Deep learning has become an increasingly powerful tool in climate science, enabling advances in tasks ranging from the identification of atmospheric circulation patterns to weather forecasting and extreme-event classification. Yet the inherent complexity of atmospheric processes-particularly those driving rare, high-impact precipitation extremes-continues to challenge the ability of neural models to generalise robustly across diferent regimes. In this study, we evaluate seven single-level predictors-spanning standard ERA5 fields (total precipitation, total cloud cover, 10 m u- and v-wind components) and physics-enriched diagnostics (convective precipitation, K-index, vertically integrated moisture divergence)-to forecast extreme precipitation (> 95th percentile) over Greece. Using inputs from a broad European domain (34°-72° N, 25° W-65° E), we train a representative deep-learning architecture on diferent subsets of these variables to isolate the single predictor that maximises classification skill. To corroborate our findings, we then apply an XGBoost classifier and analyse its split-gain importances. We find that vertically integrated moisture divergence consistently yields the highest skill in the deep-learning framework across all three forecast lead times (2, 4, and 6 days), whereas the XGBoost model most frequently splits on total precipitation. Through this dual-model approach, we pinpoint the ERA5 fields and diagnostic indices that carry the strongest signal for local precipitation extremes.
Over the past decades, the frequency and severity of climate-related hazards—such as floods, flash
lfoods, and intense rainstorms—have risen sharply, underscoring the multifaceted impacts of global
warming [
Municipal, regional, and national decision-makers therefore urgently need forecasting tools that can
resolve local hazard impacts and enable proactive adaptation. In recent years, machine-learning (ML)
and deep-learning (DL) approaches have shown great promise for predicting precipitation and related
extremes (e.g., heavy rainfall, hail), in some cases achieving performance comparable to traditional
numerical weather prediction (NWP) in both speed and skill [
Yet, an open question remains as to which predictor variables contribute most to extreme-rain
classification. While many studies either assemble broad pools of reanalysis fields for general forecasting [
From physics prespective, extreme precipitation events in Greece often arises from synoptic-scale
disturbances (e.g., Mediterranean cyclones, atmospheric rivers) that traverse a broader European domain
before impacting local systems [
In this work, we fill the gap in variable-selection methodology by conducting an evaluation of ERA5 reanalysis variables as single predictors of extreme precipitation (> 95th percentile) over Greece. We assemble a core set of single-level predictor fields—encompassing thermodynamic, dynamic, and moisture-flux drivers—and including an anomaly indexes known to flag extremes. By training a representative deep-learning architecture on varying predictor inputs, we seek to identify the single variable that maximises classification accuracy for extreme precipitation events. To validate and interpret these results, we complement our neural model with an XGBoost classifier, whose split-gain feature importances provide an independent measure of each variable’s influence. This dual-model framework ensures that our conclusions about predictor relevance are robust across both deep-learning and tree-based paradigms.
Predicting precipitation has become a core task within the new generation of “foundation” weather
models—large-scale (MLWP) systems trained on decades of ERA5 reanalysis—that aim to represent
the full state of the Earth’s atmosphere. Notable examples include GraphCast [
An ensemble of machine-learning methods has also been applied to identify the dominant drivers of
extreme-precipitation intensity and frequency on a regional scale [
Another complementary approach is provided by a recent flash-flood study in central western
Europe, which links extreme precipitation events—defined as radar-derived hourly totals exceeding
40 mm ℎ− 1 from the RADOLAN dataset—to a small set of ERA5 proxy variables via linear modeling
over 1981–2020 [
We base our experiments on the ERA5 reanalysis [
Our predictor fields cover a broad European domain (34 °–72° N, 25° W–65° E) on a 144× 261 grid, sampled at two consecutive times frames—0 and 2 = 1 + 6 hours—and used to forecast a third time = 2 + , where is 2, 4, or 6 days depending on the forecast windo. We draw these samples at four synoptic times (00, 06, 12, 18 UTC) over the period of 1980 to 2023.
From the same ERA5 dataset we derive our target variable: a binary mask of extreme precipitation over the Greek domain (34°–42° N, 19°–28° E) on a 33× 37 grid (Fig. 1). For each grid cell, we compare its total precipitation value against the the 95th-percentile threshold—computed from the 1980–2023 ERA5 record over the Greek domain (Table 2)—to determine if it exceeds this extreme cutof. At forecast time , any cell whose ERA5 tp exceeds its threshold 3 is labeled “1” (extreme), while all others are labeled “0.” (3) > 95().
