Representing the effects of subgrid-scale variations in bathymetry on light and primary production

Rates of production by primary producers in aquatic ecosystems are strongly affected by light. Traditional models of phytoplankton and other primary producers assume a single, uniform depth and hence uniform light conditions across each grid cell or model box. This introduces an error when the depth of the bed varies significantly within a cell. Accuracy can be improved by using higher-resolution models to allow production across a greater range of depths to be simulated, however, this comes at a considerable cost in terms of model complexity and CPU times. For models with many state variables simulating large domains or long periods of time, this added computational cost may prohibit detailed sensitivity analysis or parameter estimation techniques. Here, a semi-analytical approach to modelling light limitation in aquatic systems is developed and compared with both coarse-resolution and high-resolution models in a simple case study. The model is applied to simulations of both phytoplankton and microphytobenthos in well-mixed, nutrient-replete systems. It is demonstrated that the semi-analytical approach gives results that closely match those of the higher-resolution model, but at a much lower computational cost. In an example phytoplankton model presented here with bathymetry varying by 150% of the mean depth, a single-box model produces a 14% error in the predicted change in phytoplankton concentration over 10 days, while the semi-analytical model reduces this error to only 0.8%.