Dry and moist dynamics shape regional patterns of extreme precipitation sensitivity

Significance

The factors controlling the large regional variations in simulated responses of extreme precipitation to global warming are poorly understood. Standard diagnostics break the responses into thermodynamic and dynamic components associated with moisture and vertical motion. The vertical motion is the more poorly understood; we use a method to understand it by decomposing it into dry and moist components. The moist component can be predicted by a simple model that explains how dynamics and thermodynamics are coupled. This allows us to explain the regional variations in vertical motion, and thus extreme precipitation, in terms of the dry quasigeostrophic forcing and moisture, a deeper level of explanation than is available from the thermodynamic–dynamic decomposition on its own.

Abstract

Responses of extreme precipitation to global warming are of great importance to society and ecosystems. Although observations and climate projections indicate a general intensification of extreme precipitation with warming on global scale, there are significant variations on the regional scale, mainly due to changes in the vertical motion associated with extreme precipitation. Here, we apply quasigeostrophic diagnostics on climate-model simulations to understand the changes in vertical motion, quantifying the roles of dry (large-scale adiabatic flow) and moist (small-scale convection) dynamics in shaping the regional patterns of extreme precipitation sensitivity (EPS). The dry component weakens in the subtropics but strengthens in the middle and high latitudes; the moist component accounts for the positive centers of EPS in the low latitudes and also contributes to the negative centers in the subtropics. A theoretical model depicts a nonlinear relationship between the diabatic heating feedback ($\alpha$) and precipitable water, indicating high sensitivity of $\alpha$ (thus, EPS) over climatological moist regions. The model also captures the change of $\alpha$ due to competing effects of increases in precipitable water and dry static stability under global warming. Thus, the dry/moist decomposition provides a quantitive and intuitive explanation of the main regional features of EPS.

A warmer climate has more water vapor, which tends to intensify extreme precipitation events in general. Observational trends and climate simulations indicate this intensification on a global scale (1–6), but regional responses of extreme precipitation exhibit wide geographic variation (3–8). Regional patterns of extreme precipitation sensitivity (EPS) (defined here as the fractional change in extreme precipitation per degree of global warming) can be separated into a relatively homogeneous thermodynamic component representing changes in water vapor (which approximately follows the Clausius–Clapeyron [CC] scaling, 7%/K), and a dynamic component representing changes in vertical motion. The dynamic component contributes most of the regional variation in EPS (8). Thus, the key to understanding the regional patterns of EPS is to understand the changes of vertical motion in extreme precipitation events. This is a subtle task, because vertical motion and precipitation are closely coupled, making cause and effect difficult to untangle.

The dynamics that control vertical motion vary with latitude, due to variations in the Coriolis effect. In the deep tropics, ascent is closely associated with latent heating of moist convection (9, 10). In the extratropics, vertical motion is also strongly constrained by quasibalanced dynamical processes associated with the potential vorticity field, represented most simply by quasigeostrophic (QG) dynamics. Extratropical extreme precipitation events are usually associated with large-scale perturbations such as fronts and cyclones (11, 12). A given large-scale perturbation induces dynamically forced vertical motion, and would do so even in a dry atmosphere. In the real, moist atmosphere, it stimulates the development of moist convection by destabilizing the atmospheric stratification. The latent heating then released by the convection, in turn, drives further large-scale ascent. Both the dry adiabatic dynamics due to the large-scale perturbations and the diabatic heating due to the moist convection are important in generating vertical motion in extreme precipitation events (13, 14). Thus, it is useful to view extreme precipitation as a system consisting of forcing (by large-scale adiabatic perturbations) and feedback (by diabatic heating).

