The Thermodynamic and Dynamic Cause Analysis of Three Extensive Compound Heatwaves from 2011 to 2024 in Mainland Spain

Abstract

In recent years, frequent heatwaves (HWs) in Spain have increased mortality rates and impacted ecosystems. While most studies only investigate the causes of HWs in a single year, we analyzed the thermodynamic and dynamic causes of three extensive compound HWs (defined as concurrent daytime and nighttime high temperatures) over mainland Spain during the 2011–2024 summers using station and reanalysis data. In addition, we explained the differences in the duration of the three HWs in terms of thermodynamic processes and the evolution of large-scale circulation systems. For thermodynamic analysis, we applied the first law of thermodynamics to examine local temperature variations and the surface energy balance to assess solar radiation and soil moisture impacts on HWs. It was found that high temperatures occurred more frequently over mainland Spain during 2015–2024 compared with 2011–2014. The thermodynamic analysis indicates negative contributions from horizontal advection, positive contributions from adiabatic heating, and a dominant positive contribution from diabatic heating in the formation of the three HWs. Although we observed anomalously increased solar radiation during the three HWs, soil moisture deficit was the primary factor in HW formation. The dynamic analysis shows that a similar large-scale circulation configuration prevailed over mainland Spain during the three HWs. The region was simultaneously controlled by an anomalously intense Azores High and the ridge line of a warm high-pressure ridge, accompanied by a weak divergent flow. This work offers valuable insights for the study of HWs in Spain and helps to understand the universal mechanism behind the HWs.

1. Introduction

It is well known that the Mediterranean region is a hotspot of climate change [1], exhibiting significantly accelerated summer warming compared with other global regions [2,3]. Spain, in particular, has experienced frequent heatwaves (HWs hereinafter) in recent years, and the duration and intensity of HWs have increased significantly [4]. HWs are defined as prolonged periods of excessively high temperatures [5]. In July 2015, an HW in southeastern Spain lasted for almost 9 days, and in some areas even 15 days [6]. On 14 August 2021, Montoro set an all-time temperature record of 47.4 °C in Spain [7]. In the summer of 2022, mainland Spain experienced the strongest HW on record, with mean temperatures reaching 24.6 °C, 2.1 °C higher than the 1981–2010 average [8].

Frequent HWs in Spain increase the risk of human mortality. In the summer of 2022, there were approximately 5000 heatwave-related deaths in Spain [9]. Achebak et al. [10] found that the highest inpatient mortality rates in Spain in 2023 were during the summer months and were strongly associated with high temperatures. Furthermore, studies indicate that the mortality burden attributable to heatwaves in Spain has risen substantially since the COVID-19 outbreak [11]. HWs can also have an impact on ecosystems by causing a decrease in forest productivity, which may hinder the carbon sink capacity of forests [12,13]. In addition, HWs can create favorable conditions for the occurrence of wildfires, which can significantly affect groundwater quality [14]. Notably, sustained high temperatures at night can also cause a high degree of discomfort and have an impact on human health [8], potentially preventing humans from effectively recovering from the damage caused to their health by daytime HWs. When daytime and nighttime HWs occur simultaneously, the resulting phenomenon is defined as compound HWs, which may pose elevated health risks [15]. Therefore, investigating the drivers of compound HWs in Spain is important for developing effective strategies to reduce their associated risks.

Existing research has extensively investigated the dynamic and thermodynamic mechanisms of HWs in Spain through observational analyses and reanalysis data. For instance, Sousa et al. [16] conducted a comparative analysis of the large-scale atmospheric circulation configurations during the June and July 2019 HW in Western Europe using the NCEP/NCAR dataset. Demirtaş et al. [7] used ERA5 data to calculate the period mean of the 500 hPa geopotential height (GH500) and the anomaly of GH500 with respect to the base climate in order to analyze the atmospheric drivers of the 2021 HW in the Euro-Mediterranean region. Kim et al. [17] utilized the ERA5 reanalysis dataset in combination with the budget of the thermodynamic energy equation to analyze anomalies in horizontal advection, adiabatic heating, and diabatic heating, thereby discussing the causes of the rise in lower tropospheric temperatures during the 2022 HW in southwestern Europe. These methods have yielded several findings on the drivers of HWs in Spain. Sousa et al. [16] found that distinct ridge-like patterns extending from North Africa to Western Europe occurred in both the June and July 2019 HWs and that the ridge during the June HW was stronger. Zschenderlein et al. [18] demonstrated that adiabatic heating and diabatic heating contributed more than horizontal advection in HW formation from 1979 to 2016. In addition to large-scale circulation anomalies and local thermodynamic anomalies, soil–atmosphere interactions play a crucial role in HW formation, with soil moisture being a particularly significant factor [19,20]. Studies have shown that soil moisture deficits usually accompany anomalously high temperatures [21]. For instance, during the 2003 and 2010 European summer HWs, soil moisture in the core HW regions showed negative anomalies of 34% and 41%, respectively [22]. Additionally, Ribeiro et al. [23] found a strong correlation between extremely high temperatures and soil dryness in Spain.

