New, general methods to define the depth separating surface water from deep water, outflow and internal loading for mass-balance models for lakes

This paper addresses some fundamental problems related to the structure and function of lakes in general and in mass-balance calculations and modelling in particular. We have presented a new approach to define and differentiate between surface water and deep water. This approach is based on the water depth separating areas where resuspension appears from areas where continuous sedimentation is likely to prevail, the “critical” water depth. We have presented (1) new general algorithms to calculate surface water volume and deep water volume based on the critical water depth and the form of lakes, (2) algorithms to calculate concentrations of matter in the surface water and the deep water compartments, (3) methods to quantify sedimentation by accounting for the mean depths of the surface water compartment and the deep water compartment, (4) approaches to quantify internal loading via resuspension, (5) algorithms for upward and downward mixing between the surface and the deep water compartments, and (6) a new approach to calculate lake outflow of substances. The new algorithm for outflow also accounts for how variations in evaporation and precipitation influence outflow. The model has been critically tested using radiocesium as a tracer, but it should be stressed that all new sub-models are generic and meant to apply to all types of dissolved and suspended materials in lakes. These tests used data from 23 lakes (and 357 data on radiocesium in water, but also in sediments, small fish and on suspended particles) covering a wide limnological domain (latitudes from 42 to 61 V, altitudes from 0 to 1090 m.a.s.l., catchment areas from 0.17 to 114,700 km2, precipitation from 430 to 1840 mm per year; areas from 0.042 to 1147 km2; mean depths from 1.1 to 90 m, pH from 5.1 to 9; K-concentrations from 0.23 to 27.5; total-P concentrations from 8.3 to 100 μg/l and theoretical lake water retention times from 0.02 to 137 years). The model predicts well when empirical data are compared to modelled values, the slope is almost perfect (0.98) and so is the r2-value (0.96).