Factor Model-based Detection of Regime Transitions in High-dimensional Climate Data (ERA5)

Factor Model-based Detection of Regime Transitions in High-dimensional Climate Data (ERA5) | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Factor Model-based Detection of Regime Transitions in High-dimensional Climate Data (ERA5) Kuldeep Dahal, Sanjib Choudhury This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9206602/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Climate change is usually assessed by examining trends in individual variables, but changes in relationships among variables may indicate deeper structural shifts within climate systems. Here, using Exploratory Factor Analysis across five periods from 1991 to 2025 for a location at longitude 29°N, latitude 77°E, we demonstrate that this multivariate approach can detect such structural changes by identifying temporal shifts in hidden covariance patterns. Across all periods, two consistent climate regimes are identified—a thermally driven land-atmosphere mode (Factor 1) and a moisture-circulation mode (Factor 2)—showing stable core modes of variability. However, systematic redistribution of explained variance (Factor 1 increasing from 50.1% to 54.2%; Factor 2 declining from 27.5% to 20.3%) and changing loading magnitudes reveal gradual reweighting within these regimes. The thermal mode becomes more dominant as surface-boundary layer coupling weakens, while the moisture mode shows ongoing decline through reduced influence of meridional wind and humidity variables, suggesting that climate variability is reorganizing around thermally driven processes. Notably, emerging cross-loading behavior in dew point temperature—showing increasing association with both factors—suggests that structural realignment may begin at the variable level before fully manifesting as regime changes. These findings show that climate change at this location proceeds through the amplification or reduction of existing latent structures rather than sudden structural collapse. By monitoring changes in how variables relate to each other through factor loading matrices and variance redistribution, this multivariate approach offers a sensitive way to detect early signs of structural climate change in complex environmental systems. Climate Change factor loadings matrix Kaiser-Meyer-Olkin test Bartlett’s test of Sphericity eigenvalues scree plot Factor Analysis Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 INTRODUCTION Climate change is now actively altering global weather extremes and ecosystem stability. While its effect on individual variables like temperature is clear, identifying its influence on the complex, multivariate structure of the climate system, the network of relationships among temperature, pressure, humidity, wind, and other parameters/variables remains a major scientific challenge. Traditional methods that focus on single variables may overlook important shifts in how these parameters interact. Historically, climate change detection has centered on identifying long-term trends in individual climate variables such as surface temperature and precipitation. Although these methods have successfully demonstrated anthropogenic warming, they assume that climate change primarily manifests through changes in marginal distributions. Growing evidence shows this assumption is incomplete, as climate change can also be identified through shifts in the joint behavior of weather variables, even when individual trends are weak or hidden by natural variability. Recent studies showed that the multivariate configuration of the daily weather itself is impacted by a detectable climate change signal, irrespective of long-term trends. Climate change alters the relationships among variables, such as temperature, humidity, wind, and pressure, rather than simply shifting their means 1 . The impacts of climate have increasingly arisen from the interaction of multiple variables, highlighting that the isolated extreme variables have governed risk and detectability rather than dependencies. This conceptual shift establishes climate change as a problem of structural change in multivariate systems, more than solely a problem of trend detection 2 . Assessments of climate change over India reveal that it manifests through evolving interactions and changing sensitivities among monsoon-related variables, such as circulation, land–atmosphere feedbacks, and moisture pathways, which undermine stationary relationships with large-scale drivers 3,4,5 . Climate network and causal inference approaches provide complementary evidence that climate change manifests as a reorganization of system interactions. Structural changes have been identified in causal pathways and dependence networks, supporting the interpretation of climate change as a modification of climate system architecture rather than simple signal amplification 6,7 . The availability of ERA5 reanalysis has enabled systematic investigation of multivariate climate dynamics over India. These ERA5-based studies reveal that climate change is manifesting through modifications in the coupling between circulation and moisture transport, evolving nonlinear controls on precipitation variability, and shifts in the dynamical coupling of precipitable water vapor with circulation 8,9,10 . The assumption of stationary teleconnections governing the Indian climate is increasingly challenged by evidence that large-scale drivers are reorganizing under climate change, with studies documenting emerging extratropical influences on monsoon rainfall alongside time-varying relationships between El Niño–Southern Oscillation (ENSO) and hydroclimatic extremes 11,12 . This non-stationarity is further evident in the evolving influence of climate oscillations on hydrological extremes such as droughts and flash droughts, confirming that climate impacts arise from changing interactions rather than fixed forcing pathways 13 . The increasing prevalence of compound extremes over India provides direct evidence of changing dependence structures, with studies showing that hot–dry extremes have intensified due to modifications in the joint behaviour of temperature and moisture rather than independent trends 14 . Assessments of heat–humidity stress further confirm that climate change amplifies societal risk through the evolution of joint distributions of multivariate climate behavior 15 . While dimensionality reduction techniques like Empirical Orthogonal Function (EOF) analysis traditionally assume stable underlying structures of climate variability, studies applying time-dependent frameworks reveal that spatial coherence and synchronization patterns among monsoon systems evolve across decades, indicating that latent climate organization is not static 16 . Allowing spatial patterns to vary over time through time-dependent extensions of EOF analysis further demonstrates the structural evolution in dominant modes of variability that stationary frameworks fail to capture 17 . Despite this, few studies explicitly test whether the latent multivariate structure of the climate system has changed across time, and even fewer apply formal statistical methods to distinguish meaningful structural change from random variability. This study shows how Exploratory Factor Analysis (EFA) can be applied to detect the multivariate changes leading to climate change. STUDY AREA This study focuses on a geographic point at 29°N, 77°E—a location situated in northern India, proximate to Delhi—selected as a representative testbed for detecting multivariate climate change in a rapidly developing, data-rich region. While the methodological framework is universally applicable to any location with sufficient observational or reanalysis data, this site offers several strategic advantages: (1) It lies within the Indo-Gangetic Plain, a region experiencing pronounced climatic pressures, including intense urban heat island effects, shifting monsoon dynamics, and deteriorating air quality, thereby providing a strong potential signal for change detection. (2) High-quality, long-term ERA5 reanalysis data are reliably available, ensuring robust statistical analysis and (3) The area features a complex interaction of multiple climate influences (continental, monsoonal, and increasingly human-made), making it a suitable candidate for examining structural changes in a multivariate climate system. Therefore, while theoretically location-independent, this choice allows for a thorough, physically meaningful case study where emerging climate signals are likely to be identifiable. DATA We utilized the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis to obtain a physically consistent, multivariate climate dataset 18 . Daily mean values for nine surface and near-surface variables were extracted for a single grid point (29°N, 77°E) in northern India: zonal wind at 10m (u10), meridional wind at 10m (v10), 2m dewpoint temperature (d2m), 2m air temperature (t2m), mean sea level pressure (sp), skin temperature (skt), total cloud cover (tcc), soil temperature level 1 (stl1), and boundary layer height (blh). The analysis spans a historical baseline (1991-1994) and a contemporary period subdivided