1. Introduction
Consideration of atmospheric energetics has been a useful framework for understanding the response of tropical circulations and the concomitant precipitation changes to radiative forcing (Chou and Neelin 2004; Yoshimori and Broccoli 2008; Merlis 2015; Feldl and Bordoni 2016). The canonical example of this approach is the interpretation of shifts in the intertropical convergence zone (ITCZ) from hemispheric asymmetry in the top-of-atmosphere (TOA) radiative imbalance or surface fluxes. An asymmetry in forcing provokes interhemispheric energy transport by energetically direct circulations that converge water vapor into the hemisphere with the TOA energy surplus (Kang et al. 2008, 2009; Yoshimori and Broccoli 2008; Kang and Held 2012; Frierson and Hwang 2012; Donohoe et al. 2013; Bischoff and Schneider 2014). These results have been encapsulated in diffusive closures for the anomalous interhemispheric energy transport (Kang et al. 2009; Frierson and Hwang 2012; Bischoff and Schneider 2014). In practice, these approaches consider the response of annual-mean precipitation to annual-mean circulation changes that result from annual-mean changes in the spatial pattern of the TOA radiative forcing, radiative feedbacks, or surface fluxes (Frierson and Hwang 2012; Hwang et al. 2013; Bischoff and Schneider 2014).
Here, the role of the seasonal cycle of the climatological humidity on the annual-mean precipitation response to the radiative forcing of anthropogenic sulfate aerosols is assessed in an idealized atmospheric general circulation model (GCM). Anthropogenic sulfate aerosols are a forcing agent of particular interest in this context because their radiative forcing has seasonal variation that arises both from seasonality in their concentration (which can arise from precursor emissions and the physical climate’s influence on aerosol growth and aerosol sinks) and from the seasonality of insolation. Furthermore, anthropogenic sulfate aerosols have been invoked as critical to observed changes in the Indian monsoon (Bollasina et al. 2011) and zonal-mean tropical precipitation shifts (Hwang et al. 2013).
In what follows, idealized aquaplanet GCM simulations with either low or moderate homogeneous surface thermal inertias are subjected to sulfate aerosol radiative forcing to illustrate the potential importance of the seasonal cycle of the climatological humidity for annual-mean precipitation changes. The idealized simulations reveal a rectification mechanism in which seasonally varying perturbation winds and seasonally varying climatological humidity can produce an annual-mean tropical precipitation change: the annual-mean water vapor flux by the seasonally varying fields is larger than the water vapor flux of the annual-mean fields (section 3b). This mechanism implies that annual-mean precipitation changes do not directly follow annual-mean circulation changes. The geographic importance of the rectification mechanism in Earth’s climate is then qualitatively assessed in a reanalysis estimate of the seasonal cycle of humidity (section 4).
2. Idealized GCM
The GCM described in Merlis et al. (2013a), which has comprehensive radiation transfer (from the Geophysical Fluid Dynamics Laboratory’s AM2; Anderson et al. 2004) with prescribed clouds and an active hydrological cycle with an idealized quasi-equilibrium convection scheme (Frierson 2007), is used here. The prescribed cloud distribution has meridionally varying low clouds to produce an earthlike equator-to-pole temperature gradient and no high clouds [with the same parameters as in Merlis et al. (2013a)]. This GCM configuration allows for the water vapor feedback and suppresses cloud feedbacks. Suppressing cloud feedbacks will influence the magnitude of circulation changes, but these cloud-related circulation changes depend on model formulation (Voigt et al. 2014; Feldl and Bordoni 2016; Voigt and Shaw 2015). The idealized GCM, then, focuses attention on changes that depend on robust aspects of climate simulations.
