In this study, we use the simulations from 13 models participating in PlioMIP2 (Table 1). All models include a preindustrial (PI) simulation and a Pliocene climate simulation. In PlioMIP2 models, the boundary conditions have been updated using the new version of the U.S. Geological Survey PRISM4 dataset (Dowsett et al., 2016; Haywood et al., 2016), including soils, lakes, land-ice cover, vegetation, topography, and bathymetry. The CO2 levels for the mid-Pliocene and PI simulations are set at 400 and 280 ppmv, respectively. To calculate the ensemble mean, we interpolate all data onto a common grid with a 1∘×1∘ resolution using bilinear interpolation.

To examine the changes in precipitation (P) minus evaporation (E) in the PlioMIP2 mid-Pliocene experiments relative to their respective PI simulation, we decompose the moisture budget equation based on Seager et al. (2010), i.e., 1δ(P‾-E‾)≈-1ρwg∇⋅∫0ps(V‾0δq‾)dp︸δTH-1ρwg∇⋅∫0ps(q‾δV‾0)dp︸δMCD+R. Here, g is gravity, ρw is the density of water, V is the horizontal wind, q is the specific humidity, δ(⋅) is the annual mean difference in variables between the warmer climate state (mid-Pliocene) and the PI simulation, and subscript 0 represents the variables in the PI simulation. In the warmer climate, the change in P minus E (PmE, the left-hand side of Eq. 1) is balanced by the thermodynamic (δTH, induced by increased specific humidity) and dynamic (δMCD, induced by circulation anomalies) contributions and residual term (R, which is mainly involved in the contributions from high-frequency variability of transient eddies, nonlinear effects, and surface boundary terms).

As we are interested in understanding the relative contribution from zonal circulation (i.e., local Walker circulation) changes and meridional circulation (i.e., local Hadley circulation) anomalies to the changes in PmE in a warmer climate, we further apply the three-pattern decomposition of global atmospheric circulation (3P-DGAC; Hu et al., 2017; S. Hu et al., 2018a, b) method in this study. The horizontal, meridional, and zonal circulations that can be viewed as the global generalization of the Rossby wave in the middle–high latitudes and the Hadley and Walker circulations in the low latitudes are defined to decompose the global atmospheric circulation into a superposition of the horizontal, meridional, and zonal circulations by using the 3P-DGAC method.

Based on the essential features of the Rossby, Hadley and Walker circulations, Hu et al. (2017) defined the 3D horizontal circulation VR, meridional circulation VM, and zonal circulation VZ in the spherical σ-coordinate system as follows: 2VR(λ,θ,σ)=uR(λ,θ,σ)i+vR(λ,θ,σ)j,VM(λ,θ,σ)=vM(λ,θ,σ)j+σ˙M(λ,θ,σ)k,VZ(λ,θ,σ)=uZ(λ,θ,σ)i+σ˙Z(λ,θ,σ)k. Here, the following continuity equations are satisfied: 31sin⁡θ∂uR∂λ+1sin⁡θ∂(sin⁡θvR)∂θ=0,1sin⁡θ∂(sin⁡θvM)∂θ+∂σ˙M∂σ=0,1sin⁡θ∂uZ∂λ+∂σ˙Z∂σ=0. Equation (3) is the sufficient condition that the components of VR, VM, and VZ can be represented by the stream functions R(λθσ), H(λθσ), and W(λθσ), respectively, as follows: 4uR=-∂R∂θ,vR=1sin⁡θ∂R∂λ,vM=-∂H∂σ,σ˙M=1sin⁡θ∂(sin⁡θH)∂θ,uZ=∂W∂σ,σ˙Z=-1sin⁡θ∂W∂λ. Because three-pattern circulations (horizontal, meridional, and zonal circulations) exist in both the low latitudes and middle–high latitudes, the global atmospheric circulation can be expressed as the superposition of the horizontal, meridional, and zonal circulations – that is, 5V=VM+VZ+VR with the following components: 6u=uZ+uR=∂W∂σ-∂R∂θ,v=vR+vM=1sin⁡θ∂R∂λ-∂H∂σ,σ˙=σ˙M+σ˙Z=1sin⁡θ∂(sin⁡θH)∂θ-1sin⁡θ∂W∂λ. Equation (5) or (6) is called the three-pattern decomposition model.

