Dataset for "A Causal Intercomparison Framework unravels precipitation drivers in Global Storm-Resolving Models" by Ricard et al. (2025)

npj | climate and atmospheric science Article Published in partnership with CECCR at King Abdulaziz University https://doi.org/10.1038/s41612-025-01104-x A causal intercomparison framework unravels precipitation drivers in Global Storm-Resolving Models Check for updates Lucile Ricard1, Tom Beucler2,3, Claudia Christine Stephan4& Athanasios Nenes1,5 Correctly representing convective precipitation remains a long-standing problem in climate models, duetoitshighlyparameterizednature and unclear roleofdriversinteractingoverawiderange ofspatial scales. We analyze and compare simulations of Global Storm-Resolving Models, namely the DYAMOND models, using a methodology based on dimensionality reduction and causal inference, to unravel the contribution of large-scale variables and storm-scale dynamics on precipitation distribution. We derive regions of Column Relative Humidity (CRH), which exclude sharp humidity gradients and help define coherent thermodynamic environments, which are subsequently found to control precipitation throughout half of the tropics. The mean CRH is the primary large-scale driver in regions sufficiently large to maintain homogeneity that is unaffected by storms over the 30-day simulation period. The control of mean CRH on precipitation is notably amplified by considering explicitly the intermediate role of the convective area. Moreover, the effect values are consistent across models and quantiles, which could be further employed to constrain GCMs. Our results show that the most extreme intensities (99.9th percentile) cannot be adequately represented without highresolution data on vertical velocity. However, their effect on precipitation varies considerably across models and precipitation quantiles, making it more difficult to develop a constraint on storm-scale control. Precipitation plays a crucial role in the terrestrial energy balance and water cycle. Still, it is a complex, non-linear, and multi-scale atmospheric process that eludes adequate representation in models1.Inthetropics, precipitation is mostly produced through deep moist convection2and has long been poorly understood owing to a paucity in observations and the challenges associated with obtaining them (coverage by ocean, deserts, and forests). After a century of observations and study however, tropical precipitation remains one of the most uncertain aspects of atmospheric models, due to the complex relation between the convective cloud ensemble and its environment. Convection occurs when air in a small, local area becomes very buoyant, within a larger-scale disturbance3. Meanwhile, the latent heat released in tropical convective systems serves as the primary energy source in the tropics. It increases the buoyancy of the air and drives further large-scale upward motion and the global circulation system4,5. Convective precipitation occurs on spatial and temporal scales too small and too short to be explicitly resolved in traditional Global Climate Models (GCMs) with horizontal grid spacing of 50 km and above. Parametrization schemes encode our physical understanding of how small-scale processes in these models affect the grid scale, and in most cases are controlled by large-scale atmospheric state. As a result, parameterizations have been identified as the most relevant cause of systematic errors in weather prediction and climate models6. One notable bias is the drizzle bias, where GCMs typically fail to reproduce the precipitation distribution accurately, with most underestimating heavy precipitation7,8. One reason is that the exact dependency of precipitation on its environmental conditions is still unknown, especially in the tropics where large-scale forcing is weak and convective precipitation occurs over a wide range of spatial scales. Tropical precipitation is proven to be highly dependent on the columnintegrated water vapor9,10. Moisture quasi-equilibrium characterizes the 1Laboratory of Atmospheric Processes and their Impacts (LAPI), School of Architecture, Civil & Environmental Engineering, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland. 2Faculty of Geosciences and Environment, University of Lausanne, Lausanne, Switzerland. 3Expertise Center for Climate Extremes, University of Lausanne, Lausanne, Switzerland. 4Leibniz Institute of Atmospheric Physics (IAP), University of Rostock, Rostock, Germany. 5Center for the Study of Air Quality and Climate Change (CSTACC), Institute of Chemical Engineering Sciences, Foundation for Research & Technology-Hellas (FORTH), Patras, Greece. e-mail: lucile.ricard@epfl.ch;athanasios.nenes@epfl.ch npj Climate and Atmospheric Science | (2025) 8:245 1 1234567890():,; 1234567890():,; relationship between atmospheric stability and the moisture which fuels convections11. However, some variability in moisture convergence and entropy divergence is not explained by environmental parameters. This suggests there are convective-scale drivers that operate independently of the larger-scale environment. The role of the small-scale structures is also poorly understood. Tropical convection can self-organize, due to numerous positive feedbacks that maintain the moistening necessary for convection12. Thus, convective elements may group together to form Mesoscale Convective Systems (~100 km in horizontal scale), an order of magnitude larger than that of a convective cell (1–10 km)13. The degree of spatial aggregation has been shown to be strongly linked to the intensity of precipitation under certain humidity conditions14.Moreover 15, showed from observations that most of the regional increase in tropical precipitation over time (i.e., due to climate change) is associated with changes in the frequency of organized deep convection. While mean precipitation is constrained by the global energy budget, the frequency and intensity of precipitation extremes may be much less linked to global and large-scale quantities - and may be constrained by the local water vapor availability. Vertical motion and precipitation are tightly linked, which makes it difficult to assess the precipitation response to changes in dynamics. The aim of this study is to unravel the control of storm-scale dynamics (vertical velocity) and large-scale thermodynamics on the tropical convective precipitation characteristics (average and extremes). To do so, we analyze simulations from Global Storm Resolving Models (GSRM) gathered in the DYAMOND (Dynamics of the atmospheric general circulation modeled on non-hydrostatic domains) winter project16. The