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Article

Modelling Water Availability in Livestock Ponds by Remote Sensing: Enhancing Management in Iberian Agrosilvopastoral Systems

by
Francisco Manuel Castaño-Martín
*,
Álvaro Gómez-Gutiérrez
and
Manuel Pulido-Fernández
Research Institute for Sustainable Land Development (INTERRA), Universidad de Extremadura, 10071 Cáceres, Spain
*
Author to whom correspondence should be addressed.
Remote Sens. 2024, 16(17), 3257; https://doi.org/10.3390/rs16173257
Submission received: 7 July 2024 / Revised: 9 August 2024 / Accepted: 27 August 2024 / Published: 2 September 2024
(This article belongs to the Special Issue Advanced Pattern Recognition and Image Processing Technology for Agricultural Engineering)
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Abstract

:
Extensive livestock farming plays a crucial role in the economy of agrosilvopastoral systems of the southwestern Iberian Peninsula (known as dehesas and montados in Spanish and Portuguese, respectively) as well as providing essential ecosystem services. The existence of livestock in these areas heavily relies on the effective management of natural resources (annual pastures and water stored in ponds built ad hoc). The present work aims to assess the water availability in these ponds by developing equations to estimate the water volume based on the surface area, which can be quantified by means of remote sensing techniques. For this purpose, field surveys were carried out in September 2021, 2022 and 2023 at ponds located in representative farms, using unmanned aerial vehicles (UAVs) equipped with RGB sensors and survey-grade global navigation satellite systems and inertial measurement units (GNSS-IMU). These datasets were used to produce high-resolution 3D models by means of Structure-from-Motion and Multi-View Stereo photogrammetry, facilitating the estimation of the stored water volume within a Geographic Information System (GIS). The Volume–Area–Height relationships were calibrated to allow conversions between these parameters. Regression analyses were performed using the maximum volume and area data to derive mathematical models (power and quadratic functions) that resulted in significant statistical relationships (r2 > 0.90, p < 0.0001). The root mean square error (RMSE) varied from 1.59 to 17.06 m3 and 0.16 to 3.93 m3 for the power and quadratic function, respectively. Both obtained equations (i.e., power and quadratic general functions) were applied to the estimated water storage in similar water bodies using available aerial or satellite imagery for the period from 1984 to 2021.

