Advances in understanding the changes of tropical rainfall annual cycle: a review

Aided by progress in the theoretical understanding, new knowledge on tropical rainfall annual cycle changes under global warming background has been advanced in the past decade. In this review, we focus on recent advances in understanding the changes of tropical rainfall annual cycle, including its four distinct features: amplitude, pattern shift, phase and wet/dry season length changes. In a warming climate, the amplitude of tropical rainfall annual cycle is enhanced, more evidently over ocean, while the phase of tropical rainfall annual cycle is delayed, mainly over land. The former is explained by the wet-get-wetter mechanism and the latter is explained by the enhanced effective atmospheric heat capacity and increased convective barrier. The phase delay over land has already emerged in the past four decades. The pattern shift under warming is marked by two features: equatorward shift of the inter-tropical convergence zone throughout the year and the land-to-ocean precipitation shift in the rainy season. The former is explained by the upped-ante mechanism and/or related to the enhanced equatorial warming in a warmer world. The latter is suggested to be caused by the opposite land and ocean surface temperature annual cycle changes in the tropics. Over tropical rainforest regions such as Amazon and Congo Basin, the dry season has lengthened in the recent decades, but the fundamental reason is still unclear. Despite the notable progress of the last decade, many gaps remain in understanding the mechanism, quantifying and attributing the emergence, narrowing the inter-model uncertainty, and evaluating the impact of tropical rainfall annual cycle changes, motivating future work guided by some directions proposed in this review.


Introduction
Spanning the lowest latitudes on Earth, the tropics are warm and moist, with abundant rainfall falling down over the regions featuring monsoons and inter-tropical convergence zones (ITCZs).But rain does not fall evenly throughout year, as it maximizes during the local summer (i.e.wet season) while much less rainfall occurs during the local winter (i.e.dry season).This annual cycle of tropical rainfall is a dominant mode of variability in the Earth's climate and water cycle, attracting many investigations on its origins and variations.The dominant driver of the annual cycle of tropical rainfall is the seasonal north-south progression of solar radiation on the zonal mean, but at regional scale, many other factors such as land-sea distribution, topography, vegetation, ocean heat flux, can also influence the rainfall annual cycle substantially.To understand the tropical rainfall annual cycle changes, we need theoretical frameworks as cornerstones.
Fortunately, the past decade has witnessed major advances in theoretical understanding on the origins and variations of tropical rainfall (e.g.Bordoni and Schneider 2008, Schneider and Bordoni 2008, Kang et al 2008, 2009, Nie et al 2010, Hurley and Boos 2013, Boos and Korty 2016).Two atmospheric energetic frameworks and an atmospheric dynamical framework have been proposed to understand the energetic and dynamical constraints on tropical rainfall variations and changes, including the response of the annual cycle to anthropogenic forcings.Hence, we will briefly introduce these frameworks before we dive into reviewing the advances in the tropical rainfall annual cycle changes.
One energetic framework is based on the convective quasi-equilibrium (CQE) assumption first proposed by Arakawa and Schubert (1974).It assumes that atmospheric convection acts on time scales much faster than the large-scale environments, yielding fluctuations of free-tropospheric temperature that are in quasi-equilibrium with fluctuations in sub-cloud moist static energy (MSE).In other words, atmospheric convection is controlled by the large-scale forcing in a statistical sense such that the stabilization of the atmosphere by convection is in quasi-equilibrium with the destabilization by the large-scale forcing.The CQE framework has been widely used to understand the relationship between large-scale environments and convection (Emanuel et al 1994, Nie et al 2010, Hurley and Boos 2013, Harrop et al 2019).In this framework, the convective instability, measured either by the vertical gradient of MSE or by the sub-cloud (or surface) MSE (or equivalent potential temperature) when assuming the upper-troposphere MSE or temperature is spatially uniform in the tropics, is the key variable.
The second energetic framework utilizes the column-integrated atmospheric energy budget equation to derive the cross-equatorial energy transport indicative of the location of the ITCZ (e.g.Frierson et al 2013, Schneider et al 2014) or to derive the divergence of atmospheric energy transport indicative of the location of the regional rainfall peak (e.g.Song et al 2020Song et al , 2021)).Foundational in this framework is the observation that the tropical atmosphere is energetically stratified with higher MSE in the upper level and lower MSE but more moisture in the lower level.Hence, an upward motion inducing precipitation and divergence above and convergence below causes a net MSE divergence and a net moisture convergence.This relationship between MSE divergence and moisture convergence facilitated by the atmospheric overturning circulation provides an energetic perspective for understanding the response of tropical rainfall to forcings across different scales.These two atmospheric energetic frameworks provide complementary views, as one considers the atmospheric column as a whole while the other considers the vertical structure of atmospheric energy distribution.Both of these two energetic frameworks have been used to understand the tropical rainfall annual cycle changes, which will be reviewed in details in the later sections.
The atmospheric dynamical framework utilizes the atmospheric momentum equation to explain the rapid onset of tropical rainfall as a swift shift of atmospheric circulation regimes (e.g.Bordoni andSchneider 2008, Schneider andBordoni 2008), i.e. from the equinox regime to the monsoon regime.In the equinox regime, the zonal momentum is dominated by mid-latitude eddies, so the atmospheric circulation cannot directly respond to variations in the thermal driving and only responds indirectly through changes in eddy momentum flux divergence.In the monsoon regime, atmospheric circulation is close to the conservation of momentum, so it can respond directly to radiative heating.Dynamical feedbacks favor a rapid transition from the equinox regime to the monsoon regime, thus explaining why monsoon onset can be more rapid than the seasonal evolution of radiative heating.This dynamical framework has been used to understand the rapid onset of the Asian monsoon in the climatological mean, but how this framework can be used to understand the tropical rainfall annual cycle changes under global warming is still lacking.The two atmospheric energetic frameworks and the atmospheric dynamical framework have been reviewed in several papers (e.g.Biasutti et al 2018, Hill 2019, Geen et al 2020), so readers are referred to the review papers for more details on these frameworks.
Aided by advances in the theoretical understanding, much progress has been made in the past decade in understanding how global warming would impact the tropical rainfall annual cycle, which is the focus of this review.Besides the three frameworks briefly introduced above, some important concepts such as the weak temperature gradient approximation (e.g.Sobel and Bretherton 2000), the upped-ante mechanism (e.g.Neelin et al 2003), and the elevated warming in the tropical atmosphere (e.g.Hansen et al 2002) are indispensable in understanding tropical rainfall and its response to warming and will be discussed.Here, we will mainly review studies published in the past decade or so and organize our discussions based on four distinct features of tropical rainfall annual cycle, including changes in amplitude, spatial pattern, phase and wet/dry season length.We focus on the response of these features to warming while recognizing that other anthropogenic forcings such as aerosols and land use land cover change also play important roles in their past and future changes.For each feature, we will introduce the phenomenon (i.e.how the feature may change), the mechanisms of the changes and the emergence (including its attribution as supported by literature).The impact of tropical rainfall annual cycle changes is then introduced.Finally, we will provide a summary and discussion on the future work.

