**A New Tool for Assessing Environmental Impacts of Altering Short-Term Flow and Water Level Regimes**

**María Dolores Bejarano 1, \*, Jaime H. García-Palacios 2 , Alvaro Sordo-Ward 2 , Luis Garrote 2 and Christer Nilsson 3,4**


Received: 13 September 2020; Accepted: 10 October 2020; Published: 19 October 2020

**Abstract:** The computational tool InSTHAn (indicators of short-term hydrological alteration) was developed to summarize data on subdaily stream flows or water levels into manageable, comprehensive and ecologically meaningful metrics, and to qualify and quantify their deviation from unaltered states. The pronunciation of the acronym refers to the recording interval of input data (i.e., instant). We compared InSTHAn with the tool COSH-Tool in a characterization of the subdaily flow variability of the Colorado River downstream from the Glen Canyon dam, and in an evaluation of the effects of the dam on this variability. Both tools captured the hydropeaking caused by a dam operation, but only InSTHAn quantified the alteration of key flow attributes, highlighting significant increases in the range of within-day flow variations and in their rates of change. This information is vital to evaluate the potential ecological consequences of the hydrological alteration, and whether they may be irreversible, making InSTHAn a key tool for river flow management.

**Keywords:** fluvial ecosystems; hydropeaking; InSTHAn tool; short-term flow regimes; subdaily flows; sustainable river management

#### **1. Introduction**

Flow variables shape the dynamics of in-channel and floodplain conditions that determine fluvial ecosystem structure and functioning [1,2]. Whereas the ecological role of monthly and annual flow dynamics has been in focus for many years, less attention has been paid to flow variability within days [3].

Variation at such short time scales is altered by several human activities, such as land use and urbanization, and water management practices such as flood control, agricultural withdrawals and power generation [4,5]. Increasing instability of within-day flows and exacerbation of extreme flows may likely affect water quality [6], fluvial landforms [7] and aquatic and riparian organisms that are adapted to naturally less fluctuating conditions (review by Bejarano et al., 2018 [8]).

Subdaily flow regimes govern fish reproduction [9] by affecting egg viability and reproductive capacity. They also affect their behavior [10] and performance [11] by offering shelter and food, which affects their movements. Ultimately, subdaily flow regimes affect fish survival, by modulating fish energy balance with implications for growth rates and risk of illness, or due to stranding and drift [12]. Risk of desiccation [13] and catastrophic drift [14] of macroinvertebrates increases with more

recurrent daily dry periods and peak flows. Highly fluctuating short-term flow regimes may also increase propagule dispersal of aquatic and riparian plants, and interfere with germination, growth and performance, thus likely hampering recruitment and increase mortality [15,16]. At the community level, alterations of short-term flows may ultimately result in removal of intolerant species and invasion by exotic species [17].

The rise of hydropower as a renewable energy source calls for a better understanding of the ecological consequences of altered flow regimes and associated hydraulic parameters at short time scales. Hydropeaking plants usually cause frequent and rapid fluctuations in flow and water level within the day [18], and this variation is superimposed upon the seasonal changes in flow regimes resulting from water storage in upstream reservoirs. The demand for hydropower is growing, especially in Southeast Asia, Africa and Latin America [19]. In Europe, hydropower is promoted by legislation such as the Renewable Energy Directive (RES; 82 2009/28/EC). Consequently, shifting flow regimes towards preindustrial conditions in rivers affected by hydropeaking without significantly affecting hydropower production is a challenge for river managers. To cope with this challenge, scientific studies focused on the short-term variation of flow regimes are needed.

The restoration of preindustrial flow regimes requires metrics comprising of the full range of flow components (i.e., magnitude, frequency, duration, timing and rise and fall rates; [1]) and temporal variability (i.e., long- and short-term variations) is essential. Whereas studies of seasonal and annual flow patterns have been common, analysis of short-term data have suffered from a lack of computational tools. To the best of our knowledge, the first metrics accounting for short-term variability of flow regimes appeared within the last two decades (e.g., [4]) and the most comprehensive approaches date from 2014 onwards (Table 1). Unlike the recent advance in the definition of subdaily metrics, computational tools supporting metric calculation have hardly been developed. The tools devised by Hass et al. [20] and Sauterleute and Charmasson [21] (Table 1) are the only ones we are aware of to date, and at the time of writing, the former tool was unavailable for use. This is unfortunate, because the management of series of flows or water levels recorded at such a fine resolution is challenging.

Our main goal is to develop a tool for computational time series analysis that assists in a comprehensive characterization of short-term stream flow and water level regimes and assesses the alterations of such regimes and, thus, their derived potential environmental impacts. We also want the tool to provide results through charts and graphs, which are easy to interpret by a wide range of users. Additionally, in this article we also aim to validate the devised tool by applying it to a case study. This manuscript will help to transmit the utility of the proposed tool to both the scientific and professional audience.


#### **Table 1.** Review of literature dealing with subdaily flows and water levels.

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

#### *2.1. InSTHAn's Development: Underlying Theory and Methods*

We developed the new tool called InSTHAn: indicators of short-term hydrological alteration. InSTHAn allows the user to (i) summarize multiple, long series of subdaily flow or stage data into a manageable set of ecologically meaningful metrics (i.e., characterization), (ii) qualify and quantify the deviation of each series from the unaltered state to assess the hydrological alteration and its potential environmental impact and (iii) display both the short-term flow or stage pattern and its impact by using tables and graphs. The name informs on its ultimate purpose and time scale of the target regime. The pronunciation of the acronym refers to the required recording interval of the input data (i.e., instant flow or water level measured or modeled records).

#### 2.1.1. Characterization of Short-Term Regimes

The first step when analyzing a subdaily flow or water level dataset is to describe its distinctive features. For this aim, the proposed tool computes a set of descriptors, here called short-term characterization indicators (STCI; Table 2). STCI meets two requirements: it (i) captures representative information on the magnitude, frequency, duration, timing and rates of change from the subdaily flow or water level dataset and (ii) is assumed relevant for the biotic composition of aquatic, wetland and riparian ecosystems [1,34].


**Table 2.** Short-term characterization indicators calculated in indicators of short-term hydrological alteration (InSTHAn). # means "number of".


**Table 2.** *Cont.*

STCI was calculated based on an *n*-year long series of flows (*Q*) or water levels (*L*) recorded or modeled at any subdaily time scale, e.g., every 15, 30, 60 or 120 min, *T* being the time interval between records. Optionally, series of longer *T* can be derived from the original dataset upon request. For the purpose of defining indicators, each daily hydrograph (or limnograph) is divided into two characterization units: records (*R*; e.g., *Q* or *L* records; Figure 1) and periods (*P*). The number of records (*R*) per day varies according to *T*, which can be the same as that of the series input at least. Each record (*R*) of a series can be assigned one of the following patterns: (1) rise (R*R*), when *<sup>Q</sup>*(*T*)−*Q*(*T*−1) <sup>&</sup>gt; 0; (2) fall (F*R*), when *<sup>Q</sup>*(*T*)−*Q*(*T*−1) <sup>&</sup>lt; 0; (3) stability (S*R*), when *<sup>Q</sup>*(*T*)−*Q*(*T*−1) <sup>=</sup> 0; (4) change (C*R*), when *<sup>Q</sup>*(*T*−1) , the pattern in *<sup>Q</sup>*(*T*+1); (5) reversal (R*R*), when the pattern changes from F*R* to R*R* or vice versa, without considering the stability; (6) minimum (Min*R*), when *Q*(*T*) = *Q*(min); (7) maximum (Max*R*), when *Q*(*T*) = *Q*(max) and (8) mean (MeanR), when *Q*(*T*) = *Q*(mean). The threshold from which two consecutive records are considered different (or equal) may be set by the user. It could be similarly applied to *L*. Where *T* is the user-defined subdaily time interval and min, max and mean are the daily minimum, maximum and mean flows or water levels, respectively. Periods (*P*) denote

within-day portions of time of a similar pattern among records (cf. above). There may be one to several *P* per day, lasting up to 24 h, and which can be classified according to the characteristic short-term pattern into periods of rise (R*P*), fall (F*P*), stability (S*P*), minimum (Min*P*), maximum (Max*P*) and mean (Mean*P*). STCI provides quantitative information on magnitudes, rates of change and frequencies of *R* and *P* and on durations of *P*, from each day of the year (i.e., *i*th day of the year from 1 to 366). That STCI has daily values also implies information on timing (i.e., intra-annual and inter-annual) of *R* and *P*. STCI referred to *R* patterns is called record-based STCI, whereas STCI referred to *P* patterns is named period-based STCI. For comparisons of several short-term regimes, the record-based STCI must be calculated based on the same time interval between records (*T* of their *R*) for all series (Table 2).

