Neural general circulation models optimized to predict satellite-based precipitation observations

Dmitrii Kochkov; Ian Langmore; Janni Yuval; Stephan Hoyer

REVIEW 4 major objections 5 minor 3 cited by

Neural general circulation models optimized to predict satellite-based precipitation observations

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Training a hybrid general circulation model directly on satellite-based precipitation observations can make its precipitation climatology, extremes, and diurnal cycle substantially more realistic than conventional GCMs, reanalysis, and a…

desk verdict A real advance in the NeuralGCM program: training a hybrid GCM on satellite precipitation works, the forecast and mean-state claims survive an independent GPCP check, but the extremes and diurnal-cycle wins are only shown against the training target. read the letter →

arxiv 2412.11973 v1 pith:JEQD7PAT submitted 2024-12-16 physics.ao-ph cs.LG

Janni Yuval , Ian Langmore , Dmitrii Kochkov , Stephan Hoyer This is my paper · ORCID

classification physics.ao-phcs.LG

keywords NeuralGCMprecipitationparameterizationhybridmachinelearningclimatemodeldifferentiabledynamicalcoreIMERGsatellitediurnalcycleofextremeensembleweatherforecasting

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

General circulation models have persistent, societally important precipitation errors: mean biases are comparable in size to projected changes, extremes are poorly distributed, and the daily cycle peaks too early. This paper tries to remove those errors by training a hybrid atmospheric model directly on satellite-based rain observations instead of relying only on reanalysis or high-resolution simulation targets. The model is a differentiable dynamical core with a learned physics parameterization, augmented by a learned precipitation network; evaporation is diagnosed from the column water budget so the hydrologic cycle stays closed. Across 20-year simulations, the authors report that the model cuts mean precipitation error by about 40% relative to a 37-model CMIP6 AMIP ensemble, improves extreme and diurnal precipitation, and outperforms a 50-member operational ensemble in medium-range precipitation forecasts. The upshot is that observation-based training can directly improve a quantity that conventional parameterization development has struggled to fix for decades.

What carries the argument

The load-bearing object is the column water budget closure, Eq. (1): $P - E = \frac{1}{g}\int\sum_i \left(\frac{dq}{dt}\right)^{\mathrm{NNtend}}_i p_s\, d\sigma$, with $P$ the learned precipitation rate, $E$ the diagnosed evaporation, and the sum running over water-vapor, cloud-ice, and cloud-liquid tendencies from the learned physics network. A small Encode-Process-Decode network with a ReLU output predicts non-negative precipitation from the atmospheric column plus static embeddings, while the differentiable dynamical core and tendency network evolve the state. Enforcing this budget couples the precipitation loss to the physics network's moisture tendencies, which shifts the model's precipitable-water distribution toward observations and is what allows an observable (rain) to train the unresolved physics without breaking water conservation.

What would settle it

Examine the diagnosed evaporation fields in a long integration and compare them to direct flux observations or to a high-resolution water-budget product; if the fields show grid-scale artifacts that track precipitation errors, or if the model's precipitation skill collapses when the learned moisture tendencies are replaced by a trusted reanalysis budget, the water-budget closure is doing compensating work and the central claim is falsified.

Watch

Extended reading notes

Core claim

NeuralGCM was originally a differentiable dynamical core coupled to a learned physical-tendency network trained on ERA5. This paper retrains it end-to-end while adding a compact precipitation network that outputs the hourly precipitation rate, with evaporation then diagnosed as the residual of the column water budget, $P - E = \frac{1}{g}\int\sum_i \left(\frac{dq}{dt}\right)^{\mathrm{NNtend}}_i p_s\, d\sigma$. The precipitation network is trained against 6-hourly IMERG accumulations, while atmospheric state, evaporation, and other fields are trained against ERA5; the specific-humidity loss is down-weighted because ERA5 humidity itself is known to deviate from observations. In 20-year, SST-forced simulations started from 37 initial conditions, every run remains stable, and the model reproduces the IMERG precipitation-rate frequency distribution, annual-maximum daily precipitation (Rx1day), and diurnal phase more closely than ERA5, CMIP6 AMIP and historical runs, and GFDL's X-SHiELD cloud-resolving model. In forecasting, a 50-member NeuralGCM ensemble improves on the 50-member ECMWF ensemble for all 15 forecast days in CRPS, root-mean-square bias, spread-skill ratio, and Brier score at the 0.95 quantile, with the result holding against GPCP, a dataset not used in training.

