Underwater light profiles in some New Zealand lakes: A comparison of log‐linear and Weibull models

Abstract

Using irradiance profile data from 11 New Zealand lakes of different water clarity and reflectance, we tested the fit of linear regression and Weibull models to underwater light profiles. The diverse optical characteristics of the lakes provided a wider test of the applicability of the model to lakes other than the more humic stained lakes used in an earlier Norwegian investigation. Measurements comprised down and upwelling vector irradiance, scalar irradiance, and in‐air vector irradiance sampled at a frequency of once every 2 seconds with a data‐logger. Log‐linear regression models proved inferior to the non‐linear Weibull function in several respects. Owing to appreciable curvature of the light profiles, log‐linear models produced significant bias for estimates of depth‐specific irradiance, in spite of the extremely close regression fits (r² ≥ 99%). The completely specified linear model (log‐linear regression including the intercept and incident irradiance, LR2) yielded significantly biased predictions of V _m (the midpoint of the euphotic zone, taken as 10% of incident irradiance), whereas the Weibull predictions were statistically unbiased. For the 1% irradiance depth (V _eu), the LR2 model almost coincided with Weibull estimates. Employing linear models is likely to give biased estimates of underwater irradiance at depths above V _eu. We recommend that, where precise estimates of underwater irradiance are required, for example when modelling light‐dependent biological processes, non‐linear rather than the traditional log‐linear models should be applied.

Keywords:

• modelling
• non‐linear estimation
• underwater irradiance
• Weibull function

Notes

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