**Figure 1.** Patterns identified by InSTHAn (**a**,**c**; pre-dam) and COSH-Tool (**b**,**d**; post-dam) during five days in June, 2007 (**a**,**b**) and 1949 (**c**,**d**), in a hydrograph built on hourly flows recorded in the Colorado River reach downstream from the Glen Canyon dam. Dots represent the flow records, which are colored or marked according to their pattern for InSTHAn or to identify peaking events for COSH-Tool. The following figures were provided to COSH-Tool for peaking events identification: 4 and 96 as inferior and superior percentiles of the rate of change, 120 min as the minimum duration for a peak, 0.2 as the magnitude threshold to merge peaks and 180 min as the minimum duration between two consecutive peaks.

For several-year long series (*n* > 1; where *j*th denotes each year of the series from 1 to *n*), each indicator is ultimately computed as each day average for the whole *n* years dataset, getting 366 values per indicator (Equation (1); Table 2). The frequency and duration indicators report records a day of what it is being described by the indicator. Rate-related features report the rise or fall rates of the variable in its units per the time interval (*T*) between records (*R*). The units of the STCI magnitude-related indicators are the same of the selected variable (e.g., m<sup>3</sup> /s for flows or m for levels). Furthermore, for the calculation of STCI describing magnitude-related features, the series is also previously standardized by dividing between the mean flow or water level for the whole dataset. Consequently, InSTHAn also provides unitless magnitude-related indicators, which is useful when

daily flow or water level datasets. InSTHAn's

comparing series from different rivers. The tool calculates values for a total of 30 STCI, from which 14 are related to frequencies, 6 to durations and 10 to magnitudes and rates of change (Table 2).

$$\text{STCI}\_{day(i)} = \frac{\sum\_{j=1}^{j=n} \text{STCI}\_{day(i,j)}}{n} \tag{1}$$

Equation (1): *STCIday*(*i*) : short-term characterization indicator for the *i*th day from 1 to 366 of the year; <sup>P</sup>*j*=*<sup>n</sup> j*=1 *STCIday*(*i*,*j*) : sum of the short-term characterization indicator for the *i*th day from 1 to 366 of the year *j*th of the several-year long dataset from 1 to *n* and *n*: total number of years of the dataset.

#### 2.1.2. Assessment of Short-Term Hydrological Alteration and Environmental Impact

When assessing the impact of a perturbation we want to know whether the state of the perturbed system differs significantly from what it would have been in the absence of perturbation (natural onwards). Provided the difficulties in collecting direct ecological data both under perturbed and natural conditions, the here proposed tool is based on the widespread qualitative understanding of the ecological implications of the suite of hydrological indicators calculated by InSTHAn to derive the potential environmental impact of the alteration of the short-term flow or water level regimes. That is, the environmental impact is assumed in accordance with the degree and type of hydrological alteration, an assumption also applied by Bejarano et al. [35]. For the assessment of the hydrological alteration InSTHAn requires two datasets of subdaily flows or water levels to be compared, one representing the perturbed regime and the other the natural regime. The latter may come from the same location as the perturbed one as the preimpact period records or modeled records, or it may come from a comparable river reach.

The impact assessment involves a one-by-one comparison of the whole suite of STCI (record- and period-based STCI involving 366 values per indicator from each day of the averages for *n* years) from the perturbed and corresponding natural subdaily flow or water level datasets. InSTHAn's output is a suite of short-term impact indicators (STII, record- and period-based STII) obtained through Equation (2). Each impact indicator quantifies the deviation of the perturbed condition (*per*) from the natural condition (*nat*) of the corresponding characterization indicator (Equation (2)). Log<sup>10</sup> is applied to the quotient to avoid excessively high values when the averages of certain indicators in the natural conditions are very low (e.g., indicators related to flow rates of change). Impact indicators can take any positive and negative value and are unitless. Comparisons are not restricted to perturbed and natural series, but other comparisons between series may be made according to user needs.

$$\text{STII}\_{\text{day}(i)} = \text{sign}(\text{STCI}\_{\text{day}(i)}^{\text{nat}} - \text{STCI}\_{\text{day}(i)}^{\text{per}}) \log\_{10} \left| \frac{\text{STCI}\_{\text{day}(i)}^{\text{nat}} - \text{STCI}\_{\text{day}(i)}^{\text{per}}}{\left(\frac{\sum\_{i=1}^{366} \text{STCI}\_{\text{day}(i)}^{\text{nat}}}{366}\right)} + 1 \right| \tag{2}$$

Equation (2): *STIIday*(*i*) : short-term impact indicator for the *i*th day from 1 to 366 of the year; *sign*(*STCInat day*(*i*) <sup>−</sup> *STCIper day*(*i*) ): sign function for the difference between the short-term characterization indicators for the *i*th day from 1 to 366 of the year from the natural (*nat*) and perturbed (*per*) series; *STCInat day*(*i*) <sup>−</sup> *STCIper day*(*i*) : absolute value for the difference between the short-term characterization indicators for the *i*th day from 1 to 366 of the year from the natural and perturbed series and P*i*=<sup>366</sup> *i*=1 *STCInat day*(*i*) : sum of the short-term characterization indicator for the *i*th day from 1 to 366 of the year from the natural (*nat*) series.

#### *2.2. InSTHAn's Application and Validation*

We were interested in (i) characterizing the short-term flow variability of the Colorado River (USA) along the reach downstream from the Glen Canyon dam before and after its construction (i.e., 1966) and (ii) evaluating the impacts of the dam on this short-term flow regime and, thus, subsequent expected environmental impacts on the fluvial ecosystem. For this aim, and in order to verify InSTHAn's correct operation and demonstrate its advantages, we applied InSTHAn and the Computational Tool for the Characterization of Rapid Fluctuations in Flow and Stage (Sauterleute and Charmasson, 2014; COSH-Tool onwards), which was kindly provided by authors (v2016). We had two original flow (m<sup>3</sup> /seg) data series (.xlsx files). The natural series corresponded to hourly flows measured between 1943 and 1951, whereas the perturbed series corresponded to every 15 min flow measured between 2003 and 2011, both at Lees Ferry (9,380,000 gauging station code; data from https://waterdata.usgs.gov/). The former file was characterized by one column (flow) without a heading and five decimal places measurements, and the latter was characterized by three columns (date, time, and flow) with their respective headings and two decimal place measurements.

#### **3. Results**

#### *3.1. InSTHAn's Characteristics*

InSTHAn has been developed in Matlab, and the code is created and executed based on a user's actions within the graphical user interface (GUI). This approach provides convenient access to the most relevant code functions via buttons in the GUI, but translates each user action into executable code that can be captured in a script. The distribution version of the tool is encapsulated into an executable file that does not require a Matlab license for the end user. Moreover, implementing scripting within the GUI enables immediate visualization of results via graph and table-based views of the data. InSTHAn supports the commonly used .xlsx and .txt data files containing flow and/or water level records in columns, measured at any subdaily time interval and provided in any consistent system of units defined by the user. The results are generated into excel files with open code macros to help the user to zoom into long series graphs. Finally, InSTHAn may be deployed on multiple platforms (Windows, Linux and Macintosh), the installation and calculations require little disk space and computing power, respectively, and graphics have satisfactory performance on commonly used processors. Specifically, the required disk space is 27 Mb for computers with Matlab v2018, but 1.56 additional Gb corresponding to the additional libraries distributed with the MCR\_R2018a\_win64\_instaler.exe are necessary when Matlab is not installed. Concerning the computational power, it took four minutes to complete an impact analysis for the selected case study involving the management of records, in a i7, 20 Gb ram PC.

