Modelling of underwater light in freshwater lakes using survival and failure time analysis

Abstract

1. This study presents a new approach to modelling subsurface irradiance using concepts from survival and failure time analysis. The model applies a modified Weibull distribution function to predict downwelling irradiance. Data sets from forty‐seven Norwegian sites show extremely high coefficients of determination, up to 99.99%, when analysed by the Weibull model.2. The uncritical use of a single kd value to model underwater light conditions is likely to result in poor estimates of received irradiance. This error may amount to several hundred per cent. The practice of force‐fitting linear least‐squares regressions to log‐transformed irradiance data inevitably leads to highly biased estimates of the true fraction of incident irradiance entering the water.3. Wave effects causing fluctuations of subsurface irradiance are modelled with synthetic data and compared with field observations. Fluctuations of surface elevation by waves produce skewed frequency distributions of the underwater light field. The result of these effects, which are to reduce the accuracy of estimated model parameters, can be largely eliminated by carefully designing field procedures used for the acquisition of subsurface light data.