into sequential 4-year blocks (2010-2013, 2014-2017, 2018-2021, 2022-2025). To achieve a balance between temporal resolution and statistical independence while representing synoptic variability, we sampled observations on seven fixed calendar days each month (4th, 8th, 12th, 16th, 20th, 24th, and 28th), yielding 84 observations annually. All variables were standardized to z-scores (mean=0, standard deviation=1) within each analysis period to place them on a common scale for multivariate comparison. This standardization approach centers the analysis on the covariance structure between variables—the core focus of factor analysis—while the multi-year blocks allow examination of potential shifts in these relationships over time. METHODS a. Temporal Segmentation To investigate changes in multivariate climate structure over time, the full dataset is divided into non-overlapping four-year blocks: Baseline period: 1991–1994 Contemporary periods: 2010–2013, 2014–2017, 2018–2021, 2022–2025 This block-wise design balances sample size and temporal resolution, allowing comparison of factor structures across distinct climatic epochs while minimizing short-term variability. b. Data Pre-processing and Standardization For each time block, the selected variables are extracted and converted into a common tabular format. Missing observations are removed to ensure complete multivariate records. All variables are standardized using z-score normalization within each period, such that each variable has zero mean and unit variance. Standardization ensures comparability across variables with different physical units and implies that the total variance of the system equals the number of variables. This step is essential for factor analysis based on the correlation matrix. c. Assessment of Factorability Before factor extraction, the suitability of the data for factor analysis is assessed using standard diagnostic tests: Kaiser–Meyer–Olkin (KMO) measure of sampling adequacy, to evaluate whether partial correlations are sufficiently small; Bartlett’s test of sphericity, to test whether the correlation matrix significantly differs from an identity matrix. Only datasets satisfying commonly accepted thresholds (KMO > 0.7 and Bartlett’s test p < 0.05) are retained for further analysis. d. Exploratory Factor Analysis Exploratory Factor Analysis (EFA) is performed separately for each time block using the correlation matrix of standardized variables. Factors are initially extracted without rotation to obtain eigenvalues. The Kaiser criterion (eigenvalue > 1) is used to determine the number of factors retained. For interpretability, retained factors are rotated using Varimax rotation, which produces orthogonal factors and a simple loading structure. Rotation does not alter total variance explained but redistributes variance among factors to enhance physical interpretation. e. Variance Explained For each period, the percentage variance explained by each retained factor is computed by dividing its eigenvalue by the total variance and expressing the result as a percentage. Cumulative variance explained by the retained factors is also calculated and compared across periods to assess the stability of the latent structure. f. Visualization and Exploratory Analysis A suite of visualization techniques is used to support interpretation: Scree plots and variance-explained plots to justify factor retention; Dumbbell plots to illustrate loading changes relative to baseline; Alluvial diagrams to depict shifts in dominant variable–factor associations; All analyses were conducted in Google Colab using Python. RESULTS Table 1: Suitability Test Results Periods KMO value Chi-Square Bartlett's test of sphericity (p-value) 1991-1994 0.814414954 3845.4 0 2010-2013 0.809427363 3783.9 0 2014-2017 0.789636812 3545.3 0 2018-2021 0.814770975 3594.7 0 2022-2025 0.825436524 3552.3 0 As shown in Table 1, the KMO (Kaiser-Meyer-Olkin) test with values greater than 0.78 and Bartlett’s test of sphericity with p-value < 0.05 confirms that the samples/periods (1991-1994; 2020-2013; 2014-2017; 2018-2021; 2022-2025) are adequate and there is significant correlation among the variables for further analysis. Table 2: Eigenvalues Factors 1991-1994 2010-2013 2014-2017 2018-2021 2022-2025 Factor 1 4.513 4.67 4.687 4.814 4.88 Factor 2 2.471 2.237 2.079 1.918 1.827 Factor 3 0.736 0.704 0.809 0.745 0.691 Factor 4 0.522 0.627 0.548 0.65 0.649 Factor 5 0.42 0.399 0.467 0.48 0.536 Factor 6 0.211 0.205 0.268 0.245 0.256 Factor 7 0.095 0.128 0.1 0.112 0.124 Factor 8 0.018 0.017 0.025 0.021 0.022 Factor 9 0.014 0.013 0.016 0.016 0.014 The combined scree plot (as referred to Figure 1) for all five periods identified a clear elbow after the second component, representing a sharp drop in eigenvalues. Only the first two components in each period had eigenvalues greater than 1 (as shown in Table 2), representing the largest proportion of total variance. Both the scree plot and the eigenvalues table indicate that only two factors should be retained for further analysis. Table 3: Factor Loadings Matrix Period Variable Factor 1 Factor 2 1991-1994 sp -0.8477 -0.4152 v10 -0.0768 0.6757 t2m 0.9725 0.0540 tcc 0.1704 0.4508 u10 0.1623 -0.7441 d2m 0.3418 0.7533 skt 0.9952 0.0957 stl1 0.9710 0.0907 blh 0.7366 -0.3991 2010-2013 sp -0.8326 -0.4008 v10 -0.1072 0.5301 t2m 0.9660 0.0590 tcc 0.2141 0.5181 u10 0.0666 -0.7832 d2m 0.4099 0.7205 skt 0.9870 0.1576 stl1 0.9831 0.1112 blh 0.7429 -0.3251 2014-2017 sp -0.8716 -0.3431 v10 -0.0781 0.6469 t2m 0.9646 0.0462 tcc 0.1211 0.3791 u10 0.0420 -0.7098 d2m 0.5484 0.6304 skt 0.9901 0.1182 stl1 0.9735 0.0859 blh 0.6988 -0.3395 2018-2021 sp -0.8571 -0.3369 v10 -0.0184 0.5895 t2m 0.9654 0.0811 tcc 0.0900 0.4656 u10 -0.0148 -0.7021 d2m 0.5725 0.6403 skt 0.9838 0.1754 stl1 0.9751 0.1434 blh 0.6780 -0.2152 2022-2025 sp -0.8524 -0.3780 v10 -0.0189 0.5778 t2m 0.9700 0.0569 tcc 0.1468 0.5783 u10 -0.0219 -0.6385 d2m 0.5791 0.6295 skt 0.9790 0.1884 stl1 0.9758 0.1344 blh 0.6358 -0.0846 Among the nine variables considered for the analysis, the factor loading matrix displays the strength of association between each variable and the extracted factors, with the respective loading values indicating which factor each variable most strongly represents. Variables with factor loadings exceeding 0.40 are typically retained as meaningful contributors to a factor, while loadings above 0.70 are considered indicative of a well-defined structure. The table highlights all values meeting the retention criterion for their respective factors. a. Characteristics of the retained Factors We start by performing EFA on each dataset and time period (1991-1994, 2010-2013, 2014-2017, 2018-2021, and 2022-2025) separately to identify the most influential climatic factors for this location (29°N, 77°E) across different periods. The factor loading matrices show a consistent pattern of variable–factor relationships, with the same groups of climate variables mainly loading on Factor 1 and Factor 2 (Table 3). This suggests that the dominant climatic factors remain stable at this location (29°N, 77°E) throughout the study periods. However, despite this structural consistency, the size of the factor loadings varies across datasets, indicating that the strength and internal relationships of variables within each factor are changing (Table 3: Factor Loadings Matrix). Further, the total variance explained by the two factors across different time periods has changed significantly. The observed fluctuations in loadings imply that climate change at this location is not characterized by a shift to new climate regimes but by a gradual change in the coupling strength among variables within existing regimes (Fig 4: Variance Explained). We can also say that for any other location, if there is any structural change in the Factor-variable association, then it can easily be detected with the help of the factor loading matrix and alluvial plots. Focusing on the analysis, we find that the climate variables, namely t2m , skt , stl1 , sp , and blh load on Factor 1, and v10 , u10 , d2m, and tcc load on Factor 2 for all the time periods/datasets (Table 3 and Fig 2). T2m, skt, blh, and stl1 had strong positive loading, and sp had strong negative loading on Factor 1. Similarly, v10, d2m, and tcc had positive loading, and u10 had a negative loading on Factor 2. b. Changes Detected Although we found that a broadly consistent climatic pattern dominates throughout the study period, statistically meaningful variations in variable loadings are observed in the factor loading matrix (Table 3: Factor Loadings Matrix). Changes in Factor 1 T2m (air temperature), skt (skin temperature), and stl1 (soil temperature) remained extremely high (>0.96), indicating a persistent coupling between surface heating, subsurface thermal conditions, and near-surface atmospheric temperature. In contrast, blh (boundary layer height) loading shows a gradual weakening over time, decreasing from ~0.74 (1991–94) to ~0.64 (2022–25) (Table 3: Factor Loadings Matrix). This decoupling suggests that although surface and near-surface temperatures continue to rise coherently, their ability to drive vertical atmospheric mixing has diminished. This