EC-Earth is a fully coupled ocean–atmosphere GCM . We have used model version 2.2. The Integrated Forecasting System (IFS) was the atmospheric component. The spectral resolution was T159 (roughly 1.125∘×1.125∘) with 62 vertical levels. The convective scheme was used along with the H-TESSEL land surface scheme, including surface runoff. The Nucleus for European Modeling of the Ocean (NEMO, version 2) was the ocean component. The horizontal resolution was 1∘ with 42 vertical levels . NEMO includes sea-ice model LIM2. The OASIS3 coupler couples the ocean, sea ice, land, and atmosphere. EC-Earth performs well for the present day when compared to CMIP3 models in terms of climatology as well as inter-annual, spatial, and temporal variability .

The two precession extremes, precession minima Pmin and precession maxima Pmax, correspond to summer solstice at perihelion and winter solstice at perihelion, respectively (Fig. ). Table  shows the orbital configurations used. This leads to a stronger seasonal cycle in the Northern Hemisphere (NH) and a weaker seasonal cycle in the Southern Hemisphere (SH) in Pmin (Fig. ). On the other hand, the seasonal cycle is weaker in the NH and stronger in the SH in Pmax.

The model is run separately for each of the orbital configurations. The length of each simulation is 100 years, with the first 50 years being considered spinup. We have used the climatology of the last 50 years, for all our analysis. The orbital parameters remain constant throughout the simulation. All other boundary conditions (e.g., the solar constant, greenhouse gas concentrations, orography, ice sheets, vegetation) were kept constant at the pre-industrial levels. Vernal equinox has been fixed at 21 March, and the present-day calendar is used. Since the length of the season and the dates of equinoxes change along the precession cycle, the autumn equinoxes do not coincide. This is known as the “calendar effect”. It introduces some errors due to the phasing of insolation. We do not make any corrections in order to be consistent with previous studies. Further details about the experiments are provided in .

The Hadley cell is a thermally direct overturning circulation in the tropics. It takes energy away from the tropics and transports it towards the poles. The Hadley cell has a rising branch in the deep tropics and a descending branch in the extra-tropics. This leads to moisture convergence near the rising branch. The ITCZ coincides with the rising branch of the Hadley cell and is responsible for the zone of heaviest precipitation in the tropics. The characteristics of the ITCZ can be described by using the conservation equations for moist static energy (MSE) and moisture. Using this approach, proposed a simple model for ITCZ in terms of net energy input into the atmosphere and vertical stability. This is a diagnostic model that has been used to explain variations in rainfall due to global warming and the impacts of aerosols . In this section, we have discussed this simple model in detail. Equations () and () correspond to the conservation of MSE and moisture in a vertical column of the atmosphere. The first term in both the equations is horizontal divergence, with the second term being the vertical divergence of MSE and moisture fluxes, respectively.

