Multivariate Downscaling Approach Preserving Cross Correlations across Climate Variables for Projecting Hydrologic Fluxes

Most of the currently employed procedures for bias correction and statistical downscaling primarily consider a univariate approach by developing a statistical relationship between large-scale precipitation/temperature with the local-scale precipitation/temperature, ignoring the interdependency between the two variables. In this study, a multivariate approach, asynchronous canonical correlation analysis (ACCA), is proposed and applied to global climate model (GCM) historic simulations and hindcasts from phase 5 of the Coupled Model In- tercomparison Project (CMIP5) to downscale monthly precipitation and temperature over the conterminous United States. ACCA is first applied to the CNRM-CM5 GCM historical simulations for the period 1950–99 and compared with the bias-corrected dataset based on quantile mapping from the Bureau of Reclamation. ACCA is also applied to CNRM-CM5 hindcasts and compared with univariate asynchronous regression (ASR), which applies regular regression to sorted GCM and observed variables. ACCA performs better than ASR and quantile mapping in preserving the cross correlation at grid points where the observed cross correlations are significant while reducing fractional biases in mean and standard deviation. Results also show that preservation of cross correlation increases the bias in standard deviation slightly, but estimates observed precipitation and temperature with increased likelihood, particularly for months exhibiting significant cross correlation. ACCA also better estimates the joint likelihood of observed precipitation and temperature under hindcasts since hindcasts estimate the observed variability in precipitation better. Implications of preserving cross correlations across climate variables for projecting runoff and other land surface fluxes are also discussed.