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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, Ophélia Miralles, Carlos Osuna, Daniele Nerini, Andreas Pauling, Daniel Hupp, Ulrich Hamann, Mary McGlohon, Marti Bosch, Luca Lanzilao, Marco Arpagaus, Lukas Jansing, Daniel Leuenberger, Mark A. Liniger, Katrin Ehlert, Matthew Chantry, Håvard Homleid Haugen, Gert Mertes, Ana Prieto Nemesio, Mario Santa Cruz, Jasper Wijnands, Gabriel Moldovan, Harrison Cook, Oliver Fuhrer

arXiv:2610.01835v1physics.ao-phcs.LG

TL;DR

Regional forecasts need to represent few-kilometre processes that global models do not resolve, while six-hourly output misses important intermediate variability. Varda-single combines a six-hourly forecaster with hourly downscaling over a 1 km Alpine grid. It is competitive with or improves on operational NWP baselines for most headline scores, though local winds and convective precipitation remain challenging.

  • Problem

    Regional forecasting must capture few-kilometre processes unresolved by typical global grids, and six-hourly steps miss between-step extremes and process variability.

    Source: §1 · p. 2

  • Method

    Varda-single combines independently trained stretched-grid models: a 6-hourly autoregressive forecaster and a temporal downscaler that produces hourly states over a 1 km Alpine domain.

    Source: §1 · p. 3

  • Results

    Varda-single is competitive with or improves on MeteoSwiss operational NWP baselines for most headline scores and variables.

    Source: §5 · p. 16

  • Takeaways & Limitations

    Varda-single is a step toward complementing MeteoSwiss regional NWP models with data-driven alternatives for the Alpine domain.

    Source: §5 · p. 16

    The model misses high-frequency valley-wind variability, and its deterministic MSE training produces overly smooth precipitation forecasts.

    Source: §4.3.1 · p. 13, §4.3.3 · p. 14

Abstract

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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.

1 Introduction

High-resolution regional forecasting must capture kilometre-scale processes that global models miss, while six-hourly output can miss important intermediate variability. Varda-single addresses these needs with deterministic hourly forecasts over the Alpine domain using a stretched-grid system.

1 Introduction

  • Regional forecasts must resolve few-kilometre processes such as convection, orographic and valley winds, and fog that typical global-model resolutions do not capture.National meteorological services operate high-resolution limited-area systems, often with ensembles and frequent updates, at substantial computing cost.Source: §1 · p. 2
  • High-resolution data-driven regional forecasting has developed through limited-area models with external boundary conditions and stretched-grid models that refine a global grid locally.Both approaches build on encoder–processor–decoder graph neural networks suited to irregular, mixed-resolution grids.Source: §1 · p. 2
  • Six-hourly forecasts miss between-step extremes and poorly resolve the diurnal cycle and process life cycles, motivating hourly predictions for aviation, energy, and hydrology applications.Existing approaches either interpolate intermediate states with a separate model or couple learned forecasts to a shorter-step physical solver.Source: §1 · p. 2
  • Varda-single combines a 6-hourly autoregressive forecaster and an hourly temporal downscaler on a global 31 km mesh refined to 1 km over Switzerland and nearby areas.The stretched-grid choice avoids the need for externally supplied lateral boundary forecasts.Source: §1 · p. 3

2 Datasets

Varda-single pairs global reanalysis and operational analyses with regional kilometre-scale datasets across its training stages. The shared variable set and processing make the datasets usable together on a common grid.

2 Datasets

  • ERA5 provides pre-training on its native N320 reduced Gaussian grid at approximately 31 km resolution, while ECMWF IFS operational analyses are interpolated to that same grid for fine-tuning.Source: §2 · p. 4
  • The 1 km REA-L-CH1 reanalysis covers January 2005–March 2025 hourly, while hourly KENDA-CH1 operational analyses provide the initial conditions for operational ICON-CH1-EPS forecasts.REA-L-CH1 is a deterministic ERA5 downscaling with radar precipitation assimilated; KENDA-CH1 uses an Ensemble Kalman Filter and assimilates conventional and radar-derived observations.Source: §2 · p. 4

2.1 Forecasting variables

  • Models use variables shared across the global and regional datasets; prognostic variables are inputs and outputs, diagnostics are targets only, and forcings affect the state without being predicted.ICON fields are interpolated from model levels to pressure levels, with below-surface values extrapolated over complex Alpine terrain.Source: §2.1 · p. 4

3 Varda-single

Varda-single uses two independently trained Graph Transformer models on a stretched global-to-regional mesh. Its training curriculum moves from global reanalysis through regional training to operational-analysis fine-tuning.

