# Exploring Climate Change Through the Lens of Records Theory

Jinane Jouni, Anis Hoayek, Aline Mefleh, Mireille Batton-Hubert

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Jinane Jouni, Anis Hoayek, Aline Mefleh, Mireille Batton-Hubert. Exploring Climate Change Through the Lens of Records Theory. 56eme journees de Statistique de la SFdS, Jun 2025, Marseille, France. hal-05035638

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# EXPLORING CLIMATE CHANGE THROUGH THE LENS OF RECORDS THEORY

Jinane Jouni<fnref n="1" />, Anis Hoayek<fnref n="2" />, Aline Mefleh<fnref n="3" /> & Mireille Batton-Hubert<fnref n="4" />

**Résumé.** Le phénomène mondial du changement climatique est devenu l'un des défis les plus urgents de notre époque. Dans ce contexte complexe, la communauté scientifique cherche des méthodologies innovantes pour quantifier et comprendre l'occurrence et la gravité du changement climatique. La théorie de records en statistique des extrêmes offre un cadre prometteur pour détecter et vérifier le changement climatique. Notre recherche couvre plusieurs lieux géographiques et utilise une approche de notation univariée pour analyser les tendances de température et de précipitations, fournissant ainsi des informations précieuses sur l'occurrence, la fréquence et l'intensité des événements climatiques extrêmes. Nos résultats révèlent un schéma de réchauffement global, avec des scores de température en baisse au milieu du siècle avant d'augmenter brusquement, dépassant souvent les niveaux précédents. Les scores de précipitations varient selon les régions, certaines connaissant des conditions plus sèches tandis que d'autres font face à une augmentation des précipitations. Ces résultats mettent en évidence des extrêmes climatiques changeants, soulignant l'urgence d'analyser le changement climatique.

**Mots-clés.** Changement climatique, Théorie de records, Notation statistique, Température, Précipitation

**Abstract.** The global phenomenon of climate change has become one of the most pressing challenges of our time. Amidst this complex landscape, the scientific community seeks innovative methodologies to quantify and understand the occurrence and severity of climate change. The theory of records in extreme value theory provides a promising framework for detecting and verifying climate change. This research spans multiple geographic locations, employing a univariate scoring approach to analyze temperature and precipitation trends, and providing valuable insights into the occurrence, frequency, and intensity of extreme climate events. Our findings reveal a global warming pattern, with temperature scores declining mid-century before rising sharply, often surpassing previous levels. Precipitation scores vary across regions, with some experiencing drier conditions while others face increased rainfall. These results highlight shifting climate extremes, reinforcing the urgency of climate change analysis.

**Keywords.** Climate change, Records theory, Scoring system, Temperature, Precipitation

## 1 Introduction

Climate change is one of the most urgent global challenges, with its environmental and societal impacts becoming increasingly evident. Over the past several decades, scientific consensus has established that human activities are the primary drivers of climate change, with mean global surface temperature increasing and reaching 1.1°C above pre-industrial levels in 2011-2020 (IPCC, 2023). However, variability and extremes are critical to understanding the full impact of climate change beyond the global mean value (Schär et al., 2004), especially that the evolution of extreme temperatures does not always follow that of the mean (Castillo-Mateo et al., 2023). Understanding the manifestations and trends of climate change is crucial for effective mitigation strategies and informed decision-making.

In parallel, record theory provides a powerful framework for analyzing rare extreme events by examining the statistical behavior of record values in time-series data. In a time series {$X_t$}$_{1\le t\le T}$, where T is the present time, a record $R_n = X_{L_n}$ occurs at time $L_n$ when $X_{L_n}$ exceeds all previous values, that is, $X_{L_n} > \max\{X_1, ..., X_{L_{n-1}}\}$.

Four key models have been developed to characterize record-breaking events. The most fundamental independent and identically distributed model (i.i.d.) assumes records occur independently, rarely, and symmetrically (the same number of max and min records, forward and backward records) in a stationary climate context (Chandler, 1952; Arnold et al., 1998). The Discrete-Time Random Walk Model (DTRW), discussed by Majumdar and Ziff (2008), accounts for random fluctuations and increments, making it useful for short-term weather variability chaotic conditions. The Linear Drift Model (LDM) introduces a constant linear drift influencing the occurrence of records and representing a steady warming or cooling trend rather than random fluctuations steady. Lastly, the Yang-Nevzorov Model increases the likelihood of records over time as the number of record-candidate observations increases exponentially, representing scenarios with accelerated warming (Nevzorov, 1990). Table A.1 in the appendix summarizes each model.