1. Introduction

In the SW Iberian Peninsula, approximately 60% of its land surface is occupied by extensive grazing areas, either in the form of woody rangelands or treeless grasslands, which are in fact past cleared forests [1]. These systems alternate woodland and natural pastures at tree densities ranging from 15 to 80 trees ha−1, depending on the local context [2]. These pastures are usually grazed by sheep, cattle and Iberian pigs inside of large privately owned farms that exceed 100 ha in size [3]. Since traditional practices such as transhumance and transterminance have begun to be uncommon, most farmers have chosen strategies to supply food and water to livestock for the whole year. The design of watering ponds has been crucial in this matter to overcome high summer temperatures and water scarcity [4].
This kind of pond represents the majority of water bodies identified in regions such as Extremadura, in which extensive livestock farming is a common activity. In fact, Abdennour et al. [5] identified 64,896 water bodies with an area < 0.01 km2 that represent the 64.5% of the total. Water for livestock consumption in the SW of the Iberian Peninsula comes from these small ponds, which are an important resource in Mediterranean climate environments, where summers are always hot and dry and periods of drought are recurrent [6].
The suitability of these ponds depends, to a large extent, on the adequacy of their size to soften climatic fluctuations. In recent decades, the Mediterranean region has experienced significant modifications in climate patterns characterized by rising temperatures, variations in precipitations and the increased frequency of extreme weather events [7,8]. This will presumably reduce the availability of surface water in ponds for livestock consumption, being necessary to improve the management and assessment of water resources [5]. In these areas, precipitation shows a great temporal variability and runoff is highly concentrated, with 10% of months accounting for 85% of the total discharge [9]. Therefore, it is crucial to help farmers to assess the volume of water stored at a specific time (V), as well as the maximum volume (Vmax), to improve the management of this resource and monitor water resources on a regional scale [10].
Estimating V or Vmax requires a high-resolution topographic model of the pond in addition to the water level. The elaboration of this topographic model is, commonly, time-consuming and requires the use of specific surveying techniques and instruments [11]. On the other hand, rather than Vmax, the farmer is interested in V, for which it is necessary not only to have the surface topography of the pond, but also to measure the depth of the water table (h). Due to these difficulties, it is common to establish relationships between V, the area of the water table (A) and h [12,13,14,15] that allow one of these parameters to be indirectly obtained from another. For example, in this way, it is possible to determine V from the measurement of the area occupied by the water (A) in an aerial image or the depth of the water table directly measured with the help of a plumb (h). These relationships can be an important tool for landowners who can estimate the maximum or real-time water stored in a farm and thus be aware of whether the supply capacity of his farm meets the real consumption needs of the livestock [16], in addition to the losses due to evaporation or overflow [6].
The development of V-A-h relationships also relies on the existence of a high-resolution spatial topographic model of the pond, with a wide variety of techniques available for its elaboration. In the presence of water in the pond, bathymetric sonar [17,18], green airborne Light Imaging And Ranging (green LIDAR) [19], satellite radar altimetry with Sentinel-3 [20,21] or Terrestrial Laser Scanner (TLS) [22] through water are effective state-of-the-art techniques. However, they are unsuitable in water ponds of the SW of the Iberian Peninsula due to the pond size, water depth and turbidity [11]. Marín-Comitre et al. [11] overcame these limitations by employing close-range Structure-from-Motion and Multi-View Stereo photogrammetry (ahead SfM) and aerial SfM with images acquired by Unmanned Aerial Vehicles (UAVs), both obtained at the end of the summer, when the water reaches the minimum level, and combined with Global Navigation Satellite Systems (GNSS) to survey points in the submerged area.
In these previous experiences, the use of the GNSS was necessary to survey submerged points, but also to survey Ground Control Points (GCPs) that allow one to scale and georeference the photogrammetric model. In the present work, we have used a UAV equipped with an RGB sensor and a direct georeferencing system to acquire aerial images that are used later to produce a high-resolution 3D model of the pond by means of SfM. The development and use of UAVs with direct georeferencing systems is relatively recent [23,24,25] and these systems suppress the need to survey GCPs and, therefore, the use of a rover GNSS. However, in this approach it is necessary that the ponds are completely free of water.
Our work is based on Marín-Comitre et al. [11] who developed V-A-h relationships for seven water ponds in farms of the SW Iberian Peninsula. On this basis, the novelty of our work is that we have added four new cases to the dataset and surveyed and elaborated then using state-of-the-art remote sensing techniques: UAVs with direct georeferencing capabilities and SfM and we compare the resulting mathematical models and the associated errors. In addition to expanding Marín-Comitre et al.’s [11] dataset, we use a UAV with direct georeferencing through a post-processing kinematic (PPK) procedure which minimizes field work and allows for the generation of accurate and high-resolution 3D models (point clouds and Digital Elevation Models or DEM). In this regard, the efficiency of our proposal compared to the surveying techniques used by Marín-Comitre et al., 2021 [11] is based on the criteria of precision and accuracy, cost and accessibility, flexibility and mobility, time and work efficiency and, finally, data quality and spatial resolution.
Hence, the main goal of this work is to refine existing V-A-h relationships for water ponds in the SW of the Iberian Peninsula that may be useful for landowners, farmers and managers to improve the management of water resources in the current context of water scarcity. To do this, four water ponds were studied in detail in addition to the seven ponds used in the previous study by Marín-Comitre et al., 2021 [11]. Additionally, we conducted a thorough analysis of errors and uncertainties in the estimations of V using V-A-h relationships. Finally, the obtained V-A-h relationships were used to carry out a multi-temporal analysis of water availability in three representative farms (27 ponds).

