Dynamic amplification of extreme precipitation sensitivity.

A useful starting hypothesis for predictions of changes in precipitation extremes with climate is that those extremes increase at the same rate as atmospheric moisture does, which is [Formula: see text] following the Clausius-Clapeyron (CC) relation. This hypothesis, however, neglects potential changes in the strengths of atmospheric circulations associated with precipitation extremes. As increased moisture leads to increased precipitation, the increased latent heating may lead to stronger large-scale ascent and thus, additional increase in precipitation, leading to a super-CC scaling. This study investigates this possibility in the context of the 2015 Texas extreme precipitation event using the Column Quasi-Geostrophic (CQG) method. Analogs to this event are simulated in different climatic conditions with varying surface temperature ([Formula: see text]) given the same adiabatic quasigeostrophic forcing. Precipitation in these events exhibits super-CC scaling due to the dynamic contribution associated with increasing ascent due to increased latent heating, an increase with importance that increases with [Formula: see text] The thermodynamic contribution (attributable to increasing water vapor; assuming no change in vertical motion) approximately follows CC as expected, while vertical structure changes of moisture and diabatic heating lead to negative but secondary contributions to the sensitivity, reducing the rate of increase.

How will precipitation extremes respond to climate change? As climate warms, the water vapor content of a saturated air column increases with surface temperature () at a rate of following the Clausius–Clapeyron (CC) relation (1, 2), and the actual water vapor content increases similarly in both models and observations (3, 4). The response of global mean precipitation to warming is largely constrained by global energy balance () (3), while regional mean precipitation increases more variably (5). Observations of precipitation extremes, however, show that they increase more rapidly than the regional mean precipitation does in most regions, increasing even where the mean precipitation decreases, albeit with significant variability across geographic locations (6, 7). General circulation models (GCMs) project that, in midlatitudes, the rate at which precipitation extremes increase is close to CC scaling. In the tropics, some models project super-CC scaling, although with considerable intermodel spread (8–11). Given that GCMs poorly represent many characteristics of precipitation extremes in the current climate, such as their climatology (8) and dependences on temperature on the interannual timescale (12), it is appropriate to view their predictions of changes in precipitation extremes with warming with a critical eye. Simulations in regional climate models with finer horizontal resolutions usually show greater sensitivity of extreme precipitation to warming than do GCM simulations (13–19), suggesting that GCMs may underestimate this sensitivity.

By separating the sensitivity of precipitation extremes to surface temperature into a thermodynamic component—that due to the increase of atmospheric moisture with temperature (i.e., that which leads to CC scaling)—and a dynamic component, which is the change of large-scale vertical motion (1), most of the uncertainty in extreme precipitation sensitivity comes from the dynamic component (9, 10). It is suggested that the increased latent heating associated with increased precipitation may further modify the atmospheric circulations associated with extreme precipitation events, changing both the magnitude and vertical structure of their large-scale vertical motion and resulting in a feedback between the thermodynamic and dynamic components (2, 20). This feedback may be either positive or negative and is key to explaining the wide spread of extreme precipitation sensitivity in GCM simulations (9, 10) and the regional distribution of extreme precipitation sensitivity in observations (6, 7).

In this paper, we investigate the sensitivity of extreme precipitation to warming using the idealized Column Quasi-Geostrophic (CQG) modeling framework (21, 22). This framework allows for a relatively clean mechanistic interpretation of the feedbacks between the thermodynamic and dynamic contributions to extreme precipitation events. CQG extends the notion of parameterization of large-scale dynamics (23–26) from the tropics to the extratropics. In the tropics, large-scale vertical motion is almost entirely controlled by diabatic heating, while in the extratropics, dry adiabatic balanced potential vorticity (PV) dynamics also plays an important role in generating large-scale vertical motion. CQG allows interaction between large-scale vertical motion and convection in a limited domain, thus distinguishing this study from previous cloud-resolving model (CRM) studies that have examined extreme precipitation sensitivity under Radiative–Convective Equilibrium with no large-scale vertical motion (27).

The experiments here are designed based on an extreme precipitation event occurring in May 2015 over the southcentral United States. We choose a specific observed event so that we can use a realistic synoptic forcing, derived from reanalysis, and validate our method by comparing model results with observations. We argue, however, that our results have implications for other extreme events with broadly similar characteristics. We simulate the 2015 event under a wide range of with the same large-scale Quasi-Geostrophic (QG) adiabatic forcings obtained from reanalysis data. This approach is conditioned on the large-scale perturbations and considers the sensitivity only due to the slowly varying thermodynamic component of the climate—namely, the background temperature (T) and moisture (q)—thus being similar to event-based “highly conditional,” “pseudoglobal warming,” or “storyline” event attribution studies (16, 19, 28–32). We show that the positive feedback between the thermodynamic and dynamic components of the extreme precipitation sensitivity can be straightforwardly understood and quantified under CQG, thus providing a theoretical estimate of the extreme precipitation sensitivity that may be a useful complement to those from GCMs. A limitation is that, due to our focus on a single event and assumed constancy of , no statement can be made about changes in the probability of occurrence of an event of this type.

