1. Introduction
Most of the precipitation in Earth’s tropics falls in a region of relatively small meridional extent that migrates with the seasons. Dynamically, this region of strong precipitation is characterized by strong mean upward motion and low-level convergence of winds and hence this region is commonly referred to as an intertropical convergence zone (ITCZ). Simulating and understanding the mechanisms governing the meridional extent, the amount of precipitation, and the position of the ITCZ is thus a necessary component of predicting how variations and long-term trends in the climate may affect tropical precipitation. However, the full extent of mechanisms that affect the properties of the ITCZ is not yet well understood (Faulk et al. 2017) and state-of-the-art climate models struggle to represent several aspects of the ITCZ accurately (e.g., Lin 2007; Bollasina and Ming 2013; Hwang and Frierson 2013; Li and Xie 2014; Siongco et al. 2015).
A pressing problem in climate simulations when compared to observations is the too frequent and too pronounced occurrence of two ITCZs in the eastern and western Pacific and over the Indian Ocean in boreal summer (Lin 2007; Li and Xie 2014; Oueslati and Bellon 2015; Zhang et al. 2015), which may contribute to the spread of model climate sensitivity (Tian 2015). Even in the zonal and annual mean the two ITCZs in models tend to be too far from the equator when compared to observations (Lin 2007; Li and Xie 2014; Adam et al. 2016). We will refer here to this “double-ITCZ problem” in terms of the temporal- and zonal-mean distance of the ITCZs from the equator (note that other definitions exist of the double-ITCZ bias or problem). The problem is most prominent in coupled simulations but it is also apparent in simulations with prescribed sea surface temperatures (SSTs) even on hemispherically symmetric aquaplanets (completely water-covered planets; e.g., Numaguti 1993; Williamson 2012; Möbis and Stevens 2012; Landu et al. 2014; Harrop and Hartmann 2016; Fläschner 2016). The absence of hemispherical asymmetries in aquaplanet simulations has made it a popular test bed to identify and understand mechanisms contributing to the double-ITCZ problem.
So far, several factors have been identified that may contribute to the double-ITCZ problem, such as weak meridional surface-temperature gradients in the tropics (Dahms et al. 2011; Oueslati and Bellon 2013b), a low entrainment rate in the convective parameterization (Möbis and Stevens 2012; Oueslati and Bellon 2013a), the resolution of the model (Landu et al. 2014), and, most recently, weak atmospheric cloud-radiative effects (ACREs) (Harrop and Hartmann 2016; Fläschner 2016). However, the influence of ACREs on the tropical large-scale dynamics (Voigt et al. 2014a), and in particular how ACREs contribute to the double-ITCZ problem, is not well understood. Harrop and Hartmann (2016) and Fläschner (2016) show that the total ACRE pulls the ITCZ toward the equator, but it remains unclear how shortwave and longwave ACREs affect the ITCZ position individually, and a mechanism that explains the shift in ITCZ induced by the ACRE consistently across models is still missing. Therefore, this paper will investigate how the longwave and the shortwave ACREs interact with the tropical large-scale dynamics and thereby influence the ITCZ position in aquaplanet simulations. We will propose a mechanism that explains the shift in ITCZ using a framework that yields consistent results across models. We will for the first time apply and compare several diagnostic and prognostic frameworks for the ITCZ position to this problem. These frameworks are based on low-level moist static energy (MSE), gross moist stability, and the energy-flux equator.
ACREs have been shown to affect many aspects of the tropical large-scale circulation in GCMs, such as the strength of the large-scale circulation (Randall et al. 1989; Harrop and Hartmann 2016), vertical velocity (Slingo and Slingo 1988; Randall et al. 1989; Harrop and Hartmann 2016), the low-level convergence (Randall et al. 1989; Harrop and Hartmann 2016), the strength of the Walker circulation (Sherwood et al. 1994), the magnitude of El Niño–Southern Oscillation (Rädel et al. 2016), and the Madden–Julian oscillation (Crueger and Stevens 2015). Other studies suggest that ACREs influence the ITCZ position (Kang et al. 2008; Zhang et al. 2010; Hwang and Frierson 2013; Voigt et al. 2014a,b; Harrop and Hartmann 2016; Fläschner 2016) and Harrop and Hartmann (2016) recently investigated the influence of ACREs on the ITCZ systematically by using the output of six models taking part in the Clouds On–Off Klimate Intercomparison Experiment (COOKIE; see Stevens et al. 2012). We choose a different approach to study the influence of ACRE on the position of the ITCZ. We perform a multitude of simulations with a single state-of-the-art atmospheric GCM. This allows us to tailor the experimental setup and model output to our needs. Thus we can investigate for the first time how the longwave and the shortwave ACREs affect the ITCZ position separately. This is important for attributing model biases in ITCZ position to biases in ACREs, since the contribution of the longwave and shortwave ACRE biases to the total ACRE bias could differ between models. Furthermore, we modify the model to obtain specialized output for the task at hand. This allows us to put forward an alternative mechanism by which ACREs individually affect clouds.
