Temporal co-variation of surface and microwave brightness temperatures in Antarctica, with implications for the observation of surface temperature variability using satellite data

Satellite observations of microwave emission are a key resource for estimating surface temperatures in Antarctica. Use of these data to examine climate variability, however, relies on the assumption of constancy through time in the relationship between surface temperatures and the proxy brightness temperatures. Thus we are motivated to study the physical relationship between surface and brightness temperature time series, and to seek indicators of possible temporal variability in that relationship. Here we report an initial study using near-surface temperatures from the Byrd Station automated weather station in West Antarctica and 37 GHz, vertically polarized brightness temperatures from the Scanning Multichannel Microwave Radiometer. We begin with the simplest model of the relevant thermal and microwave physics and derive a convolution expression that relates surface and brightness temperatures. The convolution kernel depends on firn thermal diffusivity and the microwave extinction coefficient in a particularly simple way: solely through a single characteristic time-scale. For the Byrd data, we find that the (fractional variation in) observed brightness temperatures can be reproduced by our model in considerable detail, on scales from interannual down to a few days. The time-scale is tightly constrained by minimization of the discrepancy between observed and simulated time series, and the optimized value agrees closely with that derived from independent estimates of firn thermal and microwave parameters. We find no evidence thus far of temporal variability in the relation between surface and brightness temperatures, though investigation across a wider domain in space and time is needed before such variability can be ruled out.