Improving precipitation forecasts in an AI weather model using observational data

Precipitation forecasts shape decision making across the global economy and are particularly important for agriculture [1]. Despite recent advances, evaluating and predicting sparse, intermittent, and localized precipitation remains uniquely challenging: global observational datasets often disagree, and rain gauge data poorly represent grid-box averages [2]. Simultaneously, weather models must approximate the processes that lead to precipitation, such as convection and microphysics, because they occur at scales too small to be explicitly resolved [3]. While recently developed Artificial Intelligence Weather Prediction (AIWP) models offer a significantly faster, cheaper, and often more accurate [4] complement to traditional forecasting systems, current models consistently over-forecast drizzle and under-forecast extreme weather events [5, 6, 7, 8]. Correcting these biases is a priority as AIWP models enter operational deployment [9, 10].

These precipitation errors stem from two distinct challenges: the models’ loss function and training data biases. Standard deterministic loss functions suffer from a double-penalty bias when precipitation is merely shifted in space; effectively, they express uncertainty as a smoothing of the forecast field, resulting in overly smooth forecasts that underestimate the highest intensity events and over-predict drizzle [11]. While recent probabilistic models mitigate some of this smoothing [12], their accuracy remains fundamentally constrained by biases in the training data itself. Most AIWP models are trained on ERA5 (ECMWF Reanalysis version 5) [13] that relies on the same microphysical and convective parameterizations that make conventional precipitation forecasting challenging. By emulating the larger-scale effects of these parameterizations, AIWP models inherit their structural biases; for ERA5, this includes a systematic overprediction of drizzle [14] and underprediction of high-intensity rainfall [2, 15, 16]. In operational settings, these biases can lead to a failure to issue warnings ahead of extreme events, or delayed or suspended harvests in operations such as sugarcane harvesting [17]. Satellite-derived observational datasets, such as IMERG (Integrated Multi-satellite Retrievals for GPM) [18] provide an alternative that does not inherit parameterization biases but carries its own retrieval and calibration biases. However, observational precipitation datasets are not everywhere consistent with ERA5 atmospheric variables, such as specific humidity and vertical velocity, which physically give rise to precipitation, making training at high resolution challenging with model architectures that respect such physical constraints [19].

Here, we demonstrate that an AI model architecture, a graph-transformer, can be used to successfully map the ERA5 atmospheric state to high-resolution satellite observations to mitigate systemic drizzle and extreme-precipitation biases in current operational AIWP models. To do so, we retrain ECMWF’s operational AI Forecasting System (AIFS-CRPS) [10] directly on the IMERG dataset. To isolate the impact of the training data, we retain the same graph-transformer architecture, Continuous Ranked Probability Score (CRPS) loss function, and core ERA5 atmospheric variables as in AIFS-CRPS, but substitute IMERG data for the target precipitation field; we dub this model Laxmi. We find Laxmi improves systematic precipitation intensity biases and medium-range accuracy when compared to the operational AIFS-CRPS [10] and ECMWF’s physics-based ensemble Integrated Forecast System (IFS ENS, abbreviated to IFS henceforth) [20].

Improved precipitation distribution

Selecting a target dataset for training an AIWP model requires balancing accuracy with spatial coverage and temporal resolution. While ground-based radar-gauge datasets, such as the U.S. Multi-Radar Multi-Sensor (MRMS) system [21], are considered closest to ground truth [22], they lack coverage across much of the tropics, precluding their use in global models. Reanalyses, such as ERA5 [13], circumvent the lack of coverage by using a physical model to assimilate observations. ERA5 is widely considered to be the best reanalysis [22], yet the convection parameterization in the underlying physical model produces too frequent precipitation events, increasing the frequency of light rain and decreasing the frequency of heavy rain compared to gauge data [23]. Compared to several satellite products, ERA5 produces precipitation about twice as frequently in the tropics and at the wrong time of day [14], and it underestimates precipitation associated with tropical mesoscale convective systems—which account for over 50% of tropical precipitation—by 25-34% [24]. Over the Indian subcontinent, IMERG more accurately reproduces the observed precipitation intensity–temperature relation than ERA5 when validated against gauge-based measurements [25].

