# A new multi-expert distance for clustering climate parameters: a Caribbean precipitation case study

Emmanuel Biabiany, Ruben Bagghi, Didier Bernard, Vincent Pagé, Stéphane Cholet, Raphaël Cécé

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Emmanuel Biabiany, Ruben Bagghi, Didier Bernard, Vincent Pagé, Stéphane Cholet, et al. A new multi-expert distance for clustering climate parameters: a Caribbean precipitation case study. Computers & Geosciences, 2026, 207, pp.106058. 10.1016/j.cageo.2025.106058. hal-05293791

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# A new multi-expert distance for clustering climate parameters: a Caribbean precipitation case study

Emmanuel Biabiany<sup>a, *</sup>, Ruben Bagghi<sup>a</sup>, Didier C. Bernard<sup>b</sup>, Vincent Pagé<sup>a</sup>, Stéphane Cholet<sup>a</sup>, Raphaël Cécé<sup>b</sup>

## ARTICLE INFO

Keywords:

Machine learning

Clustering

Data fusion method

Precipitation

Tropical storm

Hurricanes

Caribbean region

## ABSTRACT

This study investigates precipitation patterns in the Caribbean region using a novel Multi-Expert Distance (MED) metric for clustering analysis. MED integrates multiple climate parameters, including Sea Surface Temperature (SST), wind components at 925 hPa, and Outgoing Longwave Radiation (OLR), with the objective of enhancing spatiotemporal precipitation analysis. This approach offers an alternative to conventional methods that rely on single datasets and Euclidean distances. It combines physical parameters during clustering to enhance accuracy and insights. The analysis encompasses a 43-year period (1979–2021), extending from the Gulf of Mexico to the Caribbean, with a spatial extent that covers the entire region. The MED metric incorporates zone-specific histograms and Kullback-Leibler divergence, enabling dynamic comparisons of atmospheric configurations. The analysis yielded six distinct clusters, each exhibiting unique seasonal and inter-annual precipitation patterns, influenced by regional atmospheric dynamics. The analysis revealed significant transitions and associations between clusters, precipitation levels, and atmospheric conditions. Clusters representing dry conditions exhibited negative SST anomalies, reflecting reduced moisture production. Conversely, clusters exhibiting high precipitation exhibited positive SST anomalies, which are conducive to moisture accumulation. Furthermore, tropical storms and hurricanes were predominantly observed in wetter clusters, underscoring the utility of MED in linking atmospheric phenomena with climatic impacts. The results highlight the effectiveness of the MED in improving both the accuracy and interpretability of clustering algorithms. Beyond its methodological contributions, this work highlights the MED’s potential to advance the understanding and forecasting of precipitation regimes, thereby contributing to more robust climate analyses. Such insights are particularly relevant for informing climate adaptation strategies in vulnerable regions, notably the Caribbean. Future research could investigate automated domain segmentation as a means of further refining and optimizing this approach.

## 1. Introduction

Rainfall is the primary factor contributing to climate variability in the Caribbean region. The analysis of cumulative rainfall is of significance in improving our knowledge of the region's climate, as well as the impacts of climate change. It is therefore essential to study the atmospheric phenomena and structures responsible for the production and distribution of precipitable volumes in the area. The automatic identification of spatio-temporal structures that are indicative of the atmosphere's low frequency variability has long been known as an important research objective (Gouriand et al., 2024; Biabiany et al., 2020; Moron et al., 2016; Bernard et al., 2019; Chattopadhyay et al., 2020; Dey et al.,

2023).

Clustering methods have been proven to be an efficient approach to identifying such complex structures. To conduct a comprehensive analysis of atmospheric configurations, it is necessary to use several physical parameters. Pre-processing and organizing data are pivotal steps in the clustering process, as they determine the relevance of the results. There are several methods for data fusion, each tailored to specific goals and applications. It is noteworthy that recent research in this area remains scarce and that these methods have not yet been applied to the analysis of complex climate data, without using artificial neural networks (Hussain et al., 2024).

In the context of relational algebra and SQL semantics, data joins,

<footnote><sup>a</sup> Laboratoire de Mathématiques, Informatiques et Applications, Université des Antilles, Guadeloupe</footnote>

<footnote><sup>b</sup> Laboratoire de Recherche en Géosciences et Énergies Mathématiques, Université des Antilles, Guadeloupe</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: emmanuel.biabiany@univ-antilles.fr (E. Biabiany).</footnote>
such as inner and outer joints, combine records based on matching values across datasets (Poliakov et al., 2017). A probabilistic approach, incorporating Bayesian probabilities and Dempster-Shafer theory, could be considered. These theories address uncertainty by leveraging conditional probabilities and belief functions. (Martin et al., 2010; Radzvilas et al., 2024). Machine learning-based methods, like neural networks and clustering algorithms, leverage deep learning models and group similar data for more effective fusion (Hussain et al., 2024; Canalle et al., 2021). Heuristic methods, such as genetic algorithms and local search algorithms, optimize data combinations by exploring neighboring solutions. These techniques are widely used in fields like environmental monitoring, security, and business decision-making to enhance the quality and reliability of fused information (Meng et al., 2020; Sharma et al., 2023). To summarize, there are three main data fusion strategies: pre-treatment fusion, post-treatment fusion and fusion during the process.