InSTHAn is organized into projects and analyses (Figure 2). A project consists of one to several analyses (e.g., Project 1 and Analyses 1, 2 and 3 in Figure 2). Any calculation of a set of indicators constitutes an analysis, being of two types: characterization analysis, aimed exclusively at characterizing a short-term flow or water level regime (calculation of STCI), and impact analysis, aimed at assessing the alteration of a short-term flow or water level regime (and thus inferring the derived environmental impact; calculation of STII). A folder is generated where specified in the computer to store the projects ("Project 1" directory; Figure 2) where data and all analyses run within the same project are stored, either in an automatically generated folder for the data files ("Excel" subdirectory), for the characterization analyses ("Characterization" subdirectory), or for the impact analyses ("Impact" subdirectory; Figure 2).

mpact analyses ("Impact" subdirectory; Figure 2).

the projects ("Project 1" directory; Figure 2) where data and all analyses run

**Figure 2.** General organization of InSTHAn.

"Raw" data and "Imported" data), or on a preprocessed data series by "Pre processed" data). Thus, each Analyses were linked to short-term data series (Figure 2) characterized by a set of flow or water level records measured (or modeled) at any subdaily time interval and from a specific time period, which was used for the calculation of indicators. Indicators may be calculated on the entire imported original data series (i.e., "Raw" data and "Imported" data), or on a preprocessed data series by changing the analysis period or the time interval between records with InSTHAn (i.e., "Pre-processed" data). Thus, each characterization analysis is linked to a single series, whereas each impact analysis is linked to two series, for example a perturbed (*per*) series and a comparable natural (*nat*) series (Figure 2). The impact assessment may be run (i) on a series of short-term flows or water levels, which can be split in InSTHAn into two independent (sub) series representing the preimpact (natural) and postimpact (perturbed) periods, or (ii) on two independent series representing the perturbed and the natural conditions. In any case, the previous characterization of each perturbed and natural series is necessary for the subsequent evaluation of the impact (Figure 2).

InSTHAn is organized into three modules corresponding to the steps that must be followed to set up and complete an impact assessment analysis, requiring the user to (i) create a project and import the data (Module I: Project management and data import; Supplementary Materials A: Figure S1), (ii) preprocess and analyze the data by calculating the STCI (Module II: Characterization; Supplementary Materials A: Figure S2) and (iii) calculate the STII (Module III: Impact assessment; Supplementary Materials A: Figure S3). Finally, outputs may be displayed in tables and graphs. Details on each module can be found in Supplementary Materials A.

#### *3.2. InSTHAn's Functionality and Comparison with Other Tools*

Both InSTHAn and COSH-Tool were launched from an executable file. Then, the main interface opened and allowed access to analysis of the time series. Both interfaces are simple and require no coding from the user (Table 3). With InSTHAn, two different projects named "ColoradoNat" and "ColoradoPer" were created (Supplementary Materials B: Figure S5). Two different characterization analyses were ran, one for the natural original series ("ColoradoNatCharacterization1") corresponding to the period before the construction of the dam, and the other for the perturbed original series ("ColoradoPerCharacterization1"), whose outputs were saved into their respective folders within "ColoradoNat" or "ColoradoPer" projects (Supplementary Materials B: Figures S4–S19). While importing the original data series we provided the required information on the series. Then, the two imported data series were preprocessed in order to set the entire available period of data as the characterization analysis period, and to round the flow measurements to two decimal places. The perturbed data series, originally characterized by every 15 min records, was also decimated in InSTHAn to get a measurement every hour.


#### **Table 3.**Comparison of the tools used in this article: InSTHAn (v2020) and COSH-Tool (v2016).

The natural and perturbed series were also loaded and prepared with COSH-Tool. Apart from small differences between the tools related to restrictions on the navigation in the PC, or on allowed variables, units and languages (Table 3), a notable difference of COSH-Tool is the non-organization of the outputs within projects or/and analyses where they may be easily found and consulted (Table 3). With a purpose similar to rounding in InSTHAn, smoothing was required by COSH-Tool at this stage. Smoothing, however, depends on a "smoothing factor" set by the user, which must be within a range of figures used during testing of the tool. Unlike InSTHAn, COSH-Tool is unable to modify the record interval of the input series, so the original every 15 min, perturbed series had to be turned into hourly time step series before loading to ensure that both natural and perturbed series had similar record intervals for later comparisons. Finally, for both natural and perturbed original series patterns were assigned to records (*R*) and periods (*P*) by InSTHAn (i.e., fall, rise, stability, change and reversal), but peaking events (i.e., rapid increases and decreases) were identified by COSH-Tool (Figure 1). Whereas the detection of such patterns in InSTHAn is based on differences between each previous and following rounded record and does not depend on predefined values, the detection of peaking events in COSH-Tool is conditional on the provision of several figures by the user, such as the inferior and superior percentiles of the rate of change, a minimum duration for a peak, the magnitude threshold to merge peaks, and the minimum duration between two consecutive peaks (Table 3). Since the subsequent characterization of the series is based on the patterns and peaking events previously identified by InSTHAn and COST-Tool, respectively, setting different figures in COSH-Tool may result in variations of the peaking events of a series, ultimately affecting its characterization (Figure 1). For the perturbed case, the whole flow series was split into many periods of rise and fall, and reversals and changes by InSTHAn (Figure 1). However, for the same series, the rapid increases and decreases were confined to the flow records that met the user-set (recommended by the users' manual) parameters (cf. above) by COSH-Tool (Figure 1). For the natural flow series, significantly more patterns through years were detected by InSTHAn compared to the almost non-existent peaking events found by COSH-Tool (Figure 1).

After data series loading and preparation, we required InSTHAn and COSH-Tool to characterize the natural and perturbed subdaily flow regimes. The records (*R*) and periods (*P*) previously assigned to different patterns were characterized by InSTHAn, whereas characterization of the identified peaking events was done by COSH-Tool. In both tools, characterization is done through metrics and statistics relating to the major flow components (i.e., magnitude, frequency, duration and rate of change; Table 3). However, a more thorough characterization representing all facets of the subdaily variation is achieved with InSTHAn, which goes into greater depth in duration metrics and provides information on periods of stability and reversals and changes (Table 3). Whereas InSTHAn's metrics (STCI) capture each day's subdaily patterns of the series, from which the user may derive longer-scale patterns through averaging the excel outputs, metrics from COSH-Tool characterize monthly, seasonal and annual patterns, which are displayed in figures (Table 3). Only a brief summary of the outputs for the whole analyzed period is provided in an excel template by COSH-Tool. Unlike InSTHAn, COSH-Tool also provides daylight patterns. Characterization metrics representative of each flow component (frequency, duration, magnitude and rate of change) have been chosen from each tool for Figure 3 (further outputs from InSTHAn can be consulted in Supplementary Materials B and in Alonso et al. [31] and Bejarano et al. [32]).

**Figure 3.** Box-and-whisker plots for selected outputs from the characterization analyses ran in InSTHAn and COSH-Tool for the pre- and post-dam (Glen Canyon dam) flow series (1943–1951 hourly flows, and 2003–2011 every-15 min flows, respectively) along the downstream reach of the Colorado River. *y*-axes represent the months in pre- (natural) and post-dam (perturbed) conditions, colored in blue and red, respectively. Black lines in the middle of the boxes are the median values for each group. The vertical size of the boxes is the interquartile range (IQR). The whiskers represent the minimum and maximum values that do not exceed 1.5 × IQR. The points are outliers. *x*-axes represent the characterization metrics related to frequency, duration, magnitude and rates of change provided by InSTHAn (i.e., short-term characterization indicators (STCI); **a**,**c**,**e**,**g**) and COSH-Tool (**b**,**d**,**f**,**h**). For InSTHAn, selected metrics are: (**a**) monthly average number of fall periods per day for the whole flow series, (**c**) monthly average duration of fall periods per day for the whole flow series, (**e**) monthly average amplitude per day for the whole series and (**g**) monthly average rate of flow decrease per day for the whole series. For COSH-Tool, the selected metrics are: (**b**) total number of rapid decreases per month for the whole series, (**d**) time span after rapid decreases per month for the whole series (not shown were three values in June, August and October for the natural period, which were higher than 15 h), (**f**) discharge after rapid decreases per month for the whole series (not shown was one value in June for the natural period, which was higher than 1000 m<sup>3</sup> /s) and (**h**) rate of flow decrease of rapid decreases per month for the whole series.