Although the above studies have explored the causes of HWs in Spain in recent years comprehensively, they mostly focus on HWs in a single year. In addition, few studies have systematically examined the factors affecting the duration of HWs by analyzing thermodynamic processes and the evolution of large-scale circulation systems. To address these gaps, we analyzed the occurrence of compound HWs during the 2011–2024 boreal summers in mainland Spain. Based on the coverage of the HWs, we selected three extensive compound HWs that affected approximately half of mainland Spain. By analyzing their thermodynamic causes (local temperature variation and soil–atmosphere interactions) and the large-scale circulation dynamic causes (Azores High anomalies and high-pressure ridge effects), this work offers valuable insights for the study of HWs in Spain and helps to understand the thermodynamic and dynamic mechanisms behind the extensive compound HWs.

2. Materials and Methods

2.1. Study Area

The study focuses on mainland Spain, located in southwestern Europe, spanning from 36°00′N to 43°47′N latitude and 9°18′W to 3°19′E longitude (Figure 1). This region features complex topography comprising plateaus, mountain ranges, and coastal plains. According to the Köppen–Geiger classification, Spain exhibits remarkable climatic diversity. Southern regions such as Andalusia and Valencia experience a Mediterranean climate characterized by hot, dry summers. Inland areas, including Zaragoza and Murcia, feature a semi-arid climate, while the central plateau and other high-altitude zones exhibit continental conditions, all of which share significant diurnal temperature variations. In contrast, the northern coastal areas maintain a temperate maritime climate with relatively mild summers. This unique combination of climatic zones and topographic complexity makes mainland Spain an ideal natural laboratory for investigating HW formation mechanisms.

2.2. Data

This paper takes daily maximum air temperature (Tmax) and daily minimum air temperature (Tmin) at meteorological stations in mainland Spain during the 1981–2024 boreal summers from the National Oceanic and Atmospheric Administration (NOAA, https://www.ncei.noaa.gov/pub/data/ghcn/daily/ (accessed on 7 January 2025)). The National Centers for Environmental Information (NCEI) oversees the standardization of meteorological station data through a systematic quality control process to guarantee data reliability before public dissemination [24]. Therefore, we directly utilized the raw meteorological station data without implementing supplementary quality control procedures during processing. Research has confirmed that ECMWF’s (European Center for Medium-Range Weather Forecasts) Reanalysis 5 data can reliably fill gaps in in situ observations, and its applicability to European heatwave studies has been validated [25]. After excluding stations with >10% missing data relative to their full expected record [26], we supplemented missing values using 2m temperature (T2M) from ECMWF’s Reanalysis 5 data (ERA5) with linear regression [27] (see Appendix A for detailed preprocessing steps), retaining 40 stations for analysis (Figure 1).

Datasets used for dynamic and thermodynamic analysis are taken from ERA5, which has been frequently used in studies about HWs [28,29,30]. In this paper, 2m temperature (T2M), surface net solar radiation (SNSR), volumetric soil water layer 1 (SoilW, used to characterize soil moisture content), surface latent heat flux (SLHF) and surface sensible heat flux (SSHF), are taken from the “ERA5 hourly data on single levels from 1940 to present” dataset (https://cds.climate.copernicus.eu/datasets/reanalysis-era5-single-levels?tab=overview (accessed on 2 February 2025)), which are grid data with a temporal resolution of 1 h and a spatial resolution of 0.25° × 0.25°. Geopotential, the v-component of wind, the u-component of wind, temperature, and vertical velocity are taken from the “ERA5 hourly data on pressure levels from 1940 to present” dataset (https://cds.climate.copernicus.eu/datasets/reanalysis-era5-pressure-levels?tab=overview (accessed on 6 February 2025)), which are grid data with a temporal resolution of 1 h, a spatial resolution of 0.25° × 0.25°, and a total of 37 unequally spaced pressure layers from 1 hPa to 1000 hPa. Given the relatively small diurnal variations in large-scale atmospheric circulation, we examined the daily large-scale circulation during three compound HWs using the 850 hPa temperature field, wind field, and 500 hPa geopotential field at 12:00 UTC in Section 3.3. The information for the datasets used in the study are listed in

Table 1. Summary of datasets used in the study.

