The role of the cloud radiative effect in the sensitivity of the Intertropical Convergence Zone to convective mixing

Studies have shown that the location and structure of the simulated intertropical convergence zone (ITCZ) is sensitive to the treatment of sub-gridscale convection and cloud–radiation interactions. This sensitivity remains in idealized aquaplanet experiments with ﬁxed surface temperatures. However, studies have not consideredthe role of cloud-radiativeeffects (CRE; atmospheric heating due to cloud–radiation interactions) in the sensitivity of the ITCZ to the treatment of convection. We use an atmospheric energy input (AEI) framework to explore how the CRE modulates the sensitivity of the ITCZ to convective mixing in aquaplanet simulations. Simulations show a sensitivity of the ITCZ to convective mixing, with stronger convective mixing favoring a single ITCZ. For simulations with a single ITCZ, the CRE maintains the positive equatorial AEI. To explore the role of the CRE further, we prescribe the CRE as either zero or a meridionally and diurnally varying climatology. Removing the CRE is associated with a reduced equatorial AEI and an increase in the range of convective mixing rates that produce a double ITCZ. Prescribing the CRE reduces the sensitivity of the ITCZ to convective mixing by 50%. In prescribed-CRE simulations, other AEI components, in particular the surface latent heat ﬂux, modulate the sensitivity of the AEI to convective mixing. Analysis of the me- ridional moist static energy transport shows that a shallower Hadley circulation can produce an equatorward energy transport at low latitudes even with equatorial ascent.


Introduction
Tropical rainfall is often associated with a discontinuous zonal precipitation band commonly known as the intertropical convergence zone (ITCZ). The ITCZ migrates between the Northern and Southern Hemispheres with the seasonal cycle, with a zonal-mean, time-mean position of approximately 68N ). The ITCZ is collocated with the ascending branch of the Hadley circulation, where strong moist convection leads to high rainfall. The upper branches of the Hadley circulation typically transport energy poleward, away from the ITCZ. Recent studies have associated characteristics of the ITCZ with the energy transport by the Hadley circulation (Frierson and Hwang 2012;Donohoe et al. 2013;Adam et al. 2016;Bischoff and Schneider 2016).
A double ITCZ bias is prominent in current and previous generations of coupled general circulation models (GCMs; Li and Xie 2014;Oueslati and Bellon 2015). The ITCZ is too intense in the Southern Hemisphere (Lin 2007), resulting in two annual-mean, zonal-mean tropical precipitation maxima, one in each hemisphere. A bias Denotes content that is immediately available upon publication as open access. remains in atmosphere-only simulations with prescribed sea surface temperatures (SSTs) (Li and Xie 2014). Aquaplanet simulations provide an idealized modeling environment in which some complex boundary conditions in tropical circulation, such as land-sea contrasts and orography, are removed. However, aquaplanet configurations of GCMs coupled to a slab ocean produce a broad range of tropical precipitation mean states (Voigt et al. 2016); even prescribing zonally uniform SSTs does not resolve the intermodel variability (Blackburn et al. 2013).

a. Modeling studies
Characteristics of the simulated ITCZ are sensitive to the representation of cloud-radiation interactions (Fermepin and Bony 2014;Li et al. 2015;Harrop and Hartmann 2016). In the deep tropics the cloud radiative effect (CRE) warms the atmosphere (Allan 2011), with important effects on tropical circulation (Slingo and Slingo 1988;Crueger and Stevens 2015). The CRE is associated with a more prominent single ITCZ (Crueger and Stevens 2015;Harrop and Hartmann 2016;Popp and Silvers 2017). Both Harrop and Hartmann (2016) and Popp and Silvers (2017) investigated the association between the Hadley circulation and CRE in a range of aquaplanet simulations with and without the CRE. In all GCMs used, the CRE is associated with increased equatorial rainfall, an equatorward contraction of the ITCZ, and a strengthening of the mean meridional circulation. The authors emphasize different mechanisms by which the CRE promotes a single ITCZ. Harrop and Hartmann (2016) propose that the CRE warms the upper tropical troposphere, which reduces the convective available potential energy and restricts deep convection to the region of warmest SSTs, while Popp and Silvers (2017) argue that the CRE strengthens the Hadley circulation and moves the ITCZ equatorward, associated with increased moist static energy (MSE) advection by the lower branches of the Hadley circulation. The strengthening of the mean circulation is associated with the CRE meridional gradient, as the CRE is positive in the tropics and negative in the extratropics ($6 458latitude; Allan 2011). However, it should be noted that the CRE reduces total tropical-mean (#6 308latitude) precipitation due to reduced radiative cooling (Harrop and Hartmann 2016).
