the Evaluation of Predictive Runo**ff **Methods**

### **José-Luis Molina 1,\*, Santiago Zazo 1, Ana-María Martín-Casado <sup>2</sup> and María-Carmen Patino-Alonso <sup>2</sup>**


Received: 31 January 2020; Accepted: 22 February 2020; Published: 25 February 2020

**Abstract:** The concept of sustainability is assumed for this research from a temporal perspective. Rivers represent natural systems with an inherent internal memory on their runoff and, by extension, to their hydrological behavior, that should be identified, characterized and quantified. This memory is formally called temporal dependence and allows quantifying it for each river system. The ability to capture that temporal signature has been analyzed through different methods and techniques. However, there is a high heterogeneity on those methods' analytical capacities. It is found in this research that the most advanced ones are those whose output provides a dynamic and quantitative assessment of the temporal dependence for each river system runoff. Since the runoff can be split into temporal conditioned runoff fractions, advanced methods provide an important improvement over classic or alternative ones. Being able to characterize the basin by calculating those fractions is a very important progress for water managers that need predictive tools for orienting their water policies to a certain manner. For instance, rivers with large temporal dependence will need to be controlled and gauged by larger hydraulic infrastructures. The application of this approach may produce huge investment savings on hydraulic infrastructures and an environmental impact minimization due to the achieved optimization of the binomial cost-benefit.

**Keywords:** runoff; temporal dependence; rivers' sustainability; predictive methods; causal reasoning; runoff fractions; water management

### **1. Introduction**

In order to implement a real integrated water resource management (IWRM), it is required the proper use and organization of a great range and amount of data sources and methods. In this context, climatic and hydrological variables are essential [1,2].

Hydrological processes' variability is increasing on a global and local scale [3,4]. Consequently, those events, with values and trends far from the historical average behavior, are more recurrent [5–7]. In order to address this new hydrological reality and aimed to anticipate and forecast it, new approaches, methodologies and techniques have emerged, incorporating this changing behavior. However, in order to build tools for the present-future, not all the reasons that explain this increasing variability are brand new (climate change and projections to the future), but also, the historical behavior should be more deeply understood [8].

Hydrological temporal behavior from a stochastic view has been usually studied, and many of those concepts, assumptions and applications are still valid today. Those concepts comprise

temporal-spatial correlation and statistical hydrological parameters, including basic, droughts and storage ones, as well as trends, shifts and seasonality testing, among others [8,9].

Traditionally, hydrological models and all their mathematical development are built based on a unique observation runoff record collected from a gauge station. Still, today, most of the hydrological tools officially implemented in water administrations are based on the previous and rudimentary approach [10]. However, the boom of very powerful analytical techniques and methods such as data mining (DM), artificial intelligence (AI) and machine learning (ML), among others, have produced a drastic change in several disciplines, including hydrology [8]. Consequently, river basins' hydrological behaviors can be currently characterized through those tools by means of huge amount of information coming from statistical or deterministic operations [11]. This massive amount of information is used for populating sophisticated expert systems that provide quantitative and dynamic results, incorporating and quantifying the inherent hydrological uncertainty [11]. However, those techniques have a high variety of performance, usage, utility, analytical power and/or accuracy, among other parameters. This heterogeneity is not properly revised or synthetized in academic studies or research articles, and, consequently, it is worthy to analyze and characterize it.

The most powerful and useful methods are the stochastic ones, which are able to incorporate and deal with the uncertainty of hydrological variables. In this sense, the discipline of stochastic hydrology is where those methods are included. Furthermore, ideas and features such as temporariness or persistence strongly related to the measure of the time series long-term memory (Hurst coefficient) [12], dependence-independence of internal data or structure and strength of causal relationships, are particularly significant.

This study is aimed to review the most popular, powerful and innovative approaches and methods for analyzing and predicting rivers' temporal behaviors. Furthermore, this paper is also aimed to provide the reader with an evaluation of the strengths, weaknesses, opportunities and threats (SWOT) of those methods and techniques set. Finally, this paper is also aimed to provide the reader with a rigorous suitability assessment focused on achieving the most suitable method for developing robust sustainable rivers' assessments. For that, the paper is structured as follows. Section 2 covers a revision of the main material and methods included in literature for developing a rigorous and updated analysis of rivers' temporal behavior and, by extension, their applications. Section 3 contains the methodology and the main results drawn from this research. This section includes the identification and assessment of parameters, a SWOT analysis of those techniques and methods and a suitability assessment for capturing the best methods for temporal rivers' sustainability. Finally, Sections 4 and 5 are dedicated for the discussion and conclusions, respectively.

### **2. Overview of Research Approaches**

Traditionally, the use of hydrological models has been extensive worldwide. A model can be in the form of a physical, analog or mathematical model [13]. Currently, mathematical models are more preferred due to the rapid development of computer technology and because of including a chronological set of relations. However, as it was aforementioned before, most of the models uniquely rely on their large set of theoretical mathematical algorithms, using for their input only the historical runoff record rather than feeding them with massive high-quality information. Predictive and descriptive methods for studying and evaluating the temporal behavior of rivers may be classified according to different criteria. In this sense, main criteria can be the following: First, considering its incapacity/capacity for explicitly incorporating and quantifying the uncertainty in their whole functioning, methods can be categorized into deterministic and stochastic [14]. Then, taking into account its capacity for dealing with massive or low amounts of data, methods are grouped into DM, big data (BD) and ML or, on the other hand, scarce-data methods. Furthermore, methods can be classified into a black or white box, in view of its transparency and manageability in their processing [15]. Additionally, stochastic methods are differentiative due to its way for dealing with the uncertainty. In this sense, there are methods like causal reasoning (CR) that uses probability [11]; other stochastic methods, such as HJ-Biplot, use multivariate analysis and techniques [16], and they are able to evaluate correlation, similarity, distance/dissimilarity and covariance [16] in the datasets. Application of different multivariate statistical techniques has increased in the recent past. The most used methods are the following ones. First, HJ-Biplot, which simultaneously interprets the position of the variables, the sets and the relationships between them [16]. Furthermore, discriminant analysis (MDA) [17] and cluster analysis (CA) allow classifying the units according to similarities [18]; factor analysis (FA) explores relationships in the few principle components [19]; principal component analysis (PCA) [17] and canonical correlation analysis (CCA) [20] select variables and identify factors influencing hydrological changes.

Given the high variability, randomness and uncertainty of hydrological processes, methods that fall on the classification of stochastic and deterministic are described in detail as follows. In this sense, according to Koutsoyiannis [21], an appropriate modeling approach for any uncertain hydrological system should necessarily include quantification of its uncertainty within a stochastic framework. Consequently, for the same previous reasons, the most adequate methods are the stochastic ones [14]. However, some new deterministic approaches can be successfully applied to some river's systems, especially for very controlled and gauged rivers' basins poorly affected by climate change [14] that are explained as follows.

### *2.1. Deterministic Methods*

### 2.1.1. Process-Based on Hydrological Models

This type of modeling has complex physical theory and usually needs to have a large amount of data and computational time. They have an initial given condition which is defined and parameterized and apply nonlinear partial differential equations which describe the hydrologic processes. Furthermore, they are usually accurate; however, they are often complex and need a lot of information as model inputs, such as river bathymetry; a complete set of meteorological information (air temperature, solar radiation, wind, etc.); inflow and outflow conditions; etc. As a result, application of such models for regions with limited data is impractical [22]. These models can be classified into black, grey, or white box, in view of its transparency and manageability in their processing [15]. Firstly, the lumped model (black model), which evaluates the response of the basin simply at the output and does not characterize the physical characteristics of the hydrological processes. Secondly, the semi-distributed model (grey model), which is partly permitted to change in space with division of catchment into an amount of sub-basins. It requires lesser amounts of input data in contrast with the fully distributed model. The final type is the distributed model (white model), which requires large amounts of data for parameterization; however, it presents some problems, such as the nonlinearity, scale and uncertainty [15]. One of the important advantages of the deterministic models is that they present the inside view of a process which enables better understanding of the hydrological system. On the other hand, their capacity for dealing (identifying, characterizing, evaluating or quantifying) with temporal behavior of rivers (dependence/memory) is very limited [14,23]. In this sense, traditional hydrological modeling codes such as HEC-HMS [24] or SIMPA [10], among others, have used the mathematical equations given by classic hydrology. They have implemented simulation models for being applied to hydrographic basins and then are compared to observational data records to get a good calibration. Those models follow the traditional hydrological scheme of procedure of routing for getting the final product of hydrographs [25–28].

