A neural network-based observation operator for weather radar data assimilation

Stefanelli, Marco; Zaplotnik, Žiga; Skok, Gregor

doi:10.48550/arXiv.2512.18289

Preprints

https://doi.org/10.48550/arXiv.2512.18289

Preprints

20 Jan 2026

| 20 Jan 2026

A neural network-based observation operator for weather radar data assimilation

Marco Stefanelli, Žiga Zaplotnik, and Gregor Skok

Abstract. In three-dimensional variational data assimilation (3DVar) for numerical weather prediction (NWP), the observation operator H plays a central role by mapping model state variables to an observation equivalent. For weather radar, however, specifying H is particularly challenging: reflectivity is a nonlinear, microphysics-dependent diagnostic quantity that only indirectly relates to the model’s prognostic variables, making traditional parameterised radar operators complex, regime-dependent and difficult to tune.

In this study, we propose a neural-network (NN)-based observation operator for radar reflectivity and apply it within a 3DVar data assimilation (DA) framework. Using five years (2019–2023) of radar reflectivity data from the Lisca radar and 4.4 km-resolution short-range forecasts from ALADIN model over Slovenia, we train a convolutional encoder–decoder neural network to map model temperature, humidity, horizontal wind components and surface pressure fields to radar reflectivity. Across independent test cases spanning clear-sky, stratiform and convective regimes, the NN-based operator accurately reproduces the spatial structure and intensity of observed reflectivity, relying primarily on the model state in the vicinity of the observation point. In the extreme precipitation case, which caused widespread floods in Slovenia on August 4, 2023, assimilating the full radar disc reduces the domain-averaged reflectivity root-mean-square error (RMSE) from 5.99 dBZ to 3.47 dBZ and improves the alignment between the analysed and observed convective bands.

Embedded within 3DVar, the Jacobian of the NN observation operator allows radar reflectivity observations to inform model state variables, producing corresponding analysis increments. The proposed NN radar observation operator offers a flexible alternative to traditional parameterised radar operators for improving convective-storm forecasts.

Received: 06 Jan 2026 – Discussion started: 20 Jan 2026

Marco Stefanelli, Žiga Zaplotnik, and Gregor Skok

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-77', Anonymous Referee #1, 24 Feb 2026
Review: A neural network-based observation operator for weather radar data assimilation by Stefanelli et al.
In this paper, the observation operator for radar data assimilation is replaced by a neural network that maps state variables such as temperature, wind, and relative humidity at different vertical levels with the reflectivity. The machine-learning-based observation operator is coupled with a 3DVar data assimilation system, and observation impact experiments are performed in order to provide a preliminary evaluation of this observation operator.
The topic is novel and is aligned with the current trend of merging data assimilation with machine learning. However, there are aspects of the obtained results that are not very clear and that should be discussed in more detail. There are also some decisions taken in the design of the experiments and the methodology that deserve further discussion. My recommendation is that the paper should undergo major revisions before being considered for publication in GMD.

Major comments:

The authors selected 4 vertical levels from different state variables to be linked with the reflectivity. These levels correspond to low levels (i.e., approximately below 2 km). What is the motivation for considering only low levels? For example, deep convection can be strongly linked with upper-level winds and perturbations in temperature and relative humidity.

The authors decided not to include hydrometeors as control variables, and because of this, these are not part of the observation operator. Since these are the variables more directly linked with radar reflectivity, some motivation should be provided. My impression is that choosing variables such as temperature and winds is an interesting approach, since this can better represent the links between radar reflectivity and the dynamic and thermodynamic fields (which are otherwise difficult to correct in a 3DVar framework). This can be an advantage of the selected approach and not a limitation, as the authors discuss at the end of the paper.

Since there are missing radar volumes (and maybe missing model outputs), it would be nice to provide more information about the actual sizes of the training, validation, and testing datasets before or after data augmentation.

Section 3.2. When the results in Figure 7 are described, there is no clear indication of the innovation that produced these analysis increments. This is said later in the discussion of Figure 8.

