Humidity Profiles Retrieved From GNSS Radio Occultations by a Non-negative Residual Constrained Least Square Error Method

Abstract

We performed some refinements to the Boundary Profile eValuation (BPV) method, developed by Vespe and collaborators (Vespe et al., 2004; Vespe and Persia, 2006; Vespe, 2016), for the retrieval of vertical atmospheric humidity profiles from Radio Occultation (RO) observations. Previous BPV models solve typical rank deficiencies in treating RO data by recurring to parametric dry atmospheric refractivity models, such as the Hopfield or the CIRA86aQ. The involved parameters were selected by fitting observed RO Bending Angles (BAs) in the stratosphere where humidity is negligible. Total refractivity was then obtained from the observed BAs via a variational method. Such approach furnishes a valid alternative to the usual Abel inversion. Humidity profiles were finally achieved by subtracting dry refractivity contribution to the total refractivity. Nevertheless, unphysical behaviors of “negative” values of humidity can occur when the dry refractivity profiles are extrapolated toward the lower part of the troposphere. In order to avoid such unphysical behavior, in this work we recur to a second fitting for the total refractivity data, through a Least Square Error (LSE) method having a non-negative residual constraint. This is mathematically achieved with a modification of the usual LSE functional to minimize, by means of an additional exponential fast increasing term with respect to negative residuals. A Levenberg-Marquardt method relative to this new functional has been developed too, in order to numerically estimates the relative minimizers. With this approach, new dry refractivity profiles, more suited to be extrapolated in the troposphere, are recovered. We tested this new method with a series of almost 450 of GPS-RO observations from the FORMOSAT-3 COSMIC-1 Space Mission in 2009. The results show that unphysical negative values for partial water vapor pressures are removed, without losing, but in most cases even improving, the accuracy of the retrieved values, as compared with data from the European Centre for Medium-Range Weather Forecasts (ECMWF) and the National Centers for Environmental Prediction (NCEP) meteorological analysis, the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) data analysis, and as the RAwinsonde Observation (RAOB) balloons excursions suggest.