Phenomenon
The amplitude of tropical rainfall annual cycle, or the annual range of rainfall, reflects the local summer-winter rainfall contrast, which can be estimated by the difference between the maximum and minimum monthly rainfall within a year (Chou and Lan 2012, Chou et al 2013, Huang et al 2013) or by the first harmonic mode of Fourier analysis (Song et al 2021).Chou et al (2007) found a hemispherical asymmetry of tropical precipitation anomalies between the two sides of the equator under global warming.In the summer hemisphere dominated by the ascending branch of the Hadley circulation, tropical precipitation (0 • -30 • ) shows an increasing trend.In the winter hemisphere dominated by the descending branch of the Hadley circulation, tropical precipitation has a slight decreasing trend or is unchanged under warming.Since summer and winter is usually the rainy and dry season respectively, the hemispherical asymmetry of tropical precipitation implies that the wet season becomes wetter, and the dry season becomes drier under global warming.In other words, the spatial pattern of precipitation changes widely known as wet gets wetter and dry gets drier (Chou andNeelin 2004, Held andSoden 2006) is also evident in the temporal variation.To our knowledge, Chou et al (2007) was the first study to identify an enhancement of the annual range of tropical rainfall under global warming.As shown in figures 1(a) and (b), rainfall increases more during the local rainy season under global warming, so the amplitude of tropical rainfall annual cycle will be enhanced, as confirmed by many studies (Chou and Tu 2008, Tan et al 2008, Chou and Lan 2012, Huang et al 2013, Dwyer et al 2014).Besides the enhanced annual cycle, the rainfall increase is found more evident at the equatorward side of the climatological rainband, suggesting the equatorward shift of the ITCZ throughout the year, which will be discussed in the section 2.
Regionally, the enhanced rainfall annual cycles can be found in most regions, except for about 20% of land areas, including the Amazon and many subtropical regions, such as central America, Mediterranean, southern edge of South America, Africa and Australia (Chou and Lan 2012, Chen et al 2020, Zhou et al 2022a).Chen et al (2020) further quantified this enhancement and found that the precipitation annual range would increase by 3.90% and 5.27% globally under 1.5 • C and 2.0 • C warming respectively.The additional 0.5 • C of warming would increase annual range of precipitation by 1.37%.Specifically, Zhang et al (2019) investigated the amplitude change in different land monsoons (figure 2).They found that in the northern hemisphere, except for the North American monsoon region, the Sahel and South and East Asian monsoon regions will experience an enhanced annual cycle; in the southern hemisphere, all monsoon regions show moderate changes but with large inter-model spread.

Mechanism
For the enhanced amplitude of tropical rainfall annual cycle, the most common explanation is the 'wet-get-wetter' mechanism (Chou and Neelin 2004, Held and Soden 2006, Chou et al 2009).Based on the moisture budget, increased water vapor under global warming is the dominant term for enhancing the amplitude of tropical rainfall annual cycle.Hence, the 'wet-get-wetter' mechanism can be understood through the simplified moisture budget equation p ∼ wq, where p is precipitation, w is vertical velocity and q is specific humidity.In the wet season, the vertical motion w is generally upward; while in the dry season, the vertical motion w is generally downward.When q increases as a response to global warming following the Clausius-Clapeyron relationship, we expect precipitation to increase in the wet season but decrease in the dry season.This enhances the annual range or the amplitude of the annual cycle of tropical rainfall, as shown in figure 1.This mechanism was first used to explain why wet region gets wetter and dry region gets drier under global warming (Chou andNeelin 2004, Held andSoden 2006), and it is straightforward to extend this mechanism to explain the amplified annual cycle (Chou et al 2007).
This 'wet-get-wetter' mechanism works much better over ocean than land, as the assumption of fixed relative humidity in the mechanism is more valid over ocean with unlimited water supply and it also works much better for larger domain averages as the changes in vertical velocity and other factors (e.g.changes in horizontal gradients of temperature and relative humidity) can become much more important at regional and local scales (Xie et al 2010, Huang et al 2013, Chadwick et al 2013a, 2013b, Byrne and O'Gorman 2015, Chen et al 2020, Geng et al 2020).Over ocean, the sea surface temperature (SST) warming pattern (figure 1(c)) may shape the spatial structure of vertical velocity and alter the precipitation response, shifting the precipitation changes more equatorward compared to the climatological precipitation (Huang et al 2013, Zhou et al 2019, 2020, Geng et al 2020).We will elaborate on this point in the section 2 about the pattern shift of rainfall annual cycle.Over land, in addition to the relative humidity change, the horizontal temperature gradient (Byrne and O'Gorman 2015) and seasonally-dependent soil moisture-atmosphere feedback (Zhou et al 2022a) are also found to be important in the precipitation amplitude changes.Responses of water cycle components to global-mean surface air temperature changes under RCP8.5 for submonsoon regions, including precipitation (P), evapotranspiration (E), P-E, total runoff (R), and surface (SMs) and total soil moisture (SMt).Results for the annual mean (blue) and wet (red) and dry (grey) seasons are shown.The surface and total soil moisture contents are scaled by 1/10 and 1/200, respectively, for display.The unit is kg m −2 K −1 for soil moisture and mm d −1 K −1 for others.Wet season refers to May-September for the NH and November-March for the SH, and vice versa for the dry season.The histograms denote the multimodel medians while the error bars denote the 25th-75th-percentile intervals among the models.The vertical axis has the same range for the submonsoon regions except for the global monsoon region.For regional divisions, the equator separates the NH from the SH monsoon region, 30 • W and 180 • separate the EH from the WH monsoon region, 60 • E separates the NH African from the South Asian monsoon region, and 20 • N and 100 • E separate the South Asian monsoon region from the East Asian monsoon region.All the regional domains are within 40 • S-45 • N. Reproduced with permission from Zhang et al (2019).© American Meteorological Society.Used with permission.
For the reduced amplitude of tropical rainfall annual cycle in the Amazon and many subtropical regions, it should be related to the changes in the vertical velocity, as moisture is generally increased everywhere.Chou and Lan (2012) thought it may be related to the tropical expansion under global warming (e.g.Fu et al 2006, Lu et al 2007; also see Staten et al (2018) for a review) as most of the reduced annual cycle occurs in the subtropical regions, but Zhou et al (2022a) offered a different explanation.They suggested the seasonally-varying soil moisture-atmosphere is responsible for this reduced annual cycle: in the dry season, the drying soil reduces evapotranspiration and modulates atmospheric circulation to enhance moisture convergence and increase precipitation but this feedback is not evident in the wet season.

Emergence
The amplitude changes in the tropical rainfall annual cycle are more evident in the ocean.However, the lack of long-term and reliable rainfall records over the ocean challenges the detection of amplitude changes in the observations.Chou et al (2013) found that the increased amplitude of tropical rainfall annual cycle has emerged from the observation based on one dataset (GPCP) during 1979-2010.Including another dataset, however, neither Marvel et al (2017) nor Song et al (2021) could support the finding of Chou et al (2013) and noted that the signal they identified is mainly evident in the high latitudes where satellite data is more prone to bias.Based on a formal detection and attribution analysis, Marvel et al (2017) found no evidence of an observed increase in the range between wet and dry season precipitation over the time period of 1979-2015 that could be attributed to anthropogenic forcing.In the future, the amplitude changes of precipitation annual cycle over tropical land should be examined to search the possible emergence signal, as land has much better observations and also sees enhanced amplitude under global warming.

