Comparison of Methods to Derive the Height-Area
Relationship of Shallow Lakes in West Africa Using
Remote Sensing

F Girard, Laurent Kergoat, H Nikiema, M Wubda, R Yonaba, T Fowé, A Abdourhamane Touré, I Mainassara, M de Fleury, M Grippa

► To cite this version:

F Girard, Laurent Kergoat, H Nikiema, M Wubda, R Yonaba, et al. Comparison of Methods to Derive the Height-Area Relationship of Shallow Lakes in West Africa Using Remote Sensing. Water Resources Research, 2025, 61, 10.1029/2024wr037411. hal-05387601

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Distributed under a Creative Commons Attribution 4.0 International License
# Water Resources Research®

## RESEARCH ARTICLE

10.1029/2024WR037411

**Special Collection:**

Hydrogeodesy: Understanding changes in water resources using space geodetic observations

**Key Points:**

* Height-area-volume relationships of small and medium-sized shallow lakes are estimated using recent remote sensing data based methods

* Radar and lidar altimetry coupled to Sentinel-2 imagery, and Pleiades Digital Surface Models perform well against in-situ data

* Inherent limits, spatio-temporal coverage, and data accessibility of each method are identified and discussed

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

F. Girard, felix.girard@get.omp.eu

**Citation:**

Girard, F., Kergoat, L., Nikiema, H., Wubda, M., Yonaba, R., Fowé, T., et al. (2025). Comparison of methods to derive the height-area relationship of shallow lakes in West Africa using remote sensing. *Water Resources Research*, *61*, e2024WR037411. https://doi.org/10.1029/2024WR037411

Received 28 FEB 2024
Accepted 5 FEB 2025

**Author Contributions:**

**Conceptualization:** F. Girard, L. Kergoat, M. Grippa

**Data curation:** H. Nikiema, M. Wubda, R. Yonaba, T. Fowé, A. Abdourhamane Touré, I. Mainassara

**Formal analysis:** F. Girard

**Funding acquisition:** M. Grippa

**Investigation:** F. Girard, L. Kergoat, H. Nikiema, R. Yonaba, T. Fowé, A. Abdourhamane Touré, M. de Fleury, M. Grippa

© 2025. The Author(s). This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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## Comparison of Methods to Derive the Height-Area Relationship of Shallow Lakes in West Africa Using Remote Sensing

F. Girard¹,² ID, L. Kergoat¹ ID, H. Nikiema³, M. Wubda⁴, R. Yonaba⁵ ID, T. Fowé⁵, A. Abdourhamane Touré⁶ ID, I. Mainassara⁷ ID, M. de Fleury¹, and M. Grippa¹ ID

¹Géosciences Environnement Toulouse (GET, Université de Toulouse, CNRS, IRD, CNES), Toulouse, France, ²Collecte Localisation Satellites (CLS), Ramonville-Saint-Agne, France, ³LERMIT, Université Joseph Ki-Zerbo, Ouagadougou, Burkina Faso, ⁴Université Joseph Ki-Zerbo, UFR-SVT/DST, Ouagadougou, Burkina Faso, ⁵Laboratoire Eaux, Hydro-Systèmes et Agriculture (LEHSA), Institut International d'Ingénierie de l'Eau et de l'Environnement (2iE), Ouagadougou, Burkina Faso, ⁶Université Abdou Moumouni, Faculté des Sciences et Techniques, Département de Géologie, Niamey, Niger, ⁷HydroSciences Montpellier (HSM, University Montpellier, CNRS, IRD), Montpellier, France

**Abstract** In West Africa, lakes and reservoirs play a vital role as they are critical resources for drinking water, livestock, irrigation, and fisheries. Given the scarcity of in-situ data, satellite remote sensing is an important tool for monitoring lake volume changes in this region. Several methods have been developed to do this using water height-area-volume relationships, but few publications have compared their performances over small and medium-sized shallow lakes. In this work we compare four methods based on recent data from high-resolution optical imagery and radar and lidar altimetry over 16 lakes in the Central Sahel, with areas between 0.22 km² and 21 km². All methods show consistent results and are generally in good agreement with in-situ data in terms of accuracy (Root Mean Squared Error below 0.42 m for heights and Normalized Root Mean Squared Error below 13% for volumes). The precision of the estimated water height is about 0.20 m for Pleiades Digital Surface Models (DSMs) and less than 0.13 m for the other methods. Inherent limitations such as DSM quality, temporal coverage of DSM and lidar data, and spatial coverage of radar altimetry data are identified. Overall, fine shape patterns are consistently observed over small height amplitudes, highlighting the ability to monitor shallow lakes with non-linear height-area relationship. Finally, we show that combining lidar and radar altimetry-based methods provides estimates of volume changes over the different water bodies of the study region accurate enough to monitor seasonal, interannual, and long-term variability.

## 1. Introduction

Lakes and reservoirs provide crucial services for humans (Reynaud & Lanzanova, 2017) and ecosystems (Schallenberg et al., 2013) such as freshwater and food supply, electricity generation, nutrients processing, provision of natural habitats and recreational services. The capability of lakes to ensure these services inherently depends on their water storage. The overall number of lakes is dominated by abundant small water bodies and ponds (Biggs et al., 2017) whereas medium-sized and large lakes (size > 1 km²) represent 85% of the global lake area (Pi et al., 2022). Monitoring lake volume change is essential as several recent studies highlighted significant variations over the past decades and different trends under the impact of climate change and human activities (Luo et al., 2022; Wang et al., 2018; Wurtsbaugh et al., 2017; Yao et al., 2023).

The hydrological functioning of water bodies in West Africa is poorly known at the large scale (Papa et al., 2023). Areas such as Central Sahel host a multitude of water bodies, ranging from reservoirs (Cecchi et al., 2009), small lakes and ponds (Gardelle et al., 2010; Grippa et al., 2019) to temporary water bodies (Haas et al., 2009). Being used for drinking water, livestock watering, irrigation and fishing, these water bodies play a vital role in such an area subject to a long dry season (Cecchi et al., 2009; Frenken, 2005). Despite the severe drought that impacted Central Sahel in the 1970 and 1980s, several studies have highlighted a paradoxical increase in the surface area of lakes and ponds (Baba et al., 2019; Gal et al., 2016; Gardelle et al., 2010), as well as an increase in runoff and river discharges (Descroix et al., 2018; Favreau et al., 2009; Mahe et al., 2010). Attempts to study the evolution of water volumes in West Africa have been carried out either at the scale of a few lakes (Fowe et al., 2015; Gal et al., 2016; Pham-Duc et al., 2020), or at a larger scale but at a specific time (Annor et al., 2009; Cecchi et al., 2009; Liebe et al., 2005). In addition, West African lakes and reservoirs have been included in global
**Methodology:** F. Girard, L. Kergoat, M. de Fleury, M. Grippa

**Project administration:** M. Grippa

**Resources:** H. Nikiema, M. Wubda, R. Yonaba, T. Fowé,

A. Abdourhamane Touré, I. Mainassara, M. Grippa

**Software:** F. Girard

**Supervision:** L. Kergoat, M. Grippa

**Validation:** F. Girard, L. Kergoat, M. Grippa

**Visualization:** F. Girard

**Writing – original draft:** F. Girard, L. Kergoat, H. Nikiema, R. Yonaba, T. Fowé, A. Abdourhamane Touré, M. de Fleury, M. Grippa

studies, but these are brief in time (Cooley et al., 2021) or cover only a few large lakes (Luo et al., 2022; Yao et al., 2023). In this regard, efforts remain to be done for both long-term and large-scale monitoring of the lake volume changes in this region.

Historically, in-situ sensors are used to measure the evolution of lake water level and volume. However, the limited spatial coverage and the global decline of in-situ operations and installations (Papa et al., 2023; Riggs et al., 2023; Schwatke et al., 2015) limit the capability to have long and large-scale time series. With periodic observations and a considerably increased spatial coverage, satellites are a relevant tool for assessing lake water volume trends globally (Gao et al., 2012; Luo et al., 2022; Yao et al., 2023).

Remote sensing allows measuring physical parameters of water bodies such as water surface height and area, enabling volume estimation. Water surface height is derived from the return time estimation of electromagnetic waves emitted by nadir-looking radar or laser altimeters. Synthetic Aperture Radar (SAR) altimeters such as those on board Sentinel-3 (S3) and Sentinel-6 are able to measure the height of small water bodies with a sub-monthly revisit time (Normandin et al., 2018; Taburet et al., 2020). However, the nadir-viewing and the inter-track distance of several tens of kilometers of the conventional radar altimeters restrict their spatial coverage. The Ice, Cloud and land Elevation Satellite-2 (ICESat-2) and the Global Dynamics Ecosystem Investigation (GEDI) missions carry on board multi-beams laser altimeters providing surface height products with along-track resolutions from tens of centimeters to tens of meters (Dubayah et al., 2020; Neuenschwander et al., 2023).

The estimation of the water extent from optical or radar imagery is based on the separation of the spectral or backscattering signature of water from that of the soil (Pekel et al., 2016; Yao et al., 2019). With a revisit time of 5 days and a spatial resolution of up to 10 m, the Sentinel-2 optical sensors can be used to monitor water surface area variations of a large number of lakes and reservoirs (Reis et al., 2021; Schwatke et al., 2019; Yang et al., 2017). Cloud cover, which is one of the main obstacles to optical observation of water bodies, is not an issue in West Africa because the dry season lasts long enough (Nicholson, 2018) to capture the entire annual dynamics of the lake water area (de Fleury et al., 2023; Robert et al., 2017).

Water surface height and area can be combined to calculate volume changes between consecutive dates (Crétaux et al., 2016; Gao et al., 2012; Li et al., 2020; Luo et al., 2022; Song et al., 2013; Terekhov et al., 2020). This can be done using simultaneous observations of water surface height and area or using the height-area (H-A) relationship (Abileah et al., 2011), which synthesizes the lake's bathymetry information into a function that describes changes in surface area as a function of water level. Once the height-area relationship has been constructed, volume change can be calculated by integration (Carabajal & Boy, 2021; Duan & Bastiaanssen, 2013; Magome et al., 2003) and using only one of the two variables.

