Ensemble quantification of short-term predictability of the ocean dynamics at a kilometric-scale resolution: a Western Mediterranean test case

Abstract

We investigate the predictability properties of the ocean dynamics using an ensemble of short-term numerical regional ocean simulations forced by prescribed atmospheric conditions. In that purpose, we developed a kilometric-scale, regional model for the Western Mediterranean sea (MEDWEST60, at 1/60∘ horizontal resolution). A probabilistic approach is then followed, where a stochastic parameterization of model uncertainties is introduced in this setup to initialize ensemble predictability experiments. A set of three ensemble experiments (20 members and 2 months) are performed, one with the deterministic model initiated with perturbed initial conditions and two with the stochastic model, for two different amplitudes of stochastic model perturbations. In all three experiments, the spread of the ensemble is shown to emerge from the smallest scales (kilometric scale) and progressively upscales to the largest structures. After 2 months, the ensemble variance saturates over most of the spectrum, and the small scales (<100 km) have become fully decorrelated across the ensemble members. These ensemble simulations can provide a statistical description of the dependence between initial accuracy and forecast accuracy for time lags between 1 and 20 d. The predictability properties are assessed using a cross-validation algorithm (i.e., using alternatively each ensemble member as the reference truth and the remaining 19 members as the ensemble forecast) together with a given statistical score to characterize the initial and forecast accuracy. From the joint distribution of initial and final scores, it is then possible to quantify the probability distribution of the forecast score given the initial score or reciprocally to derive conditions on the initial accuracy to obtain a target forecast accuracy. The misfit between ensemble members is quantified in terms of overall accuracy (CRPS score), geographical position of the ocean structures (location score) and spatial spectral decorrelation of the sea surface height 2-D fields (decorrelation score). With this approach, we estimate for example that, in the region and period of interest, the initial location accuracy required (necessary condition) with a perfect model (no model uncertainty) to obtain a location accuracy of the forecast of 10 km with a 95 % confidence is about 8 km for a 1 d forecast, 4 km for a 5 d forecast and 1.5 km for a 10 d forecast, and this requirement cannot be met with a 15 d or longer forecast.