On the persistence and related mechanisms for day–night compound humid heat extremes in the Northern Hemisphere

Hot extremes pose adverse impacts on human health and ecosystem, leading to aggravated damage when they combine high-humidity and occur in the both daytime and nighttime. Although considerable studies have focused on hot extremes, understandings about day–night Compound humid heat (quantified by Moist Enthalpy) Extremes (CMEEs) are still lacking. This work investigates their frequency, linear trends and temporal persistence in the Northern Hemisphere, and two typical vulnerable regions are selected as Central Europe (CE) and the Arabian Peninsula (AP), both exhibiting high frequency and positive trends, but with contrasting persistence, which is quantified by the bivariate Dynamical System method. Results reveal their regional dependence and physical processes: the dual importance of sensible and latent heat in CE is attributed to the combination of an anomalous anticyclone and evaporation, whereas the dominance of latent heat in AP is largely owing to the convective precipitation. CMEEs in AP can be further divided into two groups with distinct persistence, and this disparity actually depends on the preceding precipitation duration and its associated water vapor supply.


Introduction
Hot extremes have posed severe threats to society across the globe through their impacts on human health, ecological system, and economic productivity (Gasparrini and Armstrong 2011, Wernberg et al 2013, Matthews et al 2017, Mora et al 2017, Ummenhofer and Meehl 2017).In a warming climate, positive trends in hot extremes have been reported in their frequency, intensity, and duration (Meehl et al 2007, Perkins et al 2012, Suarez-Gutierrez et al 2020), and this increasing tendency is projected to exacerbate in the near future (Lee andMin 2018, Fischer et al 2021), leading to more difficulties in the related management and risk prevention for governments around the world.
Recently, some studies have noticed the great contribution of humidity to heat extremes, which plays an important role in determining the heat stress perceived by the human body (Fischer and Knutti 2013, Buzan and Huber 2020, Raymond et al 2020, Ridder et al 2020).When a hot environment is accompanied by high humidity, the efficiency of sweat evaporation will be suppressed, and any prolonged exposure to an environment with skin temperature larger than 35 • C is radically beyond tolerance.Serious health-related consequences may be aroused, resulting in the increased morbidity of chronic diseases and the associated loss of labor productivity (Sherwood and Huber 2010, Hanna and Tait 2015, Pal and Eltahir 2016).Moreover, it is not necessarily the daytime extremes always responsible for the adverse impacts, human needs cooling recuperation during the night to relieve the proceeding daytime heat stress, which is deprived by the subsequent nighttime heat.Excluding the influence from nighttime high temperature will induce significant underestimation of the heat-induced damages (Chen andZhai 2017, Wang et al 2020).Especially, sequential occurrences of hot day and hot night within 1 d (termed as compound day-night factor) are more threatening to human health (Murage et al 2017).Therefore, it is also worthwhile to consider the day-night compound factor in the investigation of hot extremes.
Humidity has been reported of vital importance in the formation of day-night compound hot extremes (Li et al 2021, Guo and Fu 2023, Wu et al 2023).While daytime high temperature is mainly attributed to the increase in solar radiation, convergent humidity is the dominant cause of nighttime hot extremes, which could absorb the long-wave radiation emitted by the ground surface and re-emit it back, thus reducing the long-wave radiative cooling and trapping more energy at night.Over most land areas in the Northern Hemisphere (NH), there is a higher probability of an ensuing hot night following a daytime hot extreme when the anomalous humidity is positive (figure S1; method in text S1).Hence, it is reasonable and imperative to combine the compound humid-hot and day-night factors jointly.
Our investigation aims to give a primary understanding of the day-night compound humid heat extremes over the NH, which accounts for most population and land area in the world.We first adopt the Moist Enthalpy (ME) to measure the humidhot factor, and define Compound day-night ME Extremes (CMEEs) as those days with ME exceeding preset criteria by both day and night (details in section 2.3).Among various characteristics of extreme events, sociometric impacts largely depend on their temporal duration.Therefore, we further utilize the Dynamical System persistence to some hotspot regions based on a bivariate framework to take into account daytime and nighttime ME concurrently.This method is established in highdimensional phase-space containing both temporal and spatial information, thus helpful in analyzing extreme events over a specific domain.Through composite analysis, we also investigate the possible mechanisms behind CMEEs regionally and figure out what physical processes cause the large discrepancy in their persistence.

