Spatiotemporal Evolution Characteristics of Summer Dry-Heat Compound Events in Liaoning Province

Abstract

In the context of global warming, the continued increase in the frequency of compound events—where drought and high-temperature extremes coincide—has led to severe natural disasters and substantial socio-economic losses. To systematically reveal the evolution of summer dry-heat compound events in Liaoning Province, this study constructs a whole-chain analysis framework of “identification–feature extraction–multivariate probability assessment”. Based on the Standardised Precipitation Index (SPI) and the Standardised Temperature Index (STI), we develop the Standardised Dry-Heat Index (SDHI) to identify dry-heat compound events. Run theory is applied simultaneously to extract key attributes for three types of events—drought, high temperature, and dry-heat compound events—and the Mann–Kendall test is used to detect their temporal mutation characteristics. By combining Copula functions with spatial analysis techniques, we further establish a whole-chain analysis method from “identification–feature extraction–hazard quantification”. The results show that during 1961–2020, summer drought, high-temperature, and dry-heat compound events occurred 4, 14, and 10 times, respectively, in Liaoning Province, with all three types showing a significant increase in frequency after the late 1990s. Spatially, zones of high drought intensity are mainly located in western Liaoning; the duration and severity of high temperatures are most pronounced in inland basin areas; and regions with high compound hazard intensity of dry-heat events largely coincide with urbanised areas. Climate propensity analyses further reveal that the province is experiencing an increasingly dry-heat-prone climate, with high temperatures being the dominant factor driving the enhanced hazard associated with dry-heat compound events. This study overcomes the limitations of traditional single-event analyses and provides a more accurate scientific basis for hazard assessment and zonal prevention and control of dry-heat disasters in Liaoning Province.

1. Introduction

A drought event is a moisture deficit caused by persistently and abnormally low precipitation; a heat event is an abnormal period during which temperatures are significantly higher than the historical mean for the same period; and a dry-heat compound event is an extreme weather event in which drought and high temperature overlap in space and time or occur consecutively, mutually amplifying their impacts. Droughts and high temperatures are among the most destructive types of summer natural disasters, with hazards closely related to ecosystem stability and socio-economic development [1]. The intensity and frequency of drought and heat events have significantly increased under global warming [2]. When high-temperature and drought events are superimposed to form a dry-heat compound disaster, the degree of ecosystem damage and the impact on various socio-economic sectors often far exceed those of single events due to the amplification of disaster effects [3]. Studies in mainland China have shown that the frequency, severity, and duration of compound dry-heat events exhibit pronounced spatial heterogeneity and a significant increasing trend, and that there is a strong positive interdependence between the occurrence of droughts and high temperatures, which contributes to the rising number of compound events [4]. McKee et al. [5] proposed the Standardised Precipitation Index (SPI), which integrates precipitation data at multiple time scales to assess drought conditions. Zhang et al. [6] adopted both SPI and the Standardised Temperature Index (STI) to identify the intensity of drought and high temperatures in North China and used Copula functions to characterise the dependence between these variables and construct their joint cumulative probability distribution, thereby analysing the spatial–temporal evolution characteristics of compound dry-heat events in that region. Wu et al. [7] used the Standardised Compound Event Indicator (SCEI) and the Standardised Dry-heat Index (SDHI), based on monthly precipitation and temperature, to assess changes in the intensity of compound dry-heat events in the mid-warm season over China from 1961 to 2012. Hao et al. [8] used the SDHI to assess global changes in the intensity of compound dry extremes and high-temperature extremes, and concluded that the intensity of these compound dry and hot extremes has increased over land globally. Alemu et al. [9] assessed meteorological, agricultural, and hydrological droughts in the Upper Blue Nile Basin using run theory to analyse key drought characteristics and performed spatial–temporal analyses of multiscale drought characteristics in the basin. Yu et al. [10] analysed the spatial and temporal evolution of drought in the Yangtze and Yellow River Basins from 1961 to 2021 using the Standardised Precipitation Evapotranspiration Index (SPEI) [11] in combination with run theory. These studies provide important references for understanding the spatial and temporal patterns of compound events and promote the application of joint multivariate analysis frameworks in extreme climate research. Meanwhile, the studies by Hao et al. [7,8] further confirm that the severity of compound dry-heat events has significantly increased across many land regions on a global scale, highlighting the importance and urgency of such events in climate and environmental research.

However, existing studies still have two main shortcomings. First, most research remains focused on the identification and frequency analysis of whether an extreme event has occurred, or is confined to the spatial–temporal dynamics of a single meteorological variable. The extraction and quantification of key attributes such as event duration and severity remain relatively weak [12,13,14]. Second, although run theory has been demonstrated to be an effective tool for identifying the duration and severity of extreme events such as droughts and heat waves, its application is mostly limited to characterising single drought events or to combining with Copula functions to analyse the joint distribution of internal drought attributes (e.g., duration and severity). There is still a lack of research on the systematic application of run theory to the characterisation of high-temperature events and dry-heat compound events [15]. High-temperature events and their compounding with droughts to form dry-heat events are key factors affecting regional environments, agriculture, and water security. Neglecting in-depth analyses of their duration, severity, and joint probability makes it difficult to comprehensively understand the multivariate dependency structure and disaster-causing mechanisms of compound events.

Since precipitation and temperature are the direct variables defining drought and heat events, standardised indices (SPI, STI, and SDHI) constructed from these variables have become preferred tools for studying their spatial and temporal evolution characteristics. These indices provide objective and standardised metrics that can comprehensively quantify the coupling characteristics of dry-heat compound events. Therefore, based on summer meteorological observation data from Liaoning Province for 1961–2020, this study first constructs the Standardised Dry-heat Index (SDHI) to accurately identify dry-heat compound events. Subsequently, run theory is introduced to simultaneously extract key features—including occurrence time, severity, and joint probability distributions—of drought, high-temperature, and dry-heat compound events. The research aims to achieve the following three advances: first, to move beyond merely analysing the evolutionary characteristics of dry-heat events by also examining the spatiotemporal differentiation patterns of their properties (duration and severity); second, to extend the application of run theory from traditional drought studies to high-temperature and compound events, thereby establishing a unified methodological framework for feature extraction across multiple types of extreme climate events; and third, to construct a joint distribution model of duration and severity using Copula functions to assess “long-duration–high-severity” extreme compound events from a probabilistic perspective, thus realising a whole-chain analysis of dry-heat compound disasters from “identification” and “feature extraction” to “multivariate probability quantification”.

