Simple equations to represent the volume - area - depth relations of shallow wetlands in small topographic depressions.

Small topographic depressions have important functions in hydrology and ecology because they store water in the form of shallow lakes, wetlands or ephemeral ponds. The relations between the area A, the volume V, and the depth h of water in depressions are important for evaluating water and dissolved-mass balances of the system. The A–h and V–h relations are usually determined from fine-resolution elevation maps based on detailed survey data. Simple equations are presented in this paper, which can be used to: (1) interpolate A–h and V–h data points obtained by a detailed survey; (2) approximate unknown A–h and V–h relations of a depression from a minimal set of field data without a time-consuming elevation survey; and (3) serve as a geometric model of depressions in simulation studies. The equations are simple power functions having two constants. The first constant s is related to the size of the depression, and the second constant p is related to the geometry of the depression. The power functions adequately represent A–h and V–h relations of all 27 wetlands and ephemeral ponds examined in this paper, which are situated in the northern prairie region of North America. Assuming that the power functions are applicable for other similar topographic depressions, an observer only needs to measure A and h twice to determine the two constants in the equation. The equations will be useful in field studies requiring approximate A–h and V–h relations and in theoretical and modeling studies.