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Stochastically Perturbed Weights: Ensembles from Deterministic Machine-Learning Weather Models

Simon Adamov, Oliver Fuhrer, Reto Knutti, Sebastian Schemm

arXiv:2609.08412v1cs.LGphysics.ao-ph

TL;DR

Deterministic ML weather models lack their own uncertainty estimates, while trained-probabilistic models require dedicated training. This paper perturbs raw weights in existing deterministic checkpoints; its supplied results show a calibration weakness for specific humidity in three non-AIFS SPW models.

  • Problem

    Deterministic checkpoints provide no estimate of forecast uncertainty, and the paper asks how much calibrated uncertainty can be recovered without retraining.

    Source: §1 · p. 4

  • Method

    The paper perturbs the raw weights of a frozen deterministic network at inference time, a scheme it calls stochastically perturbed weights (SPW).

    Source: §1 · p. 4

  • Results

    Specific humidity is the worst- or second-worst-calibrated variable for the three non-AIFS SPW models.

    Source: b. Headline intercomparison · p. 18

  • Takeaways & Limitations

    Raw-weight perturbation is a training-free post-hoc approach, and the paper identifies it as the least systematically studied variant.

    Source: §1 · p. 4

    Trained-probabilistic models require a dedicated training run, while initial-condition perturbations are spread-limited.

    Source: §1 · p. 3

Abstract

from arXiv · show

Machine-learning weather models (MLWMs) now match or outperform operational numerical weather prediction (NWP) at global medium-range forecasting, at far lower inference cost. Many deployed MLWMs are deterministic, producing a single forecast with no estimate of its own uncertainty, whereas a growing family of trained-probabilistic models generate calibrated ensembles directly, at the price of a dedicated training run. We ask instead how much uncertainty can be extracted from a deterministic checkpoint that already exists, without retraining it. Where physical ensembles represent model uncertainty by stochastically perturbing parametrisation tendencies, we perturb the network's raw weight tensors at inference time, a scheme we call stochastically perturbed weights (SPW). We also ask whether it works, where and on which scales to inject the noise, and where it fails. A three-phase ablation across four deterministic backbones, Aurora, GraphCast, SFNO, and AIFS, selects one production baseline per model, benchmarked against the trained-probabilistic AIFS-ENS, FourCastNet 3 and Atlas as well as the operational ECMWF ensemble (IFS-ENS) over 112 initialisation times. At a 240 h (10-day) lead time the SPW ensembles reach continuous ranked probability skill scores (CRPSS) between 0.04 and 0.13 below the best trained-probabilistic baseline, at zero marginal training cost. No injection site works across models: the productive tensor group is architecture-specific, so SPW is at present a tuning procedure rather than a plug-and-play recipe. Its main failure mode is a coherent whole-field offset that overdisperses the domain mean, and restricting the noise to coarse scales or perturbing the initial conditions each repair part of it.

1. Introduction

Deterministic ML weather models provide no forecast uncertainty, while trained-probabilistic alternatives require a dedicated training run. The paper asks whether uncertainty can instead be recovered by perturbing the raw weights of an existing deterministic checkpoint, and names this approach SPW.

1. Introduction

  • Deterministic MLWMs produce a single forecast without an estimate of uncertainty, despite the need for forecasts to carry uncertainty beyond a few days.The introduction frames calibrated uncertainty as central to operational use.Source: §1 · p. 3

b. Probabilistic ML weather forecasting

  • Trained-probabilistic MLWMs generate ensembles directly, but require a dedicated probabilistic training run; AIFS-ENS, FourCastNet 3, and Atlas are named benchmark comparators.The paper also distinguishes sampling-based and single-backbone ensemble approaches.Source: §1 · p. 3, b. Probabilistic ML weather forecasting · p. 5

1. Introduction

  • Post-hoc weight perturbation is training-free, unlike trained-probabilistic models and deep ensembles, and its raw-weight variant is the least systematically studied.The introduction positions this as a way to obtain spread from an existing checkpoint rather than run another training procedure.Source: §1 · p. 4
  • The central question is how much calibrated uncertainty can be recovered from an existing deterministic checkpoint that cannot be retrained.The proposed response is to perturb the network’s raw weights, calling the scheme stochastically perturbed weights (SPW).Source: §1 · p. 4

a. Deterministic ML weather models

  • Deterministic MLWMs map the global atmospheric state forward by 6 h and autoregress to multi-day forecasts, with architectures differing mainly in inductive bias.The reviewed designs include spherical or spectral operators, graph networks, and operator-learning backbones.Source: a. Deterministic ML weather models · pp. 4–5

c. Ensembling a deterministic network without retraining

This section examines inference-time ensembling by perturbing frozen deterministic weather-model weights across four backbones, using a three-phase ablation and probabilistic verification. It evaluates selected perturbations on the full production grid, including their lead-time-dependent dispersion behavior.