In contrast to the traditional 2D decomposition of the atmospheric motion into vortex and divergent parts, the continuity Eq. (5) cannot guarantee the uniqueness of the stream functions R(λθσ), H(λθσ), and W(λθσ) because the three-pattern circulations VR, VM, and VZ have three spatial dimensions, respectively (Hu et al., 2017; S. Hu et al., 2018a, b). The following restriction condition is needed to pick up the correct decomposition (Theorems 1 and 2 in Y. Hu et al., 2018): 71sin⁡θ∂H∂λ+1sin⁡θ∂(Wsin⁡θ)∂θ+∂R∂σ=0. Equation (7) guarantees both the uniqueness of the stream functions R, H, and W and the physical rationality of the 3P-DGAC method.

Using the 3P-DGAC method, we can rephrase the moisture budget in Eq. (1) to involve the contributions from zonal and meridional circulation. Here, we neglect the relatively smaller terms at low latitudes, including transient eddies, nonlinear effects, and surface boundary terms. Thus, we mainly explore the contributions from δTH and δMCD to changes in PmE in this study. Then, the δTH and δMCD can be rewritten as follows: 8δTH=-1ρg∫0psδq∇⋅VR0dp︸δTHD_R-1ρg∫0psδq∇⋅VZ0dp︸δTHD_Z-1ρg∫0psδq∇⋅VM0dp︸δTHD_M︸ΔδTHD-1ρg∫0psVR0⋅∇δqdp︸δTHA_R-1ρg∫0psVR0⋅∇δqdp︸δTHA_Z-1ρg∫0psVM0⋅∇δqdp︸δTHA_M︸δTHA,

9δMCD=-1ρg∫0psq0∇⋅δVRdp︸δMCDD_R-1ρg∫0psq0∇⋅δVZdp︸δMCDD_Z-1ρg∫0psq0∇⋅δVMdp︸δMCDD_M︸δMCDD-1ρg∫0psδVR⋅∇q0dp︸δMCDA_R-1ρg∫0psδVZ⋅∇q0dp︸δMCDA_Z-1ρg∫0psδVM⋅∇q0dp︸δMCDA_M︸δMCDA, where subscripts D and A represent the terms that are related to divergence and moisture advection, respectively. In addition, the subscripts R, Z, and M indicate the terms that are related to the horizontal, zonal, and meridional circulations, respectively. Note that VR represents the horizontal vortex winds, which are not divergent, which indicates that the terms that are related to the divergence/convergence of VR (i.e., δTHD_R and δMCDD_R) are zero. These terms can be clearly seen in Figs. 3h and 4h. In addition, we ignore these two terms in this study.

The last 100 years of individual PlioMIP2 simulations are used to calculate the multi-model mean (MMM) PmE in Fig. 1 and individual PlioMIP2 models in Fig. 2.

Figure 1a shows that most subtropical regions experience reduced PmE in the mid-Pliocene simulations with respect to the PI simulations, including the subtropical Pacific and subtropical Atlantic in both hemispheres and the subtropical Indian Ocean in the Southern Hemisphere (SH). There is also drying over the South Pacific convergence zone (SPCZ), except in the GISS-E2-1-G, COSMOS, and HadGEM3 models (Fig. 2), consistent with other studies evaluating the hydrological cycle response within the PlioMIP2 simulations (Pontes et al., 2020). Note that there is a moistening signal in the southern part of the SPCZ in the tropical southern Pacific. In contrast, the increased MMM PmE is located in the deep tropics (i.e., Pacific intertropical convergence zone, ITCZ, and northern Indian Ocean) as well as at middle–high latitudes (Fig. 1a). However, some models (i.e., the CESM2, GISS-E2-1-G, COSMOS, and HadGEM3 models) show a drier Maritime Continent (Fig. 2), which might be related to the changes in Walker circulation (we will discuss this latter in Sect. 5.3). In addition, the North African and Southeast Asian monsoon regions also show significant moistening signals, which are consistent with faunal remains and palynological transfer functions (Sanyal et al., 2004; Trauth et al., 2007; Xie et al., 2012) as well as with other modeling studies (Zhang et al., 2019; Li et al., 2020; Feng et al., 2021). Zhang et al. (2016) indicate that the combined influence of SST and CO2 level, as well as the vegetation changes, play a very important role in changing the atmospheric circulation over North Africa during the mid-Pliocene, owing to the increased net atmospheric energy there. Additionally, the expansion of vegetation into the Sahara region tends to decrease the surface albedo, which can enhance the Saharan heat low and, hence, impact rainfall over West Africa, reflecting the vegetation–albedo feedback (Charney, 1975). Recent studies indicate that the enhanced vegetation in the PlioMIP2 ensemble is likely to have contributed to increased mid-Pliocene West African summer rainfall (Haywood et al., 2020; Berntell et al., 2021). This change over Southeast Asia is robust among PlioMIP2 models, and only the COSMOS model shows a drier change over East Asia (Fig. 2e). Furthermore, the MMM PmE changes over Southeast Asia are mainly focused on the summertime (not shown), suggesting a consequence of strengthened East Asian summer monsoon circulation (Salzmann et al., 2008; Wan et al., 2010; Yan et al., 2012; Zhang et al., 2013; Li et al., 2018; Lu et al., 2021). Note that the mid- to high-latitude North Atlantic becomes drier (Fig. 1a).