Phenomenon
The wet-get-wetter mechanism suggests a simple pattern of rainfall increase and decrease in the climatological wet and dry regions, respectively.However, the spatial pattern of seasonal rainfall changes under global warming exhibits at least two evident shift changes: (1) precipitation shifts more equatorward throughout the year, which is more evident in the zonal mean (Chadwick and Good 2013, Huang et al 2013, Chadwick et al 2013a, 2013b, 2014); (2) seasonally, precipitation also shifts from land to ocean in the local rainy season (Chadwick et al 2014, He et al 2014, Song et al 2020).As shown in figure 1(a), besides the enhanced rainfall annual cycle, rainfall increases more on the equatorward side of the climatological rainfall throughout the year.This phenomenon has been referred to as 'narrowing of the ITCZ' (Byrne and Schneider 2016) and 'deep-tropics squeeze' (Su et al 2014, 2017, 2020, Lau and Kim 2015).Donohoe et al (2019) and Zhou et al (2019) found a close relationship between the annual-mean narrowing of the ITCZ and the reduced amplitude of the ITCZ seasonal migration.A year-round equatorward shift means opposite directions of ITCZ shift between the northern and southern hemispheres, resulting in insignificant changes in the annual-mean and zonal mean ITCZ location (McFarlane et al 2017, Byrne et al 2018).However, regional changes may be obscured by the zonal mean approach.Regionally, the ITCZ shifts southward in the eastern Pacific-Atlantic sector and northward in the Eurasia sector as shown in figure 3 (Mamalakis et al 2021).In addition to this meridional shift of ITCZ, previous studies also suggested that in the local rainy season, rainfall shifts from land to ocean as shown in figure 4 (Chadwick et al 2013a, 2013b, Song et al 2020).That is, in the local rainy season, ocean will receive much more rainfall than land under global warming in most model projections (figure 4(a)).

Mechanism
The first mechanism proposed for the equatorward shift of the seasonal rainband is the upped-ante mechanism (Neelin et al 2003, Chou et al 2004).According to this mechanism, in the margins of climatological convective regions, drier moisture advection caused by the mean wind and the enhanced moisture gradient will reduce the precipitation in the margins of convective zone.Bonan et al (2023) further advanced this mechanism by using a moist energy balance model and argued that both the local radiative feedback and enhanced gross moist stability favor the narrowing of the ITCZ.Hence, this upped-ante mechanism can work under uniform warming scenario and does not require a specific SST warming pattern.However, Donohoe et al (2019) and Zhou et al (2019) argued that the annual-mean narrowing of the ITCZ is caused by its reduced amplitude of seasonal migration using precipitation-related metrics, which is found to be closely related to the enhanced equatorial warming (Huang et al 2013;Huang 2014).But based on a different metric by using the latitude of the maximum/minimum zonal-mean mass streamfunction where the vertical velocity changes from ascent to descent, Byrne et al (2016) showed that the annual-mean narrowing of the ITCZ is not related to the reduced seasonal migration of the ITCZ.Thus, this sensitivity of the role of seasonal migration of the ITCZ to the choice of metrics needs to be resolved in the future.More importantly, it is urgent to clarify to what extent the upped-ante mechanism can operate in the ITCZ narrowing, in the absence of the enhanced equatorial warming.For regional shifts of ITCZ, it is argued that the enhanced land-sea contrast and Indian Ocean Dipole-like warming pattern is responsible for the northward shift of tropical rainfall over Indian Ocean and South Asia, while over the Atlantic region, the weakened AMOC is responsible for the southward shift (Mamalakis et al 2021).Over the eastern Pacific, the El Nino-like warming favors the southward shift, consistent with equatorward shift of ITCZ caused by the enhanced equatorial warming (Zhou et al 2019).This regional shift is also well consistent with the column-integrated atmospheric energetic perspective (Mamalakis et al 2021, Nicknish et al 2023).
For what causes the land-to-ocean shift in the local precipitation changes, several explanations have been provided.Chadwick et al (2013aChadwick et al ( , 2013b) ) obtained this precipitation shift by subtracting the total rainfall changes from the thermodynamic term and the weakening of atmospheric circulation term.Through moisture budget analysis, they found the rainfall shift is mainly contributed by the atmospheric circulation changes and relative humidity changes over land.Kent et al (2015) suggested that the shift is caused by the climatological land-sea contrast in specific humidity, assuming an annually uniform atmospheric mass flux change.This points to a thermodynamic reason consistent with other studies (Fasullo 2012, Chadwick et al 2013a, 2013b, Byrne and O'Gorman 2015, Kumar et al 2015, Donat et al 2016), arguing that 'wet-get-wetter' may not hold over the land.Further, Lambert et al (2017) found the land-to-ocean rainfall shift is related to the reduced relative humidity over land, based on a compositing method in which precipitation changes are linked to surface temperature and relative humidity.Song et al (2020) re-examined this land-to-ocean rainfall shift by using the column-integrated atmospheric energetic framework.They found that the land-ocean shift in the local summer precipitation changes is consistent with the atmospheric energy divergence changes (figure 4(a) vs. figure 4(b)).Further, they found that the land-ocean precipitation contrast in the peak rainy season is related to the opposite land-ocean amplitude changes of surface temperature annual cycle: seasonally-dependent wind changes enhance the amplitude over ocean, while increased effective atmospheric heat capacity and surface cooling feedback reduce the amplitude over land (figure 4(c)).In lieu of the multiple mechanisms emphasizing different processes, more research is needed to quantify the contributions from thermodynamic and dynamical factors to the land-ocean rainfall shift in the local rainy season.

Emergence
For the two distinct spatial pattern shifts, i.e. equatorward shift of the ITCZ throughout the year and land-ocean rainfall shift in the local rainy season, it is important to see whether they have emerged in the observation.Up to now, there is no report on the emergence of land-sea rainfall shift to our knowledge, but whether the narrowing of ITCZ has emerged in the observation is on debate.Some recent studies suggest that the ITCZ has already narrowed in the Pacific and Atlantic in the recent decades (Zhou et al 2011, Wodzicki and Rapp 2016, Byrne et al 2018, Lau and Tao 2020).However, in the seasonal mean, Zhou et al (2020) noticed widening rather than narrowing of the ITCZ in the recent decades mainly due to natural variability of the climate system.In other words, the equatorward shift or narrowing of the ITCZ projected under warming has not yet emerged in the observational record.The contrasting conclusions may originate from the different definitions used to define the ITCZ: one based on precipitation rate (Zhou et al 2011, Wodzicki and Rapp 2016, Byrne et al 2018) and the other based on vertical velocity (Zhou et al 2020); that is, the precipitation-based ITCZ width has narrowed but the vertical velocity-based ITCZ has widened.Future work comparing different methods in the same analysis framework is needed to further clarify the contrasting conclusions regarding the emergence of the ITCZ width changes in the recent decades.

