# Evaluation using in-situ observations from national governments and Citizen Scientists suggests nadir altimeters can accurately measure water level changes regardless of lake area

Angélica Gómez, Sylvain Biancamaria, Tamlin Pavelsky, Karina Nielsen, Grant Parkins, Megan Lane, Shahzaib Khan, Faisal Hossain, Rajat Bhattarai, Sheikh Ghafoor, et al.

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## To cite this version:

Angélica Gómez, Sylvain Biancamaria, Tamlin Pavelsky, Karina Nielsen, Grant Parkins, et al. Evaluation using in-situ observations from national governments and Citizen Scientists suggests nadir altimeters can accurately measure water level changes regardless of lake area. GIScience and Remote Sensing, 2025, 62 (1), 10.1080/15481603.2025.2543521. hal-05338826

HAL Id: hal-05338826

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Submitted on 31 Oct 2025

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# Evaluation using in-situ observations from national governments and Citizen Scientists suggests nadir altimeters can accurately measure water level changes regardless of lake area

Angélica M. Gómez, Sylvain Biancamaria, Tamlin Pavelsky, Karina Nielsen, Grant Parkins, Megan Lane, Shahzaib Khan, Faisal Hossain, Rajat Bhattarai, Sheikh Ghafoor, Jean-François Crétaux, Carlos Yanez & Nicolas Picot

**To cite this article:** Angélica M. Gómez, Sylvain Biancamaria, Tamlin Pavelsky, Karina Nielsen, Grant Parkins, Megan Lane, Shahzaib Khan, Faisal Hossain, Rajat Bhattarai, Sheikh Ghafoor, Jean-François Crétaux, Carlos Yanez & Nicolas Picot (2025) Evaluation using in-situ observations from national governments and Citizen Scientists suggests nadir altimeters can accurately measure water level changes regardless of lake area, GIScience & Remote Sensing, 62:1, 2543521, DOI: 10.1080/15481603.2025.2543521

**To link to this article:** https://doi.org/10.1080/15481603.2025.2543521

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© 2025 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

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# Evaluation using in-situ observations from national governments and Citizen Scientists suggests nadir altimeters can accurately measure water level changes regardless of lake area

Angélica M. Gómez<sup>a,b</sup>, Sylvain Biancamaria<sup>c</sup>, Tamlin Pavelsky<sup>d</sup>, Karina Nielsen<sup>d</sup>, Grant Parkins<sup>e</sup>, Megan Lane<sup>e</sup>, Shahzaib Khan<sup>f</sup>, Faisal Hossain<sup>f</sup>, Rajat Bhattarai<sup>g</sup>, Sheikh Ghafoor<sup>g</sup>, Jean-François Crétaux<sup>h</sup>, Carlos Yanez<sup>h</sup> and Nicolas Picot<sup>h</sup>

## ABSTRACT

Water level and water level changes of lentic water bodies such as lakes, wetlands, and reservoirs are rarely available, despite the relevance of these to maintain ecosystems (e.g., by providing drinking water, food, and cultural activities; and by supporting biodiversity). One alternative is to measure water surface elevation with radar nadir altimeters, whose use has increased as the capabilities of measuring inland water bodies have improved. However, their effectiveness has primarily focused on lakes larger than ~100 km², and the analysis of contributing factors to obtaining high accuracies is typically performed for a few lakes with special cases. We evaluated water surface elevation change from Sentinel-3 and Jason-3 nadir altimeter missions in lakes and reservoirs using in-situ observations from national governmental institutions and the citizen science network from the project Lake Observations by Citizen Scientists and Satellites. Utilizing the accuracy metrics of Pearson correlation coefficient, R, and the unbiased Root Mean Square Error, ubRMSE, over 27 waterbodies, we found a median ubRMSE of 0.15 m and R of 0.88. We combined the results from 61 additional lakes in a Random Forest algorithm with a permutation of importance to evaluate the impact of 7 factors on the accuracy metrics. Although water surface variability was the most contributing factor to the accuracy, we found differences in the order of variables depending on the evaluation metric used. Our results contribute to show the potential of the nadir altimeters to estimate water surface elevation changes in small lakes, present the advantages of using citizen science monitoring, and the relevance of water surface variability in relation to other factors contributing to high altimeter accuracy. Our implementation of the level of importance algorithm shows potential to systematically evaluate the nadir altimeter validation work available in the literature.

## KEY POINTS

* Water surface lake variability is a key factor impacting the accuracy metrics on radar nadir altimeter evaluation.

* Citizen Scientists contribute to evaluating nadir altimeter water surface elevation changes in small lakes, wetlands, and reservoirs.

* Radar nadir altimeter shows capabilities to measure water surface elevation in lakes smaller regardless of lake area.

## ARTICLE HISTORY

Received 9 December 2024

Accepted 31 July 2025

## KEYWORDS

Citizen science; in-situ water surface elevation change; radar nadir altimeter;

Sentinel-3; Jason-3; remote sensing

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<footnote><sup>a</sup>Department of Earth, Marine and Environmental Sciences, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA;</footnote>

<footnote><sup>b</sup>Departamento de Geografía, Universidad Nacional de Colombia - Sede Bogotá, Bogotá, Colombia; <sup>c</sup>Université de Toulouse,</footnote>

<footnote>Laboratoire d'Études en Géophysique et Océanographie Spatiales (LEGOS) (CNES/CNRS/IRD/UT3), Toulouse, France; <sup>d</sup>Geodesy and Earth Observation, Department of Space Research and Technology, The Technical University of Denmark, Lyngby, Denmark;</footnote>

<footnote><sup>e</sup>Institute for the Environment, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA; <sup>f</sup>Department of Civil and Environmental Engineering, University of Washington, Seattle, WA, USA; <sup>g</sup>Department of Computer Science, Tennessee Technological University, Cookeville, TN, USA;</footnote>

<footnote><sup>h</sup>Centre National d'Etudes Spatiales (CNES), Toulouse, France</footnote>
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# 1. Introduction

Small and medium-sized lentic systems (i.e. lakes, wetlands, and reservoirs) contribute to regulating temperature, energy, flow, and supporting biodiversity (Downing 2010; Rinke et al. 2019). Current estimates suggest that nearly 1.5 million water bodies globally have areas between 0.1 and 100 km² (Messager et al. 2016), with around 3.2 million lentic systems between 0.03 and 0.1 km² (Pi et al. 2022). In some cases, these systems are the source of benefits to society, such as irrigation, energy production, and drinking water supply (Heino et al. 2021; Inácio et al. 2022). Despite the ecosystem functions and benefits lentic systems provide, their long-term water level dynamics remain understudied at large scales.

Water dynamics has been characterized from space via satellite observations of surface water extent and level. To understand surface water extent changes, global datasets have been built in the last decade to map lake extent (Khandelwal et al. 2022), lake and reservoir surface water change, and water storage (Crétaux et al. 2016; Gao 2015; Pekel et al. 2016; Pickens et al. 2022; Verpoorter et al. 2014; Yao et al. 2019). Linking area variations with changes in lake water level and water storage is essential for understanding lake dynamics. One challenging aspect in doing this task is that lake hypsometry varies considerably among water bodies. The use of satellite-mounted nadir altimeters has contributed to characterizing surface water elevation. A radar altimeter emits radar pulses in the nadir direction (i.e. the shortest distance between the satellite and the water body underneath) (Mercier et al. 2010). Using a pulse compression technique, the altimeter records the backscattered radar echo, called waveform, within a tracking reception window (Le Gac et al. 2021). The waveforms are processed to produce the surface water elevation relative to a reference surface (geoid or ellipsoid) employing retracking algorithms (Crétaux et al. 2017; Escudier et al. 2017). The altimeter footprint captures information from an inhomogeneous surface over land that might be altered by 1) the sensor receiving signals from non-water surfaces or 2) the energy peak not coming from the nadir of the antenna (Crétaux et al. 2017). The targeted water body elevation could be missed when positioning the tracking window automatically. One of the mechanisms to improve water body elevation observations from the altimeter is the implementation of the Open-Loop Tracking Command (OLTC) (Le Gac et al. 2021). OLTC sets the appropriate reception window for the surface return signal thanks to an on-board pseudo-DEM which contains information of the overflown surface elevation (Le Gac et al. 2021).