The response of the hydrological cycle during the mid-Pliocene generally shows a wet regions getting wetter and dry regions getting drier pattern, especially over the ocean. These features are apparent in the zonal average of the PmE change (Fig. 1b), except in the GISS-E2-1-G model (Fig. 2f). The tropical regions become wetter, and subtropical regions become drier, which are similar to the results from future high-CO2 scenario experiments (Chou et al., 2009). Earlier studies have indicated that these features of changes in PmE at low latitudes are linked to the increased specific humidity (i.e., changes in the thermodynamic effect). However, there are some opposite phenomenon as well, when looking at the regional changes in PmE (i.e., northern Indian Ocean, North Africa, and the SPCZ). These may suggest that another factor, such as atmospheric circulation anomalies (i.e., changes in dynamic effect), may play an important role in changing the regional PmE pattern at low latitudes.

Multi-proxy studies are qualitatively consistent with the results of the PlioMIP2 ensemble (Feng et al., 2021). For several studies, proxy reconstructions suggest an expansion of woodland and a higher density of land cover over northern Africa, indicating moistening signals there (Salzmann et al., 2008; Bonnefille, 2010). The sedimentological indicators and pollen data also suggest a more humid climate over the Levant and Arabian peninsulas during the mid-Pliocene (Munoz et al., 2002; Heermance et al., 2013). In addition, the faunal remains or palynological transfer functions show wetter conditions in East and South Asia during the mid-Pliocene (Sanyal et al., 2004; Igarashi and Yoshida, 1988; Kou et al., 2006). However, uncertainties related to the hydroclimate of the mid-Pliocene still remain. For instance, pollen evidence suggests little hydroclimate change during the Pliocene in Qaidam Basin and southwest China's Yuanmou region (Wang et al., 1999; Chang et al., 2010; Heermance et al., 2013). Some proxies even show a drier climate over the Loess Plateau region (Ji et al., 2017; Sun et al., 2010). Note that the relatively low availability of Pliocene hydroclimate proxies makes it difficult to perform a model–proxy comparison. Furthermore, PlioMIP2 modeling experiments are designed to simulate the Marine Isotope Stage KM5c (3.205 Ma) during the mid-Pliocene, and this particular orbital interval likely does not represent the full Pliocene hydroclimate variability, adding uncertainties to model–proxy comparison (Samakinwa et al., 2020).

Figure 7a shows the changes in MMM SST superimposed on the reconstructed SST anomalies (McClymont et al., 2020). In the MMM, SSTs are between 1 and 6∘C warmer in the mid-Pliocene simulations than in the PI simulations. Note that the SST warming is amplified in the northwest tropical Indian Ocean, whereas it is reduced off the Indonesian coast, showing a pattern similar to the tropical Indian Ocean dipole (IOD). The sharp SST gradients drive strong southeasterly wind anomalies on the Equator (not shown). Xie et al. (2010) suggest that this easterly wind anomaly may shoal the thermocline in the east, helping lower the SST there via upwelling and indicating this SST anomaly over tropical Indian Ocean may be related to the Bjerknes feedback. The simulated North Atlantic warming might be related to an intensified mid-Pliocene Atlantic meridional overturning circulation (Li et al., 2020). However, Z. Zhang et al. (2021) suggest that the increased background ocean vertical mixing parameters could also contribute to the warm SSTs there. In addition, the relative smaller SST warming in Southeast Pacific and Atlantic, which is co-located with the intensified southeast trade winds, suggests the role of wind–evaporation–SST feedback (Xie et al., 2010). These SST warming patterns are consistent with current studies (Haywood et al., 2020; Williams et al., 2021). As expected, the specific humidity is increased in the low-level troposphere in the mid-Pliocene warm period (Fig. 7b) (Murray, 1966; Held and Soden, 2006). On the other hand, the sinking branch of meridional circulation in the control climate is located in subtropical regions, showing divergent circulation ∇⋅V‾>0 in the low-level troposphere; the contrary applies for the regions of deep tropics, i.e., the ITCZ and SPCZ. These two factors contribute the δTHD_M term (i.e., -1ρg∫0psδq∇⋅VM0dp) to the thermodynamic effect (Fig. 3f) and, hence, changes in PmE.