We select IMERG as our observational target, as it consistently ranks as the leading global satellite dataset when evaluated against radar-gauge networks [22]. The structural differences between IMERG and ERA5 are most visible when comparing precipitation intensity and frequency (Figure 1), both of which are important for agricultural applications. At the $99^{\mathrm{th}}$ percentile, ERA5 under-produces precipitation compared to IMERG (Figure 1A-C) by over a factor of two across the Maritime Continent, with notable deficits also occurring in major agricultural regions such as India, Brazil, West Africa, and the central and eastern U.S.

In addition to missing extremes, ERA5 exhibits a pervasive drizzle bias. While the bias is largest over the ocean, IMERG also exhibits notably less drizzle across the same or similar agricultural regions (Figure 1D-F). Accurately forecasting continuous dry periods in these regions is vital for agricultural operations, which often require continuous dry windows for planting and harvest [17]. By training directly on IMERG, Laxmi avoids inheriting these structural errors.

To quantify the learned distribution shift from training on IMERG, we evaluate the global precipitation intensity ratio (Figure 1G). Alongside IFS and AIFS-CRPS, we include the deterministic AIFS-MSE [26] to highlight recent improvements in loss function development. We find Laxmi more accurately reproduces the IMERG precipitation distribution across the tropics and extratropics (fig. S7), reducing drizzle ($<3\ \mathrm{mm}\ \mathrm{day}^{-1}$), and better capturing the frequency of precipitation above $10\ \mathrm{mm}\ \mathrm{day}^{-1}$. While all models struggle at extreme intensities, Laxmi captures 68% of the observed events exceeding $50\ \mathrm{mm}\ \mathrm{day}^{-1}$, compared to $\sim30\%$ for both AIFS-CRPS and IFS. Above $100\ \mathrm{mm}\ \mathrm{day}^{-1}$, Laxmi captures 38% of the observed events, which is double that of IFS (17%) and nearly 10 times more than AIFS-MSE (4%). Only at the extreme tail ($>300\ \mathrm{mm}\ \mathrm{day}^{-1}$) does Laxmi fail to produce precipitation, a domain where the physics-based IFS still captures about 10% of observational frequency.

Global medium-range skill

We next evaluate Laxmi’s medium-range performance across 94 ensemble forecasts over the 2024 holdout year using WeatherBenchX [27, 28] against global ($60^\circ\mathrm{S}$–$60^\circ\mathrm{N}$) IMERG observations. Evaluated at $0.25^\circ$ spatial resolution, Laxmi demonstrates substantial improvements over both operational AIFS-CRPS and IFS (Fig. 2).

At a 1-day lead time, Laxmi reduces 24-hour accumulated precipitation CRPS by 19.3% compared to AIFS-CRPS and 20.1% compared to IFS. Unbiased ensemble mean root-mean-square error (RMSE) drops by 8.7% and 8.9%, respectively. The performance gap widens for heavy precipitation: at the same 1-day lead time, Laxmi improves the Brier Skill Score at the $95^{\mathrm{th}}$ percentile by 57.2% over AIFS-CRPS and 54.4% over IFS. For all metrics, Laxmi is more skillful than both models across the entire 15-day forecast horizon.

In addition to improving global error metrics, fine-tuning on IMERG also improves ensemble calibration. Overconfidence, or an underspread ensemble, is a common challenge in AIWP models [12] as optimization tends to reduce variance for localized events like precipitation [26].

Although probabilistic loss functions, such as CRPS, yield substantial improvement [10], reanalyses still underestimate precipitation variance due to parameterization shortfalls in the underlying model [29]. We quantify calibration via the spread-skill ratio, where 1 denotes a perfectly calibrated ensemble that is neither overconfident (ratio $<1$) nor underconfident (ratio $>1$). Fine-tuning directly on IMERG substantially reduces overconfidence: Laxmi achieves a ratio of 0.83 at a 1-day lead time and exceeds 0.97 by day 15. In contrast, AIFS-CRPS and IFS have ratios of 0.50 and 0.66 at day 1 and never exceed 0.77 and 0.83, respectively. By reducing overconfidence, Laxmi provides a more trustworthy assessment of its own forecast probabilities.