### 2.1.2. Wavelets Transformation (WT)

Wavelet transform (WT) is a method that has been widely used to reveal information (signal) both over time and on a domain scale (frequency). It splits the main time series into sub-fractions, which improves the data decomposition in forecasts. Consequently, this allows capturing useful information at different levels of data resolution. It has been extensively applied in hydrology, such as rainfall–runoff relations for karstic springs [29,30], scale-dependent synthetic streamflow generation [31], temporal patterns of precipitation [32,33], variabilities of hydrological processes [34,35] and hydrological forecasting and regionalization [36,37].

The discrete wavelet decomposition is known to offer a local representation of time series data using wavelet and scaling coefficients at different resolutions obtained via Mallat's pyramidal algorithm, among others [38]. There are several researches that have employed the wavelet technique for various hydro-climatological applications [39]. For instance, Adamowski and Chan [40] developed a wavelet neural network conjunction model to forecast monthly groundwater levels using wavelet decomposed data of multiple hydrological and meteorological variables. Moosavi et al. [41] compare the forecast performance of Wavelet-ANFIS and Wavelet-ANN hybrid models to the ANFIS and ANN benchmark models. Wavelet-ANFIS model provided better groundwater level forecasts at different time horizons. Likewise, numerous groundwater level estimation studies based on hybrid Wavelet-AI models can be found in the literature [42,43]. Furthermore, such hybrid WT-ANN methods have been shown to provide good performance in hydrological studies, such as rainfall-runoff modeling [44,45] and streamflow forecasting [46,47], as well as river and groundwater level forecasting [48], among others. Several studies have also shown that the WT-ANN hybrid models perform better than some other widely used models. For example, Peng et al. [47] applied empirical wavelet transform and artificial neural networks for streamflow forecasting. They concluded that the hybrid model can capture the nonlinear features of the streamflow time series and, consequently, provide more accurate forecasts than the traditional ANN method. Adamowski and Chan [40] applied the WT-ANN method to predict groundwater level and stated that it provided better forecasting accuracy than the conventional ANN method. Similar results have also been reported by Rajaee et al. [49] and Seo et al. [50]. These studies indicate that the WT-ANN hybrid models allow users to achieve forecasts with higher accuracies.

### *2.2. Deterministic Machine Learning (ML) methods*

Some of the most widely used methods have been selected to be included in this section given its high operational capacity. Most of them belong to the ML group of methods. However, there are other methods that exceed ML influence and are also worthy to include.

There are two general categories of machine learning: supervised and unsupervised. Supervised ML techniques refer to when there is a piece of data to predict or explain. This is done by using previous data of inputs and outputs to predict an output based on a new input. By contrast, unsupervised ML is aimed to search ways to relate and group data points without the use of a target variable to predict. In other words, it evaluates data in terms of traits and uses the traits to form clusters of items that are similar to one another. To keep a robust and coherent structure, ML methods have been classified in this paper into deterministic and stochastic ones.

When there is inadequate information of influential parameters, the ML methods demonstrate higher potential and efficiency, and they are more appropriate than the conventional numerical or finite element methods [38]. The ML techniques make more reliable predictions/forecasts based on their ability to identify and reveal the nonlinear, non-stationary and discriminant features from historical time-series records and also effectively handle chaos and uncertainties associated with the input data. Furthermore, currently, the development of hybrid ML techniques for modeling hydrologic time series is also a very active area of research. For instance, the ML models developed from wavelet decomposed data have demonstrated better performance than the models provided with raw data. The description of selected methods, shown as follows, is focused on their capacity for predicting increasing hydrological condition processes, such as rivers' runoff.

### 2.2.1. Artificial Neural Networks Methods (ANN)

During the last 20 years, ANN have been increasingly used for wider applications in forecasting time series, including geophysical, meteorological and hydrological time series. Most ANN applications are used for forecasting in situations where there is an unknown relationship between the set of input factors and the outputs. Despite there is a strong criticism about the capacity of ANN for dealing with hydrological uncertainty and its reliability for semiarid regions is seriously questioned, the ANN model has become an appreciated tool for modeling nonlinear hydrometeorological phenomena, such as precipitation forecasting [51–53], streamflow forecasting [54,55] and ground water-level simulation [56,57], as well as river water temperature forecasting [58,59]. Furthermore, in regards to more specific utilities, using ANN as a tool, the NERD (neural error regression diagnosis) model of Abramowitz et al. [60] is available for data assimilation and the SOLO (self-organizing linear output) model of Hsu et al. [61], first for classifying input features into various categories, and then for performing function mapping for each category separately. Since the hydrological conditions are increasingly changing, applications of the linear and nonlinear regression models, as well as the traditional ANN models for river water temperature modeling, frequently have limitations, especially in processing of nonstationary data [62]. In this regard, wavelet transform, as a good preprocessing method for nonstationary data, can be a potential complement for the traditional methods.

### 2.2.2. System Dynamics Methods (SDs)

SDs is basically a methodology for studying complex feedback systems [63]. Consequently, this method was not originally intended to be applied for hydrological forecasting [64–67]. However, due to the inherent uncertainty and complex causal and dependency relationships within the hydrological records, it is also recommended for that. Specifically, it is particularly useful when studying complex systems with interacting elements, the behavior of which cannot be easily predicted. It allows one to examine system behavior modes and response as different variables are altered. The most well-known SDM packages include: SIMILE [68], VENSIM (www.vensim.com), STELLA (www.iseesystems.com), POWERSIM (www.powersim.com) and SIMULINK—an add-on to MATLAB (www.mathworks. com) [63].

### *2.3. Stochastic Methods*

### 2.3.1. Traditional Techniques

The traditional statistical/time series methods, such as linear and nonlinear regression models, are usually simple to develop; however, they produce, in general, large modeling errors [69]. Consequently, the way they cope with uncertainty is not recommended. It is well-known that a correlogram provides an idea of temporal dependence intensity through the correlation coefficient [70]. Furthermore, it is known that a correlogram comprises a static picture and average result of the temporal behavior of hydrological series. This fact provokes the existence of indeterminacy points for defining the temporal dependence/independence of time series [70,71]. Traditional techniques were designed exclusively for the short term through Pearson's correlation coefficient and for the long term through the Hurst coefficient, which provides an idea of the degree of dependency of hydrological events throughout time series. Within these methods, dependence has been analyzed for hydrologic studies from many perspectives and through several approaches [72]. The most common traditional measure of dependence is the Pearson's correlation coefficient, which is computed based on the assumption of normal distribution to measure the linear dependence [8]. This is commonly assumed in statistical approaches, such as autoregressive (AR) models or the autoregressive moving average (ARMA) model, to characterize the linear dependence among multivariate random variables in hydrology, such as precipitation, streamflow or runoff [73,74]. Nevertheless, the normal assumption does not hold, and the linear dependence is too basic to characterize far more complicated dependence structures [72]. Another nonparametric correlation estimator as the Spearman and Kendall has been widely used. They have also been commonly used as alternative dependence measures to characterize the nonlinear dependence of hydrological variables, as demonstrated recently with copula models [75] described later.

### 2.3.2. Multivariate Adaptive Regression Splines (MARS)

This procedure, proposed by Friedman [76], is a multivariate nonparametric model which searches over all possible univariate knot locations and across interactions among all variables by means of the use of local so-called basis functions. In this sense, MARS algorithm is based on three sequential steps [76,77]. In the first one, named "constructive phase", it is created through adding basis functions step by step. Then, in order to improve the model, the best pairs of spline functions are selected. At each step, the split that minimized some lack of fit criterion from all the possible splits is chosen on each basis function. The iterative procedure of construction finishes when the model reaches a maximum number of basic functions. Then, in the second step, "pruning phase", a backward elimination process to redefine the model fitting, is carried out. Here, basis functions are eliminated one at a time until the lack of fit criterion based on the generalized cross validation (GCV) criterion [78] is a minimum. Finally, in the third phase, the optimal model selection is done based on an evaluation of the properties of the different models.

On the other hand, recently, MARS procedure has begun to be applied in the field of hydrological forecasting due to its flexibility in modeling high-dimensional data. It is recommended and applied over a wide range of hydrological issues, like runoff prediction [79,80], drought prediction [81], water pollution prediction [82], pan evaporation modeling [83] and prediction of scour depth below free overfall spillways [84]. In most of these previous researches, the raw time-series data are fed as input. The performance of MARS was better than that of the ANN, ANFIS, support vector machine (SVM) and M5 Tree models [38].

