# A Multisensor Approach to Satellite Monitoring of Trends in Lake Area, Water Level, and Volume
## 2 Materials and Methods
### Lake Surface Area
Finally, the fractional extent of water for mixed pixels along shorelines (i.e., the boundaries between land and water) was estimated using a linear mixture model [7]. This produced two time series (nFrac and eFrac, derived from NDLI and ELI, respectively) of maps showing the fractional (0.0 to 1.0) extent of water within each pixel. Summing up the fractions for each pixel of a lake and multiplying by the pixel area (based on the sensor's spatial resolution) yielded the surface area for each lake on each date. For the period prior to the first Terra MODIS image (February 2000), the coarser-resolution AVHRR sensor was used in a similar process. Due to the lack of a blue-wavelength band on AVHRR, only an NDLI-based AVHRR dataset could be constructed, and it was used with both the NDLI and ELI versions of the MODIS time series. The same process was used to derive much finer-scale maps of lake area from a series of Landsat images. These data (30 m resolution, or nearly two orders of magnitude finer in resolution than MODIS) were used to validate the coarser-resolution lake area measurements. Likewise, the same process was used with two dates of even higher resolution (10 m)  
Figure 4: Schematic diagram of the data and methods used in this study. SPOT-5 multispectral images (2006-11-07 and 2008-04-20) to determine the appropriate threshold (-0.04) for the MODIS ELI land/water mask, by comparing MODIS land/water masks with a variety of different thresholds to area measurements from the two SPOT-5 images. The AVHRR (1998-2000) and MODIS (2000-2017) lake surface area time-series were merged using a nonparametric locally estimated scatterplot smoothing (LOESS) model, interpolating area to a daily timestep using the minimal value of \(\alpha\) = 5 data points (nominally 40 days in the post-2002 era when both Terra and Aqua were available) to minimize smoothing. Figure 5 shows this LOESS model for the period of the transition from AVHRR to MODIS (1999-01-01 to 1992-01-01). While the AVHRR data are coarser-resolution and noisier, the alignment between it and MODIS is very close. The NDLI- and ELI-derived lake area time series (nFrac and eFrac) were compared based on their detrended residuals, i.e., the individual observations minus the LOESS model, which are here considered to represent noise. Because the magnitude of this noise increases as the lake circumference (and zone of mixed pixels along the shoreline) increases, the residuals were normalized by dividing them by the square root of lake area, giving units of km\({}^{2}\)/km. These normalized residuals were used to evaluate the relative performance of NDLI and ELI as sources in the lake area algorithm. The results are presented in more detail in Section 3, but are shown and discussed briefly here because the choice between NDLI and ELI affected the subsequent methods. Examination of the residuals showed three extreme outliers among the 750 MODIS image dates: Julian days 161 and 169 in 2012, and day 353 of 2007. Visual examination of these images confirmed that these should be excluded from the analysis due to artifacts in the MOD13 source data. In addition, the lake area values from both NDLI and ELI for Aqua MODIS day 361 were anomalously noisy, yielding larger residuals in many years than other dates (Figure 6), potentially as a result of the 16-day compositing process. (The NASA Land Processes Distributed Active Archive Center (LP DAAC) reported a known issue with the MODIS MYD13Q1 v6.0 16-day composite product, resulting in \"unexpected missing data in the last cycles of each year\". The issue is being addressed in the reprocessed v6.1.) All the day 361 images were thus removed as well, and the nFrac and eFrac time series were recalculated. Figure 5: Combination of lake surface area measurements from the Advanced Very High Resolution Radiometer (AVHRR; orange squares) and MODIS (blue diamonds) with interpolation using a locally estimated scatterplot smoothing (LOESS) regression model (black line) at a daily timestep. Area (in km\({}^{2}\)) is total for all six lakes.