weakening of the temperature boundary layer linkage implies reduced vertical ventilation (a condition often associated with heat stress and accumulation of near-surface heat). The strongly negative loading throughout all time periods on sp (surface pressure) (>−0.87) confirms a recurring thermal low-pressure association (Table 3: Factor Loadings Matrix). The graphical representation of the changes occurring in Factor 1 among the variables across all five periods (1991-1994, 2010-2013, 2014-2017, 2018-2021, and 2022-2025) are shown in Figure 5 (a, c & e). Also, the total variance explained by factor 1 across all time periods has also changed significantly from 50.1% in 1991-1994 to 54.2% in 2022-2025, with a rise of 4.1%. (Fig 4: Variance Distribution Chart). This increase in explained variance insinuated that an increasingly large proportion of the multivariate climate system is governed by thermally driven land-atmospheric processes. Thus, we can say that in the case of factor 1, there is no structural change, but there is a shift in the relationship among the variables. Changes in Factor 2 Factor 2 was dominated by u10 (zonal wind), v10 (meridional wind), d2m (dew point temperature), and tcc (total cloud cover). The loadings on v10 and d2m have decreased from 0.67 to 0.57 and from 0.75 to 0.62, respectively, from the baseline period (1991-1994) to the latest period (2022-2025) considered in the study (Table 3: Factor Loadings Matrix). These decreasing loadings of both variables indicate a weakening influence of large-scale moisture transport and near-surface humidity. Hence, we can conclude that the role of meridional advection in supplying moisture to the local climate system is reduced. On the other hand, the loadings on u10 and tcc have increased significantly from -0.74 to -0.63 and from 0.45 to 0.57, respectively, compared with the 1991-1994 vs 2022-2025 time periods (Table 3: Factor Loadings Matrix). This indicates the strengthening association between the variables and the factor. The graphical representation of the changes among the variables in Factor 2 across all five periods (1991-1994, 2010-2013, 2014-2017, 2018-2021, and 2022-2025) are shown in Figures 5 (b, d & f). The total variance explained in the case of Factor 2 decreased from 27.5% to 20.3%, which is a huge decline (-7.2%) (Fig 4: Variance Distribution Chart). This means the contribution of variables associated with factor 2 to overall climate variability is decreasing. As of the time period considered for the study, we can say that there is no complete structural change in factor 2 as well. Possible Structural Change in the Future As observed from the factor loadings matrix, a possible structural change may emerge from the evolving behaviour of d2m (dew point temperature) in the near future. While d2m initially exhibits a strong association with Factor 2, its loading on this factor weakens over time. Whereas it’s loading on Factor 1 started to increase. However, in the period (2022-2025), the loadings of d2m on the two factors become nearly equal (though Factor 2 had the highest loading) (Table 3: Factor Loadings Matrix). Such convergence suggests that d2m is becoming less uniquely associated with factor 2 and increasingly influenced by Factor 1. If this trajectory continues, d2m may shift from a Factor 2-dominated variable to a Factor 1-dominated variable, potentially contributing to a future reorganization of factor structure. Also, the observed redistribution of variance between the two Factors provides insight into the possible future evolution of the multivariate climate structure of this particular location. Over the study period, factor 1 exhibited a systematic increase in explained variance, while factor 2 showed a substantial decline (Fig 4: Variance Distribution Chart). This divergence suggests that an increasing proportion of climate variability is being organized by Factor 1, with diminishing contribution from Factor 2 related variability. CONCLUSION This study shows that factor analysis acts as a sophisticated multivariate tool for detecting climate change, shifting the focus from single-variable trends to the development of interconnected structural relationships. By systematically examining factor loadings, variance redistribution, and temporal comparability, the analysis indicates that climate variability changes through a gradual reweighting of variables within relatively stable latent regimes. While the persistence of primary factor structures across different time periods suggests that the core modes of the climate system stay consistent, notable changes in explained variance and loading sizes highlight an ongoing internal restructuring. Specifically, the growing dominance (Factor 1 increasing from 50.1% to 54.2%) of one latent regime, along with the decreasing influence of another (Factor 2 declining from 27.5% to 20.3%); suggests that climate change appears as a systemic redistribution of multivariate variability rather than a sudden structural failure. Further, the appearance of cross-loading behavior in certain variables shows that structural reorganization may begin at the variable level before becoming visible at the factor level as given below: Variable like blh in Factor 1 decreasing from ~0.74 (1991–94) to ~0.64 (2022–25), variables v10 and d2m in Factor 2 decreasing from 0.67 to 0.57 and from 0.75 to 0.62, respectively, from the baseline period (1991-1994) to the latest period (2022-2025), also the variables u10 and tcc in factor 2 increasing from -0.74 to -0.63 and from 0.45 to 0.57, respectively, as compared to the 1991-1994 vs 2022-2025 time periods (Table 3: Factor Loadings Matrix). Eventually, these results support the effectiveness of factor-analytic frameworks—validated through robust statistical techniques—as a reliable, adaptable method for characterizing climate change as a continuous reorganization of interconnected processes within complex environmental systems. Declarations Ethics approval and consent to participate The study utilized publicly available climate datasets from recognized sources. No human participants were involved, and therefore ethical approval and consent to participate were not required. Consent for publication All authors have read and approved the final manuscript and consent to its publication. Competing Interests The authors have no relevant financial or non-financial interests to disclose . Author contributions Kuldeep Dahal: Conceptualization, Data Curation, Formal Analysis, Interpretation, Writing – Original Draft. Sanjib Choudhury: Methodology, Supervision, Review & Editing, Final Manuscript Preparation. Funding The authors declare that no funds, grants, or other support were received during the preparation of this manuscript. Availability of data and materials The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request. 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International Journal of Climatology , 43(2), 1034-1049. https://doi.org/10.1002/joc.7861 Deepa, J.S., Gnanaseelan, C., & Anusree, K.V. (2025). The influence of climate modes on long-term sea level variability of the Indian ocean with special emphasis on the Southern Annular Mode: A study based on Indian ocean sea level reconstructions. Theoretical and Applied Climatology 156 , 535. https://doi.org/10.1007/s00704-025-05740-4. https://cds.climate.copernicus.eu/ Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 22 Apr, 2026 Reviewers invited by journal 05 Apr, 2026 Editor assigned by journal 25 Mar, 2026 First submitted to journal 25 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9206602","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":617855091,"identity":"f170548e-d3b7-4437-aded-c011f28cefb4","order_by":0,"name":"Kuldeep Dahal","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0001-9585-6658","institution":"Indian Institute of Information Technology Senapati Manipur","correspondingAuthor":true,"prefix":"","firstName":"Kuldeep","middleName":"","lastName":"Dahal","suffix":""},{"id":617855092,"identity":"8a3f5d84-451a-48b0-a555-b03b58b8abbf","order_by":1,"name":"Sanjib Choudhury","email":"","orcid":"","institution":"Indian Institute of Information Technology Senapati Manipur","correspondingAuthor":false,"prefix":"","firstName":"Sanjib","middleName":"","lastName":"Choudhury","suffix":""}],"badges":[],"createdAt":"2026-03-24 04:36:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9206602/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9206602/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106596334,"identity":"4b6c397a-5b04-4219-abf6-b42dc582ff9e","added_by":"auto","created_at":"2026-04-10 09:35:29","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":113278,"visible":true,"origin":"","legend":"\u003cp\u003eScree Plot.\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-9206602/v1/cf8ba5027f22a47b6cfa4a63.png"},{"id":106596335,"identity":"05f45935-bd27-4008-82f7-4b9e54fa1fea","added_by":"auto","created_at":"2026-04-10 09:35:29","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":409785,"visible":true,"origin":"","legend":"\u003cp\u003eVariable -Factor Association Plot.