Load-bearing premise

The load-bearing premise is that the learned physics network's moisture tendencies are accurate enough that the evaporation diagnosed from the column water budget is physically meaningful; if those tendencies merely compensate for the mismatch between ERA5 and IMERG, the precipitation gains could come with unphysical evaporation errors.

Editorial extensions

If this is right

Training on satellite precipitation removes the need to inherit precipitation biases from reanalysis or high-resolution simulation targets, which is the main route by which current hybrid models pick up errors.
A coarse 2.8° model can beat the operational ensemble in precipitation forecast skill, implying that resolution is not the only binding constraint for rain prediction and that learned physics can compensate.
Observation-trained hybrid models can be stable over 20-year climate integrations when the loss is tuned and stability is screened across random seeds.
The computational speed (about 1200 simulated years per TPU-day) makes large ensembles practical, as demonstrated by 732 twenty-two-year runs used to estimate the sensitivity of annual-maximum precipitation to temperature.
The same end-to-end recipe can be applied to any observable whose loss can be computed from model output, such as clouds or radiative fluxes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The two configurations explored here have complementary failure modes—predicted precipitation with diagnosed evaporation creates unrealistic sub-6-hour oscillations, while predicted evaporation with diagnosed precipitation produces negative rain. Enforcing both fields as learned outputs with a hard water-budget constraint and non-negativity is the natural next step and might remove both artifacts.
The diagnosed-evaporation model shows unrealistic instantaneous evaporation fields (Fig. S21), so a key test is whether the precipitation skill survives when the learned moisture tendencies are replaced by a physically trusted budget; if it does not, the improvement may be partly owed to compensating errors rather than to a better representation of convection.
Because the model was trained jointly on ERA5 and IMERG with the humidity loss deliberately weakened, the diurnal-cycle improvement is likely attributable mainly to the IMERG precipitation loss; training identical models with and without the precipitation term would make that causal attribution quantitative.
The reported global sensitivity of annual-maximum precipitation, $4.2\%\,\mathrm{K}^{-1}$, is lower than the $5$\textendash$10\%\,\mathrm{K}^{-1}$ range often quoted, and the authors note resolution suppresses the most extreme tail; running the same training recipe at higher resolution is a direct way to test whether the sensitivity rises toward that range.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The headline result is real: a hybrid GCM trained online against IMERG precipitation, with evaporation diagnosed from the column water budget, that runs 20-year simulations stably and beats CMIP6, ERA5, X-SHiELD, and ECMWF ENS on the precipitation metrics tested. That's a genuine advance in the NeuralGCM program, not a brand-new framework—the differentiable core and online training recipe are inherited from Kochkov et al. 2024. What's new is the precipitation network, the water-budget closure that makes P a state variable with E diagnosed, and the demonstration that an observational target is usable for end-to-end training of a hybrid GCM.

Credit where it's due: the paper ships code and model outputs, compares against a real operational ensemble on proper probabilistic scores, and includes GPCP as an out-of-training reference for mean precipitation (Fig S15) and forecast skill (Fig S5). The mean-state and forecast claims hold up under that independent check. The limitations section is unusually candid—seed-dependent stability, unrealistic instantaneous evaporation (Fig S21), sub-6-hour oscillations, and an explicit recommendation against using this configuration at frequencies higher than 6-hourly. That honesty buys goodwill.

Soft spots, in proportion. The stress-test concern is correct: extremes (Figs 5, S22, S23) and diurnal cycle (Fig 6, S16–S18) are evaluated only against IMERG, the training target. The model was optimized to match IMERG's CRPS, so those scores are not independent tests of physical accuracy. This doesn't sink the paper—GPCP covers mean and forecast, and the authors flag the diurnal artifacts themselves—but 'substantially surpasses' is established for mean and forecast, and only suggested for extremes and diurnal cycle until a GPCP or gauge-based check appears. Second, the most stable seed was selected post hoc; all-seed statistics aren't reported, so the stability claim is conditional. Third, down-weighting ERA5 specific humidity by 100x means the model is pulled away from reanalysis moisture; the diagnosed E in Fig S21 shows the cost. One point in the paper's favor: the alternative NeuralGCM-evap configuration, which predicts E and diagnoses P, actually does better on most precipitation metrics (Figs S25–S27), suggesting the skill is not an artifact of the specific P/E split.

