Evaluation of Changes in Dry and Wet Precipitation Extremes in Warmer Climates Using a Passive Water Vapor Modeling Approach

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/p_s). 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.

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The temperature perturbation fields $\mathrm{\Delta }\overline{T}(\sigma ,\varphi )$ used to perturb the passive water vapor in the four experiments described in section 2c. (a) “Full Structure”: Atmospheric warming with vertical and latitudinal gradients resulting from an increased longwave optical depth (taken from the warmed experiment). (b) “Vertically Uniform”: Atmospheric warming vertically uniform with latitudinal structure, obtained by replicating the lowest atmospheric temperature change from “Full Structure” at all vertical levels. (c) “Uniform”: Homogeneous warming (∼3 K). (d) “Moist Adiabat”: Atmospheric warming following a moist-adiabatic profile, which is calculated based on the simulated surface temperature, surface relative humidity, and surface pressure (via the control and warmed simulations).

Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0048.1

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b. Passive water vapor approach

There are four existing modeling approaches with common aspects to ours:

1. 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.

2. 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.

3. Isotope-enabled GCMs, as described in the introduction.

4. 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 $\mathrm{\Delta }\overline{T}$. This is particularly a concern in the deep tropics. We choose to turn off the convection scheme even though this degrades the control simulation and can affect the response to climate change. As it becomes increasingly feasible to run GCMs near convection-resolving resolutions (or cloud-system resolving models in near-global domains), we did not pursue strategies to ameliorate this concern. We also note that isotope-enabled GCMs face issues in how convection schemes deal with the different isotopes.

c. Decomposing the temperature perturbation

We design four different experiments using different structures (latitudinal and vertical) for the temperature perturbation $\mathrm{\Delta }\overline{T}(\sigma ,\varphi )$, with the intent of isolating the relative importance of different well known features of warming that arise from a stronger atmospheric greenhouse.

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 $\mathrm{\Delta }\overline{T}(\sigma ,\varphi )=3\mathrm{K}$, but the results do not depend sensitively on the magnitude. We performed an experiment with a homogeneous temperature of $\mathrm{\Delta }\overline{T}(\sigma ,\varphi )=6\mathrm{K}$, which had similar normalized results. In the fourth and last experiment (“Moist-Adiabat,” Fig. 1d), we assume the temperature perturbation follows a moist-adiabatic profile. The moist-adiabatic profiles are calculated based on the simulated surface temperature, surface relative humidity, and surface pressure of the control and the warmed simulations, the difference between these gives the moist-adiabatic temperature perturbation. The moist-adiabatic temperature change simulation is used to compare to existing scaling theory for wet extremes, so we only present the results in section 3f. In these four experiments, the time-independent temperature perturbation is applied only to the passive water vapor [see Eq. (2)], and the control water vapor stays unchanged.

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.

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A snapshot of an individual 99.9th-percentile rainfall event (at 45°N) in the midlatitudes for (a) the control active water vapor and (b) the thermodynamically perturbed passive water vapor ($\mathrm{\Delta }\overline{T}$ Full Structure; see Fig. 1a). Precipitation rate (color-filled contours at 5 mm day⁻¹ interval) and pressure velocity at 550 hPa (gray contours at 0.1 Pa s⁻¹ interval; dashed for the negative values of upward motion).

Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0048.1

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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) = αδT_sfc(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.

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Time- and zonal-mean net precipitation changes. Comparison between the total net precipitation changes δ(P − E) (red dotted line; difference between the warmed and control simulation), the δ(P − E) thermodynamic component estimated from Held and Soden (2006) scaling αδT_sfc(P − E) (black dashed line), and the δ(P − E) thermodynamic component calculated using the perturbed passive water vapor (yellow solid line; using $\mathrm{\Delta }\overline{T}$ Full Structure; see Fig. 1a).

Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0048.1

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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.

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(a) Daily precipitation distribution for the control climate for all latitudes. Daily rainfall (color-filled contours at pseudo-log interval). The dotted gray line denotes the percentile at which a daily precipitation rate of 1 mm day⁻¹ is found, our definition of the threshold between dry and wet days. The white area indicates the days without rainfall. (b) Climatology maximum consecutive dry days (<1 mm day⁻¹ of precipitation) at each latitude.

Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0048.1

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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.

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Percentage change (normalized by the local zonal-mean surface temperature increase) of each daily precipitation percentile for all latitudes. (a) Simulated climate change (from warmed minus control simulations), which includes both thermodynamically and dynamically induced changes. (b) Thermodynamic response to the full structure of warming (see Fig. 1a). (c) Difference of (a) minus (b), the residual dynamic-induced changes to total precipitation changes. (d) Thermodynamic response to vertically uniform warming with polar amplification (see Fig. 1b). (e) Thermodynamic response to a vertically and meridionally uniform warming (see Fig. 1c). The solid gray line denotes the zero percentage change. The dotted gray line denotes the percentile at which a daily precipitation rate of 1 mm day⁻¹ is found in the control climate (see Fig. 4a). The light gray area indicates the days without rainfall in the control climate (see Fig. 4a).

Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0048.1

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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.

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Percentage change (normalized by the local zonal-mean surface temperature increase) of the maximum consecutive dry days (max CDD) for all latitudes. (a) Total changes disentangled into a thermodynamic component (from the $\mathrm{\Delta }\overline{T}$ Full Structure experiment) and a dynamic component (residual). (b) Assessment of the vertical structure vs meridional structure of warming on the dry extreme event’s thermodynamic response to warming.

Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0048.1

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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 (P_99.9). This represents events with a return period of approximately 3 years.

Figure 7a shows the simulated P_99.9 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).

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Percentage change (normalized by the local zonal-mean surface temperature increase) of the 99.9th percentile of daily precipitation for all latitudes. (a) Total changes disentangled into a thermodynamic component (from the $\mathrm{\Delta }\overline{T}$ Full Structure experiment) and a dynamic component (residual). (b) Assessment of the vertical structure vs meridional structure of warming on the dry extreme event’s thermodynamic response to warming.

Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0048.1

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The simulated thermodynamically induced changes of P_99.9 (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 P_99.9 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 P_99.9 percentage change stays near 5% K⁻¹. The P_99.9 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 P_99.9 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 P_99.9 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 P_99.9 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 P_99.9 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 P_99.9 scaling evaluated for the control and the warmed experiments.

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Percentage change (normalized by the local zonal-mean surface temperature increase) of the 99.9th percentile of daily precipitation at all latitudes. As in Fig. 7a, but here the total changes and thermodynamic and dynamic components are obtained via the scaling of O’Gorman and Schneider (2009) [see Eq. (3)]. The total percentage change is evaluated with surface pressure, pressure velocity, and temperature profiles conditioned on the extremes occurring, taken from the control and warmed simulations (red dotted line). The dynamic component of the scaling is evaluated with fixed temperature and changing pressure velocity. The thermodynamic component of the scaling is evaluated with fixed pressure velocity and temperature profile perturbed by the time-mean, zonal-mean $\mathrm{\Delta }\overline{T}$ from “Full Structure” experiment (orange dashed line). The latter is compared to the thermodynamic component obtained via the passive water vapor, for both the $\mathrm{\Delta }\overline{T}$ “Full Structure” (yellow solid line) and $\mathrm{\Delta }\overline{T}$ “Moist-Adiabat” experiments (blue dash–dotted line).

Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0048.1

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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 P_99.9 (ΔT_e,99.9) to evaluate the scaling thermodynamic component, we use the changes in the time-mean, zonal-mean temperature ($\mathrm{\Delta }\overline{T}$), similar to the passive water vapor “Full Structure” experiment (see Fig. 1a). As discussed by O’Gorman and Schneider (2009), the temperature profile when the extreme event occurs is warmer than the time-mean temperature perturbation. When we evaluate the scaling thermodynamic component using ΔT_e,99.9, predicted changes are systematically lower outside of the tropics than when using $\mathrm{\Delta }\overline{T}$ as the perturbation. This is because the extreme temperature profile is closer to a moist-adiabat in the tropics and midlatitudes, up to 60°. There are some limitations to the scaling theory at higher latitudes (poleward of 60°); the extreme temperature profile is closer to a vertically uniform profile, with the warming aloft close-to-but-lower-than the surface warming, than a moist-adiabat.

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 P_99.9 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 P_99.9 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 P_99.9 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 P_99.9 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 P_99.9 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).