highresolution fields are 40-day-long simulations (30-day without spin-up) at around 5-km resolution, in which the deep convection is explicitly resolved. The model physics is thus consistent from the planetary scale to the mesoscale and allows for a better understandingof the storm-scale processes on the convective precipitation17. We use an unsupervised dimensionality reduction technique, δ-MAPS, to identify coherent regions of Columnintegrated Relative Humidity (CRH) in the tropics (30°S-30°N), and therefore exclude sharp humidity gradients (referred to as“moist margins”). We then study the interplay between the large-scale thermodynamics, the convection-scale dynamics, and convective precipitation in these coherent regions, and their interactions both with and without considering moist margins. To do this, we propose a causal graph that represents the qualitative causal relationships between the variables of interest and constitutes our framework to compare the GSRMs, hence referred to as our causal intercomparison framework. The causal underlying structure was determined based on our expert knowledge, with the assumption that the thermodynamic and dynamical contributions are two distinct contributions. We estimate and compare the linear causal effects along the causal pathways of the graph in the different GSRMs, with the objective of determining the relative importance of the different causal pathways. Results Coherent regions of Column Relative Humidity On average, 73.7% of grid cells in the tropics in the DYAMOND models experience convective rain at least once in February 2020 (Supplementary Table 1). One possible partitioning of the tropics is the one described in ref. 18, which showed the distribution of Column-Integrated Water Vapor (CWV) is bimodal in the oceanic tropics, with a moist atmospheric regime - in which convective storms are confined in - separated from the dry regime by a moist margin occurring at synoptic scales and persisting for at least a day. Here we opt for a partitioning based on the Column Relative Humidity ðCRHÞvariable, which has the advantage to have a universal relationship with rainfall, invariant across all types of forcings19–21, while still having this signature of a dry and a moist regime separated by a moist margin. By merging grid cells into physically coherent regions using the δMAPS method22–24, we both decrease the dimensions of the original grid and define coherent large-scale thermodynamic environment. This region inference comes with a homogeneity threshold for CRH and condition it to be above this threshold. δ-MAPS is an unsupervised technique: the numbers, sizes and shapes of regions are specific to each model output (see Methods section). Here, we apply δ-MAPS to CRH fields in order to group grid cells into coherent humidity regions that differ based onthe GSRM.The number of these regions varies from 31 to 34 across the ensemble of models (Fig. 1). However, we control the area coverage in the tropics with the hyperparameter δ(Supplementary Fig. 1); with δequals to 0.30. On average 54% of the grid cells are covered across the model ensemble (Supplementary Fig. 1 | Coherent humidity regions in DYAMOND models (δ=0.30). Regions inferred in CRH fields in GEOS-3km (a), ARPEGE-NH-2km (b), ICON-NWP-2km (c), SHIELD-3km (d), UM-5km (e) and gSAM-4k (f) with δ-MAPS algorithm. Hyperparameters k, αand δmodulate the size and the number of regions, and were set to 100, 0.01, and 0.30, respectively. Grid cells within regions are moderately correlated (≥0.30). The number of regions varies from one model to another, and ranges from 31 to 34. On average, regions cover 53.73% of the tropics. Moist gradients are excluded from the regions, and colors indicate the mean of CRH in regions. https://doi.org/10.1038/s41612-025-01104-x Article npj Climate and Atmospheric Science | (2025) 8:245 2 Table 2), providing a good depiction of the tropics. This enables us to gain insights into the relationship between the extent of CRH fields and their effects on storm systems, which, in turn, are not numerous or strong enough to disrupt the homogeneity of the large-scale state over the course of the simulation. It is worth noting the distribution of CRH from coherent regions exhibits a distinct shape compared to that of the entire tropics, which shows the δ-MAPS regions here do not include very dry or very wet regimes but rather intermediate humidity levels (Supplementary Fig. 2). Thereafter, we mix the model data and the regions, in order to conduct the causal analysis both in the native regions of the models (i.e., in the coherent humidity regions) and in the external regions (called hereafter “cross-modelregions”). Concretely, with six GSRMs (noted M i ) and their inherent coherent humidity regions (noted Ri), we perform the causal effect estimation in thirty-six configurations of model data and regions (Mi;RjÞ.Themodel data are said to be extracted in coherent humidity regions when i¼jand in cross-model regions when i≠j. The former regions are the thermodynamically-controlled regions which exclude the sharp humidity gradients, and the latter regions allows us to test the validity of results out of δ-MAPS regions. The causal analysis is conducted by taking as input an ensemble of regions, where each region is considered as a realization of the same subprocesses, i.e., each region is a sample. The thermodynamic state for each region is described with the spatially-averaged Column Relative Humidity (CRH) and surface-level saturation specific humidity q surf . The CRH indicates how close to saturation the water vapor in the column is (and therefore how close to condensation and precipitation it is), while q surf measures the maximum amount of water vapor that can be held by the atmosphere near the surface, and increases quasi-exponentially with surface temperature. Thus, the two variables reflect the vertical profiles of heating and moisture, which can promote or inhibit convection. Precipitation and dynamics at the convective-scale are described by variables averaged in convective areas within the regions, i.e., where convective precipitation occurs (see Methods section). Precipitation characteristics are represented through precipitation quantiles X, which we refer to as PrX. Convective Area Fraction (CAF), or the proportion of convective grid cells in a given region at a given time, provides information about the spatial extent of convective activity. Finally, we retrieve the updraft velocity win convective areas of the regions, and more precisely, its first two moments μwand σwat 500 hPa25. Causal intercomparison framework We now