3.1 System overview

  • The system pairs a 6-hourly autoregressive forecaster with a downscaler that reconstructs the five intermediate hourly states and the sixth endpoint.The downscaler conditions on both bounding states and does not propagate errors forward, reducing the number of sequential rollout steps compared with hourly autoregression.Source: §3.1 · pp. 4–5

3.2 Graph construction

  • The stretched-grid graph embeds the 1 km regional domain within a global mesh; radial-cutoff encoder edges adapt neighbourhood size to changing node density.The hidden mesh has seven refinement levels globally and ten over the regional domain, while global pre-training uses a uniform seven-level mesh.Source: Figure 3 · p. 5, §3.2 · p. 5

3.3 Model architecture

  • Both models use encoder–processor–decoder Graph Transformers, with a 16-layer processor and residual connections; the forecaster predicts increments, while the downscaler decodes hourly states jointly.Inputs include geographic and time encodings, insolation, land-sea mask and orography; ReLU enforces nonnegative total precipitation.Source: §3.3 · pp. 5–6

3.4 Training task and objective

  • The forecaster predicts six-hour states autoregressively, while the independently trained downscaler predicts the six hourly states from the two endpoints in one pass using MSE loss.Pressure-level, variable, node-weight and uniform time-step scaling are used; the regional nodes receive 5% of total loss contribution from the stretched-grid stage onward.Source: §3.4 · p. 6

3.5 Training curriculum

  • Training progresses from global ERA5 pre-training to stretched-grid regional training, autoregressive rollout training, and operational-analysis fine-tuning.The rollout window grows from two to six; regional node reweighting increases the Alpine domain’s loss share from about 1% of area to 5%.Source: §3.5 · p. 7
  • Fine-tuning on operational analyses produces the curriculum’s largest skill improvement, including a 25% reduction in the RMSE of 2 m temperature at +60 h lead time.The downscaler is not fine-tuned because global operational analyses are unavailable hourly, so it remains trained on reanalysis data only.Source: §3.5 · p. 7

4 Evaluation and discussion

The evaluation and discussion assess Varda-single against operational analyses, station observations, and NWP and data-driven baselines, using aggregate scores, spatial-skill analysis, and case studies. They also examine precipitation in contrasting winter and summer cases and through SAL statistics for selected test-period initialisations.

4.1 Overall model performance

  • Varda-single has consistently smaller temperature bias than operational baselines and temperature-threshold ETS on par with or slightly better than operational NWP baselines except in the first few hours; precipitation RMSE matches operational NWP ensemble means, with larger negative bias after +3 h.Wet-hour ETS is higher than NWP baselines after +24 h, but unperturbed NWP members outperform it earlier; wind RMSE is similar to NWP, and Varda-single outperforms AIFS v1.1 in temperature and wind RMSE and ETS throughout the forecast range.Source: §4.1 · pp. 8–9
  • Against ICON-CH2-CTRL, Varda-single has mostly comparable or better station-based RMSE and ETS across the available lead times, but it underperforms ICON-CH1-CTRL on rare high-threshold wind and precipitation events and in complex-terrain wind ETS.Its station-based RMSE is comparable to or higher than ICON-CH1-CTRL; apparent differences between station scorecards and KENDA-CH1 maps reflect their different reference datasets. MSE training can improve RMSE through smoothing while attenuating peak intensity and variability.Source: §4.1 · pp. 9–10, Figure 6 · p. 10

4.2 Spatial distribution of forecast skill

  • Temperature skill is spatially heterogeneous, while wind skill is negative over most of the domain; wind errors reflect negative bias and elevated error variance, especially at high elevations.Temperature skill is positive over lowlands and major valleys but negative over lakes and steep, high terrain; the wind-score discrepancy between station scorecards and maps stems from their different verification datasets.Source: §4.2 · pp. 11–12, Figure 7 · p. 11

4.3.1 Thermally driven valley winds in steep terrain

  • At Sion, Varda-single reproduces the diurnal temperature cycle and valley-wind phase but predicts afternoon wind peaks of around 8 m s−1 as only approximately 5 m s−1.During convective rainfall, it misses much of the observed high-frequency wind variability: its 6-hourly forecaster steps and temporal downscaler produce conservative low-wind estimates under MSE training.Source: §4.3.1 · pp. 12–13, Figure 8 · p. 13

