Modeling the Hydrologic Response of a Lake Complex to Climate Change

Remote sensing and GIS results have shown that the numbers and water areas of lakes and wetlands in Prairie Pothole Region (PPR) follow well-defined power laws. Such relationships are helpful in understanding the behaviors of lakes to climatic variations. However, certain limitations exist with power laws derived by using observational approaches (e.g., satellite images and aerial photos) because of issues of image resolution and availability. A new Stochastic Hydrologic Model (SHM) has been developed that is capable of simulating lake complexes comprised of tens-of-thousands or millions of individual closed-basin lakes and wetlands in a homogeneous physiographic region of PPR, here the Missouri Coteau and Prairie Coteau.

The basic component in SHM is a lumped element hydrologic model. With essential enhancements and updates, the SHM is able to stochastically generate a lake complex with defined lake shapes, account for key hydrologic processes contributing to stage and mass loading, and provide plot power laws for the complex for any time or climatic condition. Preliminary simulation results for a lake complex along Missouri Coteau in North Dakota reveals continuous long-term power laws describing the frequency of occurrence of lakes of a given size. The power laws change seasonally and inter-annually as well as a function of climate. Meanwhile, the lower limit of power-law validity has also been examined. Eventually, the linear power law fails when small depressions effectively dry out, especially during hot, dry summer months.