Time-scale dependence in numerical simulations: Assessment of physical, chemical, and biological predictions in a stratified lake at temporal scales of hours to months

Abstract

We evaluated the predictive ability of a one-dimensional coupled hydrodynamic-biogeochemical model across multiple temporal scales using wavelet analysis and traditional goodness-of-fit metrics. High-frequency in situ automated sensor data and long-term manual observational data from Lake Mendota, Wisconsin, USA, were used to parameterize, calibrate, and evaluate model predictions. We focused specifically on short-term predictions of temperature, dissolved oxygen, and phytoplankton biomass over one season. Traditional goodness-of-fit metrics indicated more accurate prediction of physics than chemical or biological variables in the time domain. This was confirmed by wavelet analysis in both the time and frequency domains. For temperature, predicted and observed global wavelet spectra were closely related, while observed dissolved oxygen and chlorophyll fluorescence spectral characteristics were not reproduced by the model for key time scales, indicating that processes not modeled may be important drivers of the observed signal. Although the magnitude and timing of physical and biological changes were simulated adequately at the seasonal time scale through calibration, time scale-specific dynamics, for example short-term cycles, were difficult to reproduce, and were relatively insensitive to the effects of varying parameters. The use of wavelet analysis is novel to aquatic ecosystem modeling, is complementary to traditional goodness-of-fit metrics, and allows for assessment of variability at specific temporal scales. In this way, the effect of processes operating at distinct temporal scales can be isolated and better understood, both in situ and in silico. Wavelet transforms are particularly well suited for assessment of temporal and spatial heterogeneity when coupled to high-frequency data from automated in situ or remote sensing platforms.