1. Introduction
Climate model projections of the future daily precipitation distribution have an intensification of hydroclimatic extremes under global warming. Understanding the projected changes of both dry and wet extreme events, such as their intensity and frequency of occurrence, is crucial to grasp the full extent of their future societal impacts. Dry and wet hydroclimatic extremes are often defined as dry spells and heavy daily rainfall, respectively. While regions expected to have increased mean precipitation (deep tropics and mid- to high latitudes) generally have shorter dry spells and regions expected to have decreased mean precipitation (subtropics) have longer dry spells in future projections, heavy daily rainfall is projected to increase almost everywhere (Fischer et al. 2013; Sillmann et al. 2013; Pfahl et al. 2017; Dai et al. 2018). Dry and wet extremes do not have identical constraints, as changes in both extremes with warming are driven by combinations of dynamic processes (changes in the large-scale circulation, convective vertical velocities, and eddies) and thermodynamic processes (the dependence of atmospheric water vapor on temperature, in particular).
It is well established that thermodynamically induced rainfall changes are linked to atmospheric water vapor changes. Water vapor changes follow Clausius–Clapeyron (CC) scaling, the quasi-exponential relation between saturation vapor pressure and temperature, with a global value of 6%–7% per degree of warming because changes in relative humidity are small (Trenberth et al. 2003). Allen and Stainforth (2002) proposed that extreme precipitation changes follow the CC scaling based on the premise that an extreme event empties the air parcel of all its water vapor. The thermodynamic intensification of extreme precipitation is actually most likely to be at a sub-CC rate (Pall et al. 2007; O’Gorman and Schneider 2009; Chen et al. 2011), due to the relation between extreme precipitation and the moist-adiabatic derivative of saturation specific humidity. The change of saturation specific humidity with pressure increases at a slower rate than the CC scaling, especially at higher temperatures. This is due to the offsetting effect of the enhanced warming aloft of moist-adiabatic warming (O’Gorman and Schneider 2009). This, in turn, arises from the latent heat of condensation, which is larger at higher temperatures. Thermodynamic changes have also been invoked for the dry tail of the distribution of precipitation: if the mean precipitation increases more weakly (e.g., 2%–3% per degree of warming) than the specific humidity, this suggests there must be compensating drying in parts of the precipitation distribution should the increase in extremes exceed the mean. One of the contributions of this research is to thoroughly quantify thermodynamic changes across the distribution of precipitation.
Beyond thermodynamic changes, there is a substantial body of studies that examine the dynamic contribution to projected changes in heavy daily precipitation. The expected dynamical poleward shift of the circulation under global warming may have a large contribution to extreme precipitation intensity and frequency in the midlatitudes (Lu et al. 2014). In addition, the strengthening of midtropospheric vertical velocities can amplify heavy rainfall intensity. Some studies use the quasigeostrophic (QG) omega equation to decompose the vertical velocity changes into a dry component—the textbook ageostrophic terms in QG theory—and a moist or diabatic component—arising from latent heat release (e.g., Li and O’Gorman 2020). The moist component reveals that the latent heat released during an extreme event is linked to changes in moist static stability (a latent heat feedback) because a stability closer to moist adiabatic leads to an increased pressure depth of the upward motion (Li and O’Gorman 2020). The QG omega equation’s moist component also reveals that the nonlinear relation of the diabatic heating feedback with precipitable water can explain the super-CC sensitivity of extreme precipitation in some tropical regions. The increased water vapor with warming leads to larger diabatic heating feedback due to convection (independent of the large-scale forcing, the dry component), enhancing the sensitivity in climatologically moist regions, which explains part of the regional pattern of extreme precipitation sensitivity in the tropics (Nie et al. 2020). Heavier wet extremes are also projected in regions of mean precipitation decrease, such as the subtropics, albeit with large uncertainties (Pfahl et al. 2017; Norris et al. 2020). While weaker extreme ascent can result from increased horizontal scale of ascent and increased stability in the subtropics (Tandon et al. 2018), there is also evidence of an amplification of extreme ascent associated with the heaviest rainfall events, though this may be damped in certain regions due to the Hadley cell’s poleward expansion (Norris et al. 2020). While typical climate model resolutions rely on convective parameterization, cloud-resolving model (CRM) have also been used to investigate the convective vertical velocities changes associated with extreme precipitation. There is evidence that the vertical velocity peak shifts upward with warming (Muller et al. 2011; Abbott et al. 2020), and this influences the relevant temperatures where condensation occurs. As for droughts/dry spells, it has been shown that a simulated increase in dry extremes is the result of a modest strengthening of ascent in convective regions and the associated expansion of the surrounding dry areas (Lintner et al. 2012). It has been linked to the upped-ante mechanism proposed by Neelin et al. (2003), by which decreases in rainfall result from an increase in the required surface boundary layer moisture for convection to occur. In brief, dynamical changes, via convective velocities in low latitudes and synoptic-scale eddies in the midlatitudes, are important to precipitation extremes.