Data Source	Data Type	Temporal Range	Spatial Range	Purpose
NOAA	Tmax and Tmin at meteorological stations	1 June–31 August for each year from 2011 to 2024 (daily)	40 stations in mainland Spain	Analysis of HWs in mainland Spain from 2011 to 2024
		25 May–7 September for each year from 1981 to 2010 (daily)		Calculation of the 95th percentile of daily temperatures using a sliding 15-day window
ERA5	2m temperature, surface net solar radiation, volumetric soil water layer 1, surface latent heat flux, and surface sensible heat flux	16–18 June 2017, 16–18 June 2022, 22–24 August 2023 (hourly)	Range: 10°W–4°E, 35°N–44°N Resolution: 0.25° × 0.25°	Analysis of the soil–atmosphere interactions
		16–18 June from 1981 to 2010, 22–24 August from 1981 to 2010 (hourly)		Climatology
	v-component of wind, u-component of wind, and vertical velocity at 950 hPa; temperature at 925 hPa and 950 hPa	16–18 June 2017, 16–18 June 2022, 22–24 August 2023 (hourly)	Range: 10°W–4°E, 35°N–44°N Resolution: 0.25° × 0.25°	Analysis of the local temperature variation
		16–18 June from 1981 to 2010, 22–24 August from 1981 to 2010 (hourly)		Climatology
	geopotential at 500 hPa; v-component of wind, u-component of wind, and temperature at 850 hPa	16–18 June 2017, 16–18 June 2022, 22–24 August 2023 (daily at 12:00 UTC)	Range: 30°W–80°E, 10°N–70°N Resolution: 0.25° × 0.25°	Analysis of the large-scale dynamic circulation processes

.

2.3. Methods

2.3.1. Definition of a Compound Heatwave

For the preprocessed 1981–2024 meteorological station dataset, the 1981–2010 period served as the climatology to calculate the high-temperature thresholds for the 2011–2024 analysis period. Although the World Meteorological Organization’s (WMO) updated standard 30-year reference period (1991–2020) applies to 2021–2024, we maintained the 1981–2010 climatology throughout the analysis period to ensure threshold calculation consistency [31]. We separately determined whether 40 meteorological stations had experienced hot days (HDs hereinafter). For a given meteorological station, a day is classified as an HD when both its Tmax and Tmin simultaneously exceed their respective high-temperature thresholds [4]. Given mainland Spain’s varied topography and coastal-inland temperature differences, we used relative thresholds (the 95th percentile of daily temperatures calculated using a sliding 15-day window over the 1981–2010 period) to determine HDs, ensuring comparability across different geographic settings [32]. A compound heatwave was identified when multiple stations within the study area simultaneously reached the HD criteria for three or more consecutive days, and the stations covered > 5% of the total study area [4,33].

2.3.2. Estimation of Local Temperature Variations

We used the first law of thermodynamics to analyze the thermodynamic causes of compound HWs in mainland Spain during the 2011–2024 boreal summers. Factors influencing local temperature variations include horizontal advection ($-\mathbf{V}·\nabla \mathrm{T})$, adiabatic heating ($-{\left({\displaystyle \frac{\mathrm{p}}{{\mathrm{p}}_0}}\right)}^{{\displaystyle \frac{\mathrm{R}}{{\mathrm{c}}_{\mathrm{p}}}}}\omega {\displaystyle \frac{\mathsf{\partial }\theta }{\mathsf{\partial }p}}$), and diabatic heating (${\displaystyle \frac{1}{c_p}}{\displaystyle \frac{dQ}{dt}})$. Their relationship is expressed as

$${\displaystyle \frac{\mathsf{\partial }T}{\mathsf{\partial }t}}=-\mathbf{V}·\nabla \mathrm{T}-{\left({\displaystyle \frac{\mathrm{p}}{{\mathrm{p}}_0}}\right)}^{{\displaystyle \frac{\mathrm{R}}{{\mathrm{c}}_{\mathrm{p}}}}}\omega {\displaystyle \frac{\mathsf{\partial }\theta }{\mathsf{\partial }p}}+{\displaystyle \frac{1}{c_p}}{\displaystyle \frac{dQ}{dt}}$$

(1)

where $\mathrm{T}$ is the temperature at pressure p. $\mathbf{V} \mathrm{and} \mathsf{\omega }$ are the horizontal speed of air and speed of air motion in the downward direction. ${\mathrm{p}}_0$, R, and $c_p$ are the standard atmospheric pressure (1000 hPa), gas constant (287 J${\mathrm{k}\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$), and air-specific heat at constant pressure (1004 J${\mathrm{k}\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$). The potential temperature $\theta$ normally shows a decreasing trend as atmospheric pressure rises, which is defined as

$$\theta =T{\left({\displaystyle \frac{p_0}{p}}\right)}^{{\displaystyle \frac{R}{c_p}}}$$

(2)

Substituting this expression into Equation (1) yields:

$${\displaystyle \frac{\mathsf{\partial }T}{\mathsf{\partial }t}}=-\mathbf{V}·\nabla \mathrm{T}+\omega ({\displaystyle \frac{T}{P}}{\displaystyle \frac{R}{c_p}}-{\displaystyle \frac{\mathsf{\partial }T}{\mathsf{\partial }p}})+{\displaystyle \frac{1}{c_p}}{\displaystyle \frac{dQ}{dt}}$$

(3)