Phenomenon
The phase of tropical rainfall annual cycle is often depicted in terms of the timing of the maximum, minimum, onset or demise of the rainfall.Studies have used different ways to define the rainfall annual cycle based on rainfall in the onset month (Lee and Wang 2014), the rainfall difference between the demise and onset month (Song et al 2021), or the phase of the first harmonic mode of Fourier analysis to mimic the annual cycle (Biasutti andSobel 2009, Song et al 2018a).While some differences in the phase estimated using different methods are to be expected, the estimates should be qualitatively consistent.However, the phase changes based on different definitions are found to be substantially different, especially at the regional scale, which will be further discussed later.
The seasonal delay of global rainfall was first reported by Biasutti and Sobel (2009).In this symbolic study, empirical orthogonal function (EOF) analysis was conducted on the annual cycle of global rainfall and SST in both the 20th century and 21st century (figure 5).Rainfall exhibits a distinct zonal band with positive sign to the north and negative sign to the south (figure 5 Confirmed in many follow-up studies, the seasonal delay of rainfall is a robust phenomenon in a warming world over different regions, in the observations and under multiple future warming scenarios and across several CMIPs (Biasutti and Sobel 2009, Seth et al 2010, 2011, 2013, Biasutti 2013, Dwyer et al 2014, Ma and Zhou 2015, Song et al 2018a, 2018b, 2020, 2021).
Beyond the zonal mean, Song et al (2020) suggested contrasting phase changes between land and ocean, with a robust seasonal delay over land but the phase change is either unclear or slightly advanced over ocean.Regionally, the seasonal delay of rainfall has been reported in several land monsoon regions, including South America (Li et al 2006, Seth et al 2010), North America (Cook and Seager 2013), southern Africa (Shongwe et al 2009) and the Sahel (Biasutti and Sobel 2009, Biasutti 2013, Dunning et al 2016, 2018).Li et al (2006) found that over the Amazon region, the transition from dry season to wet season will be delayed due to the decreased wet season rainfall.To our knowledge, this is the first study to reveal the seasonal delay of rainfall in a regional monsoon.Seth et al (2013) investigated the different monsoons and found that American and African monsoon regions in both hemispheres will experience robust seasonal delay, but no consistent signal is found in South and Southeast Asia.At the regional scale, the phase change is subject to more uncertainties and depends on the study regions and the definitions used.

Mechanisms
On the mechanism of seasonal delay, Biasutti and Sobel (2009) noticed a seasonal delay of SST globally (figure 5(d)), which is closely related to sea ice melting in the high latitude.Considering the close relationship between SST and rainfall, they speculated that the seasonal delay of tropical rainfall is caused by the seasonal delay of SST.However, seasonal delay was found even in model sensitivity experiments under uniform SST warming (Dwyer et al 2014).They found the uniform SST warming can drive the seasonal delay of tropical rainfall through the seasonality changes in atmospheric circulation, of which the origin is not clear then but found to be the enhanced atmospheric heat capacity by Song et al (2018a) via conducting the column-integrated atmospheric energy analysis.Song et al (2018a) demonstrated a strong relationship between the seasonal delay of tropical rainfall and the cross-equatorial energy transport, which represents the interhemispheric energy contrast.That is, when tropical rainfall shifts from the south to the north in May, there is a northward cross-equatorial energy transport under global warming (figure 6(a)), which is facilitated by a southward shift of tropical rainfall; in contrast when tropical rainfall shifts from the north to the south in November, there is a southward cross-equatorial energy transport under global warming (figure 6(a)) facilitated by a northward shift of tropical rainfall.These changes are robust in different warming scenarios, including uniform SST warming, suggesting the cross-equatorial energy transport can well explain the seasonal delay of tropical rainfall.By decomposing the cross-equatorial energy transport into different components, it is found that the tendency of column-integrated MSE (figure 6(c)), mostly associated with the tendency of latent energy term (figure 6(d)), dominates.Song et al (2018a) further devised a simple conceptual model for the tendency of latent energy change that causes the seasonal reversal of cross-equatorial energy transport and the seasonal delay of tropical rainfall where, ∆ ∂⟨Lvq⟩ ∂t is the change of column-integrated latent energy tendency, a is a parameter related to the climatological temperature, ∆T s is the change of surface temperature, ∂Ts ∂t is the climatological temperature.Based on equation (1), during the boreal spring when the northern hemisphere is warming up ( ∂Ts ∂t > 0) and the southern hemisphere is cooling down ( ∂Ts ∂t < 0) and in a warming world (∆T s > 0), ∆ ∂⟨Lvq⟩ ∂t is positive and negative in the northern and southern hemispheres, respectively.In other words, there is an interhemispheric energy contrast between the two hemispheres in boreal spring and fall, which induces a cross-equatorial energy transport and delays the precipitation associated with the seasonal progression of the ITCZ.In this view, the temporal tendency of column-integrated MSE is key to the seasonal delay.More generally, this variable is related to the effective atmospheric heat capacity (Song et al 2020).Hence, the seasonal delay may be explained by the increase of effective atmospheric heat capacity under global warming, which delays atmosphere response to the seasonal solar forcing (Song et al 2020).
In addition to the column-integrated atmospheric energetic framework, which emphasized the increased moisture 'demand' during the onset stage of wet season, the seasonal delay may also be induced by the reduced moisture 'source' at the beginning of the rainy season.This is related to the convective barrier mechanism from the CQE framework, which was first proposed by Seth et al (2011).This convective barrier mechanism based on the competing effects between local (or bottom up) and remote (or top down) mechanisms (Giannini 2010) to explain the annual cycle changes of tropical rainfall (figure 7).They argued that during the peak rainy season in regions with sufficient surface moisture (e.g.land monsoonal regions), the greenhouse gas-induced increased downwelling radiation enhances evaporation and surface MSE and hence rainfall.This is the local mechanism in which the land response to anthropogenically enhanced terrestrial radiative forcing dominates.In the remote mechanism, they emphasized the remote SST warming leading to large-scale tropospheric warming almost uniformly across the tropics as the weak Coriolis force in the tropics cannot maintain temperature (pressure) gradient (i.e. the weak temperature gradient approximation).In regions where the surface MSE change cannot match the enhanced tropospheric warming, moist stability is enhanced and rainfall is reduced.By analyzing the whole annual cycle, they suggested that the local mechanism dominates in the wet season while the remote mechanism dominates in the dry season.During the transition from dry to wet (i.e. in spring), insufficient moisture availability at the end of an intensified dry season under warming (i.e. the enhanced annual cycle) would favor an extension of the top-down mechanism and delay the handoff to the bottom-up destabilization, resulting in diminished early season rainfall.This convective barrier mechanism emphasized that the moisture 'source' becomes more limited during the onset stage of wet season due to the enhanced dry season under warming.If this is the case, the seasonal delay of rainfall should be related to the enhanced amplitude of the annual cycle of rainfall, implying a close relationship between the phase and amplitude changes, which can be examined in the future.As mentioned in the Introduction, either the vertical gradient of MSE or surface/subcloud MSE should be an important indicator of the seasonal delay of tropical rainfall based on the CQE framework.Seth et al (2013) found the vertical gradient of MSE can explain the seasonal delay in the American and African monsoons, but not the Asian monsoon.By replacing the vertical gradient of MSE between the surface and the upper troposphere with the relative surface MSE (the difference between local surface MSE and tropical mean surface MSE), Bombardi and Boos (2021) found the seasonal phase changes in all the monsoon regions can be well explained by this convective barrier mechanism.Song et al (2022) also found the surface equivalent potential temperature, essentially the same as surface MSE but with temperature unit, can well explain the seasonal delay of rainfall over the northern tropical land.
Compared to the CQE framework, which applied to the regional monsoon since the beginning of development, the column-integrated atmospheric energy equation perspective is first applied to explain the zonal-mean rainfall seasonal delay, but it proves to be faithful in explaining the regional phase changes, including the land-ocean phase change contrast (Song et al 2020) and seasonal delay in the Sahel (Song et al 2021).It should be pointed out that although the atmospheric energy divergence is still found to be the driver of the seasonal delay at the regional scale, the dominant term may not be the enhanced effective atmospheric heat capacity by the surface warming, as the net energy input into the atmosphere and related local feedback processes may become more important.In the former case (Song et al 2020), the seasonal delay over land vs. ocean is found to be closely related to the land-to-ocean rainfall pattern shift discussed in the above section.In the latter case (Song et al 2021), the increase of effective atmospheric heat capacity in the Sahel is caused by the increased relative humidity rather than the temperature under the aerosol-only forcing.This suggests that understanding the mechanisms responsible for regional precipitation phase changes is more challenging and more efforts are needed to apply this energy framework to different monsoon regions.