This study aims to bridge the gap between theoretical record-breaking frameworks and their practical applications in analyzing, evaluating, and comparing climate data across different regions by exploring patterns of extreme events. The findings will contribute to a more detailed understanding of climate change's regional impacts and provide new

<footnote n="1">¹ Mines Saint-Etienne, Univ Clermont Auvergne, CNRS, UMR 6158 LIMOS, Institut Henri Fayol, F - 42023 Saint-Etienne France, jinane.jouni@hotmail.com</footnote>

<footnote n="2">² Mines Saint-Etienne, Univ Clermont Auvergne, CNRS, UMR 6158 LIMOS, Institut Henri Fayol, F - 42023 Saint-Etienne France, anis.hoayek@emse.fr</footnote>

<footnote n="3">³ Department of Mathematics, Holy Spirit University of Kaslik, Jounieh, Lebanon, aline.mefleh@usek.edu.lb</footnote>

<footnote n="4">⁴ Mines Saint-Etienne, Univ Clermont Auvergne, CNRS, UMR 6158 LIMOS, Institut Henri Fayol, F - 42023 Saint-Etienne France, batton@emse.fr</footnote>
statistical method for future studies. This study is organized into four sections: Section 2 reviews previous applications of record theory in climate studies, particularly for temperature and precipitation. Section 3 details the methodology, including feature selection, categorization and scoring system. Section 4 presents the results for six geographical stations, while Section 5 synthesizes the findings, discusses implications, and proposes future research directions.

## 2 Literature Review

Several studies have applied record theory to analyze temperature and precipitation trends in various regions. For example, Benestad (2003) analyzed the incidence of temperature and precipitation events (moving forward and backward in time) in multiple dependent stations of Northern Europe (1895–1999), and found a significant increase in high-temperature records moving forward compared to what is expected in a stationary i.i.d. model. Similarly, Meehl et al. (2009) observed a 2:1 ratio of high-to-low records in U.S. temperature data (1950–2006) since the late 1970s, with projections suggesting ratios as high as 50:1 by the end of the 21st century. In Europe, Elguindi et al. (2013) identified a rising trend in high-temperature records and stable to declining low-temperature records since the 1980s, consistent with regional warming patterns.

Studies have also explored the influence of trends and variability on record-breaking events. Newman et al. (2010) demonstrated that linear trends significantly alter the ratio of high-to-low record-breaking temperatures beyond 1:1, as seen at the Mauna Loa Observatory, where minimum temperature records exhibited a stronger warming trend than maximum records. Using the Linear Drift Model, Redner and Petersen (2006) and Wergen and Krug (2010) fitted a Gaussian distribution for daily temperature data in Europe and the U.S., observing a consistent increase in mean temperatures with stable variance, predicting ongoing rises in high-temperature records alongside declines in low-temperature records.

Overall, most previous studies anchor their comparisons against the i.i.d. model without attempting to fit specific record models to the data. Moreover, these studies predominantly focus on one statistic, such as record counts, max-to-min ratios, or linear trends to conclude to global warming. This study seeks to address these limitations by integrating additional variables and applying a comprehensive scoring system to analyze climate trends more holistically.

## 3 Proposed Methodology

The proposed methodology employs a uni-dimensional framework to analyze trends in climate measures—primarily temperature and precipitation—by constructing a new time series, {$S_t$}$_{1<t\le w}$ ($w$ will designate the number of subset series or so-called moving windows). This series is derived using a weighted scoring system based on a set of predefined features. This section elaborates on the methodology in three steps: feature development, feature selection and weighting, and the scoring framework.

### 1. Feature Development

Based on record theory and statistical principles, a comprehensive set of variables was developed aiming to measure or assess different aspects of records. These variables were grouped into three factors—Frequency, Intensity, and Trend—each providing distinct insights into the behavior of records.

(a) **Frequency-based features** quantify the occurrence and distribution of records within a given time frame. Examples include the record count, i.e. the number of record-breaking observations within a time frame. Another variable is the model-based score where higher values are assigned to models with greater probabilities of generating records (e.g., *i.i.d.*: 1, DTRW: 2, LDM/Yang: 3; see Figure 1). Model fitting is validated using statistical tests such as Arnold's test for *i.i.d.* models (Arnold et al., 1998), Ljung-Box for DTRW (Hamie et al., 2018), and tests described by Hoayek (2016). A third example, widely used in the literature, includes the ratio of high-to-low records which compares the frequency of higher records to lower records.