2. Study Area and Data Sources

2.1. Study Area

Liaoning Province is located between 118°53′ E–125°46′ E and 38°43′ N–43°26′ N, and is administratively divided into 14 prefecture-level cities. As a highly coupled ecological–economic region, Liaoning Province is seriously threatened by the frequent occurrence of dry-heat compound events [16,17,18], which lead to crop yield reductions, water shortages, and forest fires, with far-reaching socio-economic impacts [19,20,21]. Furthermore, repeated dry-heat events can trigger a series of cascading effects, including reduced crop yields, increased forest fire occurrence, pasture degradation, and water scarcity, which further exacerbate ecosystem instability and heighten the vulnerability of regional socio-economic development [22,23]. Therefore, systematically studying the evolutionary patterns of dry-heat compound events in Liaoning Province has become a key task for addressing regional climate change and enhancing disaster prevention and mitigation capacity. Such research is of great practical significance and urgency for developing scientific disaster response strategies and reducing socio-economic losses.

2.2. Data Sources

The meteorological observation data used in this study were obtained mainly from the China Meteorological Science Data Sharing Service “https://data.cma.cn/ (accessed on 10 May 2024)”. Daily monitoring data from 25 national standard meteorological stations in Liaoning Province were collected for 1961–2020, including records of daily precipitation and air temperature. In data processing, the continuity of the station records was first examined. Abnormal or missing data were corrected and interpolated using linear methods and information from neighbouring stations in the same year to ensure data integrity and consistency (Figure 1).

3. Methodology

3.1. Construction of Index and Classification of Ranks

The Standardised Precipitation Index (SPI) quantifies the degree of precipitation anomalies by fitting a probability distribution function to the precipitation series to classify drought [24]. The index effectively portrays precipitation climatological characteristics at different time periods and across regions, with strong spatial and temporal comparability. Because different SPI time scales reflect different hydrological balances, this study focuses on the summer season (June–August) and therefore adopts a 3-month scale (SPI-3) to better capture wet–dry variability at the seasonal scale [25]. All computations in this study were performed using PyCharm 2024.1, Spatial interpolation application ArcMap 10.2.

Calculation of sliding 3-month cumulative precipitation: the monthly precipitation series is cumulated on a sliding 3-month scale to generate a new cumulative precipitation series P₃:

$$P_3\left(t\right)=P\left(t\right) +P\left(t-1\right) +P\left(t-2\right)$$

(1)

where P₃(t) denotes the total precipitation for the last three months up to month t.

SPI-3 (3-month standardised precipitation index) formula:

$$SPI-3={\phi }^{-1}\left[F\left(P_3\right)\right]$$

(2)

where F(P₃) is the marginal probability distribution function of 3-month cumulative precipitation. F(P₃) is an empirical cumulative probability value calculated by the Gringorten plotting position formula, which characterises the relative position of the P₃ values in the historical series. This is then normalised according to the standard normal distribution $\phi$, which in turn yields SPI-3. The resulting SPI-3 is a standardised index with a mean of 0 and a standard deviation of 1. Negative values indicate drier-than-normal conditions, and the smaller the negative value, the more extreme the drought event. This approach effectively transforms precipitation information into a single comparable metric suitable for assessing the spatial and temporal variability of drought events.

Gringorten formula:

$$F\left(P_3\right)={\displaystyle \frac{i-0.44}{n+0.12}}$$

(3)

where i is the sort order number of the data in the historical contemporaneous sequence, and n is the time series length.

The Standardised Temperature Index (STI) is developed based on the same computational concept as SPI, the core of which is to classify high temperatures by fitting a probability distribution function to the temperature series and converting it to a standard normal distribution [26]. This index effectively eliminates the effects of geographic location and seasonal variations, objectively reflecting the degree of temperature anomalies relative to the historical period and providing a standardised indicator for monitoring heat events. STI is also analysed at a 3-month time scale (STI-3).

Calculation of the sliding 3-month mean temperature: The monthly temperature series is accumulated on a sliding 3-month scale and averaged to generate a new mean temperature series T₃:

$$T_3\left(t\right)={\displaystyle \frac{\left[T\left(t\right) +T(t-1)+T(t-2)\right]}{3}}$$

(4)

where T₃ (t) denotes the average temperature of the last three months up to month t.

STI-3 (3-month standardised precipitation index) formula:

$$STI-3={\phi }^{-1}\left[F\left(T_3\right)\right]$$

(5)

where T₃ represents the average temperature of 3 consecutive months and F(T₃) is the marginal probability distribution function of the 3-month average temperature. Larger values of STI-3 indicate more severe high temperatures. The STI-3 was obtained by normalising the distribution according to the standard normal distribution $\phi$, where F is again fitted by the Gringorten plotting position formula.

Gringorten formula:

$$F\left(T_3\right)={\displaystyle \frac{j-0.44}{n+0.12}}$$

(6)

where j is the rank order of the data in the historical contemporaneous sequence and n is the length of the time series.

The calculation concept of the Standardised Dry-Heat Index (SDHI) inherits and extends the standardisation concepts of SPI and STI, aiming to quantify the composite degree of anomaly of a dry-heat event by fitting a composite probability distribution. The index innovatively combines the probability distributions of precipitation and temperature and constructs a composite indicator that can reflect both water deficit and high-temperature stress through ratio operations, thus characterising the integrated deviation of dry-heat conditions relative to the same period in history [8]. Unlike SPI and STI, which focus on a single meteorological factor, SDHI captures combined water–heat anomalies through the probability ratios of precipitation and temperature, which are then fitted to a probability distribution and transformed into a standard normal distribution to obtain SDHI. The proposal of SDHI fills the gap of a single index for monitoring composite events and provides a powerful quantitative tool for the comprehensive assessment of dry-heat compound stress in the context of climate change, being particularly suitable for agricultural drought, ecological risk, and other research fields that need to consider water–heat balance in an integrated manner.

SDHI-3 (3-month standardised dry-heat index) formula:

$$SDHI-3={\phi }^{-1}\left[F\left(X\right)\right]$$

(7)

$$X={\displaystyle \frac{F\left(P_3\right)}{F\left(T_3\right)}}$$

(8)

$$F\left(X\right)={\displaystyle \frac{k-0.44}{n+0.12}}$$

(9)

where ${\phi }^{-1}$ denotes the inverse function of the standard normal distribution; X is the ratio of F(P₃) to F(T₃) derived from Gringorten’s formula; F(X) is an empirical cumulative probability value calculated based on the variable X to describe the relative position of X in the historical series; k is the ordinal number of the data in the historical contemporaneous series, and n is the time series length.