Across a hierarchy of models it has been shown that the simulation of tropical precipitation is sensitive to the representation of convection (Terray 1998;Frierson 2007;Wang et al. 2007;Chikira 2010; Mobis and Stevens 2012;Oueslati and Bellon 2013;Bush et al. 2015;Nolan et al. 2016). For example, variations in lateral entrainment and detrainment rates, which alter the representation of deep convection, affect the diurnal cycle of precipitation over the Maritime Continent (Wang et al. 2007) and South Asian monsoon precipitation rates (Bush et al. 2015). Increasing convective mixing strengthens deep convection in convergence zones, associated with an increased moisture flux from subsidence regions (Terray 1998;Oueslati and Bellon 2013).
In full GCMs, complex surface characteristics and boundary conditions, including land-sea contrasts, orography, and SST gradients, make it challenging to understand the sensitivity of tropical precipitation to the representation of convection (Oueslati and Bellon 2013;Bush et al. 2015). Even in the absence of complex surface topography, aquaplanet studies have also shown that characteristics of tropical precipitation, in particular the location and intensity of the ITCZ, are sensitive to the sub-gridscale treatment of convection (Hess et al. 1993;Numaguti 1995;Chao and Chen 2004;Liu et al. 2010;Mobis and Stevens 2012). Mobis and Stevens (2012) studied the sensitivity of the ITCZ location to the choice of convective parameterization scheme in an aquaplanet configuration of the ECHAM GCM by comparing the Nordeng (1994) and Tiedtke (1989) schemes, which vary in their formulations of entrainment, detrainment and cloud base mass flux for deep convection. The Nordeng scheme, with a higher lateral entrainment rate, produced a single ITCZ, while the Tiedtke scheme produced a double ITCZ. The authors associate the location of maximum boundary layer MSE with the ITCZ location; they argue that mechanisms that control the boundary layer MSE are important to the sensitivity of the ITCZ to the representation of convection. The boundary layer MSE distribution is predominantly controlled by the surface winds, which are influenced by convective heating, allowing variations in convective heating to influence the ITCZ structure. The importance of the surface winds is further emphasized by simulations with prescribed surface winds in the computation of the surface fluxes (Mobis and Stevens 2012). These simulations lead to the conclusion that there is a strong association between surface turbulent fluxes and the ITCZ.
While the ITCZ has been shown to be sensitive to the CRE and the convective parameterization scheme, no study has separated these effects. This paper will analyze the sensitivity of the ITCZ to convective mixing in aquaplanet simulations using the Met Office Unified Model (MetUM), and the role of the CRE in this sensitivity.

b. Atmospheric energy framework
Literature based on a hierarchy of models, as well as reanalysis data and observations, concludes that the northward displacement of the ITCZ from the equator is anticorrelated with the northward cross-equatorial atmospheric energy transport (Kang et al. 2008;Frierson and Hwang 2012;Donohoe et al. 2013). Bischoff and Schneider (2014) developed a diagnostic framework to relate the location of the ITCZ to this energy transport.
The zonal-mean atmospheric MSE budget is (Neelin and Held 1987) where AEI is the atmospheric energy input, yh is the meridional MSE flux (y is meridional wind; h is MSE), h e is the moist enthalpy, square brackets denote zonal mean time mean, hat (^) represents a mass weighted vertical integral, › y is the meridional derivative, and › t is the time derivative. Local Cartesian coordinates are printed with y 5 af, (where a is Earth's radius and f is latitude), but all calculations are performed in spherical coordinates. Bischoff and Schneider (2014) Bischoff and Schneider (2014) derive the dependence of the ITCZ location on the equatorial MSE flux and equatorial AEI: with the AEI defined as where subscript 0 denotes the equatorial value, S is the net incoming shortwave radiation at the top of the atmosphere (TOA), L is the outgoing longwave radiation at the TOA, and O is the net downward flux at the surface. Bischoff and Schneider (2016) retain higher-order terms in the Taylor expansion to derive a framework for negative [AEI] 0 . A negative [AEI] 0 is associated with a double ITCZ as [ c yh] no longer increases with latitude; energy is transported equatorward at low latitudes to achieve equilibrium. A double ITCZ is associated with two off-equatorial energy flux equators, where the total meridional energy flux equals zero. Bischoff and Schneider (2016) derive an expression for the locations of a double ITCZ: Note that Eq. (4) is from a corrigendum for the original paper. Bischoff and Schneider (2014) explore the relationship derived in Eq. (2) using an idealized slab-ocean GCM with a prescribed oceanic heat transport. They investigate the effects of the [AEI] 0 and the [ c yh] 0 through varying the imposed equatorial ocean heat flux and the atmospheric longwave absorption. Changes in both [AEI] 0 and [ c yh] 0 affect the latitude of the ITCZ; this theoretical relationship is supported in observations and reanalyses (Adam et al. 2016). Bischoff and Schneider (2016) (3)] is chosen as their simulations prescribe O, which allows only the TOA energy budget (S 2 L) to vary. This constrains the AEI response to model perturbations, as surface radiation and turbulent fluxes are constrained at equilibrium, which could reduce the impact of surface-flux feedbacks on the ITCZ. We use atmosphere-only simulations with prescribed SSTs, allowing variations in the components of O. As our experiments do not have a closed surface energy balance and we are interested in cloudy-sky radiation AEI components, we choose to write the AEI as where SW and LW represent the net atmospheric heating from shortwave and longwave radiation, respectively, and H denotes the atmospheric heating from surface sensible and latent heat fluxes. Both fixed SST and prescribed O frameworks misrepresent the real climate system by restricting air-sea coupled feedbacks (discussed further in section 4). From an AEI perspective, Mobis and Stevens (2012) severely constrain H in a subset of experiments by prescribing the surface winds when computing the surface fluxes. This reduces the sensitivity of the ITCZ to the convective parameterization scheme. Previous research on the response of the simulated ITCZ to variations in the sub-gridscale representation of convection has not considered the role of the CRE or used an energy budget framework like that proposed by Bischoff and Schneider (2014). We hypothesize that the sensitivity of the ITCZ to these factors can be linked to variations in AEI and [ c yh].

