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arxiv: 2605.26666 · v1 · pith:MZBZON7Inew · submitted 2026-05-26 · ⚛️ physics.ao-ph

A Comparative Analysis of Clustering Algorithms for Characterizing Surface Ocean Variability in the Western Mediterranean

Victor Rodriguez-Mendez , Enrico Ser-Giacomi , Jose J. Ramasco , Cristobal Lopez , Emilio Hernandez-Garcia This is my paper

Pith reviewed 2026-06-29 14:51 UTC · model grok-4.3

classification ⚛️ physics.ao-ph
keywords clusteringsea surface temperaturekinetic energywestern MediterraneanK-meansSelf-Organizing MapsInfoMapocean patterns
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The pith

K-means and Self-Organizing Maps identify four distinct seasonal clusters in western Mediterranean sea surface temperatures that remain after removing the annual cycle.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how clustering algorithms can extract recurrent patterns from daily sea surface temperature and kinetic energy data in the western Mediterranean. K-means and Self-Organizing Maps both identify four clusters for temperature that correspond to the seasons, and this holds even when the average yearly variation is subtracted from the data. This points to seasonal structures that have more than just a simple average effect. For the more variable kinetic energy field, the partition-based methods give consistent large-scale groupings while InfoMap highlights smaller features like jets and eddies and can flag extreme events.

Core claim

K-means and Self-Organizing Maps consistently delineate four distinct clusters of sea surface temperature configurations, aligned with the seasons even after removing the annual cycle, which indicates the persistence of seasonal structures beyond a mean effect in the temperature field. The study of surface kinetic energy reveals more complex circulation regimes where K-means and Self-Organizing Maps classify dominant large-scale patterns robustly while InfoMap uncovers finer-scale features such as localized jets and eddies.

What carries the argument

Clustering techniques (K-means, Self-Organizing Maps, and InfoMap) applied to daily snapshots of sea surface temperature and kinetic energy to identify regional patterns.

If this is right

  • K-means and Self-Organizing Maps produce coherent classifications of temperature patterns across methods.
  • Four clusters align with seasons for sea surface temperature even without the annual cycle.
  • Kinetic energy patterns are more complex and show finer details with InfoMap.
  • InfoMap serves as a complement that can detect anomalies and extreme events in the flow field.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar clustering could help identify persistent structures in other marginal seas or ocean basins.
  • The identified clusters may link to specific transport properties or biogeochemical processes in the region.
  • These methods could be tested on model output to see if the same seasonal clusters appear in simulations.

Load-bearing premise

That the clusters found by the algorithms represent physically meaningful and recurrent dynamical structures in the ocean rather than depending mainly on the algorithm choice or data handling steps.

What would settle it

A test showing that the four clusters disappear or change when using different spatial domains, preprocessing, or when compared to independent oceanographic observations of seasonal regimes would challenge the main result.

Figures

Figures reproduced from arXiv: 2605.26666 by Cristobal Lopez, Emilio Hernandez-Garcia, Enrico Ser-Giacomi, Jose J. Ramasco, Victor Rodriguez-Mendez.