Both InSTHAn and COSH-Tool were able to capture the hydropeaking derived from the operation of the Glen Canyon dam in the perturbed flow series. In general, from both tools the user can derive that hydropeaking is associated to significantly frequent and short fall (and rise) periods (InSTHAn) or rapid decreases (and increases; COSH-Tool); fast hourly flow changes (highlighted by both tools) and high within-day flow amplitude (InSTHAn) and discharge (COSH-Tool; Figure 3). On average, InSTHAn identified three, 5 h fall periods per day during the whole year for regulated conditions (Figure 3). Other metrics (not shown) were consistent with these figures; the more frequent the fall (and rise) periods, the more frequent the flow changes and reversals, and the more frequent and shorter the stability periods. On average, COSH-Tool identified 25 rapid decreases per month for regulated conditions and described short time spans after rapid decreases (5 h on average) for regulated conditions (Figure 3). For the series subjected to hydropeaking, InSTHAn showed that the average daily amplitude was 162 m<sup>3</sup> /s and the flow receded at a rate of (−) 21 m<sup>3</sup> /s/h, whereas COSH-Tool showed an average discharge at the end of a decrease of 263 m<sup>3</sup> /s and of rate of flow decrease per month of (−) 24 m<sup>3</sup> /s/h (Figure 3). Conversely, the characterization of the natural series did vary significantly between the tools. Whereas the patterns of the flows used by InSTHAn for the characterization are also found in the series regardless of whether it is regulated or not, the peaking events used by COSH-Tool are restricted to artificial changes of the series, such as hydropeaking, and linked to exceptional natural peaking events (Figure 3). Consequently, hardly any peaking events were found by COSH-Tool throughout the natural flow series and, thus, most metrics were not applicable or equaled zero (Figure 3). The values for the metrics mentioned above obtained by applying InSTHAn to the natural series were in general (except for the spring values) significantly lower than the values from the perturbed series. Average values were as follows: four, 3 h fall periods per day and two, 8 h fall periods per day for the spring and the remaining seasons, respectively; a daily amplitude of 79 m<sup>3</sup> /s during the flooding season and 21 m<sup>3</sup> /s for the rest of the year and an hourly flow rate of 1 m<sup>3</sup> /s/h (Figure 3).

In InSTHAn we ran an impact analysis named "ColoradoImpact1", whose outputs were saved into its corresponding folder within one of the existing projects (the project "ColoradoNat" in our case; Supplementary Materials B: Figures S20–S25). For the impact analysis we indicated the characterization files to compare natural and perturbed (i.e., "ColoradoNatCharacterization1" and "ColoradoPerCharacterization1") from the InSTHAn dropdown menu and the deviation from the naturalness of each metric for each day of an average year was calculated. Impact assessment is not available in COSH-Tool (Table 3). Described changes on each STCI are summarized by their respective STII, which evidence both the magnitude and the direction of the impact (a selection of STII is shown in Figure 4). On the one hand, the very positive STII values highlight the significant increase of the within-day flow amplitude and rates of change resulting from hydropeaking (Figure 4). On the other, the close-to-zero, positive and close-to-zero, negative STII values highlight the slight increase or decrease of the frequency and duration of the fall periods with regulation, respectively; the pattern is only unfulfilled during the flooding period (Figure 4).

mpact analysis named "ColoradoImpact1", whose outputs were s

"ColoradoNatCharacterization1" and

into its corresponding folder within one of the existing projects (the project "ColoradoNat" in our –

"ColoradoPerCharacterization1") from the InSTHAn dropdown menu and the deviation from the

**Figure 4.** Outputs from the impact analyses ran in InSTHAn for the above mentioned characterization indicators (short-term impact indicators [STII]; -I denotes the impact on each indicator). Values around 0 mean a slight impact.

#### **4. Discussion and Conclusions**

#### *4.1. Applicability*

InSTHAn assists both scientists and river managers in describing and evaluating the naturalness of short-term flow/water level regimes, thus, eventually facilitating the understanding of the potential environmental impacts of the alterations of these regimes. Results from the application of InSTHAn to the analysis of the short-term flow variation in the Colorado River denote important modifications of certain key hydrological parameters at the subdaily scale due to the operation of the Glen Canyon dam. These would, otherwise, have gone unnoticed with other tools based on daily or larger time scale flow records. The derived consequences of these changes for the fluvial ecosystem may be severe. Particularly, significantly higher amplitudes of subdaily flows due to a regulation increase of the everyday wetted area, which may remove or move upwards on riparian areas plant species less tolerant to flooding while triggering the development of aquatic or amphibian species. Such consequences were described by Bejarano et al. [16] in rivers with hydropeaking from Northern Sweden, where *Betula pubescens* survival decreased significantly whereas *Salix* and *Carex* species were favored. Additionally, the significantly faster flow rates of change may result in fish/egg stranding, macroinvertebrate drift and obstruction of germination. For example, Casas-Mulet et al. [36] related the higher mortality of *Salmo salar* eggs in a river in central Norway to rapid dewatering, and Schülting et al. [37] observed macroinvertebrate drift proportions peaked during the up-ramping phase of water in an experimental flume. Although altered to a lesser extent, the more frequent and shorter inundations within a day may also cause scouring and burial, and soil surface clogging, damage or removal of sessile organisms or life stages and habitat deterioration and loss, which was already reported by Vanzo et al. [7].

Although based on different characterization units (patterns or peaking events), both InSTHAn and COSH-Tool were reliable for the characterization of short-term scale flow and water level series. The single characterization of the short-term natural and regulated flow regimes is valuable as it increases scientific knowledge on geographic patterns of hydrological variability [38,39], and helps to understand the influence of these patterns on biological communities and ecological processes [40]. InSTHAn's added contribution lies in its ability to quantitatively assess the short-term hydrological alteration by comparing identified patterns in natural and regulated conditions. Consequently, and unlike COSH-Tool, InSTHAn brings water managers and scientists closer to the potential ecological

consequences of the hydrological alteration, and to whether consequences may be irreversible (when exceeding the ecosystem's thresholds), ultimately helping to determine the resistance and resilience of the river [41]. This knowledge is key for guiding any river management strategies [42], the assessment of its ecological status [34,43], prioritizing conservation efforts [44] and setting and measuring progress toward conservation or restoration goals [45]. Particularly, InSTHAn's results from the analyzed series would be useful when determining operational rules at the Glen Canyon plant and/or in-situ compensation measures aimed at harmonizing hydropower production and ecological integrity of the river [46]. Whatever the purpose, InSTHAn should be used in combination with other tools focused on longer time resolutions such as the IHA [34], in order to guarantee the comprehensiveness of the analyses by accounting for hydrological attributes at all time scales [47].

#### *4.2. Merits and Limitations of InSTHAn in Relation to Other Tools*

The appeal of InSTHAn is that it facilitates the analysis of long data series, which would otherwise be tedious. It offers several advantages and improvements over its peers. It allows different languages, reads widely used files of data from any source, records at any subdaily time scale and characterizes by a wide range of date styles and data units, and up to four variables in the same sheet can be imported; options that are more limited in existing tools. Additionally, InSTHAn provides a set of descriptive subdaily hydrological indicators comprehensive enough to account for the most ecologically determinant hydrological attributes [32], overcoming the limitations of other tools in duration metrics. Although it has been specially designed for flow and water level datasets, as included indicators make sense in the context of the field of stream hydrology, the user may consider it appropriate for other variable types recorded at similar short-term resolution, e.g., water temperature or water dissolved gasses in order to analyze the phenomena of thermopeaking [48] and saturopeaking [6], respectively. All these variables are usually affected by hydropower production, which has been the focus of this manuscript, but InSTHAn could be useful also in cases when flows are manipulated by dams with other purposes than electric power generation but also involving the alteration of the short-term flows.

An interesting novelty is that InSTHAn allows adaptive analyses by modifying the analysis periods (i.e., subperiods), the recording time intervals (i.e., to longer subdaily time steps) and the accuracy to detect subdaily patterns (i.e., thresholds from which a fluctuation is considered). The latter is crucial to avoid unreal fluctuations led by the influence of the accuracy of the measuring device or the model, or simply measurement or modeling errors [30], and which is lacking in existing tools. Finally, no tools to date enable the assessment of the alteration of short-term regimes (Table 1). Specifically, COSH-Tool founds the characterization of subdaily regimes on peaking events (to some extend similar to the so-called pulses by other authors) previously identified by the user based on subjectively defined thresholds (e.g., [4,21,28,30]; Table 1). As our results show, the use of peaking events as characterization units prevents the characterization of natural (or slightly affected) series usually lacking such events. This is not minor, as impact can only be assessed by comparing natural and perturbed series pairs. Characterization in InSTHAn, however, is based on patterns ultimately describing the records of the series. This, first, guarantees objectivity in the identification process of subdaily patterns, which, secondly, can be performed for any series regardless of the degree of alteration.

From a practical perspective, InSTHAn has been designed for a wide audience with different backgrounds and expertise. Although the decision-maker is often a water resources manager within a mandated organization, stakeholder participation, including water abstractors, wildlife campaigners and local community representatives, play a role in influencing decisions [49]. Unfortunately, reaching agreement is hindered by such a range of interested parties with usually conflicting goals, which can rely on InSTHAn outputs to set balanced thresholds. For this aim, InSTHAn is an easy installation tool, which requires little computer memory and optimizes the calculation time. The friendly windows within the GUI and clear results displayed through tables and graphs, which can be read and managed from Excel files, help to make the tool easy to use even for inexperienced users. Furthermore, it can be customized to change the language, units, and add/remove/zoom into graphs. Unfortunately, for the authors´ experience, the navigation through COSH-Tool and management of results was not as straightforward and intuitive.

