The complex interactions among climate variables in the Arctic have important implications for potential climate change, both globally and locally. Because the Arctic is a data-sparse region and because global climate models (GCMs) often represent Arctic climate variables poorly, significant uncertainties remain in our understanding of these processes. In addition to the traditional approach of validating individual variables with observed fields, we demonstrate that a comparison of covariances among interrelated parameters from observations and GCM output provides a tool to evaluate the realism of modeled relationships between variables. We analyze and compare a combination of conventional observations, satellite retrievals, and GCM simulations to examine some of these relationships. The three climate variables considered in this study are surface temperature, cloud cover, and downward longwave flux. Results show that the highest correlations between daily changes in pairs of variables for all three data sets occur between surface temperature and downward longwave flux, particularly in winter. There is less variability in GCM output, in part, because there is greater spatial averaging. Although the satellite products can be used to examine some of these relationships, additional work may be needed to ensure consistency between changes in radiative components of the energy budget and other retrieved quantities. The GCM's relationships between variables agree well with in situ observations, which provides some confidence that the GCM's representation of present-day climate is reasonable in high northern latitudes.