We aim to disentangle the thermodynamically induced changes from the dynamically induced changes across the full probability distribution of daily precipitation. Chen et al. (2019) developed a quantile-conditional moisture budget, which can be applied to the whole daily precipitation probability distribution function. They were able to obtain the thermodynamic and dynamic components for high percentile daily rainfall. They demonstrate the “wet-get-wetter” mechanism controls extreme precipitation increase, where the amplification is linked to an increased gross moisture stratification controlled by lower-tropospheric moisture changes. We use a different method to obtain the relative importance of thermodynamic effects over the whole probability distribution of daily precipitation, disentangled from dynamical influences. Our methodological approach involves the implementation of a passive water cycle within the GCM, which follows the dynamical flow without interacting with it. This method is similar to that of Grabowski (2014), who used two set of thermodynamic variables to study microphysical schemes impact on convection, and isotope-enabled GCMs (e.g., Lee et al. 2009; Colose et al. 2016), where multiple water isotope tracers following the same dynamical flow but with different temperature-dependent sources and sinks, that have been used to study past climates. Here, we use the simulated passive water cycle as a direct measure of the thermodynamic precipitation change from different temperature perturbations that result from warming due to a strengthened atmospheric greenhouse, akin to increased carbon dioxide concentration.
We evaluate the thermodynamically induced changes for both dry and wet extremes under global warming. The passive water vapor framework, which can be used for both individual precipitation events and climatological changes, simulates a substantial thermodynamically induced precipitation decrease of dry and wet days in the subtropics and of dry days in midlatitudes. We show an important role for the decrease in the air–sea surface temperature contrast with warming, which damps surface evaporation increases, in simulating a thermodynamically induced amplification of dry-spell length and of increased warming aloft in the tropics in simulating a small thermodynamic damping of the intensification of extreme precipitation.
2. Methods
a. Idealized general circulation model
We use the GFDL gray-radiation aquaplanet moist GCM (Frierson et al. 2006), with a T85 truncation in the spectral dynamical core (∼1.4° horizontal resolution) and 30 vertical levels. This is an extensively analyzed, idealized “rung” of the hierarchy of climate models (Held 2005; Jeevanjee et al. 2017; Maher et al. 2019). The vertical levels are in sigma (σ) coordinates, the pressure normalized by its surface value (σ = p/ps). The simulations do not include any convection scheme (the motivation for this choice is described in the following section and the appendix presents the sensitivity of key figures to this choice). There is no transport of condensates: they immediately precipitate out. Surface precipitation is then simply the mass-weighted vertical integral of the large-scale condensation tendency of water vapor.
We perform a simulation where the atmospheric optical depth is increased by 1.4 times the control distribution, following O’Gorman and Schneider (2008). This increase in optical depth provokes 6.1 K of global-mean surface temperature warming, and we will refer to this simulation as “warmed” from now on. We also examine the sensitivity of the model to using a comprehensive clear-sky radiative transfer scheme in the appendix. Both the control and warmed simulation have zonally symmetric slab ocean lower boundary conditions that simulate an energetically consistent surface temperature distribution. The difference between the warmed and control simulation is used to define the total (combined dynamic and thermodynamic) change in precipitation. The change in time- and zonal-mean temperature is shown in Fig. 1a and has substantial structural similarity to comprehensive GCMs: enhanced warming in the upper tropical troposphere and polar amplified surface warming that is associated with a lower-troposphere enhanced warming. This temperature change field plays a key role in the passive water vapor approach, described next, that we use to disentangle the effects thermodynamic changes and dynamic changes have on daily precipitation statistics.
b. Passive water vapor approach
There are four existing modeling approaches with common aspects to ours:
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The “piggy-backing” approach of Grabowski (2014) and Grabowski (2015), who examined microphysical impacts on convection. They use two sets of thermodynamic variables affected each by a different microphysical scheme. One set of the thermodynamic variables determines the dynamical flow, while the other one is “piggy-backing.” This isolates microphysical changes (e.g., changes in cloud condensation nuclei from increased aerosols) without the associated circulation-related changes that occur in time-dependent nonlinear atmospheric models.
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Regional tagging of additional water vapor tracer variables (e.g., Bosilovich and Schubert 2002), where passive water vapor tracers follow the same Eulerian moisture tendency equation, but are “tagged” to reveal the region where surface evaporation occurred.
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Isotope-enabled GCMs, as described in the introduction.
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Idealized dry GCMs with passive hydrological cycles (e.g., Galewsky et al. 2005; Ming and Held 2018), in which a standard dry dynamical core with diabatic forcing (Held and Suarez 1994) that is independent of the simulated water vapor condensation is used to advect water vapor and it is subject to condensation when it is supersaturated.