Pre-treatment fusion is a well-known fusion strategy. As the name implies, it involves fusing the data prior to processing. The most obvious way involves concatenating input datasets, grouping components (characteristics or dimensions) from different sources together. For each dataset, it becomes possible to perform dimension reduction, by performing principal component analysis (PCA) before or after concatenation (Gewers et al., 2021; Jolliffe and Cadima, 2016), creating composites (Moron et al., 2016). Concurrently, other authors have proposed the construction and utilization of combination functions, which are contingent upon the input datasets, as well as the specific outputs that are desired (Yamanishi and Kanehisa, 2004; Chen et al., 2021; Heer and Chi, 2002).

Another common fusion strategy is called post-treatment fusion. It consists of combining data or results of several clustering to later inject them into a new grouping method or function. The initial data is condensed into its representation space using an initial analysis, then grouped using correspondence or consensus functions (Ayad and Kamel, 2008; Strehl and Ghosh, 2002). These functions are used to aggregate multiple sources of information, opinions or decisions into a single representative output (e.g., majority or weighted vote, mean, median, mode, etc.).

Fusion during process is an approach that is rarely found in scientific literature. Using this type of method, the aim is to combine the characteristics of each data item at the time of processing. This approach is used in Sublemontier et al. (2011) and in Bickel and Scheffer (2005).

Following the recognition of the constraints of the Euclidean distance (also called L2), commonly used in many clustering methods, a recent dissimilarity measure, called Expert Distance (ED), was suggested by Biabiany et al. (2020). This distance is favored as it has been demonstrated to be more effective than L1 or L2 distances, which place excessive emphasis on the spatial distribution (pattern) of fields, thus neglecting their distribution density. This measure is based on spatial segmentation, quantification in histograms, and zonal analysis with Kulback-Leibler (KL) divergence (Kullback and Leibler, 1951). The divergence is symmetrized as follows:

$$D_{KLS}(h_1, h_2) = D_{KL}(h_1, h_2) + D_{KL}(h_2, h_1) \qquad (1.1)$$

$$D_{KLS}(h_1, h_2) = \sum_{i} h_1(i) \log \frac{h_1(i)}{h_2(i)} + \sum_{i} h_2(i) \log \frac{h_2(i)}{h_1(i)} \qquad (1.2)$$

where $h_1$ and $h_2$ are distributions of discrete probabilities, $i$ is the index of possible values from each distribution. The ED metric is defined as:

$$ED(d_1, d_2) = \frac{1}{n} \sum_{z=1}^{n} D_{KLS}(d_1(z), d_2(z)) \qquad (2)$$

where $d_1$ and $d_2$ are daily data, and $d_x(z)$ is the histogram of zone with reference $z$. In this case the number of zones $n$ equals four as presented in Fig. 1.

<figure><img src="image_3.png" /><figcaption>Fig. 1. Caribbean region from 98.75° W to 56.25° W and from 8.75° N to 31.25° N with a spatial subdivision into four subareas: Z1 (Gulf of Mexico), Z2 (northern tropical Atlantic), Z3 (Northern Tropical Pacific) and Z4 (Caribbean area).</figcaption></figure>

The ED offers significantly superior results, whether in terms of numerical evaluations of the quality using the silhouette index (Rousseeuw, 1987), or interpretations by domain experts, for a specific climatic parameter. Few studies have already been conducted with this metric, on different physical parameters. In these articles, the proposed EDs allow the comparison of different atmospheric configurations on a physical parameter with great efficiency and have been integrated into several clustering methods to automate the analysis (Bernard et al., 2022; Biabiany et al., 2020).

To date, ED has not been employed to simultaneously cluster multiple datasets encompassing distinct environmental parameters. This study proposes a novel iteration of the metric that facilitates such multiparameter integration.

In contrast to the conventional ED, which is predicated on a solitary variable, the recently proposed Multi-Expert Distance (MED) employs multi-parameter distributions to more accurately reflect the intricacies of atmospheric interactions. When incorporated into clustering algorithms, MED enhances automatic configuration grouping by similarity, leading to the formation of more homogeneous clusters. The distinguishing characteristic of this approach is the integration of expert-defined spatial segmentation, histogram-based representations of pre-defined classes, dissimilarity computation between distributions (via Kullback-Leibler divergence), and the fusion of various physical parameters. To the best of our knowledge, no unified clustering approach for regime identification has yet been developed that integrates multiple expert distances derived from distinct atmospheric parameters.

In the work carried out by Moron et al. (2016) on the identification of weather patterns in the Caribbean and the analysis of their impact on precipitation was reproduced. This paper extends the previous works by integrating multiple atmospheric variables into a unified clustering metric, MED, whereas their approach relied on pixel-wise Euclidean distances on precipitation alone. This new approach is introduced in section 2. The results obtained with this method are compared and presented in section 3. The spatiotemporal patterns identified are interpreted and compared with studies in scientific literature for the area of interest, in section 4. Section 5 presents the work and the main results, ending with some perspectives.

