A minimalist model of terminal lakes: Qinghai Lake (China) and Lake Chad (N Africa)

Abstract

The ratio of the areas of a terminal lake to its total basin provides a geomorphological measure, which characterises the geobotanical state of water limited climates. A minimalist model of this lake area ratio is introduced combining the water balances of lake and land, the Budyko-Schreiber rainfall-runoff chain over land and, as a closure, the land and lake potential evaporation to be of similar magnitude. The following results are analysed. (i) Model diagnostics quantify a dryness threshold separating water from energy limited climate regimes, which coincides with an upper bound for the area ratio of terminal lakes to remain hydrologically closed. (ii) Model validations for Qinghai Lake and Lake Chad demonstrate model and observed water flux budgets to be in close agreement. (iii) Finally, a paleo-climate sensitivity study for Lake Chad demonstrates that the minimalist model appears to be a viable tool for future and paleo-climate estimates based on lake area ratio changes only and a single reference water flux. Furthermore, a stochastic interpretation of the rainfall-runoff chain allows estimates of water flux variability.