Varda-single-1.0: deterministic data-driven weather forecasting at 1 km resolution over Switzerland's complex topography

Alberto Pennino; Francesco Zanetta; Michele Cattaneo; Claire Merker; Radi Radev; Jonas Bhend; Louis Frey; Hugues de Laroussilhe

physics.ao-phOct 1, 2026

Varda-single-1.0: deterministic data-driven weather forecasting at 1 km resolution over Switzerland's complex topography

Authors: Alberto Pennino, Francesco Zanetta, Michele Cattaneo, Claire Merker, Radi Radev, Jonas Bhend, Louis Frey, Hugues de Laroussilhe, +23 more

Organizations: Federal Office of Meteorology and Climatology MeteoSwiss · Swiss Data Science Center (SDSC), ETH Zürich · Center for Climate Systems Modeling (C2SM), ETH Zürich · European Centre for Medium-Range Weather Forecasts (ECMWF) · Norwegian Meteorological Institute (MET Norway) · Royal Netherlands Meteorological Institute (KNMI) · Institute for Atmospheric and Climate Science (IAC), ETH Zürich

Abstract

We present Varda-single-1.0, a medium-range data-driven weather prediction system built for the Alpine domain. It provides hourly deterministic regional forecasts on a mesh of 1 km resolution and global forecasts on a 31 km mesh. The system comprises two independently trained stretched-grid Graph Transformer models with encoder-processor-decoder architecture, developed in the Anemoi framework: a 6-hourly autoregressive forecaster and a temporal downscaler reconstructing hourly forecasts between the forecaster's steps. Its training curriculum includes pre-training on ERA5 reanalysis data, followed by training on a 20-year kilometre-scale regional reanalysis, and finally fine-tuning on operational kilometre-scale analyses. Verified over one year against operational analyses and surface station observations, Varda-single is competitive with or improves on MeteoSwiss' operational numerical weather prediction baselines for most headline scores and variables. It broadly matches the skill of the high-resolution 1 km ICON-CH1-EPS control at lead times up to +33 h and generally outperforms the 2 km ICON-CH2-EPS control at lead times up to +120 h. Despite competitive aggregate scores, Varda-single underestimates some local wind maxima and produces overly smooth convective precipitation fields, consistent with the smoothing associated with squared-error training. To gain insight into the model's behaviour, we investigate three case studies beyond the aggregated headline scores, and find particular weaknesses in Varda-single's representation of local winds over complex terrain. Varda-single represents an important step in the development of high-resolution ML forecasting over complex terrain, in complementing the operational regional numerical weather prediction models of MeteoSwiss with data-driven models and in providing a pretrained model for researchers and user-specific applications.

Figures & tables

Figure 1: Example of a Varda-single forecast initialised at 00 UTC on 6 April 2025, showing 2 $\mathrm{m}$ temperature and 10 $\mathrm{m}$ wind speed at a lead time of +12 $\mathrm{h}$ .

	Description	Type	Model
Single-level features
2t	2 $\mathrm{m}$ air temperature	Prog.	F,D
2d	2 $\mathrm{m}$ dew point temperature	Prog.	F,D
10u	10 $\mathrm{m}$ eastward wind	Prog.	F,D
10v	10 $\mathrm{m}$ northward wind	Prog.	F,D
lsm	Land-sea mask	Forc. ⋆	F,D

Table 1: Summary of features included in Varda-single. Variables used by the 6-hourly forecaster are marked with "F", while variables used by the temporal downscaler are marked with "D".

Figure 2: The Varda-single system. The forecaster model takes in the current and previous atmospheric states $x_{t,t-6}$ and propagates them forward in time by 6 hours to produce $x_{t+6}$ . The temporal downscaler model takes in inputs $x_{t}$ and $x_{t+6}$ and produces hourly outputs from $x_{t+1}$ to $x_{t+5}$ , also including $x_{t+6}$ for hourly accumulated variables, in our case total precipitation.

Figure 3: Input meshes of Varda-single. Blue nodes are obtained from the native ERA5 N320 reduced Gaussian grid and represent the spatial boundary conditions necessary to model the regional domain. Red nodes are the cell centres of the REA-L-CH1 grid at 1 $\mathrm{km}$ spatial resolution, our regional domain of interest. During pre-training, only global nodes are considered to learn global weather dynamics. In the stretched-grid training step, the regional domain is embedded within the global grid, and regional dynamics are learned conditional on the global dynamics. We display a close-up of a 24 $\mathrm{km}$ $\times$ 24 $\mathrm{km}$ cutout to depict the complex topography of the Alpine region, which spans a substantial portion of the regional domain.