## 2. Data and methods

Parameters used in this work are the same as in Moron et al. (2016) work, i.e., Sea Surface Temperature (SST), Wind Components (U, V) at 925 hPa and Outgoing Longwave Radiation (OLR). SST exerts a significant influence on air humidity through the process of increasing evaporation, thereby enriching the atmosphere with water vapor. The ascent of this warm, moist air gives rise to convection currents, which, as
they undergo cooling, enable the condensation of water vapor into clouds. This process releases latent heat, thereby fueling convection and ultimately leading to precipitation. Consequently, SST, humidity, convection and precipitation are inextricably linked in a sophisticated cycle.

A larger period is considered: 43 years in this case, from January 1st, 1979, to December 31st, 2021, instead of 34 years (1979–2013) previous works. A better resolution is also proposed for each data set (around 0.25°). The aim is to produce a joint analysis of several physical parameters related to humidity production, cloud formation and precipitation. An interesting area starting from 98.75° W to 56.25° W and from 8.75° N to 31.25° N was considered with a spatial subdivision to separate the different climate zones (see Fig. 1).

The datasets were structured into matrices, totaling 15,706 observations (rows) and 15,561 values (columns) for SST and UV, while for OLR there are only 1032 values. These matrices are the data input for our automatic clustering methods. To make them easier to handle, we have chosen to concatenate them.

## 2.1. ERA-5 datasets: production and transport of humidity

SST data were chosen as the main parameter driving the marine convection and the production of clouds. The U and V components of the wind at 925 hPa were selected to include cloud transport and, more generally, moisture of atmospheric base layers in the automatic analysis. Daily fields (at 12:00 UTC) from the hourly ERA-5 reanalysis (Copernicus Climate Change Service [C3S], 2017) datasets were used (data sources will be found in the appendix). These data are structured on uniform grids with a resolution of 0.25° (~31 km).

## 2.2. Outgoing longwave radiation data: location and density moisture-laden air masses

OLR data comes from the National Oceanic and Atmospheric Administration (NOAA) website. It is derived from satellite measurements and is also organized in the form of uniform grids with a resolution of 1° (NOAA Climate Data Record (CDR) of Daily Outgoing Longwave Radiation (OLR), 2024). OLR datasets allow to quantify the energy that Earth's surface, oceans, and atmosphere radiate into space. This conserved energy serves as an effective gauge of moisture-laden air masses density and location.

## 2.3. MSWEP data: impact on precipitations

Multi-Source Weighted-Ensemble Precipitation (MSWEP) is a globally encompassing precipitation product. It boasts a temporal resolution of 3 h and a spatial resolution of 0.1° (MSWEP v2.8, 2024). This product includes data from gauges, satellites, and reanalysis sources, thereby ensuring the procurement of the most accurate precipitation estimates at each geographical location (Beck et al., 2019). The clustering process presented in the following section included physical parameters related to moisture production, transport and spatial repartition, but the MSWEP dataset was used to analyze the impact of obtained clusters on the rainfall in the Caribbean.

## 2.4. Clustering analysis with multi-expert distance

It is worth noting that our method does not require prior upscaling or downscaling of the parameters. The number of resulting histograms, which is four, does not depend on the resolution of the data. Therefore, it prevents any artifact related to sampling low-resolution data. It also prevents data loss that may result from sampling high-resolution data. The usual K-medoid (Sureja et al., 2022; Kaufman and Rousseeuw, 1987) and Agglomerative Hierarchical Clustering (AHC) algorithms were employed in this work (Bakkelund, 2021; Ackermann et al., 2014). The choice of these algorithms relates to the fact that their only free hyperparameter is the number of clusters. As a matter of fact,

Density-Based Spatial Clustering of Applications with Noise (DBSCAN) was discarded at this time, as the choice of the proximity radius (epsilon) remains a delicate step. The epsilon parameter of DBSCAN delineates the maximum distance between two data points for one to be considered in the vicinity of the other (Ghahramani, 2003; Jain, 2008). The process essentially generates a radius around each point. This parameter must be empirically adjusted. In this work, a new approach is proposed, allowing data to be combined during the clustering (Schubert et al., 2017; Ester et al., 1996).

The first step is to calculate an ED for each climate parameter under consideration, using the classic ED method (see Eqs. (1.1) and (1.2)). The ED metric integrates a set of knowledge about the dynamics of the data to be partitioned as well as their spatiotemporal properties. Based on an empirical spatial subdivision ($d_x$ (1) to $d_x$ (4), Fig. 1) and the use of Kullback-Leibler symmetrized divergence, noted $D_{KLS}$ (Kullback and Leibler, 1951), the ED metric allows to quantify the similarity between two daily fields of data (Biabiany et al., 2020; Bernard et al., 2022) as shown in Fig. 2.

In this work, daily fields are compared by zone during clustering using predefined histogram class boundaries, obtained from the deciles of each physical parameter (Table 1). Several ED metrics are therefore calculated during processing.