The construction of the height-area relationship requires computing the height and extent of the lake banks contour lines (isobaths). With remote sensing data, isobaths are typically calculated by combining near-simultaneous observations of water surface height and area from radar or lidar altimetry data and imagery respectively (Abileah et al., 2011; Busker et al., 2019; Gao et al., 2012; Schwatke et al., 2020). Estimates of bank topography from global Digital Elevation Models (DEMs) in combination with satellite images (Avisse et al., 2017; Bhagwat et al., 2019; Terekhov et al., 2020; Tseng et al., 2016) or as stand alone (Fang et al., 2019; Pan et al., 2013; Yao et al., 2018; S. Zhang & Gao, 2020) have been also employed to construct height-area relationships. Lidar altimetry profiles of lake banks have been used in some recent studies (Arsen et al., 2013; Bacalhau et al., 2022; Ma et al., 2019; N. Xu et al., 2020). Due to the scarcity of in-situ data to perform validation, lakes in West Africa were seldom analyzed (Table S1 in Supporting Information S1). de Fleury et al. (2023) combined water levels from Sentinel-3 altimetry and water areas from Sentinel-2 imagery to assess the dry-season water height dynamics of 42 lakes in Mali, Niger and Burkina Faso (BF). These lakes were selected among the 150 lakes lying under the Sentinel-3A and -3B ground tracks within the study area, which is far below the several thousands of water bodies found in the region (de Fleury, 2023; Pi et al., 2022).

Despite the abundant literature available on the techniques summarized previously (Table S1 in Supporting Information S1), much fewer studies (Table S2 in Supporting Information S1) compared different satellite based methods for deriving lake height-area relationships and volume changes. Among these, only the study of Magome et al. (2003) was focused on West Africa. Volume changes of Lake Volta in Ghana were estimated by comparing different methods using altimetry (TOPEX/Poseidon) and optical imagery (Moderate-Resolution Imaging Spectroradiometer, MODIS) or their combination with a DEM. The authors reported better results when
<figure><img src="image_3.png" /><figcaption>Figure 1. Study area and lakes analyzed in this study.</figcaption></figure>

combining altimetry and DEM and highlighted the greater spatial coverage of the method using the combination of imagery and DEM.

In addition, to our knowledge, intercomparison of different methods has focused on lakes bigger than 10 km² and has thus not addressed small lakes. For a complete assessment of surface water resources in West Africa, all types of lakes and reservoirs should be accounted for, including small and shallow lakes, ephemeral lakes and lakes covered by aquatic vegetation which are the most commonly found in this area (de Fleury, 2023) and more generally in many semi-arid areas worldwide.

Therefore, the following questions remain to be answered: what are the capabilities of current sensors for estimating the height-area relationship of lakes in West Africa, including small lakes, ephemeral lakes, shallow lakes and lakes covered by aquatic vegetation? Which data and methods are most suited for this purpose and what are their pros and cons? What is the impact on the accuracy of volume variation estimates? Do open data provide accurate enough solutions? This work addresses the above questions by analyzing four different methods based on recent data (Pleiades, Sentinel-2, Sentinel-3, ICESat-2, GEDI) over 16 small (<1 km²) and medium-sized (1–100 km²) lakes located in Central Sahel. The results of each method are evaluated using in-situ data, available for 8 lakes, and criteria of accuracy, precision, sensitivity to land and water surface characteristics and spatio-temporal coverage.

## 2. Material and Methods

### 2.1. Study Area and In-Situ Data

The study area (Figure 1 and Supporting Information S1) is located in Central Sahel, between the 10.8°N and 15.5°N latitudes, and extends over Mali, Niger, and Burkina Faso. From North to South, the climate is semi-arid and dry sub-humid. Rainfall is driven by a tropical monsoon system and follows a latitudinal gradient with mean annual precipitation ranging from 290 mm yr⁻¹ to 1,015 mm yr⁻¹ (Funk et al., 2015). Rainfall is concentrated during the wet season stretching from June to October. The rest of the year consists of a long dry season with very
<table><caption>**Table 1**
Information and Data Availability on the Studied Lakes</caption><thead><tr><th>Lake</th><th>Country</th><th>Coord. (WGS84)</th><th>Lake area (km²)</th><th>MNDWI thresh.</th><th>References</th><th>In-situ data</th><th>Pleiades</th><th>ICESat-2</th><th>GEDI</th><th>Sentinel-3</th></tr></thead><tbody><tr><td>Agoufou</td><td>Mali</td><td>15.37°N, -1.47°E</td><td>1.98</td><td>0.09</td><td>Grippa et al. (2019), Gal et al. (2016), Gardelle et al. (2010)</td><td>water level (2015–2019)</td><td>X</td><td>X</td><td>X</td><td></td></tr><tr><td>Arzuma</td><td>BF</td><td>12.22°N, -1.31°E</td><td>1.78</td><td>-0.04</td><td>de Fleury et al. (2023)</td><td>water level (2023-)</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Babou</td><td>BF</td><td>12.88°N, -1.61°E</td><td>0.60</td><td>-0.10</td><td>de Fleury et al. (2023)</td><td></td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Bam</td><td>BF</td><td>13.38°N, -1.53°E</td><td>19.30</td><td>0.03</td><td>de Fleury et al. (2023)</td><td>H-V curve (DGRE)</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Bangou Kirey</td><td>Niger</td><td>13.50°N, 2.23°E</td><td>0.22</td><td>0.09</td><td>Touré et al. (2016)</td><td>water level (2022-)</td><td>X</td><td>X</td><td>X</td><td></td></tr><tr><td>Bangui Mallam</td><td>Mali</td><td>15.41°N, -1.36°E</td><td>3.34</td><td>0.10</td><td>Gardelle et al. (2010)</td><td></td><td>X</td><td>X</td><td>X</td><td></td></tr><tr><td>Djigo</td><td>BF</td><td>14.08°N, -0.22°E</td><td>2.50</td><td>-0.17</td><td></td><td></td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Inbanta</td><td>Mali</td><td>15.47°N, -1.96°E</td><td>2.93</td><td>-0.11</td><td></td><td></td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Kokorou</td><td>Niger</td><td>14.20°N, 0.90°E</td><td>21.33</td><td>-0.16</td><td>Baba et al. (2019)</td><td>H-A curve Baba et al. (2019)</td><td>X</td><td>X</td><td>X</td><td></td></tr><tr><td>Manga</td><td>BF</td><td>11.66°N, -1.05°E</td><td>0.71</td><td>0.10</td><td>de Fleury et al. (2023)</td><td></td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>North Tanvi</td><td>BF</td><td>12.22°N, -1.30°E</td><td>0.17</td><td>0.00</td><td>de Fleury et al. (2023)</td><td></td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Seguenega</td><td>BF</td><td>13.44°N, -1.95°E</td><td>1.40</td><td>-0.10</td><td>de Fleury et al. (2023)</td><td>H-V curve (DGRE)</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Seytenga</td><td>BF</td><td>13.96°N, 0.29°E</td><td>3.23</td><td>0.15</td><td>de Fleury et al. (2023)</td><td>H-V curve (DGRE)</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>South Tanvi</td><td>BF</td><td>12.20°N, -1.30°E</td><td>0.24</td><td>0.10</td><td>de Fleury et al. (2023)</td><td></td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Tibin</td><td>BF</td><td>13.18°N, -1.45°E</td><td>15.39</td><td>0.10</td><td>de Fleury et al. (2023)</td><td></td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Toussiana</td><td>BF</td><td>10.88°N, -4.61°E</td><td>1.34</td><td>0.00</td><td>de Fleury et al. (2023)</td><td>H-A-V curve Sanogo and Dezetter (1997)</td><td>X</td><td>X</td><td>X</td><td>X</td></tr></tbody></table>

little cloud cover, which is suited for observing water bodies using optical imagery (Figure S2 in Supporting Information S1).

Sixteen lakes have been selected (Figure 1 and Table 1). Among these, eight have been primarily chosen given the availability of in-situ data (Agoufou, Arzuma, Bam, Bangou Kirey, Kokorou, Seguenega, Seytenga and Toussiana). Eight additional lakes, of which seven covered by Sentinel-3 orbits (Babou, Djigo, Inbanta, Manga, North Tanvi, South Tanvi and Tibin) and 1 with existing documentation (Bangui Mallam, (Gardelle et al., 2010)), have been added to the analysis. Another reason that motivated the selection of these 16 lakes was the successful acquisition of clear sky Pleiades images at the end of the dry season, when water areas are at their minimum, allowing therefore maximum coverage of the lake banks. The selected lakes are spread along the climatic gradient and include three lakes in Mali, two in Niger, and 11 in Burkina Faso. Ten are reservoirs and six are natural lakes. Their mean altitude is between 200 and 500 m above mean sea level, their mean water surface area ranges from 0.22 km² (Bangou Kirey) to 21 km² (Kokorou), and most of them are relatively shallow (a few meters deep). Finally, these lakes show different optical water types (Figure S2 in Supporting Information S1). They present varied levels of turbidity (Cecchi et al., 2009), including extremely turbid lakes (e.g., Bangou Kirey, Touré et al., 2016)), some of them harbor temporary or permanent aquatic vegetation (e.g., Kokorou, (Baba et al., 2019), Babou and Seguenega, Figure S2 in Supporting Information S1) or are covered by trees (Inbanta). Last, some of these lakes are ephemeral as they dry out during the dry season (Inbanta, North Tanvi, South Tanvi).

