## 1. Introduction

[2] Characterizing changes in local climate variables is required to better understand the movement of water through the atmosphere, land surface, and subsurface interfaces at basin scales and to quantify the influence of potential changes in the hydrological system across a range of resolutions. Among other variables, the surface skin temperature (TSK), soil moisture (SMOIS), latent heat flux (LH), and vegetation fraction (VEGFRA) are key variables in coupling atmospheric forecasting models with land surface models [*Evans et al*., 2011; *McCumber and Pielke*, 1981; *Walker and Rowntree*, 1977]. These variables are inherently interrelated and combine to affect water balances across catchment scales [*McCabe et al*., 2008a]. For instance, while the amount of vegetation fraction directly influence the SMOIS, LH, and TSK, it is likewise affected by variations in each of these other related variables through complex nonlinear relationships [*Rodriguez-Iturbe*, 2000].

[3] General circulation models (GCMs) provide a mechanism through which to predict the climate under scenarios of future change. However, the output of these GCMs is often too coarse (grid cells of hundreds of kilometers) for studying the potential effects of hydrological variability and change at the regional and local scale. For example, hydrological studies related to the effect of climate change on areas such as flood prediction, groundwater recharge, agricultural water use, and urban water supply all require information at the catchment scale, which is beyond the capacity of current generation GCMs to provide. To bridge the mismatch of spatial scale between the GCM and the scale of operational interest, some form of data downscaling is necessary.

[4] There are two broad categories of downscaling approaches existing in the current literature: statistical downscaling and dynamical downscaling. Comprehensive reviews on these approaches have been provided by various researchers [*Evans et al*., 2012; *Maraun et al*., 2010; *Wilby and Wigley*, 1997; *Wilby*, 2002], so only a summary is provided here. Statistical downscaling approaches are based mainly on regression relationships between the coarse scale information obtained from GCM (predictors) and observed variables at the local or fine scale (predictands) [*Hewitson and Crane*, 1996]. Statistical downscaling approaches have their own limitations, such as (i) the selection of informative predictors is an onerous task and (ii) the predictors depend on their availability from GCM outputs and also on the region and the season under consideration. The latter limitation is crucial as it determines the characteristics of the downscaled climate scenario. In addition, the derived relationship between the predictors and predictands is assumed to be valid in a future perturbed condition, which cannot be verified [*Chu et al*., 2010].

[5] There is no universally accepted statistical downscaling approach applicable in climate change impact studies. Therefore, a recent trend in the scientific community has been to first apply several different downscaling methods and compare the results using verification data [*Raje and Mujumdar*, 2011]. The output of the “best” downscaled model is then forced into the hydrological model to assess the future scenario of climate change [*Liu et al*., 2011]. Furthermore, all relevant uncertainties stemming from the selection of the downscaling methods and hydrological methods have to be taken into account. Many researchers identify the method of statistical downscaling as a major source of uncertainty in impact studies [*Segui et al*., 2010; *Stoll et al*., 2011; *Teutschbein et al*., 2011]. Further investigation of statistical downscaling approaches is therefore warranted.

[6] Statistical downscaling approaches are often preferred as they are computationally less burdensome than the other major approach: dynamic downscaling [*Kidson and Thompson*, 1998]. In dynamical downscaling, a regional climate model (RCM) is applied using GCM outputs as boundary conditions. This approach takes into account detailed terrain and land cover information and provides physically consistent results [*Kunstamann et al*., 2004]. Dynamic downscaling also inherently accounts for the multivariate spatial dependencies and the cross-dependencies between variables, which statistical approaches often do not [*Sain et al*., 2011]. Although RCMs are useful for investigating the large-scale circulation, there are limitations to their application in impact studies at the regional and local levels [*Giorgi*, 2006], mostly related to the need to explicitly account for model biases and the difficulty to characterize downscaling uncertainty. Furthermore, the physical simulation of the climatic system in RCMs is computationally very expensive. Hence, there is growing interest in the research community to develop statistical techniques to further downscale the RCM output to the point locations required for impact studies [*Evans*, 2012; *Hoffmann et al*., 2011]. These methods vary considerably from simple spatial interpolation, weather generators and machine-learning techniques [*Evans*, 2012].

[7] Geostatistical simulation methods provide useful tools for analyzing spatially correlated variables. Whether in predicting point values from areal data for univariate problems [*Kyriakidis*, 2004; *Kyriakidis and Yoo*, 2005] or in the use of kriging and cokriging techniques to obtain fine resolution imagery from coarse scale images [*Nishii et al*., 1996], there are many applications of such approaches in geology, earth science, and remote sensing [*Atkinson et al*., 2008; *Liu et al*., 2007; *Mariethoz et al*., 2012; *Pardo-Iguzquiza et al*., 2006, 2010; *Zhang et al*., 2012]. However, most of the existing approaches are based on linear geostatistics [*Goovaerts*, 1997]. Such methods rely on assumptions of linear correlation with covariates or assume a multi-Gaussian spatial dependence, involving specific types of patterns [*Journel and Zhang*, 2006]. From the perspective of land-atmosphere interactions, it is known that the structure of land-atmosphere variables and their interrelationships can be highly nonlinear [*Wallace and Hobbs*, 2006]. As a result, new statistical downscaling approaches are needed that are capable of reproducing such nonlinear characteristics.

[8] Some geostatistical approaches to downscaling have been proposed that use multiple-point geostatistics (MPS) [*Strebelle*, 2002], a nonparametric approach that is free from simplifying assumptions such as linearity, maximum entropy, and multi-Gaussianity [*Gómez-Hernández and Wen*, 1998]. However, applications to downscaling are so far limited to cases with a single variable and, in addition, are restricted to either categorical variables such as land cover category [*Boucher*, 2009] or to self-similar images [*Mariethoz et al*., 2011]. In this paper, the geostatistical approach of direct sampling (DS), based on MPS, is applied for downscaling variables typically of interest in land-atmospheric studies of the hydrological sciences. Traditional geostatistical approaches use variograms, whereas the multiple-point statistics-based approaches use training images to describe spatial continuity. The DS algorithm, as described in *Mariethoz et al*. [2010], extends the idea of MPS to continuous and multivariate problems.

[9] The MPS approach involves deriving spatial arrangements of values from a training image and storing them in a database [*Strebelle*, 2002]. The database is used for retrieving the conditional probabilities for the simulation. In contrast, the DS approach does not require a database and can generate stochastic fields representing complex statistical and spatial properties directly from the training image. The method can use multivariate training images, generating random fields where the (possibly nonlinear) relationships between variables are reproduced as in the training image. Such an approach is used in this study, with a training image generated from 20 years of seasonal data.

[10] The rationale of our approach is to identify the dependence between coarse- and fine-scale patterns using past observations expressed as training images. Patterns contained in these training images are resampled conditionally to local coarse values, resulting in locally accurate downscaled estimates mimicking the interscale relationships as observed in training images, i.e., past observations, where the variables are informed at all scales are considered. We demonstrate the use of the DS approach with RCM simulation data at different resolutions and by comparing the downscaled results with high-resolution RCM outputs. Unlike typical statistical downscaling approaches, the proposed method provides physically consistent spatial patterns of TSK, SMOIS, and LH over different seasons, which are then used as downscaling predictive models.