Calibration of Parameter Perturbations for Ensemble Prediction Using Data-Consistent Inversion

Abstract Parameter perturbations are an attractive way to represent model errors in an ensemble prediction system due to their ability to target precise sources of uncertainty. However, most parameters do not have a linear impact on the model outputs, and therefore the distributions chosen to perturb their value influence the climatology of the ensemble system. In particular, distributions centered on the parameter’s default value are not always sufficient to prevent the ensemble average from deviating from the deterministic model. In this study, we propose to use inverse problem theory to adapt the parameter distributions in order to produce unbiased ensembles. Specifically, we use a method called data-consistent inversion to solve the inverse problem in a simplified framework of low dimensions. The updated distribution of two microphysical parameters of the model AROME is computed thanks to an ensemble of single-column simulations of a radiation fog case. This updated distribution, as well as two other standard distributions—uniform and lognormal—is then used to produce ensembles of single-column and 3D simulations. Results indicate that both 1D and 3D ensembles produced with the updated distribution are better centered on the deterministic AROME model than with the uniform or lognormal distributions, which demonstrates the potential benefit of the data-consistent inversion framework for designing parameter perturbations. However, many challenges remain to be addressed to apply this method in operational ensemble systems, especially if a large number of parameters need to be perturbed. Significance Statement Meteorological forecast uncertainty is often estimated with the help of ensemble systems, which provide sets of alternative scenarios for a given prediction. Ensembles are produced by introducing perturbations in the system which represent various sources of error. Among them, parameter perturbations are a popular way to target uncertainty coming from the meteorological model itself. However, the way in which parameter values are randomly perturbed influences the ensemble output statistics because the response of the model to changes in a parameter’s value is often nonlinear. The purpose of this study is to design appropriate distributions from which parameter values can be sampled to produce unbiased ensembles. We show how, in a simplified framework, using inverse problem theory can help to construct such distributions.