Process-aware mixture modelling of precipitation-event distributions using event-type clustering

Ortega Menjivar, Lena; Özcelik, Nur Banu; Laimighofer, Johannes; Laaha, Gregor

doi:10.5194/egusphere-2026-4282

Preprints

https://doi.org/10.5194/egusphere-2026-4282

Preprints

24 Jul 2026

| 24 Jul 2026

Process-aware mixture modelling of precipitation-event distributions using event-type clustering

Lena Ortega Menjivar, Nur Banu Özcelik, Johannes Laimighofer, and Gregor Laaha

Abstract. Accurate modelling of event-level precipitation distributions is critical for hydrological modelling, flood risk assessment, and climate studies, yet selecting suitable parametric families remains challenging. We propose a process-aware approach that first separates precipitation events into types and then constructs an overall mixture from the resulting type-specific distributions. Using 10-min precipitation records from two climatically contrasting Austrian weather stations (Graz Universität and Dornbirn, 2010–2022), we compare partitioning (k-means) with outcome-guided, model-based clustering implemented as finite mixtures of Gamma regressions (clusterwise distributional regression). Events are characterised by severity, magnitude, duration, intensity, time-to-peak, and lightning occurrence. While partitioning yields interpretable event groups, the outcome-guided approach provides substantially better distributional fit–reducing Kullback-Leibler divergence by 66–73 % relative to a single-Gamma baseline–and improves visual diagnostics. Single-distribution baselines underrepresent process heterogeneity in precipitation; process-aware clusterwise mixtures that account for event-level structure address this gap. The framework is distribution-agnostic and portable, relying on information available at the event scale and lightning data, and can support applications such as hydrological modelling and stochastic weather generation.

Received: 16 Jul 2026 – Discussion started: 24 Jul 2026

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Lena Ortega Menjivar, Nur Banu Özcelik, Johannes Laimighofer, and Gregor Laaha

Status: final response (author comments only)

RC1:
'Review of egusphere-2026-4282', Georgia Papacharalampous, 21 Aug 2026
This paper proposes a novel, process-aware framework for modeling sub-hourly precipitation distributions (e.g., for stochastic weather generation) by explicitly accounting for the underlying meteorological process heterogeneity rather than relying solely on increasingly complex single-distribution models, though it can potentially be combined with them. The proposed methodology (supplemented by open-source R code) includes the identification and characterization of precipitation events from 10-minute records using severity, magnitude, duration, mean intensity, time-to-peak and lightning occurrence as its features, with lightning serving as a proxy for convection. Two distinct clustering approaches are compared within the study’s framework, the traditional unsupervised partitioning (k-means) and an outcome-guided, clusterwise distributional regression method. Gamma models are fitted both to all non-zero values surpassing a selected wet-interval magnitude threshold and cluster-wise, subsequently aggregating the cluster-specific fits into weighted mixtures. The results show that the proposed framework offers a promising alternative to traditional precipitation modelling, with outcome-guided, process-aware clusterwise mixtures reducing Kullback-Leibler divergence by 66% to 73% relative to a standard single-Gamma baseline across two conducted case studies, outperforming also the k-means alternative.
I believe that the paper represents an important methodological advancement, making a meaningful step forward from the purely descriptive use of clustering for sub-hourly precipitation events. I have the following minor comments, which mainly concern the presentation of the work already conducted.
Minor comments
Lines 73–74: Was any additional quality control applied to the dataset beyond those originally performed by the data provider?

Lines 93–94: Maybe, something like “weights equal to the cluster share of 10-min above-threshold (wet) observations” instead of “weights equal to the cluster share of 10-min observations”?

Lines 80–81: Since the number of flashes per hour were available on a 1 km x 1 km grid, maybe something like this is closer to the approach followed: “For each station, an event was flagged as convective if at least one flash occurred during the event window within a discrete raster buffer comprising all grid cells whose centers fall within a 7 km radius from the station.” (or “all grid cells whose boundaries encompass…”)

The severity, duration and mean intensity features are all included in the k-means clustering, even though mean intensity is severity divided by duration. This could introduce some redundancy or uneven weighting of information. Were alternative combinations of driving features explored and what motivated the final choice? What are the benefits of this specific combination?

Out of curiosity, was the clustering tested without the lightning feature in the two examined locations? As noted already in the paper, the proposed framework is feature-set agnostic. Removing the dependency on lightning data in future implementations could broaden the practical applicability of the framework in regions where such data are unavailable.

Maybe another brief discussion on the extent to which the proposed framework can be applied region-wise as opposed to strictly location-wise (station-specific) could be included. Similarly, it could be relevant to discuss how useful the framework is expected to be at other temporal resolutions, and what specific adaptations would be required to handle them.

In relation to the specific questions posed and explored in the paper, it appears that the answers, particularly for question (ii), may be somewhat sensitive to the choice of case study. Under this view, maybe the paper could briefly discuss a broader, large-scale comparison of clustering approaches as a future direction towards a generalized implementation of the proposed framework.

Given that practical applications are highlighted as key motivations (such as stochastic weather generators), it would be relevant to also provide a brief conceptual outline on how the mixtures can be utilized in practice. For instance, in stochastic weather generators, this could involve simulating conditioned states and subsequently drawing precipitation values from cluster-specific distributions.

Since an important application of the proposed framework is in stochastic weather generators, the manuscript could benefit from including a few additional key references in this domain to further strengthen the context.

A few typos and notation inconsistencies exist throughout the paper and should be addressed. For instance, the symbol “k” is used both for a cluster's serial index and for the total number of clusters. Additionally, “Dimension 3” in line 205 should ideally be styled as “Dim. 3” (similarly for “Dimension 4” in line 206).
Citation: https://doi.org/10.5194/egusphere-2026-4282-RC1
- AC1: 'Reply on RC1', Lena Ortega Menjivar, 05 Oct 2026
  
  We thank the referee for the encouraging feedback, and the careful reading of our manuscript!
  
  In the attached document, we address the raised points.
  
  Citation: https://doi.org/10.5194/egusphere-2026-4282-AC1
RC2: 'Comment on egusphere-2026-4282', Anonymous Referee #2, 30 Sep 2026

Please see the file attached below.

Citation: https://doi.org/10.5194/egusphere-2026-4282-RC2

Lena Ortega Menjivar, Nur Banu Özcelik, Johannes Laimighofer, and Gregor Laaha

Data sets

Station Data-v2 (10 min): Quality-checked station data for Austria in ten-minute resolution GeoSphere Austria https://doi.org/10.60669/8fya-7x87

Model code and software

boku-stat/Clustering Rainfall: Clustering Rainfall - Version archived for Ortega Menjivar et al. (2026+) Lena Ortega Menjivar et al. https://doi.org/10.5281/zenodo.21358297

Lena Ortega Menjivar, Nur Banu Özcelik, Johannes Laimighofer, and Gregor Laaha

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Short summary

Computer models that generate artificial rainfall are widely used to plan for floods and water management, but they often struggle to represent the variety of real rain events. We grouped rainfall events from two Austrian weather stations into clusters of similar character and fitted a separate statistical model to each group. Combining these groups describes observed rainfall, including rare heavy events, better than a single model, offering a simple way to improve rainfall simulations.


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