Although the δTHD_M term is the first-order control on the thermodynamic effect in most regions, the δTHD_Z term contributes to the thermodynamic effect to some extent, especially over the adjacent northern Indian Ocean. The climate mean zonal circulation characterizes ascending motion in the tropical western Pacific, tropical African, and tropical southern American regions, favoring convergent circulation (i.e., -∇⋅V‾Z0>0) there (Fig. 6d; Hastenrath, 1991; Peixoto and Oort, 1992). With increased specific humidity (δq>0) under a warmer climate, the δTHD_Z term (i.e., -1ρg∫0psδq∇⋅VZ0dp) shows a positive contribution and, hence, increases PmE in these regions (Fig. 3g). On the contrary, the δTHD_Z favors a decrease in PmE over the western Indian Ocean, eastern Pacific, and tropical Atlantic (Fig. 3g), where the climate mean zonal circulation is divergent (Fig. 7d).

In Sect. 4, we have demonstrated that the primary dynamic contribution to changes in PmE is a consequence of anomalous meridional circulation (the δMCDD_M term). Figure 8a shows the annual mean mass stream function (MSF) of meridional circulation for the PI simulation (contours), which is similar to present-day meridional circulation (Cheng et al., 2020). During the mid-Pliocene, the meridional circulation changes are characterized by enhanced meridional circulation in the SH tropics and weakened meridional circulation in the NH tropics (shading in Fig. 8), which is caused by the northward shift of meridional circulation in the SH, as indicated in our later discussion. To quantify meridional circulation changes, we further calculated the intensity in Fig. 8b. The intensity is defined as the maximum of the absolute average MSF between 200 and 925 hPa in the range from 30∘ S to 30∘ N (Oort and Yienger, 1996) in Fig. 8a. Models simulate a consistently weakened meridional circulation intensity in the NH and a slightly strengthened intensity in the SH (Fig. 8b), which is related to the hemispheric asymmetry of the atmospheric energy budget (Feng et al., 2020).

As a result, meridional circulation anomalies could induce divergent/convergent circulation anomalies in the low-level troposphere (Fig. 9). The weakened local meridional circulation leads to anomalous southerly winds spanning northeastern South America eastward to the northwestern Pacific region. These meridional circulation anomalies induce the anomalous divergence (convergence) of circulation over the Indo-Pacific warm pool (adjacent to subtropical regions), resulting in a negative (positive) contribution from δMCDD_M (Figs. 9 vs. 4f). In fact, this anomalous meridional circulation is closely related to the strengthened Asian summer monsoon (not shown), consistent with previous studies (Zhang et al., 2013; Prescott et al., 2019). In addition, anomalous northerly winds exist in the western tropical Pacific, but southerly winds are located in the central Pacific (Fig. 9). These circulation anomalies could induce δMCDD_M, which favors moistening of the equatorial central Pacific and southern part of the SPCZ region but dries the SPCZ (Fig. 4f). Previous studies have indicated that these circulation anomalies are caused by the southward shift of the SPCZ, which is mainly modulated by the intensified and westward shift of the South Pacific subtropical high for the mid-Pliocene compared with the PI simulation (Pontes et al., 2020).

