| 16 Jul 2026
Use of a GNSS-PRO forward operator for the evaluation of global and km-scale NWP models
Abstract. A new formulation for a Polarimetric Radio Occultation (PRO) forward operator was recently developed and evaluated with the Weather Research and Forecasting (WRF) model and the European Center for Medium-Range Weather Forecasts (ECMWF) Integrated Forecasting System (IFS), representing a promising step toward the assimilation of PRO observations in numerical weather prediction (NWP) systems and a novel tool for evaluating frozen-hydrometeor microphysical parameterizations. In this study, the operator is applied for the first time across two operational Météo-France systems: the convection-permitting Applications of Research to Operations at Mesoscale (AROME) model and its overseas configuration, AROME-OM, and the global Action de Recherche Petite Échelle Grande Échelle (ARPEGE) model. Twenty-seven PRO occultations, each co-located with simulations from both AROME/AROME-OM and ARPEGE, are analyzed, spanning metropolitan France and the French overseas territories (Antilles, Southwest Indian Ocean, French Polynesia and New Caledonia) across both mid-latitude convective and stratiform precipitation, and tropical convective regimes. The PRO observations are first cross-checked against the ARAMIS ground-based radar observations over metropolitan France, providing an observation-only reference independent of either forward operator. For all AROME cases, the PRO operator is then systematically compared with the polarimetric radar forward operator (operadar) driven by the same AROME fields. The PRO operator globally achieves a better agreement with the observations than operadar across all regions, mainly because of its optimized nature, although a remarkably good agreement is found between the two operators and the observations over the metropolitan France domain. The PRO operator further serves as a diagnostic of how each NWP model partitions frozen water content among its prognostic species, and help identify the species that are the most difficult to accurately simulate with operadar (snow and wet graupel). These findings establish the PRO operator as a versatile multi-model diagnostic for frozen-hydrometeor microphysics and underline the operational potential of PRO observations as a complement to ground-based polarimetric radar networks, especially over seas.
Review of “Use of a GNSS-PRO forward operator for the evaluation of global and km-scale NWP models”
This manuscript compares PRO observations and simulations using two different forward models. Over France it also compares the PRO observations to simulations based on ground radar measurements. The work investigates the differences between the observations and the three simulations though it is not possible to come to any concrete explanations for those differences. However, the manuscript provides a good overview of the PRO technique and illustrates the possibility of using it with NWP models, both for model assessment and data assimilation. All these concepts are novel and likely of widespread interest.
The work is mostly in good shape and well presented. However, there are areas where the presentation needs to be more precise and thorough. Further, the hypotheses proposed to explain differences between the observations and various simulations are not always convincing. Therefore, there are some major issues to address, but the work would likely be suitable for publication after these are addressed.
Main issues
1) It is strange that the forward operator based on Bayesian estimation retains a bias against the observations that it was trained on (e.g. L298 - 305). Minimisation of equation 8 would naturally reduce the bias to zero over the whole profile, if the observation errors in R were constant. In practice the errors are not constant, so this effect may already explain the phenomenon. However, this needs to be explained and investigated in the manuscript. It is important to do this in order to demonstrate that the Bayesian inversion is working correctly. Further, it does not seem justified to attribute the differences to an underestimation of frozen hydrometeors in AROME: the Bayesian estimation should have already corrected this underestimation by adjusting the estimated mass scattering efficiency appropriately.
2) The negative phase shifts in the simulations based on ground radar are very interesting. It is asserted on lines 272 - 274 that this comes from vertically oriented hydrometeors but it would be important to back this up with citations or further justification. And I am not convinced by the suggestion that the ground radar simulations are not representative of the PRO full ray path. In order to generate negative phase shifts averaged along the whole simulated ray path, the negative values of K_dp must be relatively widespread across multiple radar pixels along that path. To back up these assertions, there needs to be more investigation into how this signal looks in the ground radar. In particular, the issue might be much clearer after looking at maps of K_dp at each radar elevation.
3) L295-296 assert that “both forward operators capture the leading-order vertical structure”. The evidence presented in the manuscript is not sufficient to justify this, and errors of a few mm could be quite large in profiles such as those shown in Figure 3. To provide more evidence, it would be important to show some examples of the phase shift profiles - observations versus the two simulations - and not just averaged differences.