Secondly, a combination operator (for instance, sum or average), noted $Mc$, is used to calculate a single value representing a metric. In this work, a new metric, called Multi Expert Distance (MED) was introduced. The following equation (Eq. (3)) describes its calculation:

$$MED(d_1, d_2) = Mc(i \to P) [ED_i(d_1, d_2)] \quad (3)$$

where $d_1$ and $d_2$ are daily data and $Mc$ is a combination method applied on $P$ expert distance values from different physical parameters. The computation of the MED metric for this work is presented in Fig. 3.

The new multi-parametric expert metric was incorporated into K-medoid and AHC algorithms for the purpose of daily fields comparison. In the process of clustering, a function was used to segregate the concatenated data prior to the computation of the expert distance for each parameter, whenever the distance between two elements was calculated. This methodological approach enhances the precision of the clustering process.

To compare the results with that of Moron et al. (2016), a clustering using the L2 metric on concatenated data from the same period (from January 1st, 1979, to December 31st, 2021) was carried out. The dimension of data was reduced by PCA, keeping 82 components, for 95 % inertia.

## 2.5. Clustering performance measures

The evaluation of the clustering outcomes was conducted utilizing the silhouette index (Rousseeuw, 1987). The silhouette index ($S_aM_k$), as defined by Biabiany et al. (2020), was employed for this purpose (Eq. (4)). This methodology facilitates the quantification of the quality of a clustering configuration by computing the mean quality of each individual cluster, which is in turn determined by the average of the silhouette indices, denoted as $s(i)$, across the constituent elements of the cluster. This approach provides a comprehensive assessment of the clustering configuration. This index is defined as follows:

$$S_aM_k = \frac{1}{k} \times \sum_{j=1}^{k} \frac{1}{|C_j|} \times \sum_{i \in C_j} s(i) \quad (4)$$

where $k$ is the number of clusters, $C_j$ the set of days from the cluster $j$, $i$ a day from $C_j$, and $s(i)$ the silhouette index value of day $i$. The number of clusters was determined based on index values greater than 0.2, to ensure optimal cluster coherence. In general, a new stability is sought in the evolution of the $S_aM_k$ index values to identify the appropriate number of clusters (Fig. 4).
<figure><img src="image_4.png" /><figcaption>Fig. 2. The schematic of an expert distance computation.</figcaption></figure>

<caption>**Table 1**</caption>

Boundaries of the histogram classes used to quantify daily data for each parameter; these edges were determined from each dataset deciles in the study time range and area; with SST (in K), OLR (in W.m⁻²) and wind velocity (WV in m.s⁻¹); some statistic information; (–) for the value zero.

<table><thead><tr><th></th><th>Min</th><th>0.1</th><th>0.2</th><th>0.3</th><th>0.4</th><th>0.5</th><th>0.6</th><th>0.7</th><th>0.8</th><th>0.9</th><th>Max</th><th>Means</th><th>σ</th></tr></thead><tbody><tr><th>SST</th><td>280.88</td><td>296.8</td><td>298.44</td><td>299.4</td><td>300.05</td><td>300.58</td><td>301.06</td><td>301.47</td><td>301.89</td><td>302.4</td><td>306.75</td><td>300.05</td><td>2.3</td></tr><tr><th>OLR</th><td>(–)</td><td>200.28</td><td>225.98</td><td>243.39</td><td>255.95</td><td>265.42</td><td>272.87</td><td>279.1</td><td>285</td><td>291.85</td><td>350.3</td><td>252.92</td><td>45.06</td></tr><tr><th>WV</th><td>1.e-4</td><td>2.17</td><td>3.64</td><td>4.87</td><td>5.96</td><td>7.02</td><td>8.08</td><td>9.22</td><td>10.59</td><td>12.62</td><td>65.87</td><td>7.33</td><td>4.1</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>Fig. 3. The schematic of multi expert distance computation between two days ($d_1$ and $d_2$), with input parameters: Sea Surface Temperature (SST), wind components (U, V) and Outgoing Longwave Radiation (OLR); Mc module is a combination operator (e.g., sum or average).</figcaption></figure>

The clustering results obtained using the new MED metric will therefore be compared with those obtained with the same method as Moron et al. (2016) using the $S_a M_k$ index.

## 3. Results

### 3.1. Clustering assessment

Fig. 4 shows the results of the evaluation of the two clustering processes used. The indices produced with the MED (Fig. 4b) give better results than those using the Euclidean distance and Moron et al. (2016), method (Fig. 4a). Six clusters were retained for MED, to consider the first inflection at $k = 6$ with a silhouette index $S_a M_k$ of 0.4. The elbow method involves measuring the Euclidean distance between each data point and its cluster center and choosing the number of clusters based on where the sum-of-squares (WCSS) value stabilizes. This value signifies the aggregate variance within each cluster, which is represented graphically against the number of clusters.

The interpretation of the silhouette index, ranging from -1 to 1, as indicated by extant literature, suggests that the maximum value should be utilized. However, as previously discussed, when data carries a regular temporal signal, the index decreases steadily as the number of clusters increases. In such cases, positive inflections can be interpreted as indications of renewed stability in cluster organization (Cordeiro de Amorim and Hennig, 2015). Our research focuses on these clusters due to their notable stability over time, a feature that is underlined in the present work.

In the following, results obtained for the new method are described in detail.

