Effect of satellite altimetry sampling error in estimating reservoir storage and outflow

Abstract The potential of satellite imagery to complement the in-situ gauge networks in monitoring freshwater is well established. However, Temporal Sampling (TS) intervals of satellite altimetry impart significant uncertainty compared to daily or sub-daily in-situ gauge measurements. This study examines the effect of infrequent TS from satellite altimetry, i.e. 10-Day (Jason-2/3), 21-Day (SWOT), 27-Day (Sentinel-3A) and 35-Day (SARAL/AltiKa) for the evaluation of reservoir storage and outflow. The metrics of Relative Error (RE), Root Mean Squared Deviation (RMSD), and the correlation between altimetry-based and in-situ observations have been used for the evaluation. Results show that the altimeters having a high TS frequency, such as 10-Day or 21-Day, performed well with RMSD less than 0.2 m and correlation more than 98% in estimating satellite-based storage and outflow compare to coarse 27-Day or 35-Day TS. This study improves the understanding of sampling error in satellite altimetry, which has immense potential for future SWOT altimeter mission.


Introduction
Reservoirs are the primary source of water for irrigation, hydropower production and mitigate downstream effect of hydrological extremes (Adhikari et al. 2010). Continuous monitoring of reservoir operations is needed to ensure freshwater availability during inter-seasonal months, especially during the Indian summer season (February to May). The number of gauge stations is often sparse and poses challenges in installation and maintenance, especially in remote areas. Besides, observations face restrictions due to data sharing policies among transboundary nations (Hossain et al. 2014). Additionally, human intervention and insufficient information regarding upstream water operations, i.e. storage and outflow from the reservoirs, lead to a significant challenge in water resource management such as flood to the downstream (Hossain et al. 2014). Due to these limitations, satellite altimetry is the sole accessible source, playing an essential role in hydrological monitoring Alsdorf et al. 2003;Papa et al. 2010;Siddique-E-Akbor et al. 2011). Satellite radar altimetry has shown immense potential to complement the in-situ gauge network for monitoring local hydrological processes . Satellite altimetry missions such as Topography Experiment (TOPEX)/Poseidon (Fu et al. 1994), European Remote Sensing (ERS) (Francis 1995), Environmental Satellite (ENVISAT) (Dubock et al. 2001), Joint Altimetry Satellite Oceanography Network (Jason) (Shum et al. 1995), Satellite with ARgos and ALtiKa (SARAL/AltiKa) (Frappart et al. 2015), and Sentinel-3A/3B (Donlon et al. 2012) have been extensively used for monitoring water levels in large reservoirs, rivers, and floodplains Frappart et al. 2010;Papa et al. 2012). However, the coarse Temporal Sampling (TS) interval of existing altimetry satellites induce uncertainty when comparing daily or sub-daily in-situ gauge measurements (Roux et al. 2008). A significant source of uncertainty stems from the infrequent TS of altimetry satellites, which is 10-Day for T-P/Jason-2/3, 27-Day for Sentinel-3A/3B, and 35-Day for ERS-1/2/ENVISAT/SARAL/AltiKa Biancamaria et al. 2010;Papa et al. 2010).
The Surface Water and Ocean Topography (SWOT) altimetry mission (to be launched in mid-2022) will enhance the satellite-based monitoring of reservoirs by providing high spatial and temporal resolution data (Biancamaria et al. 2016). SWOT will use 2-D wide-swath, Ka-band interferometric synthetic aperture radar to observe surface water extent along with elevations, which will be used to estimate storage (Fu et al. 2012). Additionally, the wide swath of SWOT altimetry will improve TS frequency to more than once (depending upon latitude) in 21 days, which shall allow water storage change monitoring even at the sub-monthly periods (Solander et al. 2016). The SWOT data has an expected measurement error of 10 cm for water elevation, 1 cm:1km in river slope, and 20% on water mask extent (Andreadis et al. 2007;Biancamaria et al. 2010;Durand et al. 2010). However, the effect of the TS frequency of satellite altimetry in predicting reservoir storage and outflow operations remains unknown (Dettmering et al. 2020). The present study focuses on quantifying the changes in altimetry-based reservoir storage and outflow estimation accuracy due to the infrequent TS interval of existing (Jason-2/3, Sentinel-3A, SARAL/AltiKa) and future SWOT altimetry mission over India. As the temporal sampling is a function of orbital geometry, this comparative study between previous altimetry missions and future SWOT mission will enhance understanding the number of sample points of data collected by each mission. Furthermore, this study will be useful for the data-scarce region or transboundary river basin.