4.3.2 Foehn wind

  • In the south Foehn case, Varda-single captures the cross-Alpine pressure forcing and wind-peak timing at Altdorf but attenuates the observed 15 m s−1 maximum, while overestimating some midday temperature maxima.The paper attributes the wind-intensity shortfall to small-scale terrain processes, MSE-related smoothing and possibly insufficient hidden-mesh density; the latter is supported only tentatively by preliminary experiments.Source: §4.3.2 · pp. 13–14, Figure 9 · p. 14

4.3.3 Precipitation in synoptic and convective situations

  • For widespread convection, Varda-single produces smooth, low-intensity precipitation bands instead of observed cells reaching 143 mm in 6 h, with a forecast maximum of 45 mm and SAL structure score S = +1.77.Across seasons it approximately reproduces precipitation amounts but misses spatial structure, especially in summer; this one-step smoothing follows from MSE training toward the conditional mean, motivating spatially aware precipitation verification and alternative training objectives.Source: §4.3.3 · pp. 14–15
  • Figure 10 contrasts a well-forecast winter case with a poorly forecast summer case using 6 h accumulated precipitation from Varda-single and verifying KENDA-CH1 analyses.The displayed cases are initialised at 00 UTC on 7 December 2025 (+24 h) and 12 UTC on 2 July 2025 (+6 h); their inset SAL values are for single windows, unlike Figure 11’s per-initialisation averages.Source: Figure 10 · p. 15
  • Figure 11 reports SAL statistics for Varda-single and ICON-CH1-CTRL over 6–30 h windows, including only initialisations with at least 2 mm domain-mean analysis precipitation.Circles show mean structure (S) and amplitude (A), with area scaling by mean location (L); diamonds mark seasonal means, and the subset includes 34 JJA 2025 and 35 DJF 2025/26 initialisations.Source: Figure 11 · p. 16

5 Conclusions

Varda-single is a pair of independently trained models for operational Alpine forecasting, providing a first assessment of regional medium-range data-driven forecasts at 1 km. It is competitive with MeteoSwiss NWP baselines, while limitations remain in temporal and terrain detail and deterministic forecast sharpness.

5 Conclusions

  • The system pairs a 6-hourly autoregressive forecaster with an hourly temporal downscaler, using independently trained stretched-grid Graph Transformers in Anemoi.The authors frame it as an operational Alpine system and a first assessment of regional medium-range data-driven forecasting at 1 km.Source: §5 · p. 16
  • Varda-single is competitive with or improves on MeteoSwiss operational NWP baselines for most headline scores and variables.The system is verified against operational analyses and station observations.Source: §5 · p. 16
  • The temporal downscaler is trained only on reanalysis data, without fine-tuning on operational analyses, although its inference performance is satisfactory.Future work could test fine-tuning on operational analyses or forecast data to improve hourly forecasts.Source: §5 · p. 16
  • The 6-hourly forecaster cannot fully exploit 1 km grid information because many relevant processes occur and remain predictable on timescales much shorter than six hours.The authors speculate that bypassing these timescales may harm the forecaster and, indirectly, the downscaler.Source: §5 · p. 16
  • On complex terrain, shared latent nodes make decoding difficult where neighbouring 1 km cells can have very different weather, and latent capacity may be insufficient for fine-scale variability.The authors hypothesise insufficient latent capacity and propose investigating spatial coverage, channel count, and denser latent nodes in demanding regions.Source: §5 · pp. 16–17
  • The authors plan to address deterministic over-smoothing with spatially aware losses and probabilistic models as a separate line of work.The conclusion links overly smooth forecasts to deterministic training.Source: §5 · pp. 16–17
  • Model weights and configuration files are openly available, and Varda-single is running quasi-operationally at MeteoSwiss with a 3 h cadence.The public materials include instructions and examples for producing seamless hourly forecasts over Switzerland at 1 km for several days on consumer-grade hardware.Source: §5 · p. 17

A Machine Learning Components

Varda-single uses Graph Transformer message-passing layers in its encoder, processor, and decoder. Attention weights neighbour messages before nodes aggregate them and update their representations.

