A Half-Order Derivative Based Model of Lake Heat Storage Change

Abstract

Heat storage change (HSC) is a crucial component of lake's thermal energy budget. Conventional temperature profile based models of HSC require location specific parameters such as lakebed topography. Based on the half-order time-derivative formula of heat fluxes, an analytical model was formulated for estimating HSC from water surface temperature and solar radiation without using geography dependent parameters. The proposed model was tested against field measurements at Poyang Lake, a shallow inland lake, which has pronounced seasonal variations in water level and lake area. Our analysis indicates that the model accurately simulates diurnal HSC with a coefficient of determination of 0.94 and a root mean squared error (RMSE) of 77.5 ± 21.6 Wm⁻² for the study period. Larger nighttime RMSE (75.0 ± 26.8 Wm⁻²) than the daytime value (55.1 ± 19.7 W m⁻²) is attributable to larger measurement errors of nighttime turbulent fluxes. The estimation of HSC independent of temperature profile and lake-specific parameters by the proposed model facilitates remote sensing monitoring the HSC of global water bodies.