Emergence
The seasonal delay of rainfall is linearly related to the global warming level (see equation ( 1)).With accelerated warming since 1979, it is natural to ask whether the seasonal delay of tropical rainfall has emerged from natural variability.As the seasonal delay is more evident over land (Song et al 2020) where longer and more reliable observations are available compared to ocean, there is an opportunity for more reliable detection and attribution analysis over land.As shown in figure 8, Song et al (2021) showed that seasonal delay of tropical rainfall has already emerged in the northern tropical land as a whole and in the Sahel, where the seasonal delay under global warming was first discovered based on model projections (Biasutti and Sobel 2009).Over the North America, the signal is also evident in both observation and model simulations, but not in the South Asia (figure 8).In the South Asia, the Interdecadal Pacific Oscillation, one important internal variability mode, is found an important role in the recent observed phase changes (Zhang et al 2017).Using historical simulations from CMIP6 and several large ensembles, external forcing accounts for more than half of the observed seasonal delay (Song et al 2021).Both the increase of greenhouse gases and decrease of anthropogenic aerosols are important drivers of the observed seasonal delay in the past four decades, but seasonal delay has not yet emerged in the southern tropical land (Song et al 2021).The north-south hemispheric contrast in seasonal delay warrants further research in the future.

Phenomenon
Changes in the phase can occur without changes in the shape of tropical rainfall annual cycle if changes in the onset and demise dates of the wet/dry season are similar.However, some studies have detected changes in the wet/dry season length in the past decades (Fu et al 2013, Ma and Zhou 2015, Jiang et al 2019, Xu et al 2022) and under global warming (Kitoh et al 2013, Wang et al 2020, Bombardi and Boos 2021), especially for regional monsoon systems (Xiang and Wang 2013, Watanabe and Yamazaki 2014, Zhang et al 2017).Determining the wet/dry season length requires estimating the onset and demise dates of the wet/dry season, but some conclusions change substantially depending on the methods or the thresholds used in the same method for estimating the onset and demise dates.A common method uses cumulative rainfall anomaly (Dunning et al 2016, 2018, Bombardi and Boos 2021, Guo et al 2022) where anomaly is calculated with respect to a threshold that is often set as the climatological annual-mean rainfall.Another method to determine the onset and demise dates uses a fixed threshold to define the wet and dry seasons (Wang and Linho 2002, Fu et al 2013, Kitoh et al 2013, Wang et al 2020).In this method, the climatological annual-mean rainfall is taken as the threshold or alternatively, (January for the northern hemisphere and July for the southern hemisphere) is used to define the wet and dry seasons using a fixed threshold value (5 mm d −1 or 3.5 mm d −1 ).Hence, the wet/dry season length determined using the first and second method is subject to changes in the annual-mean rainfall and amplitude, respectively.That is, when the annual-mean rainfall increases, the wet season length becomes longer based on the first method and this is also the case when the amplitude of rainfall annual cycle increases based on the second method.Bombardi et al (2020) summarized different methods to define the onset/demise dates, but their impact on the wet/dry season length changes is still unclear.Further efforts to conduct quantitative comparison and develop more objective methods to quantify the onset/demise dates changes are needed in the future.
Based on observational datasets, the dry season length has increased in recent decades in both Amazon and Congo Basin (figure 9), the two biggest tropical rainforest areas in the world (Fu et al 2013, Jiang et al 2019, Xu et al 2022).Under global warming, the dry season length is also projected to increase in these two regions but subject to large inter-model spread (Bombardi and Boos 2021).The wet/dry season length changes in the Amazon region are not sensitive to the choice of methods used to define the wet/dry season length.The lengthening of dry season in the Congo Basin is mainly obtained based on the cumulative rainfall anomaly and whether the result is sensitive to the choice of methods is unknown.The wet/dry season length changes are also examined over global monsoon regions under global warming (Kitoh et al 2013, Wang et al 2020, Bombardi and Boos 2021).Based on the second method of defining wet/dry season length using onset/retreat dates, several studies concluded the wet season will get longer in the northern hemispheric monsoon regions due to the later monsoon retreat in the future in CMIP5 (figure 10; Kitoh et al 2013) and CMIP6 models (Wang et al 2020), but these models do not produce consistent wet/dry season length changes in the southern hemisphere.By changing the threshold value (from 5 mm d −1 to 3.5 mm d −1 ) in the definition of onset/retreat dates, Moon and Ha (2020) found that regions featuring a longer wet season do not include the North and South American monsoon regions, highlighting again uncertainty due to how the wet season length is defined.
Regardless of the methods used to define wet/dry season length, many previous studies documented the large uncertainty in the wet/dry season length and its changes in climate models (Fu et al 2013, Kitoh et al 2013, Bombardi and Boos 2021, Xu et al 2022).Fu et al (2013) found that CMIP5 models underestimate the variability of dry season length and its controlling factors and concluded that models may underestimate the future changes of dry season length.Hence, both uncertainties in the definitions and models may limit our understanding of the wet/dry season length changes.