I present the results of aquaplanet simulations with 5- and 20-m slab ocean depth. The simulations with low surface thermal inertia will be referred to as continental and the higher thermal inertia simulations will be referred to as oceanic in what follows. While a 20-m slab ocean depth is shallow compared to the mixed layer depth of many regions of the ocean, it is sufficiently deep that the results are distinct from the continental regime. In all cases, there is an infinite water supply at the surface for evaporation. The use of the aquaplanet lower boundary condition is an idealization that removes the quantitatively important, but complicating, influence of spatial variations in the surface energy storage that arise from land–sea heat capacity contrasts. The insolation is that of a circular orbit (0 eccentricity) with orbital obliquity of 23.5°. Thus, the boundary conditions and forcing are hemispherically symmetric in the time mean, except for the prescribed aerosol concentration. The simulations are performed with T85 spectral resolution and 30 vertical levels, although the results are similar with T42 resolution. All other parameters follow those of Merlis et al. (2013a). Simulations are integrated for 30 yr and averages over the last 20 yr are presented.
The control simulations have prescribed preindustrial sulfate aerosol concentration with all other aerosol concentrations are zero. Following Yoshimori and Broccoli (2008), the perturbation simulations have a prescribed sulfate aerosol concentration of 2.2 times the anthropogenic perturbation (defined as the difference between 2000 and 1860) from a chemical transport model (Horowitz et al. 2003). The increased amplitude of the forcing has the virtue of generating a larger forced response and the central results presented here are unchanged in simulations with a 1 times perturbation sulfate aerosol concentration. Radiative forcing is estimated using fixed-SST simulations (Hansen et al. 2005; Yoshimori and Broccoli 2008). The forcing has largest magnitude in the Northern Hemisphere extratropics and is weak in the Southern Hemisphere (Figs. 1b and 2b). Seasonally, it is largest in Northern Hemisphere summer (Figs. 1b and 2b). Because only low clouds are prescribed, the magnitude of the radiative forcing in the idealized GCM is greater than comprehensive AM2.1 simulations by approximately a factor of 2 in the global and annual mean [−4.4 W m−2 for 5-m depth and −4.7 W m−2 for 20-m slab ocean depth compared to −2.0 W m−2 in the simulations of Yoshimori and Broccoli (2008)].
(a) Seasonal cycle of zonal-mean precipitation (color contouring with 3 mm day−1 interval) with annual- and zonal-mean precipitation for the control continental regime simulation with slab ocean depth of 5 m. (b) Seasonal cycle of hemisphere-mean sulfate aerosol radiative forcing in Northern (blue) and Southern (magenta) Hemisphere with annual- and zonal-mean radiative forcing (black) and surface temperature change (red). (c) Seasonal cycle of response of zonal-mean precipitation (color contouring with 1 mm day−1 interval) with annual- and zonal-mean response of precipitation (solid line) and evaporation (dashed line) to sulfate aerosol radiative forcing.
Citation: Journal of Climate 29, 4; 10.1175/JCLI-D-15-0388.1
As in Fig. 1, but for the oceanic regime with slab ocean depth of 20 m.
Citation: Journal of Climate 29, 4; 10.1175/JCLI-D-15-0388.1
Additional simulations with zonally symmetrized aerosol concentrations have similar zonal-mean tropical precipitation responses. This results from the zonally symmetric aquaplanet boundary condition (Kang et al. 2014), so the meridional and temporal variations in the forcing are the aspects critical to the results presented here. In section 3c, the importance of seasonal variations in the forcing is assessed by comparing to a simulation with a time-independent energy sink in the slab ocean that has the meridional structure and amplitude of the annual- and zonal-mean sulfate aerosol radiative forcing (Fig. 1b).
3. Precipitation response to sulfate aerosols
a. Simulation results
Figure 1a shows the seasonal cycle of the climatological zonal-mean precipitation and its annual mean in the continental simulations with low surface thermal inertia and the control preindustrial sulfate aerosol concentration. The ITCZ extends seasonally into the subtropics (as in similarly configured simulations; Bordoni and Schneider 2008; Merlis et al. 2013a; Donohoe et al. 2014), with a maximum latitude of ~25° following each hemisphere’s solstice. The annual-mean precipitation has two off-equatorial maxima that correspond to the seasonal excursions of the ITCZ associated with the strong cross-equatorial or “monsoonal” Hadley circulation.