As shown in

Table 1. Classification of different range index levels.

Hierarchy	SPI	STI	SDHI	Typology
1	SPI > –0.5	STI ≤ 0.5	SDHI > −0.5	Normal
2	−1.0 < SPI ≤ −0.5	0.5 < STI ≤ 1.0	−0.8 < SDHI ≤ −0.5	Mild
3	−1.5 < SPI ≤ −1.0	1.0 < STI ≤ 1.5	−1.3 < SDHI ≤ −0.8	Moderate
4	−2.0 < SPI ≤ −1.5	1.5 < STI ≤ 2.0	−2 < SDHI ≤ −1.6	Serious
5	SPI ≤ −2.0	STI > 2.0	SDHI ≤ −2.0	Extreme

, the intensity of the composite dry-heat event was classified into five classes based on the SDHI thresholds of −0.5, −0.8, −1.3, −1.6, and −2.0 [27].

3.2. Run Theory

Run theory provides a systematic analytical framework for identifying drought, high-temperature, and combined dry-heat events [11]. As shown in Figure 2, the method discretises the time series X_t by setting a threshold X: When X_t is consistently higher than X over consecutive time periods, it forms a positive run, corresponding to a high-temperature event; when it is consistently lower than X, it forms a negative run, corresponding to a drought or dry-heat event [12,13,14,15]. In the case of drought, for example, when the monthly scale SPI is consistently below a threshold (e.g., −0.5), it constitutes a negative run whose duration D characterises the temporal span of the event, and the area bounded by the cumulative below-threshold SPI values is defined as the drought severity S. Intensity refers to the SPI value during an individual drought event, while severity (S) is defined as the cumulative sum of all consecutive SPI values below a designated threshold within that event. Similarly, dry-heat events are identified based on the SDHI, and high-temperature events are identified based on the STI; dry-heat events are defined using negative runs, and high-temperature events are judged using positive runs.

In practice, drought–high-temperature compound processes often exhibit temporal complexity, and spatially and temporally correlated sub-dry-heat units may appear during the dominant event period due to precipitation or temperature fluctuations [28]. The characterisation system of the complete event, therefore, needs to be constructed by merging the duration and cumulative severity of adjacent sub-events [29]. Thus, the key steps in the identification of dry-heat compound events include run segmentation, threshold screening, and sub-event fusion. The specific threshold X used in this study is described in detail in subsequent subsections.

• Handling of small dry-heat events: to avoid attenuation of statistical significance due to interference from short-term weak signals, it is necessary to establish threshold-screening criteria to implement validity assessment and sample integration for microscale dry-heat events.
• Merging of dry-heat events: for serialised dry-heat segments separated by transient wet or cool periods, intelligent splicing of fragmented events is achieved through time-domain continuity analysis to construct complete dry-heat processes with hydrological coherence.

We set up a three-level threshold system (X₀, X₁, X₂) to realise dry-heat feature extraction based on the SDHI time series. First, the D and S parameters are obtained through run-theory analysis, where D characterises the duration of a single dry-heat (or drought) event, and S is a quantitative expression of the cumulative deviation of SDHI representing the severity of this event. The specific identification process is as follows:

• Initial dry-heat judgement: if the SDHI of a month is lower than the X₁ threshold, an initial dry-heat judgement signal is triggered.
• Single-month event filtering: for water-deficit events with a duration of 1 month, when the SDHI value exceeds the X₂ threshold, the event-culling operation is performed.
• Associated event fusion: when there is a single-month interval between adjacent dry-heat events and the SDHI for that intervening month does not reach the X₀ benchmark value, the event-fusion procedure is initiated. The total duration after fusion is the sum of the original durations plus the number of intervening months, and the total severity is the algebraic sum of the intensities of the sub-events; otherwise, the status of independent events is retained.

The cut-off level parameter system is constructed as follows. According to the mechanism of hydrological events, the first cut-off level X₀ is set to 0 (corresponding to the monthly average SDHI neutral threshold). Referring to international norms for classifying dry-heat events, when the SDHI breaks the lower limit of −0.5, it is labelled as a mild dry-heat state, and the secondary cut-off level X₂ = −0.5 is determined accordingly. For cases where SDHI lies in the interval −0.5 to −0.3 for 1 or more observation cycles, the dry-heat state judgement is maintained; therefore, the tertiary cut-off level is set as X₁ = −0.3 [30].

Among them, according to the grading criteria of dry-heat compound events, the first cut-off level is set as X₀ = 0; when the SDHI value is less than −0.5, mild dry-heat conditions occur, and the second cut-off level is set as X₂ = −0.5 (the SDHI value when mild dry-heat occurs). Dry-heat events are also considered to have occurred when the SDHI value is consistently in the range of −0.5 to −0.3 for one or more time periods; therefore, the third cut-off level is set as X₁ = −0.3.

3.3. Mann–Kendall Mutation Test

The Mann–Kendall mutation test is one of the most effective methods for testing time series mutations, and the test can specify the onset of the erosion [31]. It is particularly effective for pinpointing the onset time of an abrupt change. In this study, it is employed to analyse the change points in climatic factors and streamflow.

For a time series x₁, x₂, …, x_n with sample size n, a rank-based sequential statistic S_k is first constructed. For each time point j (j = 2, 3, …, n), compare its value x_j with all preceding values x_i (i = 1, 2, …, j − 1). The statistic Rj is the cumulative count of instances where x_j > x_i. Formally,

$$R_j={\displaystyle \sum _{i=1}^{j-1}\mathrm{sgn}(x_j-x_i)}$$

(10)

where sgn($x_j-x_i$) is the sign function:

$$\mathrm{sgn}(x_j-x_i)=\left\{\begin{array}{l}1\hspace{1em} x_j-x_i>0\\ 0\hspace{1em} x_j-x_i=0\\ -1\hspace{1em} x_j-x_i<0\end{array}\right.$$

(11)

The progressive statistic S_k is then defined as the cumulative sum of R_j up to time k:

$$S_k={\displaystyle \sum _{j=1}^k{R}_j},k=2,3,\dots ,n$$

(12)

Under the null hypothesis H₀ that the data are independently and identically distributed (no trend or change point), the mean $E_{\left(S_k\right)}$ and variance $Va{r}_{\left(S_k\right)}$ of S_k are given by the following:

$$E_{\left(S_k\right)}={\displaystyle \frac{k\left(k-1\right)}{4}}$$

(13)

$$Va{r}_{\left(S_k\right)}={\displaystyle \frac{k\left(k-1\right)\left(2k+5\right)}{72}}$$

(14)

The standardised test statistic UF_k (also known as the forward sequence) is then calculated as follows:

$$U{F}_k={\displaystyle \frac{S_K-E_{\left(S_k\right)}}{\sqrt{Va{r}_{\left(S_k\right)}}}},k=2,3,\dots ,n$$

(15)

With UF₁ = 0, UF_k follows approximately the standard normal distribution.