2. Materials and Methods

2.1. Study Area

This work was carried out at four representative ponds in three farms of Extremadura (Spain): Parapuños de Doña María, La Brava and La Barrosa, located in the municipalities of Monroy, Aliseda and Alburquerque, respectively (Figure 1). These farms represent conventionally managed woodlands and natural pastures, which include different livestock species such as the Retinta cattle, Merino sheep, Iberian pigs and goats for meat production. The climate is Mediterranean, with an average annual rainfall varying from 500 to 600 mm y−1, distributed irregularly during the autumn, winter and spring months, and an average annual temperature of 16 °C [26]. The topography in the farms is represented by an undulating landscape with altitudes slightly above 400 m. Lithology is dominated by siliceous rocks (Precambrian slates) and the remains of Tertiary deposits. Soils are, in general, shallow, classified as Leptosols and Cambisols types, slightly acidic, relatively poor in nutrients and easily erodible in overgrazed areas [27].

2.2. Data Collection and Workflow

The four ponds analysed in this study are pond no. 4 and no. 6 of Parapuños de Doña María (Par4 and Par6), pond no. 6 of La Barrosa (Bar6) and pond no. 8 of La Brava (Bra8). These were surveyed and cubed in September 2021 and 2022, when there was no water in them. The information obtained from these four ponds was integrated in the database from the previous work by Marín-Comitre et al. [11]. A Phantom 4 RTK UAV was used to acquire aerial photographs of the water ponds and the surrounding area to be postprocessed. The flight plan was designed to cover every study area with perpendicular strips, a flying altitude of 80 m above topography and a Ground Sampling Distance (GSD) of 2.54 cm. The dataset was pre-processed using a Post-Processing Kinematic Approach (PPK) with data recorded simultaneously by nearby permanent GNSS stations and the software RedToolbox v.3.0.91 [28]. The images with the corrected camera pose were used as the input in the SfM photogrammetric workflow within the software Pix4Dmapper Pro v.4.5.6 [29] to produce point clouds, Digital Elevation Models (DEMs) and orthophotographs (Figure 2).
The resulting high-resolution DEMs were used to estimate the Vmax at each pond. First, different geoprocessing steps (calculation of hillshade, slope and terrain profile analysis) were used to identify the location of the spillway. Then, the volume of water stored at intervals of 10 cm or 20 cm (at smaller ponds, such as Par6, 10 cm intervals were used, while for larger ones, such as Bra8, 20 cm intervals were used) up to the spillway altitude were estimated for each pond. The geoprocessing procedure allows one to have data of V, A and h (Table 1) for the different intervals and to estimate the relationships between these parameters for every pond.
The V, A and h data estimated from the previous step were studied using a regression analysis to establish relationships and calculate the associated errors (by means of the Root Mean Square Error or RMSE). Marín-Comitre et al. [11] established pond-specific and generalized V-A-h relationships for seven ponds surveyed using different geomatic techniques. Microsoft Excel v.2407 and RStudio v.4.2.2 software packages were used for this purpose. Power (1) and quadratic (2) functions were fit for every water pond (pond-specific) and farm (farm-specific), but also a general equation produced with data from all the ponds was estimated. Errors (3) for every function and pond were estimated using the specific and general equations and the relationship between the error and water table height was explored.
y = α x β
y = a x 2 + b x + c
Error ( % ) = A B S p o w , q u a d M D E x 100
The best-resulting equations produced for each pond were then used to estimate V in every free-available aerial image in the National Centre of Geographic Information database (CNIG) and in the Google Earth Pro v.7.3.6.9796 catalogue (Table 2). The A of the ponds was mapped using ArcGIS v.3 software for the CNIG database and Google Earth Pro for its own catalogue of images. In addition, the best-resulting equations were used to compare the maximum capacity of the total ponds in the 3 pilot farms with the actual maximum capacity of the 4 ponds analysed.