Figure 1
Figure 1. Figure 1: The study region (red box) within the broader context of the Western Mediterranean Sea. 2.2 K-means clustering K-means clustering (MacQueen et al., 1967) is an unsupervised learning algorithm that partitions a dataset into K distinct, non-overlapping subgroups or clusters. The algorithm aims to minimize the within-cluster sum of squares (WCSS): W CSS = X K k=1 X x∈Ck ∥x − µk∥ 2 , (1) where each x is a sing… view at source ↗
Figure 2
Figure 2. Figure 2: Mean silhouette scores for different clustering methods. Scores for KE and SST using K-means and SOM across varying grid sizes (number of clusters) and topologies. The significant drop in mean silhouette score around four clusters for both K-means and SOM (with 2 × 2 topology in this case), particularly pronounced for SST, supports the selection of four clusters for subsequent analyses. Winter Spring Summe… view at source ↗
Figure 3
Figure 3. Figure 3: Mean silhouette scores for SST clustering across meteorological seasons (4-clusters configuration). 3.2 Sea Surface Temperature 3.2.1 K-means for SST In this section we apply the K-means algorithm with a predetermined number of 4 clusters, as suggested by the silhouette analysis. Figure 4a shows the centroids of the SST spatial patterns in each cluster. So far, the labelling of the clusters as C1, 9 [PITH… view at source ↗
Figure 4
Figure 4. Figure 4: K-means Clustering of Sea Surface Temperature Data. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Temporal distribution, from 1987 to 2022, of SST states in the four clusters (C1–C4) identified through K-means clustering. Vertical dashed lines mark conventional seasonal boundaries (21 December, 21 March, 21 June, and 21 September). Each color represents a different SST cluster, demonstrating both seasonal patterns and inter-annual variability. cold subsets of transitional states. It should be mentioned… view at source ↗
Figure 6
Figure 6. Figure 6: K-means Clustering of Spatially detrended SST data. [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Temporal Distribution of detrended SST clusters in the Mediterranean Sea from 1987 to 2022. The plot shows daily cluster assignments (C1–C4) resulting from K-means clustering of spatially detrended SST data. Vertical dashed lines mark conventional seasonal limits. Cluster colors represent the identified distinct SST-anomaly regimes, revealing recurrent seasonal transitions and the persistence of sub-season… view at source ↗
Figure 8
Figure 8. Figure 8: Panel a) shows the codebook vectors of SOM neurons, representing the sea surface temperature profile for each of the four clusters. Panel b) shows the distribution of data samples assigned to these clusters across different seasons (winter, spring, summer, and autumn). characterized by low and uniform KE, possibly corresponding to periods with weaker currents. C2, with 13.4% of the data, reveals a medium-i… view at source ↗
Figure 9
Figure 9. Figure 9: Centroids of the four clusters obtained from the application of the K-means clustering algorithm on the KE field. Each panel shows the average spatial distribution of KE in each cluster, with the percentage indicating the proportion of total samples assigned to that cluster. The color bar indicates the magnitude of KE. It is important to note that the centroids in K-means tend to simplify complex patterns … view at source ↗
Figure 10
Figure 10. Figure 10: Codebook vectors of the four neurons encoding the representative spatial state of four clusters of KE resulting from the application of the SOM clustering method. The color bar indicates the magnitude of KE. ing mathematical principles, strongly suggests that the circulation in the Ibiza Channel oscillates between these well-defined dynamical states. 3.3.3 InfoMap for KE The centroids of the clusters of K… view at source ↗
Figure 11
Figure 11. Figure 11: Spatial distribution of KE centroids for clusters identified using the InfoMap community detection method. Each panel shows the mean KE pattern of the populations classified in each cluster (C1-C4). Color intensity indicates KE magnitude To further understand the relevance of this ’intense south jet’ energy configuration we applied K-means and SOM algorithms to subsets of the whole data set. We find that … view at source ↗
Figure 12
Figure 12. Figure 12: Jaccard similarity matrices comparing SOM and K-means clustering for (a) Sea Surface Temperature (SST) and (b) Kinetic Energy (KE). Matrix values range from 0.0 to 1.0, where darker purple indicates higher similarity (overlap). In each cell, the lower-left triangle represents the actual Jaccard index between the two methods, while the upper-right triangle represents a baseline Jaccard index calculated usi… view at source ↗
read the original abstract