The control oceanic simulation with higher surface thermal inertia has weaker seasonal off-equatorial ITCZ excursions, reaching a maximum latitude of ~12° following the solstices, and the annual-mean precipitation has a well-defined equatorial maximum (Fig. 2a). For both the oceanic and continental control simulations, the deviation from symmetry between the hemispheres arises from limited time sampling and the nonzero preindustrial sulfate aerosol concentration.
In the continental regime, the tropical precipitation response to sulfate aerosol radiative forcing features decreases in the precipitation rate in the convergence zone and increases to its south over the seasonal cycle (Fig. 1c). The precipitation response is larger in Northern Hemisphere summer and fall compared to the Southern Hemisphere summer and fall, and this seasonality follows that of the radiating forcing (Fig. 1b) with an ~1-month phase lag. The annual-mean precipitation change is generally a decrease in the tropics, with a sharp decrease of ~1.8 mm day−1 that is confined to the northern edge (~25°) of the seasonal ITCZ. Away from this region, the magnitude of the annual-mean precipitation decrease is similar to the evaporation decrease (Fig. 1c). As expected from a reduction of absorbed solar radiation at the surface, evaporation decreases under sulfate aerosol radiative forcing. It is clear from the seasonal cycle of the precipitation change that the large annual-mean decrease near 25°N arises from the convergence zone’s decrease in precipitation and southward shift in Northern Hemisphere summer. South of this (near 15°N) there are seasonally canceling changes as the southward shift in Northern Hemisphere summer increases precipitation, while there are precipitation decreases in the convergence zone in the transitions to and from the off-equatorial convergence zone extremum in the Northern Hemisphere spring and the Northern Hemisphere fall. The resulting annual-mean change in precipitation near 15°N is weak. Therefore, the annual-mean change is not simply a southward shift where the decrease in precipitation near 25°N is accompanied by an increase in precipitation to the south of this region. There are, however, regions of modest net precipitation (precipitation minus evaporation) increases adjacent to the strong decrease near 25°N.
The sulfate aerosol-forced precipitation change in the oceanic regime is a southward shift in the convergence zone that follows its seasonal off-equatorial excursions (Fig. 2). As in the continental simulations, the weakest change is in Northern Hemisphere spring, prior to the peak radiative forcing. However, the precipitation change in the oceanic regime has weaker seasonality, consistent with more of the radiative forcing being stored in the surface and affecting the surface fluxes, circulation, and precipitation in subsequent seasons. The annual-mean precipitation change has a dipole near the equator: a ~1 mm day−1 decrease in precipitation north of the equator and a ~0.7 mm day−1 increase precipitation south of the equator (Fig. 2c). This southward shift of annual-mean tropical precipitation is broadly similar to others that have been described in comprehensive GCM simulations perturbed by sulfate aerosol radiative forcing [e.g., the simulation in Yoshimori and Broccoli (2008), which has hemispherically asymmetric tropical P and P − E changes of ~1 mm day−1 in the tropics].
b. Water vapor budget decomposition
Water vapor budget decomposition of change in annual- and zonal-mean net precipitation δ[P − E] for (a) continental and (c) oceanic simulations with dynamic, thermodynamic, and residual defined in section 3b. (b),(d) The importance of seasonality in the dynamical component of the change in water vapor flux is assessed by showing seasonal time series of the largest contributors 
Citation: Journal of Climate 29, 4; 10.1175/JCLI-D-15-0388.1
Here I consider a further decomposition of the annual-mean dynamic water vapor flux change 
Figures 3a and 3c show a decomposition of the annual-mean perturbation water vapor budget into dynamic and thermodynamic components. The dynamic component of the change in water vapor flux is the largest term in both the continental and oceanic simulations, although the thermodynamic component is not negligible in the oceanic simulations. While the pattern of annual-mean surface temperature change is broadly similar between the continental and oceanic simulations (Figs. 1b and 2b), the thermodynamic component differs because of the differences in the climatological circulations.
The annual-mean dynamic component (from the convergence of 
Changes in net precipitation, the dynamical component of the perturbation water vapor flux, and the annual-mean dynamic component of the perturbation water vapor flux (defined in section 3b; in mm day−1) averaged over the regions indicated in Fig. 3.