Numerous nadir altimeter missions have been launched since the 1980s, initially to monitor changes in ocean topography (International Altimetry Team 2021). As capabilities improved to estimate surface water elevation in inland waters, the precision to detect surface water elevation has also improved (International Altimetry Team 2021; O'Loughlin et al. 2016). Initially, these capabilities have been extensively evaluated over lakes larger than approximately 100 km² (e.g., Birkett 1998; Birkett and Beckley 2010; Crétaux et al. 2016, 2017; Crétaux and Birkett 2006; Ričko et al. 2012; Sulistioadi et al. 2015 and many others). The extensive research over larger lakes motivated the implementation of applications to retrieve lake water level time series from satellite altimetry in these water bodies, e.g., G-REALM (https://ipad.fas.usda.gov/cropexplorer/global_reservoir/), hydroweb.next (https://hydroweb.next.theia-land.fr/), and DAHITI (Schwatke et al. 2015). As the capabilities improved, the evaluation extended to lakes larger than 10 km², while smaller lakes have received considerably less attention (Table 1). Recent contributions have analyzed additional smaller lakes using auxiliary data or models to improve or filter potentially incorrect water height measurements (Boy et al. 2022; de Fleury, Kergoat, and Grippa 2023). As algorithms for retrieving inland water levels from altimeters have improved, our understanding of their capabilities in the world's numerous small lakes and reservoirs has not followed suit. In addition, the literature has documented some of the factors impacting the altimeter accuracy, however, we have not found a systematic evaluation of these factors and how their relative importance ranks when evaluating them together.

One of the challenges of evaluating nadir altimeter performance in small lakes is the lack of in-situ data. It is relatively uncommon for national monitoring agencies to collect regular data in small lakes, as gauge installation and maintenance can be very expensive (Hannah et al., 2011). To our knowledge, there are no global repositories of data available for lake water levels that include smaller lakes, unlike the major repositories for river stage and discharge (e.g., the Global Runoff Data Center, https://www.bafg.de/GRDC/EN/Home/homepage_node.html). This lack of data is particularly notable for natural lakes, as small reservoirs are more likely to be monitored by local authorities. Citizen science, an approach in which the public participates in exchanging knowledge and data in one or more stages of the research, provides an
<figure><img src="image_18.png" /><figcaption>Table 1. Previous work of nadir altimeter validation on lakes smaller than 100 km².</figcaption></figure>

<table><thead><tr><th>Reference</th><th>Type waterbody</th><th>Number of water bodies</th><th>Mean area (km²)</th><th>Location</th><th>Satellite Mission</th></tr></thead><tbody><tr><td>Baup, Frappart, and Maubant (2014)</td><td>Lakes</td><td>1</td><td>0.52</td><td>France</td><td>Envisat</td></tr><tr><td>Arsen, Cretaux, and Abarca-Del-Rio (2015)</td><td>Lakes</td><td>3</td><td>8.9–88.1</td><td>Argentina/ Chile</td><td>SARAL/Altika</td></tr><tr><td>Bernatowicz and Lyszkowicz (2017)</td><td>Lakes</td><td>1</td><td>71.42</td><td>Poland</td><td>Jason-2</td></tr><tr><td>Nielsen, Andersen, and Ranndal (2020)</td><td>Lakes</td><td>15<br>22</td><td>50.69–98.68<br>52.21–97.41</td><td>US<br>Canada</td><td>Sentinel-3</td></tr><tr><td>Ribeiro Neto et al. (2021)</td><td>Reservoirs</td><td>20</td><td>4.36–67.40</td><td>Brazil</td><td>Envisat, SARAL, Jason-2/3, Sentinel-3</td></tr><tr><td>Frappart et al. (2021)</td><td>Lakes</td><td>10</td><td>7.5–88</td><td>Switzerland</td><td>Jason-1 to 3<br>ERS-2<br>Envisat<br>SARAL<br>Sentinel-3<br>ICESat-2<br>GEDI</td></tr><tr><td>Boy et al. (2022)</td><td>Lakes</td><td>7</td><td>2.8–17.3</td><td>France</td><td>Sentinel-3</td></tr><tr><td rowspan="4">de Fleury, Kergoat, and Grippa (2023)</td><td>Reservoirs</td><td>10</td><td>2.7–88.7</td><td>Switzerland</td><td rowspan="4">Sentinel-3<br>Sentinel-2</td></tr><tr><td>Lakes and reservoirs</td><td>21<br>12</td><td>0.02–28.22<br>0.3–37.91</td><td>Burkina Faso<br>Mali</td></tr><tr><td></td><td>9</td><td>0.04–19.28</td><td>Niger</td></tr><tr><td></td><td>19<br>60<br>4<br>2</td><td>20–500</td><td>US<br>Canada<br>Sweden<br>Australia</td></tr><tr><td>Nilsson and Nielsen (2024)</td><td>Lakes</td><td></td><td></td><td></td><td>Sentinel-6MF</td></tr></tbody></table>

alternative to obtaining water elevation changes in small lakes. This is possible given the relationships local communities have established with these lakes and the benefits they provide. Several projects have developed ways to work with citizen scientists to collect water level data (e.g., Lowry et al. 2019; Nath and Kirschke 2023; Metcalfe et al. 2022). One of these projects, the Lake Observations by Citizen Scientists and Satellites (LOCSS) (https://locss.org.; Ahmad et al. 2020; Little et al. 2021), primarily focuses on lakes and currently contains more than 65,000 observations across more than 260 lakes in ten countries. Some of these lakes fall beneath nadir altimetry tracks and offer the potential to evaluate nadir altimeter capabilities.

In this paper, we assess how well nadir altimeters detect water level changes in lakes and reservoirs smaller than 95 km². To do so, we evaluate the performance of three satellite nadir altimeters, Jason-3, Sentinel-3A, and Sentinel-3B, in lakes with areas between 0.24 and 95 km². For simplicity and given the context of this work, this paper uses the term lakes to refer to lakes and open-water wetlands and make the distinction to reservoirs specifically in Brazil. We use gauge/in-situ data publicly available from Argentina, Brazil, and the US national services and in-situ observations provided by the LOCSS citizen science network (Section 2.1). We combine the results of our evaluation with the performance evaluated from previously published work to systematically examine the level of importance of factors potentially impacting satellite accuracy. To evaluate this impact, we used a multiple Random Forest (RF) with Permutation of Importance approach to identify the order in which these factors impact the evaluation metrics for accuracy. The factors considered to evaluate the level of importance are the transect length (i.e. the length of the altimetry ground-track intersecting the lake), the number of matching observations between the altimeter and the in-situ data, the average lake area, the presence of nearby water bodies, water level variability, the number of altimeter observations that were averaged, and the topographic roughness (Section 3.4).

## 2. Data

### 2.1. Collection of in-situ data

#### 2.1.1. Data for nadir altimeter evaluation

In this study, we consider 27 lakes and reservoirs distributed as follows: 4 lakes in Argentina (areas between 9.03–82.24 km²), 7 reservoirs in Brazil (2.01–74.07 km²), 3 lakes in Bangladesh (3.51–66.10 km²), 1 in Canada (0.37 km²), and 12 in the US (0.24–158.36 km²). This selection was based on the availability of the data within public repositories. Additionally, we considered only those lakes where the nadir altimeter footprint was less than 1 km from the lake. We first attempted to have a diverse range of hydrological and climatic conditions,
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however, that was not possible given the lack of available and accessible data. Thirteen of the lakes, located in Bangladesh (three lakes), Canada (one), and the US (nine), are part of the LOCSS project (data available at https://locss.org.) (Table 2, Figure 1). In this project, citizen scientists collect water heights from the lakes and send them via cell phone or through the project website, where they are archived and freely available. Twelve out of the 27 waterbodies have an area of less than 20 km². The smallest lake monitored by a national agency is 9.3 km² in area. LOCSS provides data for the 10 smallest lakes, including several smaller than 1 km²