unravel the drivers of convective rainfall in the regions for each GSRM by use of a causal-intercomparison framework to quantify the information propagating between the resolved variables in the highresolution simulations, and reveal different effect sizes than those which may be obtained with a traditional linear regression approach. The causal graph encodes assumptions about the absence and presence of causal relations, which allows us to limit the effect of spurious correlations and provide more interpretable and trustworthy results than those obtained from only correlation considerations. Prior to this causal analysis, we gained an insight into the nature and persistence of the dependencies with Machine Learning (ML) approaches (see Methods and Supplementary Information). A linear regression model and two different neural networks were applied to predict PrXor CAF from the different drivers (Supplementary Fig. 3). None of the advanced deep-learning models significantly outperformed the linear regression model, neither for the prediction of quantiles nor for the prediction of the convective area fraction (Supplementary Fig. 4). Notably, the failure of a Long Short-Term Memory (LSTM) model to gain information from a sequence of input data proves that considering a range of time lags simultaneously is of limited value. Based on these results, we concluded that (i) the dependencies are linear, (ii) we can exclude a time-based sequence mode processing, (iii) storm-scale dynamics do not directly drive the convective area fraction, and, (iv) large-scale CRH controls precipitation quantiles both directly and indirectly through the CAF26. These outcomes, and notably the linear model assumption, motivated our choice to perform a causal analysis. Instead of predicting precipitation, we aim to estimate the temporal precedence of variables. The approach also enables a clearer distinction of the timescales associated with the effect of each driver. We present a causal graph (Fig. 2) which is assumed to be a good representation of convective precipitation across DYAMOND models. Our graph consists of multivariate time series data, with six components {CRH;q surf ,μw, σw,CAF;PrX}. The thermodynamic variables drive PrXthrough two causal paths: a direct path and a path mediated by CAF.CAF is referred to as mediator, as it is an intermediate process on the information transfer from CRH=q surf on PrX. Also, we assume the dynamic and thermodynamic drivers have separate influences on precipitation, and are therefore not related. Finally, the six components drive themselves (indicated by self-arrows in Fig. 2), which means that we study the influence of the other drivers on the non-persistent part of precipitation. The causal graph represents the qualitative causal relationships between the variables of interest. The most important assumption here is that the causal graph is causally sufficient, that is we assume there are no hidden common causes (common confounders). Then, with a causal inference approach, one can go further and quantify the causal effects associated with the causal pathways. Under the assumption of a linear model, the “causal pathway”method (or Wright approach) is the most suitable approach as it allows to decompose the causal effect as the sumproduct of the path coefficients, which are estimated by linear regression of every node on its parents27. Thus, the total effect of CRH=q surf on PrXis calculated as the sum of the direct and mediated effect, respectively associated to the direct path and the path mediated by CAF (Fig. 2). The mediated effect is the product of the effect of CRH=q surf on the CAF,and the effect of the CAF on precipitation. These two intermediate effects are associated with time lags τ1and τ2that sum up to τ.Valuesofτ1and τ2were selected at each time lag so the total effect of CRH on precipitation is maximized (see Methods section). The path analysis is performed with the “Linear Mediation”class of the causal inference library Tigramite28,29 and we use the measure Ifrom the information-theoretic framework30,31 to quantify the linear causal effect of perturbation, thus ICE X!Yrefers to the causal effect of the component Xon the component Y. We assume the regions in each DYAMOND model are multiple realizations of the same physical process, and the estimation of coefficients and causal effects arise from the data obtained in the ensemble of regions. Fig. 2 | Causal graph of the process-oriented intercomparison of the tropical convective precipitation in DYAMOND models.Storm-scale dynamics (moments of updraft velocity) directly drive the quantile of precipitation PrX. Large-scale thermodynamics drives the quantile of precipitation both directly and through the convective area fraction. Each variable drives itself, denoted by the self-arrows. Links are associated to a time lag τ(in hours) and to a path coefficient that expresses the strength of the direct causal effect. The sum of τ1and τ2is equal to τ. Causal effect values are calculated using the Wright approach. https://doi.org/10.1038/s41612-025-01104-x Article npj Climate and Atmospheric Science | (2025) 8:245 3 Drivers of tropical convective precipitation First, we analyze the causal effect values averaged across the DYAMOND ensemble in the coherent humidity regions. Panels of values on Fig. 3show the causal effects inferred at a specifictimelagτ, every 3 hours up to three days in the past. They show that regional-scale q surf is a weak causal driver (Fig. 3d), likely due to its low variability in the tropics where saturated temperature and water vapor gradients are weak. To first order, this means the role of the thermodynamic environment can be captured through the role of CRH.Byreplacingq surf by the standard-deviation of CRH,wedonot obtain much higher causal effects (Supplementary Fig. 5), that is the effect of storms on humidity fields is not significant enough to influence subsequent storm events. Thus, the average of CRH fields is the main (large-scale) parameter that impacts storms. Precipitation is driven by small-scale dynamics at short timescales (≤6 hours) and by regional-scale CRH at longer timescales (Fig. 3a–c). Indeed, moments of updraft velocity have their maximum causal effects ICE;max μw!prXand ICE;max σw!prXat 3 hours lag, respectively on the 25th and 99.9th percentiles (Fig. 3a, b). Mean updraft drives the light and moderate precipitation (ICE;max μw!pr25th = 0.18) while its deviation drives heavy rainfall (ICE;max σw!pr99:9th = 0.17). The influence of the thermodynamic component peaks one day before the rainfall event, with a higher magnitude (ICE;max CRH!pr99:9th = 0.31) than the dynamic effect (Fig. 3c). Also, CRH exhibits a more consistent influence on the precipitation distribution compared to updraft velocity, although the updraft velocity effect is stronger for high percentiles. We conclude that large-scale states play an important role one day prior to the precipitation, but relevant information is contained in the high-resolution updraft velocity fields. Precipitation is driven almost instantaneously by the local dynamics, with heavy precipitation being primarily influenced by the second moment of w. Enhanced large-scale preconditioning outside of moist margins We investigate whether the effect sizes hold outside coherent humidity regions, and can be extended to the whole tropics. Panels of causal effect values are reproduced in the cross-model regions (Supplementary Fig. 6). Causal effect of CRH drops (e.g., ICE;max CRH!PrXis now 0.17), while causal effects of wremain constant. This suggests thatthemomentsofupdraftvelocity drive the convective precipitation independently of the large-scale CRH gradients, and that the large-scale preconditioning is enhanced when moist margins are excluded. To confirm the above, we compare directly the causal effect values in reference regions and in cross-model regions on Fig. 4. Dynamic effects overlap well in the two ensembles of regions (Fig. 4b, c). ICE CRH!99:9th is roughly twice higher in the coherent humidity regions (Fig. 4a) where its maximum effect (τ=24h)isshiftedinthepastcomparedtothe maximum effect in the cross-model regions (τ= 18 h). In both ensembles of regions, there is a monotonic increase of ICE CRH!99:9th ,followedbyasharp monotonic decrease in the 12 hours preceding the rain, confirming that the representation of updraft velocity remains crucial for the representation of precipitation. We also assess the relative importance of the (almost) instantaneous control of storm-scale dynamics (τ= 3 h) and of the large-scale preconditioning control (τ= 24 h) in the coherent regions and in the crossmodel regions (Supplementary Fig. 7). In the coherent thermodynamic environments, the effect of the (resolved) CRH becomes stronger - on average - than the effect of updraft velocity. The mean effects across the DYAMOND ensemble suggest that the large-scale thermodynamic component dominates over the dynamic component in coherent humidity regions. However, we must ensure that the variability across models is low before concluding on a predominant causal driver. We discuss the agreement between models in the last section Inter-model differences.Werather highlight the distinct timescales at which the drivers operate, and we further investigate the reasons of such important role of CRH in coherent regions. Role of convective mesoscale organization To better understand the mechanisms behind this enhanced preconditioning, we examine the contribution of the direct and mediated effect of CRH on precipitation in the coherent humidity regions (Fig. 3e, f). The direct effect can plausibly be associated with a control ofprecipitation via the water vapor availability while the mediated effect is associated to the degree of convective organization. The two effects have comparable strengths but Fig. 3 | Thermodynamic and dynamic causal effects on precipitation in coherent humidity regions. Values of dynamic causal effects ICE μw!PrX(a) and ICE σw!PrX(b), and thermodynamic effects ICE CRH!PrX(c), ICE qsurf !PrX(d), direct Idirect CE CRH!PrX(e) and mediated Imediated CE CRH!PrX(f) over a range of quantiles and time lags. Causal effects are estimated in the coherent humidity regions and averaged across the DYAMOND ensemble. https://doi.org/10.1038/s41612-025-01104-x Article npj Climate and Atmospheric Science | (2025) 8:245 4 operate at different timescales, with a higher temporal precedence attributed to the mediated effect. Thus, we distinguish the fast direct effect (between 12 and 30 h) from the slow mediated effect (≥30 h). The clear temporal separation between the two effects is exacerbated by our way to select τ1and τ2(see Methods and Supplementary Fig. 8) The maximum direct effect occurs at a lagof 24 hours with a value of 0.21, while the maximum mediated effect peaks at a lag of 60 hours with a value of 0.19. The two effects drop in cross-model regions (Supplementary Fig.6e,f).Theenhancedlarge-scale preconditioning is very clear for both causal pathways on Fig. 4d, e. We also see the maximum mediated effect in reference regions is shifted further in the past compared to in cross-model regions (Fig. 4e). We conclude that CRH drives as much precipitation via the two causal pathways, and both effects along these pathways strengthen within the coherent CRH regions with a slightly stronger enhancement of the mediated effect (Figs. 3and 4), which explains the shift of the maximum effect towards the past. We take a closer look by representing the total, direct and mediated effects on the 99.9th percentile for the six models in their coherent humidity regions (Fig. 5). The models agree well at short timescales, and diverge at long timescales. DYAMOND models disagree both for the direct effect and mediated effect, but this matters more for the mediated effect which peaks at long timescales (Fig. 5c). Only the effects on 99.9th are represented on Figs. 4and 5,butthe enhanced large-scale control and more particularly the enhanced mediated large-scale control are shown to hold bothformedianandhighpercentiles (Supplementary Figs. 7 and 9). We also performed a causal analysis in a modified causal graph in which the links from CRH and from q surf on CAF were suppressed, leaving only direct pathways to precipitation. This ablation experiment revealed that the causal effect ICE CRH!PrXis weaker than in the original graph (Supplementary Fig. 10), which shows the explicit representation of mediated pathway contributes to a larger impact of the thermodynamic component on precipitation. We note the effects without the mediated pathway are not much weaker, which suggests that the mediated Fig. 4 | Largeand storm-scale control on the 99.9th percentile. Causal effects ICE CRH!Pr99:9th (a), ICE μw!Pr99:9th (b), ICE σw!Pr99:9th (c), direct Idirect CE CRH!Pr99:9th (d) and mediated Imediated CE CRH!Pr99:9th (e). Mean and standard-deviation of the causal effects’strengths are compared in coherent humidity regions (black) and in cross-model regions (purple). Fig. 5 | Direct and mediated causal effect of CRH on the 99.9th percentile in coherent humidity regions. Total causal effect ICE CRH!Pr99:9th (a), direct Idirect CE CRH!Pr99:9th (b) and mediated Imediated CE CRH!Pr99:9th (c) as a function of