The authors should discuss in more detail the increments presented in Figure 6. There are some aspects that do not seem to be physically consistent. For example, the increment in V changes signs in vertical levels that are very close to each other. This also happens in r, where some levels show a dominant moistening effect while others (850 hPa) show a dominant drying effect. Also, the increment is not restricted or bounded to the circle, particularly for low-level temperature and relative humidity. In the wind field, it is difficult to see a dipole consistent with low-level convergence (something that would be expected if convection intensity is enhanced within the circle). Figure A.13 also shows some of these aspects, with changing signs in the wind increment at different vertical levels and no dipole structure in the wind increments.

Following from the previous comment, Figure 9 includes the effect of spatial covariances. However, the vertical structure is still unclear. For r, some levels indicate that the observations produce a moistening (where the main precipitation band is located), while a drying effect is observed at other levels (975 and 800 hPa). Similar changes in signs are observed in the increments in V, so although the increments are aligned with the rainband, there is no consistent increase in low-level convergence (which would be the expected behavior).

I could not follow figure 8. Panel d shows the innovation. But if the innovation is defined only within the small circle, why are there shades outside the circle? And why are the values outside the circle so different from the values inside the circle?

Minor points

The quality-controlled radar observations are summed into 1-hour intervals to match the resolution of the model output. However, the model output consists of instantaneous fields, not time-averaged or aggregated quantities (at least for the variables used in the observation operator). Using a time-averaged reflectivity, on the other hand, can help to smooth out small-scale details in the radar data that are not well resolved by the model.

Radar data is interpolated to the model grid using nearest neighbor interpolation. This may not be the best approach if the resolution of the radar data is larger than that of the model. In that case, a box-averaging approach can be better.

Figure 10 is mentioned before Figure 9.

RMSE instead of RM in the caption of Figure 8.
Citation: https://doi.org/10.5194/egusphere-2026-77-RC1
RC2: 'Comment on egusphere-2026-77', Frederic Fabry, 02 Mar 2026