In-situ data are of different nature and come from different sources. Water surface height data are measured continuously, every 30 min with an accuracy of 0.5 cm, through pressure transducers on the Bangou Kirey lake and the Arzuma reservoir, respectively since July 2022 and March 2023. Additional water surface height measurements based on limnimetric scales have been collected on the Agoufou lake by the Analyze Multidisciplinaire de la Mousson Africaine - Couplage de l'Atmosphere Tropicale et du Cycle Hydrologique (AMMA-CATCH) observatory (Galle et al., 2018) between 2015 and 2019 with a weekly or monthly frequency and an accuracy of 0.5 cm. Height-volume (H-V) relationships of the Burkinabe reservoirs of Bam, Seguenega and Seytenga have
been provided by the Direction Générale des Ressources en Eau (DGRE) in Burkina Faso and come from direct leveling topographic surveys performed before the dams impoundment. The height-area relationship of the Kokorou lake is extracted from Baba et al. (2019) and derived from limnimetry, topographic map digitization. GPS field survey and Landsat-based water contouring. Finally, the height-area-volume (H-A-V) relationship of the Toussiana reservoir is derived from Sanogo and Dezetter (1997).

## 2.2. Satellite Data, Water Surface Area and Height Extraction

### 2.2.1. Water Surface Areas and Contours From Sentinel-2 Optical Images

Sentinel-2A and -2B acquire high-resolution multispectral images with a revisit time of approximately 5 days (Table 2). The MultiSpectral Instrument (MSI) onboard Sentinel-2 has 13 spectral bands from blue to Short-Wave InfraRed (SWIR), with spatial resolution from 10 to 60 m on the ground. For this study, we use the green and SWIR bands which have resolutions of 10 and 20 m. Images are Level-2A Surface Reflectance (SR) products corrected from atmospheric effects with Sen2Cor processing (Main-Knorn et al., 2017). Images are downloaded through Google Earth Engine (GEE, (Gorelick et al., 2017)) as the “COPERNICUS/S2_SR” collection, over December 2018 to December 2022. The 10 m spatial resolution bands are downscaled (nearest neighbor) to match the 20 m resolution of the SWIR bands. Images with a percentage of cloudy pixels greater than 5% are directly discarded. The residual cloudy pixels are masked using the data product's cloud and cirrus bitmasks. Following de Fleury et al. (2023), an additional threshold of 0.2 on the blue reflectance is applied. This allows removing residual clouds not detected by the cloud mask, high aerosols load situations and, particularly, sunglint effects, mostly happening for lakes situated on the east side of the Sentinel-2 orbits, that may affect water detection based on the Modified Normalized Difference Water Index (MNDWI). After these steps, a few remaining images (usually less than 5 per lake) contaminated by clouds or aerosols have been discarded by visual inspection.

To compute water surface area, we mask water pixels by applying a threshold on the MNDWI (H. Xu, 2006), which is a spectral index commonly used to detect water on optical images (Peña-Luque et al., 2021; Reis et al., 2021; Schwatke et al., 2019), based on the normalized difference between the green (B3) and the short-wave infrared (B12) bands.

$$MNDWI = \frac{\text{green} - \text{SWIR}}{\text{green} + \text{SWIR}}$$

First, we clip the images to the close surroundings of the water body to exclude close but unconnected water bodies. Then, the MNDWI is computed and the threshold, constant in time, is determined ad hoc for each lake following de Fleury et al. (2023) and Reis et al. (2021) (Table 1). Reis et al. (2021) have shown that water detection is usually accurate for a full range of MNDWI thresholds rather than a well-defined value. The water surface area is finally calculated by counting the number of pixels above the threshold and multiplying by the pixel area. The water contour is delineated using the marching squares algorithm, a 2D adaptation of the marching cubes algorithm (Lorensen & Cline, 1987) which is implemented in the “find contours” function from the Scikit-image Python package. This function takes as input the MNDWI pixels raster and the threshold value and generates iso-value contours at a sub-pixel scale by linearly interpolating the MNDWI pixel values (Figure S3 in Supporting Information S1). If the lake separates into several parts as it dries up, we keep only the largest part. For each lake, a time series of water surface areas (Figure S2 in Supporting Information S1) and water contours is generated. Despite the strict selection applied to remove clouds, aerosols and sunglint conditions, the time series obtained are dense enough to explore the full range of water area dynamics.

### 2.2.2. Pleiades Digital Surface Model

Pleiades-1A and -1B Pleiades are two satellites equipped with high-resolution optical sensors acquiring panchromatic images (480–830 nm) with a pixel size of 0.50 m (Table 2 and Figure 3). We ordered the acquisition of pairs of cloud-free Pleiades panchromatic stereo-images (Pleiades © CNES 2021, 2022, 2023, Distribution Airbus DS) over each lake, with a base-to-height ratio between 0.35 and 0.8. Pleiades images allow the creation of Digital Surface Models (DSMs) by photogrammetric processing through the computation of matching pixels displacement between two stereo-images. DSMs were processed using the DSM from OPTical stereoscopic very-
<table><caption>**Table 2**
Remote Sensing Data and Corresponding Missions Used in This Study</caption><thead><tr><th>Mission</th><th>S2</th><th>S3</th><th>ICESat-2</th><th>ICESat-2</th><th>GEDI</th><th>Pleiades</th></tr></thead><tbody><tr><td>Full name</td><td>Sentinel-2</td><td>Sentinel-3</td><td>Ice, Cloud and Land Elevation Satellite-2</td><td>Global Ecosystem Dynamics Investigation</td><td>Dec 2018</td><td>Pleiades<br>Dec 2011 (1A), Dec 2012 (1B)</td></tr><tr><td>Launch date</td><td>Jun 2015 (2A), Mar 2017 (2B)</td><td>Feb 2016 (3A), Apr 2018 (3B)</td><td>Sep 2018</td><td>L2A v2</td><td>2D surface elevation</td><td>panchromatic stereo</td></tr><tr><td>Product</td><td>L2A surface reflectance</td><td>L2 OCOG</td><td>ATL08 v6</td><td>terrain height profile</td><td>Variable</td><td>1 m × 1 m</td></tr><tr><td>Parameter</td><td>water surface area</td><td>water surface height</td><td>terrain height profile</td><td>Variable</td><td>60 m (along-track)</td><td></td></tr><tr><td>Revisit time</td><td>5 days</td><td>27 days</td><td>91 days (after Sept. 2020)</td><td></td><td></td><td></td></tr><tr><td>Posting rate</td><td>20 m × 20 m</td><td>300 m (along-track)</td><td>100 m (along-track)</td><td></td><td></td><td></td></tr></tbody></table>

high resolution imagery (DSM-OPT) online service, based on the MicMac tool (Rupnik et al., 2017) and operated by the Solid Earth ForM@Ter pole of the research infrastructure DATA TERRA. DSM-OPT also provides an ortho-image which is a panchromatic image georeferenced identically to the DSM.

We ordered Pleiades images at the end of the dry season, when water level is minimum, which allows exploring the maximum lake bank extent. We generated DSMs at 1 m × 1 m horizontal resolution, in line with Bagnardi et al. (2016). As the semi-arid landscapes of the study area often show small surface roughness (compared to mountainous or forest landscapes for instance), we adapted the correlation window size to 9 × 9 pixels and we used 0.2 as the minimum correlation coefficient for matching (Bagnardi et al., 2016). Due to the large extent of the Bam reservoir, two stereo-pairs acquisitions are needed to observe the northern and southern part of the reservoir. To end up with a single DSM, we generated a DSM for each part and we merged them after applying the Nuth and Kääb method (2011) to ensure co-registration. However, a residual elevation bias between the two parts has been observed after co-registration. We corrected it by comparing the DSM of each part with terrain ICESat-2 data and subtracting the respective mean difference.

Some Pleiades DSMs showed along-track undulations which were highlighted when computing the difference with the global 30 m (GLO-30) Copernicus DEM (European Space Agency, 2021). For instance, we observed along-track undulations of several meters in Pleiades-1B-derived DSM of the Bangou Kirey and Kokorou lakes. These undulations have been noticed on many DEMs from several space-borne missions (Hugonnet et al., 2022) and are caused by errors in the image geometry estimation due to sensor motion (jitter). Our method to correct these undulations is partly based on Girod et al. (2017). We compute the average per line of the DEM difference with GLO-30 (Figure 2) and subtract it to the Pleiades DSM (Figure S4 in Supporting Information S1).

### 2.2.3. Bank Height Profile From ICESat-2 Lidar Altimeter Data

ICESat-2 was launched in September 2018 (Table 2 and Figure 3) by NASA (Markus et al., 2017). The Advanced Topographic Laser Altimeter System onboard ICESat-2 is a photon-counting lidar with 3 pairs of laser beams emitting pulses at 10 kHz and separated by 3.3 km in the cross-track direction. The footprint size of each beam has a 14 m diameter. Each pair is composed of a strong beam and a weak beam (energy ratio of 4:1) with a wavelength of 532 nm and located 90 m from each other.

The ATL08 version 6 product is dedicated to land and vegetation and contains along-track heights above the WGS84 ellipsoid for the ground and canopy surfaces (Neuenschwander et al., 2023). We downloaded all ATL08 data over the October 2018 (first data available) - June 2023 period. The nominal posting rate is theoretically 100 m but data gaps can occur due to low signal-to-noise ratio or acquisition errors. For the midpoint of each 100 m segment, ATL08 provides three height metrics, respectively the mean, the median and the best-fit terrain height. Since the topography of the banks is likely to vary within 100 m, and as suggested by Tian and Shan (2021), we use the best-fit height in this study. Furthermore, we decided not to filter ATL08 data on the beam energy and acquisition time criteria (see Text S1 in Supporting Information S1).

The number of terrain photons detected within a segment is important to fit the 100 m height profile and derive a robust estimation of the segment height. Hence, we set a threshold of 10 on the minimum detected number of terrain photons, in line with the results of Urbazaev et al. (2022). To remove large outliers, we keep data with a photon heights STD inferior to 1 m and discard data whose best fit height is inferior to the minimum detected photon height, this being probably due to a fitting error (Figure S5 in Supporting Information S1). Finally, given that ICESat-2 beams were purposely mispointing during the first height cycles of the mission (Markus et al., 2017), that is during the two first years (nominal cycle of 91 days), certain lakes have irregular or limited temporal coverage.