In brief, our mechanism is as follows: ACREs enhance the atmospheric energy uptake in the deep tropics and the Hadley circulation responds to this by strengthening in order to export more energy away from the tropics. This circulation strengthening shifts the low-level MSE peak (and hence the ITCZ latitude) equatorward due to the negative MSE flux by the lower branch of the Hadley cell. Oueslati and Bellon (2013b) also found that changes in low-level winds are important for the ITCZ position when studying the effect of surface-temperature forcings, but this is the first study to implement the mechanism into a MSE framework and to find the mechanism for fixed surface temperatures. In contrast to the mechanism based on convective available potential energy (CAPE) suggested by Harrop and Hartmann (2016), our mechanism based on the width of the low-level MSE peak as a predictor of the ITCZ position gives consistent results across all models. A framework based on gross moist stability gives an equally good prediction of the ITCZ position, whereas estimating the ITCZ position from the zero of the mean meridional energy transport only yields mixed results.
This paper is organized as follows: In sections 2a and 2b we introduce the employed GCM and the applied boundary conditions. The experimental setup is outlined in sections 2c and 2d. We will first show how the ACREs affect the large-scale circulation in steady state (section 3a and 3b) and identify the mechanism at work. We will then investigate how changes in the distribution of low-level MSE affect the ITCZ position and we will make use of transient simulations for that purpose (sections 4a and 4b). We will also discuss in this context how the suggested mechanism relates to the width of the ITCZ (section 4c) and to the strength of the Hadley circulation (section 4d). Subsequently we will discuss the shifts of ITCZ in the framework of zonal-mean convective CAPE (section 5a), gross moist stability (section 5b), and the zero-crossing of the mean meridional energy transport (section 5c). We end the paper with a discussion of the implications of this study and with the main conclusions (section 6).
2. Methods
a. Model
Simulations are performed with a developmental version of the latest GFDL atmospheric GCM (C96L32_am4g6) referred to here as AM4d. The model uses a domain with approximately 100-km horizontal grid spacing and 32 vertical levels extending from the surface to 10 Pa. The dynamical core uses a cubed sphere with each face having 96 × 96 grid points. For the simulations presented in this study, the prognostic aerosol was turned off to allow for a simple aquaplanet experiment (APE) configuration [see Neale and Hoskins (2000) and Williamson (2012)]. Instead the cloud condensation nuclei concentration number was prescribed as 108 m−3. With the exception of the convective cloud parameterizations, the physics of AM4d is quite similar to that of AM3 (Donner et al. 2011). The convective parameterization of AM4d is a bulk two-plume mass flux scheme and is a modification of the shallow convective parameterization described in Bretherton et al. (2004). For details of the model physics see Zhao et al. (2016) and Donner et al. (2011). For the full documentation and climatology of the documented version of AM4 please refer to Zhao et al. (2017, manuscript submitted to J. Adv. Model. Earth Syst.).
To turn off a particular component of the ACREs we set the fractional cloud cover that is used for radiative computations of that component to zero at all levels. This option has been applied to both the shortwave and longwave components of the radiative transfer calculations. Turning the ACREs off only affects the radiation; the cloud condensate is still perceived by the model’s moist thermodynamics and dynamics. In that sense, this option can be thought of as making the clouds transparent to radiation in the longwave, in the shortwave, or in both parts of the spectrum.
b. Boundary conditions
We use AM4d in aquaplanet mode to utilize the interhemispheric symmetry and the shorter spinup times. Orbital parameters are set to perpetual-equinox conditions with general Earth-like settings for the rotation velocity, mass, and global- and temporal-mean insolation. The ozone concentration is zonally uniform but varies in the meridional and vertical direction according to the APE protocol (Neale and Hoskins 2000; Williamson 2012). Atmospheric concentrations of other greenhouse gases (except water vapor) are assumed to be uniformly mixed following the APE protocol (1650 ppbv for CH4, 306 ppbv for N2O, and 348 ppmv CO2). The lower boundary is set to a fixed SST pattern that varies in the meridional direction but is constant in time and zonal direction. This SST pattern was modeled with a simple mathematical function to represent the observed zonal-mean SST distributions and is referred to as QOBS following Neale and Hoskins (2000).
c. Experiments
1) Steady-state experiments
The four steady-state APE simulations presented here run for 11 years. The first six years of data are discarded to eliminate spinup noise and only the last 5 years in steady state are considered. The four experiments are both longwave and shortwave ACREs turned off (ACREoff), longwave ACRE turned on and shortwaveACREturned off (ACREonLW), longwaveACREturned off and shortwaveACREturned on (ACREonSW), and both shortwave and longwave ACRE turned on (ACREon).
