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Statistical downscaling is a useful technique to localize global or regional climate model projections to assess the potential impact of climate changes. It requires quantifying a relationship between climate model output and local observations from the past, but the two sets of measurements are not necessarily taken simultaneously, so the usual regression techniques are not applicable. In the case of univariate downscaling, the Statistical Asynchronous Regression (SAR) method of O’Brien, Sornette, and McPherron (Journal of Geophysical Research, 106, 13247–13259, 2001) provides a simple quantile-matching approach with asynchronous measurements. In this paper, we propose a bivariate downscaling method for asynchronous measurements based on a notion of bivariate ranks and positions. The proposed method is preferable to univariate downscaling, because it is able to preserve general forms of …