Methodology
We use variations of an N96 (1.258 latitude 3 1.8758 longitude) aquaplanet configuration of the Met Office Unified Model Global Atmosphere 6.0 (GA6.0) configuration (Walters et al. 2017). The deep convective parameterization scheme is an altered form of the mass flux scheme in Gregory and Rowntree (1990), including a convective available potential energy closure based on Fritsch and Chappell (1980) and a mixing detrainment rate dependent on the relative humidity (Derbyshire et al. 2004). Unless noted, all simulations are run for three years with a ''Qobs'' SST profile (Neale and Hoskins 2001), with the first 60 days discarded as spinup.
To explore the influence of the CRE on the sensitivity of the ITCZ to convective mixing we perform a companion set of experiments with cloud-radiation interactions removed: F0.28NC, F0.57NC, F0.85NC, F1.13NC, and F1.70NC (Table 1). Cloud-radiation interactions are removed by setting cloud liquid and cloud ice to zero in the radiation scheme.
Finally, a third set of simulations use a prescribed CRE (Table 2) to investigate the relative importance of f dp and the CRE to characteristics of the ITCZ. The four simulations have a prescribed, diurnally varying CRE vertical profile computed from a single-year simulation with f dp equal to 0.57 or 1.13 (PC0.57 and PC1.13, respectively). The CRE is prescribed using cloudy-sky upward and downward fluxes at each model level at every model time step. The diurnally varying CRE profile is computed as a hemispherically symmetric and zonally uniform composite of the climatological diurnal cycle at each grid point, referenced to local solar time. Two of the four simulations prescribe a CRE at a different f dp constant from that in the simulation (F1.13PC0.57, F0.57PC1.13), while the other two simulations use a CRE from the same f dp value to assess the sensitivity to prescribed cloud-radiation interactions (F1.13PC1.13, F0.57PC0.57).

Results
a. Sensitivity of the ITCZ to the convective mixing Figure 1a shows the sensitivity of the ITCZ to f dp with a single ITCZ at higher values (F1.13, F1.70). Reducing f dp promotes a double ITCZ, with peak precipitation farther away from the equator (F0.28, F0.57). F0.85 has a marginal double ITCZ with no substantial difference between equatorial and off-equatorial precipitation. Decreasing f dp is associated with a weaker horizontal gradient of the mass meridional streamfunction (Fig. 2). F0.28 is the only simulation to show a reversed Hadley circulation in the deep tropics ( Fig. 2e), associated with upper-level zonal-mean equatorial subsidence, typical of a double ITCZ. F0.57 meanwhile has a typical double ITCZ structure in precipitation but not in the mass meridional streamfunction (Figs. 1a and 2d), which we refer to as a ''split ITCZ'': two offequatorial precipitation maxima and two ascending branches of the Hadley circulation, without any substantial zonal-mean subsidence equatorward of the precipitation maxima.
Convective mixing reduces the difference in MSE between a convective plume, determined by the boundary layer MSE, and the free troposphere (Mobis and Stevens 2012), which reduces the buoyancy of the convective plume. Assuming the sensitivity of the environmental saturated MSE to f dp is small, the depth of convection will depend on the boundary layer MSE and f dp . Decreasing f dp will deepen convection for a constant boundary layer MSE, and reduce the minimum boundary layer MSE at which deep convection occurs. Following weak-temperature gradient arguments (e.g., Sobel et al. 2001) and assuming a small meridional gradient in free-tropospheric tropical temperature, and hence a small gradient in the saturated MSE across the deep tropics, the reduced minimum boundary layer MSE needed for deep convection strengthens convection in off-equatorial tropical latitudes over cooler SSTs. Stronger off-equatorial deep convection decreases equatorward low-level winds in the deep tropics, reducing equatorial boundary layer MSE.