The quantities on the right-hand side are the sum of all sources and sinks. Further details on the derivation of Eq. () can be found in . The time derivatives have been dropped in these equations because the climate is assumed to be in a steady state. The angle brackets (〈〉) indicate vertical integral. ∇⋅mU+∂mω∂p=Qdiv,∇⋅qU+∂qω∂p=E-P,A=-∫PbPtAdpg, where P is the precipitation rate (mm day-1). E is the evaporation rate (mm day-1). Qdiv is the total column energy, i.e., the sum of all the energy fluxes into the atmosphere (Eq. ) (in mm day-1; taking the latent heat of vaporization as 2.26×106 J kg-1, we get 1 mm day-1=26.16 W m-2). Over land since the storage term is small, the sum of all the energy fluxes at the surface is small. Hence, Qdiv is mainly governed by the fluxes at the top of atmosphere (TOA). However, over oceans the contribution of surface fluxes is large. q is specific humidity (kg kg-1). m is moist static energy (J kg-1), which is the sum of internal energy, potential energy, and moist energy (CpT+gZ+Lvq). Pb is the pressure at the bottom of the atmospheric column (Pa). Pt is the pressure at the top of the atmospheric column (Pa). g is the acceleration due to gravity (m s-2). The full equation for Qdiv is Qdiv=LHF+SHF+Net_Sfc_Rad︸bottom fluxes+Net_TOA_LW+Net_TOA_SW︸TOA Fluxes. where LHF is surface latent heat flux (mm day-1). SHF is surface sensible heat flux (mm day-1). Net_Sfc_Rad is net surface radiation (long wave + short wave) (mm day-1). Net_TOA_LW is net top of atmosphere longwave radiation (mm day-1). Net_TOA_SW is net top of atmosphere shortwave radiation (mm day-1). Clubbing all the radiation fluxes together into one quantity “Qrad”, we get Qdiv=LHF+SHF+Qrad. Assuming ω=0 at the top as well as the surface leaves us with the horizontal terms only. The governing equations can be combined and simplified as P-E=QdivGMS,GMS=m1-m2Lv(q2-q1),m1=∫PtPmm∇⋅Udp/g∫PtPm∇⋅Udp/g,m2=∫PmPbm∇⋅Udp/g∫PmPb∇⋅Udp/g, where GMS is the gross moist stability, as obtained by taking the ratio of Eqs. (2.11) and (2.12) from . m1 and m2 are, respectively, the total MSE in the upper (mid troposphere to top) and lower troposphere (surface to mid troposphere), normalized by the divergence of that layer. Thus, GMS is mainly a function of vertical profiles of MSE, and it provides a measure of vertical stratification of the atmosphere. Pm is pressure at the mid-troposphere level. Similarly, q1 and q2 represent the total moisture in the upper and lower troposphere, normalized by divergence. The mass convergence in the lower troposphere is the same as the mass divergence in the upper troposphere. The horizontal variations of temperature and moisture are assumed to be weak within the tropics. This implies that the horizontal advection of temperature and moisture is small. This simple model attributes the changes in P-E to either the changes in total column energy or the vertical stability.

Figure a shows a scatter of P-E as a function of Qdiv for the 3 summer months June, July, and August taken separately. The scatter is made for central India, the Bay of Bengal, and northern Africa for each of the precession extremes. We chose these three regions to highlight that neglecting the role of horizontal advection may not always be appropriate. The plot shows that the two are nearly linear, as indicated by the simple model (Eq. ). The slight deviations from linearity are due to variations in GMS. As we go from Pmax to Pmin (low to high insolation in NH summer), both Qdiv and P-E increase over central India and northern Africa (land regions). However, both these quantities decrease over the Bay of Bengal (oceanic region). The net energy input into the atmosphere and thus Qdiv is positive for all these regions during the summer.

We have shown in Fig. b a scatter of P-E vs. GMS for the same regions. The figure shows that there is no definite relation between the two. Equation () suggests that all values for GMS should be positive since P-E and Qdiv are both positive. There are, however, some points in the scatter where GMS is negative. This indicates that the assumption about the horizontal advection being small is not always valid. Hence, we modify the definition of GMS to include the horizontal advection terms.

By taking the ratio of Eqs. () and (), after multiplying Eq. () by Lv (the latent heat of vaporization for water), we get P-E=QdivTGMS,TGMS=∇⋅mU+∂mω∂p-Lv∇⋅qU+∂qω∂p, where TGMS stands for total GMS (the term “total” indicates inclusion of all advection terms). TGMS is based on only one assumption, that the time derivatives of m and q are negligible. This is a good assumption for seasonal mean conditions. TGMS is particularly useful for smaller regions, where horizontal advection can be large. TGMS represents how efficiently an atmospheric column can diverge MSE per unit moisture converged into the column. TGMS is an extension of the concept of GMS, with horizontal advection terms included. This suggests that, along with the energy fluxes and vertical stratification of a column, the lateral transport of MSE and moisture determine the precipitation. A value of TGMS similar in magnitude to GMS indicates that the horizontal transport of MSE is negligible. A change in TGMS between two climates would suggest that the transport of MSE has changed. We have used the equivalence in Eqs. () and () to estimate TGMS. Since our goal is not to estimate the changes in P-E but to diagnose the cause of these changes, there is no need to make an independent estimate of TGMS.

