Wave-optics uncertainty propagation and regression-based bias model in GNSS radio occultation bending angle retrievals

Abstract

Abstract.A new reference occultation processing system (rOPS) will include a Global Navigation Satellite System (GNSS) radio occultation (RO) retrieval chain with integrated uncertainty propagation. In this paper, we focus on wave-optics bending angle (BA) retrieval in the lower troposphere and introduce (1) an empirically estimated boundary layer bias (BLB) model then employed to reduce the systematic uncertainty of excess phases and bending angles in about the lowest 2 km of the troposphere and (2) the estimation of (residual) systematic uncertainties and their propagation together with random uncertainties from excess phase to bending angle profiles. Our BLB model describes the estimated bias of the excess phase transferred from the estimated bias of the bending angle, for which the model is built, informed by analyzing refractivity fluctuation statistics shown to induce such biases. The model is derived from regression analysis using a large ensemble of Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) RO observations and concurrent European Centre for Medium-Range Weather Forecasts (ECMWF) analysis fields. It is formulated in terms of predictors and adaptive functions (powers and cross products of predictors), where we use six main predictors derived from observations: impact altitude, latitude, bending angle and its standard deviation, canonical transform (CT) amplitude, and its fluctuation index. Based on an ensemble of test days, independent of the days of data used for the regression analysis to establish the BLB model, we find the model very effective for bias reduction and capable of reducing bending angle and corresponding refractivity biases by about a factor of 5. The estimated residual systematic uncertainty, after the BLB profile subtraction, is lower bounded by the uncertainty from the (indirect) use of ECMWF analysis fields but is significantly lower than the systematic uncertainty without BLB correction. The systematic and random uncertainties are propagated from excess phase to bending angle profiles, using a perturbation approach and the wave-optical method recently introduced by Gorbunov and Kirchengast (2015), starting with estimated excess phase uncertainties. The results are encouraging and this uncertainty propagation approach combined with BLB correction enables a robust reduction and quantification of the uncertainties of excess phases and bending angles in the lower troposphere.

Variational Assimilation of Radio Occultation Observations into Numerical Weather Prediction Models: Equations, Strategies, and Algorithms

“…Radio holographic estimates of bending angles errors were described by [65] and further developed by [66]. More advanced analysis of uncertainty propagation through the retrieval chain and resulting covariances was performed by [53,54,[67][68][69].…”

Response to Referee 1

“…In combination with the definitions of the main operators and variables in Table 1, and of the vertical grid and coordinate variables in Table 2, Fig. 2 provides a concise overview on the detailed workflow of the L1b processor. Uncertainty propagation for the WO bending angle retrieval has been implemented and demonstrated for simulated events by Gorbunov and Kirchengast (2015); estimation of Table 1. Principal variables for the rOPS L1b uncertainty propagation.…”

“…Due to strong refractivity gradients and multipath effects, the GO bending angle retrieval can be inadequate in the troposphere, and therefore WO algorithms are applied to reconstruct the geometric optical ray structure of the wave field (e.g., Gorbunov, 2002a;Gorbunov and Lauritsen, 2004).…”

“…The WO bending angle retrieval algorithm used is a canonical transform (CT2) algorithm , and the associated uncertainty propagation algorithm is not described here, but separately by Kirchengast (2015, 2018). The WO retrieval and uncertainty propagation results are supplied up to 20 km impact altitude by the WO algorithms.…”

Comparison study of COSMIC RO dry-air climatologies based on average profile inversion

“…Excess phase profiles provided by the COS-MIC Data Analysis and Archiving Center (CDAAC) of the University Corporation for Atmospheric Research (UCAR), Boulder, Colorado were used as input data. From these data bending angle profiles are calculated by applying a combined geometric optics (see Appendix A in the study by Schwarz et al, 2018) and wave optics (Gorbunov and Lauritsen, 2004;Gorbunov and Kirchengast, 2018) bending angle retrieval. To obtain ionosphere-free bending angles, the method by Sokolovskiy et al (2009) is applied on the calculated bending angles.…”