In Equation (3), Q represents the energy gained or lost per unit mass of air due to diabatic processes. The main sources of Q include the absorption of shortwave solar radiation, net longwave radiation (the difference between longwave radiation absorbed by air and that emitted outward), energy from water vapor phase changes (heat release during condensation and heat absorption during evaporation), and turbulent heat fluxes (SLHF and SSHF transferred to the atmosphere through turbulence, which is related to Equation (4)). The calculation of Q is complicated due to its multiple contributing sources, so we first calculated the temperature tendency, horizontal advection, and adiabatic heating, and then calculated diabatic heating according to Equation (3) [34]. In Section 3.2.1, we used the v-component of wind, the u-component of wind, temperature, and vertical velocity at 950 hPa to analyze local temperature variations. For the calculation of temperature tendency, T was backward-differentiated with respect to time. For the calculation of horizontal advection, we first vectorially composed the $\mathbf{V}$ wind field from v-component and u-component of wind, then applied backward differencing to T in two-dimensional space. For the calculation of adiabatic heating, ${\displaystyle \frac{\mathsf{\partial }T}{\mathsf{\partial }p}}$ was calculated by subtracting T at 925 hPa from T at 950 hPa. Finally, the hourly grid data for the calculated temperature tendency, horizontal advection, adiabatic heating, and diabatic heating were spatially averaged across mainland Spain.

2.3.3. Analysis of Land Surface Thermal Processes

To analyze the effect of land surface thermal processes on the formation of compound HWs, we used the land surface energy balance equation:

$$R_n=H+LE+G_0$$

(4)

$$R_n=S_d-S_u+L_d-L_u$$

(5)

where H and LE are SSHF and SLHF. ${\mathrm{G}}_0$ is the soil heat flux, whose magnitude is relatively small, so it can be neglected in our calculations [35]. ${\mathrm{S}}_{\mathrm{d}}-{\mathrm{S}}_{\mathrm{u}}$, ${\mathrm{L}}_{\mathrm{d}}$, and ${\mathrm{L}}_{\mathrm{u}}$ are SNSR, surface thermal radiation downwards (STRD), and ground radiation. In ERA5, SNSR, STRD, SLHF, and SSHF are provided as hourly accumulated values (in J${\mathrm{m}}^{-2}$). Additionally, ERA5 specifies downward as the positive direction, so SLHF and SSHF released from the surface to the atmosphere are represented as negative values. In this paper, to facilitate analysis of changes in surface energy output during HWs, we multiplied both SLHF and SSHF by a coefficient of −1. In Section 3.2.2, we first calculated the daily mean values of T2M, SNSR, SLHF, SSHF, and SoilW for each grid point during the study period and then determined their anomalies in the daily mean relative to the 1981–2010 climatology. Finally, we analyzed the spatial correlation between the anomalies in the daily mean of SNSR, SLHF, SSHF, and SoilW and the anomalies in the daily mean of T2M (calculating the Pearson correlation coefficient for all grid points across mainland Spain for a specific date).

3. Results and Discussion

3.1. The Selection of Three Extensive Compound Heatwaves in Mainland Spain from 2011 to 2024

Figure 2, showing the daily count of meteorological stations that reached the HD criteria throughout the 2011–2024 boreal summers in mainland Spain, reveals that compared with 2011–2014, HDs occurred more frequently in mainland Spain from 2015 to 2024, especially in 2015, 2017, 2022, and 2023. On six dates (27 June 2012, 17 June 2017, 3 August 2018, 17 June 2022, 14 July 2022, and 23 August 2023), over 50% of the total stations reached HD criteria. To ensure comparability across events with varying durations, we analyzed the coverage of six HWs using three-day windows (the minimum duration of the HW) centered on each peak date (Figure 3). It can be seen that during 26–28 June 2012 and 2–4 August 2018, only a small number of stations (black triangles in Figure 3a,c) on mainland Spain met the HW criteria. Due to the small number and scattered distribution of these stations, according to the definition in Section 2.3.1, we can even conclude that no HWs occurred on mainland Spain during these two periods. The 13–15 July 2022 event showed regional clustering but was confined to central and northwestern mainland Spain (Figure 3e). In contrast, events on 17 June 2017, 17 June 2022, and 23 August 2023 affected approximately 50% of mainland Spain (Figure 3b,d,f), qualifying as extensive HWs. Furthermore, the meteorological stations that reached the HD criteria on the peak date of these events nearly covered the entire mainland of Spain. To analyze extensive compound HWs, we selected these three events centered on 23 August 2023, 17 June 2017, and 17 June 2022 based on the spatial coverage of the HWs. To ensure consistent analysis despite duration disparities, we set three-day windows centered on each event’s peak date to analyze the peak phase of three extensive HWs.