It is important to mention that we did not include the convection tendency in the moisture equation because of an important issue with how convection schemes (e.g., Frierson 2007) and the passive water vapor interact. Because the latter always feels a temperature that is warmer than the environment temperature, it has the potential to be in constant conditionally unstable state, depending on the vertical structure of the perturbation
c. Decomposing the temperature perturbation
We design four different experiments using different structures (latitudinal and vertical) for the temperature perturbation
In the first experiment (“Full Structure,” Fig. 1a), the temperature change field is the time- and zonal-mean temperature difference between the control and the warmed simulations (with the perturbation described in section 2a). In the second experiment (“Vertically Uniform,” Fig. 1b), the temperature change is a simplification of the first one: We remove the vertical structure from the temperature perturbation by replicating the lowest atmospheric level temperature change throughout the whole atmospheric column at each latitude. This preserves the meridional structure of warming (e.g., polar amplification) and the change between the surface temperature and surface-air temperature. In the third experiment (“Uniform,” Fig. 1c), there is a homogeneous temperature perturbation at all latitudes, all vertical levels, and at the surface. This constant temperature change is set at
3. Results
a. Thermodynamic precipitation change of an individual extreme event
Figure 2a shows a map of the daily precipitation for an individual extreme event, located at 40°–50°N, 60°–75°E. This is a 99.9th-percentile event for 45°N latitude, and we can see the storm structure of a midlatitude cyclone, as the pressure velocity at the 550 hPa pressure level suggests (gray contour lines). Within the same GCM simulation, the result of the online calculation of precipitation arising from the condensation of the passive water vapor at the same time is shown in Fig. 2b. The spatial pattern is similar, but the local maxima are generally enhanced, as one expects from increased humidity. We show this sample individual extreme event to highlight that the methodology we use here can readily be applied to individual storms, in addition to performing analysis of the climatological changes in the full distribution of precipitation that we present in what follows. Previous authors have analyzed individual tropical cyclones in models where both the humidity and circulation were free to evolve (Trenberth et al. 2007; Lackmann 2015; Emanuel 2017; Reed et al. 2020) and we are applying the modeling approach introduced here to idealized GCM simulations configurations with many tropical cyclones in forthcoming work.
b. Thermodynamic changes in the time-mean net precipitation
Figure 3 shows the time- and zonal-mean net precipitation (P − E, precipitation minus evaporation) change with warming (red dotted line) for the difference between the GCM-simulated warmed and control active hydrological cycles. This change, therefore, includes both thermodynamic and dynamic changes. The thermodynamic component of these changes can be estimated as in Held and Soden (2006). The scaling, δ(P − E) = αδTsfc(P − E), is based on the principle that specific humidity will rise according to the CC relation with fixed relative humidity. This results in the widely discussed “wet-gets-wetter, dry-gets-drier” amplification of the climatological net precipitation: this is the P − E on the right side of the expression, which is multiplied by the surface warming and CC’s temperature sensitivity α = 0.07% K−1. We compare the scaling (Fig. 3, dashed black line) to the thermodynamic P − E changes obtained from the condensation and evaporation of the passive water vapor (Fig. 3, solid yellow line). They both have increased net precipitation in the deep tropics, decreases in the subtropics, and increases in the extratropics, though there are some differences in the deep tropics and midlatitudes. Having confirmed that we reproduce the key features of this well-known thermodynamic scaling for the time-mean net precipitation, we can confidently apply the passive water vapor methodology to the changes of the daily precipitation statistics.
c. Daily precipitation distribution
For a given simulation, we determine the daily precipitation distribution for each latitude by aggregating the data for all longitude grid points (which takes advantage of the zonally symmetric boundary conditions to improve the statistics for rarer events by creating a much longer time series) and then sorting these values. The cumulative density function (CDF) of the control daily precipitation is shown in Fig. 4 to provide an overview of the statistics of daily precipitation, from dry extremes to wet extremes, at all latitudes. For example, the value of the CDF’s 10th percentile at a given latitude indicates that the 10% days with the lowest rainfall, including days with no precipitation, have a precipitation rate equal or less than this value, and there are many latitudes where the 10th percentile is indeed zero.
In this study, we are specifically interested in the changes of the daily precipitation distribution with warming. We take the difference between the distributions for the control and the thermodynamically perturbed daily precipitation to obtain the simulated percentage change with warming of all daily precipitation’s percentiles for each latitude. This is undefined for percentiles with no precipitation in the control simulation.
Figure 5a shows the precipitation change obtained via the difference between the active precipitation in the warmed and control simulation. This standard GCM precipitation change (using the difference of two simulations without passive water vapor hydrological cycles) includes both thermodynamic and dynamic-related precipitation changes, and the light gray regions corresponds to the days with no rainfall in the control climate. In the midlatitudes, between latitudes ∼40° and 60°, there is a precipitation decrease with warming at lower percentiles (<40th percentile), while there is a precipitation increase with warming at higher percentiles (>60th percentile). This indicates a general tendency toward dry days getting drier and wet days getting wetter; there is a simulated shift of the CDF shape toward moderate-to-heavy rainfall events at the expense of low rainfall events. The distribution changes in the highest latitudes (poleward of ∼60°) and deep tropics (equatorward of ∼7°) are toward more precipitation for nearly all percentiles. Finally, in the subtropics, there is a precipitation decrease for all percentiles.