To train and evaluate our models, we split this dataset chronologically into three subsets: training (1980–2010), validation (2011–2020), and testing (2021–2023). All results presented in the next section are computed on the held-out testing data, ensuring that our performance metrics reflect the models’ ability to generalize to unseen, recent extreme-precipitation events. Total precipitation (tp), 10 metre u wind component,
10 metre v wind component, K index,
Vertically integrated moisture divergence (vimd) [15],
Total cloud cover (tcc) [15], Convective precipitation (cp)
Figure 2 illustrates our modeling framework. The network ingests two consecutive 6-hour snapshots of atmospheric fields—at times 1 and 2—each defined over a 144 × 261 grid spanning Europe. From these inputs, it produces at a later time = 2 + (with = 2, 4 or 6 days) a binary mask of extreme-precipitation events over the 33× 37 Greek subdomain.
To assess the predictive power of individual ERA5 variables, we keep the network architecture and hyperparameters fixed for all experiments Figure 3. This way, any diferences in forecast skill can be traced directly to the input variable set rather than changes in model complexity or training procedure. Practically, we train the same neural network repeatedly on input configurations ranging from each single predictor on its own up to the complete suite of seven fields, and evaluate performance using held-out validation metrics at lead time .
By systematically comparing these single-variable and multi-variable runs, we reveal which atmospheric fields—notably thermodynamic, dynamic, or moisture-flux diagnostics—carry the strongest signal for classifying > 95th-percentile precipitation over Greece, without confounding efects from architectural or tuning diferences.
To corroborate these findings with a complementary methodology, we also train an XGBoost classifier on the same input–output pairs. Because XGBoost expects tabular feature vectors rather than full spatial maps, we first apply an adaptive average pooling layer to downsample each 144 × 261 European predictor field to the 33 × 37 Greek grid, and then flatten these pooled maps into one-dimensional feature vectors. Unlike the deep-learning experiments—where we tested variables individually and in combinations—in the XGBoost workflow we present the full set of seven predictors simultaneously.
Furthermore, recognizing that tree-based ensembles require substantially less data to converge, we train XGBoost on a smaller time window (only the 2021–2023 samples) rather than the entire 1980–2023 record. This ensures that XGBoost sees exactly the same data representation as our neural network’s ifnal output layer, while also capitalizing on the eficiency of gradient-boosted trees. The resulting split-gain feature importances then provide an independent, model-agnostic ranking of which ERA5 ifelds carry the strongest signal for anticipating > 95th-percentile precipitation events over Greece.
Our model builds on the SmaAt-UNet [
In highly imbalanced binary-classification tasks (e.g., detecting rare “positive” pixels against an abundant “negative” background), standard binary cross-entropy tends to be dominated by easy negatives. To address this issue, we introduced the focal loss [16], which is an extension of standard binary cross-entropy.
ℒ () = − (1 − ) log (1)
We evaluate our classification models at three forecast lead times—2, 4, and 6 days—ahead, with results tabulated in (Tables 3, 4, and 5), respectively. In each case, we report the held-out test loss, precision, recall, and F1 score for the 2021–2023 period. As expected for a highly imbalanced task (few extremerain events vs. many non-extremes), recall remains low across all lead times, even as precision stays comparatively higher. Moreover, all four metrics steadily degrade as the forecast horizon lengthens—loss rises, while precision, recall, and F1 decline—highlighting the increasing dificulty of detecting rare events further into the future as it can be show Figure 6, where the deficalty of the model to predict iextremes increases with time.
Despite this overall decay, certain predictors consistently stand out. In our deep-learning architecture, vertically integrated moisture divergence (vimd) invariably ranks among the top three variables, alongside total precipitation (tp) and the K-index (kx). Figure 5 illustrates how vimd’s spatial patterns at 2 closely resemble the eventual extreme-rain mask at , underscoring its physical relevance. Although the precise ordering of tp, kx, nd vimd can shift slightly depending on whether we optimise for precision, recall, or F1, all three deliver balanced performance across metrics, confirming that their prominence is not an artifact of a particular lead time, metric choice, or data split.
When we turn to the XGBoost experiments (Table 6), the stability of variable importance is even more pronounced. Although we do not report XGBoost’s loss or precision—since our primary aim is to leverage its split-gain importances rather than its predictive scores—total precipitation and the K-index nonetheless occupy the first and second slots across all three horizons, followed consistently by total cloud cover (acc). In the middle ranks, vimd and convective precipitation (cp) trade places for the fourth position, while the 10 m u-wind component (u10) remains least important. This concordance between the tree-based and neural approaches—each with very diferent inductive biases—reinforces our conclusion that tp, kx, and vimd carry the strongest, most reliable signal for anticipating >95th-percentile precipitation in Greece.