(b) **Intensity-based features** refers to the examination of records beyond their mere count, with a focus on their magnitude and variability. For instance, the variance-to-mean ratio of records (VMR) which measures the variability of record values relative to their mean, with high values indicating significant jumps between records. Another feature is the simple dispersion measure of the whole time series $X_t$.

(c) **Trend-based features** focus on the overall direction and progression of records. A trivial variable is the slope of the trend line to assess the overall direction of the time series computed as in Newman et al. (2010). Another feature is the normalized average of observed records (divided by the first trivial record) with high comparable values related to a steep increase in record values. Besides, the percentage increase in the values of records from the first to the last one within a time window also reflects the steepness of record increases regardless of intermediate fluctuations.

### 2. Features selection and weights

An initial set of 19 features was developed based on theoretical and empirical considerations. For more information about the features, see Table B.1 in the appendix. These were refined through a two-stage process. First, features
exhibiting high multicollinearity or redundancy were identified and removed if pairwise correlation exceeds 0.9. This ensured that only independent and relevant variables were retained. Second, Exploratory Factor Analysis (EFA)<fnref n="1" /> was performed on each dataset to identify the most statistically significant variables, to validate the grouping of features into the three primary factors (Frequency, Intensity, and Trend), and to assign weights (or factor loadings) to each feature. The analysis ensured that the 12 retained features explained more than 70% of the total variance. EFA was performed across multiple datasets, yielding slightly different sets of selected features and weights for each. To maintain consistency, the features most frequently selected across all datasets were retained for the final analysis (see Table B.2 in the appendix).

### 3. Scoring system

The final scoring system integrates the selected features into a uni-dimensional score, {$S_t$}$_{1\le t\le w}$, which reflects the combined influence of Frequency, Intensity, and Trend factors. For each factor, a weighted score is computed by summing the weighted values of its associated features and normalizing the result.

$$ \text{Factor Score}_t = \sum (\text{Feature Value}_t \times w_i) / \sum w_i. \quad (1) $$

The overall final score is calculated as the average of the three normalized factor scores, ensuring balanced representation of Frequency, Intensity, and Trend.

$$ S_t = \frac{1}{3} \times [\text{Frequency Score}_t + \text{Intensity Score}_t + \text{Trend Score}_t]. \quad (2) $$

To effectively capture temporal variations and address biases from initial trivial records, a moving window approach was adopted. For each sliding subset of the time series, a global score value was computed by summing the three factor scores. Hence, each point in the resulting score series $S_t$ corresponds to a specific window, facilitating detailed analysis across geographical stations for both temperature and precipitation. The analysis began with a minimum window length of 30 observations (taking into consideration the asymptotic properties of records), sliding step-by-step through the series (the first window spanned the first 30 observations, the next started from the second observation to the 31st, and so on) and constructing the new score series. Sensitivity analysis using Dynamic Time Warping confirmed that varying window lengths had negligible effects on the resulting score series. For consistency, a window length of 50 observations was adopted, and windows with only one trivial record are ignored because of the impossibility to compute some features.

This methodology considers not only the timing, number, and intensity of climate records but also integrates non-record values, highlighting their significance in capturing fluctuations and underlying trends. The subsequent section will present the final model and analyze the scoring results for six geographical stations.

## 4 Data and Results

### 4.1 Data

The World Bank Climate Change Knowledge Portal provides complete yearly temperature and precipitation data from 1900 to 2021, including maximum, minimum, and average values. This analysis primarily focuses on average data, with maximum and minimum values specifically used to compute the "Ratio" feature<fnref n="2" />. To capture diverse climate patterns, six stations were selected to represent distinct Köppen-Geiger climate classifications<fnref n="3" />: Jambi, IDN (tropical), Cairo, EGY (arid), Beirut, LB (Mediterranean), Paris, FR (temperate), Oslo, NOR (cold) and Greenland (polar). Descriptive statistics for temperature and precipitation across these stations are summarized in Tables C.1 and C.2, while corresponding yearly trends are visualized in Figures C.1 and C.2.

Temperature levels exhibit an overall slightly increasing trend across most stations, a pattern supported by the KPSS test<fnref n="4" />, which confirms non-stationarity (exceptions include Oslo and Greenland, where temperature trends appear stationary and sinusoidal, respectively). Temperature distributions were found to be Gaussian, as expected based on climatological literature. However, this assumption is not critical in our analysis, as our methodology does not impose any distributional constraints. On the other hand, precipitation levels show a stationary behavior across all locations —though they exhibit high short-term variability and localized fluctuations.

