Parameter Optimisation in an Ocean Biogeochemical Model

As carbon dioxide emissions are intrinsically linked with global warming, we need to be sure the carbon cycle is represented correctly in the Earth System Models (ESMs) used to predict climate change. The oceans play an important role in the carbon cycle, yet the ocean biogeochemical (OBGC) models simulating this in ESMs are heavily parameterised. These parameters are rarely calibrated to observations in a global OBGC model due to the computational expense, caused by large spin up times necessary for the model to reach equilibrium.

Finding the best parameter values to use which result in the lowest model error to observations is a numerical minimisation problem. These models are very computationally expensive, therefore robust yet efficient optimisation algorithms requiring few model runs are desirable, such as those which don’t calculate derivatives (“derivative-free optimisation”, or DFO). To make the optimisation time shorter, reduced spin up times in the OBGC models are also desirable.

Here we show a comparison of several DFO optimisation methods to calibrate 6 parameters within the Model of Oceanic Pelagic Stoichiometry (MOPS). We compare the performance of the evolutionary algorithm CMA-ES which is a stochastic global optimization method requiring more model runs, to the Py-BOBYQA and DFO-LS (DFO for least squares) algorithms which are local solvers requiring fewer runs. We show how a combination of Latin Hypercube Sampling and the local solver DFO-LS can locate the optimal parameter set in fewer model runs than the global solver CMA-ES.

We also investigate the possibility of reducing the spin up time of MOPS for the optimisation process. If the model error to observations after a short spin up time (such as 500 years) is sufficiently representative for model error after 3000 years, then why spend unnecessary computational time to continue to 3000 years? We show how the model error after various spin up times relate to the model error at equilibrium, and how this relationship is influenced by the parameters you are tuning (see figure), the type and location of the observations you are optimising towards, and which general circulation model you are using to force your OBGC model. This will hopefully indicate to OBGC modellers if they can radically reduce the computational expense of a global optimisation study.