### 3.2. Spatiotemporal patterns and dynamics

Cluster sizes and precipitation values are presented in Table 2, highlighting that some weather patterns related to precipitation are found. An overview of temporal global (in terms of the total number of transitions) and relative (in terms of the number of days in each group) transitions between clusters is provided in Tables 3 and 4, respectively. It shows that only some clusters are likely to be temporally related. This finding is represented as a transition graph in Fig. 5 (relative transitions only). These day step time transitions allow to analyze links between the clusters related to atmospheric regimes. The daily time step was chosen mainly because it is the smallest unit of time that reflects possible periodicities in weather patterns, below seasons and years (Qian et al., 2010). Fig. 6 brings information about the average of cluster persistence (Fig. 6a), distribution of persistence (Fig. 6b) and its evolution over the
<figure><img src="image_6.png" /><figcaption>Fig. 4. Diagrams of the evolution of silhouette index $S_M k$, defined in Eq. (2), in the function of k the number of clusters; a) for Moron et al. (2016) method: AHC with L2 (green) and K-medoid with L2 (black); b) method using MED: AHC (broken line), K-medoid (solid line), using L2 (black) and ED (red).</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Table 2**</figcaption></figure>

Number of days in each cluster: K-medoid-C3, the most common cluster (in bold) but also the driest (in red); Kmedoid-ED-C5, the least common cluster (in italic); K-medoid-C2, the most humid (in blue); daily mean statistic for MSWEP precipitation (in mm); humid clusters and dry clusters were highlighted respectively in blue and red.

<table><caption>**Table 3**</caption><thead><tr><th>- Clusters</th><th>Sizes</th><th>(%)</th><th>Min</th><th>Means</th><th>Max</th><th>σ</th></tr></thead><tbody><tr><td>C1</td><td>2140</td><td>13.63</td><td>0.69</td><td>4.03</td><td>11.15</td><td>1.7</td></tr><tr><td>C2</td><td>2471</td><td>15.73</td><td>1.48</td><td>5.2</td><td>12.74</td><td>1.59</td></tr><tr><td>C3</td><td>3950</td><td>25.15</td><td>0.2</td><td>1.59</td><td>10.24</td><td>0.84</td></tr><tr><td>C4</td><td>1939</td><td>12.35</td><td>1.28</td><td>4.7</td><td>11.2</td><td>1.71</td></tr><tr><td>C5</td><td>1668</td><td>10.62</td><td>0.66</td><td>4.51</td><td>10.97</td><td>1.48</td></tr><tr><td>C6</td><td>3538</td><td>22.53</td><td>0.23</td><td>2.46</td><td>10.28</td><td>1.4</td></tr></tbody></table>

Temporal global transitions (in terms of the total number of transitions) between the six clusters obtained with K-medoid-ED in percentage (%); with C3-C3 the most common transition (in bold), persistence indicator (in italic) and (–) for the value zero; humid clusters (in blue) and dry clusters (in red) were highlighted.

<table><thead><tr><th></th><th>C1</th><th>C2</th><th>C3</th><th>C4</th><th>C5</th><th>C6</th></tr></thead><tbody><tr><th>C1</th><td>12.93</td><td>(-)</td><td>(-)</td><td>0.02</td><td>0.26</td><td>0.41</td></tr><tr><th>C2</th><td>0.09</td><td>15.14</td><td>(-)</td><td>0.43</td><td>0.07</td><td>(-)</td></tr><tr><th>C3</th><td>(-)</td><td>(-)</td><td>24.49</td><td>(-)</td><td>(-)</td><td>0.66</td></tr><tr><th>C4</th><td>0.17</td><td>0.53</td><td>(-)</td><td>11.57</td><td>0.08</td><td>(-)</td></tr><tr><th>C5</th><td>0.15</td><td>0.06</td><td>(-)</td><td>0.32</td><td>10.05</td><td>0.04</td></tr><tr><th>C6</th><td>0.29</td><td>(-)</td><td>0.66</td><td>(-)</td><td>0.16</td><td>21.41</td></tr></tbody></table>

years (Fig. 6c).

Eventually, the charts in Fig. 7 provide an overview of the spatial patterns characterizing the atmospheric configurations of each cluster, as well as offering information on their temporal variability. The Mann-Kendall test was employed to ascertain the significance of interannual trends within the clusters. For a better presentation and understanding, these results are discussed below per-cluster and ordered by relevance in the field of physics.

<caption>**Table 4**</caption>

Temporal relative transitions (in terms of the number of days in each group) between the six clusters obtained with K-medoid-ED in percentage (%); with C3-C3 the most common transition (in bold), persistence indicator (in italic) and (–) for the value zero; humid clusters (in blue) and dry clusters (in red) were highlighted.