With regards to the limitations of InSTHAn, we point out again that derived environmental impacts of short-term hydrological alterations are not directly provided by the tool but can be derived from the already understood ecological implications of the calculated hydrological indicators. Consequently, understanding of the ecological impacts from the outputs may require additional expertise and this may vary according to specific species, conservation objectives and site characteristics. Further research should address this issue. Another important limitation of InSTHAn derives from the requirements for the input data. Although InSTHAn may be run on daily (or longer intervals) data, results may not make sense at such time scales as indicators are focused exclusively on capturing subdaily patterns. Results should be analyzed with caution if subdaily records are few. In such cases, other tools could be more suitable (e.g., [34]). Further, for the case of hydrological datasets, measuring (especially in free-flowing rivers) and modeling at such fine resolution are still uncommon. This particularly affects the impact assessment module, which is dependent on free-flowing series. In the absence of data from free-flowing rivers, the solution would involve the restitution of the free-flowing regime at the study location. To accomplish this, at least one (representative) year of subdaily flows or water levels should be recorded at a comparable location (for example by using pressure-transducer loggers), which would provide the natural subdaily variability applied to model a longer period based on commonly available daily records (registered or modeled). In rivers with high interannual flow variability, more than one year of registered subdaily data would be desirable. A last restriction on the input data is that, with any subdaily registering interval allowed, this interval must remain constant throughout the whole study period. Finally, in the spirit of InSTHAn being a user-friendly tool that attracts a wide range of users, those who are more experienced may not like that actions are restricted to windows and cannot be ordered through commands.

#### *4.3. Future Versions*

We are working on completing existent modules and introducing new modules of InSTHAn. The modular structure and the tool architecture allow the inclusion of new modules that may extend the tool functions in future versions. Within the characterization and impact modules, new indicators will be added in future versions such as measures of central tendency and dispersion for the indicators. In addition, subdaily patterns will be summarized at other time spans apart from the daily basis (i.e., currently, indicators take an average value for each day). For example, subdaily flow fluctuations caused by hydropeaking along northern regions are higher during daytime, workdays or cold seasons following electricity demands [50]. Detecting these variations in subdaily flow patterns is key when planning strategies for sustainable hydropower management. In this regard, COSH-Tool already distinguishes between daytime and nighttime analysis. Limits on hydropower production could focus on situations when restrictions may result in great ecological gains but small economic losses. A module for the categorization of data series according to their subdaily patterns or impact will be built. We believe that it may facilitate management as similar management rules may be prescribed to all series pertaining to the same group [32]. Finally, extra ecological and economic modules, which provide the ecological and economic consequences of the already identified and quantified hydrological changes would round off the current version of the proposed tool. InSTHAn should be tested with other data series and improved accordingly. For this to be realized, our purpose is to make it generally accessible as soon as the patent is obtained by downloading it for free from a webpage with user registration as the only requirement. A user manual will be also available on the same webpage. The user may share his/her experience when using the tool, inform of the degree of satisfaction with it and ask doubts or suggest changes that could be included in future versions.

#### *4.4. Conclusions*

We introduced the new tool InSTHAn: indicators of short-term hydrological alteration. InSTHAn allows the user to (i) summarize multiple, long series of subdaily flow or stage data into a manageable set of ecologically meaningful metrics (i.e., characterization), (ii) qualify and quantify the deviation of each series from the unaltered state to assess the hydrological alteration and its potential environmental impact and (iii) display both the short-term flow or stage pattern and its impact by using tables and graphs. The name informs on its ultimate purpose and time scale of the target regime, whereas the pronunciation of the acronym refers to the required recording interval of the input data (i.e., instant records). InSTHAn represents an advance compared to existing tools. In the characterization stage, it guarantees objectivity in the identification of subdaily patterns from any (natural or altered) series, and provides a comprehensive set of ecologically meaningful hydrological indicators. In the impact stage, it enables the assessment of the alteration of short-term regimes. Finally, in terms of its functionality, it is characterized by the flexibility in the analyses (analysis periods, recording time intervals and accuracies to detect subdaily patterns) and in the supported languages, files and datasets properties (date styles, records time intervals and data units), and it is a friendly tool because its straightforward installation and use (windows within the GUI and clear display of results). InSTHAn responds to real-world needs in the fields of science and technology, and ultimately of society. By facilitating complex data management, it promotes the development of scientific studies on the short-term variability of river flows and levels—natural and altered by anthropogenic actions—underlying key ecological processes in rivers. By providing comprehensive and objective information on short-term stream flows and levels, this tool solves conflicting user perspectives and, hence, supports the sustainable integrated assessment and management of river systems. InSTHAn is particularly useful in the environmental management of rivers used for hydropower production, as it will assist in achieving the priority goal of maximizing hydroelectricity production while minimizing environmental losses.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2073-4441/12/10/2913/s1, Figure S1. Project management and data import module (InSTHAn's Module I), Figure S2. Characterization module (InSTHAn's Module II), Figure S3. Impact assessment module (InSTHAn's Module III), Figure S4. Start a new or load an existing project, Figure S5. Import the original data, Figure S6. Export "Raw" data and "Imported" data. Example from the post-dam flows, Figure S7. Export "Raw" data and "Imported" data, Figure S8. See "Imported" data. Example from the post-dam flows, Figure S9. Create a new or load an existing Characterization analysis, Figure S10. Select the Characterization analysis that we want to load from a list, Figure S11. Create and run a new Characterization analysis, Figure S12. Export Characterization analysis: main menu. Example from the post-dam flows, Figure S13. Export Characterization analysis: main results, Figure S14. Export Characterization analysis: extra results, Figure S15. See "Pre-processed" data. Example from the post-dam flows, Figure S16. See "RP Patterns" file: table sheet. Example from the post-dam flows, Figure S17. See "RP Patterns" file: graph sheet. Example from the post-dam flows (January, 2003 is represented), Figure S18. See "STCI 366" file: table sheet. Example from the post-dam flows, Figure S19. See "STCI 366" file: graph sheet. Example from the post-dam flows (The entire year values for two indicators are shown), Figure S20. Create a new or load an existing Impact analysis, Figure S21. Create and run a new Impact analysis, Figure S22. Export Impact analysis: main menu, Figure S23. Export Impact analysis, Figure S24. See "STII 366" file: table sheet, Figure S25. See "STII 366" file: graph sheet (The entire year values for two indicators are represented).

**Author Contributions:** Conceptualization, M.D.B.; methodology, J.H.G.-P. and A.S.-W.; investigation and formal analysis, M.D.B., J.H.G.-P. and A.S.-W.; resources and data curation, J.H.G.-P.; writing—original draft preparation, M.D.B.; writing—review and editing, C.N. and L.G.; visualization and supervision, C.N. and L.G.; funding acquisition, M.D.B. and A.S.-W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This manuscript was supported by funding from: the Spanish Ministry of Science and Innovation (RIHEL; Ref. PID2019-111252RA-I00 CTA and SECA-SRH; Ref. PID2019-105852RA-I00); and Universidad Politécnica de Madrid (Programa Propio: Ayudas a Proyectos de I+D de Investigadores Posdoctorales) and Comunidad de Madrid (Convenio Plurianual con la Universidad Politécnica de Madrid) (Ref. APOYO-JOVENES-PHZKKU-148- SSPVMP).

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

#### **References**


**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

© 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/).

### *Article* **Pump E**ffi**ciency Analysis for Proper Energy Assessment in Optimization of Water Supply Systems**

### **Araceli Martin-Candilejo \*, David Santillán and Luis Garrote**

Departamento de Ingeniería Civil, Hidráulica, Energía y Medio Ambiente, Universidad Politécnica de Madrid, 28040 Madrid, Spain; david.santillan@upm.es (D.S.); l.garrote@upm.es (L.G.)

