## 3 Earth Surface Modelling Advances and Links with EO Datasets
### Inland-Waters  
Globally, there are approximately 117 million lakes (>0.002 sq.km) with a combined surface area of \(~{}5\times 10^{6}\) sq.km, which is approximately 3.7% of the Earth's non-glaciated land surface [224]. Despite their relatively small spatial extent, lakes can have a disproportionately large influence on the climate, in particular within their near-vicinity [225; 226]. This occurs as a result of lakes influencing surface energy exchange with the atmosphere, which differs to those from soil or vegetated surfaces [227]. Some lakes also freeze seasonally, resulting in considerable changes in surface albedo and thermal capacity and, as a result, alterations in lake-climate interactions [228]. Although traditionally neglected in land surface models within NWP, primarily because of the computational expense, community efforts in recent years have improved our understanding of the importance of lakes and have highlighted their added-value in simulating accurately regional climatic variations [225; 229; 230]. Research aimed at introducing inland water bodies (lakes, rivers and coastal  
Figure 19: Explained spatial variance in satellite-derived soil moisture memory (e-folding time scale i.e., lag at which the autocorrelation of SMAP soil moisture drops below 1/e) within circles of radius \(0.3^{\circ}\) as a function of the standard deviation of gridded United States Geological Survey (USGS) shallow carbonate karst coverage in the corresponding circles. The karst data have been interpolated to the 9 km resolution SMAP Level-3 data grid, and the circles for comparison are centered on each land grid cell between 29–40N, 104–83W. Purple circles indicate the means of spatial explained variance in soil moisture memory within bins of width 2.0% centered on each 1.0% step of the abscissa; cyan circles are for the 90 th percentile values. Dotted lines are best-fit linear regressions. All correlations are significant at the 99% confidence level. waters) into the operational model at ECMWF has started by considering a medium-complexity scheme that satisfies the operational constraint of having low computational cost. FLake [231], a shallow-water scheme originally applied to lakes, was introduced into the IFS in progressive steps. This model is a particularly appropriate choice for NWP as it predicts the vertical temperature structure and mixing conditions in lakes of various depths and on time scales from a few hours to multiple years, while maintaining a relatively low number of prognostics variables (seven in total). The model is intended for use as a lake parameterisation scheme in NWP, climate modelling and other prediction systems for environmental applications. FLake has been implemented in the operational regional weather forecast models of Deutscher Wetterdienst (the German weather service), Finnish Meteorological Institute (FMI), Norwegian Meteorological Institute (Met.no) and Swedish Meteorological and Hydrological Institute (SMHI), and is used for research at several meteorological services across Europe including Meteo-France [232] and UK Met Office [233], and is included in several climate models. The most important external variable for lake model FLake is depth (bathymetry or mean depth at least). There were several attempts to derive lake depths from satellite observations. Already in [234], an approach for determining lake depths by using spaceborne Synthetic Aperture Radar (SAR) images was developed. For those lakes that freeze completely to the lake depth some time in the winter, the simulated ice growth curve providing the ice thickness allows to estimate the lake's maximum water depth [234]. In [235], the same idea was used and lake depth of shallow sub-Arctic lakes and ponds was determined by using Landsat Thematic Mapper (TM) and European Remote Sensing (ERS)-1 Synthetic Aperture Radar (SAR) data. Landsat TM image is used to map lake bathymetry and multi-date ERS-1 images acquired during winter are utilised to determine when and which lakes freeze to the bottom during winter.