the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 29 May 2026
Reconstruction of Global 0.25° Land Lightning Density from 1979 to 2025 based on an ensemble machine learning
Abstract. Lightning is a primary driver of severe convective hazards and wildfire ignitions, yet long-term, high-resolution gridded records have remained scarce due to the limited temporal coverage of ground-based networks and the sampling constraints of satellite observations. Here, we presented a new global 0.25° × 0.25° monthly land lightning stroke-density dataset spanning 1979–2025. To ensure robustness, we developed a ridge regression stacking ensemble that integrated four complementary machine learning architectures: eXtreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LightGBM), Random Forest (RF), and Deep Neural Network (DNN). The ensemble achieved superior performance over each single model (test R² = 0.6895, RMSE = 0.0108, MAE = 0.0030), indicating that model blending effectively enhanced predictive stability. Individual validations confirmed high spatial fidelity, as the ensemble successfully reproduced the observed large-scale spatial distribution and major tropical–subtropical continental lightning hotspots. Independent comparisons with the LIS/OTD gridded lightning climatology (±38°) further demonstrated strong spatiotemporal consistency, particularly in reproducing interannual variability. Our analysis revealed pronounced regional heterogeneity in multi-decadal trends: significant decreases were concentrated across several tropical convective centers, while localized increases emerged in specific mid-latitude regions. Attribution based on SHapley Additive exPlanations (SHAP) elucidated that these patterns were primarily governed by the coupling of thermodynamic instability (CAPE × TP), moisture availability, and ice-phase hydrometeor conditions. This dataset provided a physically constrained and spatially detailed basis for studying long-term lightning dynamics, offering practical inputs for natural-ignition modeling, lightning-produced NOx estimation, and the evaluation of lightning parameterizations in climate and Earth system models. The datasets of the 1979–2025 Global Land Lightning Density Reconstruction Version 1 (GLLDR v1) are publicly available at the Zenodo via the following DOI: https://doi.org/10.5281/zenodo.19722380 (Zheng et al., 2026a).
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Status: open (until 23 Jul 2026)
- RC1: 'Comment on essd-2026-318', Anonymous Referee #1, 03 Jul 2026 reply
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RC2: 'Comment on essd-2026-318', Anonymous Referee #2, 06 Jul 2026
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The comment was uploaded in the form of a supplement: https://essd.copernicus.org/preprints/essd-2026-318/essd-2026-318-RC2-supplement.pdf
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CC1: 'Comment on essd-2026-318', Andreas Krause, 07 Jul 2026
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The study addresses an interesting question. However, I wonder why the authors decided to randomly split the dataset into training and testing subsets. As reviewer #2 noted, machine learning model evaluation based on random splits may be overly optimistic in the presence of spatial and temporal dependence (e.g. Ploton et al., 2020). In my view, using complete years exclusively for either training or testing would provide a more robust assessment of the model's ability to generalize to unseen time periods, which is consistent with its intended use for hindcasting. To assess inter-annual variability while making use of the entire dataset, a leave-one-year-out cross validation approach could also be considered.
Additionally, given the fundamental differences between WWLLN and LIS/OTD, I am surprised by the strong correlation between the Ridge ensemble and LIS/OTD in most regions (Fig. 8d). Is the correlation indeed computed on annual mean values?
Finally, I believe the manuscript would benefit from a comparison or discussion of the reported trends in stroke density with previously published trends in thunder days over the last decades (e.g. Lavigne et al., 2019).