SWOT hydrology simulator
In the current study, the synthetic SWOT temporal sampling over the reservoirs has been simulated using Large-Scale Hydrology Simulator (LSHS) developed by Centre National d'Etudes Spatiales (CNES). The LSHS is an open-source tool that enables end-users to generate proxy SWOT data with fairly representative characteristics. The steps involved in generating proxy temporal sampling of SWOT are as follows.
Step 1: The water extent of reservoirs has been used from HydroLAKES opensource data, which is designed as a digital map repository of lakes with a surface area of at least 10ha (available for download at http://www.hydrosheds.org) (Messager et al. 2016). Further, the polygon shapefiles of water bodies have been used as input for the simulator.
Step 2: The configurational modification in LSHS, such as defining the reference gauge height (obtained from Central Water Commission) and river flag (RIV_FLAG: 0 for lakes and reservoirs), has been done to initialize the simulator.
Step 3: Finally, the proxy SWOT pass over the reservoirs has been simulated using a water body shapefile and corresponding science orbit defined for future SWOT pass.  The methodology involves generating reservoir storage and outflow times series from in-situ gauge data using the GDR orbital pass of Jason-2/3, SARAL/AltiKa, Sentinel-3A and simulated track (Table 2). To simulate the sampling error, the in-situ gauge data time series at case study region is sub-sampled by 'flying' each of the altimetry satellites and by extracting the in-situ values as observed at the overpass time of each altimetry satellites. The time series sampled by the altimeter satellite platforms are compared with the original time series. The time series of satellite-based reservoir storage and outflow has been generated such that there is no measurement error, and the sole focus is on the TS interval of each altimetry satellite. The number of satellite altimetry observations over the reservoirs per repeat orbit have been shown in Table 3. So, firstly, the analysis has been conducted using the root means squared deviation (RMSD) (1) and absolute relative error (RE) (2) using satellite-based reservoir storage (S alt ) and in-situ storage (S in-situ ). The S alt is in-situ gauge storage on the day satellite orbit pass over the reservoir. And S in-situ is the median of values from the day of satellite pass till the next orbital pass concerning the TS of altimeters.
where b y t is satellite altimetry-based reservoir storage (S alt ) andy t is observed or reference value from in-situ storage (S in-situ ) over time t.
Secondly, the outflow from the reservoir has been calculated using mass balance between hydrologic controls (Frappart et al. 2010) to evaluate the TS error in outflow (3). where O is reservoir outflow, I is precipitation-induced runoff flowing into the reservoir, DS is the change in storage, S t is the water storage at time t, S t-n denotes water storage n days prior to time t, E is reservoir loss largely due to evaporation. The TS error in reservoir outflow has been estimated using RE between satellite-based outflow (O alt ) and in-situ outflow (O in-situ ) (Figure 3).