### 2.2.4. Bank Height Profile From GEDI Lidar Altimeter Data

The GEDI mission on board the International Space Station started in December 2018 (Dubayah et al., 2020). It consists of a full-waveform lidar with 3 lasers producing a total of 8 beam ground transects spaced 600 m apart in the cross-track direction. Each ground transect has a footprint size of 30 m and samples the Earth's surface approximately every 60 m along-track (Table 2 and Figure 3). GEDI L2A
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Difference between Pleiades Digital Surface Model and GLO-30 Digital Elevation Model over Kokorou lake. X and y coordinates reference system is EPSG:32631.</figcaption></figure>

version 2 data product, distributed by NASA's Land Processes Distributed Active Archive Center (LP DAAC), provides terrain height, canopy top height and relative height metrics. The terrain height is represented by the lowest mode elevation which gives the height of the last significant energy return detected in the waveform.

We removed large outliers by rejecting data whose height absolute difference with the Shuttle Radar Topography Mission (SRTM) DEM value (parameter included in the product) at GEDI footprint location was greater than 100 m (Fayad et al., 2020). Using the dedicated flag, we also discarded data acquired during a degraded period of the instrument or platform. As for ICESat-2 ATL08 data and following the suggestions of Liu et al. (2021) who assessed GEDI L2A terrain height data accuracy as well, we considered unnecessary to discard GEDI data on the basis of beam energy and acquisition time.

### 2.2.5. Water Surface Heights From Sentinel-3 Radar Altimetry Data

The Sentinel-3 mission includes the Sentinel-3A and 3B satellites carrying on board the Synthetic Aperture Radar Altimeter (SRAL), a delay/Doppler altimeter (Table 2 and Figure 3). The altimeter operates in global mode with an along-track posting rate of approximately 300 m and an across-track resolution of several kilometers. Water surface height measurements of the same target are provided every 27 days. Water surface height data have been retrieved from the radar waveforms recorded by Sentinel-3 with the Offset Center of Gravity retracking algorithm and have been provided by the Center de Topographie des Océans et de l'Hydrosphère (CTOH). They have been processed using the Altimetric Time Series Software (AlTiS version 2.0, (Frappart et al., 2021)). The data were first selected within a polygon fitted to the lake maximum water extent derived from the corresponding water contour time series. Then, they were filtered with a threshold of 40 dB on the backscattering coefficient for data acquired before January 2020, and a threshold of 20 dB for data acquired after January 2020 (de Fleury et al., 2023). These thresholds are in line with what is suggested by Taburet et al. (2020) and Kittel et al. (2021). Besides, multi-peak waveforms or dry-lake data were rejected with an empirical threshold of 20 (unitless) on the waveform peakiness. The resulting water surface height is computed as the median of the remaining height values. Water surface heights with a Median Absolute Deviation (MAD) along the transect greater than 1 m are rejected.

## 2.3. Methods to Derive Height-Area Relationships

### 2.3.1. DEM Cut-And-Fill

The H-A relationship is processed using a standard DEM cut-and-fill method with an elevation increment of 0.1 m. Since the processing stops at an altitude defined manually, it is possible that, at a certain point, the
<figure><img src="image_5.png" /><figcaption>Figure 3. Data available over the Arzuma reservoir.</figcaption></figure>

computed water areas exceed the physical reality of the lake dynamics over the study period. The upper limit of the H-A relationship is therefore set to the maximum Sentinel-2-observed water area. For the following, this method will be referred to as the “DSM Pleiades” and is graphically represented in Figure 4a.

A Pleiades DSM footprint is at least 100 km². We first limit the processed area to the region of interest by clipping the DSM to a polygon representing the close surroundings of the water body. Water surfaces generate “No Data” values or extreme outliers on the DSM due to low pixel correlations during the stereo-matching processing, and have to be filtered out. Hence, we mask water pixels on the Pleiades orthoimage. Since orthoimage reflectance values generally follow a bi-modal distribution, we separate water from soil by defining a global threshold on the reflectance pixels. Finally, we mitigate the remaining minimal classification errors by filling the holes with a morphological closure using a square structuring element of size 9 × 9.

Once water has been masked, we determine the altitude of the water surface as the median elevation of the water pixels located along the contour. This contour is computed as the external morphological gradient using a cross structuring element of size 1. In addition, contamination by outliers is mitigated using the MAD method (Kannan et al., 2015).

### 2.3.2. Intersecting a DEM With Water Contours

This method is similar to what Mason et al. (1995) mentions as the “waterline method,” and multiple studies such as Ragettli et al. (2021) already employed it to retrieve lake bathymetry. Assuming the water surface is flat, isobaths can be computed as the intersection of water contours with a DEM. The water contour elevation is computed as the median value of the intersected DEM pixels elevations, consecutively to an outliers removal process based on the MAD method. Finally, the lower limit of the H-A relationship is set to the minimum Pleiades-observed water area. For the application of this method on Pleiades DSMs, we will use the term “DSM Pleiades/contours” (Figure 4b).

Since the Pleiades DSM are surface models, they provide elevation of the highest observed point on the ground. Thus, they are impacted by relief like buildings and, particularly for the studied lakes, trees and riparian vegetation. This is the case for the right bank of the Bangou Kirey lake which is covered by trees and was masked out using manually defined polygons derived from high resolution digital globe images. The Inbanta lake is also densely covered by trees and if all of them were masked the remaining area would be too small to compute the H-A curve. Therefore, for this lake we do not mask out any area. The resulting impact of vegetation will be discussed later.
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Schematic representation of the four methods used in this study to derive the height-area relationships.</figcaption></figure>

### 2.3.3. Intersecting Bank Height Profile With Water Contours

Instead of using a whole DEM providing continuous information of the ground elevation, this method requires one or multiple discrete terrain height profiles of the banks of the water body. Here, we use height profiles either from ICESat-2 or GEDI lidar topography measurements. This method will be referred to as the “Profile ICESat-2/contours” or “Profile GEDI/contours” method (Figure 4c). As with the DSM-based methods, the water level at the dates the height profiles were recorded determines the extent of the bank bathymetry that can be characterized. Isobaths are retrieved by calculating the intersections between the water contours and the banks height profile. For this purpose, the profiles are converted to geometric lines and we compute the crossover points with the water contour polygons. The crossover points height is linearly interpolated between the two measurement points. It is necessary to check that the pair of measurement points was acquired over the ground and not over water, and that they are located on the same bank, otherwise the resulting interpolated height will be erroneous. To do this, we mask out the measurement points acquired over water using the closest Sentinel-2 image in time.

We set a maximum threshold of 2% on the bank slope to reject crossover points located at places too steep with respect to lidar data posting rate. Slopes measured by ICESat-2 over the study lakes vary between 0% and 5% with most values lower than 3%. The 2% maximum threshold rejects no more than 6% of the total number of crossover points. Then, because it is more robust than the mean, the median value of the crossover points heights is retained for the water contour height, following Arsen et al. (2013). Finally, we filter out water contours whose height is computed from only one crossover point, as it may reflect erroneous intersections due to small water contour detection errors and affect the quality of the H-A relationship. This filter is effective for some of the lakes with an area below 2 km² such as Babou, Bangou-Kirey, Manga, North Tanvi and South Tanvi (Figure S6 in Supporting Information S1). For bigger lakes, given the multiplicity of the laser beams, we have more than two crossover points per contour.

We observe inconsistencies (tens of centimeters to tens of meters) between GEDI data from different dates of acquisition. For simplicity, we only select for each lake the acquisition date giving the most complete H-A curve.

### 2.3.4. Matching Water Surface Height With Water Surface Area Measurements

This method uses water surface height data and combines them with synchronous water surface area observations. To construct the height-area relationship, we search for the Sentinel-2 images co-dated with the Sentinel-3 data and match the height and area measurements with a temporal tolerance of 3 days. A tolerance of 3 days is appropriate given the temporal variability of the lakes studied (de Fleury et al., 2023), and provides a good trade-off with respect to data availability (Figure S2 in Supporting Information S1). If the time difference between Sentinel-2 and Sentinel-3 acquisitions is not zero, we linearly interpolate successive water area data to the water surface height date. This method will be referred to as the “Height S3/area” method (Figure 4d). All of the methods and data described above are schematized in Figure S7 in Supporting Information S1.
### 2.3.5. Combining the Height-Area Relationships Based on Open Source Data

Of the four different methods described above, the DSM Pleiades method is based on commercial data (Section 2.3.1), the DSM Pleiades/contours method uses both commercial (Pleiades) and open source (Sentinel-2, Section 2.3.2) data, and the other two methods, namely Profile/contours and Height S3/area, are based entirely on open source data (ICESat-2, GEDI, Sentinel-3, Sections 2.3.3 and 2.3.4). In this work, in addition to the performance of the individual methods, we also assess the capabilities of the combination of open source data based methods. For each lake, we fit the H-A relationship of the three methods combined with the best polynomial function of degree lower or equal to 2. Then, we discard the data outside the fit 95% confidence interval in order to remove the outliers. For the following, this method will be referred to as the “Combined open source” method.

## 2.4. In-Situ Data-Based Height-Area Relationships and Height Bias Removal

### 2.4.1. Processing the Height-Area Relationships of In-Situ Data

For three reservoirs (Bam, Seytenga and Seguenega), in-situ data provided as H-V relationships have been converted to H-A relationships, computing the areas as the derivative of the volume with respect to the height A = dV/dH (Gao et al., 2012). For three lakes (Agoufou, Arzuma and Bangou Kirey), water surface height in-situ measurements are combined with Sentinel-2 water surface areas acquired on the same day. For Agoufou, since height data are acquired at a weekly frequency, Sentinel-2 areas are interpolated between two consecutive dates to match the in-situ data.

### 2.4.2. Resolving the Bias Between Height Data

As we do not have absolute height data for all methods, the comparison of the height-area relationships requires prior height bias removal. Indeed, the in-situ data and part of the Pleiades DSMs are not absolutely leveled, GEDI data showed acquisition time-dependent biases and the other remote sensing data have different references. The height biases are removed on the height-area curves as follows. The DSM Pleiades/contours height-area method is taken as reference because it provides long and regular data sets, and the bias with the other methods is computed as the mean of the height differences:

$$bias = mean(h_{method} - h_{Pleiades})$$

The unbiased height is referred to as Height$_{Ub}$ hereafter.