Figure 5b shows the thermodynamically induced changes of the daily precipitation statistics calculated using the passive framework with the full structure ΔT (Fig. 1a). We see that the thermodynamic change (Fig. 5b) captures an important part of the total changes (Fig. 5a) in the statistics of daily precipitation. Our simulation reproduces the large precipitation rate decrease in the subtropics across nearly all percentiles and the precipitation rate increase of wet days (higher percentiles) in the deep tropics, mid and high latitudes. The difference between the standard precipitation’s total change and this thermodynamic change determined via the passive water vapor can be thought of as dynamic changes. Figure 5c shows this quantification of the dynamically induced changes to total precipitation changes (Fig. 5a). The dynamic component contributes to a precipitation decrease across all percentiles at higher latitudes and for most wet day percentiles in the midlatitudes and tropics. It contributes to a precipitation increase for dry days in the tropics and for some dry percentiles in the midlatitudes. Overall, the dynamic component typically has an opposite effect on daily precipitation distribution compared to the thermodynamic component.
The effect of the vertical structure of warming above the lower-atmospheric level (see Fig. 1) on thermodynamic precipitation changes is eliminated in Fig. 5d (cf. to Fig. 5b). The simulated precipitation rate decrease of the subtropical regions at lower percentiles does not depend strongly on the vertical structure of warming, such as the tropical upper-tropospheric amplification of warming. The simulated increase in precipitation rate in high latitudes and wet days in midlatitudes is also insensitive to the vertical structure. The thermodynamic perturbation is further simplified to a homogeneous warming (Fig. 5e), by eliminating the horizontal structure (e.g., no polar amplification) and the temperature change difference between surface and lower atmospheric level (which modifies the evaporative surface flux of the passive water vapor). With this temperature perturbation, the simulated precipitation rate decrease is limited in the lower percentiles (∼30th–40th percentiles) of the subtropics. In summary, the warming difference between the sea surface temperature and surface air temperature in a warmer climate is important to the simulated precipitation decrease in the subtropics (comparing Fig. 5d to 5c), which gets further intensified by a change in the large-scale circulation (comparing Fig. 5b to 5a). The dry and wet extremes are analyzed in more detail in the next sections.
d. Dry extreme events: Dry spells
We analyze the changes in the statistics of the lower (dry) tail of the precipitation distribution. Rather than simply focusing on a given low percentile of daily precipitation, we consider a dry extreme index that accounts for event duration. The maximum consecutive dry days (max CDD) is a way to calculate the duration of dry spells in a given climate (Sillmann et al. 2013). We use a threshold of 1 mm day−1 to separate dry days from wet days; the max CDD at each latitude is the maximum number of consecutive days with a rainfall rate under the determined threshold.
Figure 4b shows the max CDD for the control simulation, which has long duration in the subtropics and high latitudes and short duration in the deep tropics and mid latitudes. The results for the changes in CDD are typically insensitive to the threshold of 1 mm day−1, though the absolute number of CDD in the control simulation, of course, depends on the choice. Note that this index does not fully capture the whole complexity of droughts, which depend on surface changes, but is sufficient to characterize the precipitation-side of dry hydrological extremes. We have also examined the sensitivity of the max CDD to the GCM integration length. There were not any drastic changes when comparing a 1500-day (≈4 years) time series to the 6000-day (≈16 years) shown in the figures. So, 6000 days is more than sufficient to assess changes in the max CDD statistic of this idealized GCM.
Figure 6a shows the simulated max CDD percentage change (dotted red line), obtained via the warmed simulation. The simulated length of dry spells decreases with warming in polar regions, increases in the subtropical regions and midlatitudes, and stays unchanged in the deep tropics. These max CDD changes do not indicate how much more frequent dry spells are; rather, they indicate how much more intense they are in terms of duration. One can interpret longer dry spells as an indication of less frequent precipitation events. These changes in the max CDD are broadly in agreement with the consensus from the fifth IPCC assessment (Sillmann et al. 2013; Orlowsky and Seneviratne 2012) and the sixth IPCC assessment (Douville et al. 2021) reports of an intensification of wet and dry seasons under global warming, including an intensification of dry spells.
The simulated thermodynamically induced changes of the max CDD (solid yellow line) is compared to the total simulated changes from the climate change simulation (dotted red line) in Fig. 6a. The thermodynamic changes determined via the passive water vapor reproduce the higher latitude decrease of dry spell duration, as well as the intensification of subtropical dry spells. At higher latitudes (>60°), the max CDD decrease, about −5% K−1 near the poles, which is close to the thermodynamic component. The polar region’s daily precipitation is significantly increasing at all percentiles (see Fig. 5b), where polar amplification causes a larger percentage increase in water vapor and precipitation per unit of global-mean temperature change. In the subtropics (between 10° and 20°), the max CDD increases significantly, as much as 15% K−1. The thermodynamic component of the max CDD changes goes up by the CC rate in the subtropics, but it does not look like CC outside this region, as there is little-to-no thermodynamic lengthening of dry spells. The subtropical thermodynamic intensification of dry spells is also simulated in the case of the vertically uniform thermodynamic perturbation, as shown in Fig. 6b (dash–dotted blue line), while the homogeneous case simulates shorter dry spells at all latitudes (dotted dark-blue line). This indicates that the increased warming aloft in the tropics is not critical to explain the thermodynamic role of the subtropical dry spell intensification. The warming contrast between sea surface temperature and surface air temperature, which affects the evaporative flux of the passive water vapor, is important in simulating the amplification of dry spells in the subtropics, a region of water vapor divergence.
