Application of satellite imagery to update depth-area-volume relationships in reservoirs in the semiarid region of Northeast Brazil1

Reservoirs are the primary source of water supply in the semiarid region of Pernambuco state, Brazil, because of the constant water scarcity affecting this region. Knowledge of the amount of water available is essential for the effective management of water resources. The volume of water stored in the reservoirs is calculated using the depth-area-volume relationship. However, in most reservoirs in the semiarid region, this relationship is currently out of date. Therefore, the objective of this study was to explore the potential and limitations of the application of the ISODATA unsupervised classification method to calculate the depth-area-volume relationships of reservoirs in the semiarid region of Pernambuco, Brazil. The application of the ISODATA method was evaluated in three reservoirs in the state of Pernambuco, i.e., Poço da Cruz, Barra do Juá, and Jucazinho. The results were compared with the updated curves of reservoirs obtained from bathymetry and recent LiDAR surveys. The ISODATA method presented satisfactory results for the three reservoirs analyzed. The mean absolute error of the volume in Poço da Cruz and Barra do Juá was lower than 1% of the maximum capacity. The use of the ISODATA method meant that the surface area underestimation tendency in the Poço da Cruz reservoir was less than when spectral indices were used.


Introduction
The need for the construction of reservoirs in Northeast Brazil occurred because of the climate and geological characteristics of the region, which resulted in intermittent rivers and scarce groundwater (Malveira et al., 2012;Toledo et al., 2014). To perform their role satisfactorily, reservoirs must be monitored as accurately as possible. This exercise is particularly important in semiarid regions, where reservoirs are the main source of water. Accurate information about volume storage in the reservoir is essential for proper water allocation (Nascimento & Ribeiro Neto, 2017).
Such data are calculated with curves that relate water level to surface area and storage volume, also called the deptharea-volume relationship, and, in Portuguese, "cota-areavolume" (CAV). Despite federal institutions' efforts to update bathymetries, water resource management institutions still use data from the time of construction of the reservoirs (Collischon & Clarke, 2016).
Remote sensing products can be used to calculate deptharea-volume curves and reduce the cost of topo-bathymetric surveys. Satellite images are able to detect water bodies and, using spectral indices and classification algorithms, calculate their extent. The extent of water can also be useful for characterizing the geometry of lakes in combination with satellite altimetry (Arsen et al., 2014;Baup et al., 2014) and in situ water levels (Collischon & Clarke, 2016). Other approaches have been tested in Northeast Brazil using a combination of satellite imagery and field surveys (Lopes & Araújo, 2019), digital elevation models derived from synthetic aperture radar (SAR) images (Zhang et al., 2016), and supervised classification of maximum likelihood (Toledo et al., 2014).
The objective of this study was to explore the potential and limitations of the application of the ISODATA unsupervised classification method to calculate depth-area-volume relationships of reservoirs in the semiarid region of Pernambuco state, Brazil.

Material and Methods
Three reservoirs were selected to apply the method of image classification and calculation of the CAV. Poço da Cruz (Moxotó River), Jucazinho (Capibaribe River), and Barra do Juá (Riacho do Navio) are located in the state of Pernambuco, Northeast Brazil ( Figure 1). All of them are in a semiarid region, where the temperature varies between 20.1 and 29.9 °C (Jucazinho), 23.2 and 28.6 °C (Poço da Cruz and Barra do Juá), the annual precipitation is between 450 and 600 mm, and annual total evaporation greater than 1600 mm. These values were obtained from stations at the National Institute of Meteorology (INMET) and the National Water Agency (ANA).
The main characteristics of these reservoirs are listed in Table 1. The drainage area and precipitation were obtained Figure 1. Location of the reservoirs Poço da Cruz, Jucazinho, and Barra do Juá in the state of Pernambuco, Brazil The rain gauges were Surubim (735158), Inajá (837038), and Floresta (838021). Total evaporation was obtained from the INMET weather stations Floresta (82887) and Surubim (82797). The precipitation and total evaporation information for each reservoir correspond to the values of the nearest station. The maximum surface area and capacity were obtained from CAVs.
To calculate the depth-area-volume curves, in situ (bathymetry and water level) and remote sensing (satellite image and LiDAR products) data were required, as described in detail below.