Datasets
In this study, we mainly adopt ERA5 gridded reanalysis (Hersbach et al 2020) from 1981 to 2020, with a horizontal resolution of 0.25 • × 0.25 • and a temporal resolution of one hour, including 2 m temperature and dewpoint temperature, sea level pressure, precipitation, evaporation, geopotential height, vertical and horizontal winds, divergence of moisture flux, and Convective Available Potential Energy (CAPE).The selection of daytime and nighttime is based on 2 m temperature, we regard the time where the 2 m temperature reaches its daily maximum as the daytime and its minimum as nighttime.Daily sea surface temperature (SST) is provided by OISSTv2 (Reynolds et al 2002), with a 0.25 • spatial resolution and covering the same period.Outgoing long-wave radiation (OLR) is from NOAA (Lee 2011) with a 2.5 • spatial resolution.Here we primarily focus on the boreal summertime season (June-July-August; JJA).

Calculation of moist enthalpy
To describe the extent of heat and high humidity synchronously, we calculate ME according to the procedure provided by Raymond et al (2021): where ME represents moist enthalpy (kJ kg −1 ), Q h and Q l represent sensible heat and latent heat (J kg −1 ), where L v represents latent heat of vaporization (J kg −1 ), and q represents specific humidity (kg kg −1 ), where c p represents specific heat of moist air (J kg −1 K −1 ), and T represents dry-bulb temperature (K), where r represents mixing ratio (unitless),  2018).Therefore, using other metrics would not significantly change the conclusions of our study.Meanwhile, ME has more specific physical interpretations, which consists of sensible heat Q h and latent heat Q l , enables clear separation of the contribution from temperature (sensible) and humidity (latent), thus helps better understand the mechanisms driving humid-heat extremes.

Definition of day-night compound ME extremes
In order to further consider the day-night compound factor, here we define CMEEs as days when ME in daytime and nighttime (hereafter, ME day and ME night ) both exceed the 90th percentile of its corresponding distribution of the studying period based on a centered 15 d window in each grid cell (Fischer and Schär 2010).When focusing on a specific domain, regional CMEE days are defined if at least 25% of its area is affected by CMEE (approximately covering an area of 8 × 10 5 km 2 ).Different criteria (such as 15%, 20% and 30%) are tested and no qualitative difference is found.

Temporal clustering index
In this work, we adopt a temporal day-to-day clustering index following Speizer et al (2022), defined as the average number of CMEEs in a 2 week window around each CMEE, which could demonstrate the extent to which a CMEE is accompanied by others within a week before or after.

Quantification of co-persistence
Dynamical System method (DSM) considers the successive observations of a variable over a period within a given region as a trajectory x (t) in high-order dynamical phase-space, which could approximate the evolutions of states of this variable, including both temporal and spatial information (Faranda et al 2020).A given point ζ x on this trajectory indicates a latitude-longitude map for a specific day (see figure 2 in Guo et al 2022a), then a logarithmic function g(x (t), ] can be used to measure the distances between ζ x and other points on this trajectory x (t), where 'dist' denotes the Euclidean Norm.Recurrences are defined as those points close to ζ x , suggesting that they share a highly similar configuration.In this way, the exceedances u(t, ζ x ) = g(x(t), ζ x ) − s x are able to sort all analogues of ζ x out, with s x as the top 2nd quantile of g(x (t), ζ x ).The cumulative probability distribution of u(t, ζ x ) has been proved to follow the Generalized Pareto Distribution (GPD) (Lucarini et al 2012, Faranda et al 2017a) as Two Dynamical System parameters are obtained: ) is a metric measuring instantaneous dimension, which can be interpreted as the number of degrees of freedom the system can explore locally.θ −1 (ζ x ) informs on the local persistence of the system at a given time.A higher (lower) value of θ −1 (ζ x ) implies that the trajectories x (t) will evolve more slowly (rapidly) and reside a longer (shorter) time around ζ x .Here we mainly concern the metric θ −1 , since it is closely related to the duration of extreme events.The above procedure can be further extended to a bivariate system {x (t), y(t)}, then the co-persistence θ −1 x,y is derived.The physical interpretation of the bivariate metrics is analogous to that of the univariate ones, except now we consider co-recurrences of the two variables concurrently.
In this study, we apply DSM to quantify the instantaneous persistence of ME day and ME night jointly, by regarding the evolutions of these two variables as two separate dynamical systems.For more information about DSM please refer to Faranda et al (2020) and Huang et al (2022).

