## 1. Introduction

[2] A robust general circulation or “climate” model (GCM) is characterized (at least) by its ability to simulate key climate variables with correct statistical properties: modes, variability, extreme event return levels or periods, et cetera. Although GCMs are useful tools to generate spatially and temporally coherent large-scale statistics, computational limitations currently prohibit GCMs from performing global simulations at the high spatial resolution required to generate useful climate information at regional- or local-scales [*Wilks and Wilby*, 1999], indispensable to drive climate impact studies [*Giorgi et al.*, 1990]. Dynamical or statistical downscaling methods aim at bridging this gap. Regional Climate Models (RCMs) constitute the dynamical approach [*Chen et al.*, 2003]. Resolving physical equations of the atmospheric regional dynamics, RCMs are meteorologically consistent [*Wood et al.*, 2004] but are also computationally expensive and therefore restricted in their applications to few runs. On the opposite, because of their computational properties and their flexibility (e.g., for extremes, uncertainty), statistical downscaling methods (SDMs) have recently received an outburst of interest. Transfer functions [*Wilby et al.*, 2002; *Cannon and Whitfield*, 2002], stochastic weather generators [*Wilks and Wilby*, 1999; *Semenov et al.*, 1998], and weather typing approaches [*Vrac et al.*, 2007] are the main three SDM categories. Those are usually applied to GCM outputs or reanalyses to statistically generate local climate variables such as temperature or precipitation. However, they can also be applied to large-scale climate statistics to provide local-scale climate statistics [*Pryor et al.*, 2005]. This latter context is retained for this study. Hence, since our goal is here to downscale statistical characteristics, and not directly to provide local-scale values as in a usual SDM approach, we will speak of probabilistic downscaling methods (PDMs). While classical SDMs assume direct relationships between large- and local-scale climate, PDMs model relationships between their associated statistical properties. In this present work, cumulative distribution functions (CDFs) are used. In other words, the basic question we are trying to answer is: from a CDF describing a climate variable (say the wind intensity) at a large (GCM) scale, can we model the equivalent CDF at a lower scale, say at a weather station? If so, how to proceed? Remark that, if its statistical characteristics can be downscaled – i.e., CDFs in this work – local values can be easily generated to create realistic local-scale time series.

[3] Modeling this link between large- vs. local- statistics brings up two problems: (1) it can be highly non-linear and difficult to build; (2) predictands and predictors are often non-trivial and generally do not belong to a well-known distribution family such as the Gaussian family. Thus, an idea shared by the two methods presented in this work is to make assumption neither on the shape of the relationship to be modeled, nor on the family of the CDFs, but rather to use non-parametric correspondences between the predictor and predictand CDFs.

[4] In the next section, we first remind the reader of a known PDM generating local-scale quantiles, and extend it to a non-parametric approach capable of modeling stationwise CDFs based on large-scale CDFs. In section 3, the data used in this work are introduced, and the two PDMs are validated on present climate, before applying the extension method to a future climate simulation. Some conclusions and perspectives are then given in the last section.