New Approaches to the Modelling of Lake Basin Morphometry

Abstract

In lake modelling, a general and useful method of describing variations in area and volume with depth is of fundamental importance to describe processes and properties that change vertically within a given lake. In this work, two mathematical approaches to describe the shape of a lake basin are introduced and tested against empirical data. The two methods require only three easily available input parameters: maximum depth, surface area and volume. The first method is based on a traditional morphometric parameter, the volume development (V d), and the second method on the new hypsographic development parameter (H d). Both methods give area and volume at any depth of a lake and can furthermore be used to estimate lake bottom slopes. Comparisons with empirical area–depth and volume–depth distribution curves from 105 lakes that cover a wide range of lake morphometric characteristics have revealed that the two methods give very satisfactory results. The V d-model yields r 2-values of 0.924 and 0.907 for area and volume description with lake depth, respectively. The corresponding r 2-values for the H d-model are 0.988 and 0.996, respectively. Using the H d-model, an approach has also been developed to test when and by how much it is necessary to correct the empirical volume of a lake given the number of measured strata and basin shape.