4) The mathematical presentation in section 2.3 needs to be tightened up. It is current incomplete and unclear:
a) Representing water content by “WC” means the notation needs to use “.” to clarify multiplication. It would be clearer to use a single character to denote water content (W or C would be fine) and then it would be possible to drop the dot notation.
b) The A in equation 3 and A in equation 7 are different, so ideally distinguish these more clearly.
c) The notation for y, the observations or their simulated equivalent, follows two different conventions. In equation 7 the simulated observation is not distinguished (it is just Ax) but in equation 13 there are y and y_sim. I think the latter is clearest.
d) Equation 7 does not define epsilon
e) Equation 7 subtracts the liquid contribution from y, whereas Equation 13 presumably includes it. There should be some way in the notation to distinguish this.
f) Vector, matrix and dot notation in equation 7 would ideally be defined. Especially the link between x_i and bold x should be made. These things may be implicitly clear, we hope, but being precise saves the reader effort and confusion. For example, vector x could run over both vertical levels and hydrometeors, or it could be fixed across all vertical levels.
g) In particular, the dimensions of matrix A and vector x should be stated
h) Equation 10 is not enough to specify the full linear system. It needs to be stated mathematically how the “global R” is constructed and whether the global x is one vector for all locations or whether again it is a stacked vector of the kind shown in equation 10, so that a different x can be estimated for each location. Indeed, both approaches are used in this work.
5) The potential issue of non-uniform beam filling, and the treatment of sub-grid hydrometeor inhomogeneity, needs to be better discussed throughout the paper. It would be good to state already in the methods section whether and/or how these effects are represented in the various simulations. Note that on L433, it is true that (for example in RTTOV) the hydrometeor water content is normalised by the precipitation fraction before being used to generate reflectivities, but it is also then important to multiply the resulting reflectivities by the hydrometeor fraction that actually generates them. Coupled with (presumably) the lack of representation of the area being sampled normal to the ray path, the treatment of hydrometeor inhomogeneity may be one of the largest remaining errors in the forward simulations.
Minor issues
1) L64-65 (and also L509) discuss PRO being able to “constrain” snow and thermodynamic fields within NWP systems. The word “constrain” is ill defined and the wording could be read as suggesting that PRO observations could single-handedly provide all this information, without need for other observations. The remedy could be as simple as saying that the PRO observations could “contribute to constraining” the relevant parameters.
2) Figure 1 shows apparently solid coloured shapes representing the occultation rays. The caption needs to explain how a series of rays can end up being shown as a solid shape rather than a set of distinct lines.
3) Line 175: “lhy and fhy define the model’s liquid and frozen hydrometeor species.” Here or somewhere else in the introduction, there needs to be a clearer statement of what these are, and how they map onto the hydrometeor representations of AROME and ARPEGE (which are different). Note that there seem to be configurations with both 3 and 4 frozen hydrometeors, when “wet graupel” is included. It is better to introduce all these configurations in the methods section, rather than in the results section.
4) Equation 9 and L189. It needs to be explained why the standard deviation over 1 second intervals represents a sensible observation error. Further, the significance of the number 50 in equation 9 needs to be made clear.
5) Introduction of Operator in 2.4 needs to be expanded a little, specifically how the particle shape and orientation is represented in the T-matrix calculations. This is needed to support the description of canting angles on line 217.
6) L264 “the interpolation process cannot reflect exactly the real ray geometry”. I am not convinced by the hypothesis that interpolation is to blame here. It ought to be possible to represent the exact ray geometry, even if a more sophisticated approach might be needed. To explain noisier results from ground radar, this could happen if the volume sampled by ground radar were smaller than the volume sampled by PRO: there must be a finite horizontal and vertical width of the atmosphere sampled by the PRO measurement. The text needs to investigate these issues in a bit more detail.
7) L270: rho_HV is not defined.
8) The source of the reflectivity in Fig. 2 (right) needs to be stated - there are multiple simulations available.
9) L288 - 2980: The merged graupel configuration (and other configurations) need to be explained properly in the methods section (see previous comments). This is needed to better support discussions such as on L452-459. More generally, throughout the manuscript there needs to be more clarity over which configuration is being used in each set of results.
10) L292: Since section 2.5 defined the metrics RMSE, bias and chi^2, it is surprising to find the first metric presented is a median, which has not been mentioned to this point.
Typos and editorial
On page 2 lines 43 and 45 the delta Phi symbol is erroneously repeated
L110 K_dp does not seen to have been introduced at this point, either scientifically or as an acronym.
L201 the “sigma” needs explaining.