Here, we apply QG diagnostics to understand the regional patterns of EPS in climate projections from the Coupled Model Intercomparison Project Phase 5 (CMIP5). The QG$\omega$ equation is used to decompose the vertical pressure velocity ($\omega$) in extreme precipitation (excluding the deep tropics, where QG is not valid) into a part (${\omega }_D$) due to large-scale adiabatic forcings ($F$) and a part (${\omega }_Q$) due to diabatic heating ($Q$), respectively (Methods). With the previous proposed extreme precipitation scaling using vertical velocity (4), extreme precipitation ($P$) may be expressed as $P=P_D+P_Q=P_D\left(1+\alpha \right)$, where $P_D$ and $P_Q$ are the precipitation corresponding to ${\omega }_D$ and ${\omega }_Q$, respectively, and $\alpha =\frac{P_Q}{P_D}$ is a parameter measuring the diabatic heating feedback associated with moist convection. The above equation separates precipitation into a dry component ($P_D$) corresponding to the adiabatic dynamic forcing by large-scale perturbations and a moist component ($\alpha$) representing the diabatic-heating feedback associated with moist convection. The dry/moist decomposition may also be thought as an adiabatic/diabatic decomposition. Correspondingly, the dry/moist decomposition can be applied to the EPS ($\delta \ln P$):

$$\delta \ln P=\delta \ln P_D+\delta \ln \left(1+\alpha \right),$$ [1]

where $\delta \ln P_D$ includes changes in both water vapor and ${\omega }_D$, and $\delta \ln \left(1+\alpha \right)$ represents changes of the diabatic-heating feedback (15). We will show that the dry and moist components together shape the regional patterns of EPS in climate projections and provide insights into the behavior of each component, as described schematically in Fig. 1.

Fig. 1.

A proposed roadmap for understanding the EPS. The thermodynamic/dynamic decomposition (8) (light gray boxes) show that the changes of vertical motion account for most regional features, however, with causes unsolved. This study (dark gray boxes) further applies a dry/moist decomposition of vertical motion into parts due to large-scale adiabatic forcings and diabatic-heating feedback. Diagnoses from climate model outputs and a simple model link the changes in the diabatic-heating feedback to the changes in local atmospheric moisture and the dry static stability. Future studies (dashed-line arrows) should link the changes of $F$ to the changes of large-scale background conditioned on extreme precipitation or, even further, to the changes of mean states.

Methods

Daily data from 20 models in the CMIP5 archive (SI Appendix, Table S1) are used in this study. The present climate is represented by the historical simulations between 1981 and 2000, and the warmer climate is represented by the RCP8.5 scenario simulations between 2081 and 2100. The climatic response of a quantity is calculated as fractional changes (denoted by $\delta \ln$) between these two periods normalized by the global-mean surface warming. Since we are interested in regional-scale extreme precipitation in this study, extreme precipitation (denoted by $P$) of each geographic location is defined as the annual maximum daily precipitation over a surrounding $7.5^{○}\times 7.5^{○}$ regional box. At each location, diagnoses are performed on the extreme precipitation day of each year. Then, we compose all of the events during each 20-y period and apply multimodel averaging. The size of the regional box is chosen since it better suits the QG$\omega$ inversion (16). We verified the sensitivity of our results to the definition of extreme precipitation by using $3.75^{○}\times 3.75^{○}$ regional boxes. Changing to smaller regional boxes leads to larger climatological precipitation amounts; however, the EPS and its decomposition are very close to those shown here (comparing Figs. 2 and 3 with SI Appendix, Figs. S11 and S12).

Fig. 2.

The decomposition of extreme precipitation from historical simulations [$P=P_D+P_Q=P_D\left(1+\alpha \right)$]. (A–D) The multimodel mean of annual maximum daily precipitation ($P$) (A); $P_D$, component due to dry forcing (B); $P_Q$, component due to diabatic heating (C); and diabatic heating feedback ($\alpha$, color) (D). The white contours (intervals of 10 $mm$) in D show the precipitable water ($H$) conditioned on extreme precipitation day. The domain of maps (here and below) is $75^{○}$S $\sim$ $75^{○}$N. QG diagnosis are masked within $5^{○}$S $\sim$ $5^{○}$N, where the QG inversion is not applicable.

Fig. 3.

The EPS and its dry/moist decomposition [$\delta \ln P=\delta \ln P_D+\delta \ln \left(1+\alpha \right)$]. (A–D) The EPS (A), EPS approximated by the scaling using $\omega$ (B), the dry component of EPS ($\delta \ln P_D$) (C), and the moist component [$\delta \ln \left(1+\alpha \right)$] (D). In E and F, $\delta \ln P_D$ is further separated into the thermodynamic contribution (keep ${\omega }_D$ constant in the scaling) and the dynamic contribution (full scaling minus thermodynamic contribution). Stippling indicates that over 70% of the models agree on the sign of the change.