<table><caption>**Table 2.** Waterbodies used for Jason-3 and Sentinel-3 nadir altimeter evaluation. Orbit numbers and transect lengths appear in parenthesis for lakes, reservoirs or wetlands having more than one orbit of the same satellite overpassing. *the closest distance from the orbit to the lake shore is 350 m.</caption><thead><tr><th>Lake #</th><th>Gauge Name</th><th>Country</th><th>Waterbody Area (km²)</th><th>Gauge ID</th><th>Source</th><th>Orbit(s) Number</th><th>Satellite</th><th>Transect length (m)</th></tr></thead><tbody><tr><td>1</td><td>Balashur</td><td>Bangladesh</td><td>8.1</td><td>BLB2</td><td>LOCSS</td><td>318</td><td>Sentinel-3A</td><td>1778.06</td></tr><tr><td>2</td><td>Bay Tree</td><td>USA</td><td>5.77</td><td>BTN2</td><td>LOCSS</td><td>346</td><td>Sentinel-3B</td><td>2765.28</td></tr><tr><td>3</td><td>Catfish</td><td>USA</td><td>3.72</td><td>CFN2</td><td>LOCSS</td><td>18</td><td>Sentinel-3A</td><td>19.00</td></tr><tr><td>4</td><td>Deep Quarry</td><td>USA</td><td>0.27</td><td>QUL2</td><td>LOCSS</td><td>311</td><td>Sentinel-3B</td><td>429.64</td></tr><tr><td>5</td><td>Grays Lake</td><td>USA</td><td>0.27</td><td>YSL2</td><td>LOCSS</td><td>311</td><td>Sentinel-3B</td><td>0.00*</td></tr><tr><td>6</td><td>Half Moon</td><td>Canada</td><td>0.37</td><td>HMT2</td><td>LOCSS</td><td>176</td><td>Sentinel-3A</td><td>245.74</td></tr><tr><td>7</td><td>Khajura Baor</td><td>Bangladesh</td><td>2.51</td><td>KHB2</td><td>LOCSS</td><td>261</td><td>Sentinel-3A</td><td>1462.97</td></tr><tr><td>8</td><td>Mattamuskeet</td><td>USA</td><td>158.36</td><td>VCN2</td><td>LOCSS</td><td>11</td><td>Sentinel-3B</td><td>8149.53</td></tr><tr><td>9</td><td>Phelps</td><td>USA</td><td>158.36</td><td>MTN2</td><td>LOCSS</td><td>75</td><td>Sentinel-3A</td><td>2730.79</td></tr><tr><td>10</td><td>Sammamish</td><td>USA</td><td>63.55</td><td>FDN2</td><td>LOCSS</td><td>75</td><td>Sentinel-3A</td><td>2730.79</td></tr><tr><td>11</td><td>Wenatchee</td><td>USA</td><td>63.55</td><td>PHN2</td><td>LOCSS</td><td>13</td><td>Sentinel-3A</td><td>1952.93</td></tr><tr><td>12</td><td>Silver</td><td>USA</td><td>0.24</td><td>SAW2</td><td>LOCSS</td><td>319</td><td>Sentinel-3A</td><td>847.19</td></tr><tr><td>13</td><td>Tanguar Haor</td><td>Bangladesh</td><td>66.1</td><td>TAB2</td><td>LOCSS</td><td>97</td><td>Sentinel-3B</td><td>2627.69</td></tr><tr><td>14</td><td>Lago Fontana</td><td>Argentina</td><td>82.24</td><td>2316</td><td>ARHN</td><td>10</td><td>Sentinel-3B</td><td>4560.71</td></tr><tr><td>15</td><td>Lago Lacar</td><td>Argentina</td><td>51.34</td><td>2028</td><td>ARHN</td><td>281</td><td>Jason-3</td><td>3076.31</td></tr><tr><td>16</td><td>Lago Mascardi</td><td>Argentina</td><td>37.04</td><td>1824</td><td>ARHN</td><td>375</td><td>Sentinel-3A</td><td>2058.99</td></tr><tr><td>17</td><td>Lago Rosario</td><td>Argentina</td><td>9.3</td><td>2234</td><td>ARHN</td><td>(338,318)</td><td>Sentinel-3A</td><td>992.63</td></tr><tr><td>18</td><td>Açude Araras</td><td>Brazil</td><td>67.40</td><td>12030</td><td>RVBR</td><td>44</td><td>Jason-3</td><td>(690.51, 889.29)</td></tr><tr><td>19</td><td>Açude Atalho</td><td>Brazil</td><td>4.69</td><td>12036</td><td>RVBR</td><td>82</td><td>Sentinel-3B</td><td>3350.30</td></tr><tr><td>20</td><td>Açude Petronio Portela</td><td>Brazil</td><td>20.44</td><td>12327</td><td>RVBR</td><td>380</td><td>Sentinel-3A</td><td>626.28</td></tr><tr><td>21</td><td>Ney Aminthas de Barro</td><td>Brazil</td><td>74.07</td><td>19060</td><td>RVBR</td><td>38</td><td>Sentinel-3A</td><td>2527.56</td></tr><tr><td>22</td><td>UHE Machadinho</td><td>Brazil</td><td>64.98</td><td>19069</td><td>RVBR</td><td>6</td><td>Jason-3</td><td>848.71</td></tr><tr><td>23</td><td>Açude Boa Vista</td><td>Brazil</td><td>2.01</td><td>12056</td><td>RVBR</td><td>95</td><td>Sentinel-3A</td><td>4392.41</td></tr><tr><td>24</td><td>UHE Xingo</td><td>Brazil</td><td>62.36</td><td>19126</td><td>RVBR</td><td>82</td><td>Sentinel-3B</td><td>198.37</td></tr><tr><td>25</td><td>Big Spirit</td><td>USA</td><td>21.27</td><td>6604000</td><td>USGS</td><td>240</td><td>Sentinel-3B</td><td>(1131.60, 1146.30)</td></tr><tr><td>26</td><td>Tuscaloosa</td><td>USA</td><td>18.05</td><td>2464800</td><td>USGS</td><td>97</td><td>Sentinel-3A</td><td>495.14</td></tr><tr><td>27</td><td>Rathbun</td><td>USA</td><td>52.94</td><td>6903880</td><td>USGS</td><td>318</td><td>Sentinel-3A</td><td>3136.48</td></tr></tbody></table>
<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /><figcaption>**Figure 1.** Location of lakes used in each section of this paper. All the lakes were used to analyze the factors affecting the evaluation metrics (Section 3.4). Those marked with * in the legend were only used for Section 3.4, except 3 lakes in the US used in both sections.</figcaption></figure>

(Table 2). LOCSS citizen scientists can be individuals with any degree of expertise and interest in knowing the dynamics of their lakes; many live or work near the lakes, and some others are visitors. In sites in the US and Canada, data is shared via text message. In Bangladesh, lake heights were obtained from citizens engaged by the Water Development Board for Bangladesh and collected twice each time consistently (Khan et al. 2023). Little et al. (2021) have shown that water heights collected by citizen scientists are reliable and accurate compared to automated gauges, with a mean absolute error of 1.6 cm. After receiving the data from the citizens, it is visually inspected and flagged when obvious anomalies are detected. Official authorities monitor the other lakes considered in this study, from which we collected daily observations. In Argentina, data were collected from the Sistema Nacional de Información Hídrica (https://snih.hidricosargentina.gob.ar/Filtros.aspx#). In Brazil, reservoir data were available at Sistema Nacional de Informações sobre Recursos Hídricos (SNIRH) (https://www.snirh.gov.br/hidroweb/apresentacao). Data from US lakes that are not part of LOCSS were available from the United States Geological Survey, USGS, (https://www.sciencebase.gov/catalog/item/577445bee4b07657d1a991b6). For the purpose of this work, data are classified into three groups. Data collected by citizen scientists (LOCSS), data from reservoirs where they are explicitly classified as such, called Reservoirs, and data from governmental national institutions corresponding to other lakes, called National datasets. Because water level variations are higher in reservoirs, given their human intervention, we decided to distinguish them from other water bodies in the analysis.

Lakes were selected by identifying the lakes with in-situ water surface elevation measurements that fell under the satellite orbit. The area of lakes was obtained using a combination of lake polygons provided by Hydrolakes (Messager et al. 2016) and the SWOT Prior Lake Dataset, or PLD (Wang et al. 2025), in cases where the lakes were not included in the Hydrolakes database. For Brazilian reservoirs, we obtained the polygons from the SNIRH.
<figure><img src="image_22.png" /></figure>

### 2.1.2. Additional data used to evaluate factors of importance

To quantitatively explore the level of importance of different variables impacting the strength of the relationship between WSE change in-situ observations and altimeter time series, we needed to increase the number of lakes to better account for heterogeneity. This was accomplished by adding to the evaluation results 61 additional in-situ and altimetric lake WSE data derived from running the method implemented by Nielsen, Andersen, and Ranndal (2020) (Table S2). In addition to the lakes reported by Nielsen, Andersen, and Ranndal (2020), we increased the number of lakes to 61 to be able to use them in the present work.