To develop the scoring model, the Egypt station dataset ($w$ = 72 windows of $T$=50 observations) was used along with other datasets, but the former proved the best fit (higher proportion of variance explained, lower RMSEA and BIC; see Table B.2) for models comparison). EFA results identified three primary factors, which together explain over 80% of the total variance, validating our initial definition. The final model is as follows, before normalizing by each factor's weight and summing up as in eq. 1 and 2.

<footnote n="1">¹Exploratory Factor Analysis (EFA) is a statistical technique used to identify underlying factors that explain the correlations among observed variables. It is a dimension reduction technique by grouping related features into common factors, making data interpretation more intuitive. Check Tucker and MacCallum (1997) for more info.</footnote>

<footnote n="2">²The "Ratio" feature measures the proportion of high-to-low records in the dataset.</footnote>

<footnote n="3">³The Köppen-Geiger classification system, developed by Wladimir Köppen, categorizes global climates into five major types.</footnote>

<footnote n="4">⁴KPSS tests are used for testing a null hypothesis that an observable time series is stationary around a deterministic trend against the alternative of a unit root. For more info check Kwiatkowski et al. (1992)</footnote>
$$ \text{Frequency} = 0.71 N_T + 0.66 M + 0.60 R, $$

$$ \text{Intensity} = 0.88 VMR_{X_t} + 0.87 VMR_{X_t/R_n} + 0.79 \bar{L}_n, $$

$$ \text{Trend} = 0.82 \bar{R}_n + 0.80 \alpha + 0.92 P_{X_t, X_{Ln}} + 0.79 P_{R_n, R_m} + 0.90 VMR_{R_n} + 0.84 \Delta X_t. $$

## 4.2 Climate Analysis Based on Generated Scores

By definition, scores are essentially linear combinations of various features, where high score values indicate an increased likelihood of encountering extreme weather events. Higher temperature scores indicate an increased frequency of unusually high temperatures, reinforcing evidence of global warming. Conversely, high precipitation scores differentiate between excessive rainfall (e.g., IDN, NOR, GRL) and prolonged dry periods (e.g., LB, EGY, FR), which might be problematic depending on the climate's natural characteristics.

Analyzing the temperature score series reveals a consistent global pattern across all stations, which was not readily apparent from raw temperature trends. Temperature scores exhibit an "inverted bathtub" shape, regardless of the specific depth or steepness at each station (see Figures D.1 and D.3 (a)). Generally, temperatures start the century with moderate to high scores, decline to a minimum around the mid-century period, and then gradually increase, often surpassing the initial values. The beginning scores align with the early warming phase of the 20th century. The dip in the mid-century may reflect the cooling period that occurred between 1940s and 1970s. During this time, global temperatures showed a decline or stagnation after the period of warming. The last increase corresponds to accelerated global warming, largely attributed to anthropogenic greenhouse gas emissions. A case study of Beirut (Figure 2) exemplifies this trend, showing a steady increase in temperature extremes post-1970s.

Conversely, precipitation scores exhibit diverse station-specific patterns (see Figures D.2 and D.3 (b))), reflecting regional climate dynamics. In Beirut (Figure 3), precipitation scores start low, then rise steadily before plunging in mid-century, coinciding with the lowest temperature scores. This suggests that cooler temperatures during this period may have enhanced condensation, leading to increased rainfall. Subsequently, the scores rise again, signaling a decline in precipitation and a shift toward drier conditions. Other stations exhibit different behaviors. In Indonesia and Greenland, precipitation scores show a consistently positive trend, indicating increasing rainfall intensity. This is likely driven by distinct climate processes; warming temperatures in Indonesia are making rainy seasons more intense while in Greenland, higher temperatures may be shifting precipitation from snow to rain. A different pattern emerges in Paris, where precipitation scores initially rise, indicating drier conditions, but then experience a sharp drop beyond the 1950s, signaling an increase in heavy rainfall events. This same pattern is observed in Oslo, though with greater intensity, suggesting a notable rise in extreme precipitation events in Northern Europe. In contrast, Cairo's precipitation scores have increased sharply in recent decades, mirroring a similar pattern observed in the mid-century. This suggests that Egypt's climate is becoming progressively drier.