The QG$\omega$ diagnostics follows similar methods as those of refs. 13 and 14. It calculates the linear inversion of the QG$\omega$ equation to assess contributions of vertical motion from different physical processes. The QG$\omega$ equation reads

$$\left({\partial }_{pp}+\frac{\sigma }{f^2}{\nabla }^2\right)\omega =-\frac{1}{f}{\partial }_{p}Ad{v}_{\zeta }-\frac{R}{p{f}^2}{\nabla }^{2}Ad{v}_T-\frac{R}{p{f}^2}{\nabla }^{2}Q,$$ [2]

where $\sigma =-\frac{RT}{p}{\partial }_p\ln \theta$ is the dry static stability, and $f$ is the Coriolis parameter. $Ad{v}_{\zeta }=-\overrightarrow{V_g}\cdot \nabla \zeta$ and $Ad{v}_T=-\overrightarrow{V_g}\cdot \nabla T$ are the horizontal advection of geostrophic absolute vorticity ($\zeta$) and temperature ($T$) by geostrophic winds, respectively. The sum of first two right-hand-side (RHS) terms in Eq. 2 is the dry adiabatic dynamic forcings ($F$) (the dry part), and the third RHS term is the diabatic heating term (the moist part). Taking advantage of the linearity of the QG$\omega$ equation, we solve Eq. 2 on the three-dimensional spherical grids including the RHS terms one by one (detailed in SI Appendix, section S1). Thus, we have the decomposition $\omega ={\omega }_D+{\omega }_Q$, in which ${\omega }_D$ corresponds to the dry adiabatic dynamic forcings ($F$), and ${\omega }_Q$ corresponds to the diabatic heating term (the third RHS term). $\omega$ is then converted to precipitation by the scaling proposed in ref. 4.

Since the CMIP5 models do not provide the diabatic heating ($Q$), we may calculate it as the residual term in the temperature budget equation (13) and then use it to solve ${\omega }_Q$, Or we may calculate ${\omega }_Q$ as the residual term with other components of $\omega$ calculated by directly solving the QG$\omega$ equation. ${\omega }_Q$ calculated by the two methods are reasonably close to each other (SI Appendix, Fig. S2). The results presented here are with ${\omega }_Q$ calculated as the residual in the $\omega$ equation; the main conclusions are not affected by choice of methods of calculating ${\omega }_Q$ (validation in SI Appendix, section S1).

Results

First, we examine the dry and moist components of extreme precipitation in historical simulations. The extreme precipitation climatology (Fig. 2A) has a geographic distribution resembling that of the mean precipitation but with much greater intensity. $P$ in Fig. 2A is smaller than previous studies (e.g., figure 1 in ref. 8) because, here, the precipitation extremes are averaged over larger areas. $P$ from direct model outputs is well reproduced by the scaling using vertical motion (8) (SI Appendix, Fig. S7). The distribution of $P$ shows an overall decrease with latitude, since water vapor is mostly confined to the low latitudes. In contrast, the component of precipitation due to dry dynamical forcing ($P_D$) (Fig. 2B) peaks in the middle latitudes, being approximately collocated with the storm tracks in both hemispheres. The strong meridional gradient of temperature in the midlatitudes leads to baroclinic instability and actively generates synoptic storms. These midlatitude storms are very robust features even in dry climate models without water vapor (17, 18), indicating the essential role of dry QG dynamics. The large-scale dry perturbations are much weaker in the low latitudes due to the weaker Coriolis effect, resulting in small $P_D$ there. Precipitation due to diabatic heating ($P_Q$) (Fig 2C) has a greater contribution to $P$ than $P_D$ has, particularly in the low latitudes where the abundant water vapor supports strong convection. In the extratropics, the distributions of $P_D$ and $P_Q$ are closely related; the local maxima of $P_Q$ are roughly equatorward of the local maxima of $P_D$ (such as the northern hemisphere Pacific and Atlantic storm tracks and the South Pacific Convergence Zone).