## 2.5. Processing the Volume-Area Relationships

For each height-area data set associated with a specific lake and method, water volume changes are computed as the integral of the corresponding height-area function between two consecutive heights (Abileah et al., 2011; Yao et al., 2023). To do this, the H-A relationship is fitted and then integrated over H. A polynomial function (maximum degree of 5) is used for the fit and the Akaike Information Criterion (Akaike, 1973) is used to select the best fit and avoid overfitting. The volume-area relationship is finally given by cumulating volume changes. Since the height of the lake bottom is not always known, the reference is set to the “in-situ” data and all other methods are truncated to the minimum in-situ volume. Volumes from the different methods are then computed as relative volumes given by $V_{method} - V_{0,insitu}$. Moreover, since the different data sets do not start at the same water area, a dataset-specific volume offset called $V_{0,method}$ has to be resolved. The offset is computed as the mean difference with the in-situ data set.

## 2.6. Methodology for the Performance Assessment of the Different Methods

Different metrics are used to assess the dispersion, precision and accuracy of each method: the MAD, the coefficient of determination (R²), the fit Root Mean Squared Difference (RMSD), the fit Normalized Root Mean Squared Difference (NRMSD), the Root Mean Squared Error (RMSE) and the Normalized Root Mean Squared Error (NRMSE) (see Table S3 in Supporting Information S1 for their definition).
### 2.6.1. Evaluation of Height-Area Curve Dispersion

We provide information on the H-A curves dispersion using the $R^2$, height RMSD and height Normalized RMSD (NRMSD) of the A-H polynomial fits. The NRMSD is the RMSD divided by the amplitude of the height observations ($y_{max} - y_{min}$).

### 2.6.2. Evaluation of Water Height Precision

To assess the precision of the water heights retrieved by the different sources of height data, that is, how flat these height data sources observe the water surface, we use the MAD because it is more robust to outliers than the standard deviation. The MAD is computed along the water transect for Sentinel-3 data and along the water contours estimated by Sentinel-2 for methods using Pleiades, ICESat-2 and GEDI data. For the last three methods, the dispersion estimate also includes water contour detection uncertainty and therefore does not allow a strict assessment of the precision of the water level data alone.

### 2.6.3. Evaluation of Height and Volume Accuracy

For the accuracy assessment of the heights and volumes, the $R^2$, RMSE and Normalized RMSE (NRMSE) are used. Since lakes can have very different volumes, NRMSE provides a more comprehensive information compared to RMSE. In-situ H-A and A-V curves are interpolated to obtain height and volume matchups with data from the other methods.

## 3. Results

### 3.1. Height-Area Relationships

The height amplitude observed by the remote sensing-based methods is ranging from 1.5 m (Agoufou, Bangui Mallam, Inbanta, Manga) to 4 m (Arzuma, Toussiana), with most amplitudes below 3 m (Figure 5). Fine shape patterns such as slope changes are well retrieved using the different methods and are in good agreement with in-situ data (e.g., Arzuma, Djigo, Kokorou, Tibin).

The methods relying on bank height data (Pleiades, ICESat-2 and GEDI) are dependent on the acquisition dates which limit the observable extent of the H-A curves. In the case of ICESat-2 data, the low number of data over the small lakes (Bangou Kirey, Manga, North Tanvi, South Tanvi) is also due to the fact that the laser beams only overpassed the lakes during the planned first 2 years of lidar mispointing. For Bangou Kirey, Pleiades, ICESat-2 and GEDI sensors overpassed the lake at a relatively high water level, not allowing exploring the full H-A curve. Conversely, simultaneous observations of in-situ water level and Sentinel-2-derived area are not available for the highest water levels, which occur for only a few days during the rainy season when cloud cover is a problem for optical imagery. Therefore, it remains difficult to compare in-situ and satellite estimates for this lake.

Complete drying of some lakes during the dry season increases the H-A curves extent but also introduces errors in the Pleiades DSM. Indeed the H-A relationships derived by the DSM Pleiades method show hockey cross patterns for Inbanta and North Tanvi. For these lakes which dried up, the water contour could not be used to estimate the starting altitude as described in Section 2.3.1, which has been set to 310 m for Inbanta and 296 m for North Tanvi. The presence of high noise in the DSM challenged other solutions to derive the starting altitude, such as for example, using the minimum DSM elevation within the lake polygon. The location of the noisy DSM pixels is confirmed by areas of low pixel correlations corresponding to smooth surfaces such as, for instance, the lake bottom for North Tanvi (Figure 6). The noise leads to troughs several meters deep which force the starting altitude (lake bottom) to be underestimated. These pixels are filled progressively with small changes in lake area, which explains the observed hockey cross pattern. As soon as the lake is not completely dry, the average elevation computed over the smallest water area smoothes the noise and gives a correct minimum water elevation. For Inbanta, we also note a difference between the DSM Pleiades and the DSM Pleiades/contours curves reflected by overestimated water areas within the two first thirds of the DSM Pleiades curve. This difference is also attributed to the DSM noise (Figure S8 in Supporting Information S1), the resulting troughs causing a substantial quantity of pixels to be prematurely filled.
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Height-area relationships derived from all the methods (a) over the lakes with in-situ data and (b) over the other lakes.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Data available over North Tanvi reservoir. We show a zoom on Pleiades Digital Surface Model (DSM) pixels over the bottom of the reservoir. The amplitude of the DSM noise exceeds 1.5 m in some places.</figcaption></figure>

## 3.2. Volume-Area Relationships

The V-A curves also denote a generally good agreement between the different methods (Figure 7). Some small slope differences observed on the H-A curves comparison are more evident on the volume-area curves (e.g., DSM Pleiades over Kokorou lake), which is partly due to error propagation in the calculations. The largest differences with respect to in-situ data are observed over Bam and Seytenga reservoirs, where all remote sensing methods agree well with each other and differ from in-situ data. Part of these discrepancies may be due to bank erosion and sedimentation (Cecchi et al., 2020), with sediment transfer from the lake edge mainly due to land use (Tully et al., 2015) and wave-induced bank erosion (Hilton, 1985). For example, Boena and Dapola (2001) documented the Bam reservoir silting and showed that the sediment deposits in the lake could be of substantial thickness.

## 3.3. Dispersion of the Area-Height Relationships

All methods provided good fit results with almost all R² above 0.80 and most values above 0.90 (Table 3). The DSM Pleiades method outperforms all the other methods with all RMSD values below 0.03 m, except for two lakes (Inbanta and North Tanvi) where RMSD equals 0.21 and 0.15 m, respectively. The DSM Pleiades/contours, Profile ICESat-2/and Profile GEDI/contours methods show good and consistent results with all RMSD values below 0.14 m, most being below 0.10 m. The Height S3/area method tends to produce curves with dispersion values almost systematically greater than those from other methods. RMSD is between 0.09 and 0.34 m, with 4 lakes having RMSD above 0.20 m. A small part of this dispersion is inherently related to the time interpolation required to match water surface height and area measurements.
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Volume-area relationships derived from the different methods over the lakes with in-situ data.</figcaption></figure>

3.4. Precision of Water Height

The median MAD obtained using the different sources of height data (Figure 8) are respectively between 0.11 and 0.70 m with most values below 0.20 m for Pleiades, between 0.04 and 0.19 m with most values below 0.13 m for ICESat-2, between 0.04 and 0.23 m with most values below 0.13 m for GEDI, and between 0.01 and 0.12 m with most values below 0.06 m for Sentinel-3. Therefore, all sources of height data provide good results.

The number of points per contour/transect used to compute the precision varies with the methods and highly depends on lake size and, especially for Sentinel-3, and on the satellite's track attack angle with respect to the lake banks. The median number of points per contour ranges from 675 (Babou) to 4260 (Tibin) for Pleiades DSMs, from 2 (North Tanvi) to 50 (Bam) for ICESat-2, from 2 (Bangou Kirey) to 20 (Tibin) for GEDI (mainly because we selected only one acquisition date) and from 1 (Toussiana) to 12 (Bam) per transect for Sentinel-3.