One question arises regarding what causes the meridional circulation changes under mid-Pliocene conditions. At low latitudes, it is worth noting that the ITCZ lies at the foot of the ascending branch of the meridional circulation, which is highly linked to the hemispheric asymmetry of the atmospheric energy budget (Frierson et al., 2013). We further quantify the shift of the ITCZ in Fig. 8c and Earth's energy budget in Fig. 8d and e. The definition of the ITCZ location is the latitude of the maximal annual mean precipitation between 20 and 20∘ S (Frierson and Hwang, 2012; Donohoe et al., 2013). On average, ensemble models show that the NH atmosphere receives 1.5 W m-2 more net radiation than the SH (Fig. 8d), which could induce an increased cross-equatorial southward energy flux of 0.22 PW (Fig. 8e). Thus, this imbalance in the atmospheric energy budget causes a 1.1∘ northward shift in the zonal-mean ITCZ latitude. Consequently, this shift of the ITCZ reorganizes atmospheric circulation (Watt-Meyer and Frierson, 2019), leading to the northward movement of the meridional circulation in the SH (Fig. 8a). This meridional circulation shift could result in a weakened (strengthened) meridional circulation in the NH (SH) (Fig. 8b) and, hence, drive δMCDD_M (Fig. 4f) and MMTD (Fig. 6c). Pontes et al. (2021) indicated that the anomalous wind over the southern Pacific is related to the El Niño–Southern Oscillation (ENSO) weakening across models, which could favor a northward shift of the ITCZ. In addition, it should be noted that the northward shift of the ITCZ exists in both the boreal summer (June–July–August) and winter (December–January–February) seasons, accompanied by the northward shift of the meridional circulation in the SH (not shown). Pontes et al. (2021) further suggested that the northward shift of the Pacific ITCZ during austral spring–summer is remarkably related to the ENSO weakening across models, which is associated with the stronger climatological circulation in the SH.

As mentioned above, δMCDD_Z plays a key role in the changes in PmE over the northern Indian Ocean. As this term is linked to Walker circulation anomalies, we further discuss Walker circulation changes in the mid-Pliocene warm climate.

There is a noticeable diversity in the simulated Pacific Walker circulation (PWC) intensity across the models (Fig. 10a). In addition, previous work has suggested that the PWC intensity is closely tied to the zonal SST and sea level pressure (SLP) gradient during the mid-Piacenzian (Tierney et al., 2019). In this paper, the dSLP and dSST are defined as the difference in SLP and SST across the equatorial Indo-Pacific (160–80∘ W, 5∘ S–5∘ N minus 80–160∘ E, 5∘ S–5∘ N). As expected, the models with an enhanced zonal SST gradient across the equatorial Indo-Pacific tend to produce a weaker zonal SLP gradient and decreased PWC (not shown), with the inter-model correlations of -0.95 and -0.75, respectively. Note that the PlioMIP2 models produce a large spread in simulating the changes in dSST (Fig. 10c) and dSLP (Fig. 10d), which is consistent with the results in Fig. 10a. Previous studies have suggested that the east–west SST gradient was reduced in SST proxies (Tierney et al., 2019). This feature is captured by the CESM2, GISS-E2-1-G, and HadGEM3 models (Fig. 10a, b, c). However, other models (i.e., the CCSM4, CCSM4-Utrecht, EC-Earth3-LR, and NorESM-L models) consistently simulated stronger PWC intensity (Fig. 10a, b, c). That is, the results suggest that the model-simulated changes in the strength of PWC are probably highly model dependent, which might be affected by the different parameterizations (Tierney et al., 2019).

However, the westward shift of the PWC is a robust feature among these models, except the COSMOS and GISS-E2-1-G models (Fig. 10b). To discuss the impact of the PWC shift on atmospheric circulation in the tropics, we further calculate the changes in the zonal mass stream function (ZMS) for the mid-Pliocene with respect to the PI simulation in Fig. 11. As suggested in Fig. 7d, the ZMS in the PI simulation (contours in Fig. 11a) is characterized by ascending motion in the tropical western Pacific and Maritime Continent and descending motion in the western Indian Ocean and eastern Pacific, consistent with previous studies (Kamae et al., 2011; Bayr et al., 2014; Ma and Zhou, 2016; Han et al., 2020). Compared with the PI simulation, the most striking features in the mid-Pliocene simulation are weakened ascending motion over the Maritime Continent and tropical western Pacific and strengthened descending motion on the western Indian Ocean, indicating a westward expansion of the PWC (Fig. 11b).

The westward shift of the PWC can also be seen from the potential velocity (Fig. 12). This shows that the center of the anomalous positive values is located in the northern Indian Ocean. In contrast, the center of a negative value exists in the equatorial eastern Pacific and western Atlantic in the low-level troposphere (Fig. 12a). Concurrent, generally opposite anomalies can be seen in the upper-level troposphere (Fig. 12b). Indeed, these features indicate an upward (downward) motion shift from the tropical western Pacific (eastern Pacific) to the west of the Indian Ocean (central Pacific), resulting from the westward expansion of the PWC (Figs. 10b, 11). That is, when divergent/convergent circulations are combined with the climate mean specific humidity (q‾>0) in the lower troposphere, they can trigger a negative/positive contribution from the δMCDD_Z term to changes in PmE (Fig. 4g).