Simulation of Lake Complexes Using a Probabilistic Hydrologic Model with Super-Resolved Calibration

We developed a Probabilistic Hydrologic Model (PHM) capable of simulating lake complexes comprised of tens-of-thousands or more individual closed-basin lakes and wetlands. It is applied to simulate the hydrologic response of lake systems to the broad range of climatic variability of a 105-yr period (1901-2005) in the Prairie Pothole Region of North Dakota. The model is calibrated with a Genetic Algorithm by comparing the simulated results with observed lake area-frequency power-law relationships derived from Landsat images and water depths from seven individual lakes. The simulated lake behaviors show good agreement with the observations under average, dry, and wet climatic conditions. A mass balance cross comparison for Wetland P1 in the USGS Cottonwood Lake area suggests the PHM successfully simulates key hydrologic processes such as precipitation, evaporation, runoff, and groundwater flow. For example, the contributions of groundwater inflow/outflow fluxes to the wetland computed by the PHM match well with those computed by MODFLOW with differences less than 3%. Analysis over the last century shows that the power laws of medium to large lakes changed intra-annually and interannually as a function of climate. Major droughts and deluges have the ability to create marked variability of the power law function (e.g. up to one and a half orders of magnitude variability from the extreme Dust Bowl Drought to the extreme 1993-2001 deluge). Analyses also reveal that the linear power law fails for very small lakes and the features of the small-lake departure from power law are closely related to the climatic conditions. This new model provides a novel tool to examine the response of the behavior of a complex of closed lakes across size scales. Moreover, we demonstrate a powerful method for model calibration, which is especially suitable for complicated models with a large number of parameters, numerous data points, and multi-objective problems.