## 2.2. Nadir altimeter data

### 2.2.1. Nadir altimeter for evaluation

Here we used the radar altimeter level-2 (L2) product from Jason-3, Sentinel-3A and 3B satellite missions requested from the Center de Topographie des Océans et de l'Hydrosphère (CTOH). CTOH provides a software called Altis (Frappart et al. 2021) that processes each radar altimeter L2 product (https://gitlab.com/ctoh/altis/-/wikis/home). More specifically, we requested the Geophysical Data Record (GDR) and the Non Time Critical (NTC) Land Baseline products for Jason-3 and Sentinel-3, respectively. To request the data, we selected an area surrounding each lake of about 0.5 × 0.5 degrees. At each lake location, we obtained the water level and the geophysical parameters, as described by Frappart et al. (2021). Jason-3 was launched on 17 January 2016 following the previous mission Jason-2, currently operational, with a repeat track of 10 days. Sentinel-3A and 3B, developed by the European Space Agency (ESA), are part of the Sentinel family of satellites. Sentinel-3A was launched on 16 February 2016 and the identical Sentinel-3B on 25 April 2018. Sentinel-3 constellation has a repeat cycle of 27 days. As we performed a combined analysis of Sentinel-3 and Jason-3 in this evaluation, we obtained water surface elevation (WSE) estimates from Low-Resolution Mode (LRM) data for all the missions. LRM is the mode used in conventional altimetry (such as in all Jason series missions). In this mode, a radar pulse is emitted at a low rate (1–2 kHz), producing around 2000 pulses per second (Crétaux et al. 2017). The instrument uses the echo delays from within the pulse-limited footprint to estimate the WSE (Raney 1998). Sentinel-3A and 3B operate in delay-Doppler or Synthetic Aperture Radar, SAR, mode, but allow to derive LRM mode. In SAR mode, around 18,000 pulses per second are emitted at a higher frequency (~20 kHz) (Crétaux et al. 2017). The echo delays and the Doppler information (phase) of the echoes are used to focus the signal and attain an improved along-track resolution (Raney 1998). Sentinel-3, which is operated in closed burst mode, focuses the echoes within each burst to narrow the footprint in the along-track direction to around 300 m (about one order of magnitude better than the pulse-limited footprint size). To derive pseudoLRM data, Sentinel-3 ground segment processes the pulses of a radar cycle disregarding the Doppler information.

### 2.2.2. Additional nadir altimeter data for factor of importance analysis

Nielsen, Andersen, and Ranndal (2020) used the R package "tsHydro" to generate WSE time series (Nielsen et al. 2015) from Sentinel-3A and 3B using SAR mode. tsHydro operates under the assumption that the water level observed by nadir altimeter follows a mixture of Gaussian and Cauchy distributions. This means that an observation can represent the water level from a water target at nadir, or can be a response from an off-nadir target that does not represent the water level of interest. This approach attempts to decrease the effect of extreme observations (potentially resulting from observing an off-nadir target) when estimating the mean water level. Nielsen et al. (2015) presented a detailed description of the method. Given the 61 additional lakes WSE time series were processed using the SAR mode, we further compared the WSE time series resulting from LRM mode processing done in Section 2.1 with SAR WSE time series in the 27 lakes of that section to evaluate for substantial differences. Given that no statistically significant differences were found to impact the outcome of the Random Forest algorithm (Figure S4), we evaluated the factor of importance using a combination of results from the LRM and SAR processing modes.

## 2.3. Collection of data for factor of importance analysis

We evaluated the influence of seven explanatory variables, called factors, on the two evaluation metrics obtained when evaluating the altimeter time series with in-situ observations (R and ubRMSE). We selected
<figure><img src="image_23.png" /></figure>

the factors, typically reported in the literature and identified by experts, according to the surface properties that might alter the altimeter signal related to the area covered by the footprint, the unevenness of the surface (water and land), and the presence of nearby water bodies. Specifically, we used the following factors: altimeter transect length, lake area, topographic roughness, presence of nearby water in the area surrounding the lake, variability of the water surface elevation, number of altimeter observations used to generate the time series, and number of matching altimeter and in-situ observations. We checked how individual factors relate to the evaluation metrics (Figure S5).

## 3. Methods

We divide our methods into three groups. The first one describes how data from in-situ observations and nadir altimeters were prepared for the analysis, as well as the explanatory variables to evaluate the factor of importance (Section 3.1). The second group includes the methods used to evaluate the performance of nadir altimeters using three types of datasets (Section 3.2). The final group includes the methods to evaluate the factor of importance using a random forest algorithm (Section 3.4). Section 3.3 is transversal to 3.2 and 3.4 as it explains how evaluation metrics were calculated.

### 3.1. Data preprocessing

#### 3.1.1. In-situ data preprocessing

For all the in-situ gauges, dates in the time series were transformed from local time to UTC. In addition, all the units were transformed into meters. Given the nature of the LOCSS data (i.e. data collected by citizen scientists and reported through the website or via a text message), the water level is sometimes reported more than once at the same time. Measurements taken at the same time (i.e. the difference in time is less than one minute) were reduced to the median if the standard deviation of those values was less than 0.05 m; otherwise, they were removed. We found 35 measurements taken on the same date. The 0.05 m threshold is three times the mean height difference between Citizen Scientist readings and automated pressure transducers found during the LOCSS validation phase (Little et al. 2021). We used this threshold as a conservative value of potential differences in the observations due to the view angle, typing when sending the text message, or the presence of notable waves. A standard deviation greater than 0.05 m was found in 0.025% of the LOCSS data (one measurement) (Table S1, supplemental material). In Bangladesh, the gauges in Tanguar Haor and Khajura Baor needed to be repositioned during the data collection period due to the rapid desiccation that caused some areas to dry out completely during the dry months. In these cases, we repositioned the reference height for each lake associated with the shift in local datum to create a unified water surface elevation time series (See supplemental information Figure S1). We verified and manually removed outliers presented in the time series for other data sources (i.e. USGS, ARHN, and RVBR). For each time series, we extracted the data in the same range of time available in the L2 product.

#### 3.1.2. Nadir altimeter level-2 processing

To compute the WSE time series using Altis software, we created a polygon at each crossing between the satellite ground-track and a lake or reservoir defining a virtual station. This polygon uses the average lake contour and the satellite ground-track crossing as a reference and extends around 3 km outside the lake contour. We ensured in this way that all observations from the L2 footprint associated with the lake were included within the polygon. Some lakes had multiple crossings (Table 2).

Over each virtual station and for each measurement date, we calculated the median of all the WSE within the polygon, computed from the Ice-1 retracker (Bamber et al. 1994), a threshold retracker based on amplitude defined by the Offset Centre of Gravity (OCOG) method (Wingham et al. 1986). In addition, we applied atmospheric and geophysical corrections provided in the L2 file. The corrections are specifically due to the characteristics of the media in which altimeter radar signal is propagated (i.e. atmospheric refraction due to the dielectric properties of the ionosphere, the dry gas component, the water vapor, and the cloud liquid water content of the troposphere), and the Earth surface (i.e. crustal vertical motions due to the solid Earth and pole tides) (for more information, see Crétaux et al. 2017). We worked with the WSE relative to the ellipsoid as we used WSE change (Section 3.2).
<figure><img src="image_24.png" /></figure>

When more than one virtual station was identified over the same lake or reservoir, we used the time series from the virtual station with more observations. This was done to reduce the potential noise that some virtual stations have. Similarly, we have two LOCSS lakes with two gauges each (i.e. Lake Phelps and Lake Mattamuskeet). We evaluate each gauge individually to check for consistency.

### 3.1.3. Explanatory variables preprocessing

Transect length was calculated as the intersection between the nominal satellite ground track and the average lake extent. Depending on the lake, we used lake polygons from SWOT PLD, HydroLAKES, and the SNIRH database for Brazilian reservoirs. In one case, Tanguar Haor in Bangladesh, the lake extent was missing in existing databases, we calculated the area using the method described by Ahmad et al. (2020). This algorithm uses backscattered-based thresholding in Sentinel-1 SAR Ground Range Detected (GRD) images. Prior to the thresholding, the SAR angle is bounded within 31.7° to 45.4° to decrease the signal-to-noise ratio. Then water pixels are those with a backscatter of less than 13 dB. This threshold value was chosen following the work of Liu (2016) in which different backscattered values were examined considering multiple land covers surrounding the water bodies. From the lake polygons, we extracted the lake area.