c. Ensembling a deterministic network without retraining

  • The study examines the previously unstudied simplest post-hoc weight perturbation: multiplicative Gaussian noise applied to raw weight tensors and left frozen.This inference-time variant reuses one checkpoint without retraining.Source: c. Ensembling a deterministic network… · p. 6

d. Verification of probabilistic weather forecasts

  • Verification scores forecasts against WeatherBench-2 probabilistic climatology, combining CRPSS and spread-skill ratio with structural, spectral, distributional, and physical checks.The physical checks target Clausius-Clapeyron and geostrophic balance; the scoring framework follows Gneiting and Raftery (2007), with climatology from Rasp et al. (2023).Source: d. Verification of probabilistic… · p. 6

a. Models

  • Experiments perturb four deterministic backbones—Aurora, GraphCast, SFNO, and AIFS—and compare them with AIFS-ENS, FourCastNet 3, Atlas-ERA5, and IFS-ENS.The three trained-probabilistic comparators are AIFS-ENS, FourCastNet 3, and Atlas-ERA5; IFS-ENS is the classical ensemble baseline.Source: a. Models · p. 7

b. SPW framework

  • SPW perturbs a selected subset S of weights independently per ensemble member with multiplicative Gaussian noise; its two controls are S and magnitude σ.The noise is scaled to each weight, giving a weight w variance of σ^2|w|^2.Source: b. SPW framework · pp. 7–8

1) The three-phase ablation

  • At 240 h, the deterministic prior has washed out and perturbation does the work, motivating production-baseline selection by CRPSS at that lead.The selection used four ablation initialisations; the independent 112-initialisation grid served as a held-out check.Source: 1) The three-phase ablation · p. 8, Table 2 · p. 11
  • The closest rivals, GraphCast m2g and the SFNO Phase 2b encoder, sit closer to spread-skill ratio 1 but fall behind on multivariate scores.The broader comparison considered spread-skill over 120–240 h alongside structural, distributional, and multivariate metrics.Source: 1) The three-phase ablation · p. 8, Table 2 · p. 11
  • At 240 h, no runner-up displaces its ablation winner after full-production-grid comparison on common initialisations.Runner-ups were rerun because a four-initialisation sweep could not resolve the ±0.02 band.Source: 1) The three-phase ablation · p. 11
  • For SFNO, the encoder cell ties sfno modes10 at 240 h and leads at 120 h, but the coarse-mode cell is selected by the specified tie-break.The encoder perturbation overdisperses the spatial mean (240 h SSR ≈1.8), whereas coarse modes hold it near [value not supplied].Source: 1) The three-phase ablation · p. 11
  • The frozen perturbation has two limitations: a coherent whole-field shift inflates spatial-mean spread at long lead, and forecasts are underdispersed at short lead.Q3 tests refreshing perturbations across the rollout and adding perturbed initial conditions, while leaving each backbone’s ablation-selected configuration unchanged.Source: 1) The three-phase ablation · p. 12

2) Refreshing the perturbation across the rollout

The ablation compares frozen weight perturbations with noise refreshed during the autoregressive rollout. Refreshing changes the temporal path of the perturbation, and its cadence is tuned while matching accumulated perturbation variance.

2) Refreshing the perturbation across the rollout

  • Frozen noise is reused across the rollout, so it pushes the spatial mean in the same direction each step and its per-member offset accumulates with lead time.The refresh-every-N-steps variant resamples at cadence boundaries and boosts each draw to match the frozen case’s accumulated perturbation variance.Source: 2) Refreshing the perturbation across… · p. 12
  • For SFNO, the refresh cadence is tuned over N ∈ {1, 10, 20, 40} at a frozen anchor σ_frozen = 0.25.N = 1 is fresh-per-step and N = T is the frozen baseline.Source: 2) Refreshing the perturbation across… · p. 12
  • The refresh-every-20 variant is also tested on Aurora and AIFS at their production σ, with a matched fresh-versus-frozen activation-space control.Source: 2) Refreshing the perturbation across… · p. 12