To quantify the relative contribution of Qdiv and TGMS to the changes in P-E, we do the following. Writing Eq. () for Pmax, P-E=QG, where P, E, Q, and G are precipitation, evaporation, Qdiv, and TGMS, respectively. Considering Pmax as the reference case and Pmin as the perturbed case, we can write the following for Pmin: (P+ΔP)-(E+ΔE)=Q+ΔQG+ΔG, where Δ represents the perturbation from Pmax. Now dividing by P-E, we get 1+Δ(P-E)(P-E)=1+ΔQ/Q1+ΔG/G.

This equation can further be modified as Δ(P-E)︸Change inP-E=ΔQQ1+ΔGG(P-E)︸Contribution fromQdiv+-ΔGG1+ΔGG(P-E)︸Contribution from TGMS.

suggested that different response of the Indian land mass and the Bay of Bengal is due to migration of near-surface equivalent potential temperature from the Bay of Bengal over to India. This is because the rate of increase in insolation is higher in the high insolation (similar to Pmin) experiment. This causes the equivalent potential temperature θe to rise rapidly over India. It is known that the location of ITCZ coincides with that of the surface energy maxima . Hence ITCZ migrates over India quickly and remains there. However, EC-Earth simulates higher near-surface equivalent potential temperature θe over the Bay of Bengal, in both Pmin and Pmax (Fig. ). In this section, we propose an alternate mechanism for the different response of the Indian land mass and the Bay of Bengal to the changes in precession.

We have shown earlier that in Pmin there is an increase in Qdiv over the Indian land mass and a decrease over the Bay of Bengal with respect to Pmax (Figs.  and ). Here we examine the factors that caused the changes in Qdiv. Splitting Qdiv into its component fluxes (Eq. ) will help us to determine which flux contributed the most. Figure  is a spatial map of the differences in P-E, Qdiv and its component fluxes Qrad, LHF, and SHF. Qdiv has a good spatial coherence with P-E, over most of the regions except the Arabian Sea. As was discussed earlier, this is due to the changes in TGMS, which is able to counter the effect of reduced Qdiv. P-E has decreased along the southern parts of the Western Ghats but has increased in the northern parts of the Western Ghats. Qrad bears a resemblance to P-E. This suggests that radiative feedbacks from clouds are present. Changes in Qrad are not large enough to counter the decrease in latent heat flux (LHF) over the Arabian Sea and the Bay of Bengal. Thus, the decrease in LHF over these regions reduces Qdiv there. In fact, Qdiv and LHF have similar spatial patterns over the oceanic regions. The changes in sensible heat flux (SHF) are small in most places.

We take two regions: one over central India and the other over the Bay of Bengal, to identify the flux which contributes most to the changes in Qdiv. These regions are outlined with black boxes in Fig. a. The changes in the three components of Qdiv over these two regions are depicted in the bar chart (Fig. f). It shows the dominance of the radiative terms over India, and LHF over the Bay of Bengal, respectively.

LHF is a function of surface wind speed, sea surface temperature (SST), and near-surface relative humidity. LHF increases with an increase in SST and wind speed. SST has increased over the Bay of Bengal and southern Arabian Sea by about 2 ∘C (Supplement Fig. S1). Thus, it cannot explain the decrease in LHF. Hence, we look at the changes in wind speed (Fig. ). Fig. a and b show the mean winds at 850 hPa. The shading indicates wind speed and the streamlines show the direction of flow. The axis of the low-level jet (LLJ) has shifted to the north, and this has led to a decrease in winds over the Bay of Bengal. Due to LLJ, deep oceanic water upwells along the coast of Somalia. This leads to cooler SSTs over the western parts of the Arabian Sea. Since in Pmin, LLJ has shifted further north, the region of upwelling also shifts north, thus leading to cooler SSTs in the western coast of the northern Arabian Sea (Fig. S1). Hence, LHF over the Arabian Sea decreases due to weaker winds in the southern parts and colder SST in the northern parts.