3.2. Analysis of the Thermodynamic Causes of Three Extensive Compound Heatwaves

3.2.1. Local Temperature Variation

To investigate the thermodynamic processes driving local temperature variations during three compound HWs, we analyzed the hourly regional means of 950 hPa temperature tendency, horizontal advection, adiabatic heating, and diabatic heating for each event and its corresponding climatology over mainland Spain (Figure 4). As shown in Figure 4a, temperature tendency during the 2017 and 2023 HWs generally exceeded their climatological values, indicating accelerated daytime warming and weakened nighttime cooling that favored high temperatures during the day and night. Specifically, the daily maximum of temperature tendency during the 2017 HW reached 1.5 K${\mathrm{h}}^{-1}$, exceeding climatology by about 0.3 K${\mathrm{h}}^{-1}$. The 2023 HW exhibited a maximum of 1.4 K${\mathrm{h}}^{-1}$, which was about 0.2 K${\mathrm{h}}^{-1}$ higher than the climatology. The anomalies in temperature tendency during the 2017 HW were consistently higher than those in 2023, which suggests more rapid warming and slower cooling in 2017, contributing to the prolonged persistence of the HW. This aligns with the long duration of the 2017 HW shown in Figure 2. During 16–17 June 2022, anomalies in temperature tendency were intermittently positive, but the maximum reached 0.7 K${\mathrm{h}}^{-1}$. Negative anomalies emerged on 18 June 2022, indicating slower warming and accelerated cooling relative to climatology. Correspondingly, Figure 2 shows an abrupt decline in stations that reached HD criteria on 18 June 2022.

According to the thermodynamic equation for local temperature variations (Equation (3)), temperature tendency depends on horizontal advection, adiabatic heating, and diabatic heating. Horizontal advection represents heat transport by atmospheric flow. When winds blow from warmer to cooler regions, the wind vector $\mathbf{V}$ opposes the temperature gradient $\nabla \mathrm{T}$, resulting in positive horizontal advection ($-\mathbf{V}\bullet \nabla \mathrm{T}$ > 0, warm advection) that produces a warming effect at the destination region. Figure 4b demonstrates that during all three compound HWs, horizontal advection was predominantly negative except for brief periods from 16 to 17 June 2022, indicating its cooling effect opposed the development of HWs. Specifically, horizontal advection was consistently smaller than its climatological values in both 2017 and 2023, with anomalies ranging from −0.3 to −0.1 K${\mathrm{h}}^{-1}$, revealing enhanced negative contributions during these HWs. On 16 and 18 June 2022, the negative contributions of horizontal advection generally exceeded climatological norms, with anomalies reaching −0.4 K${\mathrm{h}}^{-1}$ on 18 June. Notably, the negative contribution of horizontal advection was smaller than climatology, with intermittent positive advection occurring during some hours on 17 June 2022.

Adiabatic heating describes temperature variations in an air parcel due to purely compressional or expansion processes without heat exchange. Subsiding air parcels experience pressure increases and volumetric compression, converting external work into thermal energy through the adiabatic process. Adiabatic heating was predominantly greater than zero during the initial two days of the three compound HWs and provided positive contributions to the formation of HWs. However, negative contributions increased on the final day. Compared with climatological values, anomalies in adiabatic heating during the 2017 HW were consistently positive, peaking at approximately 0.15 K${\mathrm{h}}^{-1}$. Similarly, the 2023 HW exhibited maximum positive anomalies near 0.1 K${\mathrm{h}}^{-1}$, indicating anomalously enhanced positive contributions from adiabatic heating during the HWs. Although adiabatic heating during the 2022 HW was greater than climatological values overall, the deviation was marginal (Figure 4c). Diabatic heating represents changes to an air parcel’s internal energy through energy transfer processes, including radiative flux divergence, latent heat release, and turbulent thermal diffusion. The comparison of Figure 4a,d reveals that the variation trends of the temperature tendency and diabatic heating are consistent. Relative to horizontal advection and adiabatic heating, the magnitude of diabatic heating was the largest, and its maximum value during the three compound HWs reached 1.5 K${\mathrm{h}}^{-1}$, which demonstrates diabatic heating’s dominant positive contributions to the formation of HWs. In addition, diabatic heating consistently exceeded climatological values during all three HWs, with maximum anomalies of approximately 0.4 K${\mathrm{h}}^{-1}$ in 2017, 0.75 K${\mathrm{h}}^{-1}$ in 2022, and 0.3 K${\mathrm{h}}^{-1}$ in 2023, which suggests that the warming effect of diabatic heating was anomalously large during the HWs.