A significance level of α = 0.05 is adopted in this study, corresponding to critical values of ±1.96. If the plotted UF_k curve exceeds these confidence limits, it indicates a statistically significant trend within the time series (upward if UF_k > 0, downward if UF_k < 0).

To precisely locate the potential change point, the time series is processed in reverse order (x_n, x_n−1, …, x₁), and the same procedure is applied to compute the backward sequence UB_k. The intersection point of the UF_k and UB_k curves, located between the confidence limits, pinpoints the estimated time of a mutation. A clear intersection point with a significant trend shift signifies an abrupt change in the series.

3.4. Copula Function

Copula techniques provide a flexible way to describe the dependency structure between multivariate data, independent of their marginal probability distributions, and serve as a powerful tool for modelling and sampling nonlinearly correlated multivariate data [32]. A Copula function is a joint distribution function defined on the interval [0, 1], and Copula theory was first proposed by Sklar [33] in 1959; it subsequently developed rapidly in the 1990s. A Copula is a joint multivariate probability distribution function with a domain of definition between [0, 1], constructed without explicitly considering the marginal distributions. In recent years, Copula functions have been widely used for bivariate frequency analysis in natural sciences and engineering fields such as hydrology, geology, and oceanography [34,35,36]. The emergence of Copula theory provides an efficient way to characterise the various features of composite events.

The process of applying the Copula function to construct the multivariate joint distribution function is as follows: first, the marginal distribution of each random variable is constructed; second, the Copula function is fitted and tested.

Before using the Copula function for the bivariate joint probability distribution of drought duration and severity, the marginal distribution functions of the two univariate variables—duration and severity of drought events—are determined, taking into account the dependence between these two characteristic variables. Seven common univariate distribution functions are selected, including the generalised extreme value distribution (GEV), extreme value distribution (EV), exponential distribution (EXP), Poisson distribution (POISS), normal distribution (NORM), gamma distribution (GAM), and Rayleigh distribution (RALY), to fit the two characteristic variables (duration and severity) of composite high-temperature–drought events of different degrees. These distributions are then tested by the Kolmogorov–Smirnov (K–S) method to select the optimal marginal distribution function for different grid points.

GEV (Generalised Extreme Value) distribution formula:

$$G_{\gamma }(x)=\exp \left(-{(1+\gamma x)}^{-{\displaystyle \frac{1}{\gamma }}}\right)$$

(16)

where $\gamma$ is a positional parameter.

EV distribution formula:

$$F(x)={\sigma }^{-1}\exp \left({\displaystyle \frac{x-\mu }{\sigma }}\right)\exp \left(-\exp \left({\displaystyle \frac{x-\mu }{\sigma }}\right)\right)$$

(17)

where $\mu$ and $\sigma$ are positional and scale parameters.

Exponential distribution formula:

$$F(x)={\displaystyle {\int }_0^x\frac{1}{\mu }}{e}^{{\displaystyle \frac{-(x-\alpha )}{\mu }}}dx$$

(18)

where $\alpha$ and $\mu$ are scale and positional parameters.

Poisson distribution formula:

$$P(X=k)={\displaystyle \frac{e^{-\lambda }{\lambda }^k}{k!}}$$

(19)

where $\lambda$ both mean and variance.

Normal distribution formula:

$$F(x)={\displaystyle \frac{1}{\sqrt{2\pi }\sigma }}{e}^{-0.5{\left({\displaystyle \frac{x-\mu }{\sigma }}\right)}^2}$$

(20)

where $\mu$ and $\sigma$ are the mean and variance of the sample.

Gamma distribution formula:

$$F(x)={\displaystyle \frac{{\beta }^x}{\Gamma (\alpha )}}{\displaystyle {\int }_x^{\infty }{(x-\gamma )}^{\alpha -1}{e}^{-\beta (x-\gamma )}}dx$$

(21)

where $\alpha$, $\beta$, $\gamma$ respectively shape, scale, and positional parameters.

Rayleigh distribution formula:

$$F(x)={\displaystyle \frac{x}{{\sigma }^2}}{e}^{-{\displaystyle \frac{x^2}{2{\sigma }^2}}}$$

(22)

where ${\sigma }^2$ is the variance of the sample.

Copula functions combining duration (D) and severity (S) to construct a joint probability model, before constructing the Copula model, parameter estimation and fitness testing of F_D(d) and F_S(s) are required, i.e., the marginal probability distributions of duration (D) and severity (S) are determined, and the statistical dependence structure of the two needs to be quantified.

The core of the Copula function is the joint treatment of marginal variables based on the correlation between them. According to the definition of the Copula function, the joint distribution function of the duration D and severity S can be expressed as follows:

$$\mathrm{F}\left(d,s\right)=P\left(\mathrm{D}\le d,\mathrm{S}\le s\right)=\mathrm{C}\left[{\mathrm{F}}_{\mathrm{D}}\left(d\right),{\mathrm{F}}_S\left(s\right)\right]$$

(23)

where F(d,s) is the joint distribution function of ephemeral and severity; P is the joint probability; and C is the Copula function.

Based on the extracted 2 feature variables of drought duration and severity, the empirical joint distribution function of the above theoretical Copula function was fitted separately, and the joint distribution function was fitted according to the squared Euclidean distance between the empirical distribution function and the theoretical distribution function [37] as well as the akaike information criterions (AIC) method [38], goodness-of-fit test. The smallest value of the AIC criterion indicates a better simulation of the copula function.

