Estimating time-dependent parameters for a biological ocean model using an emulator approach

We use a statistical emulator technique, the polynomial chaos expansion, to estimate time-dependent values for two parameters of a 3-dimensional biological ocean model. We obtain values for the phytoplankton carbon-to-chlorophyll ratio and the zooplankton grazing rate by minimizing the misfit between simulated and satellite-based surface chlorophyll. The misfit is measured by a spatially averaged, time-dependent distance function. A cross-validation experiment demonstrates that the influence of outlying satellite data can be diminished by smoothing the distance function in time. The optimal values of the two parameters based on the smoothed distance function exhibit a strong time-dependence with distinct seasonal differences, without overfitting observations. Using these time-dependent parameters, we derive (hindcast) state estimates in two distinct ways: (1) by using the emulator-based interpolation and (2) by performing model runs with time-dependent parameters. Both approaches yield chlorophyll state estimates that agree better with the observations than model estimates with globally optimal, constant parameters. Moreover, the emulator approach provides us with estimates of parameter-induced model state uncertainty, which help determine at what time improvement in the model simulation is possible. The time-dependence of the analyzed parameters can be motivated biologically by naturally occurring seasonal changes in the composition of the plankton community. Our results suggest that the parameter values of typical biological ocean models should be treated as time-dependent and will result in a better representation of plankton dynamics in these models. We further demonstrate that emulator techniques are valuable tools for data assimilation and for analyzing and improving biological ocean models.

► Use of emulators for data assimilation and parameter estimation in biological model.
► Clear spatial and temporal dependence of plankton model parameters.
► Improved representation of plankton in ocean models through time-dependent parameters.
► Improved state estimates of emulator in comparison to optimized fixed parameter model.