Hotspots of CMEES over the Northern Hemisphere
We find CMEEs mostly occur in the subtropical desert areas and some waterside regions in midhigh latitudes (figure 1(a)), suggesting that the physical processes behind these extremes may be regiondependent.The regions most suffering from CMEEs include the Northern Africa, the Arabian Peninsula, Central Europe, Northwestern China, and the Great Lakes region.The lack of CMEEs mainly concentrates upon the tropics and Southeast Asia, probably due to their high temperature and humidity throughout the year.Most of the NH has experienced a significant positive trend in recent decades (figure 1(b)), with the highest value appearing in the Northern Africa, the Arabian Peninsula, Central Europe, South Asia, Southeast Asia, Northeast Asia, and Northwestern China.Notable attention needs to be paid to the regions where increasing trend and fundamental frequency both show a relatively larger value, so they may suffer higher vulnerability to CMEE exposure in the future.The most prominent exception to the general increase in CMEE is located in the western North America and portions of Central Asia, which has been highlighted in previous studies (Sarhadi et al 2018, Speizer et al 2022).
Apart from the frequency and trends of CMEEs, social impacts also depend on their temporal distribution.Here we adopt a temporal clustering index following Speizer et al (2022), which demonstrates the extent to which a CMEE is accompanied by others within a week before or after (figure 1(c)).We find most regions with substantial day-to-day clustering are in desert areas: the Northern Africa, the Arabian Peninsula, Northwestern China, and parts of Iran, Afghanistan and India.One may intuitively link the clustering feature with the persistence of extreme events, which has a close connection with their socio-economic repercussions.Therefore, we apply Dynamical System persistence θ −1 to further

Characteristics of regional CMEEs in CE and AP
We first calculate the co-persistence θ −1 of ME day and ME night over the two domains and compare it with the corresponding regional averaged variables (figures 2(a) and (b)).There is a well-defined linear relationship between the daytime and nighttime ME in CE, while in AP the relationship becomes much more scattered.This difference may be associated with the relatively clearer diurnal cycle in mid-latitudes than that in subtropics and tropics.As expected, the regional averaged ME day and ME night for CMEEs are apt to be larger than those of other days in Notably, we find there are two distinct groups of CMEEs in AP, where ME day , ME night and θ −1 all exhibit large discrepancy.In case of different spatial configurations offsetting each other in the following composite analysis, we apply K-means clustering method on the basis of ME day and ME night , then utilize Calinski-Harabasz criterion to determine the optimal number of clusters (Caliński and Harabasz 1974), which is two for CMEEs in AP (for simplicity we term them as AP1 and AP2 hereafter).We also apply the same procedure to CMEEs in CE, and the classified groups show no significant difference, thus we consider the CMEEs in CE as the sole cluster.The large values of ME in CE are attributed to the combined effect of large Q h and Q l concurrently, however, in AP1 and AP2, they are related to the anomalous moisture only (figure S2).The location of the highest ME in AP1 and AP2 are also disparate.In AP1, it mainly appears along the coast of the Arabian Sea, while it extends meridionally from the Persian Gulf to the Gulf of Aden in AP2, covering a much larger area.As for their temporal features, AP2 has a higher value of persistence compared with AP1 and CE (figure 2(c)), implying that the spatial pattern of this cluster will sustain longer, in accord with the lagged spatial correlation shown in figure 2(d), where AP2 has a longer duration in both ME day and ME night fields.Furthermore, the regional averaged ME day in AP1 and AP2 are larger than that in CE, while ME night is slightly lower.Instinctively, two questions arise in our study: Are the physical processes behind the CMEEs in CE and AP different?What mechanisms cause the CMEEs in AP1 and AP2 to have different persistence?