To account for topographic roughness, we used the topographic roughness index (TRI) in the areas surrounding each lake using a 1 to 5 km buffer. Before extracting the buffer, we masked out the average area of the lake to only consider the topography around the lake. The maximum buffer distance was selected to cover a substantial part of the altimeter footprint that was also representative of the topography surround- ing the lake (Section 3.1.2). TRI is defined as the square root of the sum of the square differences between a central pixel and its surroundings as a metric to account for topographic heterogeneity. TRI was derived using the algorithm implemented by Riley, Degloria, and Elliot (1999), available through QGIS v 3.22 software (https://www.qgis.org/en/site/). QGIS uses the Geospatial Data Abstraction Library (GDAL) for raster and vector geospatial analysis.

To account for the presence of water in the land surrounding the lake, we use the 80% probability water occurrence pixels calculated by Pekel et al. (2016). We masked out the lake extent and generated a buffer at 5 km. Within that buffer, we count all the water pixels over the total area of the buffer. We accounted for the variability of the lake water level using the difference between the maximum and the minimum water elevation from each time series covering the entire period, which is also defined as the maximum amplitude of the time series (APL<sub>wh</sub>). The number of altimeter observations used to generate the time series, and the number of matching altimeter and in-situ observations were extracted from the nadir altimeter preproces- sing and the comparison between nadir altimeter and in-situ observations, respectively.

## 3.2. Matching nadir altimeter with in-situ observations

To match the time series from in-situ observations to the nadir altimeter time series dates, we first looked at the frequency of each time series. When daily gauge data was available we extracted the gauge measure- ments related to the time at the altimetry crossing. This is not possible for the LOCSS gauges due to the irregular sampling. Then we checked the linear interpolation method used in previous work (Biancamaria et al. 2017) to match in-situ observations with the nadir altimeter time series. However, this method works best when in-situ observations are relatively close in time to satellite overpasses, which is sometimes not the case for LOCSS, and for some reservoirs. Given the irregular sampling of some in-situ observation time series, we used a window of 10 days around each altimeter WSE date (i.e. 5 days prior, 5 days after a nadir altimeter WSE date including time). We chose the closest in-situ value to the nadir altimeter WSE data within the window to avoid a linear interpolation between two data points far in time. When the distance in time was the same for two values around the altimeter WSE date, we interpolated within those values. We tested 1 to 10-day window sizes to evaluate the effect of interpolating values that were far in time. We chose the window size that included enough observations around the date and where the effect of adding or removing a point was minimal in smoothing the resulting time series (Figure S2).

To compare nadir altimeter and in-situ WSE observations, we computed the WSE change by subtracting the mean of each time series (i.e. removing the bias), as our goal was to assess how well altimeters can track variations in water level within a particular lake. To calculate the mean value of each time series, we use only the data involved in the comparison to ensure we capture the same
<figure><img src="image_25.png" /></figure>

temporal scale (i.e. the same degree of variability). This approach allowed us to include in-situ data even when only available in a local vertical datum, as is the case for some LOCSS lakes. We discarded comparisons with less than seven matching data points to better justify and analyze the results.

### 3.3. Evaluation metrics

To quantify the degree of agreement between the altimeter and the in-situ WSE change time series, we considered the unbiased Root Mean Square Error (ubRMSE) and the Pearson correlation coefficient, R. The Root Mean Square Error, RMSE, or total error reports account for systematic error (i.e. the bias) and random error, which represents the variance (i.e. systematic error). We worked with WSE change obtained by subtracting the mean of each time series as described in section 3.2 Therefore, the systematic error is removed from the RMSE, which corresponds to ubRMSE. The Mean Error, ME (Equation 1), and the Variance of Error, VE (Equation 2), quantify the systematic and random errors, respectively, and RMSE accounts for these two (Equation 3) (Reyes et al. 2017). Therefore, the ubRMSE is presented in equation 4.

$$ME = \sum_{i=1}^{n} e_i/n \qquad (1)$$

$$VE = \sum_{i=1}^{n} (e_i - ME)^2/n \qquad (2)$$

$$RMSE = \sqrt{\sum_{i=1}^{n} e_i/n} = \sqrt{ME^2 + VE} \qquad (3)$$

$$ubRMSE = \sqrt{VE} \qquad (4)$$

Where $e_i=z_i - o_i$ be the error at each time i, z = altimeter WSE change values, o = in-situ WSE change values observed at the lake, and n be the number of time validation values at each lake-orbit combination.

We used R, to quantify the strength of the relationship between the altimeter WSE change and the in-situ WSE change. The selection of R is further detailed in the supplemental material section S3. Pearson correlation is calculated with equation 5.

$$R = \frac{Cov(Z, O)}{SD_Z SD_O} \qquad (5)$$

Where, Cov = Covariance, SD = Standard Deviation. The last letter represents the values to which each statistic is applied. Z = altimeter WSE change values, and O = in-situ WSE change values observed at the lake.

To evaluate how well low ubRMSE represents the accuracy of altimeter data, we compared the ubRMSE with the amplitude of the in-situ WSE change of each time series (i.e. the difference between the maximum and the minimum WSE change), APL<sub>hw</sub>. We calculated the portion of the ubRMSE over each amplitude (Equation 6).

$$ubRMSE_{ratio} = \frac{ubRMSE}{APL_{hw}} \qquad (6)$$

### 3.4. Exploring factors affecting the evaluation

A synthesis of the method and the data used to explore the factors affecting the evaluation is shown in Figure 2.

We used the Random Forest (RF) algorithm (Breiman 2001) to identify the level of importance that each factor may have in the strength of the relationship between WSE change derived from the altimeter and from the in-situ observations, and unbiased RMSE (i.e. R and ubRMSE). The summary of RF and its variable of importance estimation is based on previous work by Grömping (2009); Altmann et al. (2010); and the documentation of scikit-learn packaged for Python (https://scikit-learn.org/stable/index.html) used to implement this approach. We provide the relevant elements of this implementation, but the reader is referred to these materials for details.
<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /><figcaption>**Figure 2.** Approach to explore factors affecting the evaluation. Factors considered (right data input symbol): water level variability APL<sub>hw</sub>, calculated as the total amplitude in the time series (1); transect length (2) and Waterbody area (3); surface roughness (4) represented as topographic roughness index, TRI; number of matching observations (5); water nearby the lakes (6), accounts for the water pixels in a 5 km buffer; and number of altimeter observations after filter outliers (7).</figcaption></figure>

RF is a supervised algorithm, which means it fits a model with a set of predictors based on a known response during a training phase. It uses the fitted model to evaluate the response of new predictor values in the testing phase. During the training phase, RF builds a set of decision trees created by partitioning a randomly selected sample of factor variables and their values into multiple groups called nodes down to terminal nodes. RF is random because it selects a random sample of data to generate each decision tree and random criteria to make the partitions in the tree. It is called a forest given its bootstrapping feature (i.e. the final prediction is an ensemble of the predictions at each tree). Once the trees are built, the predicted response is estimated following the path of the decision tree from the root to the terminal nodes of each tree. This predicted response at each tree is calculated as the average response in the terminal node. Different metrics can be used to select the best quality of the split, which is determined using a loss or optimization function. In our implementation, we choose to minimize the RMSE.

Let D be the total dataset (i.e. pair predictor factors and response variable). We trained RF with 75% of D (D<sub>train</sub>) and evaluated using the remaining 25% (D<sub>test</sub>), where D represents each lake's time series. This
<figure><img src="image_28.png" /></figure>

process was randomly performed and repeated 1000 times for each response variable (i.e. R and ubRMSE) to increase the random selection of RF in ranking the factor of importance.