Hence, decreasing f dp is associated with a poleward ITCZ shift and promotes a double ITCZ. Similar arguments can be made for higher f dp promoting a single ITCZ. The sensitivity of the ITCZ to f dp is associated with AEI changes (Fig. 1b), with a change from a single (F1.13) to a double/split ITCZ (F0.28/F0.57) associated with a decrease in the [AEI] 0 (Figs. 3d,e). Simulations with a single (double) ITCZ in precipitation have a positive (negative) [AEI] 0 ( Fig. 1b), in agreement with Bischoff and Schneider (2014). Changes in cloudy-sky radiation and latent heat flux are the dominant components of AEI changes (blue and orange lines, respectively, in Fig. 3). In F1.13 the total CRE peaks at approximately 60 W m 22 at the equator and reduces to zero around 158 latitude (blue line in Fig. 3b). This equatorial warming comes almost entirely from the longwave CRE, which dominates the total CRE equatorward of 108 latitude (not shown). In the subtropics, 208 to 308 latitude, low clouds contribute to a negative CRE of '2 W m 22 , as longwave cooling from boundary layer clouds is greater than the shortwave heating. The split ITCZ in F0.57 is associated with a substantially reduced equatorial CRE and an increased off-equatorial CRE (Fig. 3d). We chose CRE profiles from one year of F0.57 and F1.13 for our prescribed-CRE simulations (Table 2), as these two simulations show CRE profiles typical of a double and single ITCZ, respectively; these simulations are analyzed in section 3d. As the Hadley circulation and ITCZ are associated with the AEI, and the CRE plays a substantial role in AEI changes when varying f dp , we hypothesize that prescribing the CRE will reduce or remove the sensitivity of the AEI and ITCZ to f dp .
b. Sensitivity of the ITCZ to convective mixing with no cloud radiative effect To test our hypothesis above, we first analyze simulations with the CRE removed (Table 1) (Table 1).
Removing the CRE at f dp 5 1.13 (F1.13NC) leads to a switch from a single to a split ITCZ, and '20% weakening of the Hadley circulation (Figs. 4a and 5b). Similar to Harrop and Hartmann (2016), removing the CRE cools the tropical (#308 latitude) upper troposphere, destabilizing the atmosphere and reducing the environmental saturated MSE. For a fixed boundary layer MSE and convective mixing rate, removing the CRE deepens convection as the buoyancy of a convective plume increases relative to the saturated MSE of the environment. Hence, removing the CRE reduces the minimum boundary layer MSE for deep convection, strengthening off-equatorial convection over cooler SSTs. Stronger off-equatorial convection decreases equatorward low-level winds in the deep tropics, reducing equatorial boundary layer MSE and promoting a double ITCZ. This mechanism is similar to that proposed for the sensitivity of the ITCZ to f dp (section 3a). However, when removing the CRE changes in the environmental saturated MSE play the dominant role, while for the sensitivity of the ITCZ to f dp , changes in the convective parcel MSE dominate.
The weaker Hadley circulation and double ITCZ in precipitation in F1.13NC is consistent with AEI changes. In F1.13NC removing CRE reduces the [AEI] 0 by '45 W m 22 , leading to a negative [AEI] 0 , and increases the subtropical AEI by up to 15 W m 22 (208 to 458 latitude) (Fig. 6f). Across the deep tropics the AEI change is not equal to the CRE diagnosed from F1.13, due to increased turbulent and clear-sky fluxes. These increased fluxes, associated with an equatorward shift of the ITCZ, partially offset the reduction in [AEI] 0 . Hence, the predicted location of the double ITCZ in section 3a when removing the CRE overestimated the poleward shift of the ITCZ. Removing the CRE reduces tropical-domain (#6308 latitude) AEI, which is associated with increased AEI at higher latitudes to maintain equilibrium. Our simulations are consistent with the suggested mechanisms proposed by Popp and Silvers (2017): the ITCZ is located at the maximum boundary layer MSE, and a weaker meridional circulation is associated with a reduced AEI gradient.
At all f dp removing the CRE reduces the maximum precipitation rate, weakens the Hadley circulation (cf. Figs. 1a and 4a), and moves the latitude of peak precipitation poleward (Fig. 7a). The sensitivity of the ITCZ structure to removing the CRE depends on the convective mixing rate: either a broader single ITCZ (F1.70NC), a poleward shift of a double/split ITCZ (F0.28NC and F0.57NC) or a switch from a single to a split/double ITCZ (F0.85NC and F1.13NC). Removing the CRE cools the upper troposphere and reduces the boundary layer MSE required for deep convection. This increases the f dp value at which the ITCZ transitions from single to split/double.
Removing the CRE changes, but does not remove, the sensitivity of the ITCZ to f dp . Quantifying the apparent effect of the CRE on the sensitivity of the ITCZ to f dp is difficult, as the effect depends on both the range of f dp considered and the metric used (Fig. 7). When an offequatorial ITCZ is simulated in CRE-off simulations (0.28 # f dp # 1.13), including the CRE increases the sensitivity of the ITCZ location to f dp by '30% (comparing the slopes of the solid regression lines in Fig. 7a). However, because F1.70NC has a single ITCZ, including the CRE cannot shift the ITCZ equatorward. Hence, when 0.28 # f dp # 1.70 the change in sensitivity reduces to nearly zero (comparing the slopes of the dashed lines). The reduction in sensitivity also depends on the chosen metric; for instance, the maximum precipitation rate has a negligible sensitivity to f dp in CRE-off simulations but a substantial sensitivity in CRE-on simulations (Fig. 7b), highlighting that the CRE has a positive feedback on convection as increasing f dp is associated with an increased CRE (Fig. 8).
