The need for prior information in characterizing snow water equivalent from microwave brightness temperatures

Microwave brightness temperatures (Tbs) contain information about snow properties, including the thickness, density, grain size, and temperature of stratigraphic layers; each of these properties generally varies vertically in the snowpack. Inverse solutions to characterize snow via Tbs have met with only limited success, not least because multiple sets of snow properties can lead to the same Tbs; the problem becomes more complex with increasing number of layers. Our objective is to address the question: Can an inverse solution be obtained with only very minimal prior information on snow properties under ideal conditions? We developed a new inverse algorithm: a Bayesian Markov Chain Monte Carlo scheme solved using the Metropolis algorithm. We allowed the number of snowpack layers itself to be unknown by generating different chains for each possible number of layers (up to a maximum of four), then selecting the optimal chain using a model selection criterion. We generated synthetic Tb observations using the microwave emission model for layered snow (MEMLS), and then used the Metropolis algorithm, MEMLS, and the synthetic observations to estimate the snow properties for 150 snowpits measurements made during the NASA Cold Land Processes Experiment (CLPX) field campaign. We evaluated algorithm results using the accuracy criteria on snow water equivalent (SWE) imposed for the planned CoreH2O satellite mission. We obtained an accurate solution to number of layers, layer thickness, density, grain size, snow temperature and ground temperature from microwave measurements for shallow snow (less than 300 mm), with an RMSE of 18.2 mm. We examined the sensitivity of these results to error in MEMLS, and found that for model error less than 8 K standard deviation, the SWE RMSE is uniformly less than 30 mm. For deep snow, however, the problem appears to be intractable, with RMS errors greater than 20% even for an assumption of zero model error. We conclude that for deep snow, additional prior information is required for accurate SWE estimation from microwave Tbs. We suggest that such prior information could come from physical snowpack models.