Application of Empirical Orthogonal Functions Parameterization in the Problem of Retrieval of the Tropospheric Thermal Structure by Radiometric Data

We describe the mathematical tools of the optimal estimation method for retrieval of tropospheric temperature profiles (0–10 km) from radiometric data with the desired profiles parameterized in the form of expansion over empirical orthogonal functions obtained by a singular analysis of the covariance matrix of the radiosonde measurement data. It is shown that within the framework of such an approach one can use a high-resolution altitude grid for a relatively small dimensionality of the inverse problem. This permits one to properly analyze the statistics of radiosonde measurements and, at the same time, retrieve the temperature profiles without using a large computing power. We have conducted test retrievals of temperature using a large ensemble of simulated noisy spectra of atmospheric self-radiation based on the statistics of radiosonde temperature measurements above Nizhny Novgorod. It is found that the r.m.s. error of temperature retrieval from spectra in frequency ranges 50–55 GHz, 55–59 GHz, and 50–59 GHz varies within the ranges 0.5–2.7 K (at altitudes of 0–10 km), 0.3–1 K (at altitudes of 0–2 km), and 0.3–2.8 K (at altitudes of 0–10 km), respectively. The optimal number of empirical orthogonal functions (dimensionality of the problem) is 6–8 in the case of the 50–55 GHz spectra, 8 in the case of the 55–59 GHz spectra, and 10 in the case of the 50–59 GHz spectra.