RamaNet: Neural Inverse Model for Atmospheric Profiling With Ramanujan Frame Expansion of Microwave Brightness Temperatures

Recovering atmospheric profiles from multichannel microwave radiometer observations is a challenging inverse problem with limited training data. The K-band and V-band observations are short vectors of lengths 8 and 14, yet they must be mapped to high-resolution profiles of water vapor density $\rho _{v}$ and temperature $T$. We introduce RamaNet, which expands these short brightness temperature vectors with Ramanujan frames to identify hidden periodic patterns across the ordered channels and then maps the resulting coefficients to the target profiles with a dense network. We evaluate RamaNet on a ground-based microwave radiometer reanalysis dataset against matched multilayer perceptron and random forest baselines over training set sizes from 150 to 11111 profiles. RamaNet yields lower test root mean squared error than the multilayer perceptron at all training sizes for $\rho _{v}$ and four of seven for $T$. At the largest training size, RamaNet performs best among all three models and requires far less storage than the random forest baseline. These results show that Ramanujan frame representation is effective for mapping short multichannel brightness temperature observations to high-resolution atmospheric profiles.