Mechanisms for CMEEs in CE and AP
Previous studies have proved the importance of precipitation in humid-hot extremes (Fischer andKnutti 2013, Rogers et al 2021), here we find it indeed playing a key role in the CMEEs over AP, which mainly comes from the convective form for both clusters, and the persistence θ −1 is closely related to the precipitation duration (figure 3(a)).In AP2, the abovenormal rainfall starts from 8 d before the CMEE day (Day −8), significantly earlier than that in AP1, which starts from Day −3, and the rainfall can also last longer in AP2, while it reaches zero rapidly on Day +3 in AP1.In CE, however, the substantial evaporation is actually the main source of the abnormal Q l (figure 3(b)), partly due to the anomalous rainfall 10 d earlier (figure 3(a)), where the rainwater is temporarily stored in the shallow soil layer, then evaporates dramatically to the atmosphere through landsurface interactions, at last the soil water reaches its minimum value on Day 0 (figures S3(a) and (b)).The corresponding evolutions of more atmospheric  variables (surface temperature, divergence of moisture flux, sensible and latent heat flux) are displayed in figure S3, where the anomalous divergence of moisture flux is much larger in AP and conforms to the characteristics of the proceeding precipitation, while the surface temperature and latent heat flux are both important in CE.These phenomena may preliminarily answer the two questions we posed before: the driving factors of the CMEEs in CE and AP are different, while the CMEEs are caused by large Q h and Q l jointly in CE, Q l is more predominant in AP; the different persistence between AP1 and AP2 largely results from the different precipitation duration.
To further investigate the underlying mechanisms responsible for the large Q h and Q l in CE, we composite some reasonable variables in figure 4.An obvious high-pressure system can be found at 500 hPa over the study region, which is usually regarded as the vital circulation to a hot extreme in Europe (Stéfanon et al 2012, Perkins 2015, Zschenderlein et al 2018).The corresponding anticyclone may lead to a clear sky and more short-wave radiation received at the surface, and the associated downdraft could also heat the surface adiabatically, in favor of the formation of large Q h .These processes have been well-documented in previous works, most of which find this positive anomaly in geopotential height is triggered by the North Atlantic Oscillation (NAO; Faranda et al 2017b, Kueh and Lin 2020).However, we find it associated with the positive North Atlantic tripole (NAT) SST mode when the hot extremes are combined with high humidity.The cooler SST in the central North Atlantic excites a low-pressure system above, then induces a zonal wave train propagating downstream and forms a southerly advection over the western part of CE, which could bring a large quantity of water vapor from the Mediterranean and Atlantic, confirming the convergent moisture flux shown in figure 4(d), eventually results in a large Q l in tandem with the abnormal evaporation (figure 4(e)).However, this southerly transfer of water vapor is insufficient during the positive-phase NAO, where the spatial pattern of geopotential height is dipolar meridionally over Europe, and the easterly advection to the south of the anomalous anticyclone will carry the lack-ofmoisture air from the inland area and lead to a dry or normal hot extreme under the high-pressure system instead of a humid one.
Compared with the approximate contribution from temperature and humidity in CE, Q l plays a dominant role independently in the CMEEs in both AP1 and AP2, mainly in virtue of the anomalous convective precipitation.In general, there are two necessary conditions for the generation of convective precipitation: strong ascending flow and abundant supply of water vapor.Here we adopt the Convective Available Potential Energy (CAPE) and moisture divergence to quantify these two factors, respectively (figures 5(a) and (b)).CAPE is the potential energy represented by the total excess buoyancy and can be used to assess the potential for the development of convection.Both AP1 and AP2 have a large CAPE exceeding 200 J kg −1 since Day −14, providing the essential energy needed for upward motion.After Day −9, CAPE in AP2 becomes slightly larger than that in AP1, and reaches 600 J kg −1 on the central day, which is nearly twice as much as that in AP1, partly explaining the difference between their precipitation duration.In fact, we find moisture convergence predominantly regulating the persistence θ −1 .Water vapor converges to the study region since Day −10 in AP2 and stays incoming until Day +3, whereas it only turns positive after Day −3 in AP1 and decays rather rapidly, which means that the study region keeps gaining moisture for more than 2 weeks in AP2, but only for 5 d in AP1, exactly confirming the rainfall period illustrated in figure 3 (a).This moisture convergence is provided by the southerly advection from the Arabian Sea, probably triggered by the wave trains from the North Atlantic to South Asia and also related to the anomalous South Asian High (SAH; figures 5(c) and (d)).The strong south or southeast wind dominates the study region from the very beginning of the precipitation in AP2, however, there always exist some northerly flows over the coastal areas of the Red Sea before the CMEE day in AP1, weakening the water vapor supply in the early stage (figure S4).