3. Results

3.1. Relationships between Variables and Mathematical Models

The maximum data of each variable, the graphs of the adjustments made in the new cases, as well as of the whole data, and the errors returned by the specific and general mathematical models to each pond are shown in this subsection. Table 3 shows the maximum value for V-A-h at every pond. The maximum storage volume varied from 771.4 m3 to 6653.6 m3, with Bra8 being the pond with the highest storage capacity. The maximum area of the water sheet varied from 860.7 m2 to 5003.9 m2, with Par4 having the largest area. The maximum height of the ponds varies between 4.3 m and 1.9 m, with Bar6 being the deepest.
Figure 3 shows illustrative scatterplots that show the relationships between V-A-h parameters for some ponds. Blue and red lines represent power and quadratic functions. Black dots represent observed vs. measured values of V-A-h. The R2 values, always above 0.9, demonstrate strong statistical relationships, with quadratic functions showing the highest R2 values. The V-h relationship in Par6 for the quadratic function returned an R2 = 1, being the most accurate. On the contrary, the A-h relationship for the power function of the Bar6 pond showed an R2 = 0.90, being the least accurate. It can be seen from the graphs that the quadratic functions are more accurate than the power functions since the latter do not fit at specific parts of the curve. For instance, the V-A relationship for Par4 shows that the blue line does not fit well in the x-coordinate in 2000 m3 and above. A similar behavior can be observed in Bar6, where the blue line does not fit in the x-coordinate at 1000 m3 and above. The V-A relationship in Par6 showed a good fit for both functions.
The specific power and quadratic functions estimated with the corresponding R2 and RMSE are shown in the Table 4. In general, the quadratic functions present a lower RMSE (%) than the power functions, with the latter showing RMSE < 4%. The V-A relationship in the Par6 pond had the lowest RMSE (1.71%), while the Bar6 showed the highest RMSE (10.26%). Regarding the V-h relationship, Par6 had the lowest RMSE with 0.16%. Bar6 was the study case with the highest RMSE in the different relationships, presenting, for instance, an RMSE in the A-h relationship of 17.06%.
Figure 4 shows the relationships for the whole dataset (n = 11), i.e., including our four cases besides the Marín-Comitre et al. [11] dataset. These plots show the fit of the power (blue line) and quadratic (red line) functions as well as their corresponding R2. In general, the quadratic functions showed the highest R2. In the case of the V-A relationship, the power function showed an R2 = 0.748 in comparison to the quadratic function with an R2 = 0.808. The A-h relationship showed the worst performance while the V-A and V-h, which are the most useful equations for farmers, showed an R2 above 0.75.
The generalized functions of the different relationships between the V-A-h parameters and their associated R2 are shown in the Table 5. Applying the general V-A power function to each pond resulted in an RMSE that varied from 1.65% (P1) to 24.24% (Bra8). The use of the general quadratic function resulted in an RMSE that varied from 8.30% (Par4) to 23.23% (Bra8). The analysis of the V-h and A-h relationships for Bar6 showed the highest RMSE (48.50%), being the worst pond for the application of the mathematical models. On the contrary, at pond P4, these models fitted quite well, with RMSEs not exceeding 4% in the V-h relationship and 7% in the A-h relationship.

3.2. Estimated Errors

Figure 5 shows the RMSE for the different models at each pond and using the generalized equations. For the V-A, the RMSE was below 25%. The quadratic and power functions showed errors of the same magnitude for each pond. The figure highlighted the large RMSE observed at Bar6 (close to 50%) for the V-h and A-h relationship. On the contrary, P4 showed the lowest RMSE in the V-h and A-h relationships.
Figure 6 shows the errors as a function of the volume of water stored using power- and quadratic-specific models. Specifically, A, B and C columns in Figure 6 show the error in the V-A, V-h and A-h relationships. The V-A relationships are of particular interest in terms of the applicability of the equations and, according to Figure 6, the errors are relevant when the volume of water stored is low. Conversely, the errors tend to be close to the 10% when the volume of water stored is medium or high. Therefore, the models developed here are useful in times of a hydrological bonanza, but they will not be practical for low water levels (something common after dry spells).
Similarly, Figure 7 presents the errors as a function of the volume of water stored but using the general equations instead of the specific ones (showed in Figure 6). In this case, the errors were estimated for the four cases analysed in the present work, but also for Marín-Comitre et al.’s [11] dataset. The plots showed a similar behavior to that described above for specific functions. The quadratic functions (red line) showed lower errors than the power functions (blue) when the volume of water stored was medium or high. Only P1, using a quadratic function, showed high errors.