### 2.3.3. ARIMA/ARMA Methods

ARIMA/ARMA methods are usually used for generating synthetic series from the historical record [8]. Before tackling this generation, historical time series need to be normalized, which is a drawback of this technique [85]. Once the normalization is done, by means of the previous model, several synthetic series are generated with the same occurrence probability of the historical one [70]. Frequently, these synthetic series are used to populate a further model/method, such as CR [23]. Consequently, this method is usually hybridized with other techniques of artificial intelligence, which provide more accurate results in the modeling of complex natural processes [73,74,86,87]. This approach is applied to the hybridization with Bayesian methods for developing CR [77].

### 2.3.4. Causal Reasoning (CR) Methods

CR is based on the propagation of probability along a Bayesian implementation through a causal model. This model is based on decision variables who represent probability distributions for temporal runoff. Most of the CR approaches are based on Bayesian networks (BNs) and dynamic Bayesian networks (DBNs). Those methods are based on probabilistic graphical models [88,89]. They easily and automatically allow defining relationships between parts into complex models, through conditional probabilities, due to both models being based on Bayes' theorem [90]. BNs are probabilistic graphical models that offer compact representations of the joint probability distribution over sets of random variables [91,92]. This property has been taken to use BNs as a decision support system (DSS), for example in [93,94], to address problems within the IWRM paradigm [95]. Dynamic Bayesian networks (DBN) are a generalization of hidden Markov models (HMM) [8,96]. One of the main advantages of BNs is that they compute inference omni-directionally. Given an observation with any type of evidence on any of the networks' nodes (or a subset of nodes), BNs can compute the posterior probabilities of all other nodes in the network, regardless of arc direction, through observational inference [97].

The inherent ability of BNs to explicitly model uncertainty makes them suitable for temporal hydrological series analysis. Another feature of BNs is the unsupervised structural learning [98], which means probabilistic relationships between a large number of variables without having to specify input or output nodes. This can be seen as a quintessential form of knowledge discovery, as no

assumptions are required to perform these algorithms on unknown datasets. Furthermore, this is strongly related to machine learning that has been applied successfully in the hydrological context in papers such as [99,100]. Consequently, the resulting product has many similarities with a neuro-fuzzy system or adaptive neuro-fuzzy inference system (ANFIS) that has been applied in works such as [101]. Finally, an important contribution of this method comprises the identification, characterization and quantification of temporal conditioned runoff fractions [8]. This represents an outstanding advance over classic or alternative methods.

### 2.3.5. Copulas Methods

In hydrology, copula applications started after the work of De Michele and Salvadori [102], who tested Frank copulas for a joint study of the negatively associated storm intensity and duration. Other research, such as that of Zhang and Singh [103], incorporated copulas for an extreme analysis of rainfall and drought events. The study of the dependence's modeling between extreme events is widely studied nowadays [104]. Dependence in extreme events needs to be evaluated through techniques focused on an extreme distribution, such as the tail-dependence coefficient. This has been commonly used in investigating hydroclimatic extremes, such as precipitation and temperature [105].

Another important and recent area of research is the construction of a multivariate distribution in modeling different dependence structures [106]. This is applied to hydrology in the form of frequency analysis, downscaling, streamflow or rainfall simulation, geostatistical interpolation, bias correction and so on. Other methods, such as multivariate parametric distribution [107], entropy [108] and copula [75], have been developed to model various dependence structures of multivariate variables through the construction of joint or conditioned distribution.

On the other hand, it should be highlighted that Copula method is based on the description and modeling of the dependence structure between random variables independently of the marginal laws involved. In this sense, there are high similarities with CR. Differences with CR lies in the fact that a Copula is a bivariate function, while CR is based on conditioned probabilistic distributions.

### 2.3.6. Kalman and Particle Filter Methods

The Kalman filter (KF) is a method that allows estimating unobservable state variables from observable variables that may contain some measurement error. It is a recursive nature algorithm that requires two types of equations: those that relate the state variables (main equations) and those that determine the temporal structure of the state variables (state equations). The estimates of the state variables are made based on the dynamics of these variables (time dimension), as well as the measurements of the observable variables that are obtained at each moment of time (cross-sectional dimension). That is, the dynamics are summarized in two steps: estimate the state variables using its own dynamics (prediction stage). Then, improve that first estimate using the information of the observable variables (correction stage). Once the algorithm predicts the new state at time, it adds a correction term, and the new "corrected" state serves as the initial condition in the next stage, *t* + 1. In this way, the estimation of the state variables uses all the available information until that moment and not only the information until the stage before the moment in which the estimation is made [109].

Recently, some novel applications, based on KF, have emerged in the field of hydrologic predictions. This is due to its features of real-time adjustment and easy implementation within a framework dynamic state [110]; one of them is an ensemble Kalman filter (EnKF). This method approximates the distributions of the system states by random samples, named ensembles and replaces the covariance matrix by the sample covariance computed from the ensembles, which is used for state updating in the KF [111]. In this sense, it is worth noting interesting approaches in the hydrological predictions field. For example, Moradkhani et al. [112] showed a dual-state estimation for parameters and state variables in a hydrologic model. For its part, Weerts and Serafy [113] compared the capability of EnKF and particle filter (PF) methods by reducing uncertainty in the rainfall-runoff update and internal model state estimation

for flooding forecasting purposes. For their part, Pathiraja et al. [114] proposed an approach to detect nonstationary hydrologic model parameters in a paired catchment system.

On the other hand, a particle filter (PF) technique has emerged as an attractive alternative to remove the unrealistic Gaussian assumption of the EnKF [115], improving the reliability of hydrologic predictions [116]. PF is able to fully represent the posterior distributions of model parameters and state variables through a number of independent random samples called particles, and the particles are weighted and propagated sequentially by assimilating available observations. Over the past few years, the PF and its variants have been receiving increasing attention from the hydrologic community due to its ability to properly estimate the state of nonlinear and non-Gaussian systems [117,118].

### *2.4. Stochastic Machine Learning (ML) Methods*

### 2.4.1. HJ-Biplot

The HJ-Biplot [119] is an extension of the classical Biplot methods [120]. This technique allows a joint representation of a data matrix in a reduced subspace dimension, usually a plane, of the rows and columns of a matrix of multivariate data *Xnxp*. It is a symmetric simultaneous representation technique that is in some ways similar to correspondence analysis but is not restricted to frequency data.

HJ-Biplot uses markers (points/vectors), denoted as g1, g2, ... , gn for each row, and h1, h2, ... , hp for each column. The markers are obtained from the usual singular value decomposition (SVD) of the data matrix *X* = *UDVT*, where *U* are the eigenvectors of XXT, *V* is the eigenvectors of *XTX* and *D* is the matrix diagonal of singular values, taking as row markers rows of *J* = *UD* and, as column markers, rows of *H* = *VD*. HJ-Biplot is widely used, because it provides a higher goodness-of-fit for rows and columns of the matrix [16].

Recently, this technique has been applied in the field of hydrology. Carrasco et al. [16] examined the relationship between the physicochemical and biological variables, as well as the sampling points through different months. Although this method has a descriptive character contributing to deepening the hydro-chemical knowledge and, consequently, improving the hydrological and hydrodynamic understanding and interpretation of water systems, which allowed generating new interpretations, knowledge and evaluations about the water quality of Gatun Lake. It also offers the advantage of providing high representation quality, both for the sampling points and for the physicochemical and biological variables.

### 2.4.2. Principal Component Analysis (PCA)

PCA analysis reduces the dimension of the original dataset. This technique uses an orthogonal transformation to convert highly correlated variables into a set of values of linearly uncorrelated, which are called principal components. Each principal component is a linear combination of the original variables. The mathematical approach for processing can be called adaptive data analysis (Table 1) that comprises mathematical processes such as orthogonal linear transformation, rank (dimensionality) reduction and visualization of latent data structures.

On several occasions, hydrological datasets contain not only useful important information but also confusing noise. Sometimes, datasets are not normally distributed or may contain outliers. Even the hydrological parameters are usually many times correlated. The correlation indicates that some of the information contained in one variable is also contained in some of the other remaining variables. In order to reveal the logical structures of the data, there are several hydrological procedures, such as PCA, which reduces the data dimensionality and gain more effective features [121]. Therefore, in several studies, the reason for selecting PCA as a statistical method was the low noise sensitivity [121].

PCA analysis has been used in numerous hydrological studies to test the water quality assessment [122], understand the role of land-atmosphere interactions in driving climate variability and the spatiotemporal variability [123] or select the redundant input variables for a prediction model of hybrid runoff models [124].

