Ocean ensemble forecasting. Part I: Ensemble Mediterranean winds from a Bayesian hierarchical model

A Bayesian hierarchical model (BHM) is developed to estimate surface vector
wind (SVW) fields and associated uncertainties over the Mediterranean Sea. The
BHM–SVW incorporates data-stage inputs from analyses and forecasts of the
European Centre for Medium-Range Weather Forecasts (ECMWF) and SVW
retrievals from the QuikSCAT data record. The process-model stage of the
BHM–SVW is based on a Rayleigh friction equation model for surface winds.
Dynamical interpretations of posterior distributions of the BHM–SVW parameters
are discussed. Ten realizations from the posterior distribution of the BHM–SVW
are used to force the data-assimilation step of an experimental ensemble ocean
forecast system for the Mediterranean Sea in order to create a set of ensemble
initial conditions. The sequential data-assimilation method of the Mediterranean
forecast system (MFS) is adapted to the ensemble implementation. Analyses
of sample ensemble initial conditions for a single data-assimilation period in
MFS are presented to demonstrate the multivariate impact of the BHM–SVW
ensemble generation methodology. Ensemble initial-condition spread is quantified
by computing standard deviations of ocean state variable fields over the ten ensemble
members. The methodological findings in this article are of two kinds. From the
perspective of statistical modelling, the process-model development is more closely
related tophysicalbalances than inpreviousworkwithmodels for the SVW.Fromthe
ocean forecast perspective, the generation of ocean ensemble initial conditions via
BHM is shown to be practical for operational implementation in an ensemble ocean
forecast system. Phenomenologically, ensemble spread generated via BHM–SVW
occurs on ocean mesoscale time- and space-scales, in close association with strong
synoptic-scale wind-forcing events. A companion article describes the impacts of
the BHM–SVW ensemble method on the ocean forecast in comparisons with more
traditional ensemble methods.