Lavigne T, Liu C T and Liu N N 2019 How Does the Trend in Thunder Days Relate to the Variation of Lightning Flash Density? J Geophys Res-Atmos 124 4955-74
Ploton P, Mortier F, Réjou-Méchain M, Barbier N, Picard N, Rossi V, Dormann C, Cornu G, Viennois G, Bayol N, Lyapustin A, Gourlet-Fleury S and Pélissier R 2020 Spatial validation reveals poor predictive performance of large-scale ecological mapping models Nat Commun 11
Citation: https://doi.org/10.5194/essd-2026-318-CC1
Data sets
Global Land Lightning Density Reconstruction version 1 (GLLDR v1) Hao Zheng et al. https://doi.org/10.5281/zenodo.19722380
Model code and software
GLLDR v1 Reconstruction Code Hao Zheng et al. https://doi.org/10.5281/zenodo.19723880
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- 1
Zheng et al. present a global, land-only monthly lightning stroke density dataset spanning the period 1979-2025. The dataset is developed using four machine learning algorithms: (i) XGBoost, (ii) LightGBM, (iii) Random Forest (RF), and (iv) a Deep Neural Network (DNN). These models are trained using several lightning-relevant meteorological variables and derived thermodynamic indices from the ERA5 reanalysis to estimate lightning stroke density. The target lightning observations are based on gridded stroke density derived from the World Wide Lightning Location Network (WWLLN). The final lightning dataset is produced by combining the outputs of the four machine learning models within a ridge regression ensemble framework.
The primary novelty of this work lies in extending the temporal coverage of lightning observations from the WWLLN record, which is available for 2013-2024, to a continuous dataset spanning 1979-2025. Overall, I find the methodology to be sound and the resulting dataset to be of high quality. The NetCDF dataset is easily accessible through the Zenodo repository and includes well-documented metadata and attributes describing the stored variables. I have a few minor comments, listed below, which are intended to improve the clarity and presentation of the manuscript.
Line 103: It is not clear what the authors mean by “stable WWLLN observations”.
Line 126: Please clarify whether the stroke density is accumulated for every month or averaged.
Lines 188-192: It is not clear what additional advantage the inclusion of tree-based models provides compared to using only the DNN, or vice versa. The authors should explain, from a theoretical perspective, how combining these different models is expected to improve the robustness and overall performance of the final ensemble.
Lines 247-248: Please refer to Table 1 here for the statistical metrics related to the ridge regression model.
Lines 258-261: What is the performance of the random forest (RF) model in this context? Figure 3f suggests that the RF model performs better than the other individual models, with a larger fraction of grid cells exhibiting high R² values, and in some cases even outperforming the ridge regression ensemble. Please discuss this result.
Section 4.1: Although RMSE and MAE are useful performance metrics, they are reported in absolute units. To better assess the magnitude of the errors, the mean value of the target variable should also be reported alongside these statistics. Alternatively, and preferably, I recommend reporting normalized RMSE and normalized MAE so that the errors are expressed as percentages rather than absolute values.
Figure 4: In line with the previous comment, please report the bias in panel (e) in percentage. Also, is the reported correlation coefficient calculated from the zonal mean comparison? If so, please state this explicitly in the figure caption.
More generally, I recommend reporting bias and other comparison statistics as percentages as well throughout the manuscript (for example, Fig. 5d) rather than in absolute units only.
Figure 6: The y-axis limits in panels (b) and (d) could be adjusted to better highlight the variations in the annual time series.
Lines 366-367: It would be helpful to introduce the distinction between flash-rate density and stroke density at this point, rather than at line 378. This would allow readers to better understand why a qualitative comparison is more appropriate than a direct quantitative assessment.
Figure 8: Since the ridge regression ensemble is trained using WWLLN data, a direct comparison between the ensemble output and LIS/OTD observations should account for the inherent differences between the WWLLN and LIS/OTD datasets. I therefore suggest including an additional panel, similar to panel (d), showing the correlation between WWLLN and LIS/OTD over their common period of availability. The corresponding discussion in the text should also be revised accordingly.
Figures 9 and 10: These figures are difficult to interpret because they use abbreviations for the control parameters without defining them. I recommend providing the expanded forms of these abbreviations in at least one of the figures/caption to improve readability.
Section 5: The discussion should also address the current challenges that prevent the development of lightning density datasets at daily resolution. A monthly temporal resolution is too coarse for many studies of lightning, which is closely associated with short-lived and extreme meteorological processes. It would also be valuable to discuss whether a pathway exists for developing a daily lightning climatology using currently available satellite observations or by combining multiple satellite products.