**\*** Correspondence: araceli.martin@upm.es

Received: 29 November 2019; Accepted: 24 December 2019; Published: 31 December 2019

**Abstract:** Water supply systems need to be designed accounting for both construction and operational costs. When the installation requires water pumping, it is key for the operational costs to know how well the pump can perform. So far, pump efficiency has been considered using conservative values, in the absence of a better estimation. The aim of this paper was to improve determining the energy costs by clarifying what the value of the pump performance should be. For this, 226 commercial pumps were studied, registering the efficiency at the optimum operating point, as well as other variables such as the flow rate, height, and pump type. As a result, a strong relationship between the pump performance and the discharge flow was spotted. That allowed the generation of an empirical curve, which can be used by designers to anticipate what pump efficiency can be expected. The results are used in a simple case study using the Granados Optimization System. These achievements can be implemented in design policies for a better energy assessment in the optimization of water supply systems.

**Keywords:** pump efficiency; water distribution systems; water supply systems; optimization; design policies; design

#### **1. Introduction**

Under the climate change threat, becoming energetically efficient is now a crucial necessity for our society. A proper energy assessment is, therefore, a key factor to account for in the developing of new policies that look after sustainable designs of water supply systems [1]. The designing stage of a water distribution system requires considering not only the construction phase, but also the operation of the facility over its entire lifespan. With this approach, energy expenditure takes a huge fraction of the final cost, and it should not be dismissed from the calculations. There are many designing approaches that do incorporate this aspect in their analysis. Mala-Jetmarova et al. [2] summarized what other authors considered in their proposals. After their review of the state of art, it seems that the design of water distribution systems is increasingly emphasizing the importance of including operation assessments.

The operational costs are often included in optimization algorithms in a single economic function that would also include construction costs of the network. This approach is used in some classical studies, like [3], but it is still the most common way to assess energy costs in the design. That is the case of [4–9] or [10]. Nevertheless, a different perspective is to treat operational and construction costs as separated objectives, as [11] does. However, this assessment confirmed that such a perspective throws back very different design solutions: the optimum design for construction costs means the highest operational investment and vice versa. This approach makes the search of the optimum for the overall installation more difficult, and therefore it is more advisable to adopt a single cost function to optimize.

In order to achieve a more precise assessment of all costs involved, multiobjective algorithms have started to incorporate in the optimization function costs of maintenance [12,13], replacement [14–16], and greenhouse gas emissions [17–20], among others. Multiobjective methods offer a very complete revision of all costs, but many times they require complex programming, resulting in being computationally expensive and hard to use. The work of [21] explained the state of the art of the multiobjective techniques.

Because operation costs are distributed along the lifespan of the installation, they need to be computed at the design stage. The equivalence is calculated using an accumulative factor that depends on the duration of the operation of the water drive considered, the duration of the construction period, and the discount rate employed. Regarding the lifespan of the facility, some methodologies consider an operative life of 20 years [3,5], but other authors [15,16,20] prefer to carry out the analysis for 100 years.

Another key variable for the operation costs is the pump efficiency. One of the most widely used methods for designing water supply systems in Spain is the Granados System [22,23], which is a gradient-based procedure. Among all variables affecting the Granados System, the pump efficiency is the key factor for calculating the diameter of the hydraulic conduction. The aim of this paper is to define the relationship between the pump's efficiency and the other parameters involved in the procedure, such as the flow rate, the pumping head and the required power. This pump efficiency analysis does not only serve for the purposes of the Granados System, but it can also help in many other methods that require the value of the pump's efficiency. This is the case of [24], where they use an estimated value of 75% in their calculations; for Wu et al. [15], the values range from 81% to 84%; Gessler and Walski [25] estimate the efficiency as 75% and so do Alperovits and Shamir [26] and Featherstone and El-Jumaily [27].

Other studies have also decided to optimize the design using as key variables the pump location [28,29], pump capacity [4], type [19], power [3], pumping head [30–32], pumping schedule [24,33], or pressure [34,35]. Water supply system design is a complex task where many variables are involved [36] and inter-connected; the decision-making needs a full comprehension of how each factor affects the installation. Some of the relationships between variables are still unknown and only intuited by experience. For this purpose, sensitivity analyses are necessary. The work [37] carries out an exhaustive sensitivity analysis using Sobol's method (a variance-based approach) to determine the variables that most affect the installation. These variables could vary from pipe diameters to tank sizes, and the degree of influence depends on each case study. In their work, they prove the computational savings that can be obtained and, therefore, how beneficial the analysis is. This paper also intends to serve as a sensitivity analysis of how much pump efficiency is influenced by other factors and how the pump's efficiency can affect the final cost of a water supply system.

Since the pump efficiency can substantially affect the design of water supply systems due to the wide range of values they can adopt, with this study we carry out an extensive study of the pump performance in order to characterize its values. For this to be made, we analyze the features of commercial pumps available in the market. The conclusions are integrated in a gradient-based procedure, using as a base the Granados System, giving rise to an optimized design method that accounts for the construction and operational costs. This procedure is also compatible with adding other variables such as the carbon footprint [38] of the design or the GHG emissions. Our new methodology is applied to a case study to illustrate its computationally straightforward conception.

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

#### *2.1. Brief Summary of the Granados System*

Granados System is a pipe-sizing method indicated for the design of branched water distribution systems. It is a gradient based methodology. It is, in fact, based on the 'change gradient' concept: The change gradient is defined as the cost of reducing one meter of head loss by increasing the pipe diameter from ∅<sup>i</sup> to the next bigger one ∅<sup>j</sup> = ∅i+1:

$$\mathbf{GC}\_{\mathcal{D}\_{\mathbf{i}} \to \mathcal{D}\_{\mathbf{j}}}^{\mathbf{q}} = \frac{\mathbf{P}\_{\mathbf{j}} - \mathbf{P}\_{\mathbf{i}}}{\Delta \mathbf{h}\_{\mathbf{i}}^{\mathbf{q}} - \Delta \mathbf{h}\_{\mathbf{j}}^{\mathbf{q}}} \,\tag{1}$$

where P<sup>i</sup> and P<sup>j</sup> are prices of pipes of length L and diameters ∅<sup>i</sup> and ∅<sup>j</sup> , respectively; ∆hi<sup>q</sup> and ∆hj<sup>q</sup> are the head losses of a pipe of length L and diameters ∅<sup>i</sup> and ∅<sup>j</sup> , respectively, when a flow rate q is circulating. When the head losses are calculated using Manning's formulation, the change gradient's expression is:

$$\text{GC}\_{\mathcal{D}\_{\text{li}} \to \mathcal{D}\_{\text{j}}}^{\mathbf{q}} = \frac{\mathbf{p}\_{\text{j}} \, \mathrm{L} - \mathbf{p}\_{\text{i}} \, \mathrm{L}}{\frac{\mathrm{L} \, \mathrm{n}\_{\text{i}}^{2} 2^{20/3} \, \mathrm{q}^{2}}{\pi^{2} \, \mathcal{D}\_{\text{i}}^{16/3}} - \frac{\mathrm{L} \, \mathrm{n}\_{\text{j}}^{2} 2^{20/3} \, \mathrm{q}^{2}}{\pi^{2} \, \mathcal{D}\_{\text{j}}^{16/3}}} = \frac{\pi^{2}}{\mathrm{n}^{2} \, 2^{20/3}} \frac{(\mathbf{p}\_{\text{j}} - \mathbf{p}\_{\text{i}})}{\left( \frac{\mathrm{n}\_{\text{i}}}{\mathcal{D}\_{\text{i}}^{16/3}} - \frac{\mathrm{n}\_{\text{j}}}{\mathcal{D}\_{\text{j}}^{16/3}} \right) \mathbf{q}^{2}} = \mathrm{K}\_{\text{CC}} \frac{1}{\mathbf{q}^{2}} \tag{2}$$

with n being Manning's friction coefficient.

The definition of the change gradient also needs to include some other associated costs such as excavation expenditure or reinforcements against chemically aggressive environment or hydraulic transients. During the optimization stage, hydraulic transients are usually taken into account in a simplified way, for instance, extra thickness of the pipes to withstand water hammer transient pressure. Once the optimum design is achieved, proper assessment of water hammer should be carried out to verify the initial hypothesis. These associated cost factors increase the pipe price, and therefore, they have to be accounted in the design through P<sup>i</sup> and P<sup>j</sup> .