2) Transient simulations
In addition to steady-state experiments, we perform two ensembles of transient simulations with 10 members each to better understand the mechanisms behind the changes in ITCZ position. Both ensembles start from the steady-state conditions of the ACREoff experiment and run for one year. In the first ensemble the longwave ACRE is turned on at the beginning of the simulations and in the second ensemble the shortwave ACRE is turned on at the beginning of the simulations.
d. Further considerations
Traditional simulations of the atmosphere (e.g., AMIP and weather prediction) correspond to our ACREon experiment. When comparing experiments with and without ACREs, the ACREon experiment has often been used as the reference state. In contrast, this study uses the ACREoff experiment as the reference because we have found it more natural to investigate the response of the climate to ACREs being turned on. Previous studies (Slingo and Slingo 1988; Randall et al. 1989; Crueger and Stevens 2015; Harrop and Hartmann 2016) of ACREs have focused on comparisons between the ACREoff and ACREon experiments. However, the strong response of land surfaces to changes of shortwave radiation makes an interpretation of the ACREoff experiment solely in terms of cloud changes difficult. Therefore, the next round of the Cloud-Forcing Model Intercomparison Project phase 3 (CFMIP3) recommends ACREonLW experiments to isolate the cloud response (Webb et al. 2017). This concern is irrelevant in our APEs because of the fixed lower boundary. As is shown in the following section, each of the four experiments investigated here reveals interesting interactions between clouds and radiation. The results obtained with our approach do not include the response of the surface temperature to changes in ACREs. However, fixing the surface temperature has the advantage of taking out a feedback and thus facilitates the interpretation of the atmospheric response to changes in ACREs, which by itself is not yet well understood. Furthermore, the fixed surface temperature experiments follow a well-defined protocol (APE) that allows us to easily compare our results to previous ones.
3. The effect of shortwave and longwave ACREs on the position of the ITCZ
a. Shifts in the ITCZ and changes in the large-scale circulation
In both the ACREoff and the ACREon simulations there are two ITCZs (Fig. 1a). We identify the ITCZ here as the hemispheric maximum in zonal-mean precipitation. The ITCZs are, however, considerably farther away from the equator in the ACREoff experiments than in the ACREon experiments. Hence, the net ACRE pulls the ITCZs toward the equator (Fig. 1a). If we turn only the longwave ACRE on, the ITCZs move all the way to the equator to form a single ITCZ. If, by contrast, only the shortwave ACRE is turned on, then the ITCZ moves farther away from the equator (Fig. 1a). So the longwave and the shortwave ACRE have opposite effects on the position of the ITCZ. The peak of the precipitation at the ITCZ increases in magnitude with decreasing latitude of the ITCZ position. The difference between experiments does not, however, exceed 0.23 mm day−1 in the global mean and 0.20 mm day−1 in the tropical mean (defined here from 30°S to 30°N) because the increase in precipitation at the ITCZ with decreasing latitude of the ITCZ is offset by a decrease in precipitation in the subtropical subsidence regions (Fig. 1a). So the closer the ITCZ moves to the equator, the less precipitation falls off the equator. This is consistent with an increase in the strength of the Hadley circulation with decreasing latitude of the ITCZ (Fig. 2): Stronger mean upward vertical velocities in the ITCZ promote an increase in zonal-mean precipitation in the upwelling region and stronger mean downward vertical velocities suppress precipitation in the subsidence region.
Zonal-mean quantities in steady state: (a) the total (convective + large-scale) precipitation, (b) the vertically integrated total (liquid + frozen) water path, (c) the atmospheric energy uptake, and (d) the ACRE. Colors represent the individual experiments ACREoff (black), ACREonLW (red), ACREonSW (blue), and ACREon (orange). The filled circles show the global and the crossed circles the tropical means (from 30°S to 30°N) of precipitation in (a). The horizontal location of the dots is only for visual separation and does not have any particular meaning. Note that the horizontal axes are scaled with the cosine of the latitude.
Citation: Journal of Climate 30, 22; 10.1175/JCLI-D-17-0062.1
Zonal-mean mass streamfunction in steady state for (a) ACREoff, (b) ACREonSW, (c) ACREonLW, and (d) ACREon. Green contours denote clockwise and violet contours counterclockwise rotation. The zero value is denoted by black contours. The depicted contours increase in steps of 0.5 × 1011 kg s−1. Note that the horizontal axes are scaled with the cosine of the latitude and that the vertical coordinates are logarithmic.
Citation: Journal of Climate 30, 22; 10.1175/JCLI-D-17-0062.1
The increase in the strength of the Hadley circulation with decreasing latitude of the ITCZ is consistent with an increase in zonal-mean atmosphere energy uptake (Fig. 1c) at the equator. The atmospheric energy uptake is defined as the net downward (=downward − upward) top-of-the-atmosphere energy flux minus the net downward surface energy flux, and corresponds to the total net energy flux into the atmosphere. Since the global and temporal mean of the atmospheric energy uptake has to be zero, the energy uptake at higher latitudes has to decrease. Therefore, the atmosphere must export more energy from the equator to higher latitudes. In experiments with prescribed sea surface temperature the energy density that is transported can only change to a limited extent. The energy transport corresponds to the transported mass multiplied with the energy density [see Eq. (8)]. Hence, a substantial increase in poleward energy transport requires an increase in the strength of the large-scale circulation, if the energy density (and the depth of the circulation) does not change substantially.