**Table 1.** Parameters assessment. Measure of the predictability and reliability. Low (\*), medium (\*\*) and high (\*\*\*).


### 2.4.3. Factorial Analysis of Variance (FAV)

Factorial analysis is usually used to help in the study of the individual and interaction effects of the parameters [125]. More specifically, the factorial analysis of variance method is used to diagnose the curve relationship between the parameters and the response [126,127]. In other words, FAV technique is used for measuring the specific variations of hydrological responses in terms of posterior distributions to investigate the individual and interactive effects of parameters on model outputs [128]. To complete this description, FAV comprises a powerful statistical tool to facilitate the exploration of the main effects. This is done by measuring the variation ranges of hydrological response under the impact of individual parameters and parameter interactions by revealing the specific variations of each parameter's effects under the impact of another parameter [129]. The FAV technique can also quantify the sensitivity of model outputs to individual parameters, as well as their interactions, through addressing the curvilinear characteristic of the hydrological response when parameters vary across their multiple levels [130,131].

Consequently, the hybridization of this method with Bayesian methods is quite appropriate, direct and powerful. This is called the Bayesian-based multilevel factorial analysis (BMFAV), and it is used to assess parameter uncertainties and their effects on hydrological model outputs. In this sense, there are several other applications aimed to approximate the posterior distributions of model parameters with Bayesian inference [128,132]. Another important application of FAV was to develop a BMFAV method to address the dynamic influence of hydrological model parameters on runoff simulation [133].

### **3. Methodology and Results**

This research comprises a methodological framework that includes the development of several consecutive phases listed as follows. First, an identification of parameters for a posterior SWOT analysis took place; then, those parameters were assessed based on a rigorous analysis of the global scientific literature; after that, a SWOT analysis was developed; finally, a suitability assessment for rivers' sustainability was developed. Results drawn from this research are largely established in terms of a comparative analysis of the aforementioned techniques aimed to reach a ranking of methods from a multidimensional way. This will allow selecting the most suitable technique for each component of rivers' sustainability included in this research.

### *3.1. Identification of Parameters*

The parameters identified and established in this research for tackling the SWOT analysis are listed as follows. **Predictability**: There is a high variability on the prediction capacity provided by the analyzed methods and techniques. A qualitative score (high, medium and low) to rank and measure that skill is established. **Reliability**: This parameter is aimed to qualitatively score the degree of confidence and/or accuracy that the generated prediction provides from a certain method. **Mathematical approach for dealing with uncertainty**: This descriptive parameter informs about which way is the method that deals with uncertainty (probability, multivariate, etc.). **Mathematical approach for processing**: This provides insights of the algorithms type and theoretical development the method relies on. **Amount of processed information**: This parameter is aimed to qualitatively score the amount of information the method requires for generating its output. A qualitative score (high, medium and low) for ranking and measuring is established. **Manageability**: This provides an idea of the ease of handling. Consequently, it measures the complexity and level of expertise required for implementing the method. A qualitative score (high, medium and low) is established. **Transparency**: This measures the ease for an external observer to look into the internal process. The spectrum is quite wide, going all the way through total transparency to complete a black box. A qualitative score (high, medium and low) for ranking and measuring is also established.

### *3.2. Assessment of Parameters*

Table 1 shows the scores and values for each method, based on a rigorous analysis of the global scientific literature and on our own experience. The reader may be referred to the previous section, where the insights of each method are described, and also to the discussion and conclusions sections, where a summary of the essential information drawn from this research is shown.

The interpretation of Table 1 is not trivial. The reader may conclude that there are several similarities among methods, and that is right. Consequently, it seems necessary to tackle a further assessment where the main strengths, weaknesses, opportunities and threats (SWOT) for each method are shown and summarized (Table 2). After that, a final assessment that comprises a suitability evaluation is carried out (Table 3). There, the degree of method suitability for assuring the highest level of rivers' sustainability depends on the final use that the method is designed to and the type of service that it is able to deliver.


**Table 2.** Strengths, weaknesses, opportunities and threats (SWOTs) analysis for methods.

1 feature pear method is included.

**Table 3.** Suitability assessment for method implementation addressing a service.


### *3.3. SWOT analysis*

This evaluation comprises the identification and inclusion of the main feature for each of the 4 characteristics of the SWOT analysis (Table 2). This deep analysis is aimed to provide a guide for the final users to get a general knowledge of each method applicability, so the usage for the goals to reach is optimum. There is a high variety in the traits across methods. However, it is worthy to mention some of the main patterns identified here. For the strength, several methods show great computation power, so make them able to cope with great amounts of data at very fast processing. Other methods are known worldwide that make their usage easier for non-specialists' users. Process-based hydrological models show their ability for capturing and reproducing physical knowledge. Other methods, such as MARS, reveals its high predictive nature and others; furthermore, KF, EnKF and PF, as well as Copulas, show their capacity for dealing with hydrological uncertainty. Regarding weaknesses, methods show also a great heterogeneity. Some of them, such as process-based hydrological models or ANN, show scarce capacity for dealing with hydrological variability and temporally runoff understanding, respectively. Then, WT and SDS reveal a hard output interpretation; traditional techniques show very high inputs requirements; others methods like MARS, Copulas, KF, EnKF and PF are very mathematically complex to deal with. CR show its great opacity in its functioning, and others show their low ability for predicting. In regards to the opportunity, the most frequent and important trait is hybridization with other methods. Finally, threats analysis also shows methods' deficiencies on opacity, as well as on inaccurate, manifold, overrated and complex usage, among others.

### *3.4. Suitability Assessment for Rivers' Sustainability*

The measure of a method suitability is a quite complex matter, and the procedure designed and followed in this research is explained as follows. In this sense, the level of suitability depends on the final use that the method is designed to. For that reason, this analysis is divided on the different services that the method may address. These services are: average prediction (AP), current conditions simulation (CCS), temporal dependence evaluation (TDE), spatio-temporal dependence evaluation (SPTDE), extreme prediction (EP) and protection actions (PA). At the end, a global suitability score (GSS) for the sustainability assessment is provided.

The quantitative score for each service/method is explained as follows (Table 3): The highest level of suitability is symbolized with (\*\*\*), the second level (\*\*), the third level (\*) and, finally, the absence of suitability leaves the cell in blank.

The analysis and interpretation of this assessment shows that the best method for predicting runoff temporal behavior is the CR. On the other hand, the worst methods for this purpose are HJ-Biplot and Hurst coefficient.

### **4. Discussion**

Hydrological processes' variability is increasing on all levels, and those extreme events are more recurrent over time. In order to address this new hydrological reality and aimed to anticipate and forecast it, new approaches, methodologies and techniques have been analyzed in this research. This analysis is articulated in three phases: identification and assessment of parameters, SWOT analysis and suitability assessment.

Seven parameters have been identified and evaluated whose behavior assessment is discussed as follows. For predictability, the methods that behaves the best are ANN, WT, CR and copulas. On the other hand, considering these methods were not initially or specifically conceived for developing predictions, the worst ones for developing a prediction are process-based hydrological models, linear and nonlinear regression models, Pearson's correlogram coefficient (correlogram)–Spearman and Kendall estimator, multivariate adaptive regression splines (MARS) and HJ-Biplot. For reliability, the best methods are CR and FAV. On the contrary, the worst methods are process-based hydrological models and Pearson's correlogram coefficient (correlogram). Regarding the mathematical approach for

dealing with uncertainty, 11 different values have been identified: null; null/scarce, scaling coefficients at different resolutions, regression, correlogram coefficient, optimization, mathematical residuals coefficients, probability, bivariate function, random samples (ensembles) and different statistical expressions. The methods that do not include any uncertainty treatment are the artificial neural networks (ANN), system dynamics (SDs) and Hurst coefficient. In regards to the mathematical approach for processing, four values are identified: theoretical algorithms, dynamic and adaptive mathematical expressions, constant mathematical expressions and matrixes visualization/cluster analysis. Then, regarding the amount of processed information, none of the studied methods requires low levels of data amounts, which is reasonable, because, usually, the more information for populating the method, the best performance level is obtained. For manageability, the easiest methods to work with are the Pearson's correlogram coefficient (correlogram) and Hurst coefficient; on the contrary, the most complicated and sophisticated methods to deal with are the ANN, WT and SDs. Finally, in regards to transparency, the clearest methods are the Pearson's correlogram coefficient (correlogram) and Hurst coefficient, while the darkest are the ANN, SDs, CR, Copulas, Kalman and particle filter.

