Shandong Province is situated between 114°48′-122°42′E longitude and 34°23′-38°17′N latitude, spanning approximately 721.03 km from east to west and 437.28 km from north to south, with a total land area of 155,800 km². As of November 2020, the province had a male population of 51,432,931 (50.66%) and a female population of 50,094,522 (49.34%), resulting in a sex ratio (males per 100 females) of 102.67, reflecting a 0.34 percentage point increase compared to the sixth national census. By the end of 2023 the population aged 60 and above reached 23.91 million, constituting 23.62% of the total population. Shandong Province has the largest elderly population in China, characterized by a high absolute number, rapid growth rate, and an accelerating aging trend, presenting significant demographic and socio-economic challenges. Land use types are shown in Fig. 2(b).

The climate data used in this study consist of bias-corrected near-surface meteorological variables from the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) Atmospheric Reanalysis (ERA5). This dataset is derived using the same methodology as the widely utilized Water, Energy, and Climate Change (WATCH) forcing data, ensuring consistency and comparability in climate analysis. The dataset has been adjusted for altitude effects and bias-corrected at the monthly scale using data from the Climate Research Unit (CRU)—which accounts for temperature, diurnal temperature range, cloud cover, wet days, and precipitation fields—and the Global Precipitation Climate Centre (GPCC), which is specifically used for precipitation fields. The data are provided on 0.5° gridded resolution. Consequently, when utilizing ECMWF’s ERA5 dataset, the critical step of data variation correction can be omitted, ensuring streamlined and reliable climate analysis.

We selected the near-surface air temperature dataset to calculate the daily maximum temperature, used Rainfall flux to calculate SPI to define drought events, and used near-surface air temperature, surface air pressure, and near-surface specific humidity to calculate the relative humidity (RH) of the surface to define humid events.

The risk assessment of urban compound events is typically conducted using the indicator-based method combined with a multi-criteria decision analysis (MCDA). In this study, four key components are considered: hazard, exposure, vulnerability, and capacity, with a total of 13 indicators quantified and analyzed to comprehensively evaluate urban disaster risk. Utilizing urban-scale weather grid data and statistical yearbook data, this study employs the entropy weight method for calculating weighing values of indicators to conduct a flood risk assessment at the urban level in Shandong Province, China. The risk scores (hazard levels) for each component are derived from the corresponding evaluation indicators within the four-part assessment framework. A higher score indicates a greater risk, highlighting the vulnerability and exposure of specific urban areas. The disaster factors considered in this study include compound hot-drought events and compound hot-humid events, both of which are primarily driven by extreme heat. High temperatures contribute to increased surface air humidity in summer while simultaneously reducing precipitation frequency across different regions. These events result from a combination of natural environmental conditions and urban development factors. Exposure broadly refers to human and material assets directly affected by disasters, encompassing a macro-level assessment of risk. Vulnerability, in contrast, provides a more detailed classification of exposure, offering a refined evaluation of susceptibility to disaster impacts. Additionally, recovery capacity reflects a city’s ability to withstand disasters by leveraging available human and material resources. This metric serves as an indicator of local government efforts in disaster mitigation and loss reduction (Table 1). This is an assessment of two compound disasters, so in the disaster part, we calculated them separately, so the weights are 1 separately.

The Standardized Precipitation Index (SPI) is well established in describing the occurrence and severity of drought events. This is a method of assessing the severity of drought in a region based solely on precipitation data and has been shown to have high reliability in analyzing specific events (Meseguer-Ruiz et al., 2024). The SPI method offers several advantages, including computational efficiency, high accuracy in drought event assessments, methodological simplicity, and minimal data requirements, making it a preferred tool in drought analysis. In this study, we employ the traditional SPI calculation method (Thomas and McKee, 1993), rather than moment estimation or maximum likelihood estimation, as these alternative approaches are more susceptible to computational errors. By adhering to the standard calculation method, we ensure greater accuracy and consistency in drought assessments.

Where P_i is the precipitation in the e^i-th month of the study period; u is the mean of the study series during the entire study period; and σ is the standard deviation.

There are multiple approaches to calculating the Standardized Precipitation Index (SPI), with the mean and standard deviation-based method being the most reliable in minimizing calculation errors. When selecting the research subject and regression period, two primary methods are commonly used: year-based selection and month-based selection (Abu Arra and Şişman, 2024).

1. Year-based selection involves calculating the SPI by aggregating precipitation over N consecutive months within a given year. A typical example is using precipitation from June, July, and August (JJA) in the year to compute the summer SPI.