3.5. Climate Propensity Rate

Climate propensity rate describes the tendency and rate of change in climate factors in a given area over a certain time frame. It can be used to characterise the trend and magnitude of climate change, as well as to study the impacts of climate change on regional environments and human activities. Trends in climate factors are expressed as best-fit straight lines, and the slopes of climate factors over time (i.e., the propensity rates) are calculated. The linear regression equation for the climate propensity rate of a time series of a meteorological element in year i is as follows:

$$X_i=a+bt$$

(24)

where a is a constant term; t is the year; and b is a regression coefficient, the positive or negative of which indicates an upward or downward trend in the climate factor, and the magnitude of the slope indicates the magnitude of the trend.

4. Results and Analysis

4.1. Characterisation of the Distribution of Summer Drought in Liaoning Province

4.1.1. Characterisation of the Temporal Distribution

Figure 3 reveals the synergistic evolution characteristics of the average summer drought duration, severity, and Standardised Precipitation Index (SPI) in Liaoning Province during 1961–2020. In order to show more clearly the correspondence between the values of SPI on the left side and the drought duration and severity on the right side, the positive and negative directions of the SPI values on the left Y-axis have been inverted in the figure, while the positive and negative Y-axis of the drought duration and severity on the right side remain unchanged.

During this period, four summer drought events (based on SPI < −0.5) occurred in Liaoning Province in 1972, 1992, 2000, and 2014, while the remaining years were normal or wet. The occurrence of drought thus exhibits evident stage characteristics.

The 2000 drought was the most severe, with a minimum SPI of −0.88, a duration of 2.4 months, and a severity of 2.72, making it one of the most severe droughts in Liaoning Province since the founding of New China [39]. During that year, the province’s summer precipitation was the lowest in 60 years, severely affecting agriculture, and many cities also experienced severe water shortages.

There is a strong correspondence between the SPI series and the peaks of drought duration and severity. Sudden changes in drought duration and severity relative to the SPI index are not obvious, and there are few occurrences of “flash droughts” (very high severity but short duration) and few droughts dominated by cumulative effects (long duration but low severity) [40].

The Mann–Kendall mutation test was further applied to examine the trend of the summer SPI in Liaoning Province from 1961 to 2020, and the results are shown in Figure 4. The UF curve is negative during 1968–1995, 1999–2012, and 2014, indicating that precipitation in Liaoning Province showed a decreasing trend in these periods and that the region was in a relatively dry state. In contrast, UF values are positive during 1995–1999 and 2012–2014, corresponding to relatively wet periods. Both the original (UF) and inverse (UB) series fluctuate within the 0.05 significance level bounds, indicating that no distinct abrupt change is detected and that the mutation trend is not obvious. The frequent crossings of UF and UB during 1961–2020 imply that the summer drought index in Liaoning Province shows considerable interannual variability, and the continuity of climate change is relatively low [41].

Overall, Figure 4 shows that the mean summer drought index in Liaoning Province over the past 60 years fluctuates considerably but remains within the significance threshold, and its long-term trend is not pronounced. However, UF values are more often negative, suggesting that relatively dry periods are more frequent than relatively wet periods, and that the overall summer precipitation in Liaoning Province exhibits a decreasing tendency. The increasing tendency of drought events in the two sub-periods also indicates that Liaoning Province is becoming more prone to summer drought.

4.1.2. Characterisation of the Spatial Distribution

The optimal marginal distribution function and optimal Copula function selection for the duration and intensity of summer droughts in Liaoning Province from 1961 to 2020 are presented in Table S1. In terms of drought duration (Figure 5a), the spatial distribution of summer drought in Liaoning Province is heterogeneous, with most areas close to the provincial mean. The Anshan, Dandong, and Xiongyue stations are centres of high values, whereas the Xingcheng, Xiuyan, and Kuandian stations exhibit shorter drought durations. Although Dandong City as a whole receives abundant precipitation, the Dandong station has a longer drought duration, which is related to its dependence on stable summer monsoon precipitation; when the monsoon is interrupted or weakened, the duration of moisture deficit becomes more pronounced. Xingcheng, as a coastal station directly regulated by the Bohai Sea, is frequently replenished by oceanic water vapour, which favours the occurrence of small-scale local precipitation processes that interrupt the continuity of drought [42]. Xiuyan and Kuandian are both located in the hinterland of the Thousand Hills mountain range, where strong topographic relief easily triggers local thermal circulations (e.g., valley and mountain winds) and convection, resulting in scattered precipitation over complex terrain and, consequently, shorter drought durations.

In terms of drought severity (Figure 5b), the high-value zones of summer drought severity in Liaoning Province are mainly distributed in western Liaosi and in parts of Dandong. These regions are classic semi-arid to arid areas characterised by low precipitation, strong solar radiation, and vigorous evaporation. During drought events, soil moisture is rapidly depleted, and the water deficit index increases sharply, leading to very high drought severity. The relatively high severity at the Dandong station suggests that under rare drought conditions, ecosystems and agricultural systems adapted to humid environments are more sensitive to water stress. Conversely, the relatively low severity at the Kuandian station in Dandong City, as well as in the Liaodong mountainous area and at the Xingcheng station, is closely related to orographic uplift, which enhances cloudiness, reduces temperature, weakens evaporation, and, together with the moderating effect of the ocean, mitigates drought severity [42].

Regarding the joint probability distribution of drought duration and severity (Figure 5c), the spatial pattern of joint probability in summer across Liaoning Province is mostly greater than or equal to the provincial mean, except in some areas of Dalian. Owing to its distinct marine climate, Dalian is not prone to high-severity droughts, and the statistical probability of simultaneously meeting the two extreme conditions of “long duration” and “high severity” is consequently very low. As a result, the joint probability in Dalian is reduced by the small likelihood of this “extreme combination” and is therefore lower than the provincial average (Figure 5).

4.2. Characterisation of Summer High Temperature Distribution in Liaoning Province

4.2.1. Characterisation of the Temporal Distribution

Figure 6 shows the synergistic evolution characteristics of the average summer high-temperature duration, severity, and standardised temperature index (STI) in Liaoning Province during 1961–2020. During this period, 14 significant heat events (STI > 0.5) occurred in Liaoning Province in summer, specifically in 1961, 1963, 1994, 1997, 1999, 2000, 2001, 2007, 2013, 2014, 2016, 2017, 2018, and 2020. The occurrence of high-temperature events exhibits clear phase characteristics and interannual fluctuations. In terms of temporal distribution, most summer high-temperature events in Liaoning Province over the past 60 years occurred after 1994, especially after 2000 [39], when the frequency of high-temperature events increased significantly. The duration and severity of high-temperature events also showed a significant long-term increasing trend over the 60-year period.