The relatively low precision of Pleiades DSMs (>0.40 m) over certain lakes can be explained either by high amplitudes of noise due to very smooth areas or by flooded vegetation and trees. It is not surprising that the precision of Pleiades is poorer than other data sources, as we have chosen to generate the DSMs at a spatial resolution of 1 m × 1 m, which introduces more pixel-to-pixel noise than a coarser resolution. The average precision of 0.04 m for Sentinel-3 must be taken carefully because for half of the lakes, the transects are made of a median number of three points or less. Except for these cases, all sources of data show a good precision stability with Inter-Quartile Ranges <0.20 m.
<table><caption>**Table 3**
Polynomial Fit Statistics of the Area-Height Relationships</caption><thead><tr><th rowspan="2"></th><th rowspan="2">DSM pleiades</th><th rowspan="2">DSM pleiades/contours</th><th rowspan="2">Profile ICESat-2/contours</th><th rowspan="2">Profile GEDI/contours</th><th rowspan="2">Height S3/area</th></tr><tr><th colspan="4">Polynomial degree/R<sup>2</sup>/RMSD (m)/NRMSD (%)</th></tr></thead><tbody><tr><td>Agoufou</td><td>5/&gt;0.99/&lt;0.01/0.04</td><td>5/0.99/0.02/1.32</td><td>4/0.99/0.04/2.1</td><td>5/0.98/0.02/0.92</td><td></td></tr><tr><td>Arzuma</td><td>5/&gt;0.99/0.01/0.23</td><td>3/0.99/0.08/2.04</td><td>5/0.8/0.09/2.26</td><td>4/0.96/0.12/3.17</td><td>1/0.81/0.34/8.59</td></tr><tr><td>Babou</td><td>5/&gt;0.99/0.01/0.62</td><td>5/&gt;0.99/0.03/1.36</td><td>5/0.98/0.05/2.23</td><td>5/0.98/0.05/2.21</td><td>4/0.96/0.12/5.58</td></tr><tr><td>Bam</td><td>5/&gt;0.99/0.03/0.82</td><td>5/0.95/0.12/3.82</td><td>5/0.97/0.09/2.93</td><td>4/0.93/0.1/3.14</td><td>2/0.98/0.1/3.23</td></tr><tr><td>Bangou Kirey</td><td>5/&gt;0.99/&lt;0.01/0.09</td><td>2/0.9/0.09/5.25</td><td>1/0.31/0.08/4.61</td><td>4/0.87/0.03/1.52</td><td></td></tr><tr><td>Bangui Mallam</td><td>5/&gt;0.99/0.01/0.4</td><td>5/0.98/0.07/2.37</td><td>5/0.97/0.08/2.78</td><td>5/0.99/0.05/1.91</td><td></td></tr><tr><td>Djigo</td><td>5/&gt;0.99/0.03/1.06</td><td>5/0.99/0.07/2.31</td><td>5/0.99/0.07/2.3</td><td>5/0.97/0.07/2.58</td><td>5/0.96/0.13/4.48</td></tr><tr><td>Inbanta</td><td>5/0.98/0.21/3.36</td><td>3/0.8/0.14/2.36</td><td>5/0.96/0.07/1.18</td><td>5/0.94/0.07/1.13</td><td>1/0.68/0.24/3.88</td></tr><tr><td>Kokorou</td><td>5/&gt;0.99/&lt;0.01/0.03</td><td>1/0.98/0.04/1.46</td><td>5/0.98/0.08/2.48</td><td>5/0.94/0.1/3.33</td><td></td></tr><tr><td>Manga</td><td>5/&gt;0.99/&lt;0.01/&lt;0.01</td><td>4/&gt;0.99/&lt;0.01/&lt;0.01</td><td>2/0.91/0.08/4.91</td><td>5/0.99/0.03/1.61</td><td>3/0.97/0.09/5.64</td></tr><tr><td>North Tanvi</td><td>5/0.99/0.15/2.63</td><td>4/0.99/0.06/1.17</td><td>5/&gt;0.99/&lt;0.01/&lt;0.01</td><td>3/0.92/0.09/1.61</td><td>5/&gt;0.99/&lt;0.01/&lt;0.01</td></tr><tr><td>Seguenega</td><td>5/&gt;0.99/0.01/0.34</td><td>2/0.98/0.06/2.14</td><td>1/0.84/0.09/3.6</td><td>5/0.95/0.11/4.36</td><td>4/0.95/0.13/4.97</td></tr><tr><td>Seytenga</td><td>3/&gt;0.99/0.01/0.25</td><td>4/0.99/0.04/1.92</td><td>5/0.99/0.03/1.58</td><td>5/0.94/0.09/4.23</td><td>3/0.94/0.1/4.9</td></tr><tr><td>South Tanvi</td><td>5/&gt;0.99/0.01/0.44</td><td>5/0.99/0.05/1.91</td><td>3/0.82/0.12/4.43</td><td>3/0.85/0.11/4.1</td><td>1/0.93/0.2/7.53</td></tr><tr><td>Tibin</td><td>5/&gt;0.99/&lt;0.01/0.05</td><td>5/&gt;0.99/0.02/0.63</td><td>5/0.99/0.06/2.32</td><td>5/0.99/0.04/1.57</td><td>2/0.97/0.1/4.02</td></tr><tr><td>Toussiana</td><td>5/&gt;0.99/0.01/0.12</td><td>4/&gt;0.99/0.03/0.79</td><td>4/0.97/0.09/2.17</td><td>2/0.99/0.07/1.8</td><td>1/0.94/0.3/7.3</td></tr></tbody></table>

### 3.5. Height-Area and Volume-Area Relationships Accuracy

The height RMSE is between 0.03 and 0.42 m with most values below 0.30 m and the height NRMSE is between 1.3% and 13.7% with most values below 8%. Some methods are missing for some lakes. The different methods perform generally well but not similarly on the same lakes. However, we do not observe systematic differences between one method and another. Heights derived from Sentinel-3 give higher RMSE and NRMSE on certain lakes. One of the reasons might be that radar altimeter waveforms are affected by crops or other water bodies surrounding the reservoir that generate relatively high backscattering (Arzuma). The other reason is the limitation of the radar altimeter along-track resolution. This can occur with small water bodies (noise observed for Babou and Manga lakes) or larger water bodies whose orientation with respect to the altimeter ground track generates narrow transects (Toussiana). Since these transects are made of very few measurements, they are more likely to provide larger errors.

For all methods, the volume RMSE is between 0.03 * 10⁶ m³ and 8.72 * 10⁶ m³ with most values below 5 * 10⁶ m³ and the volume NRMSE is between 2.3% and 12.1% with most values below 11% (Table 4 and Figure 9). Similarly to the height statistics, we do not observe systematic differences between one method and another, or between one lake and another. Nevertheless, Profile GEDI/contours and Height S3/area methods are particularly impacted by some higher RMSEs due to the dispersion in the volume-area curve. In addition, some poor performances have been improved when going from height to volume accuracy, whereas some good performances have been reduced. This observation reflects that volume accuracy is not only a matter of height-area relationship accuracy and dispersion, but also a matter of height-area shape. This statement is supported by the results over Toussiana reservoir, where the difference between the Height S3/area method and the others methods are much lower when looking at the volume accuracy than the height accuracy metrics. We think that this is mainly due to the shape of the Height S3/area-derived height-area relationship that allows the volume-area relationship to fit the in-situ data more closely (Figure 5).

### 3.6. Combining All Height-Area Curves From Open Source Data

When combining the methods based on open source data (Figure 10), the results give height RMSE between 0.05 and 0.25 m and height NRMSE between 1.7% and 8.9% with most values below 6%. The volume RMSE is between 0.04 * 10⁶ m³ and 8.72 * 10⁶ m³ with most values below 1.44 * 10⁶ m³, and the volume NRMSE is
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Box plot of the water height precision achieved by the different data sources. For each lake in x-axis, we plot the distribution of the water height precision in y-axis. The precisions computed for each transect/contour are stacked into a box reflecting the 25th, 50th and 75th percentiles of the distribution. Water heights resulting from only one measurement are rejected.</figcaption></figure>
<table><caption>**Table 4**

Accuracy Statistics of Height and Volume</caption><thead><tr><th></th><th>DSM pleiades</th><th>DSM pleiades/contours</th><th>Profile ICESat-2/contours</th><th>Profile GEDI/contours</th><th>Height S3/area</th><th>Combined open source</th></tr></thead><tbody><tr><td colspan="7" style="text-align: center;">- Height -</td></tr><tr><td colspan="7" style="text-align: center;">R<sup>2</sup>/RMSE (m)/NRMSE (%)</td></tr><tr><td>Agoufou</td><td>&gt;0.99/0.03/2.31</td><td>0.98/0.04/2.62</td><td>0.97/0.05/3.64</td><td></td><td></td><td>0.97/0.05/3.64</td></tr><tr><td>Arzuma</td><td>0.99/0.09/3.11</td><td>0.98/0.13/4.38</td><td>0.32/0.15/5.13</td><td>0.92/0.17/5.85</td><td>0.68/0.4/13.73</td><td>0.94/0.15/5.11</td></tr><tr><td>Bam</td><td>0.98/0.42/8.33</td><td>0.91/0.35/6.86</td><td>0.96/0.21/4.15</td><td>0.87/0.3/5.87</td><td>0.98/0.28/5.49</td><td>0.96/0.25/4.93</td></tr><tr><td>Bangou Kirey</td><td>0.93/0.19/7.63</td><td>0.66/0.11/4.2</td><td>0.48/0.23/8.93</td><td></td><td></td><td>0.48/0.23/8.93</td></tr><tr><td>Kokorou</td><td>0.96/0.17/6.49</td><td>0.73/0.07/2.56</td><td>0.96/0.11/3.97</td><td>0.87/0.09/3.27</td><td></td><td>0.98/0.08/3.13</td></tr><tr><td>Seguenega</td><td>&gt;0.99/0.03/1.43</td><td>0.94/0.07/3.84</td><td>0.37/0.11/5.64</td><td>0.92/0.14/7.27</td><td>0.88/0.14/7.43</td><td>0.93/0.11/5.95</td></tr><tr><td>Seytenga</td><td>0.95/0.27/6.23</td><td>0.9/0.28/6.57</td><td>0.94/0.22/5.24</td><td>0.91/0.27/6.28</td><td>0.92/0.18/4.18</td><td>0.93/0.24/5.72</td></tr><tr><td>Toussiana</td><td>&gt;0.99/0.17/1.96</td><td>&gt;0.99/0.12/1.43</td><td>0.95/0.16/1.91</td><td>0.99/0.11/1.27</td><td>0.94/0.32/3.76</td><td>0.98/0.14/1.7</td></tr><tr><td colspan="7" style="text-align: center;">- Volume -</td></tr><tr><td colspan="7" style="text-align: center;">R<sup>2</sup>/RMSE (10<sup>6</sup> m<sup>3</sup>)/NRMSE (%)</td></tr><tr><td>Agoufou</td><td>&gt;0.99/0.05/2.37</td><td>0.98/0.08/3.51</td><td>0.98/0.08/3.77</td><td></td><td></td><td>0.98/0.08/3.77</td></tr><tr><td>Arzuma</td><td>0.99/0.14/2.99</td><td>0.98/0.2/4.27</td><td>0.32/0.3/6.37</td><td>0.93/0.28/5.86</td><td>0.62/0.71/14.97</td><td>0.94/0.26/5.57</td></tr><tr><td>Bam</td><td>0.99/6.25/11.29</td><td>0.85/6.71/12.11</td><td>0.95/3.79/6.85</td><td>0.87/4.91/8.87</td><td>0.97/3.43/6.2</td><td>0.95/4.22/7.61</td></tr><tr><td>Bangou Kirey</td><td>0.94/0.03/5.47</td><td>0.66/0.03/5.74</td><td>0.48/0.03/7.23</td><td></td><td></td><td>0.48/0.04/7.66</td></tr><tr><td>Kokorou</td><td>0.96/1.99/6.03</td><td>0.73/1.56/4.71</td><td>0.96/1.75/5.29</td><td>0.87/1.92/5.79</td><td></td><td>0.98/1.39/4.22</td></tr><tr><td>Seguenega</td><td>0.99/0.07/2.83</td><td>0.91/0.12/4.72</td><td>0.37/0.17/7.0</td><td>0.9/0.15/6.03</td><td>0.87/0.16/6.27</td><td>0.9/0.14/5.74</td></tr><tr><td>Seytenga</td><td>0.92/1.55/11.11</td><td>0.87/1.6/11.46</td><td>0.93/1.33/9.49</td><td>0.91/1.43/10.25</td><td>0.9/1.0/7.15</td><td>0.92/1.35/9.68</td></tr><tr><td>Toussiana</td><td>&gt;0.99/0.22/3.6</td><td>&gt;0.99/0.17/2.78</td><td>0.95/0.24/3.89</td><td>0.99/0.16/2.51</td><td>0.92/0.46/7.37</td><td>0.97/0.21/3.44</td></tr></tbody></table>