Across all forecast horizons, the XGBoost feature-importance results mirror the deep-learning findings: vertically integrated moisture divergence (vimd) and total precipitation (tp) emerge as the top two predictors for classifying >95th-percentile precipitation events over Greece. This concordance between the tree-based and neural models underscores the robustness of these variables’ predictive power. Although each methodology—ConvLSTM-U-Net and XGBoost—learns from diferent inductive biases, they both identify vimd and tp as carrying the strongest signal for upcoming extremes. The full split-gain importances for each lead time are presented below. Convective precipitation (cp)
K index (kx) Total cloud cover (tcc)
Total precipitation (tp) Vertically integrated moisture divergence (vimd) 10 metre u wind component (10u) 10 metre v wind component (10v)
Variables Convective precipitation (cp)
K index (kx) Total cloud cover (tcc)
Total precipitation (tp) Vertically integrated moisture divergence (vimd) 10 metre u wind component (10u) 10 metre v wind component (10v)
Variables convective precipitation (cp)
K index (kx) Total cloud cover (tcc)
Total precipitation (tp) Vertically integrated moisture divergence (vimd) 10 metre u wind component (10u) 10 metre v wind component (10v)
f1
While our objective was not to build a state-of-the-art precipitation forecasting system, these experiments nonetheless revealed significant hurdles. Predicting a rare, binary extreme-event label—compounded as the precipitation which is also a cumulative variable and a heavily imbalanced dataset—proved challenging even for our fixed deep-learning architecture. As anticipated, skill declined at longer lead times, with classification performance dropping of beyond the first forecast horizon (2 days).
Notably, total precipitation (tp) emerged as the single most important predictor across all three lead times when considering the XGBoost. The K-index also delivered consistently balanced performance, underscoring its robustness for extreme-rain classification. When we examine the XGBoost results, tp and K-index occupy the top two importance slots for every forecast horizon, reflecting their dominant role in the tree-based splits. In contrast, the ConvLSTM-U-Net’s variable ranking is somewhat more lfuid: its top three predictors vary by lead time but when considering the whole picture kx, vimd, and tp where the most important predictors. This agreement on the leading variables—despite the diferent inductive biases of the two methods—reinforces our confidence that these fields carry the strongest signal for predicting >95th-percentile precipitation events over Greece.
In addition to these methodological insights, our results also align with physical expectations. Total precipitation (tp) intuitively carries direct information about extreme-precipitation and therefore should strongly influence event classification. In the XGBoost experiments—where all seven predictors were presented simultaneously—tp indeed emerges as the most important split feature, suggesting that its signal is amplified by the presence of complementary variables. By contrast, in the deep-learning tests using tp alone, it did not rank as the top predictor, indicating that tp is less informative in the absence of other fields such as the 10 m wind components (u10, v10). From a physical perspective, the finding that tp combined with wind components improves predictive skill is consistent with the idea that extreme precipitation in Greece is driven by large-scale weather systems propagating across Europe, where the wind fields govern the trajectories and moisture transport of those events.
Together, these findings highlight both the dificulty of rare-event forecasting in a pure deep-learning framework and the critical importance of leveraging physically meaningful indices like the K-index, vimd, which are not that common in deep learning forecastings. By identifying and focusing on the variables that carry the strongest signal—rather than relying on ever-larger input pools—future work can build more interpretable, eficient, and ultimately more reliable predictors of extreme precipitation.
Building on the insights gained in this study, we plan to pursue three main directions. First, we will extend our predictor set by incorporating key pressure-level variables—such as geopotential height, humidity, and wind fields at multiple atmospheric levels—to evaluate their added value for extremeprecipitation classification. Second, we will systematically explore a wider array of variable combinations and interaction efects, using our fixed-architecture framework to pinpoint the most informative subsets. Finally, we aim to compare our data-driven extreme-event classifier with outputs from numerical weather prediction models, testing its skills.
During the preparation of this work, the authors used ChatGPT to: Grammar and spelling check. After using the service, the authors reviewed and edited the content as needed and take full responsibility for the publication’s content.
This work has received funding from the European Union’s Digital Europe Programme (DIGITAL) under grant agreement No 101146490. R. Radu, I. Rozum, et al., Era5 hourly data on single levels from 1940 to present, copernicus climate change service (c3s) climate data store (cds)[data set], 2023. [15] E.-M. Walz, P. Knippertz, A. H. Fink, G. Köhler, T. Gneiting, Physics-based vs data-driven 24-hour probabilistic forecasts of precipitation for northern tropical africa, Monthly Weather Review 152 (2024) 2011–2031. [16] T.-Y. Lin, P. Goyal, R. Girshick, K. He, P. Dollár, Focal loss for dense object detection, 2018. URL: https://arxiv.org/abs/1708.02002. arXiv:1708.02002.