time lags. Colored dotted lines represent the values estimated in the individual models, and the solid black line the values obtained for the DYAMOND ensemble. Standard-deviations associated with the maximum causal effect values are specified in the titles. https://doi.org/10.1038/s41612-025-01104-x Article npj Climate and Atmospheric Science | (2025) 8:245 5 large-scale control is not entirely lost but partly transferred to the direct link, however, the interpretability is more difficult. We further examine the mediated effect of CRH on precipitation, and decompose it into the effect of CRH on CAF and the effect of CAF on Pr99:9th (Fig. 6). It is worth noting the effect of CRH on CAF does not vary with quantiles. We see the enhanced control in coherent humidity regions is fully explained by the enhanced control of CRH on CAF.Thecausaleffectin reference regions is doubled (the ratio of the causal effect in reference regions over causal effect in cross-model regions equals 2.07), and furthermore its maximum value is shifted further into the past (33 hours lag in reference regions, while the maximum value is reached at 18-hour lag in the cross-model regions). By focusing on coherent humidity regions, we increased the likelihood of capturing convective rain from organized convective systems, particularly in moist regimes. This is an interesting result because precipitation - notably precipitation extremes - is enhanced above a certain critical CAF value. This is related to the previous observations made with the effect of updraft velocity on precipitation (Fig. 4b, c): the control of the convective scale drivers - both the convective updraft velocity or the convective area - on the precipitation does not vary with the large scale CRH gradients. We evaluate the robustness of our results to the defined regions by conducting a similar causal analysis in more coherent humidity regions identified with δ= 0.60 (see Methods). The results indicate stronger largescale CRH control in these smaller, more coherent regions, while stormscale control remains unchanged (Supplementary Fig. 11). This confirms our findings and reveals a relationship between region size and the CRH effect. However, since only a small portionofthetropicsisrepresentedby these δ= 0.60 regions, there is higher model uncertainty. We conclude that the enhanced preconditioning in homogeneous regions is explained by both a stronger control of CRH on water vapor availability and convective area fraction, with the latter being more important further into the past. The effect of CRH on CAF peaks at 33-hour lag, while the effect of CAF on precipitation peaks at a 3-hour lag. Once again, the variability across models is larger over longer timescales, which means the uncertainty of the mediated effect is rather linked to the effect of CRH on CAF. Inter-model differences Until now, we have been interested in the average of the causal effects that emerge from all the GSRMs. We now analyze the individual causal effects of models. As we can see in Fig. 7, the inter-model variability is too important forustoconcludeonthedominantroleofadriverincoherenthumidity regions. The largest uncertainty is associated to ICE σw!Pr99:9th ,forwhichthe mean and standard deviation are 0.17+/−0.10. We have a closer look at the causal effects of individual models. Our previous analysis already revealed that the uncertainty across DYAMOND models accumulates over time, and becomes especially important when the mediated control of CRH is at its maximum (beyond 24 hours in the past). We can distinguish two groups of models based on the magnitude of the mediated causal effect (strong effect in ICON-NWP-2km, ARPEGE-NH-2km, UM-5km and weak effect in GEOS-3km, gSAM-4km, SHIELD-3km) on Fig. 5c. It is not possible to differentiate between these two groups of models based on the magnitude of the direct causal effect on Fig. 5b, which suggests the differences are really inherent to the modeling of convective organization32. Fig. 6 | Decomposition of the mediated causal effect. Causal effect ICE CRH!CAF (a) and ICE CAF!Pr99:9th (b). It is worth noting ICE CRH!CAF is independent of the precipitation percentile. Mean and standard deviation of the causal effect values are compared in the coherent humidity regions (black) and in the cross-model regions (purple). Standard deviations associated with the maximum causal effect values are specified in the legends. Fig. 7 | Causal graphs with effects at the 50th and 99.9th percentiles. Causal effects on 50th (a) and on 99.9th (b) precipitation percentiles in coherent humidity regions. Links are colored based on their maximum path coefficient values and labeled with the associated lead time. Means and standard-deviations are sampled over coherent humidity regions of DYAMOND models (i.e., over six combinations of model data and regions). https://doi.org/10.1038/s41612-025-01104-x Article npj Climate and Atmospheric Science | (2025) 8:245 6 The causal effects of the three drivers on Pr90th and Pr99:9th are plotted for the six models individually in Fig. 8. We visualize on it the distance between the GSRMs, and we can compare these distances for the two different quantiles (50th and 99.9th). The variability is larger Iτ¼24h CRH!Pr50th than for Iτ¼24h CRH!Pr99:9th which we can explain by the fact that medium and extreme precipitation obey different constraints. To first order, extreme precipitation is strongly correlated with the amount of water vapor in the atmosphere33, which itself scales to surface temperature via the Clausius-Clapeyron relation. During an extreme rainfall event, all the water vapor from the saturated atmospheric column precipitates out, with a limited role played by CRH, which explains the consistency among the DYAMOND models. However, the upper bound of global mean precipitation is rather dependent on the atmospheric energy budget, where changes in global-mean precipitation depend both on changes in the radiative cooling of the atmosphere and changes in surface sensible heat flux34. The straight line revealed by the effect of CRH on the 90th quantile relative to the effect on the 50th proves that the causal effects are linearly related and is a sign of consistency between the GSRMs (Fig. 8c). The proportionality between the coefficients disappears for very high quantiles, as the line flattens out (Fig. 8f). The GSRMs can ranked the same way for their control on the different precipitation quantiles, which means the role of the CRH may be generalized to all the precipitation distribution. We can conclude that the Column Relative Humidity acts as an important driver of precipitation in