Ensemble quantification of &#160;short-term predictability &#160;of the ocean fine-scale dynamics
Authors: Leroux Stéphanie , Brankart Jean-Michel , Albert Aurélie , Molines Jean-Marc , Brodeau Laurent , Le Sommer Julien , Penduff Thierry , Brasseur Pierre 
Published: March 2021

&lt;p&gt;In this contribution, we investigate the predictability properties of the ocean dynamics using an ensemble of medium range numerical forecasts. This question is particularly relevant for ocean dynamics at small scales (&lt; 30 km), where sub-mesoscale dynamics is responsible for the fast evolution of ocean properties. Relatively little is known about the predictability properties of a high resolution model, and hence about the accuracy and resolution that is needed from the observation system used to generate the initial conditions.&lt;/p&gt;&lt;p&gt;A kilometric-scale regional configuration of NEMO for the Western Mediterranean (MEDWEST60, at 1/60&amp;#186; horizontal resolution) has been developed, using boundary conditions from a larger&amp;#160; North Atlantic configuration at same resolution (eNATL60). This deterministic model has then been transformed into a probabilistic model by introducing innovative stochastic parameterizations of model uncertainties resulting from unresolved processes. The purpose is here primarily to generate ensembles of&amp;#160; model states to initialize predictability experiments. The stochastic parameterization is also applied to assess the possible impact of irreducible model uncertainties on the skill of the forecast. A set of three ensemble experiments (20 members and 2 months ) are performed, one&amp;#160; with the deterministic model initiated with perturbed initial conditions, and two with the stochastic model, for two different amplitudes of model uncertainty. In all three experiments, the spread of the ensemble is shown to emerge from the small scales (10 km wavelength) and progressively upscales to the largest structures. After two months, the ensemble variance saturates over most of the spectrum (except in the largest scales), whereas the small scales (&lt; 30 km) are fully decorrelated between the different members. These ensemble simulations are thus appropriate to provide a statistical description of the dependence between initial accuracy and forecast accuracy over the full range of potentially-useful forecast time-lags (typically, between 1 and 20 days).&amp;#160;&amp;#160;&amp;#160;&lt;/p&gt;&lt;p&gt;The predictability properties are statistically 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 specific 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 skill. In this contribution, the misfit between ensemble members is quantified in terms of overall accuracy (CRPS score), geographical position of the ocean structures (location score), and&amp;#160; spatial spectral decorrelation of the Sea Surface Height 2-D fields (spectral score). For example, our results show that, in the region and period&amp;#160; of interest, the initial location accuracy required (necessary condition) with a perfect model (deterministic) to obtain a location accuracy of the forecast of 10 km with a 95% confidence is about 8 km for a 1-day forecast, 4 km for a 5-day forecast, 1.5 km for a 10-day forecast, and this requirement cannot be met with a 15-day or longer forecast.&lt;/p&gt;