A Machine Learning Components

  • Varda-single implements Graph Transformer message-passing layers, adapted from Shi et al. (2021), in the Anemoi framework.The layers use attention to weight learnable messages from neighbouring nodes.Source: A Machine Learning Components · p. 18
  • Each node aggregates incoming messages as a learnable weighted average, then updates its representation with a feed-forward neural network, skip connections, and layer norms.The attention weights of incoming messages sum to 1.Source: A Machine Learning Components · p. 18
  • The message-passing layer is used in the model’s encoder, processor, and decoder blocks.Source: A Machine Learning Components · p. 18

B Graph Structure

Both models operate on data and hidden nodes connected through encoder, processor, and decoder graphs. A stretched icosahedral mesh provides a dense latent representation over the regional domain and a coarser one elsewhere.

B Graph Structure

  • The graph comprises data nodes on the input grid and hidden nodes for the latent state, connected through data-to-hidden, hidden-to-hidden, and hidden-to-data edge sets.These sets define the encoder, processor, and decoder graphs, processed sequentially; edges carry normalized length and direction attributes.Source: B Graph Structure · p. 18
  • Hidden nodes occupy a triangular icosahedral mesh refined coarsely globally and more densely over the limited-area domain, with a margin at the regional boundary.Each refinement level quadruples face count and roughly halves characteristic edge length; the stretched mesh keeps the global node count tractable.Source: B Graph Structure · p. 18
  • Encoder edges use radial cutoffs scaled to local hidden-node spacing, avoiding the over- and under-connection that fixed-k nearest neighbours create across a stretched mesh.The cutoff factor is 0.7 in all stretched-grid experiments.Source: B Graph Structure · p. 18
  • Processor edges unite 1-hop neighbours across mesh refinement levels, connecting both nearby and distant hidden nodes; 75% have six neighbours and 19% have twelve.The multi-scale connectivity provides a global receptive field without requiring a deep stack of purely local hops.Source: B Graph Structure · p. 19
  • Each data node connects to its three nearest hidden nodes, so decoding locally interpolates the surrounding latent state.The latent mesh is at least as dense as the data grid in the region of interest.Source: B Graph Structure · p. 19
  • Edge lengths are unit-max normalized within each edge set, while edge directions are standardized to zero mean and unit variance.Figure A1 depicts blue data nodes, red hidden nodes, and grey edges across global, boundary, and LAM-only regions.Source: Figure A1 · p. 19, B Graph Structure · p. 20

C Hardware details

Training used three supercomputers: Balfrin for the operational emulator, Santis for the temporal downscaler, and LUMI for most development and experimentation.

C Hardware details

  • Operational-emulator training used up to 64 NVIDIA A100 GPUs across 16 Balfrin nodes.Each node has four A100 GPUs with 96 GB of memory each.Source: C Hardware details · p. 20
  • Temporal-downscaler training used 64 NVIDIA GH200 GPUs across 16 Santis nodes.Santis is part of the Alps supercomputer infrastructure at CSCS.Source: C Hardware details · p. 20
  • Most development and experimentation used 128 GPU devices across LUMI nodes.Each node has four AMD Instinct MI250X modules, exposed as eight 64 GB GPU devices.Source: C Hardware details · p. 20

D Geographical information

Evaluation spans the Jura Mountains, Swiss Plateau and Swiss Alps, using SwissMetNet surface observations across four weather variables.

D Geographical information

  • The evaluation covers the Jura Mountains, Swiss Plateau and Swiss Alps, from sub-alpine ranges and low-lying hills to high-elevation terrain with peaks up to approximately 4,500 m.The Jura reaches approximately 1,700 m, while the Swiss Plateau ranges from approximately 400 to 800 m.Source: D Geographical information · p. 20
  • Surface stations measure 2 m temperature, 10 m wind speed and direction, mean sea-level pressure and precipitation.Figure A2 shows 187 temperature stations, 151 wind stations, 59 pressure stations and 277 precipitation stations.Source: D Geographical information · p. 20, Figure A2 · p. 20

Financial support

The work received support from the ECMWF Member and Co-operating States Machine Learning Project and EUMETNET’s E-AI Programme.

Financial support

  • The ECMWF Member and Co-operating States Machine Learning Project supported scientific exchanges and working visits among participating institutions.Source: Financial support · p. 21
  • Michele Cattaneo received support through EUMETNET’s Artificial Intelligence and Machine Learning for Weather, Climate and Environmental Applications Programme.Support was provided through the 2025 Research Cooperation Grant.Source: Financial support · p. 21
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