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea) \u003c/strong\u003e1991-1994 vs 2010-2013. \u003cstrong\u003eb) \u003c/strong\u003e1991-1990 vs 2014-2017. \u003cstrong\u003ec) \u003c/strong\u003e1991-1990 vs 2018-2021. \u003cstrong\u003ed) \u003c/strong\u003e1991-1994 vs 2022-2025.\u003c/p\u003e\n\u003cp\u003eThe factor loadings for the period (1991-1994) were considered as baseline and compared across all the other periods for consistency. The same variables were loaded for Factor 1 and Factor 2, respectively, in all the cases.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-9206602/v1/4858a4b348b2d479e0982b64.png"},{"id":106596338,"identity":"7f3c3ac4-f84a-490f-82f8-937237e3b161","added_by":"auto","created_at":"2026-04-10 09:35:30","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":701251,"visible":true,"origin":"","legend":"\u003cp\u003eFactor Loadings Evolution.\u003c/p\u003e\n\u003cp\u003eRed represents factor 1 and blue represents factor 2.\u003c/p\u003e\n\u003cp\u003eThe transition of factor loadings for all the nine variables considered in this study from the baseline period 1991-1994 to the recent period 2022-2025 is shown in the figure.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-9206602/v1/fa91c50c60c9d35f8444cbb4.png"},{"id":106596336,"identity":"42affe94-5495-4adb-89f5-942949a301aa","added_by":"auto","created_at":"2026-04-10 09:35:29","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":132152,"visible":true,"origin":"","legend":"\u003cp\u003eVariance Distribution Chart.\u003c/p\u003e\n\u003cp\u003eThe total variance percentage explained by Factor 1 and Factor 2, along with their cumulative variance percentage for all the periods, is shown in the figure.\u003c/p\u003e\n\u003cp\u003eThe results are statistically robust and follow a consistent pattern, providing meaningful interpretations.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-9206602/v1/c63b44746f567a3ee6476cff.png"},{"id":106596337,"identity":"fbcfc3df-5258-435e-b960-c8026f95bcf0","added_by":"auto","created_at":"2026-04-10 09:35:29","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":211018,"visible":true,"origin":"","legend":"\u003cp\u003eChange in variables (Baseline vs Each Period)\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea) \u0026amp; b) \u003c/strong\u003ecomparison of the factor 1 and Factor 2 loadings, respectively, for the periods 1991-1994 and 2010-2013.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ec) \u0026amp; d) \u003c/strong\u003ecomparison of the factor 1 and Factor 2 loadings, respectively, for the periods 1991-1994 and 2014-2017.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ee) \u0026amp; f) \u003c/strong\u003ecomparison of the factor 1 and Factor 2 loadings, respectively, for the periods 1991-1994 and 2018-2021.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eg) \u0026amp; h) \u003c/strong\u003ecomparison of the factor 1 and Factor 2 loadings, respectively, for the periods 1991-1994 and 2022-2025.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-9206602/v1/abbe0d44091e75d342fffb43.png"},{"id":106596340,"identity":"168d6222-ec6b-472f-b754-3c43e2cf63d3","added_by":"auto","created_at":"2026-04-10 09:35:36","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2408001,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9206602/v1/83e754d0-9cc1-4a47-aa3c-e15a99c3ce78.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eFactor Model-based Detection of Regime Transitions in High-dimensional Climate Data (ERA5)\u003c/p\u003e","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eClimate change is now actively altering global weather extremes and ecosystem stability. While its effect on individual variables like temperature is clear, identifying its influence on the complex, multivariate structure of the climate system, the network of relationships among temperature, pressure, humidity, wind, and other parameters/variables remains a major scientific challenge. Traditional methods that focus on single variables may overlook important shifts in how these parameters interact. Historically, climate change detection has centered on identifying long-term trends in individual climate variables such as surface temperature and precipitation. Although these methods have successfully demonstrated anthropogenic warming, they assume that climate change primarily manifests through changes in marginal distributions. Growing evidence shows this assumption is incomplete, as climate change can also be identified through shifts in the joint behavior of weather variables, even when individual trends are weak or hidden by natural variability. \u0026nbsp;Recent studies showed that the multivariate configuration of the daily weather itself is impacted by a detectable climate change signal, irrespective of long-term trends. Climate change alters the relationships among variables, such as temperature, humidity, wind, and pressure, rather than simply shifting their means\u003csup\u003e1\u003c/sup\u003e. The impacts of climate have increasingly arisen from the interaction of multiple variables, highlighting that the isolated extreme variables have governed risk and detectability rather than dependencies. This conceptual shift establishes climate change as a problem of structural change in multivariate systems, more than solely a problem of trend detection\u003csup\u003e2\u003c/sup\u003e. Assessments of climate change over India reveal that it manifests through evolving interactions and changing sensitivities among monsoon-related variables, such as circulation, land\u0026ndash;atmosphere feedbacks, and moisture pathways, which undermine stationary relationships with large-scale drivers\u003csup\u003e3,4,5\u003c/sup\u003e. Climate network and causal inference approaches provide complementary evidence that climate change manifests as a reorganization of system interactions. Structural changes have been identified in causal pathways and dependence networks, supporting the interpretation of climate change as a modification of climate system architecture rather than simple signal amplification\u003csup\u003e6,7\u003c/sup\u003e. The availability of ERA5 reanalysis has enabled systematic investigation of multivariate climate dynamics over India. These ERA5-based studies reveal that climate change is manifesting through modifications in the coupling between circulation and moisture transport, evolving nonlinear controls on precipitation variability, and shifts in the dynamical coupling of precipitable water vapor with circulation\u003csup\u003e8,9,10\u003c/sup\u003e. The assumption of stationary teleconnections governing the Indian climate is increasingly challenged by evidence that large-scale drivers are reorganizing under climate change, with studies documenting emerging extratropical influences on monsoon rainfall alongside time-varying relationships between \u0026nbsp;El Ni\u0026ntilde;o\u0026ndash;Southern Oscillation (ENSO) and hydroclimatic extremes\u003csup\u003e11,12\u003c/sup\u003e. This non-stationarity is further evident in the evolving influence of climate oscillations on hydrological extremes such as droughts and flash droughts, confirming that climate impacts arise from changing interactions rather than fixed forcing pathways\u003csup\u003e13\u003c/sup\u003e. \u0026nbsp;The increasing prevalence of compound extremes over India provides direct evidence of changing dependence structures, with studies showing that hot\u0026ndash;dry extremes have intensified due to modifications in the joint behaviour of temperature and moisture rather than independent trends\u003csup\u003e14\u003c/sup\u003e. Assessments of heat\u0026ndash;humidity stress further confirm that climate change amplifies societal risk through the evolution of joint distributions of multivariate climate behavior\u003csup\u003e15\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eWhile dimensionality reduction techniques like Empirical Orthogonal Function (EOF) analysis traditionally assume stable underlying structures of climate variability, studies applying time-dependent frameworks reveal that spatial coherence and synchronization patterns among monsoon systems evolve across decades, indicating that latent climate organization is not static\u003csup\u003e16\u003c/sup\u003e. Allowing spatial patterns to vary over time through time-dependent extensions of EOF analysis further demonstrates the structural evolution in dominant modes of variability that stationary frameworks fail to capture\u003csup\u003e17\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eDespite this, few studies explicitly test whether the latent multivariate structure of the climate system has changed across time, and even fewer apply formal statistical methods to distinguish meaningful structural change from random variability.\u003c/p\u003e\n\u003cp\u003eThis study shows how Exploratory Factor Analysis (EFA) can be applied to detect the multivariate changes leading to climate change.