SWOT analysis reveals a multidimensional analysis largely focused on the advantages and drawbacks for each method. In this sense, one feature has been identified and included for each of the four components of the SWOT analysis, which are strength, weakness, opportunity and threat (Table 2). Some of the most important traits are the following. On the strengths, several methods show great computation power, others are globally known, others are aimed to capture and reproduce physical knowledge, others have a clear predictive nature and others, such as Kalman and the particle filter, show their capacity for dealing with hydrological uncertainty. Regarding weaknesses, some of them show scarce capacity for dealing with hydrological variability and temporally runoff understanding. Then, hard output interpretations and very high input requirements are also common traits; others methods are, mathematically, very complex to deal with; opacity in its functioning and low predictive skills are also important weaknesses to mention. In regards to the opportunity, the most frequent and important trait is hybridization with other methods. Finally, a threat analysis also shows methods' deficiencies on opacity, as well as on inaccurate, manifold, overrated and complex usage, among others.

Suitability assessment for rivers' sustainability comprises an analysis of seven services, which are: average prediction (AP), current conditions simulation (CCS), temporal dependence evaluation (TDE), spatio-temporal dependence evaluation (SPTDE), extreme prediction (EP) and protection actions (PA). At the end, a global suitability score (GSS) for the sustainability assessment is provided. This evaluation reveals that the method that averagely behaves the best for achieving temporally river sustainability is causal reasoning. It is recommended to inform that this final score is an average, and, in this case, CR has an important drawback on the great opacity across the whole implementation.

It is worthy to highlight that none of the analyzed methods are too appropriate by themselves for implementing protection actions. In this service, the best methods are the traditional physical methods (process-based hydrological models) that allow changing the physical features of the hydrological model.

### **5. Conclusions**

This review paper shows an extensive analysis of the most important methods for the hydrological understanding and prediction of rivers' runoff behaviors. Of course, there is a high variability of dimensions involved in this research. Consequently, there are methods more appropriate to one dimension than to others. However, in general terms, the most recommended method is causal reasoning, despite its dark (black box) nature, need of large data amount and manageability difficulty. The reasons why CR is the best-ranked method largely comprises its flexibility, articulated by the chance for incorporating dynamic and adaptive mathematical expressions, reliability, predictability, ease to hybridize with other methods and the uncertainty treatment method, which is probability; that, in itself, is a very powerful uncertainty tool.

This research may be useful for helping to reach a much larger sustainability of rivers, since their temporal hydrological behavior is far from being well understood.

**Author Contributions:** Conceptualization, J.-L.M.; methodology, J.-L.M., S.Z., A.-M.M.-C. and M.-C.P.-A.; software, J.-L.M., S.Z., A.-M.M.-C. and M.-C.P.-A.; validation, J.-L.M. and A.-M.M.-C.; formal analysis, J.-L.M., S.Z., A.-M.M.-C. and M.-C.P.-A.; investigation, J.-L.M., S.Z., A.-M.M.-C. and M.-C.P.-A.; resources, J.-L.M., S.Z., A.-M.M.-C. and M.-C.P.-A.; data curation, J.-L.M., S.Z., A.-M.M.-C. and M.-C.P.-A.; writing—original draft preparation, J.-L.M.; writing—review and editing, J.-L.M., S.Z., A.-M.M.-C. and M.-C.P.-A. and visualization, J.-L.M., S.Z., A.-M.M.-C. and M.-C.P.-A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** Authors acknowledge the great support given by the High Polytechnic School of Avila, (Avila, Spain) and University of Salamanca to elaborate this paper.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Review* **Reviewing Arch-Dams' Building Risk Reduction Through a Sustainability–Safety Management Approach**

**Enrico Zacchei 1,2and José Luis Molina 3,\***


Received: 29 November 2019; Accepted: 31 December 2019; Published: 3 January 2020

**Abstract:** The importance of dams is rapidly increasing due to the impact of climate change on increasing hydrological process variability and on water planning and management need. This study tackles a review for the concrete arch-dams' design process, from a dual sustainability/safety management approach. Sustainability is evaluated through a design optimization for dams´ stability and deformation analysis; safety is directly related to the reduction and consequences of failure risk. For that, several scenarios about stability and deformation, identifying desirable and undesirable actions, were estimated. More than 100 specific parameters regarding dam-reservoir-foundation-sediments system and their interactions have been collected. Also, a summary of mathematical modelling was made, and more than 100 references were summarized. The following consecutive steps, required to design engineering (why act?), maintenance (when to act) and operations activities (how to act), were evaluated: individuation of hazards, definition of failure potential and estimation of consequences (harm to people, assets and environment). Results are shown in terms of calculated data and relations: the area to model the dam–foundation interaction is around 3.0 Hd 2, the system-damping ratio and vibration period is 8.5% and 0.39 s. Also, maximum elastic and elasto-plastic displacements are ~0.10–0.20 m. The failure probability for stability is 34%, whereas for deformation it is 29%.

**Keywords:** concrete arch-dams; stability scenarios; deformation scenarios; safety management; sustainability assessment

### **1. Introduction**

There are many factors, largely controlled by the structures size, that hinder sustainability in the field of dam engineering. In this sense, the height of the blocks can reach more than 100 m and the crown length can reach more than 500 m [1,2]. Dams with these dimensions are called "super-high dams" [3,4]. Then, the presence of structural elements [5], and their interactions, with different functions that increase the difficulty of calculation and modelling, e.g., the cantilevers that support and distribute the vertical loads and the arches that distribute the horizontal loads. Finally, the interaction of dam, foundation, sediments and reservoir sub-systems, requires not only the knowledge of the structural and hydraulic engineering, but also, other engineering areas are involved.

Three aspects, namely geometry, behaviour, and materials, comprise the internal and intrinsic actions, which exclude the external actions and their uncertainties of probability and occurrence. These uncertainties are called "random" and are related to the magnitude of variability and inherent randomness. Besides these types of uncertainties, there are the "epistemic" uncertainties that are related to the lack of knowledge of materials and models [6]. Random and epistemic uncertainties are studied in stochastic analyses, which are used to solve problems that cannot be deterministically solved because models are not known, or data are not available.

Due to the doubts of the input data, analyses, methodologies, and results, the concept of "risk" and quantitative risk assessment (QRA) is introduced through the following equation:

$$\text{Risk} = \int \left[ \mathbf{P}(\mathbf{L}, \mathbf{E}) \times \mathbf{P}(\mathbf{R}|\mathbf{L}) \times \mathbf{C}(\mathbf{L}, \mathbf{R}) \right] \tag{1}$$

where L = loads, E = events, and R = responses. P[R|L] is the conditional probability that R is true, given that L is true, and C stands for the consequences [7,8].

This integral is a measure of risk quantification based on the occurrence and probability of L, E and R, regarding the variability of extreme events, e.g., flooding, hurricanes, earthquakes, explosions. The interest of the concrete arch-dams is proven by the fact that several studies have been published since 1931 [9]. This interest has generated several codes/manuals/reports [10–14]. Furthermore, several academic works with the following goal have been published. First, there are researches about the definition of the shape (volume and area of concrete) optimization, aimed to minimize the cost and the impact of the dam body on the environment [15–23]. Then, publications addressing the analysis of the dam behaviour under seismic actions accounting the enormous importance of the structure [24–33]. Finally, there are studies that consider the fact that the dam body is linked with the foundation base, water reservoir, and soil sediments [34–39].

However, there are some aspects, described as follows, that are not well studied either synthetized or published in the literature. In this sense, the response estimation of arch-dams are not well studied or categorized, for example the effects of the non-uniform temperature variation due to the solar radiation and convective heat [30,40–44]. Furthermore, a good calibration between the theoretical and practical data is often difficult to obtain. In this sense, there is a lack of experimental tests made in the laboratory, which allow verifying the analytical and computational models. Also, there is a lack of practical experience of researchers and technical engineers do not easily accept the insights of researchers. In this sense, some cases about real concrete arch-dams are listed in Appendix A (see Table A1). Finally, but not least, there is a clear lack of academic papers that synthetize, integrate, and summarize most of the aspects involved in sustainability of concrete arch dam building. This review paper mainly aims to cover this deficiency, which comprises its main novelty too. This is performed herein by reviewing the existent knowledge on the development of sustainability and safety assessment through the study of structural stabilities/deformations and failure risk, respectively.