The longwave ACRE increases the meridional gradient in atmospheric energy uptake because in the deep tropics convective clouds heat the atmosphere throughout their depth, whereas the longwave ACRE at higher latitudes predominantly warms the levels below the boundary layer clouds, but cools the atmospheric column as a whole (Figs. 1d and 3). Thus the longwave ACRE acts to strengthen the large-scale circulation. By contrast, the shortwave ACRE cools the atmosphere more in the tropics than at higher latitudes and therefore tends to weaken the large-scale circulation (Figs. 1d and 3).
Our results agree well with those from other models with ACREon and ACREoff experiments (Randall et al. 1989; Harrop and Hartmann 2016; Fläschner 2016). The ITCZ moves equatorward if the ACRE is turned on and the tropical large-scale circulation strengthens as well in all the models analyzed by Harrop and Hartmann (2016) and Fläschner (2016). We also find a strong increase in total (liquid + frozen) water path when ACREs are turned on, which suggests that the precipitation efficiency decreases in our model in this case (Fig. 1b). The increase in total water path is also consistent with stronger detrainment by the convection scheme when the longwave ACRE is turned on. Since the detrainment rate depends on the formulation of the convection scheme, this result could be strongly model dependent. However, the results of previous studies suggest an increase in convective detrainment by all models when the longwave ACRE is turned on, as evidenced by the increase in total water path (Harrop and Hartmann 2016). We find a slight decrease in tropical precipitation when the ACREs are turned on, but the decrease is not substantial (from 4.13 to 3.93 mm day−1). This decrease occurs because the radiative cooling rate decreases when the ACREs are turned on (Fig. 3i). However, the clouds decrease the atmospheric cooling and thus cause a warming of the deep tropical troposphere that is then communicated effectively meridionally over the entire tropics (Fig. 4c) due to the weak Coriolis force. As a consequence, the clear-sky cooling rate increases in most of the tropical troposphere and balances most of the cloud-radiative heating by clouds. The warming of the deep tropical troposphere is mostly due to the longwave ACRE (Fig. 4b). The shortwave ACRE tends to warm only the tropopause region (Fig. 4a).
Zonal-mean cloud-radiative heating rates in steady state: (left) longwave, (center) shortwave, and (right) total (longwave + shortwave) cloud radiative heating, for (a)–(c) ACREonSW, (d)–(f) ACREonLW, and (g)–(i) ACREon. Note, that the horizontal axes are scaled with the cosine of the latitude and that the vertical coordinates are logarithmic.
Citation: Journal of Climate 30, 22; 10.1175/JCLI-D-17-0062.1
Difference in steady-state zonal-mean temperature between (a) ACREonSW and ACREoff, (b) ACREonLW and ACREoff, and (c) ACREon and ACREoff. Note that the horizontal axes are scaled with the cosine of the latitude and that the vertical coordinates are logarithmic.
Citation: Journal of Climate 30, 22; 10.1175/JCLI-D-17-0062.1
b. The low-level MSE distribution as a predictor of the ITCZ position
(a) The steady-state zonal-mean MSE at 925 hPa for ACREoff, ACREonSW, ACREonLW, and ACREon. (b) The steady-state zonal-mean CAPE as a function of latitude for the same experiments. Note that the horizontal axes are scaled with the cosine of latitude.
Citation: Journal of Climate 30, 22; 10.1175/JCLI-D-17-0062.1
4. An MSE-based mechanism for the ITCZ shift with ACREs
a. Transient simulations
To elucidate how the ACREs affect the low-level MSE we now analyze the transient simulations. All of the following analysis is performed using 3-hourly data. We first focus on an ensemble of simulations in which the longwave ACRE is turned on at the beginning of the simulations. It takes around 50 days for the ITCZs to move to the equator and form a single ITCZ (Figs. 6a,d). Therefore we will focus our analysis on this initial period. In the first days of simulation the temperature, specific humidity, and accordingly the MSE increase fastest at around 5.5° latitude and hence equatorward of the original ITCZ position at 8.5° latitude (henceforth denoted as “off the equator”) (Figs. 6b,c). As a consequence the ITCZ starts to move toward the equator (Fig. 6d). After 10 days the specific humidity and the MSE increase fastest at the equator (Figs. 6b,c). After 30 days the temperature, specific humidity, and MSE at the equator become larger at the equator than at 5.5° latitude and consequently the ITCZ moves equatorward of 5.5° (Fig. 6d). The MSE does not increase any more at 5.5° latitude after around 30 days and ceases to increase at the equator after around 40 days, coincidentally with the ITCZ reaching the equator. The higher rate of increase in MSE equatorward of the original location of the ITCZ and the prolonged increase at the equator are responsible for the larger increase in MSE at the equator than off the equator and thereby for the ITCZ moving to the equator.