models gSAM4km, ARPEGE-NH-2km, SHIELD-3km, and ICON-NWP-2km, and as a minor driver in GEOS-3km and UM-5km. On the contrary, we must distinguish medium and extreme precipitation when we rank models according to the effects of updraft velocity on precipitation. GSRMs are ranked differently along the x-axis (effects on Pr50th ) and the y-axis (effects on Pr99:9th )onFig.8e. We can not make a general statement on the role of the mean or standard-deviation of updraft velocity for a given GSRM relative to other GSRMs. We can still conclude the mean updraft velocity is the strongest causal driver of medium precipitation in model gSAM-4km and the weakest driver in model ARPEGE-NH-2km (Fig. 8a), although these observations are not valid for extreme precipitation. Interestingly, the second moment is the strongest driver on medium precipitation in model GEOS-3km and the weakest driver in model gSAM-4km (Fig. 8b). The largest uncertainty is associated with ICEðτ¼3hÞ σw!Pr99:9th (Fig. 8e). Discussion Our results show the preconditioning of the large-scale environment on precipitation significantly enhanced in the coherent humidity regions, and this preconditioning becomes stronger with increasing degree of coherence (Supplementary Fig. 11). Future studies with longer simulations should focus on the relationship between extent of CRH fields and strength of CRH control, and in turn the longer-term imprint of convective storms on homogeneity of the large-scale fields (Supplementary Fig. 5). We also show a faithful representation of precipitation extremes requires the highresolution updraft fields,whateveristhestrengthofthelarge-scale humidity gradient. The moistening of the large-scale environment preconditions the amount of extreme rainfall, while the precipitation event is driven at short timescales by the high-resolution updraft velocity. Precipitation occurs in saturated updrafts whose moisture content was set up few days in advance by the large-scale environment but varies under the control of the convective updrafts with a very small temporal precedence (≤6h). Our study shows that the large-scale control of CRH precipitation is twice as large when moist margins are excluded, which implies that greater confidencecanbegiventothemodeledrainfallinGCMsinthispartofthe tropics. We investigated further this enhanced preconditioning and show that it holds for the different quantiles of precipitation, and it may be decomposed into one “fast”control via the availability of water vapor, and one “slow”control, via the convective area fraction. The control of CRH precipitation via the CAF is the one that acts further in the past, which Fig. 8 | Inter-model differences. Inter-model differences for causal effects ICEðτ¼3hÞ μw!Pr50th (a), ICEðτ¼3hÞ σw!Pr50th (b), ICEðτ¼24hÞ CRH!Pr50th (c), ICEðτ¼24hÞ μw!Pr99:9th (d), ICEðτ¼24hÞ σw!Pr99:9th (e), ICEðτ¼24hÞ CRH!Pr99:9th (f). Dots and error bars correspond to means and standard-deviations of causal effect values estimated in all ensembles of regions (both coherent humidity regions and crossmodel regions) in order to compare the inter-model differences and the inter-region differences. https://doi.org/10.1038/s41612-025-01104-x Article npj Climate and Atmospheric Science | (2025) 8:245 7 reinforces the importance of its representation for the modeling of convective precipitation. It is worth noting that CAF indicates the proportion of the convective area within the region but does not specify whether this area consists of a few large convective cells or many small ones. Additionally, we conducted a causal analysis using an alternative metric: replacing CAF with the number of convective clusters in the region. The results were nearly identical, although the large-scale control mediated via the number of clusters was foundto be weaker than when using CAF.Onepotentialavenue for future research could be to further explore this direction and determine the optimal way to incorporate information about the degree of spatial aggregation into the causal graph, and potentially optimize the large-scale control on precipitation. It is also important to mention that our causal graph consists of a configuration with auto-links (i.e., the variables are selfdriven). The absolute values of the causal effects would be increased by removing them. Concluding, we find that convective precipitation primarily depends on the representation of updraft velocity in the models and determines its causal importance. The partitioning between inand out-of-moist margins is an efficient way forward to diagnose the role of large-scale states on convective precipitation, and can be used as a way to determine whether the balance between smalland large-scale drivers of precipitation (in its relevant percentile) is appropriate in models. This enhanced large-scale control is revealed thanks to the explicit representation of the CRH control on mesoscale convective organization (Supplementary Fig. 10). Outside of coherent CRH regions, the large-scale control on precipitation has a lower intensity and a shorter duration, and seems to be decoupled from the stormscale control. In both regions, the higher moments of the updraft field are more directly linked to the extreme precipitation quantiles at short lags, which means that the resolution of the model can only reliably constrain up to a certain percentile in the precipitation distribution. It also means that subgrid parameterizations based on large-scale forcing may struggle to accurately capture tropical precipitation extremes without a sufficiently high-resolution representation of the vertical velocity field. Our results suggest that parameterizations in GCMs are more challenging and crucial in regions of sharp gradients of humidity, where the large-scale environmental control on precipitation is weaker and more limited in time. In order to have more realistically modeled rainfall in GCMs, one could develop constraints on the thermodynamic and dynamic controls of precipitation. Future work should incorporate observational products to validate and extend the model-based findings. In this paper, we tried to identify an invariant behavior from GSRMs. We found that GSRMs can be constrained on large-scale control for all quantilesasthemodelsexhibitstablerelativeresponsestoeachother (Fig. 8c, f). Despite the mean precipitation and precipitation extremes having different responses to water vapor amount, it seems they are linked to CRH via the same underlying process in the GSRMs. Conversely, such a constraint could not be developed for small-scale control on precipitation. The relative differences between GSRMs are not consistent