The implied effect of changes in the large-scale circulation (calculated as a residual in Fig. 6a, dashed orange line) further intensifies subtropical and mid- to high-latitude dry spells. The reduction in the dynamic component from large values in the subtropics to near zero around 30° suggests a potential role for circulation shifts, such as a poleward expansion of the Hadley cell (Lau and Kim 2015) and a poleward shift of storm-track activity (Scheff and Frierson 2012). In addition to the drying effect of circulation shifts, there is a potential dynamic role for changes in eddy kinetic energy that is distinct from the thermodynamically induced drying from an increase in the existing eddy moisture flux divergence and convergence (e.g., Held and Soden 2006, who discussed the thermodynamic role of increased moisture gradients, given the diffusive nature of eddy moisture fluxes). Changes in the dry spell intensity can also be linked to a warmer moist adiabat in the core of convective regions. The surface boundary layer moisture threshold to reach convective instability increases with warming. The thermodynamic enhancement in gradients of the climatological inflow of lower energy air from non-convective regions toward the margins of convective regions makes it harder to reach the threshold convective instability under warming, and this suppresses convection at the margin [the “upped-ante mechanism,” (Chou and Neelin 2004; Neelin et al. 2003)]. That thermodynamic suppression of convection at the margin of these regions will alter vertical velocity statistics and, therefore, is a dynamical change that can length the dry spells (Lintner et al. 2012). This potentially explains the transition from near-zero dynamic changes in the deep tropics to the dynamic dry spell lengthening in the subtropics.
e. Wet extreme events: 99.9th percentile of daily rainfall
We analyze the changes in the statistics of the upper (wet) tail of the precipitation distribution. Similar to many past studies (e.g., O’Gorman and Schneider 2009), we define wet extremes as events reaching a rainfall corresponding to the 99.9th percentile of the daily precipitation distribution (P99.9). This represents events with a return period of approximately 3 years.
Figure 7a shows the simulated P99.9 percentage change (dotted red line), obtained via the warmed simulation. Extreme precipitation intensifies everywhere; the smallest increase (near-zero) is located in the subtropics, there is a 7%–8% K−1 increase in the mid- and high latitudes, and an increase that approaches 10% K−1 in the deep tropics. These simulated changes are in agreement with previously published changes (e.g., Pfahl et al. 2017).
The simulated thermodynamically induced changes of P99.9 (solid yellow line) are compared to the total simulated changes from the climate change simulation (dotted red line) in Fig. 7a. The thermodynamic changes determined via the passive water vapor reproduce the increase in heavy daily rainfall at all latitudes. At higher latitudes (>50°), the P99.9 increase is almost completely explained by the thermodynamic component. The simulated percentage increase in water vapor is the largest in polar regions due to local amplified warming and increased moisture transport. Throughout the tropics, the thermodynamic P99.9 percentage change stays near 5% K−1. The P99.9 percentage change gets larger (6%–7% K−1) and more homogeneous when the thermodynamic perturbation does not include the vertical structure of warming, as shown in Fig. 6b (dash–dotted blue line). The surface air temperature change is around 4 K throughout the tropics, and is repeated through the whole atmospheric column in the “Vertically Uniform” experiment, which explains the more spatially homogeneous simulated P99.9 changes. The contrast with the “Full Structure” simulation (Fig. 6b, solid yellow line) indicates that the upper-troposphere amplification in the tropics damps the simulated P99.9 changes. As the climate warms, we expect to see a larger temperature increase in the upper troposphere than at the surface in the tropics (i.e., a more stable tropical atmosphere). In our simulations, precipitation occurs immediately after condensation takes place, when the relative humidity reaches a value of 100%. The large-scale condensation tendency decreases significantly in the tropical lower-troposphere because of the increasing temperature change with height. As a simple diagnostic, this would suggest an upward shift of the level of condensation (this is in line with Wright et al. (2010), who use a tracer of last saturation to decouple temperature and circulation fields to diagnose the mechanisms influencing relative humidity). If air parcels reach saturation at a higher altitude, where the environment temperature is much colder than at lower altitudes (higher pressures), a smaller amount of water vapor can condense. Compared to a homogeneous warming (∼3 K) perturbation (Fig. 7b, dotted dark-blue line), the P99.9 percentage changes outside the tropics is smaller due to the normalization by the local zonal-mean surface temperature increase, which is polar amplified. One can note that the simulated P99.9 change from the homogeneous warming experiment (dotted dark-blue line) goes from 6% K−1 in the deep tropics to 9% K−1 at the poles, which corresponds roughly to what we expect from the Clausius–Clapeyron (CC) theory. The nonlinear relationship between saturation specific humidity and temperature has a higher sensitivity at colder temperatures; a smaller specific humidity increase at colder temperatures leads to a larger percentage change per degree of warming than it does for a larger specific humidity increase at warmer temperatures. This is because the actual specific humidity content is much lower in colder temperatures than in warmer temperatures.
