## 1. Introduction

Atmosphere–ocean general circulation models (AOGCMs) and the new generation of earth system models provide insights into the dynamic nature of possible climate responses to anthropogenic forcing. With spatial scales typically on the order of one half degree or coarser, however, they are unable to simulate climate at the local to regional scale. To compensate for this relatively coarse resolution, a number of dynamical and statistical techniques have been developed to downscale climate model outputs to the impact-relevant spatial and temporal scales at which observations are made.

Despite the plethora of downscaling methods in the literature (Crane and Hewitson, 1998; Wilby *et al*., 1998; Huth *et al*., 2001; Stehlik and Bardossy, 2002; Wood *et al*., 2004; Haylock *et al*., 2006; Schmidli *et al*., 2006; Kostopoulou *et al*., 2007; Hidalgo *et al*., 2008; to name just a few out of hundreds), relatively few downscaling methods have been applied to quantify potential impacts of climate change at the local to regional scale for a broad cross-section of regions and sectors across North America. The majority of studies of climate change impacts in the United States, for example, rely on one of five methods: a delta approach whereby a change or ‘delta’ is added to observed mean annual, seasonal, or monthly values in order to get future values (Hay *et al*., 2000; as used in USGCRP, 2000); simulations from a regional climate model (e.g. Mearns *et al*., 2009; as used in NARCCAP); the Bias Correction-Statistical Downscaling model originally developed as a front end to the hydrological variable infiltration capacity model, which uses a quantile mapping approach to downscale monthly AOGCM-based temperature and precipitation to a regular grid (Wood *et al*., 2004; as used in Hayhoe *et al*., 2004, 2008; Luers *et al*., 2006; USGCRP, 2009); a constructed analogue approach that matches AOGCM-simulated patterns to historical weather patterns (Hidalgo *et al*., 2008; as used in Luers *et al*., 2006); and a linear asynchronous regression approach that downscales daily AOGCM-based temperature and precipitation to individual station locations (Dettinger *et al*., 2004; as used in Hayhoe *et al*., 2004, 2008, 2010).

Each of these methods has its own benefits, and each can be sufficient for certain applications. For example, the simple and transparent delta approach can yield a nearly identical downscaled annual or seasonal mean temperature value as a more complex statistical model. At the other end of the spectrum, complex regional climate models are computationally demanding, but provide consistent high-resolution projections for a plethora of surface and upper-air variables. None of these five methods, however, allows for using multiple climate models and scenarios as input while downscaling to any spatial scale (including both station-based and gridded), simulating additional impact-relevant variables (such as solar radiation and humidity), and adequately resolving projected changes in daily climate extremes, at the same time.

For that reason, we have developed a new statistical downscaling model, the asynchronous regional regression model (ARRM). ARRM builds on the same statistical technique used by the last downscaling approach listed above (Dettinger *et al*., 2004), asynchronous quantile regression, to define a quantitative relationship between any daily observed and simulated surface variable that has a symmetric distribution, with particular emphasis on accurately resolving the relationship at the tails of the distribution in order to capture simulated changes in extremes. Asynchronous quantile regression removes the time stamp from historical observations and simulations, reordering each time series by value before matching quantiles of observed data with those from AOGCM output. This is important because coupled AOGCM simulations generate their own patterns of natural variability, meaning that no day-to-day or even year-to-year correspondence with observations should be expected.

The general concept of quantile regression was originally developed in the field of econometrics by Koenker and Bassett (1978) to estimate conditional quantiles of the response variable as opposed to the conditional mean estimated by the orthodox least-squares regression method. The quantile regression approach is of particular utility to geospatial data, in that it can be used to determine relationships between two quantities that are not measured simultaneously, such as an observed and a model-simulated time series. It takes advantage of the hypothesis that although the two time series may be independent, their distributions may be similar.

The general technique of quantile regression has been used in a variety of applications, including by O'Brien *et al*. (2001) to determine relationships between measurements of relativistic electron conditions measured from two different satellites passing over the same area at different times. Dettinger *et al*. (2004) were the first to apply this method to downscaling AOGCM output, to examine simulated hydrologic responses to climate change. In this application, the first time series was observations and the second, historical model simulations. The regression model derived from these two distributions was then applied to transform the distribution of, or downscale, future model simulations.

The objective of this study is to build on the foundation of quantile regression to develop a relatively straightforward, flexible, efficient, and robust statistical model that is capable of downscaling any atmospheric variable, measured on a daily or monthly basis, which has, or can be transformed into, an approximately symmetric distribution. Section 'Model development' describes the statistical basis of the model and refinements that improve its ability to downscale global model outputs. Section 'Data and simulations' describes the long-term weather station observations and the AOGCM outputs used to evaluate the downscaling model in terms of its ability to simulate observed temperature and precipitation, using the same variables from the AOGCMs as predictors. Section 'Model evaluation' describes how the model was developed in multiple steps, each of which is successively tested to ensure that the additions improve the model's ability to reproduce historical climate. Section 'Future projections' discusses the results of applying the downscaling model to end-of-the-century temperatures and precipitation and the changes between downscaled and raw AOGCM output compared with present conditions. Finally, Section 'Conclusions' summarizes the findings of this study.