Summary evaluation
I was intrigued by the premise and results of the manuscript EGUSphere-2026-77v1 entitled “A NEURAL NETWORK-BASED OBSERVATION OPERATOR FOR WEATHER RADAR DATA ASSIMILATION” by Stefanelli et al.. The authors have used a very unusual approach to obtain expected radar observations given model fields, a necessary first step towards radar data assimilation. Instead of trying to simulate the radar reflectivity from the model fields, they devised an approach that learned how to reproduce what an actual radar observes from model fields by training a machine-learning based machine to do so. They then demonstrated the use of the machine by showing that radar data could be used to find new model states that would reduce the mismatch between simulated and observed radar data.
That stated, I believe the authors focused too much of their attention on studying the more expected results of their work while not critically analyzing the much more interesting and novel ones. The norm in observation operators H() is to only use model variables x to devise H. You chose the unusual path to use a combination of observations y and model variables x to determine H. This has a set of advantages (fewer assumptions on microphysics and scattering, natural ability to simulate many radar artifacts…) and pose additional challenges (decoupling between the real world shaping observations and the simulated world shaping model fields due to initial condition and model errors) compared to the traditional approach. And while a few of the advantages were mentioned in the introduction, none of the challenges were, and they were not reflected upon after the Introduction. And while the machine was trained with 4 years of data with 2023 being used for testing, I only found results for four radar maps. Critically analyzing the performance of your indirect approach to devising H() should have been given considerably more emphasis, as the follow-up results, and your planned future work, are, in my opinion, expected: Once you have an H function, it is a trivial result that you can use 3-D Var to modify x and find a new one whose H(x) would be a better match to y than the original H(x). Given that the key novelty of your approach now and in the future rests on your ability to find a good H() using a combination of model and radar data, a better critical analysis of its performance would have been expected. Ideally, a comparison with a more traditional H() would be best, but I’d be happy with some longer-term statistics (echo coverage, biases, standard errors, etc.).
Because I am uncertain that these and other changes can be made in the time constraints associated with a conditional acceptance, I will recommend rejection of the current manuscript in its current form. But I encourage you to make the necessary modifications to your manuscript as your approach has the value of being much more original than many others.
Specific comments
i) The title does not reveal the key novelty, namely that you are devising and evaluating a “measurement-based observation operator” as opposed to the more traditional “simulation-based observation operator” (I find myself having to invent new terminology to express what you have designed; if you can find a better way to express this, please do so!). One could devise a NN-based OO by having it learn to imitate a simulation-based OO, and your current title would apply to such a work; but this is not what you did. It would be better if your title would better express or describe your unusual approach.
ii) Methodology, 2^nd sentence: I propose the following edit, if you believe it is still correct: “The NN observation operator is trained to determine the expected reflectivity averaged over the previous hour from fields of temperature (t), horizontal wind components (u and v), relative humidity (r), at four pressure levels (975 hPa, 925 hPa, 850 hPa, and 800 hPa) and three surface variables, 2m temperature (t2m), 2m relative humidity (r2m) and mean sea level pressure (msl) from the ALADIN numerical weather prediction model (hereafter ’ALADIN model outputs’ refers to the listed fields)".
iii) Last paragraph of 2.1, also related to ii: “The quality-controlled radar observations were subsequently summed into 1-hour intervals to match the temporal resolution of the ALADIN model outputs”. First, this choice of using hourly averages or sums of reflectivity is interesting per se, because you could have chosen to use the radar data closest to the hour, and the temporal resolution would still be matched. Why that choice? I personally believe it is a good idea, but I believe it needs to be articulated here. Then, a few more details are required: a) How is the sum done (in dBZ, in Z, in R)? b) Are the radar maps shown in all figures the hourly sums, the hourly averages, or something else? c) Is the 13.5-dBZ thresholding done before or after the summing or averaging? d) How do you handle the NaN resulting from that thresholding in the summing (if the thresholding is done before) and in the training of the machine?
iv) Second paragraph of 2.4: “All such timesteps are extracted and augmented (Aggarwal et al., 2018) by rotating both the input ALADIN fields and the corresponding radar reflectivity by 90°, 180°, and 270° around the vertical axis”. I presume you changed what was u-winds and v-winds in response to that rotation. More importantly, this rotation will hamper your radar field statistics (average, standard deviations) and make it less representative by combining points occurring at the right geographical location with three times more points occurring at another geographical location and having different averages and standard deviations, introducing location-dependent biases. Can you justify this choice? Wouldn’t a simple repetition (or weight increase in the loss function) or a minor displacement of a model pixel (4.3 km) in each direction be a better choice?
v) Figure A.11 (which should be A.1) could use units to x and y. Kilometers? Grid points?
vi) Errors, differences, bin sizes, and standard differences in reflectivity should have units of “dB” or “dB(Z)” (better choice), but not “dBZ”. I counted 16 corrections to make on the text and figure captions, plus a few more on the figures themselves.

Citation: https://doi.org/10.5194/egusphere-2026-77-RC2

Marco Stefanelli, Žiga Zaplotnik, and Gregor Skok

Data sets

LISCA-ALADIN HNN Marco Stefanelli https://zenodo.org/records/17880623

Model code and software

3DVar Neural Network-Based Observation Operator Marco Stefanelli https://zenodo.org/records/17898084

3DVar for Neural Network-Based Observation Operator Marco Stefanelli https://zenodo.org/records/17899025

Marco Stefanelli, Žiga Zaplotnik, and Gregor Skok

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Short summary

Weather radars provide storm intensity and location, but weather forecasting systems do not readily use them. We trained a neural network on 5 years of reflectivity radar and model output data to map model fields into radar reflectivity space, allowing forecasts to be corrected with radar data. In a major flood case, this cut errors in storm position and strength. Broadly speaking, the methodology provides a simplified solution for assimilating observations with no direct model-equivalent field.


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