# A Multisensor Approach to Satellite Monitoring of Trends in Lake Area, Water Level, and Volume
## 2 Materials and Methods
### Lake Surface Area  
The process used to estimate lake surface area was based upon that described in [7]. For this study, the MODIS MOD13Q1/MYD13Q1 16-day composite product (hereafter \"MOD13\") was used, rather than the Level-1B imagery of [7]. MOD13 includes two vegetation indices, the normalized difference vegetation index (NDVI) and the enhanced vegetation index (EVI; [61]), as well as surface reflectance in selected MODIS bands, data quality flags, and other data. Two lake indices were derived from MOD13, the aforementioned NDLI [18; 23] and the new ELI. NDLI is given by Equation (1):  
\[NDLI=\ \frac{R_{RED}-R_{NIR}}{R_{RED}+R_{NIR}}\, \tag{1}\]  
where \(R_{RED}\) and \(R_{NIR}\) are the spectral reflectance or spectral radiance in red and near-infrared wavelength bands, respectively. Note that NDLI is equivalent to a sign-reversed version of NDVI; i.e., values of NDLI >0 are increasingly likely to be water, and are equivalent to NDVI <0. Due to the high correlation between visible wavelength spectral bands, NDLI is generally very similar to the NDWI [20; 21] but does not require the use of a green-wavelength band. Similarly, the new index ELI (Equation 2) is a sign-reversed version of EVI:  
\[ELI=G\times\frac{R_{NIR}-R_{RED}}{R_{NIR}+C_{1}R_{RED}-C_{2}R_{BLUE}+1}\, \tag{2}\]  
where \(R_{NIR}\), \(R_{RED}\), and \(R_{BLUE}\) are the near-infrared, red, and blue wavelength bands, \(C_{1}\) and \(C_{2}\) are wavelength-specific aerosol resistance terms (6 and 7.5, respectively, for MODIS, [61]), and G is a gain factor of \(-2.5\) (versus +2.5 for EVI). High values of ELI (= low values of EVI) are increasingly likely to represent water. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data Source** & **Resolution** & **Dates** & **Role** \\ \hline Terra Moderate Resolution Imaging & & 403 images: & \\ Spectroradiometer (MODIS) 16-day vegetation & 250 m & 2000-02-18 to & Lake surface area \\ index composite V.006 (MOD13Q1) [55] & & 2017-08-13 & \\ \hline Aqua MODIS 16-day vegetation index & & 349 images: & \\ composite V.006 (MYD13Q1) [56] & 250 m & 2002-07-04 to & Lake surface area \\ \hline Advanced Very High Resolution Radiometer (AVHRR), Level-1B Local Area Coverage (LAC) & 1100 m & 62 images: & \\  & 1998-09-26 to & Lake surface area \\ \hline Landsat-5 Thematic Mapper (TM), Landsat-7 & & 100 images: & Lake surface area \\ Enhanced Thematic Mapper (ETM+), and Landsat-8 Operational Land Imager (OLI) [57] & 30 m & 2017-09-15 & (validation) \\ \hline SPOT-5 High Resolution Geometric (HRG) & & 2006-11-07 and & Threshold \\ multispectral & 10 m & 2008-04-20 & selection \\ \hline Shuttle Radar Topography Mission (SRTM) & 30 m & 2000-02-11 to & Water level (Lake \\ digital elevation model (DEM) [58] & & 2000-02-22 & 5 only) \\ \hline Advanced Spaceborne Thermal Emission and & & 12 DEMs: & Water level and \\ Reflection Radiometer (ASTER), DEMs from & 15 m & 2014-11-18 to & \\ bands 3N and 3B (AST14 DEM) [59] & & 2017-10-09 & \\ \hline Ice, Cloud, and Land Elevation Satellite (ICESat)-1 Geoscience Laser Altimeter System & 70 m & 54 orbit tracks: & Water level \\ (GLAS) [60] & & 2009-03-29 & (validation) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Remote sensing data sources. For this study, NDLI and ELI were each used to map lake surface area, using the same methodology. Firstly, the data were reprojected to the Universal Transverse Mercator (UTM) zone 36 North coordinate system and subset to the study region. Secondly, a constant threshold value (0 for NDLI, \(-\)0.04 for ELI) was used to create a binary land/water mask for each date. Thirdly, the binary-mask time series was smoothed by comparing each pixel on date \(t\) to its value on dates \(t\)-8 and \(t\)+8 days (i.e., the previous and subsequent MOD13 dataset; prior to the first Aqua image in mid-2002, with only Terra imagery available, this was \(t\)-16 and \(t\)+16). If the pixel's land/water value differed on both the comparison dates, it was switched.