<table><thead><tr><th></th><th>C1</th><th>C2</th><th>C3</th><th>C4</th><th>C5</th><th>C6</th></tr></thead><tbody><tr><th>C1</th><td>94.91</td><td>(-)</td><td>(-)</td><td>0.14</td><td>1.92</td><td>3.04</td></tr><tr><th>C2</th><td>0.57</td><td>96.24</td><td>(-)</td><td>2.75</td><td>0.45</td><td>(-)</td></tr><tr><th>C3</th><td>(-)</td><td>(-)</td><td>97.37</td><td>(-)</td><td>(-)</td><td>2.63</td></tr><tr><th>C4</th><td>1.34</td><td>4.33</td><td>(-)</td><td>93.71</td><td>0.62</td><td>(-)</td></tr><tr><th>C5</th><td>1.38</td><td>0.54</td><td>(-)</td><td>3.06</td><td>94.66</td><td>0.36</td></tr><tr><th>C6</th><td>1.3</td><td>(-)</td><td>2.91</td><td>(-)</td><td>0.71</td><td>95.05</td></tr></tbody></table>

- Cluster C3 is the most common cluster and holds 3950 days (approximately 25 % of the dataset), ranging from January to April and returning to December, with a maximum in February, when the region is drier, with a daily average precipitation of 1.59 mm. Cluster C3 covers a temporally continuous period, confirming a well-established seasonal pattern. A *p-value* of $3.4 \times 10^{-5}$ shows that there is a decreasing inter-annual trend. This cluster has high persistence and only one possible transition to C6, the second driest cluster (Tables 3–4 and Figs. 5 and 6).

- Cluster C2 covers 2471 days (approximately 16 % of the dataset). Intra-annual dynamics show an atmospheric pattern that ranges from June to October, with a peak in September (Fig. 7). This is the wettest cluster, with 5.2 mm. The covered period coincides with that of the passage of tropical storms and hurricanes in the area (Table 5). Cluster C2 significantly tends to become more frequent over the years, with a *p-value* of $3.6 \times 10^{-8}$. It also has a high persistence and can only transit to the other wet clusters (C4, C1 and C5 as shown in Tables 3–4 and Figs. 5 and 6).

- Cluster C4 covers 1939 days (approximately 12 % of days) and appears mainly in July, then gradually disappears until October, during the area's wet season. This cluster seems to be particularly related to hurricane events (Table 5). It is worth noting that it is the second wettest with 4.7 mm of average daily precipitation (Table 2). Cluster C4 significantly tends to become less frequent over the years, with a
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Graph of temporal relative transitions between the six clusters obtained with K-medoid-ED in percentage (%); humid clusters (in blue) and dry clusters (in red) were highlighted.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Persistence graphs: average persistence per cluster (a); probability distribution (in blue) and cumulative probability (in red) of cluster persistence (b); short cluster transitions (≤2 days) over the years (c), with a significative Mann Kendall trend test.</figcaption></figure>

p-value of 1.9 × 10⁻⁶). It also has a high persistence (Tables 3–4, Figs. 5 and 6) and can only transit to the other wet clusters.

- Cluster C1 contains 2140 days (approximately 14 %) mainly located at the limits of the temporal range of C2, but more often during the outer transition from wet to dry. This cluster is humid, with approximately 4 mm of daily averaged precipitation, and can evolve towards C4 and C6 (Tables 3–4 and Figs. 5 and 6). Cluster C1 does not have a significant trend over the years (Fig. 7).

- Cluster C5 covers 1668 days (approximately 11 % of the dataset) during the transition from dry season to wet season with a maximum in June. This is a wet cluster with a daily average precipitation of 4.51 mm. Cluster C5 also has a high persistence and is related to all clusters excluding C3 which is the driest one.

- Cluster C6 covers 3538 days (approximately 22 % of the dataset) and is mainly located at the limits of the temporal range of C3, but more often during the transition from dry season to wet season. Cluster C6
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** LEFT: Patterns of each cluster from K-medoid-ED, with *k* = 6; CENTER: Chart of intra-annual variabilities over the years for the period 1979 to 2021; RIGHT: Chart of inter-annual variabilities with a dashed line for trends and the validity indexes (with significative *p*-value were highlighted in yellow).</figcaption></figure>

is the second driest cluster with 2.46 mm of daily averaged precipitation (Table 2).

As shown in Fig. 6, it presents the average persistence (in days) of each cluster, the atmospheric regimes are constant while around 20 days

(Fig. 6a). A substantial proportion of persistent cases, approximately 80 %, have a duration of less than 50 days, with a notable 17 % lasting less than a single day (Fig. 6b). Short transitions lasting ≤2 days are infrequent but tend to increase significantly over the years (Fig. 6c).
<caption>**Table 5**</caption>

Descriptive statistics and probabilities analysis of distribution of tropical storms and hurricanes in the six clusters of K-medoid-ED method; for a given cluster C (from C1 to C6), $P_{TS}(C)$ expresses the probability that a TS is in C, $P_H(C)$ expresses the probability that a H is in C, $P_C(TS)$ expresses the probability that C produces a TS, and $P_x(H)$ expresses the probability that C produces a H; with the maximum of each column (in bold); (–) for the value zero; humid clusters (in blue) and dry clusters (in red) were highlighted.