We used the Permutation of Importance algorithm, PIMP, implemented in scikit-learn for Python, to rank factor importance across the trees. PIMP inspects each RF, measuring the contribution of each factor to the performance of the fitted model. The algorithm shuffles the order of each dataset in the model and computes a metric score compared with the model's score metric (Altmann et al. 2010). We found PIMP more appropriate for our analysis because 1) the multiple orders of variables are selected based on maximizing the trees' accuracy at each RF, i.e. minimizing the variance; and 2) to allow for multiple combinations of the order of factors in multiple RF and explore the level of agreement. The algorithm shuffles the order of each dataset in the model and computes a metric score compared with the model's score metric (Altmann et al. 2010). Let s be the scoring metric (i.e. RMSE score) of each factor in the RF fitted model, k, the number of times the dataset is shuffled, and $s_{i,j}$, the scoring metric calculated at each shuffle, i, and for each factor j. For each shuffled $D_{test,k}$, the feature of importance of each factor j, $fi_j$, is computed as Equation 7:

$$fi_j = s - \frac{1}{k} \sum_{i=1}^{k} s_{i,j} \quad (7)$$

# 4. Results

## 4.1. Evaluation of nadir altimeter WSE

The median ubRMSE of water level change was 0.15 m and the median R 0.88, where R presents more variability in lakes monitored by LOCSS relative to the national datasets of lakes and reservoirs (Figure 3A). Disaggregating the evaluation metrics by each group of datasets, we found more dispersion in the ubRMSE,

<figure><img src="image_29.png" /><figcaption>**Figure 3.** Summary of the results in the nadir altimeter evaluation. A. Results of evaluation metric R by each dataset's group. B. ubRMSE results by each dataset's group. Dots show the distribution of the values. Average R is 0.83 ± 0.16 and ubRMSE 0.22 ± 0.21 m. C. Relationship between ubRMSE and lake variability measured as the maximum amplitude of each time series APL<sub>hw</sub>.</figcaption></figure>
<figure><img src="image_30.png" /></figure>

for the Brazilian reservoirs, ranging from 0.09–0.96 m, than in the other datasets ([0.09–0.24] for National Datasets, and [0.07–0.78] m for LOCSS) (Figure 3B).

In general, ubRMSE is less than 30% of the lake water variability, APL<sub>hw</sub> (i.e. APL measured as the maximum amplitude of the time series) (Figure 3C). ubRMSE is higher in lakes with higher water level variability (i.e. maximum amplitude of the time series), although it is similar relative to APL<sub>hw</sub>. The relation ubRMSE/APL<sub>hw</sub> is greater than 20% in 5 lakes and 1 reservoir (Lakes Catfish, Balashur, Deep Quarry, Kahura Baor, and Açude Boa Vista's reservoir). In these lakes, R is less than 0.65 and is not significant in all these cases. Lake area for these lakes varies from 0.24 to 63.55 km².

Figures 4-6 presents the results for each of the 27 lakes. Although R and ubRMSE are obtained by comparing only the matching observations, Figures 4-6 include the in-situ time series available in the

<figure><img src="image_31.png" /></figure>

**Figure 4.** Evaluation of altimeter WSE time series in LOCSS lakes by gauge. Notice one lake can have more than one gauge. Each panel presents the time series and results for each gauge. **indicate not significant R in the evaluation (i.e. p-value ≥ 0.05). Comparisons were performed only in matching observations (Figure S6). Each plot shows all the in-situ data for the period of analysis. A line connects two in-situ observations if these are 10 or less days close to each other.
<figure><img src="image_32.png" /></figure>

<figure><img src="image_33.png" /></figure>

**Figure 5.** Evaluation of WSE change in lakes whose water level is reported in national datasets from the U.S. and Argentina by satellite overpass. Different panels with the same lake name happen when a lake has more than one satellite overpass. The comparison of water level change between altimeter and in-situ observations shows generally strong relationships. Comparisons were performed only in matching observations (see Figure S7). Each plot shows all the in-situ data for the period of analysis. A line connects two in-situ observations if these are 10 or less days close to each other.

evaluation range. The matching in-situ and nadir altimeter WSE change observations are provided in Figures S6 to Figure S8 in the supplemental material.

Across all 27 lakes, R was significant (p-value < 0.05) in 81% of lakes. Generally, for all the lakes in which R was not statistically significant, the correlation result is less than 0.65. Despite being not significant, only one of the reservoirs showed no clear correspondence between altimeter WSE change and in-situ data (Açude Boa Vista reservoir) even though Sentinel-3B overpasses it (Figure 6G). The other case corresponds to Grays Lake (Figure 4E), in which Sentinel-3A does not directly overpass the lake (Figure S9).

The Brazilian reservoirs present the best results of R (R > 0.97 above the 25th percentile) (Figure 3A). Among the Brazilian reservoirs, Açude Atalho (Figure 6E) results in the highest ubRMSE (0.96 m). For this reservoir, prior to 2019 we found no consistency between nadir altimeter and in-situ data (Figure S10). In Açude Araras prior to July 2018, the altimeter signal did not match in-situ observations (Figure S10).

Among the smaller lakes (area less than 20 km²), Half Moon showed the best R (0.88) while ubRMSE/APL<sub>hw</sub> was less than 0.2 (ubRMSE 0.068) during the months in which the lake is not frozen. In the smaller lakes (area less than 20 km²), APL<sub>hw</sub> ranged from 0.52 to 2.56 m and ubRMSE represents less than 25% of APL<sub>hw</sub>.
<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /><figcaption>**Figure 6.** Evaluation of WSE change in Brazilian reservoirs by satellite overpass. Different panels with the same lake name happen when a lake has more than one satellite overpass. \*\* indicate not significant R in the evaluation (p-value<0.05). Comparisons were performed only in matching observations (Figure S8). Each plot shows all the in-situ data for the period of analysis. A line connects two in-situ observations if these are 10 or less days close to each other.</figcaption></figure>

## 4.2. Factors influencing the evaluation

Factors influencing the accuracy of nadir altimeters were tested with the permutation of importance algorithm, which evaluates how much a single value contributes to (high fi) or degrades (very low to negative fi) the model score. We found that WSE variability as represented by APL<sub>hw</sub> is the most important factor contributing to R and ubRMSE (Figure 7). However, the rank of importance varies relative to the metric used as a response variable in the RF algorithm. As contributors to R, the factors ranking higher besides APL<sub>hw</sub> are, in order of importance, the number of matching observations between the altimeter and the in-situ data, the topographic roughness (represented by TRI), and the water pixels outside the lake in their surroundings. For ubRMSE, the most important factors in order after APL<sub>hw</sub> are TRI, lake area, number of matching observations, transect length, and water pixels surrounding the lake. These results were consistent even when the metric assessing permutation of importance accuracy changed to the root mean square (Figure S11). When R is the response variable, lake area, number of altimeter observations, and transect length have a very low and almost equal contribution to R. For ubRMSE, the variable that contributes the least is the number of altimeter observations.
<figure><img src="image_36.png" /></figure>

<figure><img src="image_37.png" /><figcaption>**Figure 7.** Factor of importance impacting the nadir altimeter evaluation with in-situ observations. The x axis corresponds to the feature of importance, fi. Metric R and ubRMSE are the response variables of each of the 1000 combinations of RF algorithms.</figcaption></figure>

# 5. Discussion

In this study, we considered 88 lakes located in Argentina (areas between 9.03–82.24 km²), US (0.24–158.36 km²), Canada (0.37–96.48 km²), and Bangladesh (3.51–66.1 km²), and 7 reservoirs from Brazil (2.01–74.07 km²) (Figure 1). A summary of the results for all lakes can be found in the supplemental material (Figure S12). 27 out of the 88 lakes were used explicitly to evaluate the performance of Sentinel 3 satellites and Jason 3 in observing water surface elevation changes (Section 2.1 and Section 3.1). We combined these evaluation results with results from 61 additional lakes to test factors impacting the evaluation metrics.

## 5.1. Nadir altimeter evaluation

Results of this study reinforce that, in general, modern nadir altimeters are capable of measuring water level variations even in lakes smaller than 1 km². Our ubRMSE results are comparable with other studies that report ubRMSE lower than 1 m in lakes (Nielsen, Andersen, and Ranndal 2020) and RMSE similarly below 1 m in reservoirs (Ribeiro Neto et al. 2021), but our results extend these observations to smaller lakes and suggest that in these lakes (< 1 km²) ubRMSE values are generally substantially less than 1 m. We further evaluate ubRMSE relative to the total water surface variability APLhw, finding that ubRMSE represents up to 30% of APLhw. The relatively low ubRMSE values observed in most lakes, combined with a high R, suggest that ongoing improvements have substantially improved the capabilities of nadir altimeters such as Sentinel-3A and 3B in data processing algorithms (e.g., implementation of OLTC).