3) Augmenting with perturbed initial conditions

The paper combines perturbed initial conditions with weight perturbations, defines separate grids and verification metrics, and selects architecture-specific SPW production baselines. In the Milton case study, SPW uses initial-condition augmentation because weight-only perturbations are underdispersed at short leads.

c. Evaluation grids

  • The ablation grid supports per-model baseline selection, while the independent 112-initialisation production grid supports headline evaluation.The selection uses only four ablation initialisations.Source: Table 3 · p. 13, c. Evaluation grids · p. 13

d. Metrics

  • Scalar scores average seven variables, while multivariate scores retain 12 variable-level channels; the verification includes scoring, calibration, structural, spectral, threshold, and distributional metrics.For scalar CRPSS and RMSE, 3D variables are first averaged over 500 and 850 hPa.Source: d. Metrics · p. 13

e. Hurricane Milton case study

  • The Milton stress test uses IC-augmented SPW because weight-only perturbation is underdispersed at short leads, the regime probed by this rapid-intensification case.The SPW case-study rows use IC-augmented configurations; TP and IFS-ENS use their native ensembles.Source: e. Hurricane Milton case study · p. 14

a. Ablation: per-model production baselines

  • The four production picks differ by architecture: Aurora uses Phase 2b encoder, GraphCast Phase 1 all-weights, SFNO Phase 3 coarse-mode, and AIFS Phase 2 decoder.The selected noise scales are 0.025, 0.01, 0.25 (ℓ < 10), and 0.028, respectively.Source: a. Ablation: per-model production… · p. 16
  • A single perturbed member is consistently worse than the unperturbed control, but the ensemble mean beats the control at all but the shortest lead times.The ensemble-mean gain is largest where the unperturbed model is weakest, declining from SFNO to AIFS.Source: a. Ablation: per-model production… · p. 16

b. Headline intercomparison

AIFS-ENS leads the production-grid comparison, while perturbed AIFS is the strongest SPW baseline across almost every metric. SPW ensembles are close on per-pixel spread calibration but can overdisperse the spatial mean; initial-condition augmentation and, in some cases, noise refresh address parts of this gap.

b. Headline intercomparison

  • Specific humidity is the worst- or second-worst-calibrated variable for the three non-AIFS SPW baselines, while geopotential is best calibrated.The authors attribute the humidity result to its heavy non-Gaussian tail, which a frozen perturbation cannot reproduce.Source: b. Headline intercomparison · p. 18
  • AIFS-ENS leads the proper scoring rules, while perturbed AIFS is the strongest SPW baseline across almost every metric; SPW mainly trails on multivariate and spread-calibration scores.The SPW baselines retain a smaller fraction of AIFS-ENS’s skill beyond 240 h.Source: b. Headline intercomparison · p. 18

c. The spatial-mean spread-skill gap and its resolution

b. Headline intercomparison

c. The spatial-mean spread-skill gap and its resolution

  • Each member’s single perturbed weight set shifts the whole field together, producing nearly constant offsets and excess spatial-mean spread.Per-pixel spread averages many local perturbation directions and remains calibrated.Source: c. The spatial-mean spread-skill gap… · p. 20
  • Refresh improves SFNO’s 240 h spatial-mean SSR from 0.66 to 0.83, but it barely changes Aurora and AIFS overdispersion and does not generalise across backbones.For GraphCast, refreshing coarse activation noise moves SSR farther from 1, from 0.27 to 0.15.Source: c. The spatial-mean spread-skill gap… · pp. 20–21
  • Initial-condition augmentation raises AIFS’s 24 h MSL SSR from 0.65 to 0.79 and reduces GraphCast’s 240 h spatial-mean SSR from 3.20 to 1.90, while leaving long-lead spread unchanged.It incurs a 0.06–0.10 CRPSS reduction at 6 h; weight perturbation supplies 86–97% of combined variance at 240 h, versus 8–17% at 6 h.Source: c. The spatial-mean spread-skill gap… · p. 21

d. Inference cost and environmental footprint

SPW reuses existing checkpoints at zero marginal training cost, while Atlas has markedly slower inference than the other six baselines. The Hurricane Milton case study finds differences in storm detection and position error, but its intensity comparisons are constrained by the verification grid’s resolution.

e. Case study: Hurricane Milton (October 2024)