2. Month-based selection calculates the SPI for a specific month over multiple consecutive year. For instance, selecting June precipitation over 40 consecutive years allows for the identification of long-term precipitation patterns.

The month-based method enables the identification of long-term precipitation trends while providing valuable insights for sustainable urban system development. effectively minimizing errors caused by intra-annual seasonal precipitation variability. Given these advantages, this study adopts the month-based method for SPI calculation. Additionally, the China Meteorological Administration (CMA) provides a classification system for drought events based on SPI thresholds (Table 2).

The definition of hot events varies across different studies, with two commonly used approaches: threshold-based methods and observation-based methods (Yu et al., 2022). The threshold-based method effectively identifies hot anomalies by setting predefined temperature thresholds; however, it has regional limitations. For instance, the 90th percentile temperature threshold in equatorial regions is significantly higher than that in polar regions. Conversely, the observation-based method may not fully capture the spatial variability of hot anomalies but provides a more intuitive reflection of critical temperature thresholds relevant to human activities and ecosystems. For example, agricultural crop growth depends on a specific temperature range rather than an absolute hot threshold. Considering these factors, this study adopts the hot event criterion of T 35 ℃, as defined by the China Meteorological Administration, to identify hot events in the study area.

Relative humidity (RH) is used as a criterion for defining wet events (Kohonen, 1982). According to the China Meteorological Administration (CMA), human discomfort increases significantly in summer when air temperatures exceed 33 ℃ and RH surpasses 60%. Given this threshold, humid events cannot be analyzed as independent occurrences, as they are strongly influenced by air temperature. Therefore, after identifying humid events, it is essential to integrate air temperature data to examine the patterns of Hot-Humid event and assess the associated risks faced by different cities. Based on available ERA5 reanalysis data, the calculation of relative humidity (RH) requires specific humidity, atmospheric pressure, and air temperature (Anderson, 1936; Castellví et al., 1996; Sahin and Cigizoglu, 2013). The specific calculation process is outlined as follows:

Where t air temperature (℃); q is specific humidity; p is surface air pressure (Pa); e is e is water vapor pressure; e_s is saturated water vapor pressure (hPa).

This study defines two types of compound event: composite compound Hot-Drought event and humid and hot event. These events are determined by the occurrence of individual events, with matching determined based on predefined threshold criteria. The criteria for defining individual events are based on fixed thresholds, as detailed in Table 3.

Since the Standardized Precipitation Index (SPI) is predominantly calculated on a monthly scale, it provides a more accurate representation of seasonal variations and historical trends. Consequently, if the SPI value for a given month is determined to be -1.4, this implies that when analyzing compound events, the SPI value for each day within that month is uniformly considered to be -1.4.

After identifying the compound events, the next step involves quantifying the frequency across 16 prefecture-level cities in Shandong Province, China. By integrating the data presented in Table 1, an original dataset for evaluating urban compound disasters is established. In general, hazard part, exposure part, and vulnerability part contribute to an increased risk of urban compound event, whereas capacity part serves to mitigate these risks. Consequently, when applying min-max normalization, the capacity part must be inversely standardized to ensure proper representation. The entropy weight method is utilized to quantify the relative importance of each factor (Feng et al., 2024), the specific weighting steps are as follows:

Where, x_ij is membership degree; f_ij is overall sample entropy information; H_j is entropy value; j^* is entropy weight vector.

Fig. 3(a) illustrates that the difference in the number of humid events between coastal and inland cities is not particularly pronounced. A superficial examination of the total number of events suggests that coastal cities, such as Qingdao and Yantai, experience more humid events than inland cities like Dezhou and Zibo. However, geographical location alone does not fully account for this pattern. Notably, cities such as Jining and Binzhou, which contain numerous lakes and artificial water bodies, exhibit a higher frequency of humid events. This suggests that local hydrological conditions, rather than mere coastal proximity, serve as a key regulatory factor in the formation of summer humid events.