An important step in water-extent determination is the validation of the results obtained using satellite imagery. In this study, the surface area and volume were compared to CAVs generated using a digital terrain model (DTM) calculated from bathymetric and LiDAR surveys. The DTM, which represents the topography of the Poço da Cruz and Jucazinho reservoirs, was generated after the integration of the aerophotogrammetric survey of the non-water part, and the bathymetric survey of the inundated area carried out by the Agência Nacional de Águas (here called DTM ANA ).
The survey was supported by the implantation of geodetic networks of altimetric and planimetric references connected to the Brazilian Geodetic System (SGB), and the LiDAR technique was used for the non-water terrain survey. The final result had a density of 2 points m 2 in a 3D representation with the planimetric and altimetric references, defined as SIRGAS2000/ UTM and the reference ellipsoid GRS80, respectively. The bathymetry was accomplished with an echosounder using a single beam for shallow water and a multibeam for deep water. The coordinate information of the altimetric and planimetric geodetic networks was used in the unification of LiDAR plus bathymetry reference systems.
Three-Dimensional Pernambuco (PE3D) was a project of the Government of Pernambuco state, which resulted in a database of DTM and orthophotos of high-resolution using LiDAR technique (here called DTM PE3D ). The survey was carried out between March 2014 and December 2016, and the final product had the following characteristics: a scale of 1:5000, a spatial resolution of 1 m, and an altimetric accuracy of 25 cm, covering the entire territory of the state (Nascimento & Ribeiro Neto, 2017). The PE3D is another data source for calculating the bathymetry and CAVs of reservoirs in Pernambuco state. This is possible in cases where the reservoir was empty on the date of the measurement, as demonstrated by Nascimento & Ribeiro Neto (2017). The Barra do Juá reservoir is one of these cases, allowing the updating of its bathymetry.
The water level in the reservoirs was monitored daily by the Agência Pernambucana de Água e Clima (APAC). The altimetric reference of the stations was obtained based on DTM ANA and DTM PE3D .
The selection of the images was based on the following criteria: representation of the range of water levels observed in the reservoirs, cloud-free images, period covering approximately 15 years, and availability of in situ water level on the day of the satellite pass. Images from Landsat-5 and -8 were selected and downloaded using the Google Earth Engine (Gorelick et al., 2017). The process was carried out using JavaScript language with a cloud cover criterion of less than 10% and a mask of the reservoirs.
The images were obtained from the collection Tier 1 TOA reflectance because corrections had been applied to these images (Li et al., 2013). The CAV curves were calculated using 31 images from Poço da Cruz (13 Landsat-5 and 18 Landsat-8), 17 images from Barra do Juá (6 Landsat-5 and 11 Landsat-8), and four images from Jucazinho (two Landsat-5 and two Landsat-8). The small number of images for the Jucazinho reservoir was due to the high cloud incidence in the region.
ISODATA applies the concept of minimum distance to classify the images based on the spectral signatures of the pixel and the average of the class, associating the pixel with the class with the lowest spectral difference (Memarsadeghi et al., 2007). First, the method defines a vector of arbitrary classes with N centers of spectral averages and assigns each pixel to the class with the nearest spectral average. After allocating all the pixels, a new spectral average is generated for the classes, and then the pixels are reallocated again in the classes with the nearest spectral average. This process is repeated iteratively until the allocation converges. This unsupervised method was chosen to overcome the problem associated with the definition of threshold values in applications using water indices.
An RGB composition was created with bands 2, 4, and 5 from Landsat-5 and bands 3, 5, and 6 from Landsat-8. In both satellites, these bands correspond to green, near-infrared, and shortwave infrared, respectively. They are the same bands as those used in the Normalized Difference Water Index (NDWI) and the Modified NDWI (MNDWI) and have good performance in distinguishing the presence of water.
The System for Automated Geoscientific Analysis (SAGA) was used to apply the ISODATA method. The input parameters were: i) the maximum number of iterations, ii) the initial number of classes, iii) the maximum number of classes, and iv) the minimum number of pixels in one class. The centers of the initial classes were defined randomly using the value of parameter ii. Then, the image was classified for the first time, and later the classes with the number of pixels lower than the parameter iv were removed (added to other classes), adjusting the number of classes limited by the maximum value adopted in parameter iii. In addition, during the process, classes with Table 1. Geometric characteristics of the reservoirs selected and hydrometeorological characteristics of the regions where they are sited spectral proximity between them could be merged into one class.