3.3. Applicability of Models

The temporal dynamics of the volume of water stored in the studied ponds for each farm is shown in the Figure 8. The volume of stored water showed a large variability that is given by the seasons, but also by the inter-annual variability of the Mediterranean climate. The dynamics is similar for each pond and for each type of function used to estimate the volume of water. For the Parapuños farm, the quadratic function overestimates the values produced by the power function, whereas in La Brava and La Barrosa farms, the opposite occurs.
By means of pond-specific high-resolution DEMs, the Vmax of every pond was calculated and compared with the Vmax estimated using the power (blue) and quadratic (red) functions (Figure 9). According to this comparison, in small ponds like Par6 or Bar6, both functions estimated a volume of water stored close to the volume calculated using their high-resolution DEMs. For large ponds like Par4 and Bra8, the volume of water determined using their DEMs is close to that estimated by means of the quadratic function, while the power function clearly overestimates the Vmax.

4. Discussion

The availability of water in extensive livestock farming systems of Mediterranean countries is increasingly threatened by climate change, which could compromise ecosystem maintenance, human development [31] and land management due to, on the one hand, the increase in the average stocking rates [32] and, on the other hand, land abandonment [33]. The survivorship of these kinds of farms is crucial both for their provision of ecosystem services as well as for their role in preventing fires, a serious threat in the Iberian Peninsula [34]. In addition, these ponds are also vital for many hunting animals as well as for birds and amphibians [35].
It is still uncommon, at least in the Extremadura region, that many farmers, advisors and/or stakeholders make a forecast on the amount of available water and if it is in accordance to the needs of the livestock in spite of existing accurate formulas that allow for estimating the water consumption per individual [16] and losses by evaporation [36]. It is often due to the fact of many of them (especially farmers) can know or easily estimate the maximum depth and the current water surface, but they are not mindful that parametric relationships with volume also exist. In other words, by knowing one of these parameters, the estimation of volume is an easy task.
Marín-Comitre et al. [4,6,11] have already provided useful formulas in this matter but the V-A relationships performed here provided a substantial improvement in terms of accuracy (assessed by R2 and RMSE: 0.75 vs. 0.57 (power); 0.81 vs. 0.60 (quadratic); 25% vs. 39%) thanks to the addition of four new study cases (each case supposes several months of work from a field survey in September until the final calculations). However, in order to simplify this process of estimation, we suggest the use of the following formula V = −0.00003 A2 + 1.3416 A − 356.86 that it is well-fitted both for large and small ponds and its accuracy is pretty high (see Table 5).
Another interesting thing is the threshold of 2000 m2 (pond size). This is the limit that Marín-Comitre et al. [4,6,11,26] mentioned that is necessary to overcome if one farmer can guarantee a water supply to the livestock every summer and also after a dry spell lasting over 12 months. In addition, this is the limit at which the water quality (assessed by fecal coliforms, presence of E. coli, turbidity, dissolved oxygen, etc.) is considerably reduced if not reached. In fact, the farmers that admitted having problems related to water availability recognized that their farms have a low number of ponds and most of them are smaller than 2000 m2 in size [37].
From the point of view of the estimation of the volume, small ponds are easily quantifiable by power and quadratic functions, but for larger ponds, only quadratic functions returned accurate estimations. We have been able to identify this fact thanks to the analysis of the errors conducted, which has not been provided yet in any previous work (up to our knowledge). Nonetheless, when the water level is too low (almost empty ponds), none of our equations are useful to estimate the actual volume of water. Additionally, farmers refuse to put their livestock in fences in which ponds are almost empty, particularly in summertime, because the presence of E. coli is too high and it provokes diarrhea in them [26].
From the methodological point of view, it is also fruitful to discuss the suitability of the materials, and the tools used in this study. The obtention of the actual volume (ground truth) of each pond has supposed (i) fieldwork with sophisticated tools such as laser scanners, UAVs, GNSS-IMU, bathymetry in the flooded area, etc., and (ii) data processing to generate high-resolution (20 cm) pond-specific DEMs and mathematical models by using specific software packages. In addition, these models must be worked with GIS software such as QGIS v.3.28.7 and ArcGIS Pro v.3. Therefore, to properly know the volume of a pond requires a laborious task that demands time consumption, expensive apparatus and skilled workers. On the other hand, there are also some limitations for the application of the methodology used here. Firstly, the ponds need to be completely empty during data collection which is not always possible for large ponds. Secondly, in the PPK procedure, the positional accuracy of the 3D models is unknown until the post-processing is carried out. Thirdly, there are the usual limitations of photogrammetry, caused by the vegetation cover, although the water pond area is commonly bare. Finally, we have surveyed a small number of cases (n = 4), similar in magnitude to previous studies ([11]: n = 7). After validating the methodology used here, efforts in future work will focus on increasing the number of cases to achieve a sample size that allows the application of the obtained equations to the entire southwestern Iberian Peninsula.
The use of the quadratic equation proposed above means that every person can know the volume of water of these kinds of ponds from a previous knowledge of the pond’s size and/or depth (maximum capacity) or know the surface occupied by water. The latter can be estimated by using an aerial or satellite image. The use of aerial imagery requires a UAV or an image has to be downloaded from an official data repository. The problem, at least in Spain, is that these images are taken in a single moment of the year. The use of satellite images such as Sentinel provides a larger temporal resolution, but their spatial resolution (10 m) makes them unsuitable for the present application.
High-resolution satellite imagery may be an interesting alternative for those tasks that require the monitoring of the water volume throughout the whole year since the installation of water-level sensors is not an easy process and it is almost mandatory to hire an external service to check and download their data. Another cheaper option would be the installation of a level type to assess the depth, but this requires being personally in the pond to write down the value of each single moment. The results obtained in previous works that estimated the water volume from remote-sensing images were very consistent with the volume derived from the fitted equation of the lake storage capacity curve based on the observed data [38]. For long-term monitoring in countries like Spain, the current frequency of aerial images (spatial resolution: 0.25 m, images every 2 years) will allow the comparison between the dry, normal and wet periods and it can be particularly helpful for foreseeing water availability under certain circumstances.