Mechanisms
The physical mechanism responsible for the change in wet season length is still unclear as even if any changes have occurred globally is still in debate.Nevertheless, some studies have attempted to explain the regional wet/dry season length changes.Over the Amazon, the increased dry season length is mainly due to the delayed ending of the dry season (Fu et al 2013), but in the Congo Basin, the longer dry season is mainly due to the earlier dry season onset (Jiang et al 2019).Fu et al (2013) suggested a role of greenhouse gases in the delayed dry season end in the recent decades by increasing the convection inhibition energy and shifting the subtropical jet poleward, while land use/land cover, ozone reduction, biomass burning aerosols and natural variability (such as Pacific Decadal Oscillation and Atlantic Multidecadal Oscillation) may not be as important.However, they found that models cannot reproduce the extent of the observed dry season length changes, pointing to model biases in representing the Amazon rainfall annual cycle.Over the Congo Basin, the earlier dry season onset has been linked to the decreased pre-dry season (April-June) rainfall (Jiang et al 2019), which is caused by the Indo-Pacific SST variations (Hua et al 2016).

Emergence
As discussed above, studies on the wet/dry season length changes (Fu et al 2013, Jiang et al 2019, Xu et al 2022) have concluded that in the satellite period (since 1979), the dry season in the two largest tropical rainforest regions, Amazon and Congo Basin, has become longer.However, these studies did not conclude whether the observed changes are driven by external forcing and instead, underscored the significant model biases in representing the observed wet/dry season length (Fu et al 2013, Bombardi and Boos 2021, Xu et al 2022).Hence, it is unclear whether the observed wet/dry season length changes are due to global warming or natural variability.Both model bias and observational uncertainty limit detection and attribution of wet/dry season length changes.

Impacts of tropical rainfall annual cycle changes
In the above sections, we reviewed the four aspects of tropical rainfall annual cycle changes, including amplitude, pattern shift, phase and wet/dry season length.The tropical rainfall annual cycle changes would exert significant climate impacts, which is just beginning to be explored and will be briefly reviewed here.The amplified annual cycle will likely increase the frequency of extreme precipitation, flood (due to enhanced runoff) and drought (Zhang et al 2019), but quantitative analysis is still lacking.Using modeling experiments, Liang et al (2020) found that enhanced amplitude of Amazon rainfall annual cycle enhances the seasonality of Amazon River discharge and hence the seasonality of ocean salinity in the Amazon plume region (figure 11).Narrowing of the ITCZ may cause a southward shift of the subtropical East Asian rainband (Zhou et al 2019).The narrowing of the tropical rain belt has caused a net reduction of tropical climate land area with global warming (Adam et al 2023).The land-to-ocean rainfall shift in the rainy season may cause opposite phase changes of rainfall annual cycle between land and ocean, making them more in sync in the future (Song et al 2020).Changes in the onset and demise dates of tropical rainfall annual cycle may have far-reaching impacts.For example, seasonal delay of tropical rainfall is accompanied by seasonally-dependent subtropical high changes, i.e. larger strengthening of subtropical high in spring is than summer in the northern hemisphere and vice versa for the southern hemisphere (Song et al 2018a(Song et al , 2018b)).These changes in the subtropical highs would have great impacts on the subtropical climate, as the subtropical highs are well known to play an important role in the moisture transport, typhoon/hurricane tracks and marine heat waves (e.g.Wu et al 2005, Zhou and Yu 2005, Stowasser et al 2007, Amaya et al 2020).Fang et al (2022) found a delayed timing of floods over the global monsoon regions in the past four decades, which might be connected with the emergence of the seasonal delay of tropical land rainfall (Song et al 2021) and indicative of the hydrologic impact of monsoon rain changes.
Dry season length is thought to be among the most important factor limiting the sustainability of rainforests (Jiang et al 2019).Increased dry season length and amplified dry season intensity (i.e.dry season get drier) could reduce the tropical ecosystem productivity (Murray-Tortarolo et al 2016).Fu et al (2013) also suggested a contribution of the prolonged dry season length to the enhanced fire counts in the Amazon region.Changes in the wet/dry season length may also impact agriculture and food security, thus can be a fruitful area for interdisciplinary studies in the future.

Summary and future work
Here, we summarized recent advances in understanding and quantifying the changes of tropical rainfall under global warming.Four aspects of the tropical rainfall annual cycle are discussed including amplitude, pattern shift, phase and wet/dry season length.For each feature, we broadly discussed the phenomenon, mechanisms and emergence.Finally, we briefly reviewed the impacts of tropical rainfall annual cycle changes.For amplitude, the well-known 'wet-get-wetter' mechanism well explains the enhanced amplitude of rainfall annual cycle in the tropics, especially over the ocean.The enhanced amplitude of rainfall annual cycle will tend to increase the probability of extreme precipitation, flood, drought and runoff.Whether the enhanced amplitude has emerged in the observation is debatable as the observations over the ocean are scarce and subject to large uncertainty.For pattern shift, two features are evident with warming: equatorward shift of the ITCZ throughout the year and a land-to-ocean precipitation shift in the rainy season.The former is explained by the upped-ante mechanism and/or related to the enhanced equatorial warming in the future.The latter is recently suggested to be caused by the opposite land and ocean surface temperature annual cycle changes in the tropics but it is also subject to some uncertainty.For phase, the seasonal delay of tropical rainfall annual cycle has been observed in many tropical land areas, including the Sahel and Central America, and will be further intensified in the future.Both the CQE perspective and the column-integrated atmospheric energetic perspective have been used to explain the seasonal delay of tropical rainfall, providing complementary and/or competing views to understand the seasonal delay of tropical rainfall.Over tropical rainforest regions such as Amazon and Congo Basin, an increased dry season length has been observed in the recent decades, but the fundamental reason is still unclear.Considering what we have achieved in the past decade regarding the tropical rainfall annual cycle changes, we suggest future studies can focus on the following four aspects to further our knowledge on the tropical rainfall annual cycle changes.

Uncertainty
Long-term precipitation observations are subject to large uncertainty, especially over the ocean.This limits the detection of the emerging changes in the observed tropical rainfall annual cycle.Although uncertainty in the annual cycle of precipitation may be smaller than that of annual mean (Marvel et al 2017), different observational datasets still do not converge on a consistent answer on how the amplitude of tropical rainfall annual cycle has changed in the past decades (Chou et al 2013, Song et al 2021).In addition to observational uncertainty, uncertainty in methods and definitions should also be resolved in the future.For example, many definitions exist for amplitude, phase, ITCZ width/location, and wet/dry season lengths, leading to different conclusions on their emergence and future changes.Besides the definitions of individual components of tropical rainfall annual cycle introduced above, there are also comprehensive metrics on the seasonality (e.g., Feng et al 2013), so how each individual component contributes to the total seasonality of tropical rainfall also deserves further investigation.A systematic comparison of the different definitions and the development of more robust and reliable definitions may help resolve conflicting quantifications of changes in the tropical rainfall annual cycle, which is an important step towards a better understanding of future changes.
Tropical rainfall is closely related to atmospheric convection, which is not explicitly resolved in the current generation of climate models.Parameterizations of atmospheric convection in climate models are subject to large uncertainty and contribute to large model biases in the ITCZ and monsoons, including the well-known double-ITCZ bias (e.g.Tian andDong 2020, Zhou et al 2022b), underestimation of monsoon precipitation in several regions (e.g. Lee and Wang 2014), and erroneous timing of monsoon rainfall annual cycle (e.g.Bombardi and Boos 2021), with consequences for the future projection of tropical rainfall annual cycle (Mamalakis et al 2021).While global convection-permitting models are more skillful in simulating many aspects of weather and climate (e.g.Stevens et al 2019), their use in conducting simulations under present-day and future warming scenarios is limited by computational resources, but season-to-decade long simulations are feasible.The latter will be useful for understanding cloud feedbacks and providing important constraints on climate sensitivity which has important implications for the magnitudes of tropical rainfall annual cycle changes.