The close coupling between $P_D$ and $P_Q$ is quantified by the diabatic-heating feedback $\alpha$ (Fig 2D). $\alpha$ decreases with latitude, reflecting the shift in the dominant dynamics responsible for generating vertical motion from convective heating in low latitudes to large-scale dry dynamics in higher latitudes. In addition, $\alpha$ shows longitudinal variations that significantly contribute to the heterogeneity of $P$. Along the same longitude, $\alpha$ over the western parts of the oceans is much greater than $\alpha$ over either the eastern parts of the oceans or land. Interestingly, the geographic distribution of $\alpha$ is highly correlated with water vapor abundance (i.e., precipitable water $H$, the white contours in Fig. 2D), indicating the dominant role of moisture in determining the responses of convection to large-scale perturbations (19).

Inspired by the strong correlation between $\alpha$ and $H$, we developed a theoretical model of $\alpha$ capturing the essential dynamics. The model simplifies the structure of large-scale dynamics, while highlighting the dependence of convection on local thermodynamic conditions. It uses a reduced static stability (${\sigma }_e$) (9, 20, 21) to link precipitation and the effects of the associated diabatic heating. Assuming that a large-scale disturbance associated with extreme precipitation has a characteristic horizontal length scale with corresponding wave number $k$ (which can be location-dependent), the QG$\omega$ equation may be rewritten as

$$\left({\partial }_{pp}-{\sigma }_e\frac{k^2}{f^2}\right)\omega =F.$$ [3]

We further assume the vertical structures of $F$, $Q$, and $\omega$ may be approximated by a single mode. We then obtain a simple formula for $\alpha$ (detailed derivation in SI Appendix, section S2):

$$\alpha =\frac{bH}{1-bH}.$$ [4]

The coefficient $b$ is inversely proportional to the dry static stability ($\sigma$) and proportional to the ratio of the disturbance length scale to the Rossby radius of deformation (discussion of the role of this length scale is in refs. 22 and 23). The scatter plot of $\alpha$ and $H$ from climate-model outputs fits the theoretical curve obtained from Eq. 4 well, even with a horizontally uniform $b$ (Fig. 4A). The map of $\alpha$ provided by Eq. 4 with the fitted $b=0.017\hspace{0.17em}m{m}^{-1}$ also matches that from QG diagnostics (SI Appendix, Fig. S8 and Fig. 2D) reasonably well. The simple model also provides a theoretical formula of $b$, which predicts $b$ in the same order of magnitude as the diagnosed $b$ but with uncertainties in the choices of parameters (discussion in SI Appendix, section S2). The factors that could potentially lead to substantial geographic variations in $b$ largely cancel, resulting in a nearly horizontally uniform $b$ that absorbs all of the complexity in convective responses. The nonlinear relationship in Eq. 4 quantifies the rapid intensification of the diabatic heating feedback (thus, precipitation extremes) with increasing moisture. Nonlinear relationships between precipitation and moisture have been found in other contexts with different formulas (24, 25); the present context differs in that $\alpha$ is not the total precipitation but the diabatic response to dry adiabatic forcing. The simple model works not only for the multimodel mean but also for individual models (SI Appendix, Fig. S4); the intermodel spread in $\alpha$ (SI Appendix, Fig. S4) is presumably mainly due to differences in model convective parameterizations (26).

Fig. 4.

Understanding the moist component of EPS [$\delta \ln \left(1+\alpha \right)$]. (A) Scatter plot of $\alpha$ and $H$ for each geographic grid. Red is for the historical period, and blue is for the warmer period. The solid lines are the best-fit lines denoted by the equations in the legends. The subtitle indicates correlation ($R$) between $\alpha$ and $H$, and rmsd of $\alpha$ between model outputs and the theoretical lines for the historical runs. (B) Map of the reconstructed $\delta \ln \left(1+\alpha \right)$ using Eq. 4 with the fitted $b$ in A. For demonstration, changes of $\alpha$ in two representative regions (black rectangles) are marked as arrows in A. The starting and ending points of the arrows correspond to the historical and the warmer period, respectively. The dashed-line arrow is with $\alpha$ from model diagnoses, and the solid-line arrow is with $\alpha$ estimated using Eq. 4.