3.2.2. Soil–Atmosphere Interactions

The analysis in Section 3.2.1 reveals that diabatic heating played the primary role in the formation of the three compound HWs. Soil–atmosphere coupling directly drives diabatic heating through sensible heat, latent heat, and radiative fluxes and is a central part of the land–atmosphere system’s energy balance [36,37]. Therefore, we utilized the soil–atmosphere coupling framework to conduct a detailed analysis of the roles of solar radiation, SLHF, SSHF, and soil moisture in the formation of HWs. As can be seen in Figure 5, anomalies in the daily mean of T2M (T2M-DM) during the three compound HWs were almost universally positive over mainland Spain. Moreover, the spatial distribution of the maximum T2M-DM anomalies for each event consistently exhibited an evolution pattern from the west to the north. Among them, the 2022 HW displayed the largest positive T2M-DM anomaly, which exceeded 10 °C across most regions. Analysis combining Figure 5 and Figure 6 indicates that when T2M-DM anomalies were entirely positive over mainland Spain on 18 June 2017 and 18 June 2022, anomalies in the daily mean of SNSR (SNSR-DM) were predominantly negative over most areas, which contradicts the commonly observed phenomenon of increased SNSR during HWs [38]. Additionally, on 22 and 23 August 2023, SNSR-DM anomalies were the largest, with anomalies of about 4 × 10⁵ Jm⁻² in northern mainland Spain. However, the corresponding T2M-DM anomalies on these days were relatively small, generally below 5 °C across most regions. To analyze the relationship between T2M-DM anomalies and SNSR-DM anomalies during the three compound HWs more clearly, we calculated the spatial correlation coefficients between the two (

Table 2. Correlation coefficients between anomalies in the daily mean of SNSR, SLHF, SSHF, and SoilW and anomalies in the daily mean of T2M (Blanks indicate values that did not pass the 0.05 significance test).

	16–18 June 2017			16–18 June 2022			22–24 August 2023
T2M-SNSR	−0.123		−0.432	−0.353	0.521	−0.284	0.121	0.321	0.133
T2M-SLHF	−0.330	−0.496	−0.511	−0.395	−0.347	−0.288	0.221	−0.131	−0.128
T2M-SSHF	−0.104				0.236	−0.075	−0.281	−0.223
T2M-SoilW	−0.223	−0.643	−0.500	−0.207	−0.600	−0.460	0.116	−0.476	−0.334

). The results show that, except for 18 June 2017 and 17 June 2022, the spatial correlation between the two was weak (|r| < 0.4) during most periods. This phenomenon indicates that the contribution of solar radiation to the formation of three HWs exhibited spatiotemporal heterogeneity, meaning that it may exhibit a positive contribution in certain regions or periods, while under other conditions it may exhibit a negative contribution.

As shown in Figure 7, most of mainland Spain during the three compound HWs exhibited negative anomalies in the daily mean of SLHF (SLHF-DM). Except for 23 August 2023, SLHF-DM anomalies and T2M-DM anomalies showed a consistent negative correlation overall (Table 2). When the T2M-DM anomalies were the largest on 18 June 2017 and 18 June 2022, the spatial extent of the negative SLHF-DM anomalies was also the largest, covering nearly the entire mainland of Spain. In particular, the SLHF-DM anomalies in northern mainland Spain were less than −3 × ${10}^5$ J${\mathrm{m}}^{-2}$, corresponding to the distribution in which the maximum positive T2M-DM anomalies occurred in the north. On 23 August 2023, positive SLHF-DM anomalies were observed over western mainland Spain, with anomalies in the northwest reaching 2 × ${10}^5$ J${\mathrm{m}}^{-2}$. On this day, positive T2M-DM anomalies in western Spain were generally below 5 °C, and some parts of the western border even exhibited negative anomalies. The negative SLHF-DM anomaly indicates a reduction in latent heat flux released from the surface to the atmosphere compared with the climatology during the HWs. Although the correlation between anomalies in the daily mean of SSHF (SSHF-DM) and T2M-DM anomalies was weak (Table 2), the SSHF-DM anomalies were overall positive across mainland Spain during the three compound HWs (Figure 8). In other words, the sensible heat flux released from the surface to the atmosphere increased during the HWs. However, the positive SSHF-DM anomalies in eastern mainland Spain were larger than 3 × ${10}^5$ J${\mathrm{m}}^{-2}$ on 22 and 23 August 2023, yet the positive T2M-DM anomalies were smaller than in surrounding areas. Notably, the SSHF-DM anomalies over western mainland Spain on 23 August 2023 reached approximately 3 × ${10}^5$ J${\mathrm{m}}^{-2}$, but T2M-DM anomalies were negative in that region at the same time. The above analysis indicates that while SLHF release decreased and SSHF increased anomalously during HWs, positive SSHF anomalies caused excessive energy loss from the surface, which was not conducive to the formation of the HWs.

Figure 9 indicates that soil moisture anomalies were predominantly negative over most of mainland Spain during the three HWs. According to Table 2, except for 23 August 2023, T2M-DM anomalies and anomalies in the daily mean of SoilW (SoilW-DM) showed a negative spatial correlation. On 18 June 2017 and 18 June 2022, when the T2M-DM anomalies were largest, the soil dryness was also most severe, with anomalies ranging between approximately −1.5 and −1 ${\mathrm{m}}^3{\mathrm{m}}^{-3}$. On 23 August 2023, soil in western mainland Spain was wetter than normal with anomalies greater than 0.5 ${\mathrm{m}}^3{\mathrm{m}}^{-3}$, coinciding with relatively small T2M-DM anomalies. In summary, the soil was anomalously dry during the HWs. This occurred because lower soil moisture reduced soil evaporation, thereby decreasing the latent heat flux released from the surface to the atmosphere while increasing the sensible heat flux. SSHF can directly heat the atmosphere, and its effect is more pronounced than SLHF [39]. This finding aligns with our analysis of Figure 7 and Figure 8. Overall, SLHF and SSHF are two crucial factors in the diabatic heating process, directly impacting the surface energy balance. Soil moisture played a significant role in the formation of the three compound HWs, and it indirectly affected the generation of HWs by modulating changes in SLHF and SSHF.