Similar to Lang et al. [10], we find a substantial improvement on medium-range metrics when using a higher-resolution model. We compared Laxmi against two coarser models trained on IMERG precipitation: a $1^\circ$ graph-transformer, IMERG-O96-CRPS (Figure 1), and NeuralGCM-precip at $2.8^\circ$ [19] (fig:8). When conservatively regridded to each model’s native resolution, Laxmi outperforms both across all error metrics. The sole exception is the spread-skill ratio, where all three models perform similarly. Rather than a uniform increase in skill with resolution, we find different error growth profiles when Laxmi is compared to each of the lower-resolution models. When compared to NeuralGCM-precip at $2.8^\circ$, we find that the largest skill gains are at the shortest lead times, consistent with better emulation of small-scale processes and higher topographic detail. However, when compared to IMERG-O96-CRPS at $1^\circ$, the largest benefit occurs at 5- to 12-day lead times. This contrast suggests that, unlike for physics-based systems, the observed performance gains cannot be attributed to spatial resolution alone; the architecture and training schedule also dictate how errors propagate at longer lead times.

An example with Indian tropical storms

To evaluate real-world early-warning capability, we examine hindcasts of the tropical monsoon systems making landfall in India over the evaluation period, a region chosen due to its heavy reliance on precipitation for agriculture and well-known vulnerability to extreme rainfall [30].

Forecasts of precipitation totals for four named storms (Asna, Dana, Fengal, and Remal) are shown in Figure 3 [see eq:31 for details]. We evaluate Laxmi against both operational AIFS-CRPS (10) and IFS (20). Across the forecasts, we find our model more reliably places heavy precipitation in the correct locations.

Across all ten events, Laxmi achieves a competitively-low average False Alarm Rate (FAR) while producing the highest Probability of Detection (POD) and Critical Success Index (CSI), a metric that both rewards correct detection and penalizes false alarms (fig:4a-fig:4c). This combination indicates that Laxmi is substantially better calibrated because it accurately forecasts heavy precipitation without additional false alarms. While IFS tends to overforecast heavy precipitation, as evidenced by its large FAR at high precipitation thresholds, Laxmi successfully detects heavy precipitation (high POD) without additional false alarms, suggesting that the model avoids a simple distributional shift toward more precipitation and instead captures both event location and intensity more accurately.

In addition to these categorical metrics, we also evaluate models on Brier score, which measures the accuracy of probabilistic predictions (calculated as the mean squared difference between the predicted probabilities and the observed outcomes). Across the 10 Indian tropical storms, Laxmi demonstrates the lowest average Brier score (Supplementary fig:10) across all precipitation intensity thresholds. However, evaluating how frequently each model delivers the best ensemble forecast, as measured by the lowest Brier score, demonstrates how Laxmi and IFS can complement each other operationally (fig:4d). At the 50 and 100 mm thresholds, Laxmi produces the best Brier score 12 of 20 times compared to 4 for AIFS-CRPS and 4 for IFS. However, at the 250 mm threshold, IFS produces the best forecast 5 of 10 times with Laxmi producing the best forecast the remaining 5 times. AIFS-CRPS is not competitive at any threshold. Thus, while Laxmi is substantially better calibrated to observation-based precipitation than AIFS-CRPS, IFS forecasts are essential at very high precipitation thresholds.

As an additional demonstration of generalizability, we also evaluate the five hurricanes that made landfall in the United States over the evaluation period and find that Laxmi provides the best forecast, as measured by Brier score at the 100 mm day$^{-1}$ threshold, for four of the five events. The case studies are shown in Supplementary fig:11 and the metrics for all 46 tropical cyclones globally are shown in Figure S12.

