Thermodynamic and dynamic responses of the hydrological cycle to solar dimming

The fundamental role of the hydrological cycle in the global climate system motivates a thorough evaluation of its responses to climate change and mitigation. The Geoengineering Model Intercomparison Project (GeoMIP) is a coordinated international effort to assess the climate impacts of solar geoengineering, a proposal to counteract global warming with a reduction in incoming solar radiation. We assess the mechanisms underlying the rainfall response to a simplified simulation of such solar dimming (G1) in the suite of GeoMIP models and identify robust features. While solar geoengineering nearly restores preindustrial temperatures, the global hydrology is altered. Tropical precipitation changes dominate the response across the model suite, and these are driven primarily by shifts of the Hadley circulation cells. We report a damping of the seasonal migration of the Intertropical Convergence Zone (ITCZ) in G1, associated with preferential cooling of the summer hemisphere, and annual mean ITCZ shifts in some models that are correlated with the warming of one hemisphere relative to the other. Dynamical changes better explain the varying tropical rainfall anomalies between models than changes in relative humidity or the Clausius–Clapeyron scaling of precipitation minus evaporation (P −E), given that the relative humidity and temperature responses are robust across the suite. Strong reductions in relative humidity over vegetated land regions are likely related to the CO2 physiological response in plants. The uncertainty in the spatial distribution of tropical P −E changes highlights the need for cautious consideration and continued study before any implementation of solar geoengineering.

trial land cover and atmospheric compositions (Kravitz et al., 2010). The GeoMIP G1 experiment counteracts the forcing from quadrupled atmospheric CO 2 levels with a simple reduction of the solar constant across all wavelengths and spectra. The G1 experiment was run from the steady state preindustrial control run, followed by an abrupt quadrupling of CO 2 , and a simultaneous solar constant reduction for 50 years. The idealized nature of this simulation is conducive to multimodel comparison.
It superimposes two large and opposite climate forcings, which offset one another nearly completely in terms of global mean 5 net radiation balance at the top of the atmosphere and near-surface atmospheric temperature, but do not totally cancel in their hydrological effects, especially on local scales (Kravitz et al., 2013c).
Thirteen fully coupled models participated in the G1 experiment (though only twelve are included in the present study), and they differ in their ocean, ice sheet, land surface and atmospheric components. The latter two components are particularly relevant for this study. Some, but not all models, feature dynamic vegetation distributions. The twelve models include a wide 10 range of parametrizations and configurations, allowing for strong conclusions about robust climate responses that appear across models (Kravitz et al., 2013a).
The water cycle impacts agriculture, economies, as well as the welfare of ecosystems and human civilizations (IPCC, 2014).
It is imperative to understand the effects of solar geoengineering on global hydrology, to evaluate whether such an approach to climate change mitigation is feasible or desirable. In order to help improve our understanding of this issue, we analyze the 15 contributions of several different effects to changes in precipitation minus evaporation (P-E) in the GeoMIP G1 experiment.
These include the thermodynamic scaling of P-E with temperature (Section 2.1), changes in relative humidity (Section 2.2), and changes in atmospheric circulation patterns (Section 2.3).

Thermodynamic Scaling of P-E 20
Surface heating increases the temperature and the evaporation rate, which increases the atmospheric moisture content, or specific humidity q (Trenberth, 1999). We have confidence about certain aspects of the hydrological cycle's response to greenhouse gas warming, particularly those tightly coupled to the increase in saturation vapor pressure with warming (Held and Soden, 2006). The Clausius-Clapeyron expression (Eq. (1)), 25 where R is the gas constant, L the latent heat of vaporization, and α is the Clausius-Clapeyron scaling factor, relates the derivative of the natural log of saturation vapor pressure e s with respect to temperature (T) to temperature itself. At typical near-surface temperatures, saturation vapor pressure increases at 7 %K −1 .
Precipitation minus evaporation determines the amount of runoff on land, and the salinity of the water column over ocean.
Precipitation minus evaporation follows Clausius-Clapeyron scaling, as in Eq.
(2), given three important assumptions (Held 30 and Soden, 2006). First, it assumes small meridional gradients of temperature relative to P-E. Second, the relationship assumes no change in near-surface relative humidity between climate states. Third, it assumes that there is no change in the atmospheric flow. This thermodynamic scaling equation represents the component of P-E change driven directly by surface temperature perturbations.
P-E changes not captured by this scaling are driven by non-thermodynamic mechanisms, including changes in relative humidity or atmospheric dynamics.