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSTUDY AREA\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study focuses on a geographic point at 29\u0026deg;N, 77\u0026deg;E\u0026mdash;a location situated in northern India, proximate to Delhi\u0026mdash;selected as a representative testbed for detecting multivariate climate change in a rapidly developing, data-rich region. While the methodological framework is universally applicable to any location with sufficient observational or reanalysis data, this site offers several strategic advantages:\u003c/p\u003e\n\u003cp\u003e(1) It lies within the Indo-Gangetic Plain, a region experiencing pronounced climatic pressures, including intense urban heat island effects, shifting monsoon dynamics, and deteriorating air quality, thereby providing a strong potential signal for change detection.\u003c/p\u003e\n\u003cp\u003e(2) High-quality, long-term ERA5 reanalysis data are reliably available, ensuring robust statistical analysis and\u003c/p\u003e\n\u003cp\u003e(3) The area features a complex interaction of multiple climate influences (continental, monsoonal, and increasingly human-made), making it a suitable candidate for examining structural changes in a multivariate climate system. Therefore, while theoretically location-independent, this choice allows for a thorough, physically meaningful case study where emerging climate signals are likely to be identifiable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDATA\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe utilized the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis to obtain a physically consistent, multivariate climate dataset\u003csup\u003e18\u003c/sup\u003e. Daily mean values for nine surface and near-surface variables were extracted for a single grid point (29\u0026deg;N, 77\u0026deg;E) in northern India: zonal wind at 10m (u10), meridional wind at 10m (v10), 2m dewpoint temperature (d2m), 2m air temperature (t2m), mean sea level pressure (sp), skin temperature (skt), total cloud cover (tcc), soil temperature level 1 (stl1), and boundary layer height (blh). The analysis spans a historical baseline (1991-1994) and a contemporary period subdivided into sequential 4-year blocks (2010-2013, 2014-2017, 2018-2021, 2022-2025). To achieve a balance between temporal resolution and statistical independence while representing synoptic variability, we sampled observations on seven fixed calendar days each month (4th, 8th, 12th, 16th, 20th, 24th, and 28th), yielding 84 observations annually. All variables were standardized to z-scores (mean=0, standard deviation=1) within each analysis period to place them on a common scale for multivariate comparison. This standardization approach centers the analysis on the covariance structure between variables\u0026mdash;the core focus of factor analysis\u0026mdash;while the multi-year blocks allow examination of potential shifts in these relationships over time.\u003c/p\u003e"},{"header":"METHODS","content":"\u003cp\u003e\u003cstrong\u003ea. Temporal Segmentation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo investigate changes in multivariate climate structure over time, the full dataset is divided into non-overlapping four-year blocks:\u003c/p\u003e\n\u003cul type=\"disc\"\u003e\n \u003cli\u003eBaseline period: 1991\u0026ndash;1994\u003c/li\u003e\n \u003cli\u003eContemporary periods: 2010\u0026ndash;2013, 2014\u0026ndash;2017, 2018\u0026ndash;2021, 2022\u0026ndash;2025\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThis block-wise design balances sample size and temporal resolution, allowing comparison of factor structures across distinct climatic epochs while minimizing short-term variability.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eb. Data Pre-processing and Standardization\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFor each time block, the selected variables are extracted and converted into a common tabular format. Missing observations are removed to ensure complete multivariate records.\u003c/p\u003e\n\u003cp\u003eAll variables are standardized using z-score normalization within each period, such that each variable has zero mean and unit variance. Standardization ensures comparability across variables with different physical units and implies that the total variance of the system equals the number of variables. This step is essential for factor analysis based on the correlation matrix.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ec. Assessment of Factorability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eBefore factor extraction, the suitability of the data for factor analysis is assessed using standard diagnostic tests:\u003c/p\u003e\n\u003cul type=\"disc\"\u003e\n \u003cli\u003eKaiser\u0026ndash;Meyer\u0026ndash;Olkin (KMO) measure of sampling adequacy, to evaluate whether partial correlations are sufficiently small;\u003c/li\u003e\n \u003cli\u003eBartlett\u0026rsquo;s test of sphericity, to test whether the correlation matrix significantly differs from an identity matrix.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eOnly datasets satisfying commonly accepted thresholds (KMO \u0026gt; 0.7 and Bartlett\u0026rsquo;s test p \u0026lt; 0.05) are retained for further analysis.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ed. Exploratory Factor Analysis\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eExploratory Factor Analysis (EFA) is performed separately for each time block using the correlation matrix of standardized variables. Factors are initially extracted without rotation to obtain eigenvalues.\u003c/p\u003e\n\u003cp\u003eThe Kaiser criterion (eigenvalue \u0026gt; 1) is used to determine the number of factors retained.\u003c/p\u003e\n\u003cp\u003eFor interpretability, retained factors are rotated using Varimax rotation, which produces orthogonal factors and a simple loading structure. Rotation does not alter total variance explained but redistributes variance among factors to enhance physical interpretation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ee. Variance Explained\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFor each period, the percentage variance explained by each retained factor is computed by dividing its eigenvalue by the total variance and expressing the result as a percentage. Cumulative variance explained by the retained factors is also calculated and compared across periods to assess the stability of the latent structure.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ef. Visualization and Exploratory Analysis\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eA suite of visualization techniques is used to support interpretation:\u003c/p\u003e\n\u003cul type=\"disc\"\u003e\n \u003cli\u003eScree plots and variance-explained plots to justify factor retention;\u003c/li\u003e\n \u003cli\u003eDumbbell plots to illustrate loading changes relative to baseline;\u003c/li\u003e\n \u003cli\u003eAlluvial diagrams to depict shifts in dominant variable\u0026ndash;factor associations;\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eAll analyses were conducted in Google Colab using Python.\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cp\u003e\u003cstrong\u003eTable 1: Suitability Test Results\u003c/strong\u003e\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003ePeriods\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003eKMO value\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003eChi-Square\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003eBartlett\u0026apos;s test of sphericity\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;(p-value)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e1991-1994\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cem\u003e0.814414954\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cem\u003e3845.4\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cem\u003e0\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e2010-2013\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cem\u003e0.809427363\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cem\u003e3783.9\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cem\u003e0\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e2014-2017\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cem\u003e0.789636812\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cem\u003e3545.3\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cem\u003e0\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e2018-2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cem\u003e0.814770975\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cem\u003e3594.7\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cem\u003e0\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e2022-2025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cem\u003e0.825436524\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cem\u003e3552.3\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cem\u003e0\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eAs shown in Table 1, the KMO (Kaiser-Meyer-Olkin) test with values greater than 0.78 and Bartlett\u0026rsquo;s test of sphericity with p-value \u0026lt; 0.05 confirms that the samples/periods (1991-1994; 2020-2013; 2014-2017; 2018-2021; 2022-2025) are adequate and there is significant correlation among the variables for further analysis. \u003cstrong\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2: Eigenvalues\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable style=\"width: 3.9e+2pt;\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003eFactors\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e1991-1994\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e2010-2013\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e2014-2017\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e2018-2021\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e2022-2025\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eFactor 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e4.513\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e4.67\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e4.687\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e4.814\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e4.88\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eFactor 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e2.471\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e2.237\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e2.079\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e1.918\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e1.827\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eFactor 3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.736\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.704\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.809\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.745\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.691\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eFactor 4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.522\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.627\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.548\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.649\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eFactor 5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.399\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.467\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.536\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eFactor 6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.211\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.205\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.268\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.245\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.256\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eFactor 7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.095\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.128\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.112\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.124\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eFactor 8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.018\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.017\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.022\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eFactor 9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.014\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.013\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.016\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.016\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.014\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;The combined scree plot (as referred to Figure 1) for all five periods identified a clear elbow after the second component, representing a sharp drop in eigenvalues. Only the first two components in each period had eigenvalues greater than 1 (as shown in Table 2), representing the largest proportion of total variance. Both the scree plot and the eigenvalues table indicate that only two factors should be retained for further analysis.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 3: Factor Loadings Matrix\u003c/strong\u003e\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003ePeriod\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003eVariable\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003eFactor 1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003eFactor 2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\" rowspan=\"9\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e1991-1994\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003esp\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.8477\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e-0.4152\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003ev10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e-0.0768\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.6757\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003et2m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9725\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.0540\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003etcc\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.1704\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.4508\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eu10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.1623\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.7441\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003ed2m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.3418\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.7533\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eskt\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9952\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.0957\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003estl1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9710\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.0907\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eblh\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.7366\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n 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nowrap=\"\"\u003e\n \u003cp\u003et2m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9660\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.0590\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003etcc\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.2141\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.5181\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eu10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.0666\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.7832\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n 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nowrap=\"\"\u003e\n \u003cp\u003eu10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e-0.0148\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.7021\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003ed2m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.5725\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.6403\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eskt\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9838\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.1754\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003estl1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9751\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.1434\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eblh\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.6780\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e-0.2152\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\" rowspan=\"9\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e2022-2025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003esp\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.8524\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e-0.3780\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003ev10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e-0.0189\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.5778\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003et2m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9700\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.0569\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003etcc\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.1468\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.5783\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eu10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e-0.0219\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.6385\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003ed2m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.5791\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.6295\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eskt\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9790\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.1884\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003estl1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9758\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e0.1344\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003eblh\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.6358\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd nowrap=\"\"\u003e\n \u003cp\u003e-0.0846\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;Among the nine variables considered for the analysis, the factor loading matrix displays the strength of association between each variable and the extracted factors, with the respective loading values indicating which factor each variable most strongly represents. Variables with factor loadings exceeding \u003cstrong\u003e0.40\u003c/strong\u003e are typically retained as meaningful contributors to a factor, while loadings above \u003cstrong\u003e0.70\u003c/strong\u003e are considered indicative of a well-defined structure. The table highlights all values meeting the retention criterion for their respective factors.