Increasing f dp is associated with an increased tropicaldomain CRE (Fig. 8), which is counterintuitive as one might expect that increasing f dp will lead to lower cloud tops and hence a reduced CRE. However, the maximum cloud top height at the ITCZ is insensitive to f dp (not shown), but the minimum temperature where the cloud fraction goes to zero (cloud top temperature) is sensitive to f dp in both CRE-on and CRE-off simulations (Fig. 8). The cloud-top temperature decreases as f dp increases ( Fig. 8), associated with a cooler upper-troposphere. Furthermore, the increase in SST at the ITCZ location, associated with equatorward contraction of the ITCZ, also contributes to an increased CRE at higher f dp . Removing the CRE decreases the sensitivity of the AEI to f dp (comparing Figs. 1b and 4b). The reduced sensitivity of the AEI is associated with a reduced sensitivity of the ITCZ. Latent heat flux variations account for most of the remaining AEI sensitivity to f dp (Fig. 6). In simulations with a double ITCZ (F0.28NC, F0.57NC, and F0.85NC), changes in the latent heat flux and AEI have a bimodal structure, indicating reduced latent heat flux at the location of maximum precipitation in F1.13NC (Figs. 6c-e). Changes in the latent heat flux are predominantly controlled by alterations in near-surface wind speed rather than changes in near-surface specific humidity (not shown).
Simulations so far agree with the association in Bischoff and Schneider (2016) between a negative [AEI] 0 and a double ITCZ. However, the negative [AEI] 0 in F0.57, F0.85NC, and F1.13NC requires an equatorward transport of energy at low latitudes, but the mean mass meridional streamfunction suggests a poleward transport of energy (Figs. 2b and 5c,d). In the following subsection we discuss mechanisms for an equatorward energy transport.

c. Mechanisms responsible for an equatorward energy transport
To better understand the response of the mean circulation, associated with ITCZ changes, to varying f dp and removing the CRE, we partition the divergence of the MSE flux › y [ c yh] into two components: the mean circulation › y ([ŷ][ĥ]) and the eddy contribution › y [ c yh] 2 › y ([ŷ][ĥ]). In these simulations it has not been possible to close the atmospheric energy budget (1) due to local energy conservation issues (discussed further in section 4); however, the sign of the [AEI] 0 is consistent with the sign of the › y [ c yh] in simulations so far. In all simulations the eddy contribution to the meridional MSE flux is substantial across the tropics, highlighting that the mean atmospheric circulation is not solely responsible for transporting energy. Furthermore, one should not necessarily assume a correspondence between the required MSE transport and the transport by the mean meridional circulation. In simulations with a single (double) ITCZ, both the mean circulation and eddies transport energy poleward (equatorward) at low latitudes. In F0.57, which has a negative [AEI] 0 and a split ITCZ, equatorward transport of energy at low latitudes is achieved solely by eddies. When f dp 5 0.85 and 1.13, a change in the sign of the energy transport by the mean circulation › y ([ŷ][ĥ]) occurs at low latitudes when removing the CRE; however, there is still equatorial ascent across most of the troposphere (Figs. 5b,c). To understand the sensitivity of the mean circulation to removing the CRE at these convective mixing rates, we partition the change in the MSE flux [ŷ][ĥ] into mean circulation changes and MSE variations.
First, the meridional mass flux, denoted by V, in F1.13NC (V e ) is partitioned into two components: Subscripts c and e represent the zonal-mean, time-mean value of the control and experiment simulation (in this case F1.13 and F1.13NC respectively). Also, a is a globally uniform scaling term calculated using the dot product of the meridional mass fluxes in the tropics (308N to 308S). We account for variations in density in V. The term V c (1 1 a) represents a change in strength of the control circulation; V r represents a change in circulation structure. Next, the MSE (c p T 1 gz 1 Lq) in the experiment simulation h e is written as where subscript p represents the zonal-mean, time-mean difference between the two simulations. The change in the MSE flux between the experiment and control simulation can therefore be written as V e h e 2 V c h c 5 aV c h c 1 V r h c 1 V c h p 1 (aV c 1 V r )h p . (10) Each term in Eq. (10) represents a mechanism by which yh can vary: aV c h c represents circulation intensity changes, V r h c represents changes in circulation structure, V c h p represents MSE profile changes, and (aV c 1 V r )h p , FIG. 7. Diagnostics for determining the sensitivity of the ITCZ to f dp in CRE-on (green) and CRE-off (blue) simulations. (a) Latitude of maximum precipitation (8). (b) Precipitation rate at ITCZ (mm day 21 ). Four regression lines are plotted in each subplot. Solid lines where 0.28 # f dp # 1.13 and dashed lines where f dp # 1.70. The slope of each regression line is printed in the legend. The first value indicates where 0.28 # f dp # 1.13 and the second value where f dp # 1.70.
represents MSE profile changes correlated with changes in circulation structure and strength.