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This project evaluates the extent to which the basic physical relation between saturation vapor pressure and temperature accounts for the climate response to a combination of large-magnitude forcings: greenhouse gas warming and solar dimming.
We investigate how well thermodynamic scaling predicts hydrologic changes in a geoengineered climate for each model by comparing the prediction using Eq.
(2) to the annual and zonal mean P-E anomaly between G1 (years 11-50) and the Preindustrial (all years) climate in the model simulations. We also consider the annual-mean global distribution of precipitation minus evaporation anomalies. In order to better understand the contribution of relative humidity changes to the P-E response, we also calculated an "extended scaling" adapted from Byrne and O'Gorman (2015). Our extended scaling includes the first two terms from Byrne and O'Gorman's equation, where H s is the relative humidity at the surface. The calculation takes local changes in H s into account, but for the sake 15 of simplicity it excludes changes in the horizontal gradients of H s . We calculated the difference between the zonal mean P-E anomalies in the extended and simple scalings to quantify the influence of changes in H s . We also calculated the difference between simulated P-E anomalies and the extended thermodynamic scaling, to isolate the role of dynamics in the simulated hydrological response. This analysis and the streamfunction analysis in section 2.3 were completed for a subset of the ensemble due to limited functionality of the central GeoMIP model data server, the Earth System Grid Federation (ESGF).

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The experimental design results in minimal temperature anomalies between G1 (years 11-50) and the preindustrial control (all years) ( Fig. 1), but does not eliminate hydrological effects (Fig. 2). The ensemble mean change in P-E shows greater hydrological changes (up to 1 mm/day) in the tropics than at higher latitudes (Fig. 2). Figure (3), which separates the precipitation and evaporation changes from solar dimming, reveals that most of the spatial structure in the P-E anomaly (Fig. 4A) comes from the precipitation change. 25 The thermodynamic scaling predicts virtually no change in global P-E patterns, since by experimental design the temperature anomaly is minimal between the G1 and preindustrial scenarios (Fig. 4B). Temperature anomalies between G1 and the preindustrial control show variations within 1 K, with some residual warming at high latitudes as a robust feature across the suite ( Fig. 1). The ensemble mean simulated precipitation minus evaporation deviates from the thermodynamic scaling by around 1.0 mm/day in the tropics, but due to the averaging of opposite responses among the models this understates the magnitude of 30 the contrast between the scaling and the simulated P-E response (Fig. 2). The most pronounced differences occur in the tropics, where temperature anomalies are minimal compared to the high northern latitudes and thus cannot account for the hydrological change. The exception to this is BNU-ESM, for which there is a pronounced P-E response at high latitudes, likely due to the poor compensation for the temperature response to quadrupled CO 2 levels in that model.
The ensemble mean reflects strong reductions in precipitation in the subtropics (Fig. 3). Previous research has suggested that this is a result of the nature of the G1 experiment forcing. Solar geoengineering might suppress tropical precipitation since the reduction in shortwave radiation cools the surface more than the mid-troposphere, increasing atmospheric stability and reducing The deviations of the extended scaling from the simple scaling are less than 0.1 mm/day in all models ( Fig. 4C). This demonstrates that local changes in relative humidity under solar dimming play a modest role in the zonal mean P-E response. Figure 4D indicates that most of the zonal mean P-E anomalies are not captured by the Clausius-Clapeyron scaling or by local 15 relative humidity changes. We interpret this component of the hydrological response to be driven by atmospheric circulation changes. To better understand the influence of relative humidity changes on smaller spatial scales, we investigate the global distribution of H s changes in the following section. We will then investigate the dynamical changes in the tropics in Section 2.3.