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea. Characteristics of the retained Factors\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe start by performing EFA on each dataset and time period (1991-1994, 2010-2013, 2014-2017, 2018-2021, and 2022-2025) separately to identify the most influential climatic factors for this location (29\u0026deg;N, 77\u0026deg;E) across different periods. The factor loading matrices show a consistent pattern of variable\u0026ndash;factor relationships, with the same groups of climate variables mainly loading on Factor 1 and Factor 2 (Table 3). This suggests that the dominant climatic factors remain stable at this location (29\u0026deg;N, 77\u0026deg;E) throughout the study periods. However, despite this structural consistency, the size of the factor loadings varies across datasets, indicating that the strength and internal relationships of variables within each factor are changing (Table 3: Factor Loadings Matrix).\u003c/p\u003e\n\u003cp\u003eFurther, the total variance explained by the two factors across different time periods has changed significantly. The observed fluctuations in loadings imply that climate change at this location is not characterized by a shift to new climate regimes but by a gradual change in the coupling strength among variables within existing regimes (Fig 4: Variance Explained).\u003c/p\u003e\n\u003cp\u003eWe can also say that for any other location, if there is any structural change in the Factor-variable association, then it can easily be detected with the help of the factor loading matrix and alluvial plots.\u003c/p\u003e\n\u003cp\u003eFocusing on the analysis, we find that the climate variables, namely \u003cstrong\u003et2m\u003c/strong\u003e,\u003cstrong\u003e\u0026nbsp;skt\u003c/strong\u003e,\u003cstrong\u003e\u0026nbsp;stl1\u003c/strong\u003e,\u003cstrong\u003e\u0026nbsp;sp\u003c/strong\u003e, and \u003cstrong\u003eblh\u0026nbsp;\u003c/strong\u003eload on Factor 1, and \u003cstrong\u003ev10\u003c/strong\u003e,\u003cstrong\u003e\u0026nbsp;u10\u003c/strong\u003e,\u003cstrong\u003e\u0026nbsp;d2m,\u003c/strong\u003e and\u003cstrong\u003e\u0026nbsp;tcc\u003c/strong\u003e load on Factor 2 for all the time periods/datasets (Table 3 and Fig 2). \u003cstrong\u003eT2m, skt, blh,\u003c/strong\u003e and \u003cstrong\u003estl1\u003c/strong\u003e had strong positive loading, and \u003cstrong\u003esp\u003c/strong\u003e had strong negative loading on Factor 1. Similarly, \u003cstrong\u003ev10, d2m,\u003c/strong\u003e and\u003cstrong\u003e\u0026nbsp;tcc\u003c/strong\u003e had positive loading, and\u003cstrong\u003e\u0026nbsp;u10\u003c/strong\u003e had a negative loading on Factor 2.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eb. Changes Detected\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAlthough we found that a broadly consistent climatic pattern dominates throughout the study period, statistically meaningful variations in variable loadings are observed in the factor loading matrix (Table 3: Factor Loadings Matrix).\u003c/p\u003e\n\u003col style=\"list-style-type: lower-roman;\"\u003e\n \u003cli\u003e\u003cstrong\u003eChanges in Factor 1\u0026nbsp;\u003c/strong\u003e\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003e\u003cstrong\u003eT2m\u003c/strong\u003e (air temperature), \u003cstrong\u003eskt\u003c/strong\u003e (skin temperature), and \u003cstrong\u003estl1\u003c/strong\u003e (soil temperature) remained extremely high (\u0026gt;0.96), indicating a persistent coupling between surface heating, subsurface thermal conditions, and near-surface atmospheric temperature. In contrast, \u003cstrong\u003eblh\u003c/strong\u003e (boundary layer height) loading shows a gradual weakening over time, decreasing from ~0.74 (1991\u0026ndash;94) to ~0.64 (2022\u0026ndash;25) (Table 3: Factor Loadings Matrix). This decoupling suggests that although surface and near-surface temperatures continue to rise coherently, their ability to drive vertical atmospheric mixing has diminished. This weakening of the temperature boundary layer linkage implies reduced vertical ventilation (a condition often associated with heat stress and accumulation of near-surface heat). The strongly negative loading throughout all time periods on \u003cstrong\u003esp\u003c/strong\u003e (surface pressure) (\u0026gt;\u0026minus;0.87) confirms a recurring thermal low-pressure association (Table 3: Factor Loadings Matrix). The graphical representation of the changes occurring in Factor 1 among the variables across all five periods (1991-1994, 2010-2013, 2014-2017, 2018-2021, and 2022-2025) are shown in Figure 5 (a, c \u0026amp; e).\u003c/p\u003e\n\u003cp\u003eAlso, the total variance explained by factor 1 across all time periods has also changed significantly from 50.1% in 1991-1994 to 54.2% in 2022-2025, with a rise of 4.1%. (Fig 4: Variance Distribution Chart). This increase in explained variance insinuated that an increasingly large proportion of the multivariate climate system is governed by thermally driven land-atmospheric processes. Thus, we can say that in the case of factor 1, there is no structural change, but there is a shift in the relationship among the variables.\u003c/p\u003e\n\u003col start=\"2\" style=\"list-style-type: lower-roman;\"\u003e\n \u003cli\u003e\u003cstrong\u003eChanges in Factor 2\u003c/strong\u003e\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eFactor 2 was dominated by \u003cstrong\u003eu10\u0026nbsp;\u003c/strong\u003e(zonal wind), \u003cstrong\u003ev10\u0026nbsp;\u003c/strong\u003e(meridional wind), \u003cstrong\u003ed2m\u0026nbsp;\u003c/strong\u003e(dew point temperature), and \u003cstrong\u003etcc\u0026nbsp;\u003c/strong\u003e(total cloud cover). The loadings on \u003cstrong\u003ev10\u0026nbsp;\u003c/strong\u003eand\u003cstrong\u003e\u0026nbsp;d2m\u0026nbsp;\u003c/strong\u003ehave decreased from 0.67 to 0.57 and from 0.75 to 0.62, respectively, from the baseline period (1991-1994) to the latest period (2022-2025) considered in the study (Table 3: Factor Loadings Matrix). These decreasing loadings of both variables indicate a weakening influence of large-scale moisture transport and near-surface humidity. Hence, we can conclude that the role of meridional advection in supplying moisture to the local climate system is reduced.\u003c/p\u003e\n\u003cp\u003eOn the other hand, the loadings on \u003cstrong\u003eu10\u003c/strong\u003e and \u003cstrong\u003etcc\u0026nbsp;\u003c/strong\u003ehave increased significantly from -0.74 to -0.63 and from 0.45 to 0.57, respectively, compared with the 1991-1994 vs 2022-2025 time periods (Table 3: Factor Loadings Matrix). This indicates the strengthening association between the variables and the factor. The graphical representation of the changes among the variables in Factor 2 across all five periods (1991-1994, 2010-2013, 2014-2017, 2018-2021, and 2022-2025) are shown in Figures 5 (b, d \u0026amp; f).\u003c/p\u003e\n\u003cp\u003eThe total variance explained in the case of Factor 2 decreased from 27.5% to 20.3%, which is a huge decline (-7.2%) (Fig 4: Variance Distribution Chart). This means the contribution of variables associated with factor 2 to overall climate variability is decreasing. As of the time period considered for the study, we can say that there is no complete structural change in factor 2 as well. \u0026nbsp;\u003c/p\u003e\n\u003col start=\"3\" style=\"list-style-type: lower-roman;\"\u003e\n \u003cli\u003e\u003cstrong\u003ePossible Structural Change in the Future\u003c/strong\u003e\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eAs observed from the factor loadings matrix, a possible structural change may emerge from the evolving behaviour of d2m (dew point temperature) in the near future. While d2m initially exhibits a strong association with Factor 2, its loading on this factor weakens over time. Whereas it\u0026rsquo;s loading on Factor 1 started to increase. However, in the period (2022-2025), the loadings of d2m on the two factors become nearly equal (though Factor 2 had the highest loading) (Table 3: Factor Loadings Matrix). Such convergence suggests that d2m is becoming less uniquely associated with factor 2 and increasingly influenced by Factor 1. If this trajectory continues, d2m may shift from a Factor 2-dominated variable to a Factor 1-dominated variable, potentially contributing to a future reorganization of factor structure.