3.3. Large-Scale Dynamic Circulation Processes During Three Extensive Compound Heatwaves

In the atmospheric vertical structure, the 850 hPa level (lower troposphere) minimizes direct surface interference while capturing low-level thermal advection, and the 500 hPa level (mid-troposphere) depicts mid-tropospheric steering flows, critical for tracking large-scale dynamic processes. To investigate the anomalies in large-scale dynamic circulation processes during the three compound HWs, we analyzed the daily distributions of the 850 hPa temperature and wind fields and the 500 hPa geopotential height field over the domain of 10°N–70°N and 30°W–80°E (Figure 10). The 500 hPa geopotential height field indicates that mainland Spain was under the combined influence of the Azores High (black 588dagpm line range) and a high-pressure ridge during the three compound HWs. The northern part of the standard climatological normals (blue 588dagpm line range) is located around 30°N, not extending to cover mainland Spain. However, during all three compound HWs, the Azores High exhibited an anomalous eastward and northward extension. It extended northward to approximately 50°N and dominated the whole of mainland Spain. Furthermore, geopotential height values within the core region of the Azores High reached 592dagpm or even 594dagpm. The mean of 500 hPa geopotential height (GH500) anomalies across mainland Spain generally exceeded 10dagpm in the initial two days of the three HWs, with the exception of 23 August 2023, when the value was slightly less than 10dagpm (

Table 3. The daily mean 500 hPa geopotential height anomalies averaged over the region 10°W–4°E, 35°N–45°N during the three HWs.

	16–18 June 2017			16–18 June 2022			22–24 August 2023
Z500 anomaly (dagpm)	+12.92	+11.02	+7.02	+10.97	+12.33	+6.30	+10.29	+9.59	+8.44

). These patterns confirm an anomalously intensified Azores High. On the one hand, strong subsidence airflow is typically prevalent within the core control region of the Azores High, which is conducive to adiabatic heating. On the other hand, suppressed convective activity, clear skies, and minimal precipitation under the Azores High’s dominance will lead to soil drying and elevated land surface temperatures. These higher surface temperatures, in turn, further promote soil moisture evaporation. This positive feedback mechanism collectively contributes to the generation and maintenance of HWs [40]. The region under the control of the high-pressure ridge corresponds to a warm air mass at 850 hPa with temperatures around 20 °C, and the ridge line of the high-pressure ridge crosses mainland Spain. This indicates that mainland Spain was controlled by the ridge line of the warm high-pressure ridge during the three compound HWs. Regions under the influence of the warm high-pressure ridge exhibit similar weather characteristics to the region under the control of the Azores High, with the same strong subsidence airflow and suppressed precipitation. However, compared with the Azores High, high-pressure ridges are typically less stable and have shorter durations. Analysis of the 850 hPa wind field reveals the presence of a weak divergent flow over mainland Spain during the three compound HWs. The divergent flow is also conducive to adiabatic heating. In summary, a similar large-scale circulation configuration prevailed over mainland Spain during the three compound HWs. Mainland Spain was simultaneously controlled by an anomalously intense Azores High and the ridge line of a warm high-pressure ridge. Under this dual influence, subsidence in the vertical direction is enhanced, leading to more pronounced adiabatic heating near the surface. The Azores High provides a stable, large-scale circulation background, while the high-pressure ridge further hinders the propagation of planetary-scale waves in the westerlies, increasing the stability of the system and making it more resistant to disruption by cold air masses. Under the influence of a stable system, exacerbated soil drying can increase the intensity and prolong the duration of the HW [41].

The intensity and duration of HWs are often closely linked to the evolution of large-scale circulation systems [42]. Although the structure of the large-scale circulation system was similar among the three compound HWs, their evolution differed. For the 2017 compound HW, the high-pressure ridge gradually evolved from a narrow shape to an omega-shaped configuration. On 18 June 2017, a cut-off low appeared upstream, and the high-pressure ridge tended to evolve into a blocking high. The structure of blocking high is stable, which is conducive to the maintenance of HWs [43]. This feature is consistent with the long duration of the 2017 HW shown in Figure 2. During 16–18 June 2022, the high-pressure ridge exhibited an omega shape, with a cut-off low forming upstream. The high-pressure ridge also possessed characteristics of a blocking high. However, both the high-pressure ridge and the Azores High gradually shifted eastward. On 18 June 2022, the Azores High’s influence was confined to central and eastern parts of mainland Spain, during which mean of GH500 anomalies across the mainland Spain rapidly decreased to 6damgp. This marked a weakening of the Azores High’s dominance over the region, ultimately leading to the gradual dissipation of the HW. This is consistent with the rapid decline in the number of meteorological stations meeting the HD criteria after 18 June 2022 in Figure 2. On 22 August 2023, the Azores High dominated nearly all of Southern Europe, extending anomalously eastward to approximately 80° N, and its central pressure reached 594dagpm, covering the entirety of mainland Spain. Consequently, the Azores High was exceptionally strong in 2023, which led to the highest intensity of the compound HW in 2023, with the highest number of meteorological stations reaching the HD criteria (Figure 2). However, the rapid evolution of the high-pressure ridge, whose axis shifted from central to eastern mainland Spain, hindered the prolonged persistence of the HW over the region.