Increasing the pipe's diameter means a reduction in the head loss along the pipeline, but it has the extra cost of the wider and more expensive tube. Since the change gradient is the cost of reducing the head loss by one meter, it needs to be compared to the cost of the energy required for pumping the water at one meter height throughout the entire life of the facility, CE1, which reads:

$$\mathbf{C\_{E1} = Ca\_{E1} \cdot f\_A = f\_A \ 9.81 \ \frac{\text{V}}{3600} \ \frac{1}{\mu\_\text{B}} \ \frac{1}{\mu\_\text{M}} \ \mathbf{p\_{E'}}} \tag{3}$$

$$\mathbf{f\_A} = \frac{(\mathbf{1} + \mathbf{i})^{\mathbf{n}\_\mathrm{U}} - 1}{(\mathbf{1} + \mathbf{i})^{\mathbf{n}\_\mathrm{U}} \mathbf{i}} \cdot \frac{1}{(\mathbf{1} + \mathbf{i})^{\mathbf{n}\_\mathrm{C}}} \,\tag{4}$$

where CaE1 is the annual energy cost per meter, f<sup>A</sup> is the discount factor, n<sup>c</sup> is the duration of the construction period, n<sup>u</sup> is the useful life of the installation, i is the discount rate, V is the annual volume of water to pump, µ<sup>B</sup> and µ<sup>M</sup> are the pump and engine efficiency, and lastly p<sup>E</sup> is the unit price of energy.

As it is justified in Granados' work, with the exception of the pump performance µB, the other variables in the previous equation are relatively known data: V is the total demanded volume to pump, p<sup>E</sup> is the unit price of the energy that has been hired, and f<sup>A</sup> is calculated from the discount rate i, the service life n<sup>U</sup> of the water pipeline which depends on the chosen material, and the construction period nC. Regarding the engine efficiency µM, although it varies theoretically depending on the model chosen and the operating point of the pump, the variations in engine performance are so small that it can be considered constant across different models and manufacturers. Therefore, the above equation can be simplified to:

$$\mathbf{C\_{E1}} = \mathbf{K C\_{E1}} \frac{1}{\mu\_{\mathbf{B}}}.\tag{5}$$

As previously said, Granados System consists of comparing the cost of building a wider pipe (change gradient) and reducing the head loss by a meter, to the cost of pumping one meter of head loss (CE1). The reasoning is the following:


But since CE1 depends on the pump efficiency µB, the procedure changes to:


This means that, whenever there is a pump on the market whose efficiency can be greater than the calculated <sup>µ</sup>B, the optimum diameter will be ∅<sup>i</sup> . In the event that no commercial pump can reach that performance because it is very high, it will be necessary to move to the next diameter ∅i+1. Therefore, to apply this method it is necessary to know the maximum efficiency that pumps can reach. This is an uncertainty of the Granados System, and up to now, typically, pump efficiency values around 80% are already indicative.

#### *2.2. Methodology*

Among all variables affecting Granados System, the pump performance is the key factor for calculating the diameter of the hydraulic conduction. Nevertheless the results may vary significantly depending on the pump efficiency; indeed, µ<sup>B</sup> presents a wide range of possible values that typically goes from 70% up to 90%. This means a variability of almost 20% in the estimation of the cost, which is a substantial difference. Therefore the aim of this paper is to define the relationship between the pump's performance and the other parameters involved in the procedure, such as the flow rate, the pumping head or the required power. For this to be done, we select 400 commercial pumps from the catalogues of several manufactures. We discard custom-made pumps since the cost of these pumps is much higher than the ordinary ones listed and the offering in commercial catalogues is already very wide. The selected pumps vary from each other in their type, impeller diameter, number of stages, rotation speed (electrical current frequency, number of poles), brand, etc. For all these models, we study the pump efficiency; in particular, we register the optimum value together with the correspondent flow rate, head and power consumed. Nevertheless, some pumps are ruled out of the sample and presentation of the results because they either were similar to those of other manufacturers, or because they were very specific for some industrial or sanitary engineering uses. In the end, the sample consists of 226 hydraulic pumps.

For the detailed study of the pump performance, this research has focused on the most common type of pump for the applications in civil engineering (supply, irrigation, sanitation, etc.)—centrifugal pumps. Within centrifugal pumps, both horizontal and vertical axes are selected, mostly with a radial flow configuration, with the exception of submersible pumps, for which the axial arrangement is more common. The sample includes regular horizontal and vertical pumps, split case pumps, multistage and submersible pumps. The manufacturers used for this analysis were IDEAL, WILO, ESPA and HASA. More specifically, the commercial models were:


Multistage pumps perform with the same efficiency for a specific flow rate and different heights (which is the number of stages multiplied for the unitary head). To avoid this dispersion that could make it difficult to draw conclusions, it was decided to only use the optimum operating point correspondent to a single stage.

Using the data collected for the optimum operating points for all the 226 hydraulic pumps previously mentioned (pump's optimum efficiency and associated flow rate, head, speed, power, frequency, diameter, etc.) we carried out an analysis to establish relationships among the design variables of a water drive.

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

Figure 1a shows the values of the optimum efficiency of the pump and the flow rate correspondent to that point. From it, it can be seen that there is a relationship between both variables: the performance of the pump improves as the discharge increases, although it seems to reach a horizontal asymptote for µ<sup>B</sup> around 90%. In this same figure, it can be spotted that the relationship between the two variables is more precise for flow rate values that are greater than 500 L/s. Below this value, as it can be seen in Figure 1b, there is more dispersion. Also, when the discharge is at least 100 L/s, the pump efficiency can be expected to be better than 80%, but under it, the dispersion is stronger. On the other hand, it has been studied whether the type of pump has any relation with the efficiency. For that, Figure 1 also shows the distribution of the operating points for the split case pumps, horizontal and multistage (both horizontal and vertical).

**Figure 1.** (**a**). Optimum pump efficiency and the correspondent flow rate at that operating point, classified by the pump type. (**b**) Detail of the previous figure for smaller discharges.

Regarding the pump type, we conclude that:


When the pumping height and the efficiency are plotted together, as shown in Figure 2, there is no clear sign of a relationship between the two variables since the dispersion is too strong for any head value. There is a very light tendency of high pump performances (around 80%) for under 40 m head, but over 60 m the distribution of µμ<sup>B</sup> is too scattered.

μ To test out what the relationship between the optimum µB and the required power for that operating point is, Figure 3 was elaborated.

The main conclusions drawn from Figure 3 are:


(**a**)

**Figure 3.** (**a**) Optimum pump efficiency and the correspondent pump power at that operating point. (**b**) Detail of the previous figure.

To summarize, this first assessment concludes that the strongest of the relationships with the pump efficiency is that of the flow rate, especially when the flow is greater than 100 L/s and it is almost linear.

భ On the other hand, the relationship between the specific speed of the pump and the efficiency is shown in Figure 4. The specific speed of the pump is defined as:

୬౨∙୯

మ ൗ

$$\mathbf{n}\_{\mathbf{s}} = \frac{\mathbf{n}\_{\mathbf{r}} \cdot \mathbf{q}^{\frac{1}{2}}}{\mathbf{H}^{\frac{3}{4}}},\tag{6}$$

where n<sup>s</sup> is the specific speed; q, H and n<sup>r</sup> are the flow rate, pumping head and the rotation speed, respectively, at the optimum operating point [39]. It is interpreted as the rotation speed that a geometrically similar pump should have in order to elevate a discharge of 1 m<sup>3</sup> /s at 1 m height.

**Figure 4.** Optimum pump efficiency and the correspondent specific speed of the pump, classified by the pump type.

μ μ Low specific speed indicates that the pump is suitable for small flow rates and great heights. This means that, since small flow rates have a poorer relationship with the pump efficiency, pumps with a low specific speed will have the worst performance values. This is shown in Figure 4. On the contrary, high specific speed is an indicator of a pump suitable for great flow rates and low heights. According to the previous analysis made from Figure 1, greater discharges correspond to better performances, and therefore, a high specific speed can be associated with a good µB, as Figure 4 shows. The scattering of the figure is caused by the poor relationship that the pumping height and the rotation speed have with the pump efficiency. However there is a diffuse tendency of increasing µ<sup>B</sup> as the specific speed grows. As far as pump type is concerned, the types of pumps that operate at higher flow rates will be the ones with a greater specific speed and therefore, better performance: These are split case pumps, as shown in Figure 4. Vertical multistage pumps also give good results in the smaller flow rate ranges.

#### *3.1. Relationship between the Flow Rate and the Pump E*ffi*ciency*

From the previous figures, it seems that there are three flow rate ranges where the relationship with the pump efficiency is different. The first one would be from 0 to 100 L/s, the second from 100 to 500 L/s and the last one over 500 L/s. Nevertheless, in order to be more precise, instead of three zones, the curve has been fitted using up to fourteen flow rate subdivisions. Table 1 shows the average optimum pump efficiency for each interval, as well as the maximum and minimum found among the studied pumps.