Discussion
Compared with considerable studies focusing on CE, limited work are devoted to the extreme events in AP.Notably, the SAH exhibits a large discrepancy between AP1 and AP2 in the developing stage of CMEEs (figure S4).The intensity of SAH in AP1 has experienced a significant weak-to-strong transition, with its position moving northwest gradually.This can be partly explained by the temporal distribution of the CMEEs in AP1, most of which occur in early summer (figure S5), coinciding with the climatological development of the SAH.Gui et al (2022) have summarized the position of SAH in boreal summer and found that the core of SAH lies over the northwestern Indochina Peninsula in May, and jumps onto the Tibet Plateau (TP) in June, then shift northwestward to the western edge of the TP in July, which justifies the results shown in figure S4(a).In AP2, however, the SAH presents a much wider zonal expansion, and maintains from Day −6 to Day +2 steadily.
It is also worth noting that there seems a positive interdecadal Pacific oscillation (IPO) phase in AP1, as well as a La Niña-like pattern in AP2 (figure S6).Many studies have verified the close relationship between the SAH and the anomalous SST (Xue et al 2018, Huang et al 2020, Tang et al 2023).During the positive IPO phase, a low-pressure system dominate the Central equatorial Pacific as a response to the warmer SST.Consequently, an anomalous divergence appears in the local upper troposphere, while an anomalous convergence covers the area of the Indochina Peninsula and Bay of Bengal, as a result of the enhanced vertical circulation, which favors the intensification of SAH southeastward to its climatology (Chinta et al 2021, Yang et al 2022).However, considering the way longer time scale of IPO than that of SAH, the abrupt increase of CMEEs over AP1 since 2010s (shown in figure S7) seems to be more related to the on-going global warming rather than the phase of IPO.It is also widely believed that the JJA SAH intensity is positively correlated with the strength of El Niño in proceeding winter (Cao et al 2016, Xue et al 2017).Here we find most CMEEs in AP2 occur in the second year of the rapid transition from El Niño to La Niña (figure S7), where SST exhibits negative anomaly in the current JJA but positive in the proceeding winter.Due to the westward Rossby wave excited by El Niño, the SST in tropical Indian Ocean (TIO) will get higher than normal and persist until the next summer owing to its long-term memory, known as the famous 'Capacitor Effect' (Xie et al 2009).The warmer SST in TIO may affect the Asian monsoon and cause more precipitation over the TP, then lead to an intensification of SAH through condensational heating (Ren et al 2015, Zhang et al 2016).Notably, the convective activities over the TP in AP2 show a western decrease-eastern increase dipolar pattern, and the positive anomaly even extends to the coastal area (figure 5(d)), which could result in a more eastward-extended SAH in response to the warmer SST in TIO (Liu et al 2021, Wang et al 2022).However, the association between the CMEEs in AP and the feature of SAH still calls on more investigations in our future work.