The shift in LLJ leads to lesser moisture flux along the southern part of the Western Ghats. Hence, P-E decreases there. At the same time, the LLJ brings more moisture into the northern parts of the Western Ghats, leading to increase in P-E. The shift of the LLJ can be seen more clearly in Fig. c, where the difference in winds between Pmin and Pmax is shown. Along the Equator, there exists an anomalous low-level easterly over the Indian Ocean. This meets an anomalous westerly from over equatorial Africa, at around 40∘ E. This indicates low-level convergence. Furthermore, on the same meridian, there exists a cyclonic circulation to the north (over the Middle East) and an anti-cyclonic circulation to the south (over Madagascar). This resembles the response of the winds to the heating of an atmospheric column as shown by .

proposed a simple shallow water model on an equatorial β plane to elucidate the role of latent heating on surface winds. In order to represent convective heating due to latent heat release, he introduced mass divergence in the atmospheric column. When this model was forced with “heating” over a region at the Equator and another region to the north of the Equator, it produced a Kelvin wave and a mixed Rossby-gravity wave. The Kelvin wave leads to an anomalous low-level easterly and an anomalous low-level westerly along the Equator. The easterly is to the east of the heat source and the westerly to the west of the heat source. These anomalous winds thus lead to low-level convergence at the Equator, near the region of the heat source. The mixed Rossby-gravity wave has a cyclonic circulation to the north of the Equator and an anti-cyclonic circulation to the south of the Equator. The wind response of EC-Earth hence, suggests that the wind patterns over the Indian subcontinent, are driven by atmospheric heating near the Equator and off-Equator. Examining Fig. a shows that the heat sources correspond to convective heating of the column due to increased precipitation over the West Equatorial Indian Ocean (WEIO) and over the Middle East (particularly the Red Sea). There are, however, some important differences between EC-Earth and the Gill model. EC-Earth is a full GCM with non-zero mean background winds, whereas Gill model is linearized with respect to zero mean background winds. Thus, the EC-Earth’s response includes non-linear terms as well.

To summarize, the decrease in Qdiv over the Bay of Bengal is due to lower wind speeds. The winds decrease because of convective heating over west equatorial Indian Ocean and the Red Sea. The convection over the Red Sea is an extension of the African monsoon. Hence, we examine the factors which lead to an increase in precipitation over these regions. The prevailing conditions in the pre-monsoon month of May, leads to enhanced convection over these regions, later in the summer. Figure a and b, show the difference in Qdiv and P-E for the month of May. Figure b shows changes in P-E in shading and the streamlines represent the changes in the wind direction. Qdiv is higher over Africa, and this causes early onset of the African monsoon (Fig. b) and changes the low-level winds along the eastern coast of Africa. The SST along the eastern coast depends on the coastal upwelling. The changes in winds thus reduce upwelling and increase SST. This enhances convection over the West Equatorial Indian Ocean, further leading to low-level convergence. This positive feedback is responsible for the convective heating that persists through the summer months. As the season advances from May onwards, the African monsoon propagates northward. The region of convection over the eastern side of Africa moves over to the Red Sea. This becomes the off-equatorial heat source.

showed that the Southeast Asian monsoon and the Northeast Asian monsoon are out of phase owing to the El Niño-like SST pattern in Pmin. Here we are addressing the differences in the precipitation changes over Southeast Asia (land) and the adjacent ocean. The domain for Southeast Asia is shown in Fig. b. Based on the analysis using Eq. (), we find that the increase (decrease) in P-E over the land (ocean) grids is mainly due to the increase (decrease) in Qdiv (Fig. ). Even though Qdiv is dominant, the contribution of TGMS is higher over Southeast Asia (oceanic regions) when compared to the Bay of Bengal. Once again decomposing Qdiv into its component fluxes suggests a similar mechanism that leads to the Indian Bay of Bengal redistribution of precipitation (Fig. f). The increase in insolation leads to an increase in Qdiv over the Southeast Asian land, whereas a decrease in LHF over the oceanic regions leads to a decrease in Qdiv. The convective heating over WEIO and the Red Sea leads to reduced winds, and hence decreased LHF in the northwestern Pacific.