In the context of the decay of strong El Niño and La Niña events [43], the STI series corresponds well with the peaks of drought duration and severity. In 1994, 1997, and 2000, ENSO affected summer wind and precipitation through a remote correlation mechanism, which led to increased drought susceptibility in Liaoning under specific ENSO phases. In these years, high temperatures were widespread across the country, and the cold air from the north was weak, making it difficult to generate effective precipitation and cooling. Consequently, Liaoning Province also experienced rare high-temperature events.

During this period in Liaoning Province, the STI and high-temperature severity reached extremely high values of 4.62–5.3, with high temperatures persisting for nearly the entire three-month summer period. Since then, high-temperature events have occurred frequently. In 2007, the high temperature was relatively short-lived but of high severity, which may be characterised as an “outbreak-type” high-temperature event, whereas the long-lived high-temperature event in 2013 had a moderate average severity, reflecting the continuing cumulative effect of high temperatures [40].

The Mann–Kendall mutation test was used to further examine the trend of the summer STI in Liaoning Province from 1961 to 2020, and the results are shown in Figure 7. The figure shows that the UF curve has negative values during 1961–1998, indicating that the STI exhibited a “downward” trend and that this period was characterised by relatively “low” temperatures. From 1998 to 2020, the UF values are positive, indicating a relatively “high” temperature period. The original series (UF) and inverse series (UB) curves intersect in 2011, after which UF continues to increase and exceeds 2, surpassing the 0.05 significance level, indicating that the high-temperature index increased significantly after 2011 [41].

Taken together, Figure 7 shows that the UF value is positive and continues to increase after 1998, demonstrating that the summer temperature index in Liaoning Province is higher in the latter 30 years than in the first 30 years, and that it exhibits an overall increasing trend over the 60-year period. The intersection of UF and UB and the rise in UF above the significance level in 2011, along with the occurrence of six high-temperature events in the eight years after 2013, provide further evidence that the frequency of summer high-temperature events in Liaoning Province has gradually increased over the past 60 years. The data in the figure indicate that Liaoning Province is likely to remain susceptible to summer heat events in the future [44].

4.2.2. Characterisation of the Spatial Distribution

The best-fit marginal distribution function and optimal Copula function selection for the duration and intensity of summer heatwaves in Liaoning Province from 1961 to 2020 are presented in Table S2. In terms of high-temperature duration (Figure 8a), most of the summer high-temperature durations in Liaoning Province are higher than the average duration, which is consistent with the results in Figure 5 for the overall temperature increase in Liaoning Province. Chaoyang, Benxi, and Xinbin, as well as the Kuandian site, are centres of high-duration values. Although Kuandian is a mountainous area, its county and meteorological stations are likely located in a relatively open mountain valley or basin. This terrain is associated with low wind speeds and poor ventilation, forming a “heat basin” [45]. In Kuandian, drought duration is shorter, while the high-temperature duration is very long. Under the influence of oceanic regulation, Dalian has the lowest high-temperature duration in Liaoning Province, followed by shorter durations at the Jianchang, Changtu, and Dandong sites.

In terms of high-temperature severity (Figure 8b), the high-severity areas in Liaoning Province are mainly located at the Benxi and Xinbin stations, which again confirms the “heat gathering” effect of mountainous basins or river valleys. These topographic conditions not only make high temperatures persistent but also exacerbate their severity. The lowest values are observed in Dalian and at the Jianping County station, which, although located in western Liaoning, is at a relatively high altitude within Chaoyang City and has a more open topography and possibly better ventilation than the Chaoyang Basin, thereby mitigating extremes of high temperature to some extent.

Regarding the joint probability distribution of high-temperature duration and severity (Figure 8c), the spatial distribution of joint probability in Liaoning Province in summer shows a pattern of “high in the east and low in the west”. Low values are found at the Dalian, Zhuanghe, and Anshan sites, whereas high joint probabilities are concentrated at the Qingyuan, Xinbin, Xinmin, and Kuandian sites. For Qingyuan, Xinbin, and Kuandian, this is mainly attributed to the “heat gathering” and “enhancement” effects of their mountainous basin topography on the stable high-pressure system, which makes “long duration–high severity” a typical feature of high temperatures in these areas. Thus, the joint probability is high. The high joint probability at Xinmin is mainly attributed to the consistent and strong response of the homogeneous plain underlying surface to the stable high-pressure system.

4.3. Characterisation of the Distribution of Summer Dry-Heat Complexes in Liaoning Province

4.3.1. Characterisation of the Temporal Distribution

Figure 9 reveals the synergistic evolution characteristics of the mean summer dry-heat duration and severity and SDHI values in Liaoning Province during 1961–2020. In order to present more clearly the correspondence between the SDHI values on the left side and the dry-heat duration and severity on the right side, the positive and negative directions of the SDHI values on the left Y-axis of the figure have been inverted, while the positive and negative directions of the dry-heat duration and severity Y-axis on the right side are kept unchanged.

During this period, 10 dry-heat events (as measured by SDHI < −0.5) occurred in Liaoning Province during the summer months, specifically in 1961, 1963, 1997, 1999, 2000, 2007, 2014, 2017, 2018, and 2020. As shown in Figure 9, there were two dry-heat events in the first 30 years and 8 in the second 30 years, corresponding to frequencies of 6% and 26%, respectively, indicating that dry-heat events were concentrated in the latter 30 years. The most severe of these was the dry-heat event in 2000, with a minimum SDHI of −1.19, a duration of 2.8 months, and a severity of 3.56.

There is a strong correspondence between the SDHI series and the peaks in duration and severity, with 2000 being the most prominent year for extreme events in this period, while such extreme events appear to have become more common after 2014. The figure shows that 1997–2000 was a peak period for the duration and severity of dry-heat events, and after 2012, both duration and severity gradually increased.

The Mann–Kendall mutation test was used to further confirm the trend of the average summer SDHI in Liaoning Province from 1961 to 2020, and the results are shown in Figure 10. The figure shows that the UF curve is negative after 1998, indicating that SDHI has exhibited a “downward” trend during this period and that the region has been in a relatively dry and hot state. Before 1998, UF values are generally positive (except in 1963, 1983, 1984, 1991, 1992, and 1994), corresponding to a period of relatively “high” precipitation and “low” temperatures. A mutation occurred in 2012, when the original series (UF) curve intersected the inverse series (UB) curve, and UF continued to decrease thereafter. The UF value exceeded the 0.05 significance level in 2015, indicating that the dry-heat index declined significantly after 2015, which is consistent with the plot of dry-heat duration versus severity [41].