across the PrX. Beyond 90th percentiles, the rainfall is very dependent on the second moment of updraft velocity whose effect varies greatly with models and quantiles, complicating the model’s reliability and interpretation (Fig. 8e). Methods DYAMOND model outputs We have access to the 15-min precipitation two-dimensional outputs, and to 3-hour three-dimensional (3D) outputs. To study the role of large-scale thermodynamics and small-scale dynamics, we used the 3-hour vertical wind velocity outputs. The vertical velocity is selected in the midtroposphere at 500 hPa, where deep convection is at its strongest25,35.The vertical motions are studied by selecting the updraft velocity (positive verticalvelocity)intheconvectiveareas.Tostudytheroleofthethermodynamic large-scale environment, we extract the 3-hour pressure and temperature 3D outputs and the 3-hour column-integrated water vapor (CWV) and specific humidity at the surface q surf outputs. The horizontal grid spacing ranges from 2 to 5 km, depending on the model. We extract fields with 0.10° grid spacing, which correspond to grid cells of about 11 km in the tropics. The time period simulated lasts 40 days, starting from 20 January 2020, but we restrict ourselves to a 30-day period to avoid the spin-up period. We restrict our investigation to a subset of six models for which the vertical velocity field is available: GEOS-3km, ARPEGE-NH-2km, ICON-NWP-2km, SHIELD-3km, UM-5km, and gSAM-4km. Names, frequencies, and simulation periods of variables are summarized in Supplementary Table 3. Additional information on the models is provided in Supplementary Tables 4 and 5. Time series are standardized by removing the diurnal mean and then dividing by the diurnal variation. δ-MAPS regions Low-level representations of the high-resolution outputs are obtained with the δ-MAPS algorithm, which identifies coherent regions in 3D datasets. δMAPSis a correlation-basedmethod that merges iteratively contiguousgrid cells that share similar temporal fluctuations (i.e., grid cells that “behave together”). Coherent regions are areas where grid cells are highly interconnected, meaning their time series data are temporally correlated. Similarity measures, such as the Pearson correlation coefficient, provide insight into these coherent regions. Mathematically, these regions correspond to non-random correlation structures, because there is a high probability that they would not have been generated with a stochastic model. They also correspond to different physical regimes because grid cells are spatially aggregated depending on the state of the atmosphere. δ-MAPS is applied to Column Relative Humidity fields in order to group grid cells into coherent humidity regions. By doing so, we both reduce the original grid and condition the large-scale environment. The two hyperparameters number of neighbors kand the homogeneity threshold, δ allow us to modulate the numbers and sizes of regions, and therefore control the proportion of tropical areas covered by the regions. Supplementary Fig. 1 shows the relationship between the hyperparameter δand the fraction of grid cells covered in the tropics. Results presented here are produced in CRH regions inferred with ksets to 100 and δsets to 0.30 (Fig. 1), which guarantees to cover half of the spatialgrid with the regions (Supplementary Table 2) and therefore to get a gooddescription of the tropics. The sensitivity of the causal analysis to the homogeneity threshold (δ) is tested by comparing the CE derived from δ= 0.30 regions to the ones derived from δ=0.60regions (Supplementary Fig. 11). The direct large-scale control is significantly higher in the smaller and more coherent regions, likely because CRH results from more local processes. Interestingly, this increased effect does not affect the other CE values (i.e., the mediated thermodynamic effect and the dynamic effects). This suggests the mediated effect is independent of the degree of homogeneity once passed a certain level, and this confirms the (average) dynamical effects are independent of the large-scale regions. Still, the choice of the coherent regions matters to reduce the uncertainty of the dynamic effects. The model uncertainty increases for all effects because small regions captured with δ= 0.60 are less comparable to each other, which shows the choice of δvalue is a compromise between stronger thermodynamic control and generalization of results (i.e., description of the tropics). Large-scale thermodynamics The control of the large-scale environment on precipitation is comprised in the profile of moisture and temperature. The working assumption is that regions correspond to regimes of column relative humidity whose structures were shaped by the large-scale environment. We derive the time series of CRH from the grid cells within regions, and obtain as many time series as the number of regions. We detail here the calculation of the CRH and the q surf from the temperature and pressure fields. The saturated specific humidity qis derived from the 3d pressure and saturation vapor pressure fields as in Eq. (1). The saturated column-integrated water vapor CWVis then obtained by integrating qover pressure coordinates (Eq. (2)), and serves to calculate the column relative humidity CRH along with the CWV outputs (Eq. (3)). https://doi.org/10.1038/s41612-025-01104-x Article npj Climate and Atmospheric Science | (2025) 8:245 8 CRH is a measure of how much water vapor a quantity of air contains in comparison with its capacity for water vapor at that temperature36,andwas found to follow more universal laws than CWV 19,21,37,38 qðT;PÞ¼Rv Rd esat ðTÞ Pð1Þ CWV¼ZPq gdP ð2Þ CRH ¼CWV CWVð3Þ Convective updraft velocity and precipitation We are interested in convective precipitation and its associated vertical motions in regions. At each timestep, it rains in only a small proportion of the regions. Convective grid cells are identified as grid cells for which the precipitation rate is above or equal to 0.7 mm/h. The robustness of the results is assessed with a convective rainfall threshold equal to 2 mm/h (Supplementary Fig. 12). The sensitivity test reveals a slightly higher direct control of CRH on precipitation, reflected then in the total CRH !PrX effect, due to a higher dependence of precipitation on humidity levels. Also, models agree better on the σw!Pr99:9th effect. Overall, the results are not too dependent on the convective rainfall threshold, which is in line with ref. 39, who provided that the threshold could be independently chosen within the range 0.7 to 2.5 mm/h. It is important to consider the spatial extent of convective systems as