(a) The zonal- and ensemble-mean total precipitation as a function of latitude and time for the 10-member ensemble of transient simulations starting from steady-state ACREoff conditions with the longwave ACRE abruptly turned on at the start of the simulations. The latitudes of ±0.5° are denoted with gray lines, the latitudes of ±5.5° with magenta lines, and the latitudes of ±8.5° with orange lines. (b) The temporal evolution of the change in MSE (solid) and of the contributions of the specific humidity (dashed) and of the temperature (dotted) to the change in MSE in the same simulations in zonal and ensemble mean at 0.5° latitude (gray), 5.5° latitude (magenta), and 8.5° latitude (orange) averaged over both hemispheres {e.g., h(ϕboth = 0.5°) = [h(ϕ = 0.5°) + h(ϕ = −0.5°)]/2}. (c) The difference in change in MSE between 0.5° and 8.5° latitude (blue) and between 5.5° and 8.5° latitude (green) averaged over both hemispheres. (d) The latitude of the ITCZ evaluated as the maximum in ensemble-mean zonal-mean precipitation on average over both hemispheres. (e) The change in zonal- and ensemble-mean meridional wind at 925 hPa at 0.5° latitude (gray) 5.5° latitude (magenta), and 8.5° latitude (orange) averaged over both hemispheres.
Citation: Journal of Climate 30, 22; 10.1175/JCLI-D-17-0062.1
b. A mechanism for the ITCZ shift with ACREs
Temporal evolution of the change in zonal- and ensemble-mean MSE tendencies from the initial state at latitudes 0.5° (gray) and 8.5° (orange) due to (left)–(right) the radiative flux-divergence, the turbulent fluxes at the surface, the zonal-mean meridional advection of MSE, and the residual terms. Results are from the 10-member ensemble of transient simulations starting from steady-state ACREoff conditions with the (a)–(d) longwave or (e)–(h) shortwave ACRE abruptly turned on at the start of the simulations. As in the previous two plots, averages are taken over latitudes on both hemispheres.
Citation: Journal of Climate 30, 22; 10.1175/JCLI-D-17-0062.1
The mechanism for the ITCZ shift due to the longwave ACRE also occurs with the shortwave ACRE, but in the opposite sense. The shortwave ACRE reduces solar absorption by water vapor both on and off the equator and leads thus to a negative radiative tendency of MSE (Fig. 7e) at low levels. The decrease in vertically integrated shortwave heating at low latitudes (10°S–10°N) is larger than at higher latitudes (around 20°N and 20°S; not shown) and therefore the meridional heating gradient decreases. The decrease in meridional heating gradient leads in turn to a decrease of large-scale circulation and thus to a slowdown of the zonal-mean meridional wind off but not at the equator (Fig. 7g). As a consequence, less MSE is advected off the equator, which leads to a positive change in the tendency of MSE. This positive change counteracts the shortwave cooling and leads to a decrease in MSE that is smaller than at the equator. This contributes to a flattening of the meridional MSE profile at low latitudes and thus to the ITCZ moving farther away from the equator (Fig. 5a). However, other terms like the change in MSE tendency due to the turbulent fluxes are considerably larger in absolute magnitude than that from the zonal-mean meridional advection off the equator (Fig. 7f). The residual is positive and considerably larger than the change in tendency from the zonal-mean meridional advection (Fig. 7h). The tendencies from the meridional advection by eddies and from the vertical advection are of about the same magnitude and sign as the tendencies from the zonal-mean meridional advection (not shown). The remainder of the residual is due to the numerical residual.
The mechanism introduced above, by which changes in the Hadley circulation influence the advection of MSE and thereby lead to different responses in MSE on and off the equator, only accounts for ACREs through the changes in heating/cooling rates. In principle, this mechanism could therefore be applicable to other perturbations of the atmospheric energy balance. Oueslati and Bellon (2013b) found a similar feedback mechanism by which an increased large-scale circulation increases the advection of colder air more off than at the equator when studying the influence of meridional SST gradients on the ITCZ position. Since colder air contains less water vapor at the same relative humidity and since the relative humidity tends to be lower in the subtropics, the advection of colder and drier air from the subtropics corresponds to the advection of air with lower MSE. In this regard, despite the different forcings and approach by Oueslati and Bellon (2013b), the mechanisms by which the ITCZ moves toward the equator are similar in the two studies. The “upped ante” mechanism (Neelin et al. 2003), by which larger horizontal gradients of moisture in a warmer climate increase the advection of dry air into the margins of tropical convective regions, thereby reducing convection in the margins, is similar to our mechanism in that increased advection of air of low MSE suppresses convection. However, in our simulations the key is an increased large-scale circulation whereas the key of the upped-ante mechanism is an increased MSE gradient.
c. The relation between the position and the width of the ITCZ
Our results suggest that the distribution of precipitation around the equator narrows as the ITCZs move toward the equator. This is consistent with the behavior of other models (Harrop and Hartmann 2016). Byrne and Schneider (2016b) show that total top-of-the-atmosphere cloud-radiative effects (CREs) affect the width of the ITCZ in climate change experiments. This raises two questions: Are the width and the position of the ITCZ linked, and are they controlled by similar mechanisms? Byrne and Schneider (2016a) suggest that a narrowing of the upwelling region of the Hadley circulation is consistent with an increased contribution to the tropical atmospheric energy uptake from that region. This mechanism causes the strengthening of the Hadley circulation and thus the ITCZ to move toward the equator in our simulations as well. Furthermore, Byrne and Schneider (2016b) find that an increase in zonal-mean meridional advection of MSE contributes to a narrowing of the ITCZ in climate change experiments. This mechanism is similar to the one we suggest to be responsible for the ITCZ moving toward the equator with the difference that the change in meridional MSE gradient is key for the change in MSE advection in Byrne and Schneider (2016b) whereas the acceleration of the meridional wind is key in our study. So the processes that govern the width of the ITCZ and the position of the ITCZ appear to be related. The width but not the position of the ITCZ is also influenced by the MSE advection by the eddies (Byrne and Schneider 2016b). This either could be due to the poleward margins of the ITCZ being at higher latitude than the peaks where eddies tend to play a larger role in the energy transport or could be due to the differences in experimental setups. A detailed analysis of this would go beyond the scope of our discussion, and is therefore left to future studies.
