Assessing Climate Model Performance in Simulating Temporal Clustering of Extreme Precipitation in Europe

1. Introduction

Heavy precipitation is one of the most damaging climate hazards in Europe, causing serious impacts on infrastructure, agriculture, and human safety [1]. Beyond the magnitude of individual events, the temporal clustering of heavy rainfall—defined as multiple intense precipitation days occurring within short intervals—can greatly amplify flood risk because soil moisture remains high and infiltration capacity cannot recover between storms, leading to rapid runoff and river response [2]. Therefore, understanding the temporal organization of extremes is increasingly recognized as a critical component of flood risk assessment and water-resource management. Recent advances in global climate models (GCMs), particularly those participating in CMIP6, have improved the representation of large-scale precipitation patterns and extreme rainfall statistics [3]. Many models reasonably reproduce seasonal cycles and the spatial distribution of extreme events over Europe [4]. However, their ability to simulate short-duration extremes remains limited because such events are strongly influenced by mesoscale weather systems and convection, which remain unresolved in coarse grids [5]. Regional analyses further indicate that GCMs tend to underestimate consecutive wet days and underestimate the occurrence of temporally organized extreme events, especially in coastal and mountainous regions such as the Alps and the Mediterranean [6].

Model resolution is a key factor affecting performance. Coarse-resolution GCMs often fail to capture convective systems and underestimate storm duration in central Europe [7], whereas high-resolution simulations better reproduce storm structure, spatial organization, and clustered heavy precipitation [8]. Nevertheless, most work has concentrated on traditional intensity- or frequency-based indices (e.g., annual maxima, percentile thresholds), while the temporal order of extremes has been evaluated only sparsely [9]. A notable example is an early evaluation of CMIP GCMs, which showed clear regional dependence and large inter-model spread in simulating clustering behavior and emphasized that temporal structure may be more challenging than intensity alone [10]. Observational uncertainty also contributes to model–data discrepancies. Continental-scale gridded datasets such as E-OBS provide long records but can smooth local heavy rainfall due to sparse station density in several European regions, particularly southeastern Europe, limiting their ability to represent short-range variability and cluster metrics derived from daily fields [11,12]. Moreover, existing studies often focus on individual countries or limited time spans, making it difficult to form consistent conclusions at the pan-European scale. Only a few studies have systematically assessed clustering in GCMs across Europe. One key contribution evaluated the ability of GCMs to capture temporal clustering of heavy precipitation and found substantial underestimation of cluster persistence and large spatial variability in model performance [13]. However, this assessment was limited to a smaller model ensemble and lacked detailed analysis at climate-zone scales. There is still a need for systematic evaluation using the full CMIP6 dataset and consistent cluster metrics.

Given these limitations, this study examines how CMIP6 GCMs simulate temporal clustering of heavy precipitation across Europe. Using observational datasets as reference, we evaluate model skill in reproducing key cluster indices, including maximum consecutive wet days and mean cluster length. Spatial patterns, inter-model variability, and performance differences among major European climate zones are also assessed. By shifting the focus from isolated extreme events to their temporal structure, this work provides a more realistic perspective on GCM capability for compounding precipitation hazards. The results highlight remaining challenges in simulating organized storm systems and underscore the need for improved representation of convection, with implications for future flood-risk projections and adaptation planning.

2. Materials and Methods

2.1. Study Region and Data Sample

The study area covered the European continent, ranging from 35°N to 70°N and 10°W to 30°E. Daily precipitation data from 1981 to 2020 were collected. Observations were based on the E-OBS v25.0e gridded dataset at 0.1° resolution, supported by more than 2,000 ground stations. For model evaluation, ten global climate models (GCMs) from CMIP6 were selected, each downscaled to the same spatial grid. Heavy precipitation was defined as daily rainfall exceeding the 95th percentile at each grid cell, which produced more than 12,000 extreme events for analysis.

2.2. Experimental Framework and Control Groups

The evaluation framework used GCM simulations as the experimental groups and the E-OBS dataset as the control. Both were processed under the same thresholds and clustering definitions to ensure comparability. The analysis was structured across three spatial domains: northern Europe, central Europe, and southern Europe. This design tested whether models captured differences between maritime, continental, and Mediterranean climates. Temporal clustering was quantified for both observed and simulated series to compare their consistency.

2.3. Measurement Techniques and Data Quality Control

Observed data were checked for completeness before use. Records with more than 5% missing values were excluded. Short gaps were filled using linear interpolation, and suspicious outliers were flagged when exceeding four standard deviations from the local mean. To align with model data, all observations were aggregated to a daily scale. The GCM outputs were interpolated to the same grid using conservative remapping. These procedures reduced inconsistencies and minimized potential bias in comparisons.