The definition of the parameters followed the standard values suggested by the SAGA (the modification of these values did not significantly alter the classification). The values are 20 for the maximum number of iterations, 16 for the maximum number of classes, and five for the minimum number of pixels in a class. The initial number of classes was the most sensitive parameter, directly influencing the final number of classes. The values were determined for each classification, always aiming at the greatest number of classes possible. The greater the number of classes, the easier it is to aggregate pixels in homogeneous groups because ISODATA classifies all pixels of the image.
To calculate the surface area, power-law regression was used with the auxiliary parameter h 0 (Eq. 1), applied to several reservoirs in the Northeast (Collischonn & Clarke, 2016). where: i -elements of the CAV; n -number of elements of the CAV; E -area or volume estimated using the CAV SI ; and, M -area or volume measured using the CAV REF .
The flowchart presented in Figure 2 summarizes the methodology.
where: A -surface area; h -water level; h 0 -auxiliary parameter; and, a, b -coefficients of the power law.
The incremental volume between two consecutive images was calculated as a truncated pyramid (Abileah et al., 2011). where: V n+1 -incremental volume between surface areas A n+1 and A n ; and, h n+1 and h n -water level corresponding to the surface areas A n+1 and A n .
The total volume is calculated by summing the successive values of ∆V based on Eq. 2:  Figure 3 presents the steps of the classification process for a Landsat-5 image in the Barra do Juá reservoir. The color composition with bands 4, 5, and 2 for the Landsat-5 image ( Figure 3A) was used in the ISODATA classification method ( Figure 3B). The pixels representing water were grouped into two classes ( Figure 3C), which were aggregated to represent the class water ( Figure 3D).

Results and Discussion
The value of the pixels is sensitive to water depth, amount of chlorophyll, and suspended solids in water, which influences the classification, especially in composition with bands from the near-infrared (Elmi, 2019). Because of this interference, the pixels of water can be erroneously classified as non-water, affecting the surface area estimate. For this reason, more than one class was classified as water, which was later grouped into one class. Figure 4A presents the relationship between water level and surface area, and water level and stored volume ( Figure 4B) in the Poço da Cruz reservoir (CAV REF calculated with DTM ANA and CAV SI ). As can be seen in Figures 4A and B, the interval between 425 and 430 m has no information on the volume calculated with the image. This situation occurred because of the lack of water level data. Nevertheless, the number of values obtained from the images was sufficient to establish the deptharea-volume relationship.
The comparison of the surface area calculated with satellite images and given by the CAV REF showed a trend of underestimation, especially at high water levels ( Figure 4A). At the maximum water level of 435.00 m, the underestimate was 3.98% (56.34 km 2 for CAV REF and 54.09 km 2 for CAV SI ). When the volume was calculated using Eqs. 2 and 3, there was an attenuation of the underestimation. For the maximum water level, the accumulated volume estimated with the images was 3.08% lower (483.72 hm 3 for the CAV REF and 468.82 hm 3 for the CAV SI ).
There was a different pattern in the area estimated at low and high water levels. Until 420.00 m, the area was overestimated, while above this level, the volume was underestimated. This is consistent with other studies, such as Collischonn & Clarke (2016), who attribute this characteristic to the spatial resolution of the images. As the water extent decreases, the error increases. The mean absolute error was 0.84 km 2 for the surface area and 4.52 hm 3 for the volume.
