Object-oriented processing of CRM precipitation forecasts by

stochastic filtering

Philippe Arbogast

∗

and Olivier Pannekoucke

CNRM/GAME

Etienne M´ emin INRIA, FRANCE

∗

Corresponding author address:

FRANCE E-mail: [email protected]

Philippe Arbogast, CNRM/GAME 31057 TOULOUSE, CEDEX,

ABSTRACT The poor predictability in current MCS permitting models based on the NH assumption and with horizontal grid mesh size about 2km does not allow the direct use of model outputs such as precipitations. It is suggested in this paper to postprocess the model outputs following an objectoriented approach with a lower resolution but a better predictability with respect to the model itself. Moreover the present approach based on the particle filter method since an ensemble is involved provides probabilistic forecasts that take into account the texture of the model outputs.

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1. Introduction The poor predictability in current Non-Hydrostatic models at the km scale resolution does not allow the direct use of model output of, say, variables associated to the water cycle such as precipitation. Though, these models succeed in simulating a wide variety of convective dynamics they also eventually fail in representing mesoscale features at the appropriate location or appropriate time. Thus, the need for advanced postprocessing method is obvious and has been pointed out by numerous papers on mesoscale forecast verification in the recent past. The first qualititative method that allow to cope with phase errors is to check the model against observations “by eyes”. Let us move on to objective methods. The first approach is to achieve scale separation to distinguish between predictability at different scales (Clarke et al., 199X; Roberts and Lean, 2008). Briggs and Levine (1997) used wavelet transforms for that purpose. ZepedaArce et al (2000) considered that a successful forecast does not necessarily match the observations. Therefore they introduced the concept of local neighbourhood of the observations in the verification process. In Atger (2001) the notion of multiple thresholds related to the distance of the forecasted event to the observations is introduced. Upscaling by averaging or thresholding are not the only way to take account phase errors. One may also handle forecasts and observations as probability densities (Ebert, 2008). Decision models must be introduced to decide what is a satisfactory forecast. In the same vein Damrath (2004) uses fuzzy logic. The most straightforward approach is to consider forecast and observations as objects in the spirit of Ebert and McBride (2000).

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Therefore, in that framework it becomes possible to address the splitting of the phase, size, and amplitude errors. Different approach are currently used (Baldwin et al., 2002; Brown et al., 2004; Nachamkin, 2004; Davis et al, 2006; Marzban and Sandgathe, 2006, 2008; Wernli et al. 2008; Michaes et al. 2007; Keil and Craig , 200x). The purpose of the present paper is to demonstrate that it is possible to consider largescale features, with respect to the model resolution, that are not just based on spatial filtering but that take into account the rich forecast signal at full horizontal resolution. It is suggested in this paper to postprocess the model outputs following an object-oriented approach. The object is defined here as a closed smooth curved. The main attribute of the object is the probability density functions of precipitation issued from AROME model ran at 2.5 km resolution (citation). As the definition of such object is a fuzzy problem we introduce the notion of probabilistic object (Avenel et al., 200X). We then consider an ensemble of objects that allows, for instance, the computation of the local probability to lie within the object or without. We expect to get weak, resp. large, uncertainty of object edge location in case of, simple shape, resp. complicated, precipitation patterns. The probabilistic object detection and tracking which are an application of the stochastic filtering approach will be presented in the section to come. Then, it will be applied to a case study to figure out what is behind the concept of probabilistic object edge. Finally, the skill of the forecast using the object-oriented approach is addressed by a comparison with direct model output using probabilistic verification tools.

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2. The particle filter algorithm a. Basics on stochastic filtering

Stochastic filters constitute well known procedures to estimate the posterior probability density function (pdf hereafter) p(xk |z1:k ) (called the filtering distribution) of a state variable xk of interest at any measurement instant k, given the discrete measurements series z1:k = (z1 , ..., zk ) until instant k, and an initial distribution p(x0 ). The inference of the posterior pdf may be obtained in two successive stages: a prediction step and a correction step. The prediction uses the transition distribution p(xk |xr