Discussion

Laxmi demonstrates the advantages of incorporating satellite-based observations into AIWP models. First, it achieves superior medium-range skill across global error metrics and produces a better-calibrated ensemble, yielding more accurate uncertainty quantification. Notably, it reduces CRPS by 19.3% at day 1 and 3.4% at day 10 compared to AIFS-CRPS, and rivals or exceeds the 6.4% maximum improvement achieved by AIFS-CRPS over the physics-based IFS. Second, Laxmi addresses structural intensity biases associated with the standard AIWP training dataset: dramatically improving the representation of heavy precipitation (30 to 200 mm $\mathrm{day}^{-1}$), and simultaneously reducing the pervasive overprediction of light rain [14]. Third, for tropical storms, the model generates higher detection rates without inflating false alarms for moderate-to-heavy events. However, we find IFS, a physics-based model, remains essential for forecasting the highest precipitation events. Finally, we demonstrate that higher spatial resolution is crucial for AIWP precipitation accuracy; Laxmi ($\sim$25 km) systematically outperforms its $\sim$100 km variant and surpasses NeuralGCM-precip [19] ($\sim$280 km) by over 10%, while resolving features at ten times finer scale.

Further development should address the remaining intensity biases and explore training to other precipitation datasets. Progress will likely require loss functions that more aggressively penalize drizzle [32], alongside methods that resolve the spatial mismatch between satellite precipitation and the reanalysis atmospheric state to better capture heavy rainfall. Although training on IMERG successfully mitigates the drizzle and extreme-precipitation biases inherited from reanalyses, it introduces its own retrieval and calibration biases. Future efforts could fine-tune models on regional datasets, such as MRMS [21], the Indian Monsoon Data Assimilation and Analysis (IMDAA) [33], and networks of rain gauges. While each of these datasets has its own limitations, they provide superior targets for customizing forecasts to region-specific tasks. Finally, real-time deployment will require fine-tuning on operational analysis to ensure compatibility with real-time initial conditions.

Our results indicate that further progress in AIWP is likely to be made by adding more satellite-based observations as fields into these models. Other currently available satellite-derived datasets, including ocean temperatures, soil moisture [34], and radiation variables [35] could enhance the learned dynamics of AIWP models, thereby extending predictability horizons even further.

References and Notes

Acknowledgments

We thank Ferran Alet, Aaron Bell, Janni Yuval, Timothy Lee, Aman Gupta, Alfred Piccioni, William Boos, and Pedram Hassanzadeh for their help. Prithvi Nambiar, Mohil Patel, and Josh DeAndria contributed to discussions and related applications.

Author contributions: Conceptualization: A.S., R.J., B.D. Methodology: J.S., A.S., R.J., B.D. Software: J.S., B.D., R.K. Y.P. Formal analysis: J.S. Writing—Original draft: J.S., Writing—Review and Editing: J.S., T.S., R.J., R.K., B.D., A.S. Supervision: R.J., A.S. Project administration: R.J. Visualization: J.S., R.K.

Competing interests: J.S., B.D., R.K., Y.P., R.J., and T.S. are employees of Alphabet. B.D., R.J., and Y.P. own Alphabet stock. Professor Aditi Sheshadri’s contribution to this publication was as a paid consultant and was not part of her Stanford University duties or responsibilities. The authors declare no other competing interests related to the paper.

Data, code and materials availability: The ERA5 dataset was downloaded and is available from the Climate Data Store (https://cds.climate.copernicus.eu/) and the IMERG data was downloaded and is available from the NASA Global Precipitation Measurement website (https://gpm.nasa.gov/data/imerg). The IBTrACS tropical storm tracks were downloaded and are available from NOAA (https://www.ncei.noaa.gov/products/international-best-track-archive). IFS ensemble forecasts were downloaded in July 2026 using Herbie [38] and are provided by ECMWF [20]. For training we used the open source Anemoi framework [39] with all evaluations conducted using WeatherBenchX [27, 28]. Graphics were generated using matplotlib [40] and cartopy [41].

Supplementary materials

Materials and Methods

Supplementary Text

Figs. S1 to S13

References (7-44)

Supplementary Materials for Improving precipitation forecasts in an AI weather model using observational data

Julian F. Schmitt; Bertrand Delorme; Robert C. King; Yashica Patodia; Tapio Schneider; Aditi Sheshadri; Ravi Jain

*Corresponding author. Email: [email protected]

This PDF file includes:

Materials and Methods

Supplementary Text

Figures S1 to S13

Materials and Methods

Data and pre-processing

We rely on two primary datasets for model training and evaluation: the ECMWF Reanalysis version 5 (ERA5) [13] and the Integrated Multi-satellitE Retrievals for GPM Version 07 Final (IMERG) [18]. Model variables match the operational AIFS configuration specified by Moldovan et al. [26] and comprise a 13-level ERA5 atmospheric state and 31 surface variables. To prevent physical inconsistencies when substituting the target precipitation field with IMERG observations, we explicitly exclude ERA5 convective precipitation, surface runoff, and snowfall. The forward map is formulated as $x_{i+1} = \mathcal{M}(x_i, x_{i-1})$, where $x_i$ defines the discrete global atmospheric state at a 6-hour interval $i$.