  • On Milton, TP baselines have the highest detection rates at 86–89%, versus 66–76% for SPW and 71% for IFS-ENS; Aurora, GraphCast, and AIFS SPW lead on IBTrACS position error.The IFS-ENS detection rate is a lower bound because archive gaps omit many leads; interpolation raises it to 80% without changing the ordering.Source: e. Case study: Hurricane Milton… · pp. 22, 24
  • The 0.25° ERA5/WeatherBench-2 grid cannot represent a Category 5 inner core: Milton bottoms out at 976 hPa versus the 895 hPa IBTrACS peak.Every baseline’s deepest member crosses the ERA5 floor of 942–967 hPa, so the track-mean MSL bias is not a baseline-quality discriminator.Source: e. Case study: Hurricane Milton… · pp. 22, 24

d. Inference cost and environmental footprint

  • Atlas takes 38 min per member, 18–39 times longer than the other six baselines, while SPW reuses existing checkpoints at zero training cost.Reported training costs for AIFS-ENS and FCN3 are of order 20,000 and 80,000 GPU-hours; training-cost comparisons depend on hardware and accounting.Source: d. Inference cost and environmental… · p. 22, Table 6

e. Case study: Hurricane Milton (October 2024)

  • For AIFS, initial-condition augmentation roughly doubles early-lead track-cone width from 48 to 96 km and increases intensity spread from 1.1 to 1.9 hPa.The two AIFS SPW columns are nearly identical in their ensemble-mean fields, consistent with augmentation changing spread rather than the mean.Source: e. Case study: Hurricane Milton… · pp. 24–26

5. Discussion

The productive perturbation site differs by architecture, with successful choices generally near the low-resolution latent rather than at a shared network position. The discussion qualifies the findings with limits on tuning cost, sampling, ensemble setup, verification, variables, and forecast horizon.

a. Architecture-specific tuning, not a plug-and-play recipe

  • Aurora favors its encoder, GraphCast its full weight set, SFNO its coarsest spectral modes, and AIFS its decoder for productive perturbations.GraphCast's shared mesh weights do not provide a scale-restricted subset, while AIFS has no coarse-scale phase.Source: a. Architecture-specific tuning, not a… · p. 27
  • Productive sites border the low-resolution latent, while central normalization layers damp variance and produce underdispersion.The productive sites do not share a common position, and AIFS-ENS injects learned noise in a processor the authors cannot exploit.Source: a. Architecture-specific tuning, not a… · p. 27
  • SFNO's low-ℓ perturbation avoids the overdispersion shared by its all-weight and encoder/decoder alternatives.SFNO is the weakest model on absolute CRPSS at 240 h, making its exposed coarse-scale modes a clean probe of the pattern.Source: a. Architecture-specific tuning, not a… · p. 27

b. Limitations

  • Each full 10-member ablation cell adds sweep cost, the price paid for selecting a configuration without a training run.The authors caution that four models cannot establish a general rule for the shared features of winning sites.Source: b. Limitations · p. 27, a. Architecture-specific tuning, not a… · p. 27
  • The 112 initialisations are dependent, making effective sample size closer to weekly blocks than to 112; the eight-block bootstrap is indicative.Its 95% intervals exclude zero for every 240 h headline CRPSS gap to AIFS-ENS, spanning 0.036 [0.031, 0.041] for perturbed AIFS to 0.131 [0.121, 0.141] for sfno modes10.Source: b. Limitations · p. 28
  • The study uses M=10 rather than operational ensembles' 30–50 members, and the four mid-season CRPSS values remain biased in absolute terms.Under exchangeability, the fair-CRPS expectation is M-independent, and the authors say M=10 supports the ranking.Source: b. Limitations · p. 28
  • Initial-condition augmentation depends on an external perturbed-analysis ensemble; cruder substitutes may not transfer its calibration.The IFS-ENS comparison also uses a smaller, potentially correlated valid subset, and its verification reference differs from the ERA5-native ML baselines.Source: b. Limitations · p. 28
  • The evaluation excludes precipitation and other highly intermittent fields, where added spread cannot restore sharpness smoothed out by the deterministic parent.Specific humidity, the most non-Gaussian variable scored, is already the worst-calibrated variable for the SPW baselines.Source: b. Limitations · pp. 28–29

6. Conclusions

The three-phase procedure turns four deterministic ML weather models into ensembles, but the best injection site depends on architecture. At 240 h, the SPW baselines trail AIFS-ENS by 0.04–0.13 CRPSS; their main calibration failure is overdispersion of the spatial mean.