Three out of the four mechanisms are important in reducing the poleward MSE transport by the Hadley circulation in F0.85NC and F1.13NC (Fig. 9): a reduction in Hadley circulation strength (Fig. 9e), a shallower mean circulation (Fig. 9f), and a reduced MSE export at the top of the Hadley circulation due to lower MSE associated with upper-tropospheric cooling (Fig. 9g). MSE profile changes correlated with changes in circulation strength and intensity [(aV c 1 V r )h p ] are small compared to the other three mechanisms (Fig. 9h). As changes in circulation strength (aV c h c ) cannot change the direction of energy transport, the reduced upper-tropospheric MSE (V c h p ) and shallower Hadley circulation (V r h c ) must be responsible for the change in energy transport direction by the mean circulation. At the equator, circulation strength changes (aV c h c ) contribute '16% of the reduced › y ([ŷ] c [h]); reduced MSE export by the upper branch of the mean circulation (V c h p ) and a shallower Hadley circulation (V r h c ) contribute approximately 34% and 50%, respectively (not shown). Therefore, at certain convective mixing rates, in our case when f dp 5 0.85 and 1.13, removing the CRE is not associated with a substantial double ITCZ in the mass meridional streamfunction, even though MSE is transported equatorward at low latitudes and the [AEI] 0 is negative. Similar behavior has also been concluded by Popp and  Silvers (2017), who found that in certain simulations the zero mass meridional streamfunction remained at the equator even when the [AEI] 0 was negative.
Removing the CRE and varying f dp are associated with substantial AEI changes that require MSE transport variations. In the two sets of simulations discussed so far, we identified three mechanisms to transport MSE equatorward at low latitudes; which mechanisms dominate depends on the CRE and f dp . First, in F0.28, F0.28NC, and F0.57NC, subsidence across the equatorial region is associated with an equatorward MSE flux at low latitudes (Figs. 2e and 5d,e) To further understand the role of the CRE on the sensitivity of the ITCZ to convective mixing, we perform prescribed-CRE simulations and vary f dp ( Table 2). The prescribed CRE is diagnosed from single-year simulations with f dp equal to 1.13 or 0.57 (section 2). The effect of prescribing the diurnal cycle of the CRE in a simulation with the same f dp is minimal; for example, the ITCZ is similar in F1.13PC1.13 and F1.13 (Figs. 1 and 10). Hence, we only discuss the mean circulation in F1. 13PC0.57 and F0.57PC1.13 (Figs. 11a,c).
Similar to CRE-off simulations, the sensitivity of the ITCZ to f dp reduces in prescribed CRE simulations (Fig. 10a) compared to CRE-on simulations (Fig. 1a), associated with a reduced sensitivity of the AEI to f dp (Figs. 10b and 12a,c). The prescribed CRE heating acts as a fixed MSE source, which requires an increase in MSE export and hence increased convective activity. In PC1.13 simulations the CRE maximizes at the equator, which is associated with increased equatorial convective activity and a single ITCZ. In PC0.57 simulations on the other hand, the CRE peaks off the equator and promotes a double ITCZ. The root-mean-square difference of tropical precipitation and the mass meridional streamfunction illustrates that prescribing the CRE reduces the sensitivity of the ITCZ and Hadley circulation to f dp by '50% (Table 3). While the CRE plays a role in the sensitivity of the ITCZ to convective mixing (e.g., comparing F1.13PC1.13 and F1.13PC0.57 in Fig. 10a), the ITCZ and Hadley circulation are still sensitive to f dp . For example, reducing f dp (F0.57PC1.13) leads to a weakening in the upper branch of the mean circulation while changing the prescribed CRE (F1.13PC0.57) intensifies the upper branch of the Hadley circulation as the higher f dp value is associated with a cooler upper-troposphere, and hence an intensified upper branch of the mean circulation is required for similar MSE transport (comparing F1.13 in Fig. 2b to F0.57PC1.13 and F1.13PC0.57 in Figs. 11c and 11a, respectively). The response of convection to changes in convective mixing is partially offset by the effect of prescribing the location of the CRE.
As in CRE-off simulations, AEI changes in prescribed-CRE simulations when varying f dp are predominantly driven by latent heat flux variations. For example, between F1.13PC1.13 and F0.57PC1.13, the equatorial latent heat flux reduces while the off-equatorial latent heat flux increases (Fig. 12a). These changes are partially offset by changes in the clear-sky radiation, associated with a decrease in the TOA outgoing longwave radiation, due to an increase in atmospheric water vapor content. As changes in the ITCZ are associated with AEI changes, we conclude that the remaining sensitivity of the ITCZ to f dp in prescribed CRE simulations is associated with latent heat flux variations. In simulations where the prescribed CRE is varied but the same f dp value is used, AEI changes are mostly associated with cloudy-sky radiation (Fig. 12b,d). However, latent heat flux variations are of the same order of magnitude as when varying f dp . Using the same technique described in section 3c, we conclude that a shallower, weaker Hadley circulation is primarily responsible for changes in the MSE transport by the mean circulation when reducing f dp or changing the prescribed CRE from PC1.13 to PC0.57 (not shown).