Nadir altimeter evaluation over Brazilian reservoirs was performed mostly after 2018. Initially, after computing the available time series in the Açude Araras reservoir (Figure S10), we found noise in the signal at the beginning of the water level time series. This behavior resulted in an increase in the ubRMSE. Açude Araras started operations in 1958 (Rodrigues and Magnel, 2019) and experienced a drought during 2012–2017, which impacted the water level change detection by Jason-3 and Sentinel-3. This impact on the performance has been reported by Ribeiro Neto et al. (2021), who also evaluated the performance of Jason-2 over this reservoir. Wet sand can cause water-like echoes when the body is empty, which is conducive to outliers (de Fleury, Kergoat, and Grippa 2023).

We found a poor performance of altimeter WSE change in two reservoirs, Açude Atalho and UHE Machadinho, during our study period (Figure S10 and Figure 6K, respectively). At Atalho reservoir, Jason-3 low performance happened when the tracking command control was operating in closed loop and improved once it was shifted to open loop tracking control in September 2020 (Boitard et al. 2020) (Figure
<figure><img src="image_38.png" /></figure>

S10B). Open loop tracking command controls the reception window of the altimeter, allowing better identification of water surface elevation (Le Gac et al. 2021). In the case of UHE Machadinho, the survey of this reservoir with Sentinel-3A was done in closed loop tracking mode at the beginning of the mission. The complex topography led to mismeasurements of around half of the satellite passes as the altimeter got locked on surrounding hills. To better monitor UHE Machadinho, it was decided to pass this reservoir to open loop tracking mode with the OLTC update V5 (March 2019) (Details on OLTC updates can be found at https://www.altimetry-hydro.eu/learnmore), but the tracking command value was based on an inaccurate lake database, missing the reservoir backscattered signal from that moment. The issue was solved in the next OLTC update onboard (V6 August 2020), and UHE Machadinho has been regularly monitored by Sentinel-3A since then. We removed the inconsistent values of the problematic periods from the analysis, significantly increasing the correlation coefficient (from 0.37 to 1) and reducing ubRMSE (from 24.22 m to 0.21 m).

Some of our results provide an update on prior analyses of altimeter performance in our study lakes. For example, Arsen, Cretaux, and Abarca-Del-Rio (2015) used water surface elevation of Lake Rosario in Argentina to evaluate the performance of Envisat, producing an R of 0.06 and RMSE of 5.4 m (Arsen, Cretaux, and Abarca-Del-Rio 2015). We obtained consistently better accuracies and levels of agreement with Sentinel-3A in the two orbits that overpass the lake (i.e. R of 0.66 and ubRMSE of 0.12 m). This improvement demonstrates the enhanced capabilities of the nadir altimeter in more recent missions, including through use of open loop tracking (Biancamaria et al. 2017, 2018; Le Gac et al. 2021). Another reason for such improvement is the preprocessing (i.e. before comparisons) steps in the WSE nadir altimeter signal. Rather than a pure automatic process, as the one used in Arsen, Cretaux, and Abarca-Del-Rio (2015), in this work, we filtered the anomalies using the results from Altis software after exploring the time series.

High RMSE for some time series could be due to multiple factors. For Jason-3, some sensor saturation could occur, impacting the waveform and making it impossible to accurately compute the range. The instrument footprint could be multiple kilometers wide in LRM mode or in the across-track direction in SAR mode. Therefore, various water bodies and specular targets could be present in the radar footprint and send back energy to the instrument. In these cases, multiple peaks will be present in the waveforms (e.g., Biancamaria et al. 2017; Crétaux et al. 2017). Ice-1 retracker will only provide range for one of these peaks, which might not correspond to the studied lakes. The use of a new retracker more adapted to these complex waveforms (e.g., Boy et al. 2022), using ancillary data, might help to lower RMSE.

In general, lakes and reservoirs observed by national agencies produced consistently high correlation, while those monitored by LOCSS presented more variation. This variation in the strength of the relationship between WSE change from the altimeter and the in-situ observations can be attributed primarily to the smaller lake level variability in lakes monitoring by LOCSS than in other lakes. If lake water level variability is of a similar magnitude to the random error from the satellite observations, which is sometimes true in small natural lakes, then it will be more challenging to accurately detect these water level variations. Given that the LOCSS monitoring network has been operating since 2017 with irregular sampling, another factor contributing to the results is the number of matching in-situ and altimeter observations, which is often lower than for lakes and reservoirs monitored by national agencies. Nevertheless, the results also showed the ability of nadir altimeters to identify lake water level changes in small lakes, most of them monitored by LOCSS, with an average R = 0.6.

## 5.2. Level of importance

We systematically evaluated the level of importance of seven variables (i.e. variability of the surface water, transect length, lake area, topographic roughness, presence of water in the land surrounding the lake up to 5 km, number of altimeter observations used to generate the time series, and number of matching altimeter and in-situ observations) in impacting R and ubRMSE of nadir altimeter evaluations in 88 lakes distributed across the American continent and Bangladesh. We found that for the two metrics, the variability of the surface water level, expressed as the amplitude of the time series, is the most important factor impacting good R and ubRMSE. Lake variability allows to identify how good ubRMSE is. Depending on the magnitude of the lake water variability, a small ubRMSE can represent more of that variability.

We found that the factors that best explain lake-to-lake variations in altimeter performance in this study are not always those commonly explored in previous studies. Lake area, which has often been analyzed in
<figure><img src="image_39.png" /></figure>

previous studies (Gao et al. 2013; Nielsen, Andersen, and Ranndal 2020; Nielsen et al. 2017; Ribeiro Neto et al. 2021), is not a major contributing factor in R and ranked third in ubRMSE. Previous work has suggested different results regarding the impact of lake area in the evaluation. While lake area does not seem to have a dominant effect on Sentinel-3A's ability to capture lake level variations calculated by Nielsen, Andersen, and Ranndal (2020), Ribeiro Neto et al. (2021) found a relation between reservoir area and RMSE (i.e. the larger the area, the smaller the RMSE). However, Ribeiro Neto et al. (2021) questioned the causality of this finding given the small sample size of reservoirs in their study (20 in total). This difference between Ribeiro Neto et al. (2021) and our result could be explained by the level of specularity of the studied lakes. More water at the nadir would mean potentially more energy backscattered toward the satellite if the lake surface is very specular (i.e. low roughness of the lake at the radar wavelength scale). However, lake roughness can change considerably in time, because of, for example, wind speed, and can even be quite heterogeneous in space. Therefore, a higher lake area does not necessarily mean more energy backscattered to the signal and a more accurate WSE. Such effects in space and time have been observed in the recent Surface Water and Ocean Topography (SWOT) satellite mission data (e.g. Chen 2024), which is a swath altimeter, providing an image of WSE, contrary to the nadir altimeter. Similar effects affect Ku-band nadir altimetry data (in a different manner) and explain our results.

Transect length ranked less important in our analysis compared to the other variables analyzed (not important in R, ranking fifth in ubRMSE). A possible explanation of the small contribution of lake area and transect length to high R and ubRMSE is the improvement in the nadir altimeter techniques to correctly adjust the range window (International Altimetry Team 2021). In addition, the response variables for the random forest algorithm are relatively good (i.e. high R and low ubRMSE) and statistically significant. In our analysis, there is only one lake in which the satellite does not pass directly over the lake. Previous studies argue the influence of track location relative to the water body as a source of decreasing accuracy. However, in some cases, results are inconclusive (Ribeiro Neto et al. 2021, Gao 2015). TRI was found to be the second most important variable in explaining the ubRMSE. As the nadir altimeter signal can return to the sensor from different places, rough topographies may increase the ubRMSE (Biancamaria et al. 2018). Our results suggest that the variability of the water surface level should be considered a key variable in determining the nadir altimeter capabilities.

Our work did not attempt to formally compare different nadir altimeter processing modes (LRM and SAR) and their impact on small lakes. However, a comparison based on 27 lakes was performed to verify whether the two datasets could be used together in the order of importance approach. Despite not finding statistically significant differences that impact the outcome of the RF algorithm, we identified a substantial improvement in accuracy at Grays lake, the only off-nadir lake, in our records, when using the SAR mode (Figure S9). R was -0.12 and ubRMSE 0.34 m, when using LRM data, compared to 0.77 and 0.19 m respectively in SAR mode. The capabilities of SAR mode with the enhanced along-track resolution have resulted in an improvement of altimeter accuracies in lakes (Nielsen et al. 2017).