6. Conclusions

  • At 240 h, SPW trails AIFS-ENS by 0.04 (perturbed AIFS) to 0.13 CRPSS on a 112-initialisation grid, at zero marginal training cost.Production runs take 59–125 seconds per member; the gaps narrow at 360 h as every baseline converges toward climatology.Source: §6 · p. 29
  • The selected noise target is architecture-specific: Aurora’s encoder, all GraphCast weights, SFNO’s ℓ<10 modes, and AIFS’s decoder.The winning sites lie near each architecture’s low-resolution latent, a hypothesis the authors say needs testing on more models.Source: §6 · p. 29
  • At 240 h, three of four SPW baselines overdisperse the spatial mean while remaining pointwise calibrated, with per-pixel SSR of 0.94–1.11.A frozen perturbation shifts each member’s whole field coherently; refreshing the noise repairs mean spread only for scale-localised perturbations.Source: §6 · p. 29
  • Initial-condition augmentation supplies early-lead spread that weight noise alone under-resolves, complementing the weight-only approach for any backbone.The authors report that early-lead spread is almost entirely the analysis.Source: §6 · p. 30
  • Where a trained-probabilistic ensemble covers the required variables, it remains the better product; SPW is intended for uncovered checkpoints and centres.The paper identifies heavy-tailed fields as SPW’s weakest case and calls trained-probabilistic models safer when those fields must be calibrated and training budget exists.Source: §6 · p. 30
  • The proposed next step is to replace the injection-site sweep with a principled selection criterion and steer perturbations toward physically consistent extremes.The paper names Fisher information as one candidate criterion and cites storyline and rare-event-sampling approaches.Source: §6 · p. 30

APPENDIX

Appendix A specifies how perturbation magnitude is rescaled across tensor groups and rollout schedules. Appendix B documents the scored variables, evaluation metrics, and CRPSS tables.

APPENDIX A

  • The spatial rescaling increases σ as the perturbed subset shrinks, using perturbed-unit counts anchored to the Phase 1 reference σ_full = 0.01.The count proxy seeds the search; production σ values come from CRPSS magnitude sweeps, while exact Frobenius-norm alternatives can overweight large, effectively low-rank matrices.Source: Appendix A · pp. 30–31
  • The perturbation unit varies by target: whole weight tensors, Aurora blocks, SFNO low-wavenumber degrees of freedom, or GraphCast coarse mesh nodes.GraphCast perturbations act in activation space because its mesh weights are shared across the graph.Source: Appendix A · p. 31
  • A frozen perturbation reuses one draw at every rollout step, whereas refresh-every-N resamples at segment boundaries; the former accumulates coherently and the latter partly cancels.The appendix compares these schedules at equal accumulated perturbation variance.Source: Appendix A · p. 31

APPENDIX B

  • The evaluation covers seven paper variables, including five upper-air variables at 500 and 850 hPa, for twelve variable-level channels overall.The appendix lists the variables and their metadata in Table B1.Source: Appendix B · p. 32, Table B1 · p. 32
  • The climatology reference uses 1990–2019 ERA5 forecasts matched by calendar date and hour, scored with fair CRPS at the same lead time.CRPSS is defined against this probabilistic climatology; raw CRPS is unreported because geopotential’s numerical scale dominates the variable mean.Source: Appendix B · p. 32
  • Per-pixel and spatial-mean SSR distinguish local-error calibration from global coherence, with 1 as the reliable target and values above 1 indicating overdispersion.The appendix standardises channels by fixed 1990–2019 climatological scales so the multivariate scores remain proper.Source: Appendix B · pp. 32–33
  • Table B2 consolidates variable-mean CRPSS across 112 initialisation times and gives a 240 h per-variable breakdown.Its headline panel reports lead times 72, 120, 240, and 360 h; the appendix passage provides scope but not unseen cell values.Source: Appendix B · p. 34, Table B2

APPENDIX C

Multivariate scores place perturbed AIFS third of seven, while geostrophic and thermodynamic checks find no systematic SPW physical-consistency excess. Temporal-path and spectral diagnostics reveal deficiencies that single-lead scores do not capture.