To further assess the magnitude and origin of the discrepancy between the annual-mean dynamic component and the full dynamic component, the water vapor flux is expressed as 
Figures 3b and 3d show the seasonal cycle near-surface specific humidity 
In contrast, the oceanic regime has relatively mild seasonality in both the climatological humidity and the perturbation convergence of the horizontal wind (Fig. 3d). Replacing the seasonally varying humidity by the annual mean does result in differences (an underestimate in Northern Hemisphere summer and an overestimate in Northern Hemisphere winter), although these largely cancel in the annual mean (Table 1). Therefore, the annual-mean rectification of the seasonal cycle is weak and the approximation of neglecting seasonality in humidity is adequate to determine annual-mean precipitation changes. The error of a few percent is similar to or smaller than the other approximations employed when the energetic framework has been applied to annual-mean tropical precipitation changes (e.g., holding the diffusivity used to parameterize energy transport fixed as the climate changes).
c. Time-independent versus seasonal forcing in the continental regime
The rectification mechanism described here relies on the combined effects of seasonally varying circulation changes and the seasonally varying climatology of humidity, so I present a simulation designed to assess the importance of the seasonally varying radiative forcing in producing the seasonally varying circulation changes. The annual- and zonal-mean radiative forcing (Fig. 1b) is applied as a time-independent sink in the slab ocean’s surface energy evolution equation with the continental heat capacity of 5 m. The simulation with time-independent forcing has a weaker magnitude net precipitation change (~40%) and this is largely from a weaker magnitude dynamic component of the precipitation change (~35%) compared to the time-dependent aerosol forcing (Fig. 4a, Table 1). In both cases, the Northern Hemisphere summer change dominates the annual-mean circulation response, consistent with the monsoonal circulation approaching the angular momentum–conserving limit in which the atmospheric energy balance, rather than eddy momentum fluxes, controls its strength (Schneider 2006; Bordoni and Schneider 2008; Merlis et al. 2013b). Therefore, the simulation with time-independent forcing, with weaker forcing in Northern Hemisphere summer, has a weaker circulation change in both that season and in the annual mean relative to the simulation with time-dependent aerosol forcing (Fig. 4b). Since the seasonal dependence of the circulation change can result from either the seasonality in the radiative forcing or the seasonality in the regime of the momentum balance, the simulation with the time-independent forcing also has an ~30% discrepancy between the annual-mean dynamic component and the full dynamic component (Table 1).
(a) Dynamic component of the water vapor budget decomposition of change in annual- and zonal-mean net precipitation δ[P − E] for continental simulations with time-dependent aerosol radiative forcing AERO and time-independent surface energy sink QFLUX. (b) The importance of seasonality in the dynamical component of the change in water vapor flux is assessed by showing seasonal time series of the largest contributors 
Citation: Journal of Climate 29, 4; 10.1175/JCLI-D-15-0388.1
An important role for seasonally varying forcing was also found in comprehensive GCM land-use change simulations analyzed in Kang et al. (2015): the Northern Hemisphere fall is less effective at provoking tropical precipitation changes than Northern Hemisphere spring because of a differences in the extent to which the forcing is balanced by local perturbations to the TOA budget rather than affecting meridional energy transport. Taken together, the results presented here and those in Kang et al. (2015) suggest that a full understanding of the tropical circulation response to extratropical forcing depends on 1) the seasonality of the forcing, 2) the accompanying local response of the TOA energy budget, and 3) circulation’s seasonal momentum balance. With the knowledge of the seasonally varying circulation change, the analysis of the water vapor budget presented here demonstrates that one must additionally consider the seasonal cycle of the climatological humidity to determine the annual-mean precipitation change.
4. Seasonality of the earth’s humidity
The magnitude of the seasonality of the earth’s near-surface humidity can be assessed in a reanalysis estimate to identify regions in which the rectification mechanism identified here is likely to be important for Earth’s climate. Figure 5 shows the ratio of the first annual harmonic of surface specific humidity 
Ratio of the first annual harmonic of monthly mean surface specific humidity to its annual mean in ERA-Interim for the climatology of 1981–2000.