The implied dynamical change (Fig. 7a, residual, dashed orange line) is most important within the tropics, and it intensifies extreme precipitation in the deep tropics and weakens it in the subtropics. One can note the dominance of the thermodynamic effects over the dynamically induced changes related to strengthened/weakened vertical motion, particularly outside the tropics.
f. Comparison with theory for wet extreme events
In Fig. 8, we present the same decomposition of the 99.9th percentile of daily precipitation response to warming as in the previous section but evaluated with the scaling [Eq. (4)]. The total percentage change (dotted red line) is calculated by taking the difference between the P99.9 scaling evaluated for the control and the warmed experiments.
We evaluate the thermodynamic component of the scaling (solid gray line) by keeping the pressure velocity fixed. The moist-adiabatic derivative of saturation specific humidity term is perturbed by a change in temperature. Rather than using the changes in the conditioned temperature on P99.9 (ΔTe,99.9) to evaluate the scaling thermodynamic component, we use the changes in the time-mean, zonal-mean temperature (
We compare the thermodynamically induced changes simulated via the passive experiment “Full Structure” (Fig. 8, solid yellow line) with the thermodynamic component of the scaling (Fig. 8, solid gray line). They both show a large sensitivity of P99.9 to warming that increases poleward, the lowest sensitivity in the tropics. They differ the most outside the tropics, where the passive framework predicts a large sensitivity of the P99.9 thermodynamic component to warming (solid yellow line compared to solid gray line). Outside the tropics, the estimated dynamic component from the passive framework has a near-zero or somewhat negative contribution by the dynamic component (as seen in Fig. 7a, dashed orange line).
The scaling explains the thermodynamically induced effects on extreme precipitation via the changes in the vertical gradient of saturation specific humidity along a moist adiabat. O’Gorman and Schneider (2009) assume an atmosphere in a moist-adiabatic state when P99.9 extreme events occur. As we mentioned earlier, when looking at the actual temperature profile during extreme events, this assumption is the most accurate for latitudes lower than 60°. A moist-adiabatic state moderates the changes of saturation specific humidity increases with height. For weaker changes in the vertical gradient of saturation specific humidity, fewer changes in condensation occur with the same vertical velocity. We can make a similar assumption, one of an atmosphere with a saturated moist-adiabatic lapse rate, for the passive water vapor GCM experiment “Moist-Adiabat,” described in section 2c (see Fig. 1d). In this experiment, the upper troposphere warms more than the surface everywhere. The simulated thermodynamically induced P99.9 changes based on a moist-adiabat profile are compared to the scaling thermodynamic component predictions in Fig. 8 (dot–dashed blue line compared to solid gray line). The magnitude of differences between the passive water vapor GCM estimate of the thermodynamic changes and the scaling theory contrast is significantly reduced, in the tropics and midlatitudes, when the passive water vapor is perturbed with the moist-adiabatic temperature change, in comparison to the full structure one (solid yellow line compared to dot–dashed blue line in Fig. 8). In the previous subsection, we mentioned how the increasing temperature change with height moderates the P99.9 sensitivity relative to surface warming. The role of vertical structure of warming is similar here.
We evaluate the dynamic component of the scaling (dashed orange line) by keeping fixed the temperature, which means there are no changes in the moist-adiabatic derivative of saturation specific humidity term. Similarly to previous results, changes in the pressure velocity statistics have a significant impact on the predicted changes in extreme precipitation intensity. There is a dynamical strengthening of extreme precipitation at higher latitudes and in the deep tropics. The latter actually depends on the choice to forgo a convection parameterization (cf. Fig. 8b of O’Gorman and Schneider 2009). In the case of no convection scheme, there are difference between how the extreme dynamic changes and the mean circulation changes. There is a weakening of the Hadley cell in the lower troposphere, with a small strengthening along the equator, but the pressure velocity during extreme events strengthens significantly in the deeps tropics. We note that this estimate of the dynamic component of changes to precipitation extremes is higher at most latitudes than the residual calculation shown in Fig. 7a. These dynamic changes differ partly because of the discrepancies between the thermodynamic changes obtained via the passive water vapor and via the scaling. Since the dynamic changes in Fig. 7a are simply calculated as a residual, the fact that the estimates of the thermodynamic changes differ (solid yellow line compared to solid gray line in Fig. 8) is the main factor that leads to large differences for the dynamic component to extreme precipitation changes. Hence, calculating the residual from the thermodynamic changes with moist-adiabatic temperature change (Fig. 8, dot–dashed blue line) would reduce the differences between the estimates of the dynamic changes (not shown). Also, it is worth noting that there are differences in the assumptions made by the scaling and by our current approach that could impact the results (e.g., the scaling does not include horizontal advection of water vapor or evaporation in its approximation to the atmospheric water vapor budget).