Thermodynamic and state-dependent checks

  • Forecasts retain members within the Clausius–Clapeyron envelope, with supersaturated tails of 0.02–1.3% versus ERA5’s 0.1%.The forecast distributions are marginally narrower in specific humidity than ERA5.Source: Appendix C · pp. 35–36

Multivariate verification

  • Perturbed AIFS ranks third of seven on both Energy Score and Variogram Score, while AIFS-ENS leads and the worst baseline trails by 14%.The ordering matches per-variable CRPSS, so the multivariate gap is not an aggregation artefact.Source: Appendix C · p. 36

Physical-consistency checks

  • Across all eight baselines, only 0.6–1.4% of mass lies beyond 15 m s−1 from geostrophic balance, with no systematic SPW excess.SPW ranges from 0.6–1.3% and trained-probabilistic baselines from 0.7–1.4%, bracketing ERA5’s 1.0%.Source: Appendix C · p. 36

Temporal path structure

  • The three trained-probabilistic baselines take the top temporal-path score positions, while perturbed AIFS leads the SPW group.SIGK diverges from ES for GraphCast all: fifth of seven under ES, it is worst by a wide margin under SIGK, which detects temporally over-coherent frozen perturbations.Source: Appendix C · p. 37

Spectral bias with lead time

  • All baselines accumulate small-scale spectral power with lead time, most strongly for GraphCast all and perturbed AIFS, while planetary scales stay near truth.FCN3 remains closest to the truth spectrum.Source: Appendix C · p. 38

APPENDIX D

Appendix D adds calibration, variance-attribution, refresh, and Hurricane Milton diagnostics. Spread carries case-to-case information, but its magnitude and the effects of refresh vary by backbone and lead time.

State-dependent spread

  • At 240 h, every curve rises monotonically with spread, and binned RMSE from the lowest to highest decile grows by a factor of 4.0–7.3 for SPW baselines and 8.9–14.0 for trained-probabilistic ones.Source: Appendix D · p. 40
  • At 240 h, SPW spread-normalised RMSE is 0.92–1.47, not separable from trained-probabilistic baselines at 1.17–1.30; at 24 h SPW is 2.19–3.52 versus 1.10–1.20.The short-lead deficit reflects spread magnitude rather than discrimination: SPW identifies uncertain cases but spreads too little around them.Source: Appendix D · p. 40

Refresh cadence

  • Refreshing perturbations lifts underdispersed SFNO toward the target SSR of 1, barely moves Aurora, and worsens AIFS overdispersion at short-to-mid leads.The effect does not generalise across backbones.Source: Appendix D · p. 42

Hurricane Milton

  • In the Milton case, member minimum pressures span 942–967 hPa across baselines; each deepest member crosses the 976 hPa ERA5 floor, but none reaches the 895 hPa best-track value.Source: Appendix D · p. 43

APPENDIX E

The Hurricane Milton appendix compares storm structure, track errors, and ensemble dispersion across SPW and reference systems. Weight and initial-condition perturbations contribute differently across lead times, and their combination restores some dispersion absent from weight-only perturbation.

Warm-core structure

  • Every baseline reproduces Milton’s warm-core maximum; SFNO peaks at 61.9 m, 24% above ERA5’s 50.1 m reference.AIFS-ENS and FCN3 are within 3% of ERA5, while Aurora, AIFS, and Atlas are 1–8% below.Source: Appendix E · p. 44

Track evaluation

  • Milton track error grows from under 100 km at 0–24 h to as much as about 2,000 km by roughly 230 h, with Aurora encoder IC and GraphCast all IC among the lowest-error systems.The trained-probabilistic baselines detect the storm more often.Source: Appendix E · p. 45

Member-level wind fields

  • In the illustrated Milton forecast, member-to-member spread forms a compact ring around the vortex in the IC-augmented SPW, trained-probabilistic, and operational ensembles.The IC-augmented SPW spread has comparable magnitude and structure to the reference ensembles.Source: Appendix E · p. 46

Milton ensemble dispersion

  • For Milton, IC noise dominates short-lead spread and weight noise long-lead spread; weight+IC roughly doubles the early track cone relative to weight-only.Weight+IC also widens intensity spread at every lead, while both reference ensembles retain larger intensity spread than all AIFS SPW configurations.Source: Appendix E · p. 47

APPENDIX F

Appendix F collects acronym expansions, acknowledgments, and data and code availability information. The authors report that inputs are public and provide code to regenerate results, but do not redistribute forecast outputs or derived table and figure values.

Acronyms

  • The glossary expands the paper’s model, forecast, verification, and ensemble acronyms, including SPW as Stochastically Perturbed Weights.Source: Appendix F · p. 48

Author disclosures

  • The authors disclose AI assistance with drafting, table and caption polishing, script refactoring, and intermediate-result tabulation, while assigning scientific decisions and content to the authors.Source: Appendix F · p. 49

Data availability

  • Input data are public, and the code to regenerate results is released with the SwissClim Evaluations verification package; forecast stores and derived values are not redistributed.Source: Appendix F · p. 49
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