2.4. Data Processing and Statistical Formulations

The temporal clustering of heavy precipitation was assessed by grouping consecutive days above the percentile threshold. Two indices were calculated: the mean cluster length (MCL) and the maximum consecutive wet days (CWD). For model–observation comparisons, a regression approach was used [14]:

$$\mathrm{MC}{\mathrm{L}}_{\mathrm{obs}}=\mathsf{\alpha }+\mathsf{\beta }\mathrm{MC}{\mathrm{L}}_{\mathrm{mod}}+\mathsf{ϵ}$$

where $\mathrm{MC}{\mathrm{L}}_{\mathrm{obs}}$ and $\mathrm{MC}{\mathrm{L}}_{\mathrm{mod}}$ are the observed and modeled mean cluster lengths, and $\mathsf{ϵ}$ is the residual. Model skill was also evaluated using the Nash–Sutcliffe Efficiency (NSE) [15]:

$$\mathrm{NSE}=1-{\displaystyle \frac{\sum ({\mathrm{X}}_{\mathrm{obs}}-{\mathrm{X}}_{\mathrm{mod}}{)}^2}{\sum ({\mathrm{X}}_{\mathrm{obs}}-{\stackrel{\mathrm{̄}}{\mathrm{X}}}_{\mathrm{obs}}{)}^2}}$$

where ${\mathrm{X}}_{\mathrm{obs}}$ and ${\mathrm{X}}_{\mathrm{mod}}$ are observed and modeled values, and ${\stackrel{\mathrm{̄}}{\mathrm{X}}}_{\mathrm{obs}}$ is the mean of observations.

2.5. Statistical Testing and Analysis Tools

Statistical differences between modeled and observed indices were tested using paired t-tests at the 95% confidence level. Robustness was examined through bootstrap resampling with 1,000 iterations. In addition, spatial variations in clustering metrics were summarized by regional averages and standard deviations. All analyses were conducted using R version 4.3.1 and Python 3.11, ensuring reproducibility of results.

3. Results and Discussion

3.1. Overall Performance and Temporal Consistency

Across European regions, the models reproduced broad patterns of extreme precipitation but underestimated the persistence of clustered events. In maritime and northern Europe, correlations between observed and simulated mean cluster length reached 0.55–0.65, with mean absolute error close to 1 day. In Mediterranean and Alpine areas, the underestimation was stronger, with modeled sequences shorter by 15–30 %. This indicates that while the models capture the spatial occurrence of extremes, they often split multi-day events into shorter segments [16]. Figure 1 illustrates this behavior through a Taylor-diagram comparison of modeled and observed precipitation statistics.

3.2. Sensitivity to Threshold and Event Definition

Changing the definition of clustering had a marked effect on results. Using a higher threshold (99th percentile instead of 95th) reduced the number of clusters by about one-third and increased average cluster length by ~0.5 days. Adjusting the linking window from two days to one day shortened clusters by 0.4–0.6 days, particularly in coastal regions. These shifts show that the choice of thresholds and linking rules strongly influences clustering outcomes. Similar sensitivities were also reported in regional studies of precipitation persistence, underlining the need for standardized definitions when comparing models [17,18].

3.3. Spatial Patterns and Regional Transferability

Bias patterns were not uniform across Europe. Over Atlantic and North Sea regions, clustering differences stayed within ±10 %, but in southern and mountainous areas, underestimation exceeded 20 %. Models calibrated for maritime climates lost accuracy when applied to Mediterranean basins, suggesting that storm dynamics and terrain play a key role in clustering skill. Figure 2 shows spatial distributions of maximum consecutive wet days for one representative model, highlighting underestimation in southern Europe and some overestimation in northern coastal areas [19,20].

3.4. Comparison with Existing Work and Study Limitations

Our findings are consistent with earlier analyses showing that climate models often reproduce total rainfall and single-day extremes more reliably than multi-day persistence. Barton et al. (2022) also reported underestimation of cluster duration in European datasets, while Tuel et al. (2022) emphasized that clustered events have stronger hydrological consequences than isolated ones. The present work adds to this by showing how sensitivity to thresholds and regional transfer explains part of the model spread. Limitations include reliance on gridded observations that may smooth local extremes, the evaluation of only a subset of global models, and the unresolved nature of convection in coarse model grids. Future research should include convection-permitting models, denser observational networks, and more consistent cluster metrics.

4. Conclusions

The evaluation of European climate models shows that they reproduce the general occurrence of extreme precipitation but underestimate the persistence of multi-day clusters, especially in Mediterranean and Alpine regions. Using standardized clustering metrics and sensitivity tests on event definitions, this study finds that the way clusters are defined has a strong impact on model performance and explains part of the differences between models. The focus on temporal clustering rather than single events underlines its importance for flood risk assessment and hydrological impacts. The results suggest that models need better representation of persistence and transition probabilities, particularly for convective and orographic processes. The study is limited by the coarse resolution of gridded observations and the restricted number of models evaluated, but it provides a useful basis for assessing clustering skill across different European climates. Future work should include convection-permitting simulations, denser observational networks, and harmonized clustering definitions to improve the reliability of projections and to support flood risk management under climate change.