The rest of this paper is organized as follows: Section 2 shows a background about the data and mathematical modelling. Section 3 describes some main key findings about an operating system and the project variables in a managerial context [7,12,14]. Section 4 is dedicated to the materials and methodologies followed in this research, describing the structure gand content of the different stages. Regarding materials, Random Variables (RVs) are showed; on the other hand, methods such as Monte Carlo Simulation (MCS), sustainability assessment framework and seismic hazard assessment are described. Then, Section 5 comprises the description of results, largely addressing the sustainability assessment of structural stability and deformations. Finally, Section 6 is dedicated to show the main conclusions drawn from this research.

### **2. Data and Mathematical Modelling Background**

The case study is the Rules Dam, which is situated on the Guadalfeo River in the Granada province, Southern Spain. It is a super-high concrete arch-gravity, formed by 32 blocks, with single curvature, 509 m of crown length and maximum height of the vertical cantilever Hd 132 m. The Down-Stream (DS) and Up-Stream (US) slope faces are 1:0.60 and 1:0.18, respectively. The capacity and area for the

maximum operating level Ho,r (i.e., water depth of 113 m) of the reservoir are 117.07 Hm<sup>3</sup> and 308 Ha, respectively. The area of the water basin is 1070 km2 [1,2].

The whole system of concrete arch-gravity dams is composed by four sub-systems, i.e., dam, foundation, reservoir and sediments. Usually, only the dam-reservoir-foundation system is studied, and, in many analyses, sediments are not considered as a separated system, but they are included in the reservoir or foundation sub-system. The parameters of the sediments as well as the foundation are very complicated to estimate, unless specific analyses "in situ" are developed. Moreover, it is very complicated to model them because they are not visible without adequate means.

Considering the precedent studies of the authors about the dam [45–49], more of 100 technical data regarding the system dam-reservoir-foundation-sediments have been summarized and shown in the Appendix A (see Tables A2–A7). The subscripts represent the four parts of the system, i.e., d = dam, f = foundation, r = reservoir, and s = sediments.

### *2.1. Dam Sub-System*

Concrete arch-gravity dams are designed to be stabilized by equilibrium forces (horizontals and verticals). Each section of the dam must be stable and independent of any other section.

The dam body is formed by several arch and cantilever units. Arch refers to a portion of the dam bounded by two horizontal planes. Arches have uniform or variable thickness, i.e., the arches may be designed so that their thickness increases gradually on both sides of the reference plane. Cantilever is a portion of the dam contained between two vertical radial planes [10].

The function of arches is to distribute the horizontal stresses along the dam body, whereas the function of cantilevers is to transmit the vertical stresses from the top to the bottom. Moreover, the arch has an important role respect to the stiffness which increases on the dam body.

Dam sub-systems can be modelled using several theories and models that are briefly mentioned as follows.


Moreover, dam sub-systems can be modelled accounting the vertical joints, as follows.


• Solid elements joints. The solid element joint model simulates the joints, connected to the ashlars, as independent solid elements, separating the discontinuity surface and spacing the blocks. These joints are characterized by mechanical models (i.e., elastic or elasto-plastic model) [54,55].

### *2.2. Foundation Sub-System*

Even if it is possible to analyse the four systems separately, it is too approximate to approach some aspects without considering the interactions. In this sense, the foundation sub-system is usually studied including the dam-foundation interactions.

The model that describes the dam base and top foundation contact is Mohr-Coulomb model. This model, used in the literature to evaluate base sliding [57], constitutes a simplified procedure to model a nonlinear single-degree-of-freedom system [58] and the failure mode under a reliability-based approach. This is performed as such due to the failure analysis of the dam–foundation interface being characterized by complexity, uncertainties on models and parameters, and a strong non-linear softening behaviour [59].

The foundation sub-systems can be modelled by a massed, massless, rigid, flexible model.


### *2.3. Reservoir Sub-System*

The main actions produced by water mass are the pressures, which can be static or dynamic pressures and act in horizontal or vertical directions. Reservoir sub-system can be approached by considering "rigid" or "flexible" dam, respectively. In this sense, it can be modelled as:


A very popular modelling approach is the "acoustic elements". This model simulates the pressure distributions of the fluid considering the compressibility of the fluid through the "bulk modulus". To find a solution it is necessary to define appropriate boundary conditions, where the most important one takes place on the contact between fluid and structure [63–65]. Acoustic elements are used for modelling an acoustic medium undergoing small pressure changes. The solution in the acoustic medium is defined by a single pressure variable, which represents its degree of freedom [64,65].

### *2.4. Sediments Sub-System*

Sediments can be modelled as a liquid (viscous model) or as a solid (elastic–plastic model). This is, because two cases should be considered: full and empty reservoir. In the first case, sediments are totally submerged, and therefore sediments can be considered in a more similar way to the liquid hydrodynamic behaviour. In contrast, in the second case, sediments can be dry (solid) or yet submerged (semi-solid) depending on the material of which sediments are made: if the predominant material is the sand soil, the liquid drains easily and thus sediments can be idealized as solid, whereas if it is made of clay soil, the liquid does not drain and so it can be idealized as a liquid.

Considering the two extreme cases, the liquid behaviour tends to the reservoir sub-system behaviour, whereas the solid tends to the foundation sub-system (liquid sediments → like reservoir sub system. Solid sediments → like foundation sub-system). The presence of sediments can affect the behaviour of the whole system. This is because, the reservoir bottom absorption affects the stiffness and damping ratio of the structure [34,66,67].

### *2.5. Interactions of Sub-Systems*

By means of the aforementioned parameters of the four sub-systems, it is possible to define some parameters that account the interactions among sub-systems. By considering these values, it is possible to estimate some general relations that can be used to the design, for instance: (i) the area of rigid foundations under the dam can be estimated as ~ 3.0 Hd 2; (ii) the contribution of the damping ratio of each sub-system respect to the damping ratio of the system is ξ<sup>d</sup> = 0.05 (26%), ξ<sup>f</sup> = 0.1 (51%), ξ<sup>r</sup> = 0.005 (3%), ξ<sup>s</sup> = 0.04 (20%); (iii) the contribution of the vibration period of each sub-system respect to the system vibration period is T1,d (s) = 0.284 (40%), T1,f = 0.09 (13%), T1,r = 0.314 (45%), T1,s = 0.014 (2%).

These percentages show the weight of each sub-system respect to the total response. However, it is important to note that these values refer to this specific case study or, more in general, to concrete arch-gravity dams under specific conditions.

Finally, a modelling process should be calibrated for accurately identifying the problem to be analysed. There is a closer correlation between models and types of analysis: The choice of a model (software) is based on the specific problem to be solved. Although nowadays, there are extremely complex models [68] that consider all the phenomena together, it is good to define and focus a specific problem aspect and then to converge and resolve it by using a unique model.

Each model is made to study a specific problem. It is important to consider all the parts of the whole system, but it is also necessary not to lose control of the parameters and their interactions.

### **3. Management Operating Systems**

The managerial procedures that account for the risk analysis are studied in reliable papers [7,8,69] and guidelines [12,14]. Moreover, in the literature, it is possible to find several contributions regarding stability optimization for concrete arch-dams [17,18,22,36,45]. However, the search of a safety and no-safety domain by taking into account the stability and deformation of arch-dams in a managerial context, by considering some parameters (see Table 1 later) obtained from several data, has not been carried out. In this sense, this paper provides a novelty for the research.


**Table 1.** Probabilistic parameters (collected results from [47–49]).

Note: PGA = Peak Ground Acceleration. SD = Standard Deviation. N = Normal (Gaussian) distribution. <sup>a</sup> CV is the Coefficient of Variation defined by: CV = (SD/Mean RV) × 100.

The project management is formed by design phases, which are called "project baselines", "project procedures", and "project systems". Each phase contains several sub-phases listed in the Figure 1.

**Figure 1.** Operating system requirements.

In this paper, a particular attention about the "management level schedules" and "risk assessment" is considered; the former estimates the possible scenarios, whereas the latter defines the hazards.

In analyses there are different parameters/values that usually are adopted: deterministic parameters (DP), probabilistic parameters (PP), semi-probabilistic parameters (SPP), semi-deterministic parameters (SDP) and super-probabilistic parameters (SP2). SPP are the parameters obtained by combining DP and PP, whereas SDP are obtained by DP and SPP. SP2 are obtained by a probabilistic analysis, which are recalculated and re-estimated using one or more probabilistic approaches. Deterministic parameters are usually well known through the literature (papers, books, codes, guidelines), experience (real projects, academic works, research projects), and empirical experimentation (laboratory work, building sites). Probabilistic parameters are not known, and therefore are subject to aleatory (inherent randomness) and epistemic (lack of knowledge of materials/models) uncertainties, as have already been introduced.