5. Conclusions

The specific relationships between the different V-A-h variables were very precise. Their use can be extrapolated to other types of studies such as, for example, establishing the water balance of the farms under study, which will help the landowner to make the right management decisions. The analysis of the four new cases, added to what was studied, obtaining a total of 11 cases, has allowed us to obtain a general relationship between the variables Volume and Area, whose function can be used for the calculation of the storage capacity of the ponds in any extensive livestock farm of the SW of the Iberian Peninsula. Quadratic functions are considered suitable regardless of the level of water available in the ponds, while the potential functions overestimate the capacity of the ponds when the water levels are high. Considering the easy visualization of the water sheet by means of GIS software, these models can be a simple tool to estimate the water volume of livestock farms. Regarding the analysis of the root mean square errors at different depths of the models developed here, very high error percentages can be observed at shallow depths, but these are quite accurate when the ponds are full or half full. Nonetheless, a larger number of cases should be studied to obtain a larger sample size and greater geographic and morphological variability of the ponds, thus obtaining more accurate models.

Author Contributions

Conceptualization: Á.G.-G., F.M.C.-M. and M.P.-F.; Methodology: Á.G.-G., F.M.C.-M. and M.P.-F.; Software: Á.G.-G.; Validation: Á.G.-G. and M.P.-F.; Formal analysis: F.M.C.-M. and Á.G.-G.; Investigation: F.M.C.-M. and Á.G.-G.; Resources: Á.G.-G.; Data curation, F.M.C.-M. and Á.G.-G.; Writing—original draft preparation: F.M.C.-M.; Writing—review and editing: Á.G.-G. and M.P.-F.; Visualization: F.M.C.-M.; Supervision: Á.G.-G.; Project administration: M.P.-F.; Funding acquisition: M.P.-F. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by the IB20036 Research Project “Los recursos hídricos en fincas de ganadería extensiva: estado actual, riesgos emergentes y propuestas de gestión (GANAWA)”, co-funded by the Consejería de Economía, Ciencia y Agenda Digital de la Junta de Extremadura and by the European Regional Development Fund (ERDF) of the European Union. This paper was funded from the European Union NextGenerationEU/PRTR-C17.I1 and Junta de Extremadura.

Data Availability Statement

The entire dataset used and/or analyzed in this research is available from the corresponding authors upon a reasonable request.