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Relative humidity is the ratio of actual vapor pressure to saturation vapor pressure ( e es ), or almost equivalently, specific humidity to saturation specific humidity ( q qs ). It can change with the evaporation rate or temperature, with the latter affecting the saturation vapor pressure as in Eq. (1). The near-surface atmosphere provides moisture to the free troposphere, where water vapor plays an important role in radiative transfer, the hydrological cycle, and climate sensitivity (Willett et al., 2010). The near-surface relative humidity parameter is also of interest in climate change studies for evaluating the risk of human heat 25 stress, under both high and low H s extremes (Sherwood et al., 2010;Souch and Grimmond, 2004).
The assumption of constant relative humidity in the simple thermodynamic scaling of P-E (Eq. (2)) relies on the availability of moisture. In a moisture-limited regime (i.e. over land) the specific humidity q may not increase proportionally with temperature, breaking the assumption of constant relative humidity. Under this circumstance, relative humidity adjustments would contribute to non-thermodynamic changes in the P-E between climate states. An observational study found decreasing surface 30 relative humidity from 1998-2008 over low and midlatitude land areas due to inhomogeneities in surface heating and moisture availability (Simmons et al., 2010). While relative humidity has been found to be nearly constant in global warming simulations with high vertical resolution (Allen and Ingram, 2002), the assumption of constant H s may not be sound when insolation rather than temperature is perturbed, as in the G1 experiment. We consider the absolute changes in the relative humidity distribution to explain precipitation anomalies between G1 (years 11-50) and the preindustrial (all years) simulations unaccounted for by thermodynamic or dynamic mechanisms. Any changes in relative humidity between G1 and the preindustrial climate are due to changes in evaporation or evapotranspiration (Fig.   3), since saturation vapor pressure is maintained along with temperature in G1. In six of the eight models presented here, relative humidity is reduced over land and conserved over ocean (Fig. 5). The relative humidity reductions are largest over  (1)). In response to elevated ambient CO 2 concentrations, plants constrict their stomata, which reduces evapotranspiration in the high CO 2 simulations, including the G1 simulations (Kravitz et al., 2013c;Cao et al., 2010). In the global warming (abrupt4xCO2) GeoMIP simulations, this effect is partially offset by the increased net primary productivity in a warmer world. However, in G1, this net primary productivity effect is muted by the reduction in insolation. Tilmes et al. (2013) found that the physiological response to G1 is qualitatively the same as for abrupt4xCO2. Biogeochemical cycling has been found to influence global precipitation as much as the radiative reduction itself (Fyfe et al., 2013). 15 Bala et al. (2008) investigate changes in global mean precipitation in a single climate model. They note a greater hydrological sensitivity to solar versus greenhouse forcing and attribute it to global energy budget constraints. Solar forcing heats the surface directly, while greenhouse forcing heats the troposphere. Changes in the insolation therefore have a greater effect on surface net radiation fluxes (i.e., latent and sensible heat fluxes change more than in the CO 2 case). When the downward shortwave flux decreases, the surface fluxes must respond, and in this case the latent heat flux dominates the response. Evaporation decreases, 20 and precipitation follows. Bala et al. do not address how this global mean equilibrium constraint will manifest regionally, but our analysis (e.g. Fig 3) is consistent with this reasoning..
In the National Center for Atmospheric Research (NCAR) Community Land and Community Atmosphere Model, Cao et al.
isolated the CO 2 physiological effect from a doubling of atmospheric CO 2 (2010). They reported patterns of reduced latent heat flux and relative humidity from this vegetative forcing that closely resemble those we observe in the GeoMIP suite, in Fig.   25 3 and Fig. 5. In the present study, since strong and significant reductions in relative humidity over land are largely constrained to regions with extensive vegetation in the form of boreal, temperate or tropical forests, we consider the biogeochemical effect of CO 2 to be the dominant cause of the relative humidity change. The role of these biogeochemical H s changes is minimal in zonal mean climate (Fig. 4C) but could have significant influence at smaller spatial and temporal scales. Convergence Zone (ITCZ), and there is evidence that its position is determined by meridional gradients in the verticallyintegrated atmospheric energy budget (Shekar and Boos, 2016). The Hadley circulation is crucial for balancing global energy, so high-latitude temperature anomalies can drive shifts of the ITCZ (Yoshimori and Broccoli, 2008). The ITCZ is sensitive to interhemispheric energy contrasts set up by aerosols, clouds, or antisymmetric heating (Seo et al., 2014). A thorough analysis of Hadley circulation changes is a crucial outstanding task for understanding the hydrological response to solar geoengineering 5 (Kravitz et al., 2013c). We will quantify changes to the Hadley circulation with the meridional streamfunction. The meridional streamfunction is derived from the continuity equation, and eitherv orw can be used to fully define the two-dimensional, overturning flow (Eq. (4)):

