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.

Highlights

  • We investigate the performance of Derivative Free Optimisation by Least Squares” (DFO-LS), a local, derivative-free optimisation algorithm which has been designed for computationally expensive models with irregular model5 data misfit landscapes typical of biogeochemical models

  • We find that DFO-LS successfully 10 recovers 5 of the 6 parameters in approximately 40 evaluations of the misfit function, while Covariance Matrix Adaptation Evolution Strategy” (CMA-ES) needs over 1200 evaluations

  • We find that the performance of DFO-LS is not significantly affected by observational sparsity, fewer parameters were successfully optimised in the presence of observational uncertainty

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Summary

Introduction

Ocean biogeochemical models are a key tool in understanding the cycling of nutrients and carbon in the ocean. In global ocean biogeochemical models the complex interactions between biota, nutrients, oxygen and carbon are typically heavily parameterized The performance of such models can be improved by either subjective manual or systematic tuning of the parameter values against observations. CMA-ES was applied by Kriest et al (2017) to optimise six parameters within the Model of Oceanic Pelagic Stoichiometry (MOPS; Kriest and Oschlies, 2015), by minimising a globally averaged misfit incorporating annual mean dissolved inorganic phosphate, nitrogen and oxygen. This constituted one of the first successful attempts at systematic tuning of a relatively complex global 45 biogeochemical model. Onto a regular grid, introducing significant error, especially in regions such as the Southern Ocean with poor data coverage. 60 The structure of the paper is as follows: Section 2 describes the methodology, Section 3 the results, 4 the discussion and 5 the conclusions

Ocean biogeochemical model
Biogeochemical model parameters
Optimisation Algorithms
CMA-ES
DFO-LS
Misfit functions
Optimisation experimental design and solver settings
Results
Noise-free experiments
Discussion
345 Acknowledgements
10: Update covariance matrix
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