We now consider the simulated responses of extreme precipitation to climate change. The EPS from model outputs (Fig. 3A) shows distinct regional patterns similar to those found in previous studies (6, 8). The EPS is positive in most regions, with maxima in the equatorial Pacific, South Asian monsoon, and polar regions. It is negative in several regions over the subtropical oceans to the west of continents. The EPS calculated by the scaling of $\omega$ (Fig. 3B) again reproduces that from direct model outputs well. Applying the dry/moist decomposition of EPS with Eq. 1 shows that the dry component ($\delta \ln P_D$) (Fig. 3C) accounts for most of the positive values in the middle and high latitudes. $\delta \ln P_D$ is weakly positive or even negative in the low latitudes. In contrast, the moist component [$\delta \ln \left(1+\alpha \right)$] (Fig. 3D) is only weakly positive in the middle and high latitudes. It contributes to the negative centers in the subtropics and accounts for the regions of super-CC sensitivity in low latitudes.

The dry component of EPS ($\delta \ln P_D$) includes changes of water vapor—inasmuch as those cause changes in precipitation for a fixed vertical velocity, that is, it excludes the diabatic feedback—and changes of ${\omega }_D$ with warming. The thermodynamic contribution, calculated as changes of precipitation using the scaling without changing ${\omega }_D$, increases pervasively, with a relatively homogeneous spatial distribution (8) (Fig. 3E). The dynamic component—the rest of $\delta \ln P_D$ excluding the thermodynamic component—is negative in most subtropical and midlatitude regions, particularly over the northern subtropical Atlantic Ocean (Fig. 3F). Changes in both the amplitude (quantified as ${\omega }_D$ at 500 $hPa$) and vertical shape of ${\omega }_D$ contribute to the dynamic component (15); the former makes the dominant contribution, as indicated by a comparison between the change in 500 $hPa\hspace{0.17em}{\omega }_D$ (SI Appendix, Fig. S9 and Fig. 3F). Changes in the vertical shape of ${\omega }_D$ make a sizable contribution only in high latitudes. The changes in ${\omega }_D$ are mostly due to the changes of dry dynamic forcing $F$ (SI Appendix, Fig. S9). The systematic weakening of ${\omega }_D$ and $F$ in lower latitudes and strengthening in higher latitudes are likely due to changes in the large-scale circulation, which modifies the atmospheric baroclinicity and propagation of disturbances (27–30). Further studies are needed to link the changes of dynamic forcing ($F$) to general circulation changes, such as Hadley cell expansion (31) and poleward shifts of the storm tracks (32).

Next, we examine the moist component of EPS [$\delta \ln \left(1+\alpha \right)$]. As indicated by both direct diagnosis of the CMIP5 model output and the simple model (Fig. 4A and Eq. 4), the diabatic heating feedback ($\alpha$) nonlinearly depends on atmospheric moisture, as does its change:

$$\delta \ln \left(1+\alpha \right)=\alpha \left(\delta \ln H+\delta \ln b\right).$$ [5]

Global warming increases both $H$ and $\sigma$ (since the temperature profile roughly follows a moist adiabatic lapse rate, which decreases with warming) with opposite effects on $\alpha$ (SI Appendix, Fig. S10). The increases of $H$ amplify $\alpha$ by increasing diabatic heating associated with condensation (33), while the increases of $\sigma$ decrease $\alpha$ by inhibiting convection. A curve fit to the diagnosed $\alpha$ (Fig. 4A) shows that $\delta \ln b\approx -6.5\%$, which is consistent with the changes of $\sigma$ ($\delta \ln b\approx -\delta \ln \sigma$, neglecting changes of $L_h$). The competing effects of increased $H$ and $b$ determine the sign of the local $\alpha$ changes. More importantly, the total effect of $\delta \ln H+\delta \ln b$ is amplified by the climatological $\alpha$ (Eq. 5). In regions with large climatological $\alpha$—such as the low latitudes and monsoon regions (Fig. 2D)—the changes in the moist component (Fig. 3D) are much greater than in the regions with small climatological $\alpha$. Reconstructions of $\delta \ln \left(1+\alpha \right)$ using $H$ from model outputs and the fitted constant $b$ approximately reproduce its regional patterns as found from the direct calculations (Figs. 3D and 4B). The negative centers in the subtropics and the positive maxima in the tropical Pacific and South Asia Monsoon region are captured by the simple model, albeit with some discrepancies such as the underestimation of the subtropical negative centers. The simple model indicates that the diabatic heating feedback and its response to warming are largely explained by the local convective thermodynamic conditions, and independent of the large-scale forcing (dry dynamics), lending further support to our dry/moist dynamics decomposition.