precipitation has the property to self-aggregate in the tropics. Water vapor may accumulate and condense but not precipitate if the vertical dynamics do not favor the growth of cloud droplets. For this reason, we retrieve various rainfall statistics, calculated upon the convective grid cells in the different regions: •Themeanconvectiverainfall •Percentiles 25th,50 th,75 th,90 th,95 th,99 th and 99.9th of convective rainfall •Theconvectiveareafraction(CAF) CAF is calculated as the number of convective grid cells within the regions divided by the total number of grid cells within the regions (at each timestep). This corresponds to the spatial extent of convective activity in each region. Regarding the vertical motions, we select vertical velocity in the midtroposphere (500 hPa), where deep convection is at its strongest. We retrieve moments of the positive vertical velocity distribution, namely mean updraft velocity (μw) and standard-deviation of updraft velocity (σw)inconvective grid cells. Setting up the mediated effect The aim is to compare the effects of direct and indirect paths for the same lag τ.Todothis,theCRH !CAF effect is associated to time lag τ1and the CAF !PrXeffect is associated with time lag τ2,suchthatτ1þτ2=τ.For τ¼1 (i.e., 3-hour lag), we consider exceptionally an instantaneous effect: τ1=0andτ2=1,orviceversa.Foreachlagτ≥2, there are τ1configurations possible with τ1≥1andτ2≥1. We select the configuration that leads to the strongest total effect CRH !PrXamong the τ1configurations. This is worth noting, this configuration may not necessarily be the one leading to the strongest mediated effect. The evolution of τ1and τ2 values in the six GSRMs is shown in Supplementary Fig. 8. The mediated effect becomes important once the lag time associated to CRH !CAF increases, which only happens in a second time after the one associated to CAF !PrXincreases. The two τ1and τ2values increase one after the other, with a clear shift around a 30-hour lag, which explains the abrupt increase of the mediated effect in Fig. 3e, f. This temporal pattern likely arises from the timescales of atmospheric processes, where moisture buildup initially drives convection directly, but longer lags are required for the effect CAF to influence precipitation more substantially. An area for improvement would probably be to consider all the possibilities in parallel mediated paths, which could contribute to attenuate the abrupt change around 30 hours and eventually reveal a stronger CRH control. Spatially-generalized Machine Learning models We applied one linear regression model and two deep learning models to learn dependencies between the set of largeand storm-scale drivers and the rainfall statistics (both CAF and PrX). Advantages of the Multiple Linear Regression (MLR) model are its closed-form solution and its interpretability. As an alternative approach, we trained a Multilayer Perceptron (MLP) model, which is a densely connected network able to learn nonlinearities. In addition, a Long Short-Term Memory (LSTM) model was trained to learn non-linear and complex long-term dependencies. This Recurrent Neural Network (RNN) developed by ref. 40 is able to understand temporal dynamics by processing sequences of inputs. The models are further described in the Supplementary Note. The models were trained across the ensemble of CRH regions, and hence are referred to as “spatially generalized models”. They were all trained with the set of inputs {μw,σw, CRH}, from which we obtain the most information on quantiles of precipitation (Supplementary Fig. 3). None of the advanced deep-learning models significantly outperformed the linear regression models, neither for the prediction of quantiles nor for the prediction of the CAF (Supplementary Fig. 4). The r2 scores obtained with the MLR are presented on Supplementary Table 6. We concluded that the dependencies are linear, justifying a linear causal effect estimation along the causal paths of a causal graph. We also found there is a high covariability between the quantiles of precipitation and the associated updraft velocity, and also that moments of updraft velocity are not predictors of the CAF. Instead, the large-scale CRH accounts for a portion of the variability in CAF through a relationship that operates on longer timescales. Multi-data inference of causal effects The Linear Mediation class from Tigramite allows us to quantify the causal effects from one variable or a set of variables on another28,29.Thecausal(time series) graph is in fact a multivariate time series dataset, from which the precipitation variable can be expressed as a linear combination of its parent variables (plus an error term). The aim is to quantify how each parent variable influences precipitation for a range of lead times. The fundamental assumption in causal effect estimation is the causal sufficiency, which implies that there are no hidden cofounders in the graph. In this specific study, each region has one of these multivariate datasets. This means we have multiple datasets originating from the same set of variables but recorded at different locations. One additional assumption is that we treat these regions as different instances of the same subprocesses. Using these multiple datasets, we estimate causal effects, a method we refer to as multidata inference of causal effects27. For linear models and graphs without hidden variables, the path method (or Wright approach) is suitable for thecausaleffectestimation.The path coefficients are associated to causal links, and causal effects are associated with causal pathways. The causal pathway from one component to another may be composed of a single causal link, or of a succession of causal links where intermediate nodes (e.g., CAF) act as mediators. The causal effects are estimated by considering all the causal pathways, and doing the sum-products of the path coefficients following the Wright approach. This approach is very suitable to estimate therelativeimportanceofthedifferent causal pathways under the assumption of a linear model, as it allows to decompose the causal effects into its different contributions (e.g., the contribution of a direct pathway versus the contribution of an indirect pathway)28,41. In the case where there isonly one link between a component itoward a component j, the causal effect is equal to the path coefficient Φi!j. Here, this is the case for the causal effects of CRH and q surf on CAF, and also the causal effects of CRH and q surf on PrX. The causal effects of CRH and q surf on the https://doi.org/10.1038/s41612-025-01104-x Article npj Climate and Atmospheric Science | (2025) 8:245 9