### **4. Materials and Methods**

### *4.1. Materials*

This research comprises the analysis of probabilistic approaches which are the most reliable and precise ones for analysing the stability of dams. In this sense, these analyses are based on the definition of probability density functions (PDFs) through several random variables (RVs). The parameters used to develop the analysis in this paper are listed in Table 1. These parameters come from precedent studies [47–49], and here are considered as RVs to carry out a sustainability assessment, and are therefore plotted by a probabilistic distribution with a mean and standard deviation (SD).

### *4.2. Methods*

### 4.2.1. Monte Carlo Simulation (MCS)

To estimate possible scenarios, MCS, which generates RVs, has been used in following way. Limit State (LS) function G(X) is defined. When the domain G(X) < 0, the LS is called "no safety", whereas when G(X) > 0, the LS is called "safety". The separation of both domains is given when G(X) = 0 (limit domain). Given a random variable vector X = {x1, ... ,xj} = {xi} for a LS function G(X) and fX(xi), which is the joint PDFs of xi, the general probability x% that G(X) takes on a value less than 0 (called here probability of failure pf) is [70,71]:

$$\mathbf{p}\_{\mathbf{f}} = \mathbf{P}[\mathbf{G}(\mathbf{X}) < 0] = \int\_{\{\mathbf{X} \colon \mathbf{G}(\mathbf{X}) < 0\}} \mathbf{f} \mathbf{x}(\mathbf{x}\_1, \dots, \mathbf{x}\_l) d\mathbf{x}\_1 \dots d\mathbf{x}\_l = \int\_{\{\mathbf{X} \colon \mathbf{G}(\mathbf{X}) < 0\}} \mathbf{f}\_{\mathbf{X}}(\mathbf{x}\_l) d\mathbf{x}\_l \tag{2}$$

Equation (2) represents the cumulative failure probability (CFP), which represents the area of the PDF within a defined interval.

By using MCS, Equation (2) can be rewritten as:

$$p\_f = \int\_{\{\mathbf{X} \colon G(\mathbf{X}) \prec \mathbf{0}\}} I(\mathbf{x}\_i) f\_{\mathbf{X}}(\mathbf{x}\_i) d\mathbf{x}\_i \tag{3}$$

where *I*(·) is an indicator function, defined by:

$$I(\mathbf{x}\_i) = \begin{cases} 1, \text{ for } G(X) \le 0 \\ 0, \text{ for } G(X) > 0 \end{cases} \tag{4}$$

Finally, *pf* can be considered as the mean value of *I*(*xi*), i.e., ¯ I(*xi*) = E[*I*(*xi*)], therefore Equation (3) becomes:

$$p\_f = \frac{1}{N} \sum\_{i=1}^{N} I(\mathbf{x}\_i) = \frac{N\_f}{N} \tag{5}$$

where *N* is the number of simulations (or samples) and *Nf* is the number of simulations with *I*(*xi*) ≤ 0. It is note that the result of *pf* is more accurate when *<sup>N</sup>* → ∞. In practice, samples required are 1 <sup>×</sup> <sup>10</sup>Nk where the choice of Nk is due to the computer power and available computational time.

### 4.2.2. Sustainability Assessment Framework

Sustainability has been assessed in this research from a double perspective. First, the perspective of temporal sustainability, closely related to the duration and useful life of arch dam infrastructures. This dimension is specifically articulated and assessed through the design parameters of "stability" and "deformation". Secondly, sustainability has been assessed from a safety perspective articulated through risk calculation. Consequently, in a broad scale, sustainability assessment is developed from a dual sustainability/safety management approach (Figure 5). On the other hand, in a detailed scale, the sustainability of concrete arch dams is evaluated from a design optimization perspective, specifically, for dams´ stability and deformation. Additionally, the safety perspective is directly related to the reduction and consequences of failure risk. For this, several scenarios about stability and deformation, identifying desirable and undesirable actions, were estimated. Quantitative results on both dimensions of sustainability are provided and explained in results section.

There are several types of actions that are generated either by human or by nature. These actions can be catalogued as either "environmental actions" or "human actions". All aspects regarding these actions are included in "impact matrices" where they are identified as "hazards". Several hazards can affect the durability of structures, e.g., environmental, social and economic impact; population and consumptions growing; climate change (temperature and humidity) [72]; flooding; hurricanes; explosions of blast waves in the terrorist attacks [73] or in demolitions [74]; seismic hazard [75]; corrosion [76,77].

Here, the last two hazards are introduced since are known by authors. However, in this analysis only seismic hazard assessment is considered.

Structures are subjected to internal and external stresses and deformations due to (1) excitation of masses by seismic vibrations or general dynamic loading by extreme events, and (2) the corrosion of the reinforced concrete (RC) elements.

Table 2 shows both hazards (as a succession: hazard → approach → scenarios), the relative approach and its scenario type.


**Table 2.** Identification of impacting hazards.

Figure 2 shows the inter-combinations among the four sub-systems of the concrete arch-dams. It is possible to see all the possible combination among the dam-foundation, dam-sediments, dam-reservoir, foundation-sediments, foundation-reservoir and sediments-reservoir. By knowing the variables of the project, it is possible to treat the hazards in a practical way.

**Figure 2.** Inter-combinations of the sub-systems (the number in the brackets indicates the quantity of the used data provide in the Appendix A) and the impacting hazards.

### 4.2.3. Seismic hazard assessment

The seismic events are extreme events that may be accurately studied. The seismic hazard is usually estimated by using two approaches: probabilistic and deterministic. The former, probabilistic seismic hazard analysis (PSHA) is based on the Cornell method [80] and Poisson distribution [71]. To apply it, it is necessary to know seismogenic zones, i.e., zones where the earthquakes are equally likely and independent of each other at any location (e.g., in Spain [81]).

The probability that a ground motion parameter *S* exceeds the ground motion level *S*<sup>0</sup> in i-th source area is defined by Λ*i*, which depends on: the PDF of the magnitude *fm*(*m*) and of the site-source distance *fr*(*r*), the standardization Normal distribution *f*ε(ε) [71] with the ground motion randomness ε and, the average annual rate of exceedance λ*<sup>c</sup>* of an event with magnitude m described through the Gutenberg–Richter trend line [82], which provides the ratio between the number of small and large events and the level of seismicity [83].

The probability is defined by:

$$
\Lambda\_i = \lambda\_\varepsilon \int\_{\mathfrak{m}} \int\_\tau \int\_\varepsilon P[S > S\_0 | m, r, \varepsilon] f\_\mathfrak{m}(m) f\_\mathfrak{r}(r) f\_\mathfrak{r}(\varepsilon) dm \, dr \, d\varepsilon \tag{6}
$$

If the analysis involves more of one seismogenic zones (where *Ns* = number of seismogenic zones), the probability of exceedance is defined by:

$$\Lambda\_{\mathcal{S}\_0} = P[S > \mathcal{S}\_0] = \sum\_{i=1}^{N\_s} \Lambda\_i \tag{7}$$

Figure 3 shows some curves (as results example) in terms of accelerations vs. structural period (Figure 3a) and hazard contribution respect to the magnitude and fault-site distance (Figure 3b).

**Figure 3.** Example of hazard curves (**a**) and hazard contributions (**b**).

MCS is used to analyse the sustainability of the structure respect to the stability and deformations. LS function is written as the difference between the stable actions As, and unstable actions Au: G(X) = As(X) – Au. When As < Au, G(x) < 0, the failure is achieved.

Figure 4a,b shows the generated MCS points, whereas Figure 4c–d shows an example how to identify the LS function (Figure 4c) and the PDF in 3D (Figure 4d). To the left of the intersection point (Figure 4c), between stable and unstable trend line, there is the "no safety" state (G(X) < 0), whereas to the right of this point there is the "safety" state (G(X) > 0). The PDF in the (xi, xi+1) point represents the value of the probability around (xi, xi+1) point in relation to the amplitude of this around (density).

**Figure 4.** *Cont*.

**Figure 4.** MCS points for 1 <sup>×</sup> 104 simulations in spread form (**a**) and linear form (**b**). Individuation of the LS (**c**) and PDF (**d**) respect to RVs for G(X) = 0.