Quantification
Although qualitative knowledge on the changes in the tropical rainfall annual cycle such as the enhanced amplitude and delayed phase has been advanced in the recent decade, quantitative understanding is still lacking because of uncertainty in factors such as climate sensitivity, internal variability, and the roles of different anthropogenic forcings.In addition, tropical rainfall is produced by different cloud and storm systems, such as monsoon depressions, typhoons (hurricanes), mesoscale convective systems and the Madden-Julian oscillation.Some pioneering studies have been done for the annual cycle changes of typhoons/hurricanes (Shan et al 2023) and Madden-Julian Oscillation (Bui and Hsu 2023) and definitely more researches are needed in the future.Quantifying rainfall changes requires understanding the contributions of different storm types to the tropical rainfall annual cycles and how they respond to global warming.In addition, it is also important to quantitatively compare different contributions of several well-established mechanisms responsible for the tropical rainfall annual cycle changes.For example, for the narrowing of the ITCZ, the upped-ante mechanism can operate under uniform SST warming, so the contributions from the uniform SST warming and SST warming pattern such as the enhanced equatorial warming pattern can be quantified in the future.Moreover, assessing the relative importance of the two atmospheric energetic frameworks in the phase changes of rainfall annual cycle or better connecting the two energy frameworks will be helpful in delineating the various mechanisms of phase changes proposed so far.This may be achieved by conducting some model sensitivity model experiments, such as fixing soil moisture in the land model under global warming.This kind of experiment may also help quantify the relative roles of tropical expansion and soil moisture-atmosphere feedback in the reduced amplitude in the subtropics.

Understanding
Currently, we have well established the theoretical understanding on the zonal-mean amplitude and phase changes, as well as the narrowing of the zonal-mean ITCZ.We need to bear in mind that when we go down to smaller scales, the simple and elegant theories may not work well as many factors can drive the local changes and some new insights will definitely be gained about the regional phase and amplitude changes.Moreover, further understanding on the mechanisms responsible for the regional rainfall annual cycle changes, especially the land-ocean rainfall shift in the local rainy season and wet/dry season length changes, will be needed to determine the robustness of future changes projected by climate models.The land-ocean rainfall shift occurs in each continent and adjacent ocean, so it should be controlled by some simple rules.Song et al (2020) did some attempts by designing an energy balance model considering atmosphere-land surface interaction and gained insights on the important role of opposite amplitude changes of surface temperature annual cycle between land and ocean.In the future, more hierarchal model experiments are needed to further our understanding on this part.For the regional ITCZ shifts, the recent understanding focuses on the local SST forcing (e.g.Mamalakis et al 2021), however the remote mechanisms such as ice albedo, cloud radiation effects, ocean heat uptake may be closely linked to the local SST changes when we take a global angle.These efforts can be pursued in the future work.For the regional phase changes, in addition to the two energetic frameworks, dynamical feedbacks (Bordoni andSchneider 2008, Schneider andBordoni 2008) may also be important at the regional scale, highlighting the need for more efforts to further understand regional phase changes by combining the energy and dynamical frameworks.
Many gaps remain in our current understanding of the wet/dry season length changes.As the wet/dry season length changes are related to the asymmetry of onset and demise changes of wet/dry season, examining the asymmetry of phase changes may provide clues on what controls the wet/dry season length changes.Since the reported wet/dry season length changes mainly occur in the two largest tropical rainforest areas (Amazon and Congo Basin), land-vegetation-atmosphere interaction may play an important role.Compared to other tropical land regions, tropical rainforests, often referred to as 'green ocean' , feature persistent cloudiness and abundant water availability, but how tropical rainforest may respond to different anthropogenic forcings remains unclear.

Impact
The climate impact of tropical rainfall annual cycle has only begun to be revealed and not much effort has been devoted to this topic, but it is very important for the future adaption and mitigation, as some climate effects may be overlooked when we only focus on the annual-mean changes.As mentioned in the section 5, there are already pioneering investigations and more researches are needed to reveal the climate impacts of tropical rainfall annual cycle changes.For example, the seasonally-dependent subtropical high response due to the seasonal delay of tropical rainfall may impact the regional climate in the subtropics.For example, the East Asian summer monsoon is closely related to the Western North Pacific Subtropical High (e.g.Zhou and Yu 2005), which is usually the strongest during summertime.If the Western North Pacific Subtropical High also becomes stronger in spring following the North Pacific subtropical high (Song et al 2018b), a phase advance of the East Asian summer monsoon may be favored, which is found to be the case in the recent decades (Zhan et al 2016, Song et al 2021) and under global warming (Chiang et al 2019).The link between the seasonal delay of tropical rainfall and the seasonal advance of East Asian summer monsoon should be investigated in more details in the future.To better connect tropical rainfall annual cycle changes to their impacts, multidisciplinary cooperation may be needed to expedite the research for societal benefits.

Figure 1 .
Figure 1.(a) Precipitation change (b) precipitation climatology and (c) SST change in RCP 4.5, all in zonal and CMIP5 MME mean.In a, the red curve marks the latitude of the climatological maximum mean precipitation.Reproduced from Huang et al (2013), with permission from Springer Nature.

Figure 2 .
Figure 2. Responses of water cycle components to global-mean surface air temperature changes under RCP8.5 for submonsoon regions, including precipitation (P), evapotranspiration (E), P-E, total runoff (R), and surface (SMs) and total soil moisture (SMt).Results for the annual mean (blue) and wet (red) and dry (grey) seasons are shown.The surface and total soil moisture contents are scaled by 1/10 and 1/200, respectively, for display.The unit is kg m −2 K −1 for soil moisture and mm d −1 K −1 for others.Wet season refers to May-September for the NH and November-March for the SH, and vice versa for the dry season.The histograms denote the multimodel medians while the error bars denote the 25th-75th-percentile intervals among the models.The vertical axis has the same range for the submonsoon regions except for the global monsoon region.For regional divisions, the equator separates the NH from the SH monsoon region, 30 • W and 180 • separate the EH from the WH monsoon region, 60 • E separates the NH African from the South Asian monsoon region, and 20 • N and 100 • E separate the South Asian monsoon region from the East Asian monsoon region.All the regional domains are within 40 • S-45 • N. Reproduced with permission fromZhang et al (2019).© American Meteorological Society.Used with permission.