Lastly, we provide a zonally averaged view of the dry/moist decomposition of EPS (Fig. 5). The dry component (blue line), while it dominates the EPS in the high latitudes, decreases to values close to zero in the low latitudes. This latitudinal dependence is partly due to the latitudinal distribution of the thermodynamic component (Fig. 3E, higher values in high latitudes related to polar amplification) (34) and partly due to the substantial weakening of dynamic forcing in the low latitudes (Fig. 3F). On the contrary, the moist component (red line) increases sharply as latitude decreases into the tropics. Again, the simple model (red dashed line) captures the latitudinal dependence reasonably well; the discrepancies that remain may be alleviated by allowing latitude-dependent parameters. The blue and red lines intersect in the subtropics, corresponding to the local minimum of EPS. The nonlinear relationship between $\alpha$ and moisture (Eq. 5) indicates a large amplification of the diabatic heating feedback under warming in climatologically moist regions, providing a simple explanation for the super-CC sensitivity at low latitudes.

Fig. 5.

A zonally averaged view of the dry/moist decomposition of EPS. The black solid line is EPS from model outputs, and the black dashed line is EPS approximated by the scaling using $\omega$. The blue (red) solid line is the dry (moist) component of EPS. The red dashed line is the moist component calculated using the fitted Eq. 4.

Conclusions and Discussion

This study applies a dry/moist dynamic decomposition on extreme precipitation on a near-global scale to understand the regional patterns of extreme precipitation sensitivity from the CMIP5 simulations (schematic in Fig. 1). The dry component ($\delta \ln P_D$) represents changes of precipitation due to changes in QG forcing and atmospheric moisture (but without considering how the changes in moisture affect the large-scale vertical motion). It shows weakening in the subtropics and strengthening in the middle-high latitudes with warming. Future studies may further link this latitudinal pattern to changes in the general circulation. Model simulations with idealized configurations (35) or even only dry atmospheres (18) could be good starting points and provide insights for understanding the comprehensive climate simulations. The moist component [$\delta \ln \left(1+\alpha \right)$] represents the changes of diabatic-heating feedback due to convection. A simple model of the diabatic heating feedback captures the geographic distribution of $\alpha$ and its changes in model simulations and shows the competing effects of increased water vapor and dry static stability. The nonlinear dependence of convective responses on moisture, depicted by the simple model, greatly enhances the regional heterogeneity by amplifying sensitivity over climatologically moist regions.

There are some limitations of this study, which may be remedied in future work. The dry/moist decomposition based on QG theory works reasonably well for regional-scale precipitation extremes. However, for extreme precipitation on smaller scales, where the QG approximation is poor, other factors, such as mesoscale organization (36), may play important roles. Unlike previous analyses that emphasized the role of changes in the horizontal length scale of precipitating disturbances (23), the results here suggest that changes in length scale play only a secondary role. Nevertheless, relaxing approximations in our simple model to include either multiple horizontal length scales or multiple vertical modes will allow more detailed analyses of the mechanisms of regional EPS. In addition, examining the characteristics of the cyclones producing precipitation extremes and their changes with climate (29, 30, 37) will provide a synergistic understanding of the conclusions here.

The dry/moist decomposition can be used to gain understanding of other aspects of extreme precipitation variations besides their long-term responses to forced climate change. For instance, does dry or moist dynamics contribute more to the interannual variation of extreme precipitation? How does large-scale variability—e.g., the El Ni$ñ$o/Southern Oscillation (38) and the Annual Modes (39)—affect extreme precipitation, through modulating the large-scale disturbances or local thermodynamic conditions? Examining the intermodel spread of dry and moist components and comparing with reanalysis may help identify key factors leading to the biases and guide further improvement of climate models; for example, correcting the sensitivity of parameterized convection on thermodynamic conditions (26) may reduce the biases in the moist component and improve the simulation of extreme precipitation.

Data Availability.

The CMIP5 data archive is available at https://esgf.llnl.gov. The analysis and codes are available at https://www.jiniepku.com/download.html.