Figure 5 shows the methodology by the flow chart used in the analysis. The flow chart is divided in two principal parts: general and specific part. In the first one, the process and operation phase are defined. Here, choices, decisions, individuation of the structure (issue), hazards, and the possible approaches are established. Then, the technical actions are analysed in terms of data and control of modelling and analyses. Here, a specific concrete arch-dam is individuated (case study), by defining sub-systems data, RVs, methods and approaches (if the modelling and analysis are not satisfactory and are not consistent to the individuated hazards, it is necessary to start over). Finally, scenarios are estimated in terms of stability and deformations of the dam by providing safety and no-safety domain (sustainability assessment) and probability of failure (safety assessment). The flow chart concluded by taking a final decision from managers and technical engineers.

**Figure 5.** General methodology flow chart.

### **5. Results**

### *5.1. Sustainability Assessment*

Here, six scenarios to evaluate the sustainability assessment accounting the deformation and stability of concrete arch-dams are shown. Stable actions refer to the probabilistic parameters in Table 1. By knowing the mean RV and SD for each parameter it is possible to generate a several points by MCS.

To the left of the Figures 6 and 7 the trend lines of the stable and unstable actions are shown. The horizontal dashed line indicates the LS line (i.e., the mean line when the stable line intersects the unstable line). For the stable action, its logarithmic trend line is also plotted, which shows better the progress of an action that starts from zero and reaches its maximum value. The logarithmic trend intersects the unstable line before respect to the linear stable trend. This gap could represent a security factor that increase the "safety" LS. When the dashed horizontal line rises, the pf increases and so the "no safety" state is more probable.

**Figure 6.** Three scenarios (**I**–**III**) regarding dams' deformation. Trend lines of stable and unstable actions vs. number of simulation (**left**); PDF when As = Au (**right**).

**Figure 7.** Three scenarios (**IV**–**VI**) regarding dams' stability. Trend lines of stable and unstable actions vs. number of simulation (**left**); PDF when As = Au (**right**).

To the right of the Figures 6 and 7, the PDFs when (As = Au) are plotted. The solid curves represent the PDFs by mean RVs, whereas the dashed curves represent the PDFs by negative SDs.

### *5.2. Safety Assessment*

Finally, the risk management model defined in literature [12,14] show the need of defining the undesirable event with the potential for harm or damage in these following steps: individuation of hazards → defining of potential for failure → estimating of consequences (harm to people, assets, environment). These steps are needed to design and justify engineering activities (why act?), to propose activities maintenance (when to act) and to tackle operations activities (how to act).

In this sense, the safety management assessment can be evaluated by quantifying the pf. Table 3 and Figure 8 summarize the results in accordance to Figures 6 and 7.


**Table 3.** Identification of impacting hazards.

### **6. Summary**

This paper mainly aimed to review the knowledge on the development of sustainability and safety assessment through the study of structural stabilities/deformations and failure risk consequences, respectively, for concrete gravity arch-dams.

In order to carry out the main analysis, several aspects have been defined: materials regarding the sub-systems (dam, foundation, reservoir, sediments) and their interactions; methods respecting to the operating systems of a project; deterministic and probabilistic variables; modelling and methodologies.

From precedent-specific studies of the authors investigating dam design, more than 10 theoretical modelling, 10 modelling types by software, more than 100 specific parameters, and more than 100 references are summarized.

This paper addresses and comprises critical aspects that are summarized as follows: (i) to show innovative approaches respecting to the enormous quantities of variables that are involved for concrete arch-dams; (ii) to provide numerical values of parameters to design concrete arch-dams; (iii) to show the project phases and methodologies; (iv) to estimate different scenarios respecting to the main actions on the dam system; (v) to contribute to the knowledge of the state-of-the-art about concrete arch dams.

The first results are shown in terms of new estimated data provided in the Appendix A. Other results concern the parameters of the interaction between dam–foundation–reservoir–sediments with respect to the area of rigid foundations under the dam (~ 3.0 Hd 2), the contribution of each sub-system damping ratio respect to the system damping ratio (8.5%), and the contribution of each sub-system vibration period respect to the system vibration period (0.393 s). These values are useful to estimate some general relations that can be used to aid design. Moreover, the maximum elastic and elasto-plastic displacements are of the order of ~ 0.10–0.20 m that, in relation to the maximum dam height, is Hd/1000, in accordance with the literature [6].

Furthermore, the sustainability assessment demonstrates that the mean probability of failure of the stability of dam body and its deformation is about 32%. In particular, that for stability is 34%, which is higher than for the deformation at 29%. These mean percentages are quite large because unstable actions have been taken. When the intersection point between the stable and unstable line rises, the pf increases, and so the "no safety" state is more probable. However, this raises the level of attention during the design of a monitoring method for concrete arch-dams, and in this sense, risk management can be carried out satisfactory.

**Author Contributions:** Conceptualization, E.Z. and J.L.M.; methodology, E.Z. and J.-L.M.; software, E.Z.; validation, E.Z. and J.L.M.; formal analysis, E.Z.; investigation, E.Z.; resources, E.Z.; data curation, E.Z.; writing—original draft preparation, E.Z.; writing—review and editing, J.L.M.; visualization, E.Z. and J.L.M.; supervision, J.L.M.; funding acquisition, E.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** The study was funded by Coordination of the Improvement of Graduated Professionals (CAPES), Support Program for Foreign Students of Doctorate (PAEDEX) and Ibero-American University Postgraduate Association (AUIP) (reference number: 3.224.803.003.569).

**Acknowledgments:** The first author acknowledges the University of Salamanca to pay the rights (when applicable) to completely download all papers in the references.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Appendix A**


**Table A1.** Some cases of real concrete-arch dams studied for scientific purposes.


**Table A2.** Collected data relative to dam sub-system.

Note: \* = Estimated value. US = Up-Stream. DS = Down-Stream. max. = Maximum. min. = Minimum. long. = Longitudinal. trans. = Transversal. fcd = Design compressive strength. fcm = Mean compressive strength at 28 days. σ<sup>c</sup> = Compressive stress. Ecm = Secant modulus of elasticity. Eep = Secant elasto-plastic modulus. εc1 = Strain at peak stress. ε<sup>c</sup> = Shortening strain. ν<sup>d</sup> = Poisson's ratio of the concrete. fctd = Design tensile strength. Gd = Shear modulus. cd = Cohesion of the concrete. φ<sup>d</sup> = Angle of friction of the concrete. Ti,d = Structural period for i-th mode. MPMR = Modal participating mass ratios. eq. = Equivalent. εlt = Limit dynamic tensile strain. ac = Effective crack length. wc = Characteristic micro-crack opening that propagate through the aggregates. Gt = Tension specific fracture energy. h0 = Size of the element that model lc for the linear analysis. lc = Crack band width of the fracture.

**Table A3.** Collected data relative to foundation sub-system.


Note: \* = Estimated value. cf = Cohesion of the foundation. φ<sup>f</sup> = Angle of friction of the foundation. ν<sup>f</sup> = Poisson's ratio of the foundation. Gf = Shear modulus. Ef = Elastic modulus of foundation. Vs,f = Shear wave velocity in rock. Vp,f = Compressive wave velocity. Eo,f = Oedometric modulus. T1,f = Foundation's first period.


**Table A4.** Collected data relative to reservoir sub-system.

Note: \* = Estimated value. DS = Down-Stream. Vp,r (or Cr) = Compressive wave velocity. Eb = Bulk modulus of reservoir. T1,r = Reservoir's first period.

**Table A5.** Collected data relative to sediments sub-system.


Note: \* = Estimated value. cs = Cohesion of the sediments. φ<sup>s</sup> = Angle of friction of the sediments. ν<sup>s</sup> = Poisson's ratio of the sediments. Gd,s = Shear modulus. Ed,s = Elastic modulus. Vs,s = Shear wave velocity in sediments. Vp,s = Compressive wave velocity in sediments. Eo,s = Oedometric modulus. T1,r = Sediments' first period.


**Table A6.** Parameters accounting the interactions.

Note: \* = Estimated value. q = Admittance coefficient. α = Wave reflection.


### **Table A7.** Modelling types.

Note: FEM = Finite Element Method. BEM = Boundary Element Method. UAV = Unmanned Aerial Vehicle. N/A = Not applicable. <sup>a</sup> Coupled BEM-FEM is used to study the fluid-structure interactions [19]. Also, accurate computation of fluid-structure nonlinear interaction is analysed by the immersed boundary method (IBM) proposed in [41]. <sup>b</sup> The reader can refer to specific bibliographies in the area of the design and/or architecture.

### **References**


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