# A Multisensor Approach to Satellite Monitoring of Trends in Lake Area, Water Level, and Volume
## 2 Materials and Methods
### Water Level, Mean Depth, and Volume  
Water level was derived by cross-referencing the lake surface area dataset (Section 2.2 above) with a digital elevation model (DEM). Based on the water level, mean and maximum depths were calculated on each date, hypsographic curves were computed for each lake, and lake volumes were estimated. Two different methods were used for the water level analysis, and the results were validated using ICESat-1 GLAS laser altimetry data, which were completely independent of the DEM-based methods. The first DEM for the study region was obtained from the SRTM [62] dataset. This DEM was produced using interferometric analysis of synthetic aperture radar (SAR) data from 11-22 February 2000. The basins for Lakes 1-4 had already filled by this date, so the bathymetry of those lakes could not be determined from SRTM. A second DEM was developed from photogrammetric analysis of stereoscopic ASTER bands 3N and 3B. Twelve individual ASTER DEMs were used, from images in 2014-2017 when all lakes except Lake 4 had dried up, thus allowing the bathymetry of each lake basin (except Lake 4) to be mapped directly. The ASTER DEMs had large vertical offsets relative to SRTM (and to each other),  
Figure 6: Comparison of residuals from lake surface area time-series nFrac and eFrac, as a function of the seasonal cycle (Julian Day). (**a**) Normalized residuals (km\({}^{2}\)/km) for all years, by day; (**b**) standard deviation of normalized residuals (km\({}^{2}\)/km) by day. Excluded data from Aqua MODIS Day 361 are shown as open circles. and various other artifacts. The cause of these offsets is undetermined, but they are reflective of the fact that the relative accuracy of these DEMs (i.e., the reported difference in elevation between any two points within a single DEM, compared to their true difference in elevation) is better than their absolute accuracy (the absolute elevations of points in the DEM compared to their true elevations); the latter are expected to be better than 25 m root mean squared error (RMSE) [59]. To prepare these DEMs for use, the following process was followed:  
1. Calculate each ASTER tile's mean and standard deviation of elevation differences from the SRTM DEM, using a subset of the area with no visible artifacts. 2. Adjust the ASTER DEMs to match the SRTM DEM by adding each tile's mean elevation difference, excluding areas that are more than three standard deviations from the SRTM elevation and were not covered by water at the time of the SRTM mission. 3. In the ASTER tile covering the (small) remaining water in the Lake 4 basin, exclude ASTER DEM pixels falling within the extent of the water area. 4. Create an initial mosaic of all ASTER DEM tiles, averaging elevation values in areas of overlap. 5. Aggregate to 150 m spatial resolution, and convert grid cells to points. 6. Delete points in no-data areas (areas where the ASTER DEM was more than three standard deviations from SRTM, or within the remaining Lake 4 water area). 7. Perform a \"tension\" spline interpolation (weight = 0.1, 100 points per region for local approximation) to fill in the gaps. The result was an ASTER DEM mosaic for the entire area, with artifacts removed and the small residual area covered by water in Lake 4 modeled by spline interpolation. This ASTER DEM was used to calculate elevation, depth, and volume for all lakes on all dates, while the SRTM DEM was used as a comparison on Lake 5 only. Table 3 lists the ASTER DEM tiles used in the DEM mosaic. Two different methods were used to estimate water levels from the lake surface area maps and the DEMs. In Method 1, the shoreline (where pixel fractional water extent crossed 0.5) was identified from the eFrac surface area maps, and the mean elevation of this line was found in the DEM(s). In Method 2, the area of pixels at or below each increment of elevation was calculated directly from the ASTER DEM, and then the observed area on a given date (from eFrac) was used to look up the corresponding water level that would produce that observed area.