Conclusions
In this study, we first introduce the conception of CMEE, which considers the compound humid-hot and day-night factors concurrently, and investigate its frequency, linear trends and day-to-day clustering features over the NH.We identify some hotspots vulnerable to CMEEs: the Northern Africa, the Arabian Peninsula, Central Europe, and Northwestern China.All exhibit high frequency and positive trends in recent decades, thus are severely subject to CMEEs.Large discrepancy is found in the temporal clustering feature between the CE and AP, therefore we further apply DSM persistence θ −1 to the two areas and aim to find the mechanisms responsible for the CMEEs and their related disparate persistence.
By means of θ −1 , we find there is a group of CMEEs in AP (AP2) more prolonged than those in CE, while the other group (AP1) shares a similar persistence.Concerning the different mechanisms between CE and AP, the large value of ME in CE results from the combination of Q h and Q l jointly, whereas Q l independently dominates the ME in AP.During the CMEE days in CE, an anomalous anticyclone can be found over the study region, leading to the decrease in local cloud cover and increase in solar radiation received, thus favoring the formation of hot extremes.This large-scale atmospheric circulation is more likely triggered by the positive NAT SST mode rather than the NAO pattern, which is generally regarded as a key system to heatwaves over Europe in previous studies.The above-normal Q l in CE is associated with the local evaporation and the supply of water vapor carried by the southerly advection, serving as the western flank of the anticyclonic circulation.Nevertheless, the anomalous latent heat in AP mainly arises from the convective precipitation, whose duration highly affects the persistence θ −1 of CMEE.To further investigate the different duration of precipitation between AP1 and AP2, we compare their time series of CAPE and moisture divergence.Results suggest that the rainfall period primarily depends on the convergent water vapor, which is supplied by a southerly wind carrying plenty of moisture from the Arabian Sea to the study region.However, no qualitative difference is found in the CAPE between AP1 and AP2, both exhibiting a large value and providing enough potential energy for the upward motion.
This study provides primary knowledge of CMEEs both globally and regionally, contributing to the better forecasts and improvements of the risk assessment and management of these extremes.Nevertheless, there still exist some ambiguities about the physical processes behind each kind of CMEE, full understanding of CMEEs still needs further efforts.

Figure 1 .
Figure 1.(a) Frequency and (b) linear trends of CMEEs in the Northern Hemisphere from 1981 to 2020.(c) Clustering feature: average number of CMEEs in a 2 week window around each CMEE.Stippling in (b) denotes where trends are statistically significant at 0.05 significance level.The green rectangles denote the two hotspots as Central Europe (CE) and the Arabian Peninsula (AP), respectively.

Figure 2 .
Figure 2. Scatter plots of the regional averaged ME day and ME night over (a) CE and (b) AP in JJA.(c) Same as (a) and (b), but for the classified CMEEs in CE and AP.The color of the dots represents the value of co-persistence θ −1 of ME day and ME night .(d) Time delayed spatial correlation of ME day (solid lines) and ME night (dotted lines).The dashed line represents the value of 1/e.

Figure 3 .
Figure 3.Time series of anomalous (a) precipitation and (b) evaporation averaged upon those grids which meet the CMEE requirement.Negative values in (b) indicate evaporation and positive values indicate condensation.

Figure 4 .
Figure 4. Composite anomalies of (a) geopotential height at 500 hPa, (b) vertical velocity (shading) and horizontal winds (vectors) at 850 hPa, (c) sea surface temperature, (d) vertical integral of divergence of moisture flux, and (e) evaporation.Negative values in (e) indicate evaporation and positive values indicate condensation.Stippling denotes statistical significance at the 0.05 significance level by Student's t test, and only vectors passing the significance test either zonally or meridionally are illustrated in (b).The green rectangle represents the study region as CE.

Figure 5 .
Figure 5.Time series of (a) CAPE and (b) anomalous vertically integrated moisture divergence averaged upon those grids which meet the CMEE requirement.Composite anomalies of outgoing long-wave radiation (shading), horizontal winds (vectors) at 850 hPa, the 12520 gpm contour (solid line) and its climatology in JJA (dash-dotted line) at 200 hPa in (c) AP1 and (d) AP2.Stippling denotes statistical significance at the 0.05 significance level by Student's t test, and only vectors passing the significance test either zonally or meridionally are illustrated.The green rectangle represents the study region as AP.