Acknowledgments

This work has been possible thanks to the collaboration of the owners and workers of the three pilot farms where the studied ponds are located. Their availability has been crucial in the field work. We would also like to thank the collaboration of colleagues from our research institutes for their availability for travel and transportation as well as for teaching us some key aspects of the work. Special thanks to the researcher Ubaldo Marín-Comitre for his suggestions and guidance.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Geographical location of the pilot farms and their watering ponds in Extremadura (A). (B) Parapuños de Doña María (PAR4 and PAR6), (C) La Brava (BRA8), (D) La Barrosa (BAR6).
Figure 1. Geographical location of the pilot farms and their watering ponds in Extremadura (A). (B) Parapuños de Doña María (PAR4 and PAR6), (C) La Brava (BRA8), (D) La Barrosa (BAR6).
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Figure 2. Example of image data obtained of the workflow in pond no. 8 of La Brava. (A) Orthophotography, (B) DEM and (C) Cloud point RGB image [30].
Figure 2. Example of image data obtained of the workflow in pond no. 8 of La Brava. (A) Orthophotography, (B) DEM and (C) Cloud point RGB image [30].
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Figure 3. Illustrative scatterplots of the V-A-h parameters measured (represented by black dots) and obtained power (blue) and quadratic (red) regression lines. V-A: Par6, V-h: Par4, A-h: Bra8.
Figure 3. Illustrative scatterplots of the V-A-h parameters measured (represented by black dots) and obtained power (blue) and quadratic (red) regression lines. V-A: Par6, V-h: Par4, A-h: Bra8.
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Figure 4. Scatterplots of the V-A-h parameters measured (represented by dots) and obtained power (blue) and quadratic (red) relationships using the whole dataset (11 ponds).
Figure 4. Scatterplots of the V-A-h parameters measured (represented by dots) and obtained power (blue) and quadratic (red) relationships using the whole dataset (11 ponds).
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Figure 5. Comparison of the RMSE values from using the different general equations.
Figure 5. Comparison of the RMSE values from using the different general equations.
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Figure 6. Errors as function of the volume of water stored. Column (A): V-A relationships. Column (B): V-h relationships. Column (C): A-h relationships.
Figure 6. Errors as function of the volume of water stored. Column (A): V-A relationships. Column (B): V-h relationships. Column (C): A-h relationships.
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Figure 7. Plots of the analysis of errors as function of the volume of water stored using general equations in V-A relationships of the whole data available.
Figure 7. Plots of the analysis of errors as function of the volume of water stored using general equations in V-A relationships of the whole data available.
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Figure 8. Temporal evolution of the average water-storing capacity of each farm.
Figure 8. Temporal evolution of the average water-storing capacity of each farm.
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Figure 9. Power (blue bar) and quadratic (red bar) functions applied to Vmax for all ponds in the pilot farms. The real maximum volume (green bar) is also shown for the four ponds where the real volume was available.
Figure 9. Power (blue bar) and quadratic (red bar) functions applied to Vmax for all ponds in the pilot farms. The real maximum volume (green bar) is also shown for the four ponds where the real volume was available.
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Table 1. Data analysis of the ponds for estimating relationships between variables. Spillway level: maximum height of the pond, i.e., the point where water overflows. Minimum elevation: pond depth point. Height: pond depth. Interval (cm): analysis distance of the V-A-h ratio. Intervals (n): number of analysis repetitions.