When these values are adjusted through a doubly logarithmic curve, the relationships for both the average and maximum values fit satisfactorily (*r* <sup>2</sup> > 98% and *r* <sup>2</sup> > 90%, respectively), as can be seen in Figure 5. The empirical equations that relate the optimum pump efficiency and the flow rate are:

$$
\mu\_{\text{B}}^{\text{Average}} = 0.1286 \ln \left( 2.047 \ln \text{q} - 1.7951 \right) + 0.5471 \quad r^2 > 98\% \tag{7}
$$

$$
\text{Maximum} \quad \text{a.o.277c 1 (2.0471 \quad 4.7954) + 0.744 \quad \text{ $\gamma$ } \quad \text{a.o.d} \quad \text{ $\gamma$ } \quad \text{a.o.d} $$

$$
\mu\_{\text{B}}^{\text{Māximum}}\_{\mu} = 0.0576 \text{ ln} \left( 2.047 \text{ ln} \,\text{q} - 1.7951 \right) + 0.741 \quad r^2 > 90\% \tag{8}
$$

where q is the flow rate in liters per second (L/s).

**Figure 5.** Adjusted curves. The curves are elaborated using 14 intervals of the collected data.

Finally, Figure 6 shows the adjusted curves along with the collected data. Both curves fit satisfactorily for most flow rate ranges, especially for the bigger ones; nevertheless the dispersion is higher for the small discharge values (under 50 L/s), but still, it gives a valid reference. To facilitate the visualization, Figure 6b shows the results in logarithmic scale.

**Figure 6.** (**a**) Optimum pump efficiency curve: database and mathematical adjustment; (**b**) mathematical adjustment in logarithmic scale.

#### *3.2. Application of the Pump E*ffi*ciency Curves to the Granados System*

For a better comprehension, the full procedure is shown in Figure 7. On the figure, all variables affecting the change gradient and the energy cost are graphically represented: flow rate, pump efficiency, energy price, annual volume of water, engine efficiency, useful life of the installation, construction period, discount rate, commercial diameters, pipe prices and pipe roughness.

**Figure 7.** Pipe sizing methodology representing the steps for the design and the shapes that curves might present depending on the variables.

The design process represented in Figure 7 consists of the following steps:


Since the aim is to compare the construction costs to those of the energy, excavation costs also must be considered and added to these figures.

3. Calculate the expected pump efficiency using the average pump efficiency equation (Equation (7)).

It is always more conservative to use the average pump efficiency equation rather than the maximum one, nevertheless this one can also be used but it would require a much more exhaustive pump search.


At this point, different alternatives might be considered for various energy prices, etc.


### *3.3. Case Study: Navas del Marqués*

To exemplify the application of the previous design procedure, the method will be used in a case study. It is based on the dam project in the Navas del Marqués locality, Ávila, Spain, which was carried out by the Tagus Hydrographic Confederation [40]. In this section we intend to compare the design results obtained in the project to the ones that would be obtained with the proposed procedure. The project included the following works:


Figure 8 shows the schematic works that the project included, along with some relevant altitudes, and input data. This paper is concerned about the sizing of first part of the water drive, i.e., Pipe 1 (remember that the tunnel section, Pipe 2, was to remain in the original state).

**Figure 8.** Case study at Navas del Marqués.: Pipe 1 is the only one to replace.

The project data that are used can be summarized in the following list:




<sup>1</sup> The project includes a limited series of ductile cast iron pipes in the estimated budget documents. These start from 150 mm.

This design process can be also followed throughout all series of Figure 9. These figures follow the same color code and symbology as Figure 7. The calculation followed the steps listed above:


This will allow a sensibility analysis to see how robust the design is against energy price changes. The first price, 0.072 €/kWh, corresponds to the energy price used in the project, and the second alternative, 0.125 €/kWh, corresponds to a higher energy price. These results can be seen in Figure 9a.

5. Once the annual unit pumping cost is obtained, the total accumulated cost is calculated using Equation (3). We assume a life span for the cast iron pipe of 31 years. Likewise, the duration of the expected construction period according to the project is 30 months, which corresponds to 2.5 years. We analyzed the sensibility of the design for the discount rate. In this line we adopt three values of the flow rate, where *i* equals 3%, 4% and 5%. With all this, the results obtained in each situation of energy prices and discount rate are shown in Table 3 below and in Figure 9b.

6. Once the full energy cost has been obtained, as well as the change gradients, the comparison is made, following the reasoning previously described. The selected pipes are compiled in Table 3 and shown in Figure 9c,d.

→ → **Figure 9.** Case study of the Navas del Marqués. (**a**) Step 4: Calculation of the annual energy cost; (**b**) Step 5: Calculation of the capitalized energy cost throughout the entire life of the installation. (**c**,**d**) Both panels show steps 1 and 5 of the procedure. This means that both the change gradient calculation (red curves) and the pipe selection is shown in the figures. In (**c**), the change gradients are calculated using the Canal de Isabel II commercial diameters, and in (**d**), they used the project data. The big orange circle in (**d**) represents the main solution, whilst the small orange circles represent the solutions for the other alternatives evaluated in the case study. For the main solution, as the energy cost per meter CE1 is greater than CGØ350→Ø400, it is more convenient to choose Ø400 mm. But because CE1 is smaller than CGØ400→Ø450, it should not be passed onto Ø450 mm and remain with Ø400 mm. The same reasoning applies to the other solution alternatives.


**Table 3.** Selection of the pipe diameter, depending on the energy prices, diameter series and discount rate considered.

\* The letters in brackets indicate the graphical solutions in Figure 9c,d.

As it is shown, most of the alternatives throw back a pipe diameter solution of 400 mm; this is not too far from the solution taken in the project, which is 500 mm. The diameter selected in the project implies a facility with higher costs than the design obtained with the optimization of this research. However the project solution is energetically less consuming, and this is a positive fact because energy prices tend to increase with time, leading to significant increases in the energy cost. Nevertheless, when the sizing is made for project energy prices, the solutions oscillate between 350 and 400 mm. Although the project and presented method give close results, the new methodology can help to optimize the full cost of the facility.

An economic evaluation has been conducted using the project energy prices and pipe prices. This can be seen in Table 4 and Figure 10.

**Figure 10.** Economic evaluation of the case study at the Navas del Marqués.

**∆**


**Table 4.** Economic evaluation for the case study using the project prices for the pipes, once a diameter of 400 mm has been selected, to prove the least cost result.

Table 4 and Figure 10 show how diameters Ø400 mm and Ø350 mm give very close results for the total cost, since they only differ in approximately 4000 €. Nevertheless, the cost variation increases compared to diameter Ø500 mm and it is significantly higher, as it can be seen in Figure 10 even though the results only differ in 100 mm wide. When the sizing is made for higher energy prices, the most common result is 400 mm. As a conclusion, although the experience of the designer can never be replaced, this method is a very convenient tool to find the optimum diameter of a pipe.

#### **4. Conclusions**

The present pump analysis is a useful tool to help with the uncertainties regarding decision-making in water supply system design. Because the relationship of the pump efficiency with the other variables involved in the design process has been elucidated, the understanding of such a complex procedure as the design of a water supply system is improved.

The definition of the pump-efficiency–flow-rate curve reduces the conflict resolution involved in gradient-based methods, avoiding iterations regarding the pump efficiency. This automatically leads to less computational effort. In this sense, the Granados method is a straightforward procedure.

Some current methods are somewhat black-boxes, losing part of their utility by not being easy to comprehend for design engineers. The visual representation of our design methodology presented in this paper facilitates the understanding of the influence of each variable and allows to have a clear picture of the process. This simplicity is one of the main necessities to aim for when it comes to water supply system design.

As the case study shows, energy costs are proved to be a great fraction of the full cost of the installation, and they need to be considered from the first phase of the design. In contrast with other methodologies that do not consider these energy cost, this analysis aims for an integrated water assessment where all costs of the water–energy nexus are integrated.

Here, we obtain empirical equations that define the average and maximum optimal pump efficiency to expect depending on the flow rate of the installation. These results can be incorporated to elaborate a proper energy assessment of the operational costs. As the case study has shown, the design of a water supply system is also very much influenced by the construction costs (the design differs when Canal de Isabel II or project pipe prices are used) and by the energy rates (centesimal order variations will throw back different results). This reinforces the importance of carrying out a sensitivity analysis when it comes to designing a water supply system. These conclusions can be used for policy assessment in integrated water management as well as supply system design.

**Author Contributions:** Investigation, A.M.-C., D.S. and L.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by CARLOS GONZÁLEZ CRUZ Grant.

**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/).

*Article*
