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

Abstract

We review different approaches to the variational assimilation of radio occultation (RO) observations into models of global atmospheric circulation. We derive the general equation for the bending angle that reduces to the Abel integral for a spherically layered atmosphere. We review the full 3-D observation operator for bending angles, which provides the strictest solution, but is also most computationally expensive. Commonly used is the 2-D approximation that allows treating rays as plane curve. We discuss a simple 1-D approach to the assimilation of bending angles. The observation operator based on the standard form of the Abel integral has a disadvantage, because it cannot account for waveguides. Alternative approaches use 1-D ray-tracing. The most straightforward way is to use the same framework as for the 3-D observation operator, with the refractivity field reduced to a single profile independent from the horizontal coordinates. An alternative 1-D ray-tracing approach uses the form of ray equation in a spherically layered medium that uses an invariant. The assimilation of refractivity has also 1-D and 3-D options. We derive a new simple form of the refractivity-mapping operator. We present the results of numerical tests of different 3-D and 1-D observation operators, based on Spire data.

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

“…As a consequence, the functioñ n (x) is now multivalued, each ramification giving rise to the same bending angle profile. From a deeper analysis (Sokolovskiy, 2003;Gorbunov et al, 2019), refractivity profiles recovered by Abel inversion (13) are actually under-estimated below this super-refraction quote.…”

“…In this case, distances are to be measured with respect to the local symmetry center, determined for example by local center of curvature of the Earth WGS84 ellipsoid, or even of the Geoid, which accurately models the Earth shape. In general, BAs defined by Equation ( 3) are often denoted as the effective BAs (Gorbunov et al, 2019), to be distinguished from the real BAs when atmospheric spherical symmetry is not verified. The approach described so far, based on GO approximation, actually works for ray deviations taking place in the upper part of the stratosphere.…”

“…In the case of ROs, y may represent atmospheric refractivity or rawer experimental data such as BAs or excess Doppler shifts (Kuo et al, 2000) (we describe these quantities in section Radio Occultation Observations). Various comparative studies (Zou et al, 2000;Cucurull and Derber, 2013;Gorbunov et al, 2019), have shown that BAs assimilation should be preferred. A lot of efforts is nowadays dedicated to a correct estimation of the error covariance matrices, in particular to error propagation from RO experimental observations to thermodynamic atmospheric data (Schwarz et al, 2017(Schwarz et al, , 2018Li et al, 2019;Innerkofler et al, 2020); however the main sources of errors in 1DVAR method result in the uncertainty in background data (Cucurull and Derber, 2013).…”

“…This increases the complexity of the required background model, and a considerable mole of data are to be treated, with high computational cost. For this reason, mixed procedures are often adopted (Gorbunov et al, 2019). The Boundary Profile eValuation (BPV) method (Vespe et al, 2004;Vespe and Persia, 2006) can be considered as a simple model, even if it avoids the use of external information.…”

Comparisons of Different Methods to Determine Starting Altitudes for Dry Air Atmosphere by GNSS-RO Data

“…where stays for the observed data, x for the data to be recovered, related to the observed data by the forward model , represents the background information, while , and are the covariance error matrices, respectively, for the background data, the observed data and the forward model. In the case of ROs, may represent atmospheric refractivity or rawer experimental data, such as bending angles (BA) or excess Doppler shifts [23][24][25][26], is usually given by atmospheric models [27] or by forecasting [5], while, as far as the error covariance matrices estimations are concerned, there is nowadays a wide literature [28][29][30][31]. On the other hand, simple models recover humidity concentration profiles by determining dry refractivity first and then operate a simple subtraction from the total refractivity (refractivity due to dry air plus water vapor molecules).…”