The CAV REF for comparison with CAV SI in Barra do Juá was obtained using DTM PE3D . The altimetric reference of the in-situ station is different from the altimetric reference of the DTM PE3D . The technical information of the dam informs the elevation of the spillway, which can also be identified on the DTM PE3D . The difference between these elevations is the factor that must be added to the water level measurement at the station to have the same reference as the DTM PE3D . The depth-area-volume relationships are shown in Figures 5A and B.  Few images were available during the drought 2012-2017, especially in the first years of this period. In just one image during low water (November 10, 2017), there was also water level measurement. The variation of the water level was between 395.05 and 403.53 m. The differences in the maximum water level (405.3 m) were 13.64% for the surface area (13.96 km 2 for the CAV REF and 12.06 km 2 for the CAV SI ) and 3.44% for the volume (59.52 hm 3 for the CAV REF and 57.47 hm 3 for the CAV SI ). The MAE was 0.39 km 2 for the surface area and 0.43 hm 3 for the volume. Figures 4 and 5 show the values of the coefficients in Eq. 1, the coefficient of determination, and the 95% confidence intervals for the depth-volume curves (CAV REF and CAV SI ). The application of the Student's t-test with the samples of volume (CAV SI and CAV REF ) showed that the null hypothesis could not be rejected (H0: µ 1 -µ 2 = 0) in both reservoirs.
Despite the small number of images, the result in the Jucazinho reservoir covered 80% of its capacity (from 14.90 to 178.57 hm 3 in the CAV REF ). Four pairs of values are not enough to establish a depth-area-volume relationship but could be useful to test the ISODATA method for the water extent calculation. For this reason, it is not presented in Figure  6 the coefficients of Eq. 1, and confidence intervals.
Like the other reservoirs analyzed, the surface area calculated with the satellite images was underestimated. The four processed surface areas had values lower than the CAV REF , which confirms the results obtained in Poço da Cruz and Barra do Juá. The MAE calculated for the surface area was 0.13 km 2 .
There are two main difficulties with the application of images to achieve the objectives of this study. The period between the oldest and newest images cannot be too long.
Reservoirs are susceptible to sedimentation over time, which alters their geometry and CAVs. Ideally, the period should not be longer than 15 years. In addition, the presence of clouds in the images can affect classification (also mentioned in Toledo et al., 2014). This requirement can affect the use of optical images near the coast, where the presence of clouds is almost constant.
In addition to remote sensing products, water level data are indispensable for the calculation of CAVs. Despite advances in technology for monitoring and improving investments, there are still long periods for which water level data is missing. Sometimes, there is an image of good quality, but it is not possible to use it because there is no information on the water level.
On the other hand, the results encourage the application of the ISODATA method for the calculation of CAVs in other reservoirs in the Northeast semiarid region. Unsupervised methods such as ISODATA do not need to determine the threshold to classify water, as verified in applications using spectral indices (NDVI, NDWI, MNDWI, among others) (Arsen et al., 2014, Feyisa et al., 2014, Schwatke et al., 2019. The results obtained with the ISODATA in the Poço da Cruz reservoir, for example, were better than the application of NDWI carried out by Costa (2019) and had a reduced tendency to underestimate the surface area. The underestimation tendency was also observed in the calculation of a simplified bathymetry using satellite imagery in the Pentecoste reservoir (state of Ceará) (Lopes & Araújo, 2019). This topic should be investigated in more detail to minimize the effects of the underestimation of the surface area calculation.
High-resolution DTMs can be considered an accurate source of data for use as a reference in validating imagebased methods. In this study, the DTM PE3D from Nascimento & Ribeiro Neto (2017) proved to be useful for validation of the results in the Barra do Juá reservoir. The DTM obtained using TanDEM-X (Zhang et al., 2016) can also be considered for this purpose.
The CAV REF for Poço da Cruz and Barra do Juá remained within the 95% confidence interval of the CAV SI . The same result was achieved by Collischonn & Clarke (2016) in the Boqueirão reservoir, State of Paraíba, Brazil. The volume error was comparable to other studies that estimated the lake volume using satellite images, as reported by Baup et al. (2014) (error of 7.4%) and Asfaw et al. (2020) (error of 2.9%). The mean absolute error of volume was 0.94 and 0.71% of the maximum capacity in Poço da Cruz and Barra do Juá, respectively. It is recommended that the ISODATA method should be applied to small reservoirs (Pereira et al., 2019) and macrophytecovered reservoirs (Zhang et al., 2018) to test it under different conditions in the Northeast semiarid region.

Conclusions
1. The ISODATA method presented satisfactory results for the three reservoirs analyzed. The mean absolute error of volume in Poço da Cruz and Barra do Juá was lower than 1% of the maximum capacity.
2. The ISODATA method had a decreased tendency to underestimate the surface area in the Poço da Cruz reservoir compared to the use of spectral indices.