Who this is for: anyone working on ML parameterization or hybrid GCMs, and anyone who cares about precipitation fidelity in climate models. It deserves a serious referee. The fixes are straightforward—report all-seed stats, add GPCP numbers for extremes and diurnal phase, state the valid time scales—and I'd expect a conditional accept after those additions.

Referee Report

4 major / 5 minor

Summary. The paper presents a hybrid neural general circulation model (NeuralGCM) trained end-to-end on satellite-based precipitation observations from IMERG, together with ERA5 atmospheric fields. Precipitation is predicted by a small neural network, and evaporation is diagnosed from the column water budget, so that precipitation is consistent with the model's moisture tendencies. The authors report substantial improvements over CMIP6 models, ERA5, and the X-SHiELD global cloud-resolving model in simulated mean precipitation, extreme precipitation, and diurnal cycle, and also report that a 50-member NeuralGCM ensemble outperforms the ECMWF ensemble in precipitation forecast skill out to 15 days.

Significance. If the claims hold, the paper is a significant advance: it demonstrates that a differentiable GCM can be trained directly on an observational precipitation product, that the resulting model remains stable in multi-decadal simulations, and that it produces competitive or superior precipitation forecasts at 2.8 degrees resolution. The work is supported by extensive evaluation on two datasets (IMERG and GPCP), open code and data availability, and a proof-of-concept large ensemble for extreme-precipitation sensitivity. The central claims, however, are weakened by the fact that the headline metrics for extremes and the diurnal cycle are evaluated only against IMERG, the very dataset used in the training loss, and by the paper's own documentation of unrealistic sub-6-hourly precipitation variability and unrealistic instantaneous evaporation. These issues are acknowledged in the supplementary material but need to be addressed in the main text and through additional independent evaluation.

major comments (4)

[Results, 'Precipitation extremes and precipitation rate distribution' and 'Diurnal cycle of precipitation'; Figs.] The extreme-precipitation and diurnal-cycle metrics are computed exclusively against IMERG, which is the precipitation product used in the CRPS training loss. The model was optimized to match IMERG precipitation, so its IMERG-based scores are not an independent test of physical accuracy. The paper does provide independent GPCP-based evaluation for mean precipitation (Fig. S15) and forecast skill (Fig. S5), but not for extremes or diurnal phase/amplitude. Since the central claim in the Discussion is that the model 'substantially surpasses' GCMs and ERA5 in 'mean state, extremes, and the diurnal cycle,' the authors should either add GPCP-based evaluation of extremes (e.g., Rx1day or 99.9th percentile, which are computable from GPCP daily data) and diurnal cycle if possible, or explicitly limit the claim to IMERG-defined skill and discuss the risk that IMERG-specific biases (e.g., overestimation of heavy precipitation) are being learned and reported as improvement.
[Results, 'Diurnal cycle of precipitation'; Figs.] The paper's own text states that 'the diurnal cycle in NeuralGCM exhibits unrealistic features, with certain times of day experiencing significantly more precipitation than others (Figs. 6e-g, S7), likely due to the model being optimized for 6-hourly precipitation accumulation,' and recommends against using this configuration at frequencies higher than 6-hourly. Yet the abstract and Discussion claim 'a more accurate diurnal cycle' and 'substantially surpasses ... the diurnal cycle.' The MAE-based harmonic metrics (Fig. 6a-d) may still favor NeuralGCM, but the model's diurnal precipitation shape is visibly unrealistic at sub-6-hour scales (Fig. 6e-g). The claim should be qualified to distinguish harmonic phase/amplitude skill from the model's unphysical high-frequency variability, and the implications for the 'accurate diurnal cycle' statement should be discussed in the main text.
[Methods, Eq. (1); Supplementary Eq. (S4); Supplementary Fig. S21] The diagnosed evaporation field E = NN_precip(X) - (1/g)∫∑(dq/dt)_NNtend ps dσ has the potential to be unphysical if the learned moisture tendencies from the physics network carry ERA5 biases. The supplementary material itself shows unrealistic instantaneous evaporation fields for this configuration (Fig. S21). If the precipitation improvement is achieved by compensating, unphysical evaporation errors, the attribution of the improvement to learning from observations is weakened. The authors should validate the diagnosed evaporation more directly, or at least analyze whether the water-budget closure relies on cancellation between the precipitation network and the moisture tendencies. As written, the paper's central mechanism—training precipitation while enforcing column conservation—is not fully supported for the diagnosed evaporation component.
[Discussion, 'Our work retains some noteworthy limitations'] The statement that 'the stable model was still obtained by training several models with varying random seeds and choosing the most stable one' is a selection procedure that could bias the reported stability. The 37-initial-condition and 732-run stability experiments are impressive and partially mitigate this concern, but the selection procedure and its potential effect on the stability and climate statistics should be described in the Methods and discussed. Without this, the 'remains stable for decadal simulations' claim is presented more strongly than the training procedure warrants.