\u003c/p\u003e\n\u003cp\u003eAlso, the observed redistribution of variance between the two Factors provides insight into the possible future evolution of the multivariate climate structure of this particular location. Over the study period, factor 1 exhibited a systematic increase in explained variance, while factor 2 showed a substantial decline (Fig 4: Variance Distribution Chart). This divergence suggests that an increasing proportion of climate variability is being organized by Factor 1, with diminishing contribution from Factor 2 related variability.\u003c/p\u003e"},{"header":"CONCLUSION","content":"\u003cp\u003eThis study shows that factor analysis acts as a sophisticated multivariate tool for detecting climate change, shifting the focus from single-variable trends to the development of interconnected structural relationships. By systematically examining factor loadings, variance redistribution, and temporal comparability, the analysis indicates that climate variability changes through a gradual reweighting of variables within relatively stable latent regimes. While the persistence of primary factor structures across different time periods suggests that the core modes of the climate system stay consistent, notable changes in explained variance and loading sizes highlight an ongoing internal restructuring. Specifically, the growing dominance (Factor 1 increasing from 50.1% to 54.2%) of one latent regime, along with the decreasing influence of another (Factor 2 declining from 27.5% to 20.3%); suggests that climate change appears as a systemic redistribution of multivariate variability rather than a sudden structural failure.\u003c/p\u003e\n\u003cp\u003eFurther, the appearance of cross-loading behavior in certain variables shows that structural reorganization may begin at the variable level before becoming visible at the factor level as given below:\u003c/p\u003e\n\u003cp\u003eVariable\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003elike\u003cstrong\u003e\u0026nbsp;blh\u0026nbsp;\u003c/strong\u003ein Factor 1 decreasing from ~0.74 (1991\u0026ndash;94) to ~0.64 (2022\u0026ndash;25), variables \u003cstrong\u003ev10\u0026nbsp;\u003c/strong\u003eand\u003cstrong\u003e\u0026nbsp;d2m\u0026nbsp;\u003c/strong\u003ein Factor 2\u0026nbsp;decreasing from 0.67 to 0.57 and from 0.75 to 0.62, respectively, from the baseline period (1991-1994) to the latest period (2022-2025), also the variables \u003cstrong\u003eu10\u003c/strong\u003e and \u003cstrong\u003etcc\u0026nbsp;\u003c/strong\u003ein factor 2\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eincreasing from -0.74 to -0.63 and from 0.45 to 0.57, respectively, as compared to the 1991-1994 vs 2022-2025 time periods (Table 3: Factor Loadings Matrix).\u003c/p\u003e\n\u003cp\u003eEventually, these results support the effectiveness of factor-analytic frameworks\u0026mdash;validated through robust statistical techniques\u0026mdash;as a reliable, adaptable method for characterizing climate change as a continuous reorganization of interconnected processes within complex environmental systems.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe study utilized publicly available climate datasets from recognized sources. No human participants were involved, and therefore ethical approval and consent to participate were not required.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll authors have read and approved the final manuscript and consent to its publication.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors have no relevant financial or non-financial interests to disclose\u003cstrong\u003e.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eKuldeep Dahal:\u003c/em\u003e Conceptualization, Data Curation, Formal Analysis, Interpretation, Writing \u0026ndash; Original Draft.\u003cbr\u003e\u003cem\u003eSanjib Choudhury:\u003c/em\u003e Methodology, Supervision, Review \u0026amp; Editing, Final Manuscript Preparation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that no funds, grants, or other support were received during the preparation of this manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eSippel, S., Meinshausen, N., Fischer, E. M., Sz\u0026eacute;kely, E.\u0026amp; Knutti, R. (2020). Climate change now detectable from any single day of weather at global scale. \u003cem\u003eNature Climate Change, 10\u003c/em\u003e, 35\u0026ndash;41. https://doi.org/10.1038/s41558-019-0666-7\u003c/li\u003e\n\u003cli\u003eZscheischler, J., Westra, S., van den Hurk, B. J. J. M., et al. (2021). Future climate risk from compound events. \u003cem\u003eNature Climate Change, 8\u003c/em\u003e, 469\u0026ndash;477. https://doi.org/10.1038/s41558-018-0156-3\u003c/li\u003e\n\u003cli\u003eGoswami, B.N., Chakraborty, D., Rajesh, P.V. \u003cem\u003eet al. \u003c/em\u003e(2022). Predictability of South-Asian monsoon rainfall beyond the legacy of Tropical Ocean Global Atmosphere program (TOGA). \u003cem\u003enpj Climate and Atmospheric Science\u003c/em\u003e\u003cem\u003e \u003c/em\u003e\u003cstrong\u003e5\u003c/strong\u003e, 58 (2022). https://doi.org/10.1038/s41612-022-00281-3\u003c/li\u003e\n\u003cli\u003eSahastrabuddhe, R., Ghausi, S. 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The influence of climate modes on long-term sea level variability of the Indian ocean with special emphasis on the Southern Annular Mode: A study based on Indian ocean sea level reconstructions. \u003cem\u003eTheoretical and Applied Climatology\u003c/em\u003e\u003cem\u003e \u003c/em\u003e\u003cstrong\u003e156\u003c/strong\u003e, 535. https://doi.org/10.1007/s00704-025-05740-4.\u003c/li\u003e\n\u003cli\u003ehttps://cds.climate.copernicus.eu/\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"climatic-change","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"clim","sideBox":"Learn more about [Climatic Change](https://www.springer.com/journal/10584)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/clim/default.aspx","title":"Climatic Change","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Climate Change, factor loadings matrix, Kaiser-Meyer-Olkin test, Bartlett’s test of Sphericity, eigenvalues, scree plot, Factor Analysis","lastPublishedDoi":"10.21203/rs.3.rs-9206602/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9206602/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Climate change is usually assessed by examining trends in individual variables, but changes in relationships among variables may indicate deeper structural shifts within climate systems. Here, using Exploratory Factor Analysis across five periods from 1991 to 2025 for a location at longitude 29°N, latitude 77°E, we demonstrate that this multivariate approach can detect such structural changes by identifying temporal shifts in hidden covariance patterns. Across all periods, two consistent climate regimes are identified—a thermally driven land-atmosphere mode (Factor 1) and a moisture-circulation mode (Factor 2)—showing stable core modes of variability. However, systematic redistribution of explained variance (Factor 1 increasing from 50.1% to 54.2%; Factor 2 declining from 27.5% to 20.3%) and changing loading magnitudes reveal gradual reweighting within these regimes. The thermal mode becomes more dominant as surface-boundary layer coupling weakens, while the moisture mode shows ongoing decline through reduced influence of meridional wind and humidity variables, suggesting that climate variability is reorganizing around thermally driven processes. Notably, emerging cross-loading behavior in dew point temperature—showing increasing association with both factors—suggests that structural realignment may begin at the variable level before fully manifesting as regime changes. These findings show that climate change at this location proceeds through the amplification or reduction of existing latent structures rather than sudden structural collapse. By monitoring changes in how variables relate to each other through factor loading matrices and variance redistribution, this multivariate approach offers a sensitive way to detect early signs of structural climate change in complex environmental systems.","manuscriptTitle":"Factor Model-based Detection of Regime Transitions in High-dimensional Climate Data (ERA5)","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-10 09:35:05","doi":"10.21203/rs.3.rs-9206602/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2026-04-23T02:05:24+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-05T17:58:37+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-26T02:06:53+00:00","index":"","fulltext":""},{"type":"submitted","content":"Climatic Change","date":"2026-03-25T08:15:49+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"climatic-change","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"clim","sideBox":"Learn more about [Climatic Change](https://www.springer.com/journal/10584)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/clim/default.aspx","title":"Climatic Change","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"ab76c31b-ff4e-472c-ba50-b1dc1830dfa6","owner":[],"postedDate":"April 10th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-10T09:35:06+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-10 09:35:05","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9206602","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9206602","identity":"rs-9206602","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}