Table 1. Data analysis of the ponds for estimating relationships between variables. Spillway level: maximum height of the pond, i.e., the point where water overflows. Minimum elevation: pond depth point. Height: pond depth. Interval (cm): analysis distance of the V-A-h ratio. Intervals (n): number of analysis repetitions.
PondSpillway Level (m)Minimum Elevation (m)Height (m)Interval (cm)Intervals (n)
PAR6381.15379.251.91019
PAR4401.56398.463.11031
BAR6314.10310.703.451034
BRA8316.65312.354.352023
Table 2. Aerial images used in this study (available in June 2022). CNIG: Spanish National Centre of Geographical Information.
Table 2. Aerial images used in this study (available in June 2022). CNIG: Spanish National Centre of Geographical Information.
Acquisition DateSpatial Resolution (m)Source
19840.5CNIG
20050.5CNIG
20070.5CNIG
2009UnknownGoogle Earth
2010UnknownGoogle Earth
20110.5CNIG
20130.5CNIG
2015UnknownGoogle Earth
20160.5CNIG
2017UnknownGoogle Earth
2018UnknownGoogle Earth
20190.5CNIG
2020UnknownGoogle Earth
2021UnknownGoogle Earth
Table 3. Maximum values of each parameter at every pond. * Source: Marín-Comitre et al. [11].
Table 3. Maximum values of each parameter at every pond. * Source: Marín-Comitre et al. [11].
PondV Max (m3)A Max (m2)h Max (m)
Par6771.4860.71.9
Par45401.25033.93.1
Bra86653.62511.73.4
Bar62270.21745.54.3
P4*2157.61957.62.5
B6*3350.72005.53.4
B8*2282.01711.32.5
P3*3635.33392.72.8
P1*1680.11764.72.5
P5*4978.04916.43.1
B3*5439.92923.43.3
Table 4. Performance values of the pond-specific mathematical models.
Table 4. Performance values of the pond-specific mathematical models.
Power FunctionsQuadratic Functions
PondEquationR2RMSE (%)EquationR2RMSE (%)
V-A relationship
Par6y = 0.0011x1.99680.9971.71y = 0.0009x2 + 0.1219x − 13.1860.9992.06
Par4y = 0.0036x1.70380.9849.61y = 0.00009x2 + 0.7028x −165.440.9961.92
Bra8y = 0.0002x2.18940.9675.99y = 8 × 10−7x3 − 0.0016x2 + 1.6942x − 209.25 0.9943.93
Bar6y = 0.0449x1.40570.97210.26y = 0.0008x2 − 0.063x + 20.3550.9981.55
V-h relationship
Par6y = 195.95x2.33680.9974.98y = 223.93x2 − 21.151x + 0.36211.0000.16
Par4y = 367.8x2.20550.9945.12y = 756.09x2 − 741.96x + 223.180.9981.57
Bra8y = 420.93x1.91360.9991.59y = 296.9x2 + 291.73x − 122.590.9990.76
Bar6y = 33.264x3.63660.9878.96y = 303.98x2 − 433.71x + 130.630.9991.12
A-h relationship
Par6y = 421x1.17040.9982.44y = 18.796x2 + 417.95x − 13.2860.9990.91
Par4y = 847.26x1.35450.9796.12y = 457.7x2 + 98.615x + 128.740.9971.53
Bra8y = 797.88x0.86950.9814.91y = −88.807x2 + 983.1x − 50.5790.9981.35
Bar6y = 111.56x2.54980.90517.06y = −71.174x3 + 467.31x2 − 295.75x + 47.0390.9961.94
Table 5. Performance values of the generalized mathematical models.
Table 5. Performance values of the generalized mathematical models.
Power FunctionsQuadratic Functions
ParametersEquationR2EquationR2
V-Ay = 0.0093x1.61120.75y = −0.00003x2 + 1.3416x − 356.860.81
V-hy = 210.87x2.57440.82y = 373.77x2 − 11.259x − 60.1040.84
A-hy = 515.67x1.48130.66y = −47.233x2 1035.6x − 275.290.69
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Castaño-Martín, F.M.; Gómez-Gutiérrez, Á.; Pulido-Fernández, M. Modelling Water Availability in Livestock Ponds by Remote Sensing: Enhancing Management in Iberian Agrosilvopastoral Systems. Remote Sens. 2024, 16, 3257. https://doi.org/10.3390/rs16173257

AMA Style

Castaño-Martín FM, Gómez-Gutiérrez Á, Pulido-Fernández M. Modelling Water Availability in Livestock Ponds by Remote Sensing: Enhancing Management in Iberian Agrosilvopastoral Systems. Remote Sensing. 2024; 16(17):3257. https://doi.org/10.3390/rs16173257

Chicago/Turabian Style

Castaño-Martín, Francisco Manuel, Álvaro Gómez-Gutiérrez, and Manuel Pulido-Fernández. 2024. "Modelling Water Availability in Livestock Ponds by Remote Sensing: Enhancing Management in Iberian Agrosilvopastoral Systems" Remote Sensing 16, no. 17: 3257. https://doi.org/10.3390/rs16173257

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