A dilemma of the uniqueness of weather and climate model closure parameters

Abstract

Parameterisation schemes of subgrid-scale physical processes in atmospheric models contain so-called closure parameters. Their precise values are not generally known; thus, they are subject to fine-tuning for achieving optimal model performance. In this article, we show that there is a dilemma concerning the optimal parameter values: an identical prediction model formulation can have two different optimal closure parameter value settings depending on the level of approximations made in the data assimilation component of the prediction system. This result tends to indicate that the prediction model re-tuning in large-scale systems is not only needed when the prediction model undergoes a major change, but also when the data assimilation component is updated. Moreover, we advocate an accurate albeit expensive method based on so-called filter likelihood for the closure parameter estimation that is applicable in fine-tuning of both prediction model and data assimilation system parameters. In this article, we use a modified Lorenz-95 system as a prediction model and extended Kalman filter and ensemble adjustment Kalman filter for data assimilation. With this setup, we can compute the filter likelihood for the chosen parameters using the output of the two versions of the Kalman filter and apply a Markov chain Monte Carlo algorithm to explore the parameter posterior distributions.

• model tuning
• Markov chain Monte Carlo
• likelihood
• filter formulation

4. Acknowledgements

We would like to acknowledge the National Center for Atmospheric Research for making the Data Assimilation Research Testbed available on-line. The research has been financially supported by the Academy of Finland (project numbers 127210, 132808, 133142, 134935 and 134999) and the Centre of Excellence in Inverse Problems Research. Additionally, this work was funded by the European Commission's 7th Framework Programme, under Grant Agreement number 282672, EMBRACE project, and the Nessling Foundation.