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Spatiotemporal simulation of minimum and maximum temperature is a fundamentalrequirement for climate impact studies and hydrological or agricultural models.Particularly over regions with variable orography, these simulations aredifficult to produce due to terrain driven nonstationarity. We develop abivariate stochastic model for the spatiotemporal field of minimum and maximumtemperature. The proposed framework splits the bivariate field into twocomponents of "local climate" and "weather." The local climate component is alinear model with spatially varying process coefficients capturing the annualcycle and yielding local climate estimates at all locations, not only thosewithin the observation network. The weather component spatially correlates thebivariate simulations, whose matrix-valued covariance function we estimateusing a nonparametric kernel smoother that retains nonnegative definiteness andallows for substantial nonstationarity across the simulation domain. Thestatistical model is augmented with a spatially varying nugget effect to allowfor locally varying small scale variability. Our model is applied to a dailytemperature data set covering the complex terrain of Colorado, USA, andsuccessfully accommodates substantial temporally varying nonstationarity inboth the direct-covariance and cross-covariance functions.

Daily minimum and maximum temperature simulation over complex terrain