### 5.3. Perspectives on improving WSE observations from space

New mechanisms to process altimeter data offer the potential to continue improving the accuracy of radar altimeters. Some examples are the Lake Physical Processing, LPP, a method that considers parameters such as acquisition and surface roughness in order to improve the retracking model (Boy et al. 2022). Applying this method over SAR data resulted in RMSE of less than 10 cm over lakes smaller than 20 km². Another example is the use of Fully Focused SAR (FFSAR) in Sentinel-6 mission that further increases the along-track resolution of SAR altimetry to the theoretical limit of half the antenna length (Egido and Smith 2017). This is an area of exploration for future nadir altimeter evaluation over small water bodies. New research (Nilsson and Nielsen 2024) has revealed the potential of Sentinel-6 to accurately observe water levels (obtaining ubRMSE of 6.4 and 12.3 cm for High- and Low Resolution Mode respectively, in lakes between 20 and 500 km²). Another direction of research is the use of deep learning approaches to derive WSE from altimeter waveforms. To our knowledge, only Niño et al. (2022) have investigated this approach. They computed a more robust estimation of WSE compared to Ice-1 using a deep neural network. However, it is computationally expensive, it is difficult to generate a large enough training database, and difficulties exist in applying this method to measurements taken in closed-loop mode. Therefore, a lot of work is still needed to go in this direction and
<figure><img src="image_40.png" /></figure>

provide an operational WSE time series processing chain as easily as it is currently done with the approach used in our study.

Our ability to observe water storage variations in small lakes will be substantially aided by the launch in 2022 of the SWOT satellite, which is specifically designed for this purpose (Biancamaria, Lettenmaier, and Pavelsky 2016; Chen 2024). Because SWOT's orbit repeats every 21 days, it does not provide sufficient temporal observations globally for all purposes. By combining SWOT data with nadir altimeters data as suggested here, our ability to observe many small lakes frequently and with high accuracy is likely to substantially improve our understanding of surface water hydrology at a global scale.

## 6. Conclusion

In this study, the results suggest that, with some caveats, it should be possible to directly observe water levels in many more lakes worldwide than are included in past studies with altimeters such as Sentinel-3A/B and Jason-3. Most previous studies of lake water surface elevation and water storage using nadir altimeters have focused mainly on lakes larger than 50 km² (e.g., Nielsen, Andersen, and Ranndal 2020; Shu et al. 2021; Yao et al. 2023). This approach may still be necessary when attempting to analyze time series dating back to the launch of TOPEX/Poseidon in the early 1990s and considering that most lake water is stored in large lakes. However, small lakes can provide important measures of local and regional water balance variations and are therefore potentially useful for understanding global hydrological patterns.

To improve the accuracy of WSE from nadir altimeter, the use of more recent retracker algorithms and nadir altimeter SAR data processing adapted to small lakes will be necessary (e.g., the approach proposed by Boy et al. (2022)). We were able to increase the representation of small lakes by using citizen scientists' data. In exploring nadir altimeter accuracy, regular sampling frequency is key for lakes with high water level variability. However, in lakes with small WSE change, interpolation methods are an alternative. As more citizens engage in this type of initiative, it is more likely to explore ungauged systems and better understand the cases in which nadir altimeter is an adequate tool to estimate WSE. Nevertheless, applications of WSE from nadir altimeters at small lakes still have some limitations. We suggest proceeding with caution for forecasting applications. Using the nadir altimeter as exploratory observations can help identify needs for local monitoring. In addition, linking in-situ and nadir altimeter observations can be useful to improve resolution when irregular sampling occurs in places in which WSE nadir altimeter accuracy is high. Our order in the factor of importance indicates that lake variability is an important factor impacting WSE nadir altimeter accuracy. Depending on the range of variability, ubRMSE can represent more of that variability and be a key factor along with topographic roughness and water features surrounding the lakes. Despite the novelty of our results, we acknowledge some limitations to our approach. Most of the world's lakes are located in northern latitudes, and the available in situ data comes mainly from those regions. However, it is still necessary to have a better representation of tropical and southern latitudes to understand better nadir altimeter capabilities in these regions and the potential applications.

## Acknowledgments

We thank LOCSS Citizen Scientists who collect and report the data, as well as our local partners who work directly with citizen scientists at each location. Specifically, thanks to the Water Development Board of Bangladesh and the Alberta Lake Management Society in Canada. In North Carolina - USA, thanks to NC State Parks (Or Jones Lake State Park and Phelps State Park); US Forest Service (or Croatan National Forest); US Fish and Wildlife Service (or Mattamuskeet National Wildlife Refuge). In Illinois, - USA, Chicago Metropolitan Agency for Planning; Lake County Health Department; DuPage County Forest Preserve District. In Washington state, thanks to WA State Parks (or Lake Wenatchee State Park); and City of Sammamish Parks and Recreation. We thank some of our citizen scientists who continuously measure the water levels at specific lakes: Richard Normandeau - Half Moon Lake Alberta; Dan Grigas - DuPage County, IL Forest Preserve District; Darren Kelly - Bay Tree Lake; Alana Bartolai - Lake County IL Health Department; and Holly Hudson - Chicago Metropolitan Agency for Planning. We also thank the Sistema Nacional de Información Hídrica (https://snih.hidricosar.gentina.gob.ar/Filtros.aspx#), the Sistema Nacional de Informações sobre Recursos Hídricos (SNIRH) (https://www.snirh.gov.br/hidroweb/apresentacao) and the United States Geological Survey, USGS, (https://www.sciencebase.gov/catalog/item/577445bee4b07657d1a991b6) for making the data publicly available. We thank Daniel Moreira from the Geological Survey of Brazil, who guides us to access Brazilian reservoirs.
<figure><img src="image_41.png" /></figure>

## Author contributions

CRediT: **Angélica M. Gómez**: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing; **Sylvain Biancamaria**: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Supervision, Validation, Visualization, Writing – review & editing; **Tamlin Pavelsky**: Conceptualization, Funding acquisition, Project administration, Resources, Supervision, Writing – review & editing; **Karina Nielsen**: Data curation, Formal analysis, Investigation, Methodology, Validation, Visualization, Writing – review & editing; **Grant Parkins**: Resources, Writing – review & editing; **Megan Lane**: Resources; **Shahzaib Khan**: Data curation, Resources, Writing – review & editing; **Faisal Hossain**: Resources, Writing – review & editing; **Rajat Bhattarai**: Resources; **Sheikh Ghafoor**: Resources; **Jean-François Crétaux**: Writing – review & editing; **Carlos Yanez**: Writing – review & editing; **Nicolas Picot**: Resources, Writing – review & editing.

## Disclosure statement

No potential conflict of interest was reported by the author(s).

## Funding

This research was funded by the NASA Citizen Science for Earth Systems Program (CSESP) Grant number [80NSSC22K1913], managed by G. Guala.

## ORCID

Angélica M. Gómez http://orcid.org/0000-0001-7073-4841
Sylvain Biancamaria http://orcid.org/0000-0002-6162-0436
Tamlin Pavelsky http://orcid.org/0000-0002-0613-3838
Karina Nielsen http://orcid.org/0000-0002-0035-1869
Grant Parkins http://orcid.org/0000-0002-8167-6787
Megan Lane http://orcid.org/0009-0005-4051-4203
Shahzaib Khan http://orcid.org/0000-0002-0851-0385
Faisal Hossain http://orcid.org/0000-0001-6192-3157
Rajat Bhattarai http://orcid.org/0009-0000-5519-2693
Sheikh Ghafoor http://orcid.org/0000-0001-7175-1619
Jean-François Crétaux http://orcid.org/0000-0002-4038-7719
Carlos Yanez http://orcid.org/0000-0002-1664-9205
Nicolas Picot http://orcid.org/0000-0001-5224-7660

## Data and software availability statement

All the nadir radar altimeter evaluation data used for Section 3.4 and cited as Table S2 is publicly available on Zenodo (https://doi.org/10.5281/zenodo.11087254). (License Creative Commons Attribution 4.0 International). Software to produce the results of the paper and data (input and results) is available at Zenodo (https://doi.org/10.5281/zenodo.11174371).

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