F1.13PC0.57 and F0.57PC1.13 have similar split ITCZs (Fig. 10a), yet very different AEI profiles (Figs. 10b and 11b,d). F0.57PC1.13 highlights that a double ITCZ in precipitation does not require a negative [AEI] 0 or an equatorward MSE transport (green and black line respectively in Fig. 11d), illustrating that a double ITCZ in precipitation is not necessarily associated with an equatorward MSE flux at low latitudes. Instead a negative [AEI] 0 is a sufficient but not a necessary condition for a double ITCZ in precipitation. Because of local energy conservation issues, which are discussed further in section 4, it is challenging to understand F1.13PC0.57, which shows a negative [AEI] 0 and a positive equatorial › y [ c yh] (Fig. 11b) [contradicting Eq. (1) as steady state has been reached].

Discussion
We have analyzed aquaplanet simulations with variations to convective mixing to show an association between resultant variations in the AEI and characteristics of the ITCZ. Using the AEI framework we have shown the importance of the CRE in the sensitivity of the ITCZ to convective mixing. In a single ITCZ   Harrop and Hartmann (2016), we observe that removing the CRE cools the tropical upper troposphere, reducing atmospheric stability and resulting in deep convection over cooler SSTs. Stronger convection at higher latitudes reduces equatorial moisture convergence and is associated with a double ITCZ. Removing the CRE also weakens the Hadley circulation, which is associated with a reduced AEI gradient between the tropics and subtropics, in agreement with Popp and Silvers (2017). The sensitivity of the ITCZ to f dp reduces when removing the CRE, agreeing with our hypothesis that prescribing the CRE would either remove or reduce the sensitivity of the ITCZ to convective mixing. Quantifying the reduction in sensitivity of the ITCZ to f dp when removing the CRE remains a challenge due to strong dependence on the chosen metric and range of f dp . It should also be noted that when removing the CRE other AEI components change, such that the AEI change is not equal to the total CRE that is removed.
In prescribed CRE simulations, ITCZ characteristics are sensitive to both the prescribed CRE and f dp , however the sensitivity of the ITCZ to f dp reduces by '50% (Table 3). In prescribed CRE simulations the response of convection to changes in convective mixing is offset by the effect of prescribing the location of the CRE. Heating associated with the prescribed CRE is a MSE source; therefore, to increase the MSE exported, convective activity increases. The reduction in sensitivity compliments work by Voigt et al. (2014), who found that prescribing the CRE reduced the sensitivity of the ITCZ to hemispheric albedo perturbations to a similar degree. Thus, the role of the CRE in the sensitivity of the ITCZ to both variations in the convection scheme and boundary forcing appear similar, based on these two studies.
In both CRE-off and prescribed CRE simulations, latent heat flux alterations, associated with circulation changes, are the predominant cause of AEI changes when varying f dp . Circulation changes when varying f dp in CRE-off simulations are not associated with clear-sky flux variations, consistent with Harrop and Hartmann (2016), who concluded that changes in the clear-sky radiative cooling do not change the modeled circulation. Mobis and Stevens (2012) highlighted the importance of surface fluxes in reducing the sensitivity of the ITCZ to the convective parameterization scheme when prescribing the wind speeds in the computation of surface fluxes. Numaguti (1993) and Liu et al. (2010) also concluded that variations in surface evaporation are associated with the ITCZ structure. We highlight that the sensitivity of the ITCZ to convective mixing is predominantly associated with surface fluxes in the absence of cloud feedbacks.
As noted earlier in sections 3c and 3d, the balance between the diagnosed AEI and diagnosed › y [ c yh], Eq. (1) (Fig. 11b). While the local energy imbalance is a concern for F1.13PC0.57, we argue that in all other simulations the local energy imbalance does not affect our conclusions. There are a number of possible reasons for the localized imbalance of the AEI budget including nonconservation associated with the semi-Lagrangian advection scheme in MetUM; the use of dry and moist density in different components of the MetUM dynamics and physics, errors in our diagnosis of the MSE budget (e.g., not considering density changes within a time step), or using an Eulerian approach for diagnosing the energy transport, which is inconsistent with the semi-Lagrangian advection scheme. It is worth noting that other studies using the AEI framework have not shown that the MSE energy budget is locally closed, and this problem may not be unique to our study. Nevertheless, the local energy imbalance has challenged our interpretation of some simulations, and highlights that future modeling studies using an atmospheric MSE budget should be cautious.