d. The relation between the strength of the Hadley circulation and the ITCZ position
Does a strengthening of the Hadley circulation trivially lead to the ITCZ position moving toward the equator? From a circulation standpoint alone, this is certainly not the case. We can illustrate cases with weaker large-scale circulation and an ITCZ closer to the equator (Fig. 8) or conversely a stronger large-scale circulation with the ITCZ farther away from the equator (Fig. 8). This is because the location of the ITCZ is where the low-level convergence of 
Sketches of the Eulerian zonal-mean mass streamfunction in different hypothetical cases. Contours always are equally spaced and the circulation is clockwise. Wind speeds are highest were the streamlines are densest. Thus, the ITCZs are the locations (indicated by orange lines) where the vertical streamlines are densest on the equatorward side of the Hadley cell. The total strength of the Hadley circulation corresponds to the total number of streamlines. The horizontal red line indicates the top of the boundary layer. We sketch five different changes in Hadley circulations from (a) the default double-ITCZ case by leaving or adding extra streamlines (in blue). Adding streamlines corresponds to a strengthening of the Hadley circulation and removing to a weakening. We thus show that without further mechanisms to constrain possible changes the ITCZ can move equatorward with a (b) weaker or (e) stronger circulation than in the default case, that it may stay with a (c) weaker or (f) stronger circulation, and that (d) it can move poleward with a stronger circulation. Thus, the strength of the Hadley circulation alone does not constrain the position of the ITCZ.
Citation: Journal of Climate 30, 22; 10.1175/JCLI-D-17-0062.1
In principle, any strengthening of the Hadley circulation leads to a larger increase of MSE advection off the equator than at the equator, because any strengthening of the Hadley circulation leads to an increase of 
5. Previous frameworks for interpreting changes in ITCZ position
a. Atmospheric stability and CAPE
As one of the motivations for using the low-level MSE, we mentioned that the mean meridional gradient of the upper-tropospheric MSE is small in the tropics. However, the value of mean MSE in the upper troposphere may change between experiments and thus the mean atmospheric stability may change as well. In agreement with previous work (Harrop and Hartmann 2016), we find that the net ACRE has an increasing warming effect with height in the tropics (Fig. 4c). This suggests that the mean stability of the atmosphere is higher when ACREs are turned on. A way of measuring the stability of the atmosphere is CAPE. Smaller values of CAPE tend to indicate a more stable atmosphere. Consistent both with an increase in mean static stability and with most previous results, we find that the mean CAPE is indeed considerably smaller in the ACREon than in the ACREoff experiments and also has a narrower distribution around the equator (Fig. 5b). Landu et al. (2014) suggest that a decrease in mean CAPE could cause an equatorward shift of the ITCZs, because a reduction of mean CAPE would make the atmosphere more stable, such that convection only occurs where the SSTs are highest around the equator. So this mechanism suggests that the changes in stability induced by the ACREs directly cause the ITCZ position to change, whereas our mechanism suggests that the strengthening of the large-scale circulation as a response to the ACREs drives the change in ITCZ position. The mechanism based on the reduction of CAPE does not, however, explain our ACREonSW experiment, which has a smaller peak of mean CAPE than the ACREoff experiment but whose ITCZ is farther away from the equator. It is also noteworthy that Harrop and Hartmann (2016) find that the mean CAPE is even larger in the ACREon experiment with the CNRM model, even though the ITCZs lie closer to the equator in that case. So in at least two simulations the reduction of CAPE cannot explain the shift in ITCZ position whereas our MSE framework explains the change in ITCZ position consistently in all simulations. This suggests that the reduction of mean CAPE that occurs in most simulations when cloud-radiative effects are turned on could be an effect of the changes in convection in these particular models. So while CAPE is a useful quantity for many purposes, the shift of the ITCZ due to ACREs is better described by the MSE mechanism illustrated here.
b. A gross-moist-stability perspective
1) A gross-moist-stability framework
Recently a variation of the gross moist stability framework has been used (Fläschner 2016) in which the gross moist stability is used to infer the mean vertical velocity (e.g., Neelin and Zeng 2000; Back and Bretherton 2006; Raymond et al. 2009). While this framework gives an accurate prediction of the ITCZ position (Fläschner 2016), it requires the prescription of the mean horizontal advection to infer the vertical velocity and is therefore less well suited for the task at hand than the framework we use here.