between 4.2% and 12.1% with most values below 10.3% (Table 4). These results are comparable to those obtained with the Profile ICESat-2/contours method alone as, for example, the average difference of volume NRMSE between both methods is −0.27%. Furthermore, the average difference of RMSE and NRMSE between the Combined open source and the DSM Pleiades methods is −0.02 m and 0.20% for heights and −0.33 * 10⁶ m³ and 0.25% for volumes. This indicates that the accuracy of the height-area relationships based on open source data is similar to that obtained using high-resolution commercial surface topography data such as Pleiades DSMs.

# 4. Discussion

## 4.1. Comparison With the Literature

### 4.1.1. Precision and Accuracy of the Height-Area Relationships

Many publications (Busker et al., 2019; T. Chen et al., 2022; Li et al., 2020; Schwatke et al., 2020) show similar results to those shown in 3.3.1 about the dispersion in the area-height relationships, and reported high values of R² (>0.90). Our results with the Height S3/area method (RMSD values between 0.09 and 0.34 m, with average being 0.16 m) are slightly better than those of Schwatke et al. (2020) who reported RMSD values between 0.15 and 0.53 m, and average of 0.27 m, over 6 Texan lakes having a number of points comparable to that of our curves (e.g., 32 points or less). Schwatke et al. (2020) used altimetry data from multiple missions with different accuracy, allowed a time lag of up to 10 days between water surface height and area data acquisitions, and did not perform time interpolation to generate the matchups, which may cause slightly larger RMSD.

Regarding the height-area relationship accuracy, most RMSE values are below 0.30 m. Li et al. (2020) obtained RMSE values of 0.06 m, 0.47 m, 0.76 m and 1.20 m over four medium-sized lakes (1–100 km²) when validating their height-area curves derived from the combination of either ICESat, Hydroweb (Crétaux et al., 2011) or GREALM (Birkett et al., 2011) altimetry data with water areas from the Joint Research Center Global Surface
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Comparison between relative volumes from in-situ (x-axis) and from other methods (y-axis). The 1:1 curve is plotted as gray dashed line.</figcaption></figure>

Water (GSW) data set (Pekel et al., 2016), respectively. Part of the difference with our results may be explained by height biases between remote sensing and in-situ data reported in the study of Li et al. (2020).

The slope breaks and curvatures consistently observed on the height-area relationships of some lakes such as Djigo, Kokorou and Tibin (Figure 5) are of particular interest as they reveal fine shape behaviors. Many existing studies (Bhagwat et al., 2019; Busker et al., 2019; J. Chen et al., 2019; Crétaux et al., 2015; Fang et al., 2019; Gao et al., 2012; Li et al., 2020; Smith & Pavelsky, 2009; S. Zhang & Gao, 2020) consider linear, quadratic or power-law regressions to fit the height-area relationship. Our results show that such assumptions might be unsuited to capture complex shape patterns in the case of small and medium-sized lakes. Using multi-
<figure><img src="image_12.png" /><figcaption>**Figure 10.** Combination of height-area curves from ICESat-2-, GEDI- and Sentinel-3-based methods for (a) lakes with in-situ data and (b) other lakes.</figcaption></figure>
polynomial regressions is the best option in this case provided that the height-area relationship has the proper resolution to resolve small scale details.

4.1.2. Precision of the Height Estimates

The water height precision along lake contours has been assessed in Section 3.4, with values ranging between 0.04 and 0.19 m, and most values below 0.13 m. Five lakes show a precision better or equal to 0.08 m. These values are in line with Arsen et al. (2013) who reported water contour height standard deviations ranging from 0.02 to 0.11 m when intersecting ICESat 170 m posting rate banks height profiles with water contours over lake Poopo in Bolivia.

For GEDI, we did not find assessment of the water height precision along contour lines in the literature. If we compare the water contour height precision with values obtained along transects over water from other publications, our results (precision between 0.04 and 0.23 m, with most values below 0.13 m) are in line with Z. Zhang et al. (2023) who studied the water level dynamics of Qinghai Lake with GEDI data. The large biases noted on GEDI profiles from different acquisition dates were also pointed out by Fayad et al. (2020), and require further investigations.

For Sentinel-3, Taburet et al. (2020) reported a median standard deviation of water height of 0.17 m. This is consistent but slightly higher than our results, which is expected as Taburet et al. (2020) studied thousands of water bodies, including rivers. Also, the use of the MAD in our study provides better results compared to using the standard deviation. More generally, standard deviations of a few centimeters have already been achieved over larger lakes with radar altimeters previous to Sentinel-3 (Crétaux & Birkett, 2006). This study shows that such a performance can be achieved on small and medium-sized lakes as well.

4.1.3. Water Area Estimates

The MNDWI threshold for water classification has been determined ad hoc for each lake. Using the same spectral index, we also tested automatic methods based on histogram analysis such as Otsu (1979) and Minimum Error Thresholding (Kittler & Illingworth, 1986). Both methods assume that the MNDWI distribution is bi-modal with two classes respectively associated with land and water. The Otsu's method determines the optimal threshold as the value which maximizes the inter-class variance and the MET method assumes that the histogram is a mixture of two gaussian-like distributions associated with the respective classes. Both methods were found to perform poorly in particular for lakes covered by aquatic vegetation (tri-modal histograms) or for lakes almost dried out (monomodal histograms for some dates). Consequently, we decided to follow de Fleury et al. (2023) and use ad hoc MNDWI thresholding. For some lakes, fairly negative threshold values have been selected to account for aquatic vegetation (Table 1). We acknowledge that spatio-temporal variations in spectral signature of the lake or atmospheric conditions may lead to underestimation or overestimation of the water surface area, but ad hoc thresholding allows for a more consistent time series. The accuracy of the water surface areas has not been directly assessed but the results of Section 3.4 indicate that the precision of the water contours height is of the order of 0.10–0.20 m. This, combined with the satisfactory height-area relationships dispersion and accuracy, reflects a good water contours detection accuracy and proves ad hoc MNDWI thresholding to be efficient for our study.

4.1.4. Accuracy of the Volume-Area Relationships

We reported volume NRMSE between 2.3% and 15.8%, with most values below 11%. This is in line with Busker et al. (2019) who validated volume variations derived from the combination of radar altimetry and GSW monthly areas over 18 global lakes and reservoirs and obtained NRMSE between 1.784% and 18.872% with most values below 11% (extrapolated volumes excluded). Schwatke et al. (2020) also obtained similar results with NRMSE (defined as the RMSE divided by the difference of the 95% percentile and the 5% percentile of the height variations) varying between 2.8% and 14.9%, with an average of 8.3%, when validating against in-situ volume variations. The in-situ data used in our study come from various sources (with errors difficult to estimate) and may induce different uncertainties during the comparisons.
## 4.2. Pros and Cons of Each Method

### 4.2.1. DEM-Based Methods

#### 4.2.1.1. Pleiades

Pleiades-based height-area relationships show generally good performance in terms of accuracy, water height precision and dispersion. In particular, those derived from the DSM Pleiades method have the advantage of relying on a single data source. However, our study shows that despite their very high spatial resolution, Pleiades DSMs should be subjected to preliminary quality checks for issues related to jitter and high noise due to low pixel correlation, which can introduce errors of several meters. Dried out lake Pleiades DSMs allow characterizing the topography of the whole lake bathymetry but also represent a challenge for the estimation of the lake bottom altitude. Indeed in the absence of water, determining the starting altitude of the height-area relationship is not straightforward as the lake bottom may show high noise. In this study we manually selected a starting altitude from which water areas increase significantly. Alternative options might be to use the elevation from an external water contour intersected with the DSM, or to correct for the amplitude of the noise estimated over a flat area. If the noise is more widely spread over the banks (not only on the lake bottom but also on higher parts of the banks), reducing the starting altitude is mandatory in order not to underestimate the water areas subsequently computed.

The DSM Pleiades/contours method, which combines Pleiades DSMs with water contours, requires an additional data source compared to the DSM Pleiades method but is not affected by the effect of dry lake noise on the starting elevation of the curves, as these are truncated to the minimum water contour extent. More generally, Pleiades DSMs represent the surface elevation, and thus remain affected by all kinds of relief such as vegetation whose footprint on the DSMs is often wider due to smoothing in the DSM generation processing.