Figure 10 shows that most of the summer dry-heat events in Liaoning Province over the past 60 years occurred after 1998. The UF value after 1998 is negative and continues to decline until 2015, when it breaks through the critical value, and the dry-heat index shows a “downward” trend, indicating that the occurrence of summer dry-heat events in Liaoning Province has a “rising” trend with increasing years. The frequency of dry-heat events in summer in Liaoning Province gradually increases over time. The data in the figure indicate that Liaoning Province is prone to future dry-heat events in summer.

4.3.2. Characterisation of the Spatial Distribution

The best-fitting marginal distribution functions and optimal Copula function selections for the duration and intensity of summer high temperatures in Liaoning Province from 1961 to 2020 are presented in Table S3. In terms of dry-heat ephemeral time (Figure 11a), the dry-heat ephemeral time is relatively short over most parts of Liaoning Province in summer, with the Kaifuyuan site forming the centre of higher values. Kaifuyuan is located in the northern Liaobu Plain, where the terrain is low, flat, and open. This topography facilitates the build-up and spread of dry heat under the control of a stable warm high-pressure system. Low values are mainly distributed at the Qingyuan, Xinbin, Anshan, and Xiongyue stations. Qingyuan and Xinbin are located in the mountainous areas of Liaodong; although they may be hot, their humidity and cloudiness are usually higher than those of the plains, and the complex local circulation is more likely to trigger small-scale precipitation or cloudiness, which frequently interrupts the continuous dry-heat state and shortens its persistent duration.

In terms of dry-heat severity (Figure 11b), dry-heat severity is high in most parts of Liaoning Province in summer, with the areas of highest severity mainly located at the Dandong, Wafangdian, Changtu, and Kaiyuan stations. When a rare, strong continental dry-heat mass breaks through the mountain barrier and affects the area, the drop in relative humidity can be unusually sharp, resulting in a high value of the combined dry-heat index. Wafangdian is located in the interior of the peninsula and, due to the influence of topography and local circulation, can receive sufficient solar radiation for heating while not being easily and continuously moistened by sea breezes, making it prone to short but unusually intense dry-heat events. Low values are mainly found at the Qingyuan and Dalian sites, which are related to the mountainous terrain, dense vegetation, and oceanic regulation [42].

From the joint probability distribution of dry-heat duration and severity (Figure 11c), most of the joint probabilities in Liaoning Province are around the average value in summer. The Shenyang site is the centre of high joint probability. The process of urbanisation in Shenyang has created a local environment that can simultaneously support “long duration” and “high severity” dry-heat events, making their co-occurrence more likely and resulting in the highest joint probability. In contrast, Wafangdian is the centre of low joint probability, indicating that “long dry-heat duration” and “high dry-heat severity” are unlikely to occur simultaneously there.

4.4. Climate Propensity for Summer Drought, High Temperature, and Dry-Heat Events in Liaoning Province

Figure 12 shows the spatial distribution of the average decadal propensity rates of SPI, STI, and SDHI in summer in Liaoning Province from 1961 to 2020. As can be seen from the SPI propensity rate in Figure 12a, the spatial distribution exhibits the typical feature of “wet east and dry west”. The northeastern region (especially the western foothills of the Changbai Mountains) shows a slight wetting tendency, mainly due to the uplifting effect of the mountainous topography on the water vapour transported by the East Asian summer monsoon, which is conducive to the formation of orographic rainfall. The most severely aridified area is located at the Chaoyang site in western Liaoning Province.

From the STI propensity rate in Figure 12b, it can be seen that the STI propensity rate is positive across the whole province in summer, indicating that all 25 stations in Liaoning Province exhibit an overall warming trend in summer. However, there are obvious spatial differences in the magnitude of warming. The Anshan and Dalian stations have become significant warming centres, which is closely related to their high degree of urbanisation. The urban heat island effect (UHI) amplifies the regional warming signal in these industrial and densely populated agglomerations, and the warming in southern coastal cities (e.g., Dalian) reflects a specific response to global warming in coastal areas. As shown by the SDHI propensity rate in Figure 12c, SDHI is negative across the province, indicating a general increase in the hazard of dry-heat events. The warming core areas, such as Dalian and Anshan, are likewise the most severely dry-heated areas, while the Shenyang, Benxi, and Wafangdian sites experience relatively less dry heat.

Overall, the spatial analyses indicate that the province is generally dry and hot, but with significant spatial heterogeneity. Specifically, aridity (declining SPI) and hyperthermia (increasing STI) are strongest in the western region, whereas the eastern region is relatively mild or even exhibits a wetting trend. It is noteworthy that the intensification trend of composite dry-heat events (SDHI) is more consistent with the spatial distribution of high temperatures (STI), especially in more urbanised areas such as Dalian and Anshan, suggesting that summer warming is the dominant factor driving the intensification of dry thermal conditions in Liaoning Province [46].

5. Discussion

In terms of temporal distribution, summer drought events in Liaoning Province exhibit distinct temporal characteristics, with four drought events identified in 1972, 1992, 2000, and 2014. Among these, the drought in 2000 was the most severe, showing the lowest SPI value, the longest duration, and the highest severity, consistent with records that it was one of the most severe droughts since the establishment of New China [39]. The MK test indicated an overall non-significant decreasing trend in the SPI but an increasing trend in the frequency of drought events over two equal periods, suggesting that Liaoning Province may face more frequent summer droughts in the future [41], echoing the global trend of increasing compound extreme events [47,48]. In terms of spatial distribution, drought severity was highest in western Liaoning (e.g., Chaoyang) and parts of Dandong, which usually have dry climates with low precipitation and strong evaporation. In contrast, coastal sites (e.g., Xingcheng) and mountainous sites (e.g., Xiuyan and Kuandian) experienced shorter drought durations due to oceanic water vapour transport and orographic precipitation [42]. The SPI climate propensity further confirms the pattern of “wet east and dry west”, with the most significant drought trend in western Chaoyang. This spatial heterogeneity suggests that western Liaoning, as an important agricultural area, is particularly vulnerable to increasing drought, which may threaten local crop yields and water security [49,50]. Future drought hazard assessment and water resource management should therefore prioritise this region.