minor comments (5)

[Supplementary Figure S24] The caption contains a typo: 'NeruralGCM-evap' should be 'NeuralGCM-evap'.
[Supplementary Figure S22] The phrase 'Mean absoulute error' should be 'Mean absolute error'.
[Methods, 'Neural network for predicting precipitation'] The description says the precipitation network predicts precipitation 'at 1-hour intervals,' but the training loss is on 6-hour accumulated precipitation. Clarify whether the network is trained on instantaneous 1-hour rates or on 6-hourly accumulations, since this distinction is relevant to the sub-6-hour precipitation artifacts.
[Results, 'Precipitation extremes and precipitation rate distribution'] The sentence 'We find similar conclusions when studying the 99.9th percentile (Fig. S22)' would benefit from the numerical MAE reduction for the 99.9th percentile, to match the quantitative context given for Rx1day.
[Introduction, third paragraph] The phrase 'stochastic training approach of [29]' is slightly ambiguous; it could be read as stochastic gradient descent rather than the rollout-length randomization described later. Consider rewording to 'the training approach of [29], which progressively increases rollout length.'

Circularity Check

1 steps flagged · score 4.0 of 10

Extremes and diurnal-cycle skill are evaluated against IMERG, the very precipitation product used in the CRPS training loss; independent GPCP checks cover only mean state and forecast skill.

fitted input called prediction [Training (p.3-4) and Results: 'Precipitation extremes and precipitation rate distribution' (Fig. 5), 'Diurnal cycle of precipitation' (Fig. 6); Discussion]
"We optimize for ... 6-hour accumulated precipitation (from IMERG). ... We compare the frequency distributions of NeuralGCM, ERA5, and a single CMIP6 model (IPSL-CM6A-LR) to that of IMERG. ... Fig. 6 demonstrates that NeuralGCM more accurately captures the timing of peak diurnal precipitation compared to ERA5 and GFDL AMIP run."

The network parameters are fitted by minimizing CRPS between predicted and IMERG 6-hour accumulated precipitation over 2001-2018. The headline climate statistics — precipitation-rate frequency distribution, Rx1day, 99.9th percentile, and diurnal phase/amplitude (Figs. 5, 6, S16-S18, S22, S23) — are then computed against the same IMERG product over 2002-2014, i.e., largely within the training period. Optimizing a precipitation loss against IMERG makes the model's precipitation distribution resemble IMERG by construction, so reporting superior extremes and diurnal-cycle scores relative to models not trained on IMERG is partly a restatement of the training objective. The paper's independent GPCP checks (Fig. S15 for mean climate; Fig.

full rationale

The paper's central mechanism — training a differentiable hybrid GCM on IMERG precipitation while diagnosing evaporation from the column water budget — is not derivationally circular: evaporation is defined by water conservation (Eq. 1 / Eq. S4), not by the precipitation target, and the GPCP results (a dataset not used in training) independently support the mean-state and forecast improvements. The self-citations to the authors' prior NeuralGCM paper [29] for the differentiable core and training recipe are normal methodology citations to a published, code-released framework; no uniqueness theorem or ansatz is smuggled in through those citations. The substantial circularity concern is narrower but real: the headline claims for extremes and diurnal cycle are evaluated exclusively against IMERG, which is the precipitation product used in the CRPS training loss, over the training period. This is a training-target evaluation, not an independent physical test, so those two aspects of the 'substantially surpasses' claim are partly forced by the fit. Because the mean-state and forecast claims have independent support and the architecture itself is externally grounded, the overall circularity is partial rather than total.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central result is a trained model; its claimed improvements depend on the training data, loss weighting, stability selection, and the water-budget diagnostic. We list the hand-chosen loss weights, the learned location embeddings, and the key data and modeling assumptions. No new physical entities are introduced.