4. Summary and discussion
We performed an online calculation of the thermodynamic precipitation changes using an additional passive water vapor variable that undergoes evaporation and condensation at a climate change-perturbed temperature. This methodology can be applied both to individual storms (Fig. 2) and across the whole probability distribution of daily rainfall (Fig. 5). We simulate a thermodynamically induced precipitation rate decrease in the subtropics at almost all percentiles (all dry and most wet days). In the midlatitudes, there is a thermodynamically induced precipitation rate decrease at lower percentiles (dry days), which is further amplified by dynamical changes. With this approach, we can identify which aspects of the temperature change structure are important to simulating particular aspects of the changes in the precipitation distribution.
The dry tail of the daily precipitation distribution can be described using the maximum consecutive dry day (CDD) index, a measure of dry spell length. We demonstrated that there is a thermodynamically induced intensification of dry spells in the subtropics, which is further amplified by dynamical changes. Most latitudes with a simulated daily precipitation rate decrease for dry days (percentiles with rainfall lower than the 1 mm day−1 threshold, red contours to the left of the gray dotted line in Fig. 5) correspond to the latitudes with longer dry spells (Fig. 6). The subtropical thermodynamically induced intensification of dry spells is simulated when the warming difference between sea surface temperature and surface air temperature is included. The reduction in this temperature contrast affects the evaporative flux here and in comprehensive simulations of climate change (e.g., Richter and Xie 2008). We show that the thermodynamic changes of CDD has a nearly CC increase in the subtropics and decreases in high latitudes. Previous thermodynamic discussions comparing the mean hydrological cycle response to global warming to wet extremes changes have been able to give information on the sign of dry extremes changes but not on their magnitude. We have a unique quantitative approach that allows us to actually quantify the magnitude of thermodynamic changes for dry spells.
The upper, wet tail of the daily precipitation distribution can be described using the 99.9th percentile of daily precipitation, a heavy rainfall event. We demonstrate that the thermodynamically induced increase in extreme precipitation dominates over dynamical effects outside the tropics. We show a damping of the extreme precipitation intensification from the moist-adiabatic warming in the upper troposphere. We can interpret this as the result of weakening vertical gradients in the saturation specific humidity, consistent with previous theory for precipitation extremes.
This passive water vapor, online approach can be extended to additional categories of extreme events and comprehensive models. We are pursuing the analysis of simulations that contain a large number of tropical cyclones. Adapting comprehensive GCMs with isotope-enabled versions could also be used to examine climate change’s effect on precipitation, rather than the fractionation of heavy isotopes. In addition, this methodological approach can be used to understand mean precipitation changes under global warming, including assessments of the role of the vertical and spatial distribution of warming, which we examine in forthcoming research.
Acknowledgments.
We acknowledge the support of an NSERC Discovery grant and Canada Research Chair (Tier II) and the Canada Foundation for Innovation for a Compute Canada allocation. We thank Isaac Held for helpful discussions, and reviewers for all valuable comments and suggestions. We are grateful to Pablo Zurita-Gotor and Isaac Held for sharing their results that demonstrated the existence of ITCZ instability, which affects the results in the appendix.
Data availability statement.
The GCM source code for the passive water vapor version of the idealized GCM is available at https://github.com/marielabonte/GCM-passive-hydro.git.
APPENDIX
Sensitivity to Convection and Radiative Transfer Schemes
In this appendix, we present two sensitivity analyses of the key measures of the precipitation distribution and its response to warming to aspects of the idealized GCM configuration. First, we show the effect of having a convection scheme in simulations with gray radiation, a more widely analyzed configuration of this GCM. Second, we show simulations with a comprehensive radiative transfer scheme for clear-sky radiation instead of gray radiation in simulations without a convection scheme. Here, we assess the sensitivity of standard model simulations (e.g., the difference of the active precipitation between warmed and control simulations) to one aspect of the configuration with and all other aspects of the simulations the same as in our standard configuration.
a. Simulations with gray radiation and a convection scheme
This set of simulations uses the quasi-equilibrium convective scheme described in Frierson (2007). It relaxes unstable columns to moist adiabats with constant relative humidity over a 2-h time scale.
Figures A1a and A1b shows the climatological distribution of daily precipitation and its changes with warming for the GCM configuration in the main text (GCM simulations using gray radiation without a convection scheme, same as Figs. 4a and 5a in this paper). These can be compared to Figs. A1c and A1d, the sensitivity experiment where the convection scheme is turned on in simulations with gray radiation. In the control climate (Fig. A1a versus Fig. A1c), the main differences are the increase in daily precipitation rates at low-to-moderate percentiles and less intense extreme precipitation in the deep tropics and the more frequent wet days (daily precipitation rate higher than 1 mm day−1) in the subtropics. Outside of the tropics, the effect of having a convection scheme is less obvious. In the extratropics advection by resolved larger, synoptic-scale flows dominates, thus convection is not directly critical to the simulate precipitation. For the daily precipitation distribution changes with warming (Fig. A1b versus Fig. A1d), the main difference is the wider region of increase daily precipitation rate in the deep tropics. The daily precipitation decrease in the subtropics has a larger sensitivity to warming in the lower percentiles (<50th percentile) and it changes sign (increase instead of decrease) at the higher percentiles (>90th percentile) when the convection scheme is active.