Figure 3 .
Figure 3. (a) Difference in the probability density function (∆PDF) of the location of the ITCZ in May-October between 2075-2100 and 1983-2005.In each period, the location of the ITCZ is defined by tracking the location of maximum precipitation and minimum OLR in overlapping longitudinal windows (we use the joint statistics of the two variables; supplementary figures 1 and 2 and Methods).(b) Same as in a, but for November-April.(c) Same as in a, but the changes in the annual distribution are shown.In all plots, the multimodel mean across 27 CMIP6 models is presented for the SSP3-7.0scenario; stippling indicates agreement (in the sign of the change) in more than three-fourths of the models considered.Results indicate a robust northward ITCZ shift over eastern Africa and the Indian Ocean and a southward ITCZ shift over the eastern Pacific and Atlantic oceans.Reproduced from Mamalakis et al (2021), with permission from Springer Nature.

Figure 4 .
Figure 4. Box plots for the change (RCP85-HIST) in land-sea difference of (a) precipitation (unit: mm d −1 ) and (b) divergence of atmospheric heat transport (∇ (AHT); unit: W m −2 ) regressed on the precipitation EOF1 among the CMIP5 models.The horizontal lines in (a) and (b) represent the 25th percentile, median, 75th percentile, and the whiskers are the maximum and minimum values of the multimodel ensemble.(c) Change in the TS (shaded; unit: K) regressed on PC1 of precipitation annual cycle, with positive values indicating increase and decrease of the amplitude of the TS annual cycle in the NH and SH, respectively.The purple contours over ocean are the changes in the 1000 hPa wind speed congruent with EOF1.The solid and dashed lines over ocean represent positive and negative values, respectively, with an interval of 0.2 m s −1 , separated by the bold contour of 0 value.The orange and blue contours over land indicate the 0.5 and −0.5 mm d −1 contours of precipitation EOF1 shown in figure 2(a) of Song et al (2020), respectively, demarcating the boundaries of the land monsoonal regions.The purple dots over land indicate regions of increased surface cooling feedback parameter β under global warming.Song et al (2020) John Wiley & Sons.©2020.American Geophysical Union.All Rights Reserved.

Figure 5 .
Figure 5. Annual cycle of precipitation and sea surface temperature in the 20th and 21st Century.First CMIP3 ensemble mean EOF of the 20th century climatology of (a) precipitation (shading interval 1 mm d −1 ) and (b) SST (shading interval 1 • C).21 • C-20 • C difference in PC1 of (c) precipitation and (d) SST in each calendar month and for each CMIP3 model (PC1s are normalized to unit variance).Blue and orange background shadings indicate months in which PC1 is negative or positive, no shading indicates a transition month.Biasutti and Sobel (2009) John Wiley & Sons.Copyright 2009 by the American Geophysical Union.
(a)).Under global warming, PC1 (the first Principal Component) shows negative changes in May and positive changes in November between the 21st and 20th century in almost all climate models examined (figure 5(c)).As May and November are the two transition seasons for the northern tropics, representing the beginning of wet season and dry season, respectively, the consistent negative change in May and positive change in November indicate clearly a delay in seasonal cycle.

Figure 6 .
Figure 6.The seasonal cycle of cross-equatorial energy transport and its each component under AMIP4K-AMIP (blue), AMIPFuture-AMIP (red) and RCP8.5-HIST (purple).The blue, pink and plum shadings represent the standard deviation among models for the AMIP4K, AMIPFuture and RCP8.5 changes, respectively.Reproduced from Song et al (2018a), with permission from Springer Nature.

Figure 7 .
Figure 7. Schematic representation of changes in the tropical troposphere and effects of remote and local mechanisms: Z indicates height above the surface and T air temperature.A change in the lapse rate is given by status quo vertical profile (blue) and projected change (brown or green).In all seasons the temperature increase in the upper troposphere results in increased dry static energy.Nearer the surface, the change in MSE is small during the dry season and large in the wet season.During the transition, increases in surface MSE are dominated by increasing temperature.Reproduced with permission from Seth et al (2013).© American Meteorological Society.Used with permission.

Figure 8 .
Figure 8. Linear trends of precipitation inter-seasonal difference (SON-MAM) during 1979-2019.(a), (b), OBS (a) and EXT (b).Black dots indicate the trend is significant at the 90% confidence level based on Student's t test.Black box marks the Sahel region (10-20 • N, 20 • W to 35 • E).Reproduced from Song et al (2021), with permission from Springer Nature.

Figure 9 .
Figure 9.The consistency of trends in dry season length (a) and water deficit (b) under each of the three definitions of 'dry season' was assessed as the variation among the eight precipitation datasets.'Very likely' , 'Likely' and 'Probably' indicate that the sign of the trend was the same and significant in 6-8, 4-5, and 1-3 precipitation datasets, respectively, while the other datasets showed no significant change.'Uncertain' indicates conflicting trends among datasets, with some showing a significant increase and some showing a significant decrease.'No Change' indicates that all eight datasets showed no significant change.The histograms in the right column of (a) and (b) show the percent area with consistent increase or decrease trends.Arid and humid regions (solid gray shaded area) were excluded when calculating the percent area, since there was no climatologically wet or dry season, thus no trends calculated under definitions of P < Ep or P < E. This analysis combined both dry seasons for regions with two dry seasons (individual trends for each distinctive season are shown in supplementary figure 9 of Xu et al (2022)).Consistency of trends in dry season length and water deficit for the other two Ep products (MERRA-2 and GLDAS-v2.0)based on P < Ep definition were shown in supplementary figure 8 of Xu et al (2022).Reproduced from Xu et al (2022).CC BY 4.0.

Figure 10 .
Figure10.Future changes (days) in monsoon onset date (ONS), retreat date (RET) and duration (DUR) over each regional land monsoon domain.For calculation of the global monsoon domain statistics in figure10(a), the seven regional monsoon domain statistics were averaged with weighting based on their area in the present-day.The 10th, 25th, 50th, 75th, and 90th percentiles refer to the 3rd, 6th, 11th, 16th, and 19th values in ascending order among the 21 models, respectively.Seven monsoon regions: North America (NAM), South America (SAM), North Africa (NAF), South Africa (SAF), East Asia (EAS), South Asia (SAS), and Australia (AUS).See the domain of these seven monsoons in figure5(a) of Kitoh et al (2013) John Wiley & Sons.©2013.American Geophysical Union.All Rights Reserved.

Figure 11 .
Figure 11.(a) The seasonality of the precipitation forcing used in the global land model control and experimental simulations.(b) Seasonality changes in Amazon River discharge in the land model experiments.(c) Similar to (a), but for Amazon River runoff forcing used to force the ocean model experiments.In (a), (c), the dashed lines are linear fits to determine trends.(d) Similar to (b), but for seasonality changes in Amazon Plume Region (APR) ocean salinity in the ocean model experiments.The black star is the APR salinity seasonality trend, averaged over five spin-up cycles.Reproduced from Liang et al (2020).CC BY 4.0.