Understanding regional dynamical structures in the sea is fundamental to characterize energy transfer and transport properties, with implications in physical and biogeochemical modeling and characterization. In this work, we study the potential of clustering techniques to identify regional patterns, persistent or recurrent configurations, out of daily snapshots of sea surface temperature and kinetic energy in a region of the western Mediterranean Sea. From the methodological perspective, we use different clustering techniques: K-means, Self-Organizing Maps and InfoMap to verify if the patterns found are coherent across methods. Our results show that K-means and Self-Organizing Maps consistently delineate four distinct clusters of sea surface temperature configurations, aligned with the seasons even after removing the annual cycle, which indicates the persistence of seasonal structures beyond a mean effect in the temperature field. The study of surface kinetic energy, characterized by higher spatial and temporal variability, reveals more complex circulation regimes. While K-means and Self-Organizing Maps provide a robust and convergent classification of the dominant large-scale energy patterns, InfoMap uncovers finer-scale features such as localized jets and eddies. InfoMap, in particular, provides a complementary perspective to the partition-based methods, validating subtle yet significant hydrodynamic structures and acting as an anomaly detector for extreme events.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript applies K-means, Self-Organizing Maps (SOM), and InfoMap clustering algorithms to daily sea surface temperature (SST) and kinetic energy (KE) fields from the western Mediterranean Sea. It reports that K-means and SOM consistently identify four clusters in both raw and annual-cycle-removed SST data that align with seasonal configurations, while KE exhibits more complex regimes where InfoMap additionally detects finer-scale features such as localized jets and eddies; the work positions the cross-method agreement as evidence for persistent structures beyond mean effects.

Significance. If the qualitative alignments hold under quantitative scrutiny, the comparative framework demonstrates complementary strengths of partition-based versus network-based clustering for characterizing regional ocean variability, with direct relevance to energy transfer and modeling applications noted in the abstract.

major comments (1)
  1. [Results] Results section (and abstract): the central claim that K-means and SOM 'consistently delineate four distinct clusters... aligned with the seasons even after removing the annual cycle' rests entirely on qualitative description of cluster-season correspondence; no quantitative validation metrics, inter-method agreement indices (e.g., adjusted Rand index), silhouette scores, or error estimates on the detrended fields are reported, leaving the persistence claim without measurable support.
minor comments (1)
  1. [Methods] Methods: while the choice of k=4 is stated for both K-means and SOM, the rationale or sensitivity analysis for this number of clusters (a free parameter) should be expanded for reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment on strengthening the quantitative basis of our claims. We address the point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Results] Results section (and abstract): the central claim that K-means and SOM 'consistently delineate four distinct clusters... aligned with the seasons even after removing the annual cycle' rests entirely on qualitative description of cluster-season correspondence; no quantitative validation metrics, inter-method agreement indices (e.g., adjusted Rand index), silhouette scores, or error estimates on the detrended fields are reported, leaving the persistence claim without measurable support.

    Authors: We agree that the persistence claim would be strengthened by quantitative metrics. In the revised manuscript we will compute and report silhouette scores for the K-means and SOM clusterings on both raw and annual-cycle-removed SST fields, the adjusted Rand index between the two methods to quantify inter-method agreement, and basic stability/error estimates (e.g., via bootstrap resampling of the detrended fields). These results will be added to the Results section with a brief reference in the abstract. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The manuscript applies standard, off-the-shelf clustering algorithms (K-means, SOM, InfoMap) directly to preprocessed observational SST and KE fields. No equations, derivations, fitted parameters, or self-referential definitions appear; the reported four-cluster seasonal alignment is an empirical output of the algorithms rather than a quantity constructed from itself. Cross-method comparison and anomaly removal are described as preprocessing choices without any reduction of the central claim to a self-citation chain or input-by-construction step. The analysis is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The interpretation that clusters represent dynamical structures rests on the domain assumption that the chosen algorithms recover physically meaningful regimes from the chosen fields; no free parameters beyond the implicit choice of cluster number are described, and no new entities are postulated.

free parameters (1)
  • number of clusters
    Set to four for SST to align with seasonal regimes; value chosen to match observed seasonal structure.
axioms (1)
  • domain assumption Clustering partitions of daily ocean fields correspond to persistent or recurrent dynamical configurations.
    Invoked when interpreting the four SST clusters as evidence of seasonal structures beyond the mean annual cycle.

pith-pipeline@v0.9.1-grok · 5763 in / 1184 out tokens · 35499 ms · 2026-06-29T14:51:30.474105+00:00 · methodology

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Reference graph

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