4. Conclusions

We utilized NOAA meteorological station data to statistically analyze the occurrence of compound HWs during the 2011–2024 boreal summers in mainland Spain. The study reveals that HDs occurred more frequently over mainland Spain during 2015–2024 compared with 2011–2014, particularly in 2015, 2017, 2022, and 2023. Pérez-García et al. [44] also detected HWs in 2017, 2022, and 2023 in their study of HWs in northwestern Spain from 2001 to 2023. Based on the spatial extent of the HWs, we selected three compound HWs occurring in 2017, 2022, and 2023 that affected approximately half of mainland Spain as our study cases.

Using ERA5 reanalysis data, combined with the first law of thermodynamics for local temperature variations and the surface energy balance, we analyzed the thermodynamic causes (local temperature variation and soil–atmosphere interactions) and the large-scale circulation dynamic causes (Azores High anomalies and high-pressure ridge effects) of the three extensive compound HWs. Our study shows that the three HWs had similar thermodynamic heating processes and large-scale dynamic circulation backgrounds. For the three factors determining temperature tendency—horizontal advection, adiabatic heating, and diabatic heating—horizontal advection exerted a larger negative contribution relative to the climatology in the formation of the three compound HWs. In contrast, the positive contributions of adiabatic heating during the HWs were anomalously large compared with the climatology. Most significantly, diabatic heating made a major positive contribution to HW formation, and the positive contribution of diabatic heating was anomalously large during the HW. From the soil–atmosphere coupling perspective, solar radiation and soil moisture are two key factors contributing to HW formation. In this study, although we observed anomalously increased solar radiation during the three compound HWs, its contribution to the formation of the three HWs exhibited spatiotemporal heterogeneity. Soil moisture deficit was the primary factor in the formation of the three HWs. Analysis of large-scale circulation processes indicates that a similar large-scale circulation configuration prevailed over mainland Spain during the three compound HWs. The region was simultaneously controlled by an anomalously intense Azores High and the ridge line of a warm high-pressure ridge, accompanied by a weak divergent flow. Serrano-Notivoli et al. [8] also found the role of subtropical ridge patterns and persistent blocking in their study of the 2022 summer HW in Spain. In addition, we explained the differences in the duration of the three compound HWs in terms of thermodynamic processes and the evolution of large-scale circulation systems.

Although our study has conducted a comprehensive analysis of the similarities and differences in the formation mechanisms of three extensive compound HWs over mainland Spain during 2011–2024 from both large-scale circulation dynamics and local thermodynamic perspectives, several limitations should be acknowledged. To ensure comparability across events, our analysis focused specifically on the peak phases (defined as a three-day period centered on the day with the highest number of meteorological stations meeting the HD criteria) of three HWs, which may not fully capture the complete evolution of HW processes. Furthermore, while we examined the overall characteristics and causes of HWs across mainland Spain, localized contributing factors such as urban heat island effects were not considered. Future research should expand the selection criteria, such as HWMI values for HWs, and increase the number of analyzed cases to better understand the full-range characteristics (including duration and propagation patterns) and formation mechanisms under different classification frameworks. Additionally, investigating regional variations in HW formation by accounting for factors like NDVI, urban heat islands, and land cover types represents an important research direction. Beyond soil moisture anomalies during HWs, analysis of anomalies in parameters such as precipitable water (PW) and groundwater content would further our understanding of interactions between Earth systems.

According to our study findings, the occurrence of HDs on mainland Spain has become more frequent in recent years, and the occurrence frequency of extensive HWs has also increased. Therefore, the development of an early warning system for HWs is highly necessary. Our study indicates that the large-scale circulation patterns underlying extensive HWs over mainland Spain exhibit distinct anomalous characteristics. Consequently, by predicting the evolutionary trends of large-scale circulation systems, timely warnings for extensive HWs can be issued. Additionally, our study has revealed a correlation between soil moisture and temperature. Therefore, installing misting systems in urban areas with low vegetation coverage, such as city squares, can help mitigate land surface temperature increases to some extent. In summary, our study provides a reference for studies on HWs in Spain while also offering a theoretical foundation for the development of HW mitigation strategies.