Fig. 3(b) presents the frequency of drought events, revealing a clear distinction between inland and coastal cities. Inland cities such as Heze and Linyi exhibit a significantly higher frequency of drought months compared to coastal cities like Weihai and Rizhao. From an economic perspective, cities with a high occurrence of drought events are predominantly agricultural, characterized by relatively underdeveloped economies and high population densities. Consequently, their water demand is substantially higher than that of other urban areas, exacerbating the severity of drought conditions and increasing the vulnerability of these regions to water scarcity. The results in Fig. 3(c) indicate that, similar to drought events, hot events exhibit a distinct geographical distribution pattern. Coastal cities such as Qingdao, Rizhao, Weihai, and Yantai experience significantly fewer hot days compared to inland cities like Heze, Liaocheng, and Dezhou. In certain years, some coastal cities recorded no hot events at all. Consequently, analyzing individual events in isolation provides only a limited understanding of the influence of factors such as geographical location and population density. A more comprehensive approach, incorporating multiple interacting variables, is necessary to fully capture the underlying drivers of hot events. The statistical and computational results presented in Fig. 4 reveal distinct trends in the frequency of different extreme climate events. While the overall frequency of humid events has been declining, hot events have exhibited a significant upward trend with pronounced interannual variability. In contrast, the frequency of drought events follows a fluctuating pattern rather than a consistent trend. Given that the occurrence of individual events is influenced by multiple interacting factors, a more systematic approach is required—one that integrates these events for a comprehensive analysis of compound climate risks.

The statistical results of compound events, as illustrated in Fig. 4(a), indicate that inland cities generally experience a higher frequency of compound Hot-Humid event. While the occurrence of humid events as independent phenomena remains relatively low in inland regions, the consistently high summer temperatures in these areas exacerbate the impact of compound Hot-Humid event, posing significant risks. Similarly, inland cities are more vulnerable to compound Hot-Drought events, further intensifying climate-related challenges.

Comparing the decadal trend analysis in Figs. 4 and 5 projections suggest that the impact of compound events on inland cities will continue to increase in the future. This trend underscores the necessity for enhanced climate adaptation strategies and risk mitigation measures tailored to inland regions.

The weights of each evaluation criterion and the comprehensive disaster risk ranking of the 16 cities were determined using the Entropy method. Computed weight values are presented in Table 4. Since capacity serves as a resilience indicator, and the objective is to assess disaster risk, Eq. (8) was applied to derive the final risk ranking.

The calculation results presented in Figs. 6 and 7 indicate that coastal cities generally have a lower probability of experiencing compound event disturbances and impacts compared to inland cities. Although coastal regions exhibit higher humidity levels, their relatively lower summer temperatures and more humid climate create a more favorable environment for human habitation. In contrast, inland cities are more frequently affected by compound events.

Regarding exposure and vulnerability, these factors are primarily influenced by economic activity and population mobility rather than geographical location. Regions with high exposure and vulnerability risks are characterized by dense populations and developed economies, making them particularly susceptible to significant socio-economic disruptions in the event of a compound event.

In terms of capacity, cities with advanced economies and high population densities tend to exhibit stronger disaster resilience due to well-developed infrastructure and sufficient governmental resources for rapid disaster response and recovery. Conversely, areas with weaker capacity are primarily concentrated in Shandong Province’s major grain-producing regions, particularly Linyi and Dezhou, which are situated on expansive plains. As a result, these agricultural cities face greater challenges in disaster response and recovery when confronted with compound events, highlighting the need for enhanced adaptive capacity in such regions.

The final calculation results, as shown in Fig. 8, reveal distinct spatial and socio-economic patterns in compound event risk across Shandong Province. From a socio-economic perspective, Qingdao and Jinan—two cities characterized by developed economies and high population densities—exhibit the highest compound event risks. Geographically, inland cities located in the western and southwestern regions of the province face greater exposure to compound disasters, whereas coastal areas generally experience lower risk levels. In terms of disaster-driving factors, although Weihai City has seldom encountered compound events, its relatively underdeveloped economy, severe population aging, and inadequate infrastructure contribute to an elevated disaster risk. These findings highlight the multifaceted nature of compound event vulnerability, emphasizing the need for region-specific mitigation strategies.

The ERA5 dataset has a spatial resolution of 0.5° × 0.5°, which is insufficient for detailed urban-scale analysis. To enhance spatial resolution, Kriging interpolation was applied, refining the dataset to 0.25° × 0.25°. However, since the dataset consists of gridded reanalysis data rather than direct observations from meteorological stations, the effectiveness of resolution enhancement through Kriging interpolation remains limited. Notably, when attempting to further interpolate to 0.1°, significant information loss occurs. Thus, despite the bias correction applied to the climate dataset, the relatively coarse spatial resolution may introduce uncertainties in statistical analyses and computational outcomes.

In assessing the compound disaster risk of 16 cities in Shandong Province, the climate dataset is based on historical records from 1979 to 2019, while socio-economic indicators, including population, land use, and GDP, are derived from the 2019 statistical baseline. These temporal discrepancies may influence the accuracy of risk assessments.