2) Prediction of the ITCZ position with the gross-moist-stability framework
We test the ability of the gross-moist-stability framework to predict the position of the ITCZ as follows. We assume that Δh does not change between simulations, implying a constant atmospheric stability. We estimate Δh by fitting a fourth-order polynomial to the Δh calculated from our simulations (Fig. 9a). By applying the model output from our simulations for 
(a) The zonal-mean gross moist stability calculated from the model output as well as the analytical function used to approximate the gross moist stability (turquoise line) as a function of latitude. (b) The implied 
Citation: Journal of Climate 30, 22; 10.1175/JCLI-D-17-0062.1
Despite some differences in the maximum and minimum values, the thus predicted 
(a) The implied split in latitude between the two ITCZs [as defined in Popp and Lutsko (2017)], as a function of the actual split between the two ITCZs in the four experiments. In the hemispherically symmetric setup used here, the split should approximately correspond to twice the distance of each of the ITCZs from the equator. In a perfect prediction the implied split by a certain framework would be equal to the simulated split and would thus lie on the gray dashed line. The splits of the actual simulations are 2° (ACREonLW), 9° (ACREon), 15° (ACREoff), and 17° (ACREonSW) latitude. The marks shown are for the energy-flux framework [magenta asterisks; see (b)], the gross-moist-stability (GMS) framework (orange squares; Fig. 9b), and the GMS framework with fixed turbulent fluxes (blue dots; Fig. 9c), with fixed radiative fluxes (red triangles; Fig. 9d), with fixed specific humidity (black circles; Fig. 9e), and with the all-sky fluxes replaced by the clear-sky fluxes (turquoise crosses; Fig. 9f). (b) The vertically integrated zonal-mean meridional energy flux as a function of latitude (solid) and a third-order Taylor expansion thereof (dashed) following the approach by Bischoff and Schneider (2016). The vertical lines denote the ITCZ positions according to the zonal-mean precipitation maxima in our simulations.
Citation: Journal of Climate 30, 22; 10.1175/JCLI-D-17-0062.1
3) Contributions of changes in radiative, turbulent fluxes, and humidity to the changes in ITCZ position
Since the gross-moist-stability framework can qualitatively predict the ITCZ position, we can ask how other factors like changes in turbulent surface fluxes, changes in radiative heating, or changes in humidity affect the position of the ITCZ in this framework. We apply again the polynomial fit of Δh to all simulations (Fig. 9a), implying no change in moist stability between experiments. By allowing only the quantity of interest to change, we find that the changes in radiative cooling together with the implied changes in circulation explain most of the changes in ITCZ position (cf. the ITCZ positions in Figs. 9d and 9b, and see Fig. 10a), whereas the changes in turbulent fluxes (cf. the ITCZ positions in Figs. 9c and 9b, and see Fig. 10a) and humidity (cf. the ITCZ positions in Figs. 9e and 9b, and see Fig. 10a) and their implied changes to the circulation have almost no influence on the ITCZ position. A previous study found that imposed changes in the entrainment rate of deep convection could change the ITCZ position by changing the turbulent fluxes at the surface (Möbis and Stevens 2012). This effect may have a small influence on the ITCZ position, but is apparently not the main effect that changes the ITCZ position when changes in ACREs are driving the changes.
4) Can changes in ITCZ position be predicted from the ACREon experiment alone?
Using the gross-moist-stability framework, we perform the same analysis as previously, but instead of using the fluxes and humidity from the ACREoff experiment we use the fluxes and humidity from the ACREon experiment and replace the all-sky fluxes by the clear-sky fluxes. Similarly, to mimic the ACREonLW experiment, we replace the shortwave all-sky fluxes by the clear-sky fluxes and mimic the ACREonSW experiment by only replacing the longwave all-sky fluxes by the clear-sky fluxes. This analysis shows that the qualitative change in ITCZ position due to the ACREs can be directly inferred with this approach (cf. Figs. 9f and 9b, and see Fig. 10a). However, correctly predicting the magnitude of 
5) Comparison between the gross-moist-stability framework and the low-level MSE framework
(a) The implied energy uptake by the atmosphere obtained by evaluating the left-hand side of Eq. (7) using the analytical fit (Fig. 9a) for the gross-moist stability. (b) The divergence (dotted) and the advective (solid) terms in Eq. (7). (c) The implied divergence term obtained, if we subtract the advective term of the ACREon experiment from the implied energy uptake shown in (a) for all four experiments.
Citation: Journal of Climate 30, 22; 10.1175/JCLI-D-17-0062.1
c. Energy flux perspective
In our simulations the zero mass streamfunction remains at the equator and thus only coincides with the ITCZ position in the ACREonLW experiment (Fig. 2). In the ACREon simulation, the transported MSE is larger in the upper branch of the Hadley circulation than in the lower branch, and thus the energy uptake remains positive at the equator (Fig. 1c). Since this means that the energy flux is a monotonically increasing function of latitude, there can only be one energy flux equator (but nonetheless two ITCZs). In the ACREonSW and ACREoff simulations the atmospheric energy uptake becomes negative near the equator (Fig. 1c), whereas the zero mass streamfunction remains at the equator. This means that the lower branch of the Hadley circulation is transporting more energy than the upper branch in this region (Fig. 2). A similar behavior has also been found by Byrne and Schneider (2016a). In this case the location of zero meridional energy transport is linked to where the low-level MSE equals the upper-level MSE rather than to where the meridional gradient of the streamfunction and hence the upward vertical motion is largest. Therefore, the position of zero meridional energy transport does not give accurate approximations of the ITCZ position in these simulations. The net import of energy at the equator from higher latitudes by the large-scale circulation could be an artifact of our model setup, but scenarios where the tropical large-scale circulation imports energy occur in the Pacific in regions of shallow circulations (Back and Bretherton 2006) and are therefore plausible.