<table><thead><tr><th>Clusters</th><th>TS</th><th>H</th><th>Cluster sizes</th><th>P<sub>TS</sub>(C)</th><th>P<sub>H</sub>(C)</th><th>P<sub>C</sub>(TS)</th><th>P<sub>C</sub>(H)</th></tr></thead><tbody><tr><td>C1</td><td>199</td><td>113</td><td>2140</td><td>0.1831</td><td>0.1633</td><td>0.1150</td><td>0.0528</td></tr><tr><td>C2</td><td><strong>562</strong></td><td><strong>409</strong></td><td>2471</td><td><strong>0.5170</strong></td><td><strong>0.5910</strong></td><td><strong>0.3043</strong></td><td><strong>0.1655</strong></td></tr><tr><td>C3</td><td>2</td><td>1</td><td><strong>3950</strong></td><td>0.0018</td><td>0.0005</td><td>0.0005</td><td>0.0003</td></tr><tr><td>C4</td><td>208</td><td>147</td><td>1939</td><td>0.1914</td><td>0.1073</td><td>0.1398</td><td>0.0758</td></tr><tr><td>C5</td><td>77</td><td>10</td><td>1668</td><td>0.0708</td><td>0.0462</td><td>0.0474</td><td>0.0060</td></tr><tr><td>C6</td><td>39</td><td>12</td><td>3538</td><td>0.0359</td><td>0.0110</td><td>0.0133</td><td>0.0034</td></tr><tr><td>Total</td><td>1087</td><td>692</td><td>15706</td><td></td><td></td><td></td><td></td></tr></tbody></table>

### 3.3. Links with hurricanes season

Hurricanes are a major concern for populations of studied areas. Thus, it is of interest to analyze the distribution of cyclonic days in clusters. In order to understand how they are related, tracking points of tropical storms (further denoted as TS) and hurricanes (further denoted as H) recorded by the National Oceanic and Atmospheric Administration (NOAA) from 1979 to 2021 were cross-referenced with the data from the clusters selected for K-medoid-ED. Atlantic hurricane database (Landsea and Franklin, 2013) (HURDAT2, 2024) was used to select the dates of occurrence of TS and H in the studied area (Fig. 1). The proposals and probabilities are presented in Table 5.

Clusters C2, C4, and C1 predominantly contain almost all the TS and H, which seems consistent with their classification as wet weather clusters, as discussed in previous sections. Notably, C2 had the highest concentration of TS, making it the most common cluster during stormy days, with approximately 52 % of such days falling into this category ($P_{TS}(C)$ in Table 5). Additionally, C2 also encompassed most hurricanes, accounting for 59 % ($P_H(C)$ in Table 5). The clusters in question delineate spatial zones exhibiting low OLRs, which correspond to the passage zones of HC and TS, or American monsoon episodes (Fig. 7).

In contrast, clusters C3 and C6 exhibited only a few TS events, primarily occurring towards the end of the year (from November to December), and contained very few hurricanes. This observation agrees with their classification as dry weather clusters. For these clusters, the low OLR zones completely occupy the Caribbean zone (Fig. 7).

### 3.4. SST anomalies and mean rainfall

Fig. 8 presents the spatial dynamics of moisture production (left) and spatial distribution of rainfall (right) for each K-medoid-ED cluster. By their very pattern, some clusters can be gathered in order to create two main configurations:

- Clusters C3 and C6 are the driest. They show negative SST anomalies, particularly at the north of interest area. Moisture production is generally lower than average in these clusters. Overall, the resulting rainfall is very low overall and only occurs in the vicinity of high altitudes.

- Clusters C1, C2, C4 and C5 are the rainiest. They present positive SST anomalies, that are in favor of moisture production. Rainfall is heavier in these clusters.

## 4. Discussions

Previous works identified eight weather types (WT) in the Caribbean

basin, clearly distinguishing winter and summer seasons. Summer WT (corresponding to WT 4–6) contribute to 70 % of annual precipitation, with *el Niño*-southern oscillation events influencing their frequency and resulting in varying precipitation anomalies across regions like Cuba, Puerto Rico, and Martinique (Moron et al., 2016).

Gouriand et al. (2024) have developed a method to detect the onset and the end of the mid-summer drought (MSD) with greater precision than local precipitation-based methods. Their findings indicated that the MSD is starting earlier, lasting longer, but becoming less intense, with its onset linked to increased subsidence and Caribbean low level jet index (CLLJ) acceleration, and its end associated with decreased sea-level pressure and CLLJ weakening.

Most recent articles in climate research use artificial intelligence methods based on neural networks, because they are effective and widespread in solving automatic classification problems with supervised learning (Rasp and Thuerey, 2021; Weyn et al., 2019, 2020; Velasco et al., 2019). For cases of automatic identification such as that described in this work, the use of clustering methods is still interesting (Bernard et al., 2022; Chattopadhyay et al., 2020; Biabiany et al., 2020).

However, clustering methods applied to climate data over a long period may not produce results that are easy to interpret. Indeed, clustering algorithms tend to group together elements whose characteristics are similar according to one or more parameters, which is generally beneficial (Park and Jun 2009; Day and Edelsbrunner, 1984). It would be convenient if weather patterns or seasons could be identified by these methods. However, in the context of climate change, it has been remarked that over a long period of time, only weather patterns that are distinctly marked and stable are identified, so a certain temporal continuity is generally assumed (C3, C2 and C4). The other clusters represent finer meteorological situations, occurring sparsely during inter-seasonal transitions or extreme events (C1, C5 and C6).

