A derivative-free optimisation method for global ocean biogeochemical models

Abstract

Abstract. The performance of global ocean biogeochemical models, and the Earth System Models in which they are embedded, can be improved by systematic calibration of the parameter values against observations. However, such tuning is seldom undertaken as these models are computationally very expensive. Here we investigate the performance of DFO-LS, a local, derivative-free optimisation algorithm which has been designed for computationally expensive models with irregular model-data misfit landscapes typical of biogeochemical models. We use DFO-LS to calibrate six parameters of a relatively complex global ocean biogeochemical model (MOPS) against synthetic dissolved oxygen, inorganic phosphate and inorganic nitrate observations from a reference run of the same model with a known parameter configuration. The performance of DFO-LS is compared with that of CMA-ES, another derivative-free algorithm that was applied in a previous study to the same model in one of the first successful attempts at calibrating a global model of this complexity. We find that DFO-LS successfully recovers 5 of the 6 parameters in approximately 40 evaluations of the misfit function (each one requiring a 3000 year run of MOPS to equilibrium), while CMA-ES needs over 1200 evaluations. Moreover, DFO-LS reached a baseline misfit, defined by observational noise, in just 11–14 evaluations, whereas CMA-ES required approximately 340 evaluations. We also find that the performance of DFO-LS is not significantly affected by observational sparsity, however fewer parameters were successfully optimised in the presence of observational uncertainty. The results presented here suggest that DFO-LS is sufficiently inexpensive and robust to apply to the calibration of complex, global ocean biogeochemical models.

A CMA‐ES Algorithm Allowing for Random Parameters in Model Calibration

“…Indeed, Kriest et al (2017) observed the most insensitive parameter subject to their optimization experiment to converge the slowest. The same behavior was recently observed by Oliver et al (2021) who applied an even faster (but less explorative) search algorithm to the same coupled BGC model setup, using twin experiment data. However, fixing some parameters from the start might impact the optimization of the other parameters.…”

“…The TMM represents advection and mixing in terms of transport matrices which are precomputed from an online ocean circulation model simulation. Here, as in Kriest et al (2017) and also in Oliver et al (2021), we apply monthly mean transport matrices from a 2.8° global configuration of the MIT general circulation model (MITgcm), having 15 depth levels (Marshall et al, 1997). MOPS coupled to the TMM simulates globally the concentrations and biogeochemical turnover of seven tracer components, namely phyto-and zooplankton, dissolved and particulate organic matter, phosphate, nitrate and oxygen.…”

“…We provide an efficient way to deal with the given problem by introducing the new R-CMA-ES (a modification of the CMA-ES where R stands for random) in this study. We will examine the effects of the proposed optimization procedure by applying it to the same global BGC model setup as used in Kriest et al (2017) and Oliver et al (2021).…”

Influence of GEOTRACES data distribution and misfit function choice on objective parameter retrieval in a marine zinc cycle model

“…CMA-ES has been shown to be a reliable and highly competitive evolutionary algorithm for both local (Hansen and Ostermeier, 2001) and global optimisation (Hansen and Kern, 2004;Hansen, 2009). It has been tested on real-world problems includ- ing parameter calibration in a biogeochemical ocean model by Kriest et al (2017), whose implementation of CMA-ES in C++ we employ here, via the OptClimSO package (https://doi.org/10.5281/zenodo.5517610; Tett et al, 2013;Oliver et al, 2022). In order to apply CMA-ES to a constrained problem, we use the boundary handling described in Hansen et al (2009), in which boundaries are imposed by adding a penalty function to the calculated misfit when a parameter's distribution mean is out of bounds.…”