Necessary conditions for algorithmic tuning of weather prediction models using OpenIFS as an example

Algorithmic model tuning is a promising approach to yield the best possible forecast performance of multi-scale multi-phase atmospheric models once the model structure is fixed. The problem is to what degree we can trust algorithmic model tuning. We approach the problem by studying the convergence of this process in a semi-realistic case. Let M(x, θ) denote the time evolution model, where x and θ are the initial state and the default model parameter vectors, respectively. A necessary condition for an algorithmic tuning process to converge is that θ is recovered when the tuning process is initialised with perturbed model parameters θ′ and the default model forecasts are used as pseudo-observations. The aim here is to gauge which conditions are sufficient in a semi-realistic test setting to obtain reliable results and thus build confidence on the tuning in fully realistic cases. A large set of convergence tests is carried in semi-realistic cases by applying two different ensemble-based parameter estimation methods and the atmospheric forecast model of the Integrated Forecasting System (OpenIFS) model. The results are interpreted as general guidance for algorithmic model tuning, which we successfully tested in a more demanding case of simultaneous estimation of eight OpenIFS model parameters.