High-temperature events show a more pronounced upward trend. A total of 14 high-temperature events were identified, with a significant increase in their frequency since 1994, especially after 2000. The duration and severity of high temperatures increased significantly over the 60-year period, and a significant abrupt climate change was detected in 2011, after which the STI increased markedly [41]. This is consistent with the increasing frequency of global and regional warming and drying [44]. Spatially, inland basins and river valleys (e.g., Benxi, Qingyuan, and Xinbin) exhibited the most significant duration and severity of high temperatures. These regions are affected by a topographic “heat concentration effect”, whereby poor ventilation in valleys or basins leads to prolonged and intensified high temperatures [45]. By comparison, the duration of high temperature is shortest in coastal Dalian, which is affected by the moderating influence of the ocean. The positive STI propensity rate across the province indicates an overall sustained warming, with highly urbanised regions such as Anshan and Dalian emerging as significant warming centres. This pattern reflects the superposition of global warming and the urban heat island effect (UHI), which substantially amplifies regional temperature increases [51,52,53]. High-temperature hazards are therefore highly concentrated in topographically susceptible and urbanised areas, highlighting the urgent need for targeted heat protection strategies, with particular emphasis on public health and the stable operation of power systems.

Dry-heat compound events show the most pronounced temporal clustering characteristics, with 10 events identified, 8 of which occurred in the latter 30 years (1991–2020). The event frequency in the latter period reached 26%, compared with only 6% in the first 30 years, indicating a substantial increase. In recent years, global climate extremes have continued to intensify, with successive overlapping droughts and heatwaves reported in Europe, North America, and Asia [54]. El Niño events and the 2000 mega high-temperature and drought event in Liaoning have demonstrated that compound disasters can exacerbate water scarcity, reduce crop yields, and trigger energy crises [39]. The 2000 event was the most extreme, and such compound events became more frequent after 2014. The SDHI decreased significantly after 2015, exceeding the significance level, confirming that dry-heat events are showing a trend towards increasing frequency and intensification [41]. Spatially, the Shenyang region has the highest joint probability of long-duration and high-severity dry-heat events, which is closely related to its high degree of urbanisation. Urban expansion alters the surface energy and water balance, creating local environments prone to sustaining the coexistence of heat and dryness [55]. In contrast, the joint probability in mountainous areas (e.g., Qingyuan and Xinbin) and coastal areas (e.g., Dalian) is significantly reduced due to the effects of orographic precipitation and oceanic regulation [42]. Province-wide, the propensity rate of dry-heat compound hazard is negative, and its spatial distribution pattern is much more strongly correlated with high temperature (STI) than with drought (SPI), suggesting that summer warming is the dominant factor exacerbating dry-heat compound hazard in Liaoning [46].

In this study, we constructed a unified framework for identification–feature extraction–hazard quantification based on run theory and the Copula function, which overcomes the limitations of traditional univariate extreme-event analysis. By extending run theory from drought to high temperature and compound events, the study achieves multi-hazard feature extraction, while the Copula function jointly characterises duration and severity and constructs their joint probability distribution, thereby enabling probabilistic hazard assessment of “long duration–high severity” extreme compound events [15,56]. This provides key methodological support for the formulation of targeted disaster prevention strategies [57,58]. For Liaoning Province, an important grain-producing region, the hazard assessment in this study indicates that western Liaoning and highly urbanised areas are at high hazard of compound dry-heat events, posing a direct threat to the stability of maize yields [59,60]. The spatial mismatch between these high-hazard zones and the areas covered by modern irrigation infrastructure highlights critical gaps in current agricultural water management [61]. Adopting climate adaptation strategies (e.g., adjusting crop sowing dates to avoid sensitive growth stages during peak dry and hot periods) can effectively reduce yield losses [62,63].

The results of this study reveal significant spatial divergence between drought and high-temperature events, especially in the mountainous and coastal areas of Liaodong. The findings not only provide a scientific basis for dynamic monitoring, hazard zoning, and zonal prevention and control of summer dry-heat disasters in Liaoning Province, but also offer empirical reference for understanding the synergistic effects of climate warming and local factors such as topography and urbanisation on compound extreme events. It should be noted that, due to the limited spatial density of existing meteorological stations, there may be some uncertainty in the spatial interpolation results for the Liaodong Mountain Range and other complex terrain areas, and potential local dry and hot “aggregation zones” or “sheltered zones” in mountainous regions may not have been fully captured. Therefore, it is recommended that future efforts strengthen monitoring and early warning in high-hazard areas and consider supplementing mountainous observations or adopting methods such as dynamical downscaling to improve the accuracy of analyses in complex terrain. Ultimately, dynamic hazard assessments should be integrated into regional climate adaptation and territorial spatial planning systems to enhance food security, water resource sustainability, and the overall resilience of socio-ecological systems [64,65].

6. Conclusions

Analysing the spatial and temporal characteristics of droughts, high temperatures, and combined dry-heat events provides a scientific basis for dynamic monitoring and hazard zoning of regional dry-heat disasters. The main conclusions of this study are as follows:

• Drought events occur frequently and show a westward shift in spatial pattern. Although the overall drought trend is not statistically significant, frequency is increasing. High-severity drought areas are concentrated in western Liaoning and parts of Dandong, while coastal and mountainous areas experience shorter durations due to orographic uplift and oceanic regulation. Climate tendency confirms a “wet east and dry west” pattern, with the Chaoyang area exhibiting the most significant drying trend.
• High-temperature events have intensified markedly, with abrupt changes after 1994 and a detected shift in 2011. Spatially, high-temperature areas are distributed in inland basins and valleys due to terrain “heat-gathering” effects, while highly urbanised areas such as Anshan and Dalian show pronounced warming from urban heat islands. The province exhibits positive STI tendency rates, indicating that topography and human activities shape heat hazard under climate warming.
• The frequency of combined dry-heat events has increased significantly, with the latter 30 years experiencing over four times more events than the first 30 years. The year 2000 recorded the most extreme event, and a notable decline in the SDHI after 2015 suggests more frequent and intense compound events. Shenyang, due to urbanisation, has become a high joint-probability centre, whereas mountainous and coastal areas face lower hazards. SDHI tendency rates are negative and spatially consistent with STI, indicating climate warming dominates the intensification of dry-heat compound hazards.

The results provide a scientific basis for dynamic monitoring, hazard zoning, and zonal management of summer dry-heat disasters in Liaoning, and offer an empirical case on the synergistic impacts of climate warming, topography, and urbanisation. Future work should enhance monitoring in high-hazard areas and integrate dynamic hazard assessment into climate adaptation and spatial planning.