<figure><img src="image_2.png" /><figcaption>Figure 1: Probability of observing records at different time (t) across four different models</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2: Temperature Scores for Beirut</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 3: Precipitation Scores for Beirut</figcaption></figure>
Overall, these patterns highlight significant climate changes across different regions. Table 1 summarizes the analysis about the scores obtained for each station. The variation in precipitation scores tells us how rainfall is changing according to different climate areas, while consistency in temperature scores reflect a common high temperature danger across the globe.

<table><caption>Table 1: Stations Scores Analysis</caption><thead><tr><td>Station (Climate)</td><td>Temperature Scores</td><td>Precipitation Scores</td><td>Interpretation</td></tr></thead><tbody><tr><td>Jambi, Indonesia (Tropical)</td><td>Stable and moderate initially, then decline mid-century, followed by a rapid increase.</td><td>Initially low, followed by a consistent increase.</td><td>Increased temperature and rainfall suggest intensifying extreme weather events, including heatwaves and flooding. This aligns with the expectation of a warmer, wetter climate in tropical regions.</td></tr><tr><td>Cairo, Egypt (Arid)</td><td>Initially high score and then rapid increase post deep dip mid-century.</td><td>Alternate between low initially, high in mid-century, and low again</td><td>The temperature increase after mid-century, coupled with precipitation fluctuations, indicates a growing risk of prolonged heatwaves and intensified drought periods. This pattern highlights increasing aridity and worsening water shortages.</td></tr><tr><td>Beirut, Lebanon (Mediterranean)</td><td>Start high, decline mid-century, and gradually increase, with a steeper rise in recent periods.</td><td>Initially low, fluctuate mid-century, then decline in recent decades.</td><td>Rising temperatures, along with decreasing precipitation in recent years, suggest a transition toward drier conditions, increasing the likelihood of droughts.</td></tr><tr><td>Paris, France (Temperate)</td><td>Initially low and stable, then rise sharply post-1950s.</td><td>Initially low, increase after the 1940s, then decline sharply in recent decades.</td><td>The post-1950s warming trend, combined with recent increased precipitation might indicate increased weather variability, potentially leading to more frequent heavy downpours.</td></tr><tr><td>Oslo, Norway (Cold)</td><td>U-shaped pattern, declining mid-century, then rising gradually at slow pace.</td><td>Fluctuate sinusoidally with a decline in recent periods.</td><td>Recent warming phase with increased rainfall may lead to heightened flood risks and changes in snow-pack accumulation.</td></tr><tr><td>Greenland (Polar)</td><td>U-shaped curve, dipping mid-century with rapid increase afterwards.</td><td>Continuous increase since the beginning of the century.</td><td>Rapid temperature increases, alongside growing precipitation, signal accelerating ice melt. This contributes directly to rising sea levels. The shift in precipitation may also indicate a transition from snowfall to rainfall, further accelerating glacial retreat.</td></tr></tbody></table>

# 5 Conclusion

Our study employing records theory as a lens for examining climate change has provided valuable insights into the shifting patterns of temperature and precipitation across six diverse cities. Records theory, with its inherent properties and characteristics, has captured hidden climate behaviors that are not immediately apparent from traditional trend analysis. We have adapted three attributes to formulate a diverse set of variables, each designed to measure distinct aspects of weather patterns. Our scoring approach extended beyond only the frequency of records to their intensity, temporal patterns, and variability. Moreover, records were studied not only in isolation but also in relation to non-record events. The analysis of score levels underscores the urgency of addressing climate change on a global scale.

While our study has shed light on climate change, several promising avenues for future research in this area can enrich our understanding of the relationship between climate change and records theory. First, variables in the score we constructed can be refined. New variables can be added, and others can be removed or combined. Second, we can explore other methodologies than EFA or refine the weights assigned to variables within the current framework. The study was limited to six regions and two climate variables which can be extended to include more vulnerable regions and climate variables to provide broader insights. Multivariate framework can be built by mitigating the current framework and using a different definition of records, highlighting the interacting relationship between climate variables.

The score we developed is not exclusive to weather or climate data; we can explore its application to any dataset where changes in patterns and intensity need to be assessed. Replicating the study with a different dataset could yield interesting insights and validate the approach's applicability. Last but not least, while our study has demonstrated the efficacy of records theory in assessing climate change, collaborating with other statistical approaches, such as Extreme Value Theory (EVT), could unlock additional dimensions of insight and enhance our methodological framework. Integrating current climate models for simulations and forecasts with records theory could also improve the obtained model's results.
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