Training	Global	Regional	Training	Steps	GPUs	Global	LR	Rollout
stage	dataset	dataset	period			batch size		length
6-hour forecaster
Global pre-training	ERA5 N320	–	1979–2023 (45 yr)	50,000	32	32	$10^{-5}$	1
Stretched-grid training	ERA5 N320	REA-L-CH1	2005–2023 (19 yr)	100,000	32	16	$6\times 10^{-6}$	1
Rollout training	ERA5 N320	REA-L-CH1	2005–2023 (19 yr)	8,000	64	16	$6\times 10^{-6}$	2–6
Operational fine-tuning	IFS N320	KENDA-CH1	2024–2025 (2 yr)	1,000	64	16	$10^{-6}$	6

Table 2: Curriculum training stages for the 6-hourly forecaster and the hourly temporal downscaler. LR denotes the peak learning rate. For the forecaster, a cosine schedule with 10 warm-up steps is used. For the temporal downscaler, the learning rate is linearly warmed up over 100 steps and subsequently annealed with a cosine schedule to

3\times 10^{-7}

at the final step. The effective number of samples seen by the model is the number of steps multiplied by the global batch size.

Figure 4: Forecast performance by forecast lead time for Varda-single and the operational baseline forecasts from ICON and AIFS v1.1. RMSE (top row), bias (second row) and ETS (bottom rows) have been computed against the operational KENDA-CH1 analysis and averaged across all initialisations in the test period and all grid points in the inner verification domain. Forecasts from the 6-hourly forecaster are indicated with dots.

Figure 5: An example of a single 6-hourly forecasting step of Varda-single initialised at 06 UTC on 6 April 2026. The left column shows the model output for 2 $\mathrm{m}$ temperature, 10 $\mathrm{m}$ wind and 2 $\mathrm{m}$ dew point temperature; the middle column shows the corresponding operational KENDA-CH1 analysis. The right column shows the pixel-wise difference between the forecast and the analysis.

Figure 6: Station-based scorecards: relative percentage difference for RMSE and ETS comparing Varda-single with ICON-CH1-CTRL (panel a) and ICON-CH2-CTRL (panel b). Blue dots: Varda-single better than the baseline NWP. Red dots: NWP baseline better than Varda-single. The size of the dots scales with the magnitude of the relative difference.

Figure 7: Pointwise MSE skill score of Varda-single against the ICON-CH1-CTRL baseline at +6 h lead time, accumulated over all initialisations and verified against the KENDA-CH1 analysis. Top row: 2 $\mathrm{m}$ temperature; bottom row: 10 $\mathrm{m}$ wind speed. Left column: total skill score $S$ ( Equation 1 ). Right column: the contribution $S_{\mathrm{BIAS}}$ of the systematic error; the random contribution $S_{\mathrm{STDE}}$ is the difference between the two columns. Blue indicates that Varda-single outperforms the baseline, red that it underperforms. Both columns share the colour scale, which saturates beyond $\pm 0.65$ .

Figure 8: Meteograms for the forecast initialised at 18 UTC on 27 June 2025 for 2

\mathrm{m}

temperature and 10

\mathrm{m}

wind speed and direction. The left column shows the valley station in Sion (SIO) and the right column the flat-region reference in Kloten (KLO), for SwissMetNet station observations (green), ICON-CH1-EPS (light blue) and ICON-CH2-EPS (dark blue) ensemble means, and Varda-single (red).

Figure 9: Meteograms for the forecast initialised at 00 UTC on 21 March 2025 for 2

\mathrm{m}

temperature (a), 10

\mathrm{m}

wind direction (b) and speed (d) in Altdorf (ALT), and the mean sea-level pressure difference between ALT and Lugano (LUG, c), for SwissMetNet station observations (green), ICON-CH1-CTRL (light blue) and ICON-CH2-CTRL (dark blue), and Varda-single (red).

Figure 10: 6 $\mathrm{h}$ accumulated precipitation for a well-forecast winter case (top; initialised at 00 UTC on 7 December 2025, lead time +24 $\mathrm{h}$ ) and a poorly forecast summer case (bottom; initialised at 12 UTC on 2 July 2025, lead time +6 $\mathrm{h}$ ). Left: Varda-single. Right: the verifying KENDA-CH1 analysis. Inset boxes give the SAL components for the displayed 6 $\mathrm{h}$ window. Note that these are single-window values, whereas the values in Figure 11 are per-initialisation averages over the 6–30 $\mathrm{h}$ windows and are therefore numerically different.

Figure 11: SAL statistics over a subset of the test period for (a) Varda-single and (b) ICON-CH1-CTRL. Each circle is one initialisation, positioned by its mean structure ( $S$ ) and amplitude ( $A$ ) components over the 6–30 $\mathrm{h}$ windows, with the circle area scaling with the mean location component ( $L$ ); diamonds mark the seasonal means. Only initialisations with at least 2 $\mathrm{mm}$ of domain-mean precipitation in the KENDA-CH1 analysis over the scored window are shown (34 in JJA 2025, 35 in DJF 2025/26). The two events shown in Figure 10 are labelled.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Figure A1: Graph connectivity shown across three representative regions (left to right in each row: global ERA5 region, boundary between global and LAM, LAM-only region). Blue dots are data nodes, red dots are hidden nodes, and grey lines are edges.

Figure A2: Map of Switzerland showing the Jura Mountains, the Swiss Plateau and the Swiss Alps, together with the surface stations used in the evaluation. There are a total of 187 stations measuring 2 $\mathrm{m}$ temperature, 151 stations measuring 10 m wind speed and direction, 59 stations measuring mean sea-level pressure and 277 stations measuring total precipitation.

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