Dynamically Driven Precipitation
where φ is the latitude, p is pressure, a is the Earth's radius,v is the meridional velocity, and g is gravity.
10 Changes in TOA energy fluxes influence the direction and strength of ITCZ shifts (Kang et al., 2008). Numerous studies have noted the strong relationship between ITCZ position and the hemispheric temperature contrast as well. The correlation between interhemispheric temperature contrasts and annual mean ITCZ position is a robust result and is related to extratropical energy transport (e.g., Broccoli et al., 2006;Toggweiler and Lea, 2010). Schneider et al. explain how this is consistent with an energetic framework: the hemisphere with the higher average temperature typically has a smaller meridional temperature respectively, are dynamically driven (Fig. 6). The anomalous ascent at the equator in CCSM4 and NorESM1-M accounts for the narrowing of the ITCZ noted in the zonal mean P-E figure. The mean circulation does not seem to provide a dynamical basis for the annual mean constriction of the ITCZ in the MPI-ESM-LR and IPSL-CM5A-LR models, in which anomalies are less than 10 kgs −1 × 10 9 . Small changes in the latitudinal range and strength of the Hadley circulation and associated precipitation have large local implications, especially on subannual scales (Kang et al., 2009). We find that summer (July-August-September, or We find that the shifts of annual mean tropical rainfall in the models are correlated with the interhemispheric surface tem-10 perature contrasts (r = 0.638, Fig. 7). Models with higher annual mean surface temperatures in the Northern Hemisphere under geoengineering tend to display northward shifts of the ITCZ. This is consistent with previous research that shows a strong relationship between the ITCZ position and the hemispheric temperature contrast (e.g., Kang et al., 2008;Frierson and Hwang, 2012). Despite the hemispherically symmetric forcing induced by solar dimming, the ensemble mean residual high-latitude warming is larger in the Arctic than in the Antarctic (Fig. 1), and in 9 out of 11 models the northern hemisphere is warmed 15 relative to the southern hemisphere after geoengineering (Fig. 7). This suggests that there could be an intriguingly close relationship between the degree of Arctic warming amplification and the tropical hydrological response to geoengineering in models. The relationship between ITCZ shifts and energy transport in G1 will be further explored in a future study.

Conclusions
There is not a single mechanism driving the P-E changes in climate model simulations of uniform solar dimming. Rather, a 20 combination of thermodynamic scaling of precipitation minus evaporation, relative humidity changes, and Hadley circulation shifts contribute to the hydrological response, to different extents in each model. In the 11-member ensemble, there is variability not only in the spatial distribution of precipitation changes, but also in the underlying causes. P-E changes were generally driven more by dynamics than by relative humidity changes or thermodynamics.
The models can be divided into three groups characterized by different precipitation responses to geoengineering: either a 25 southward shift, northward shift, or narrowing of the ITCZ. Our results support that changes in tropical dynamics, namely shifts of the Hadley circulation, are in part responsible for these alterations to the P-E distribution. In a previous study, convection scheme parameters were determinative of the tropical precipitation response to extratropical forcings (Kang et al., 2009). The partitioning of cross-equatorial fluxes between atmospheric and oceanic components is also important for the resulting ITCZ shift, so differences in the oceanic component of the models could emerge as significant (Kang et al., 2008). 30 We also present evidence that land-sea contrasts in evaporation rates, resulting in land-sea contrasts in relative humidity anomalies, contribute to changes in P-E with solar dimming. We propose that these relative humidity changes are related to the effect of CO 2 on the stomatal conductance in plants. This study demonstrates that tropical precipitation is sensitive to solar perturbations and would be altered by an implementation of solar geoengineering. The basis of this alteration is primarily dynamical. Based on our inter-model comparison, there is substantial uncertainty regarding the nature of the tropical precipitation response, in terms of the direction and strength of the ITCZ shift, as well as its variation on seasonal time scales. We present evidence that residual warming of one hemisphere relative to the other under geoengineering draws annual mean tropical rainfall into that hemisphere. The ramifications of this 5 result on seasonal timescales requires further study. Our findings strengthen the conclusion that solar geoengineering cannot restore preindustrial conditions in terms of P-E patterns, a fundamental aspect of climate.