  Spatiotemporal simulation of minimum and maximum temperature is a fundamental
requirement for climate impact studies and hydrological or agricultural models.
Particularly over regions with variable orography, these simulations are
difficult to produce due to terrain driven nonstationarity. We develop a
bivariate stochastic model for the spatiotemporal field of minimum and maximum
temperature. The proposed framework splits the bivariate field into two
components of "local climate" and "weather." The local climate component is a
linear model with spatially varying process coefficients capturing the annual
cycle and yielding local climate estimates at all locations, not only those
within the observation network. The weather component spatially correlates the
bivariate simulations, whose matrix-valued covariance function we estimate
using a nonparametric kernel smoother that retains nonnegative definiteness and
allows for substantial nonstationarity across the simulation domain. The
statistical model is augmented with a spatially varying nugget effect to allow
for locally varying small scale variability. Our model is applied to a daily
temperature data set covering the complex terrain of Colorado, USA, and
successfully accommodates substantial temporally varying nonstationarity in
both the direct-covariance and cross-covariance functions.