It should be noted that the results obtained in climate studies based on clustering integrating an ED metric generally have a high level of spatial and temporal consistency (Biabiany et al., 2020; Bernard et al., 2022). It is therefore easier to interpret them. This work shows that it is also the case for the use of the MED metric. One can observe that OLR patterns and intra-annual distributions shown in Fig. 7 are different, and most of the clusters have a significant trend in terms of frequency of occurrence.

It is interesting to note that the use of the MED results in a Silhouette index value that is twice as strong as the value obtained from the concatenation of the data (Fig. 4a). This is also the case when using the Euclidean distance. This appears to be due to its ability to summarize in a single value the differences in distribution between two temporal situations on several zones separately for each parameter. The distinct characteristics of each zone are meticulously considered during the
<figure><img src="image_11.png" /><figcaption>Fig. 8. LEFT: Spatial anomaly patterns for each cluster of K-medoid-ED; RIGHT: Spatial rainfall averages for each cluster of K-medoid-ED.</figcaption></figure>

establishment of the histogram classes employed to depict the distri-
butions. The outcome of this process is the transfer of expertise
regarding the physical parameters considered for the specific zones via a
MED that can be used by different clustering algorithms.

Transitions of duration ≤2 days are rare, but have increased signif-
icantly over time, as demonstrated in the accompanying Fig. 6. This
phenomenon could be regarded as one of the deleterious consequences
of climate change, leading to atmospheric instability. This phenomenon
could be indicative of a destabilization of atmospheric regimes, as hy-
pothesized by Zhang and Zhou (2019), who associate increased

variability with climate warming.

Notwithstanding the originality of these results, they are inadequate
for the complete identification of the underlying atmospheric dynamics
in the Caribbean. It is evident that this approach alone is inadequate for
comprehensively representing the intricate dynamics, as it risks over-
simplifying the multifaceted interactions among the various climatic
factors.
# 5. Conclusion

Based on the analysis of the clustering processes and the results obtained, it is important to highlight that the Multi-Expert Distance provides a more accurate representation of the spatiotemporal patterns and dynamics of precipitation in the studied region compared than the Euclidean distance. The six clusters identified using the MED reveal distinct seasonal and inter-annual trends, with significant implications for understanding the region's precipitation patterns and their relationship with atmospheric conditions.

The clusters produced by this work exhibit varying degrees of persistence and transition. This results in an average stability of around 20 days for the atmospheric regimes, though this is subject to disruption over the years. Future research could explore transiogram-based approaches, resembling variograms, to validate persistence windows in a more continuous framework. The clusters obtained show notable differences in precipitation levels and their link with tropical storms and hurricanes. The driest clusters (C3 and C6) are characterized by negative SST anomalies and lower moisture production, while the wettest clusters (C1, C2, C4, and C5) show positive SST anomalies and higher rainfall.

This work highlights the importance of considering both spatial and temporal variability in precipitation patterns to better understand and predict the impacts of atmospheric conditions on the region. The findings also underscore the relevance of clustering methods in identifying and analyzing complex environmental patterns, providing valuable insights for future research and practical applications in climate science and meteorology. It would be also interesting to be able to automate domain separation, to converge on zones with their own atmospheric dynamics.

# CRediT authorship contribution statement

**Emmanuel Biabiany:** Writing – review & editing, Writing – original draft, Validation, Supervision, Software, Methodology, Investigation, Formal analysis, Conceptualization. **Ruben Bagghi:** Software, Investigation, Data curation. **Didier C. Bernard:** Writing – review & editing, Writing – original draft. **Vincent Pagé:** Conceptualization. **Stéphane Cholet:** Writing – review & editing. **Raphaël Cécé:** Writing – review & editing.

# Data and computer code availability

Copernicus Climate Change Service (C3S). (2017). ERA5: Fifth generation of ECMWF atmospheric reanalyses of the global climate. Copernicus Climate Change Service Climate Data Store (CDS). Retrieved from https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-pressure-levels?tab=overview

National Centers for Environmental Prediction (NCEP). (2024). Climate Data Record (CDR) of Outgoing Longwave Radiation (OLR). NOAA National Centers for Environmental Information. Retrieved from https://www.ncei.noaa.gov/data/outgoing-longwave-radiation-daily/access/

MSWEP V2 Global 3-Hourly 0.1° Precipitation: Methodology and Quantitative Assessment. Bulletin of the American Meteorological Society: https://drive.google.com/drive/folders/1gWoZ2bK2u5osJ8Iw-dvguZ56Kmz2QWrL

National Hurricane Center. (2024). HURDAT2: Atlantic hurricane database (1851–2024). National Oceanic and Atmospheric Administration (NOAA). Retrieved from: https://www.nhc.noaa.gov/data/hurdat/hurdat2-atl-02052024.txt

Data from this research is not publicly available. Interested researchers can contact the corresponding author of this article. A GitHub repository has been set up for the resources, algorithms and Python code developed in this work: https://github.com/ebiabiany/med-2025.

# Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

# Data availability

Data will be made available on request.

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