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A multivariate multi-site statistical downscaling model (MMSDM) was developed for simultaneous downscaling of climate variables including daily maximum and minimum tempera- tures (Tmax and Tmin) for multiple observation sites. The MMSDM employs multivariate multiple linear regression (MMLR) to simulate deterministic series from large-scale reanalysis data and adds spatially correlated random series to the deterministic series of the MMLR to complement the underestimated variance and to reproduce a spatial correlation of Tmax and Tmin from multiple sites and an at-site temporal correlation between Tmax and Tmin. The MMSDM model is called MMLRc. The downscaled results of the MMLRc were compared to those of MMLR without random noise (MMLRn) and MMLR with uncorrelated random noise (MMLRi) over the southern Quebec area of Canada. The MMLRc almost exactly reproduced the cross-site correlation of Tmax and Tmin among multiple observation sites, and it accurately reproduced the at-site temporal correlation between Tmax and Tmin at each observation site. The MMLRi and MMLRc reproduced monthly standard deviations of daily Tmax and Tmin, the 90th percentile of Tmax (Tmax90), the 10th percentile of Tmin (Tmin10), and the frost and thaw cycle (Fr-Th) more accurately than the MMLRn model. However, both MMLRc and MMLRi yielded a larger standard error for the monthly mean of daily Tmax and daily Tmin, frost season length (FSL), and growing season length (GSL). For the Fr-Th and diurnal temperature range, the MMLRc performed better than the MMLRn and MMLRi. We conclude that the MMLRn may serve as an alternative to downscaling deterministic signals of a predictand, con- sistent with global climate model predictors, and it may serve to project the averaged central ten- dency of a predictand. The MMLRc, however, is recommended for reproduction of variance, extreme events, and the inter-annual variability of the predictands.

A multivariate multi-site statistical downscaling model for daily maximum and minimum temperatures