This paper introduces a fast emulator for the means and covariances of spatially resolved monthly climate fields. It projects climate-model output onto empirical orthogonal functions and learns how the reduced statistics depend on global mean surface temperature. Transforming back to physical space allows the emulator to estimate changes in regional averages and their variability. Examples with surface temperature and relative humidity show how it can generate inexpensive projections for warming scenarios absent from training. Readers get an interpretable approach to emulating spatial climate uncertainty, including the assumptions that come with a reduced basis and a global-temperature predictor.