free parameters (3)

Specific humidity loss scaling factor (relative to standard NeuralGCM) = reduced by factor of 100
Set to relax the fit to ERA5 specific humidity so precipitation can move toward IMERG (Methods, Variable re-scaling for losses).
Precipitation and evaporation loss weights = empirically tuned to ~10% and ~20% of total loss
Chosen by hand to balance conflicting ERA5/IMERG objectives; affects the final model's precipitation-evaporation trade-off (Methods).
Per-grid-point location embedding (8-dim) = learned during training, 8 values per grid point
Randomly initialized and optimized to represent static location-specific precipitation information for the precipitation network (Methods, Neural network for predicting precipitation).

assumptions (6)

domain assumption NeuralGCM differentiable dynamical core solves the large-scale atmospheric dynamics accurately
The model inherits the dynamical core from [29]; the paper patches stability issues (log surface pressure drift) but does not re-derive the core.
standard math Column water budget P - E = integral of NN moisture tendencies (Eq. 1)
Conservation of atmospheric water, used to diagnose evaporation from predicted precipitation; assumes negligible storage or condensation outside the tracked moisture variables.
domain assumption IMERG V07 final is an adequate proxy for true precipitation at 2.8 deg and 6-hour accumulations
Used as training target and primary evaluation; known IMERG biases (light/heavy rain) are acknowledged but assumed small at coarse scales.
domain assumption ERA5 reanalysis is reliable for atmospheric state and evaporation training targets
All non-precipitation targets come from ERA5, including winds, temperature, humidity, cloud water, and evaporation; the authors relax humidity only.
domain assumption Prescribed SST and sea ice are adequate for AMIP-style 20-year simulations
Standard protocol for atmospheric model evaluation; enables comparison to CMIP6 AMIP runs.
ad hoc to paper The small precipitation network with static embeddings can represent the mapping from column state to precipitation
A design choice; no guarantee of sufficiency, and the unrealistic sub-6-hour oscillations suggest a partial failure.

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Cite this review

Pith. "Pith review of Neural general circulation models optimized to predict satellite-based precipitation observations." pith.science (2026). https://pith.science/paper/JEQD7PAT

@misc{pith2026241211973,
  author       = {Pith},
  title        = {Pith review of: Neural general circulation models optimized to predict satellite-based precipitation observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JEQD7PAT}},
  note         = {Machine review of arXiv:2412.11973}
}

abstract

Climate models struggle to accurately simulate precipitation, particularly extremes and the diurnal cycle. Here, we present a hybrid model that is trained directly on satellite-based precipitation observations. Our model runs at 2.8$^\circ$ resolution and is built on the differentiable NeuralGCM framework. The model demonstrates significant improvements over existing general circulation models, the ERA5 reanalysis, and a global cloud-resolving model in simulating precipitation. Our approach yields reduced biases, a more realistic precipitation distribution, improved representation of extremes, and a more accurate diurnal cycle. Furthermore, it outperforms the mid-range precipitation forecast of the ECMWF ensemble. This advance paves the way for more reliable simulations of current climate and demonstrates how training on observations can be used to directly improve GCMs.

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Forward citations

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Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages · cited by 3 Pith papers

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

Kochkov, D. et al. Neural general circulation models for weather and climate. Nature 1–7 (2024)

work page 2024

[2] [2]

& Kiladis, G

Wheeler, M. & Kiladis, G. N. Convectively coupled equatorial waves: Analysis of clouds and temperature in the wavenumber–frequency domain. Journal of the Atmospheric Sciences 56, 374–399 (1999)

work page 1999

[3] [3]

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work page 2023

[4] [4]

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work page 2019

[5] [5]

V., Zwiers, F

Kharin, V. V., Zwiers, F. W., Zhang, X. & Wehner, M. Changes in temperature and precipitation extremes in the cmip5 ensemble. Climatic change 119, 345–357 (2013)

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[6] [6]

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