As IMERG observations (available from June 2000 onward) are distributed as instantaneous precipitation rates at a 30-minute, $0.1^\circ\times0.1^\circ$ resolution, we convert them to 6-hour accumulated totals by multiplying the instantaneous rate by the duration and summing. For training, these accumulations are conservatively regridded to the model grids (O96, $\sim1^\circ$; and N320, $\sim0.25^\circ$). The training period for IMERG-trained models is June 2000 through December 2023, with 2024 and 2025 held out for validation. Global evaluations are strictly bounded between $60^\circ$S and $60^\circ$N because beyond these latitudes, IMERG passive microwave retrievals are masked over frozen surfaces and cannot be reliably substituted by geostationary infrared estimates [42].

Model architecture and optimization

Laxmi utilizes a graph-transformer architecture identical to AIFS-CRPS [10] and was trained using the open-source Anemoi framework [39]. Like other more recent AIWP models [10, 12, 19], we use a probabilistic loss function, the almost fair Continuous Ranked Probability Score (afCRPS$_\alpha$), which substantially reduces the over-smoothing of the precipitation field. Training requires an ensemble to compute probabilistic scores and is therefore several times slower than training a deterministic model. During training, the forecast distribution $\{x_i\}_{i=1}^{M}$ is verified against a target state vector $y$ of ERA5 reanalysis or IMERG observations via the objective function defined by:

where $M = 4$ is the ensemble size, $\epsilon:= \frac{1-\alpha}{M}$, and $\alpha$ is a model hyperparameter governing the tradeoff between deterministic loss and ensemble spread, which we set to $\alpha= 0.95$.

Optimization is performed using the Adam optimizer ($\beta_1 = 0.9$, $\beta_2 = 0.95$, weight decay $= 0.1$) and a cosine learning rate schedule across a three-stage autoregressive rollout. Differing slightly from AIFS-CRPS [10], stage 1 uses a 1-step rollout for 75,000 steps with a maximum learning rate of $1.6 \times10^{-3}$. Stage 2 extends this to a 2-step rollout for 20,000 steps (maximum learning rate $1 \times10^{-5}$). Stage 3 increments the rollout from 3 to 12 steps once per epoch for 3,100 steps (maximum learning rate $2 \times10^{-6}$). The batch size is 32 for N320 models and 20 for O96 models. Unlike previous implementations that utilized operational analyses for the final stage [10], we perform all three training stages against ERA5 due to data availability, except for precipitation, which is scored against IMERG. We trained the O96 models on 10 NVIDIA A100 (80 GB) GPUs and the N320 model on 128 NVIDIA A100 (40 GB) GPUs. Both configurations took approximately 10 days to train.

Probabilistic climatology baseline

To establish a probabilistic baseline, we generate $M = 50$ member climatological forecast ensembles by resampling historical IMERG observations [19]. For any given target initialization time $t$, we construct an ensemble of forecasts by resampling historical IMERG observations, $X_{\mathrm{hist}}$. Each ensemble member, $m \in\{1, \ldots, M\}$ is derived by selecting a random source time, $s_m$, where the year is drawn uniformly from 2001–2019 and the day of the year is selected within a 15-day window centered on the target date. While the source year and day vary, the specific time of day is held constant to match the target initialization. The resulting forecast for any lead time $\tau$ is defined by $x_{\mathrm{clim},m} = X_{\mathrm{hist}}(s_m + \tau)$, with all $M = 50$ members sampled without replacement.