Results and discussion
The Taylor diagrams comparing the metrics for the 10-, 21-, 27-and 35-Day TS of satellite altimeters over reservoirs have been shown in Figure 4. It quantifies a concise summary of how closely the S alt matches with the S in-situ using RMSD, correlation, and standard deviation (SD). We observed that the observations with fine TS such as 10-Day and 21-Day appeared on the lower-right corner of the Taylor diagram, representing the higher accuracy zone compared to course TS of 27-Day and 35-Day. A 10-Day TS has shown a high correlation ranging from 0.95 to 0.99, low RMSD (0.1 m to 0.5 m), and good agreement of SD with in-situ storage of reservoirs. In comparison, the 35-Day TS resulted in RMSD of 0.15 m for R1 with the maximum of 1.99 m for R3. We observed that the rapid variation in the reservoir storage (Supplementary material, Figure S1) affects the TS error. The altimeters having coarse TS (i.e. 27-Day and 35-Day) would not be able to capture the storage variability till 27th and 35th day respectively and result in high TS error. The correlation in R2 was found to be a minimum of 0.51 with an SD of 0.3 m due to sudden change in water storage variation from 0.15 billion cubic meters to 1.5 billion cubic meters, especially during the monsoon season (June to September). Contrary, the gradual variation in the storage of reservoir R1 and R5 during the pre- monsoon (March-May) and post-monsoon (October-December) season resulted in a good correlation of 0.99 for 10-Day TS. The number of altimetry cycles that passed over the reservoir is the function of latitude and track spacing which finally affects the TS error. In addition, the number of altimetry orbital passes increases with the size of a reservoir, which interns into more TS. As in R3, due to large size, the SARAL/AltiKa and Sentinel have more orbital passes (Table 3) compared to R1, R4 and R5. However, the size of the reservoir is the crucial factor if considered, along with the latitude (Dettmering et al. 2020). As in the case of the R1 and R4, the latitude of reservoirs lie near the crossover of SARAL/AltiKa hence acquired two orbital passes (Table 3) even though the areas are smaller among all reservoirs (Table 2). For 27-Day TS, an increment in the number of observations (Table 3) has shown a better correlation with in-situ observations than 35-Day TS. 27-Day TS has shown improved RMSD by 35% (1.2 m) for R3, with correlation increased by 33% (0.68) for R2 compared to 35-Day TS. Comparatively, the 21-Day repeat orbit of SWOT has 2 to 6 times TS intervals due to wide swath (Supplementary material, Table S1), resulting in the highest sampling frequency compared to existing altimetry missions (Supplementary material, Figure S2 and Table 2). In 21-Day TS, the RMSD has estimated less than 0.2 m and correlation more than 98% over all the reservoirs except R3. The reservoir R3 exhibits the maximum RMSD of 0.97 m because of the steep water storage variation ranging from 1 billion cubic meters to 7 billion cubic meters, especially during the post-monsoon season. Even though the TS of SWOT is higher than all altimeters due to the wide swath, the higher anomalies in water storage in less time span introduces error in the satellite-based storage estimation.
The comparison and quantification of RE due to TS of altimetry satellite over reservoirs have been shown in Figure 5. The x-axis lists the altimetry missions, and the y-axis Figure 4. Taylor diagram showing the correlation, root-mean-square difference (RMSD), and standard deviation between satellite-based storage (S alt ) and in-situ storage (S in-situ ) in reservoir R 1 , R 2 , R 3 , R 4 , R 5 and R 6 .
represents the RE between the S in-situ and S alt . For 10-Day TS, the RE in reservoir storage ranged from 2.5% in R6 to 20% in R4. And for 35-Day TS, a minimum of 10% RE has been encountered within the interquartile range in R6 and a maximum of 32% in R5. The higher RE represents the overestimation of satellite-based storage due to fewer observations in a 35-Day TS over the reservoir (Supplementary material, Figure S3). We observed the increase in TS frequency from 10-Day to 35-Day (Table 3), the RE impounded from 2.5% to 10% in the R6 reservoir. Similarly, with an increase in TS frequency from 27-Day to 21-Day over R1 (Table 2), the RE reduced from 15% to less than 5%. Additionally, a maximum of 10% RE has been observed in 21-Day TS in R4 and R5.
The error associated with reservoir storage and irregular TS also affects reservoir outflow ( Figure 6). The effect of TS intervals in the outflow analysis using reservoir storage (3) has been examined over reservoirs R3 and R5. We have observed the outflow of reservoir R3 from the year 2015 to 2019 and found an improvement in the RE with an increase in the number of TS observations. In 10-Day TS, the RE of 2% in storage increased to 75% in estimating the reservoir outflow ( Figure 6). However, in 21-Day wide-swath TS, the RE in outflow was found less than 25% due to an increase in TS observations (Table 2) and repeated orbit (Table 3).
Similarly, in reservoir R5, the RE in reservoir outflow has been found to increase with the decrease in TS of altimeters from 10-Day to 35-Day. In Figure 5, we observed that in reservoir R5, the RE increased from reservoir storage to outflow by 5% in 21-Day, 20% in 10-Day, 38% in 27-Day, 45% in 35-Day repeat orbit. The results show that high TS frequency such as 10-Day (Jason-2/3) and 21-Day (SWOT) have less error increment from storage to outflow than 27-Day and 35-Day repeat orbit.

Conclusion
This study has analysed the error associated with TS frequency of altimeters for 10-Day (Jason-2/3), 21-Day (SWOT), 27-Day (Sentinel-3A) and 35-Day (SARAL/AltiKa) and shows the significant impact in estimating reservoir storage and outflow. The altimetry satellites having a high TS frequency, such as 10-Day (Jason-2/3) and 21-Day (SWOT), have less error increment in storage and outflow compared to 27-Day and 35-Day repeat orbit. Additionally, the coarse TS leads to overestimation during satellite passes at high water storage in two continuous repeat orbits and vice-versa. However, for the satellite altimetry, a 10-Day or 21-Day repeat orbit has performed well for all the reservoirs.
Since the SWOT mission will have wide-swath and exhibit the highest number of observations per revisit time, compare to existing altimetry missions. We have analysed the satellite-based storage and outflow data extracted from in-situ when the SWOT altimetry orbital pass over the reservoir. We found that in 21-Day TS, the RMSD is less than 0.2 m except for R3, and the correlation is more than 98% for all the reservoirs. In the outflow analysis from reservoirs R3 and R5, we found that the outflow from the reservoir is highly sensitive to errors available in storage due to TS of altimetry. We found that the TS error in the storage of R3 propagated to more than ten times in the estimation of outflow from the reservoir in 35-Day TS interval while in SWOT (21-Day TS), the error has not exceeded more than five times of storage for both the reservoir R3 and R5. We observed the RE in estimating reservoir storage and outflow majorly affected by two factors, such as the number of TS observations and repeat orbit. The overall comparison among altimeters shows that the future SWOT mission would perform better in estimating reservoir storage and outflow due to wide-swath TS. This study improves the understanding of TS error in altimetry-based monitoring of Indian reservoirs due to the infrequent TS interval of satellite altimetry. The accuracy of altimetry-based measurement of reservoir storage and outflow also depends on other factors such as measurement error, geophysical correction, and propagation corrections, which have not been considered here and need to be addressed in future works.