#### 4.2.1.2. Other DEMs

Pleiades images are commercial data, not open-access. We tested the potential of open-access global DEMs such as SRTM data, used in several studies (Fang et al., 2019; Pan et al., 2013; Yao et al., 2018; S. Zhang & Gao, 2020), to produce height-area relationships. The cut-and-fill method has been applied on the SRTM DEM of each of the 16 lakes studied. With the exception of the Tibin reservoir, which is among the largest studied lakes (mean area of 15.39 km²) and was not impounded yet during the SRTM acquisition, the resulting height-area relationships do not agree with all other methods. They are systematically steeper except for four lakes (Bangou Kirey, Bangui Mallam, Kokorou and Tibin). Moreover, the 1-m vertical resolution of SRTM, as used in several studies, and that of other global DEMs such as the ALOS Global DSM (AW3D30) or the ASTER Global Digital Elevation Map, is insufficient to capture water surface height variations of a few meters observed in the study region. GLO-30 Copernicus DEM has a better vertical resolution but represents a 2011–2015 averaged topography from multiple DEMs derived from the TanDEM-X mission and acquired with different water levels. Hence, bank topography must be regarded carefully as it may contain contributions from water.

### 4.2.2. Lidar-Based Methods

Profile ICESat-2/and Profile GEDI/contours methods are able to generate accurate height-area relationships over small to medium-sized lakes with sometimes a single but more often a few numbers of bank height profiles. Furthermore, these relationships are consistent with very high resolution DSM-based curves and highlight the potential of existing lidar altimetry missions for lake volume changes monitoring. We also note that the satisfactory water height precision obtained with ICESat-2 and GEDI data suggests that the algorithm implemented in the respective operational products used in this study properly separate echoes from tree canopy and ground. Nonetheless, the methods face some limitations. Among them, the height-area relationship quality depends on the lake's shape and the attack angle of the lidar altimeter ground tracks with respect to the water contours. The more parallel to the lake the trajectory is, the bigger the impact of water detection errors on the resulting contour height will be. The location of the lidar profiles is important as well since it also conditions the sensitivity of the methods to water detection errors (as it could be the case for dendritic lakes or profiles located close to the shore). The lidar data posting rates of respectively 60 and 100 m represent a limitation with respect to the range of bank slope that can be observed. A threshold on the bank slope must be applied to prevent errors induced by linear interpolation of the topography or water detection which is more challenging as the banks get steeper. Another limitation of ICESat-2 (nominal revisit time of 91 days, drifting orbit during the first 2 years of the mission) and GEDI (variable
revisit time) data is the temporal coverage which conditions the observable volume dynamics. In addition, GEDI suffers from some degraded acquisition periods (Urbazaev et al., 2022). Finally, being optical sensors, lidars are not suited to areas with important cloud cover. In this study we were not significantly impacted by this effect as the dry season, with very low or absent cloud cover, represents the major part of the year in the study area.

### 4.2.3. Height S3/Area Method

As well as lidar data, Sentinel-3 data are less impacted by relief than the Pleiades DSMs and better separate water from flooded vegetation, as suggested by the comparison between Height S3/area and Pleiades-based height-area relationships over the Inbanta lake. One of the advantages of Sentinel-3 data, in addition to having no trouble with cloud cover, is also the temporal coverage (revisit time of 27 days) which excludes the acquisition dates dependency associated with the other methods and may allow observing a greater water volume dynamics. Even more frequent revisit time is possible with Sentinel-6 data (10 days) but the spatial coverage decreases substantially (e.g., only one of the lakes studied is covered by Sentinel-6). Nonetheless, despite good water surface height precision (below 0.10 m for most lakes), the Height S3/area method tends to generate height-area relationships with more dispersion (Section 3.3). In addition to the impact of time interpolation for matching S2 and S3 data, part of these errors might be attributed to contamination of the radar waveform by surrounding bright surfaces such as crops, humid soils or neighboring water bodies which challenge the retracking (Boy et al., 2022). As the height-area relationship is then integrated to calculate volume changes, a higher dispersion in the curve will introduce additional uncertainty into the volume change estimates (Busker et al., 2019).

### 4.3. Spatial and Temporal Coverage

As already mentioned in the introduction, the spatial coverage of the radar altimetry missions is limited to the lakes below the satellite tracks. Multi-beams lidar altimetry data from ICESat-2 and GEDI missions provide open-access surface height data with enhanced spatial coverage compared to that of radar altimetry missions. Indeed, T. Chen et al. (2022) showed for example, that the ICESat-2 along-track inland surface water (ATL13) product allowed observing 2 to 7 times more global water bodies than those covered by traditional altimetry. Still, the ATL13 product is spatially limited by a shape mask derived from existing inland water bodies databases (Jasinski et al., 2023). The ATL08 product used in this work allows for an even better spatial coverage.

Intersecting the lidar bank height profiles with water contours derived from satellite imagery allows going from lidar multi-monthly revisit time to imagery weekly revisit time. This represents a significant increase in temporal coverage compared to using surface water lidar data.

## 5. Summary and Conclusion

The height-area relationships of 16 lakes and reservoirs in West Africa have been derived from four different methods. These methods used different data sources such as Pleiades DSMs, Sentinel-2 optical imagery, ICESat-2 and GEDI lidar altimetry and Sentinel-3 radar altimetry. We found a generally good agreement with in-situ data (height RMSE values below 0.42 m and volume NRMSE values below 13%) and among the methods. With the exception of the Sentinel-3-based method which tends to produce higher dispersions, all methods provide curves with very low noise (fit RMSD values below 0.10 m for most lakes). Fine shape patterns were consistently observed over small height amplitudes, highlighting the ability of the different methods to monitor shallow lakes with non-linear height-area relationships. We found satisfactory water height precisions, with values close to 0.20 m using Pleiades DSMs and slightly better values of the order of 0.13 m or less using the other methods.

Overall, consistent and accurate height-area relationships were obtained over small and medium-sized lakes with areas ranging from 0.1 to tens of km², with small height amplitudes (from about 1.5 to 4 m) and with different characteristics (i.e., turbidity levels, aquatic vegetation, tree cover). This result represents a step forward for volume change monitoring of shallow lakes (Figure S9 in Supporting Information S1) with respect to seasonality, interannual variability and trends in water storage.

We showed that combining the methods based on non-commercial data mitigates some of the limitations of the individual methods, provides more robust curves and performs similarly to methods based on high-resolution commercial DSMs. The Profile/contours method, which only requires few lidar acquisitions per lake, allows monitoring an increased number of lakes, including small and ephemeral lakes, in landscapes where topography is
quite flat. The temporal coverage (sub-monthly revisit time) of radar altimetry data and the spatial coverage of lidar data improve the height-area curves extent and the number of water bodies observed, respectively. Combining radar and lidar altimetry data provides an open source solution for upscaling volume dynamics analysis to a wider range of lakes, as the methods are easily transferable to other lakes. This could be of particular interest for the monitoring of ungauged lakes or lakes with outdated in-situ data.

Finally, benefiting from its wide-swath Ka-band radar interferometer (KaRIN), the Surface Water and Ocean Topography (SWOT) mission, launched on 16 December 2022, will be able to observe 90% of the inland areas and all lakes larger than 250 × 250 m² (requirements) located between 78°N and 78°S (Biancamaria et al., 2016). With a minimum revisit time of 21 days, SWOT will thus provide height and area change estimates for the majority of the lakes and reservoirs in the study area, further expanding the number of water bodies that could be addressed by remote sensing. The H-A-V relationships derived in this study will provide a valuable database to assess SWOT performances in this area.

## Data Availability Statement

The in-situ water surface height data on Bangou Kirey and Agoufou lakes are available in the AMMA-CATCH observatory database (www.amma-catch.org, https://doi.org/10.2136/vzj2018.03.0062). For the height-volume relationships of Bam, Seguenega and Seytenga reservoir, please contact the Institut International d'Ingénierie de l'Eau et de l'Environnement (2IE, ousmane.yonaba@2ie-edu.org, tazen.fowe@2ie-edu.org). The height-area relationships of the Kokorou lake and Toussiana reservoir have been extracted respectively from Baba et al. (2019) and Sanogo and Dezetter (1997).

The Sentinel-2 L2A Surface Reflectance (SR) images are available on Google Earth Engine (GEE, (Gorelick et al., 2017)) as the "Sentinel-2 MSI: MultiSpectral Instrument, Level-2A" collection (https://developers.google.com/earth-engine/datasets/catalog/COPERNICUS_S2_SR). The Sentinel-3 Sar Radar Altimeter (SRAL) data and the Altimetric Time Series Software (AlTiS, (Frappart et al., 2021)) are provided by the Centre de Topographie des Océans et de l'Hydrophère (CTOH, https://www.legos.omp.eu/ctoh/catalogue/). The Ice, Cloud and land Elevation Satellite-2 (ICESat-2) L3A Land and Vegetation height data product (ATL08) is accessible on the National Snow and Ice Data Center (NSIDC) website (https://nsidc.org/data/atl08/versions/6). The Global Dynamics Ecosystem Investigation (GEDI) L2A Geolocated Elevation and Height Metrics (GEDI02_A) are downloaded from the NASA Land Processes Distributed Active Archive Center (LP DAAC, https://lpdaac.usgs.gov/products/gedi02_av002/).

The data set containing the height-area-volume relationships of the remote sensing-based methods is provided as a CSV file accessible through https://doi.org/10.23708/CRZE9K. The data set also includes the in-situ data-based height-area-volume relationship of the Arzuma reservoir. In order to allow a direct comparison, the provided relationships are all unbiased with respect to the DSM Pleiades method.

## Acknowledgments

This work was supported by CNES through the APR program funding the SPLASH project, in the framework of the pre-launch activities related to the SWOT mission. Occitanie Region and Collecte Localisation Satellites (CLS) also supported this work by funding Félix Girard's PhD thesis. We acknowledge CNES and Airbus DS for providing the Pleiades images, and the AMMA-CATCH observatory for in-situ data supply in Niger and Mali. We are very grateful to Nicolas Taburet and Nicolas Picot for discussions on the altimetry data, to Etienne Berthier for sharing his expertise on DSM processing and analysis, to Guillaume Favreau for sharing his knowledge of water bodies in Niger, and to Jean-Marie Dipama for information on reservoirs in Burkina Faso. Finally, we thank the anonymous reviewers for their comments and thorough review of the previous version of this manuscript.

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