6. Implications and conclusions
Many of the models taking part in the CMIP5 experiments exhibit two strong ITCZs in the eastern Pacific too frequently (Li and Xie 2014). A recent study has shown that the hemispherically symmetric component of model biases in precipitation, with which a double ITCZ can be associated, is anticorrelated with the atmospheric energy uptake in the deep tropics (Adam et al. 2016). This is in good agreement with our results, in which the simulations with less deep-tropical energy uptake are the ones with the ITCZ farther away from the equator. The results in Adam et al. (2016) also suggest that the total (top of the atmosphere) CRE in the CMIP5 models is smaller than in observations. If ACREs and CREs affect the ITCZ in a similar way, this would be consistent with a preference for a double ITCZ in our framework and thus with our results. Too small a CRE could be caused by too small a longwave CRE or too large a (negative) shortwave CRE, which both favor ITCZs farther away from the equator according to our simulations. The tropical shortwave CRE bias is larger than the longwave bias in both CMIP and AMIP simulations [see Fig. 7b in Li and Xie (2014)]. If ACRE and CRE affect the ITCZ in a similar way, then these results and the less pronounced double ITCZ in the AMIP than in the CMIP simulations are consistent with the shortwave CRE being responsible for the bias according to our framework. A too strong shortwave ACRE leads to a poleward shift of the ITCZ in our simulations (as seen as well in the AMIP simulations). Furthermore, the shortwave CRE interacts with the surface energy balance (where its effect is largest) in the CMIP but not in the AMIP simulations. Therefore, we would expect larger biases in the ITCZ position in CMIP than in the AMIP simulations for a similar shortwave CRE bias, whereas a similar longwave CRE bias should result in approximately the same bias in ITCZ position in CMIP and AMIP simulations.
To conclude, we have demonstrated with a state-of-the-art atmospheric GCM that ACREs have a large influence on the tropical large-scale circulation and in particular on the position of the ITCZ. The longwave ACRE pulls the ITCZ toward the equator, thereby substantially reducing the double ITCZ found in simulations with ACREs turned off. By contrast, the shortwave ACRE pushes the ITCZ away from the equator. In our simulations the longwave ACRE has a stronger influence on the ITCZ than the shortwave ACRE does. We have introduced a mechanism to explain these shifts in ITCZ position as a result of ACREs. The mechanism is as follows. The ACREs enhance the atmospheric energy uptake in the deep tropics. This causes the Hadley circulation to respond by strengthening in order to export more energy away from the tropics. This circulation strengthening leads to an acceleration of the low-level zonal-mean meridional wind off the equator and thereby to a negative tendency in low-level MSE due to the increased upgradient advection of MSE. This negative tendency is absent at the equator because the zonal-mean meridional wind is constrained to remain zero at the equator because of the hemispheric symmetric experimental setup. Therefore, the peak of low-level MSE and hence the ITCZ move equatorward. Changes in turbulent surface fluxes appear to play only a minor role in driving the change.
Our framework based on gross moist stability suggests that the ACREs diagnosed from a single simulation are sufficient to predict the qualitative response of the ITCZ to changes in ACREs, but that additional experiments similar to the ones here are necessary in order to infer the change in the amount of precipitation due to the ACREs. Our results suggest, furthermore, that the energy-flux framework yields inaccurate predictions of the ITCZ position if there is a change in sign of the gross moist stability far away from the zero mass streamfunction, or if the maximum upward vertical velocities do not coincide with the zero mass streamfunctions.
By tinkering with the interaction between clouds and radiation we have demonstrated the importance of ACREs to the ITCZ and developed a physical mechanism that explains how the ACREs influence the circulation, the energetics, and the resultant precipitation. In addition, we have compared and contrasted several different frameworks that have previously been used to analyze the ITCZ. Helpful future research would focus on closing the budget of moist static energy in models, reanalyses, and observations in order to apply the different frameworks discussed in our study to these cases, and an analysis of interactions with the ocean through the surface.
Acknowledgments
We thank Isaac Held and Yi Ming for thorough and constructive internal reviews with many valuable suggestions and three anonymous reviewers for their constructive and helpful reviews. We thank Chris Golaz and Ming Zhao for their lead in developing the employed model and for many valuable suggestions in setting up the experiments. This report was prepared by Max Popp and Levi Silvers under Award NA14OAR4320106 from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce. The statements, findings, conclusions, and recommendations are those of the authors and do not necessarily reflect the views of the National Oceanic and Atmospheric Administration or the U.S. Department of Commerce.
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