Indian monsoon case study setup

To evaluate model performance during localized high-impact events, we analyzed hindcasts for all 10 tropical monsoon systems that made landfall in India between February 8th, 2024 and September 30th, 2025 and achieved depression strength or higher in the International Best Track Archive for Climate Stewardship (IBTrACS) [36, 37]. The evaluation period was bounded by the date when IFS began providing operational forecasts at $0.25^\circ$ and the end of availability for our observational target, the IMERG v7 Final dataset. Forecasts for each event were initialized using the latest 06:00 or 18:00 UTC cycle that provided a lead time of at least 72 hours prior to the IBTrACS estimated landfall. Precipitation accumulation was calculated over a 4-day event-integrated window, spanning 1 day prior to landfall through 3 days post-landfall.

Evaluation metrics

Standard global medium-range forecast metrics, including CRPS, unbiased ensemble mean RMSE, and Spread-Skill Ratio are calculated using WeatherBenchX [27, 28].

To evaluate probabilistic predictions of extreme precipitation at a given threshold $q$ (e.g., the 95{sup}th` percentile), we convert an $M$-member ensemble forecast $\{x_m\}_{m=1}^{M}$ into an exceedance probability $p = \frac{1}{M} \sum_{m=1}^{M} \mathbb{I}(x_m > q)$, where $\mathbb{I}(\cdot)$ is the indicator function. We then compute the fair Brier score (abbreviated as Brier score or BS throughout the text), which corrects for the variance penalty inherent in finite ensemble sizes ($M$):

where $o = \mathbb{I}(y > q) \in\{0,1\}$ is the binary observation derived from IMERG precipitation $y$, and the second term applies the finite-sample correction.

To measure skill relative to climatology, we calculate the Brier Skill Score (BSS) as:

where $\mathrm{BS}_{\mathrm{climatology}}$ is the fair Brier score computed identically using the exceedance probability $p_{\mathrm{clim}} = \frac{1}{M} \sum_{m=1}^{M} \mathbb{I}(x_{\mathrm{clim},m} > q)$ over the $M = 50$ member resampled IMERG climatology.

For localized event evaluations, such as evaluating heavy precipitation associated with storms, we constrain our calculations to an “active region.” The region is defined as a bounding box covering the IBTrACS best-track estimate [36] for the 4-day accumulation period plus a 500 km buffer that is further restricted to grid cells where either the observations or any evaluated model outputs a non-zero probability of exceeding the target precipitation threshold.

To assess models within an operational decision-making context, we convert each forecast ensemble into a deterministic binary warning using a fixed threshold. The optimal choice of threshold, defined as a fraction of the ensemble which detects an event, varies based on the costliness of the event and the cost to take action. For events where the cost of inaction is the same as the cost of action, the best threshold is 50%. Since large event-total precipitation generally has higher costs for inaction we select a threshold of 30% [43, 44]. Grid points within the active region are classified into hits ($H$), misses ($M$), and false alarms ($F$). From these frequencies, we compute the Probability of Detection (POD $= \frac{H}{H+M}$), the False Alarm Ratio (FAR $= \frac{F}{H+F}$), and the Critical Success Index (CSI $= \frac{H}{H+M+F}$).

Supplementary Text

Custom Models Evaluated

In the main text we present Laxmi, a graph-transformer trained on an N320 grid, which is roughly $0.25^\circ$. In order to separately study the effect of model resolution and changing the precipitation training data, we also trained two additional models on an O96 grid ($\sim1^\circ$): one with ERA5 as the precipitation target, and a second with IMERG. We introduce the following triplet nomenclature to identify this models that identifies the precipitation training data, IMERG or ERA5, the model resolution (O96 or N320) and the loss function (CRPS or MSE). Thus, Laxmi is equivalent to IMERG-N320-CRPS. The additional models, trained at O96 resolution are ERA5-O96-CRPS, and IMERG-O96-CRPS. AIFS-CRPS would be “ERA5-N320-CRPS”, however we preserve the name given to it in the original paper [10].

We compare our model to another AIWP model, NeuralGCM-precip [19], that was trained directly on IMERG precipitation observations. Metrics shown here are the same as Figure 2 with panels (A) CRPS, (B) ensemble mean RMSE, (C) Brier skill score, and (d) spread skill ratio. Model initializations include 104 initializations at 00:00 and 12:00 UTC for 2024.