# A Multisensor Approach to Satellite Monitoring of Trends in Lake Area, Water Level, and Volume
## 1 Introduction
### Objectives  
This study had two overarching objectives. The first was to develop and test methodological improvements in the use of remote sensing for monitoring water storage in lakes. This contributes to the development of an automated system that integrates a wide range of remotely sensed data sources and analytical methods to simultaneously measure trends in lake surface area, water level, and volume, building upon and improving the methods previously described in ([PERSON] et al., 2002). The second objective was to apply these data and methods for a comprehensive assessment of the evolution of the Toshka Lakes over the two decades of their existence, producing daily estimates of each lake's surface area, water level, and volume. To meet these dual objectives, the following tasks were performed:  
Lake surface area assessment:  
* Quantitative comparison of two remotely sensed spectral lake indices, NDLI and the enhanced lake index (ELI), for lake surface area estimation, using an adaptive algorithm for sub-pixel analysis. * Construction of a daily time-series of lake surface area over two decades (1998-2017) from AVHRR and MODIS imagery. * Validation of the AVHRR/MODIS lake surface area dataset in comparison to higher-resolution image sources. Water-level assessment:
* Quantitative comparison of multiple algorithms and data sources for estimating water levels from integration of DEMs and lake surface area datasets. * Construction of a daily time-series of water levels and depth statistics for each lake. * Validation of the water level dataset by comparison to laser altimetry. Lake volume assessment:* Construction of hyposographic curves for each lake, representing the relationship between lake surface area and water level. * Derivation of a daily time-series of lake volume, by cross-referencing the lake surface area dataset and each lake's hyposographic curve. Note that, while the term \"validation\" is used here for the lake surface area and water level assessments, no direct, in-situ measurements of area or water level were available. Instead, in both cases the validation process involved comparison to another remotely sensed data source. For surface area, the measurements made here from coarse-resolution sensors (AVHRR and MODIS) were compared to equivalent measurements from much higher-resolution Landsat images. For water level, the results from different algorithms and DEMs were compared to ICESat-1 GLAS laser altimetry, a completely independent and previously-validated source of water level data [7; 25; 27]. In the course of addressing the first objective, the following hypotheses were tested (stated here informally, rather than in formal null-and-alternative hypothesis language):  
Hypothesis 1: The use of sub-pixel analytical methods allows for coarser-resolution imagery (e.g., AVHRR and MODIS) to produce lake surface area estimates that are compatible with each other and equivalent to those from much higher-resolution imagery (Landsat). Hypothesis 2: A new numerical lake index for multispectral optical imagery (ELI) will yield better (i.e., less noisy) estimates of lake surface area than the existing index, NDLI. Hypothesis 3: DEMs obtained when lakes are at low water-levels, or dry, can be combined with maps of surface area to provide estimates of water level that are similar to those from laser altimetry. Rather than being framed in terms of specific hypotheses to test, the second objective involves production of new datasets, providing a comprehensive, daily record of the dynamic expansion and contraction of the Toshka lakes during the two decades from 1998-2017, encompassing the formation of all six lakes, and the subsequent disappearance of five of the six. Comparison to measured evaporation rates (from nearby Lake Nasser) supports inferences about the relative proportion of water lost to evaporation vs. groundwater recharge. Finally, the results of this study will provide guidance for similar remote-sensing-based assessments of lake hydrology in other regions.