Figure A2 shows the changes of the maximum consecutive dry days with warming. We compare the original simulations with no convection scheme and gray radiation (Fig. A2, solid red line) to the ones with convection scheme and gray radiation (Fig. A2, dotted red line). There is no major effect of having a convection scheme on the regional changes of dry spells length, although the magnitude can differ. In the subtropics, dry spells lengthen with warming with or without convection, with a somewhat more moderate increase with the convection scheme (peak values of ≈10% versus ≈15%). Note also that the region of dry spell intensification in the subtropics is more poleward and the cross-over latitude to shorter dry spells is equatorward when the convection scheme is active (solid red line compared to dotted red line). Finally, we note that there are still hemispheric asymmetries in this metric, suggesting that these are primarily the result of our 6000 day integrations, rather than the absence of a convection scheme in our primary set of simulations.
Figure A3 shows the changes of the 99.9th percentile of daily precipitation with warming. We compare the original experiment with no convection scheme and gray radiation (Fig. A3, solid red line) to the one with convection scheme and gray radiation (Fig. A3, dotted red line). The effect of the convection scheme is to significantly reduce the sensitivity of extreme precipitation to warming (≈5% K−1 lower increases) in the deep tropics and slightly reduce the sensitivity in the midlatitudes (≈2% K−1 lower increases). A large difference from the case of no convection scheme is that the pressure velocity during extreme events weakens instead of strengthening in the deeps tropics when we include a convection scheme (not shown). This results in more moderate sensitivity to warming of extreme precipitation in the deep tropics. Dynamic-induced changes in this case would decrease extreme precipitation across the tropics, instead of showing the increase/decrease pattern seen in the no convection scheme case.
b. Simulations with comprehensive clear-sky radiative transfer without a convection scheme
While the gray radiation scheme uses a prescribed optical depth as a simple function of latitude and pressure, the comprehensive radiative scheme includes prescribed ozone, carbon dioxide and other greenhouse gases and depends on the time-dependent water vapor distribution. In these new simulations, the planetary albedo is set at 0.1, as opposed to 0.38 in the original experiments. This is because we set the albedo at a higher value to account for clouds albedo when using the gray radiation scheme. In the comprehensive radiative scheme, we can prescribe low cloud fraction from the equator (0.02) to the poles (0.4). This radiative transfer and simulation set up is identical to the one described in Merlis et al. (2013). The warmed climate is performed by doubling the CO2 concentration (from 300 to 600 ppm).
For the climatological distribution of daily precipitation and its changes with warming, we compare the original experiment (Figs. A1a,b) to Figs. A1e and A1f, the sensitivity experiment where the gray radiation is replaced by a comprehensive radiative scheme and neither use a convection scheme. In the control climate (Fig. A1a versus Fig. A1e), the main difference is the lack of days without precipitation (light gray area) in the tropics, which suggests more frequent drizzle. The deep tropics region (with the characteristic of more frequent wet days) is wider, and dry days in the midlatitudes are less frequent with comprehensive clear-sky radiation. As for the daily precipitation distribution changes with warming (Fig. A1b versus Fig. A1f), the structure of changes is quite similar to the original experiment, even though the magnitude of changes, especially for the precipitation decrease in the subtropics, are smaller. There is a wider region of increase precipitation rate for dry days in the tropics, essentially increased drizzle, and we note that these large percentage changes at low climatological values are small in an absolute sense.
For the changes of the maximum consecutive dry days with warming, we compare the original experiment with no convection scheme and gray radiation (Fig. A2, solid red line) to the one with no convection scheme and comprehensive radiative scheme (Fig. A2, dot–dashed red line). There is an intensification of dry spells length in the subtropics, and a significant shortening of dry spells in the deep tropics and midlatitudes. The subtropics intensification of dry spells is also more poleward than in the original experiment case (solid red line compared to dot–dashed red line).
For the changes of the 99.9th percentile of daily precipitation with warming, we compare the original experiment with no convection scheme and gray radiation (Fig. A3, solid red line) to the one with no convection scheme and comprehensive radiative scheme (Fig. A3, dot–dashed red line). Outside the tropics, the effect of the comprehensive radiative scheme is quite negligible on the sensitivity of extreme precipitation. In the deep tropics, there is a simulated decrease in extreme precipitation with warming, while the increase with warming in the deep tropics is of a smaller magnitude than the original experiment case (solid red line compared to dot–dashed red line).
There is an apparent asymmetry between the hemispheres in the changes with warming of the daily precipitation distribution, the maximum CDD, and the extreme precipitation. The ITCZ shifts toward the Northern Hemisphere in the warmed climate, even though the radiative forcing and the surface boundary conditions are hemispherically symmetric. This hemispherically asymmetric behavior has been found in GCMs that have no convection scheme and a comprehensive clear-sky radiative transfer scheme (P. Zurita-Gotor and I. Held 2022, personal communication). In the Southern Hemisphere, we interpret the larger extreme precipitation decrease in the subtropics, the smaller dry spell lengthening in the subtropics, and the larger dry spell shortening in the midlatitudes as a consequence of the ITCZ shift to the Northern Hemisphere.
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