Variations in the CRE when varying f dp can lead to a negative [AEI] 0 associated with a net equatorward MSE energy transport at low latitudes. While the predominant response to a negative [AEI] 0 is a double ITCZ associated with equatorward energy transport at low latitudes by the mean circulation (F0.28, F0.28NC, and F0.57NC), F0.57, F0.85NC, and F1.13NC have shown that a net equatorward MSE transport can occur at low latitudes even with a poleward energy transport by the mean flow at the tropopause. Two mechanisms can lead to this. First, the MSE flux due to eddies contributes a substantial proportion to the total MSE flux (as seen in Figs. 11 and 12b,d), and this can support equatorward MSE transport. In F0.57, the MSE flux due to eddies is responsible for a net equatorward energy transport in the deep tropics. This invalidates the assumption that the energy flux equator is associated with zero MSE transport by the mean circulation, as in Bischoff and Schneider (2016). This is also supported by the equatorward displacement of the energy flux equator [(from Eqs. (2) and (4)] relative to maximum precipitation in all simulations except for F0.85NC and F1.70NC (Table 4). The second mechanism (F0.85NC and F1.13NC) is a change in the MSE transport direction due to a shallower Hadley circulation and a lower MSE in the uppertroposphere (section 3c). These changes reduce the MSE export in the upper branch of the Hadley circulation, resulting in an equatorward MSE transport by the mean circulation at low latitudes.
In our aquaplanet configuration SSTs are fixed which implies an arbitrary but varying oceanic heat transport to maintain SSTs given a net surface heat flux  imbalance. Thus, our aquaplanet experiments may be viewed as energetically inconsistent. In Bischoff and Schneider (2014) and Voigt et al. (2016) ocean heat transport, and hence the net downward flux at the surface, is fixed, constraining the response of AEI components and potentially reducing the sensitivity of the ITCZ to model perturbations. In reality the ocean circulation, and thus ocean heat transport, is sensitive to changes in the surface wind stress. Therefore, both the SST and ocean heat transport could change in response to tropical circulation changes from variations to f dp or the prescribed CRE. Recent work has shown that the ocean circulation plays an important role in the meridional transport of energy (Green and Marshall 2017), and that sensitivities of the ITCZ found in atmosphere-only simulations do not necessarily hold in a fully coupled model. For example, coupling reduces the sensitivity of the ITCZ to an interhemispheric albedo forcing [e.g., comparing Kay et al. (2016) and Hawcroft et al. (2017) to Voigt et al. (2014)]. The radiative effect of clouds on the surface and Ekman heat transport associated with a single ITCZ would be expected to reduce the equatorial SST gradient, which would promote a double ITCZ (Numaguti 1995;Mobis and Stevens 2012) and may reduce the sensitivity of the ITCZ to convective mixing. Coupled simulations with an interactive ocean are required to further investigate the sensitivity of the ITCZ to the CRE and convective mixing.

Conclusions
The double ITCZ bias is a leading systematic error across a hierarchy of models (Li and Xie 2014;Oueslati and Bellon 2015). Intermodel variability in the ITCZ structure persists even in a highly idealized framework such as an aquaplanet with prescribed SSTs (Blackburn et al. 2013). This study confirms and extends previous research that variations in the convective parameterization scheme and convective mixing can alter the ITCZ ( Fig. 1a; Hess et al. 1993;Numaguti 1995;Chao and Chen 2004;Liu et al. 2010;Mobis and Stevens 2012). Higher convective mixing rates are associated with a single ITCZ while lower rates are associated with a double ITCZ. As the convective mixing rate reduces, convection at higher latitudes strengthens, decreasing equatorward low-level winds at low latitudes, promoting a double ITCZ structure. The sensitivity of the ITCZ to convective mixing is associated with AEI changes, predominantly caused by CRE variations. For example, the CRE plays an important role in maintaining a positive equatorial AEI, and is therefore associated with a single ITCZ structure [consistent with Harrop and Hartmann (2016) and Bischoff and Schneider (2016)'s framework]. When removing the CRE, the response of the ITCZ depends on the convective mixing rate. At low convective mixing rates, where a double ITCZ is simulated with the CRE, precipitation bands shift poleward. At high convective mixing rates the ITCZ broadens, while at certain convective mixing rates the ITCZ structure changes from single to double. Quantifying whether the sensitivity of the ITCZ to convective mixing reduces when removing the CRE is challenging, as the sensitivity depends on the range of convective mixing rates and the chosen metric. Prescribing the CRE reduces the sensitivity of the ITCZ to convective mixing by '50%. When removing or prescribing the CRE other AEI components, in particular the latent heat flux, play a role in the sensitivity of the ITCZ to convective mixing. Hence, simulations where the ocean heat transport is fixed, thereby constraining surface fluxes, may underestimate the sensitivity of the ITCZ to changes in model formulation. We have also shown two mechanisms responsible for a net equatorward MSE transport even with no equatorial subsidence: MSE transport by eddies, and a reduced MSE export in the upper branch of the mean circulation due to a shallower Hadley circulation. These mechanisms highlight that caution should be taken when associating changes in the AEI to the ITCZ structure.