Citation: Journal of Climate 29, 4; 10.1175/JCLI-D-15-0388.1
5. Discussion and conclusions
By considering the role of seasonality in determining annual-mean tropical precipitation changes, I have identified a mechanism that produces annual-mean precipitation as the result of the water vapor flux of the seasonally varying perturbation tropical circulation and the seasonally varying climatological humidity. To date, the seasonal cycle of humidity has not been included in applications of the energetic framework to tropical precipitation shifts, which have considered the perturbation water vapor flux from the climatological annual-mean humidity and the perturbation annual-mean circulation. The magnitude of the mechanism identified here depends on the magnitude of the climatological seasonal cycle of specific humidity (Figs. 3 and 5). Therefore, the answer to the question posed by the title, “Does humidity’s seasonal cycle affect the annual-mean tropical precipitation response to sulfate aerosol forcing?” is yes in continental regions with strong seasonal cycles of humidity, and, for practical purposes, no in oceanic regions with weak seasonal cycles of humidity.
A key part of this rectification mechanism is the seasonal amplitude and phase of the perturbation circulation. The simulations here have a radiative forcing agent (sulfate aerosols) with strong seasonality that arises for the same reason as the climatological humidity seasonal cycle: Earth receives more sunlight in summer than winter. Replacing the time-dependent aerosol radiative forcing by its annual- and zonal-mean reduces the annual-mean precipitation change. However, even in the simulation with time-independent forcing, there is seasonality to the perturbation circulation, which can arise because of seasonality in the regime of the circulation’s angular momentum balance, and the combined effects of the seasonality of the perturbation circulation and the climatological humidity will affect the annual-mean precipitation (Fig. 4).
The results described here have implications for the interpretation of past climate changes recorded in the proxy records of paleoclimate changes. First, the large-amplitude seasonal cycle of humidity in continental regions suggests knowledge of the seasonal cycle of climate perturbations would quantitatively alter the results of applications of the energetic framework to interpret the hydrological cycle changes recorded terrestrial paleoclimate proxies (cf. Schneider et al. 2014). Second, the simulation results in the continental regime have a substantial reduction in the (net) precipitation at the northern edge of the convergence zone that is not accompanied by a corresponding increase to the south (Figs. 1 and 3). Therefore, the expectation of a dipole pattern of compensating increases and decreases that underlies many discussions of convergence zone shifts may not be relevant to the seasonal extremum of convergence over continents.
Assessing the water vapor budget seasonally in monsoon regions (e.g., Clement et al. 2004; Li et al. 2015) readily captures the role of humidity’s seasonality on precipitation changes. From this seasonal perspective, the challenge is to relate the seasonal circulation changes to the radiative forcing. In this case, one must consider the seasonality of the forcing and the concomitant differential surface energy storage between land and ocean (e.g., Chou and Neelin 2003; Merlis et al. 2013b).
Acknowledgments
I thank the European Centre for Medium-Range Weather Forecasts for providing the ERA-Interim data and Luke Davis for his assistance in preparing the reanalysis. This work benefitted from discussions at the May 2015 California Institute of Technology Keck Center workshop on Monsoons: Past, Present and Future and reviews from Aiko Voigt and an anonymous reviewer. The program code for the simulations, based on the Flexible Modeling System of the Geophysical Fluid Dynamics Laboratory, and the simulation results themselves are available upon request. I acknowledge the support of Compute Canada and Natural Science and Engineering Research Council Grant RGPIN-2014-05416.
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The thermodynamic rectification mechanism described in Merlis et al. (2013c) is distinct: it results from seasonal correlations between the perturbation specific humidity 
The first annual harmonic does not capture the seasonal cycle well in certain continental regions with wet-to-dry season humidity variations that exceed 100%, such as the African Sahel. In this case, the underestimate from neglecting the deviation from the annual-mean humidity is greater than suggested by (3).