Methods

Our implementation of CQG uses a CRM, here the System for Atmospheric Modeling (33), to explicitly resolve small-scale convection in a limited domain. As in our previous studies (21, 22), we parameterize the large-scale vertical motion using the single-wavenumber () QG equation: is pressure-coordinate vertical velocity, is dry static stability, is the Coriolis parameter, and is diabatic heating (here computed explicitly by the CRM). and are the large-scale horizontal advections of absolute vorticity and temperature, respectively. The first two right-hand side (RHS) terms represent the adiabatic QG forcing () (34), while the last RHS term represents the effects of the diabatic heating on . After each CRM time step, the large-scale is diagnosed with Eq. ; then, the vertical advection of and associated with are applied on the CRM domain, thus coupling convection and large-scale dynamics. Comparing with conventional CRM simulations in which is prescribed, in CQG, we only need to prescribe , while convection, precipitation, and are simulated interactively. Additional details of the model and experiments are in .

Numerical simulations are based on the extreme precipitation event occurring in Texas and Oklahoma during May 22–26, 2015. Meteorological variables from the European Center for Medium-Range Weather Forecasting’s interim reanalysis (35) are used in this study both to force the CRM and as a reference against which to compare the simulations. Based on the rainfall distribution associated with the event, we define a latitude–longitude box (Fig. 1) as the target region from which data are extracted for deriving and where modeled precipitation is compared with observations.

Fig. 1.

(A) Ertel PV (in PV units; color) on the 330 K isentropic surface on May 24 and areas (blue contours) where the cumulative precipitation [Climate Prediction Center precipitation data (36)] between May 22 and May 26 was greater than 50 mm. (B) Precipitable water (PW; color) and the 850-hPa horizontal winds (black arrows) on May 24. The black rectangles indicate the regional box ( and ) within which most of the rain during the 2015 event fell.

The experiments consist of a control case and a series of perturbed cases. The objective in the control case is to reproduce the extreme precipitation that was observed under the current climate in the actual event, while the perturbed cases aim to simulate precipitation from events with the same synoptic forcing in climates with varying background and profiles that depend on in a systematic way. The perturbed cases are constructed with the help of the Coupled Model Intercomparison Project (CMIP5) simulations (). In each case, the model is forced with the same large-scale adiabatic QG forcings and the large-scale horizontal moisture advection () () taken from the reanalysis to isolate the dependence of extreme precipitation on background conditions. This implies an underlying hypothesis that changes in thermodynamic environment will dominate changes in synoptic-scale PV dynamics in determining changes in precipitation extremes with warming. We view this as a plausible starting hypothesis given the much larger uncertainties in circulation changes compared with thermodynamic changes (37).

Results

Preceded by several days of heavy rain, a slowly propagating storm led to even heavier precipitation across Texas and Oklahoma during May 24–26, 2015 (Fig. 2), causing record-breaking floods. This extreme event was caused by a strong upper level PV intrusion from higher latitudes to the west of the precipitating region (Fig. 1). Associated with the PV tongue was a low-pressure trough extending down to the lower troposphere. Correspondingly, a lower level southerly jet brought very humid air from the Gulf of Mexico to the precipitating region (Fig. 1). The advection of the upper level PV anomalies induced ascending motion in the free troposphere, reducing free tropospheric stability and encouraging convection. This event produced one of the largest 5-d cumulative precipitation totals for the box of interest during the period 1948–2015, causing May of 2015 to be the wettest month among all Mays in the record ().

Fig. 2.

(A) Daily precipitation from the Climate Prediction Center (CPC) data, the Global Precipitation Climatology Project (GPCP) precipitation data (38), ERA reanalysis (12-h reforecast), and CRM simulation of the control case. The blue line is the mean of the three observations and reanalysis dataset. (B) Daily precipitation of the control case and two perturbed cases. Error bars indicate the SD among six ensemble members, which are different realizations with small random noise in the initial conditions (). Numbers in brackets are the mean precipitation between May 22 and 26 (marked by the black vertical dash lines).

The simulated precipitation using CQG in the control case matches the observed precipitation series reasonably well (Fig. 2). It reproduces the maximum in rainfall around May 24 and other minor peaks mostly within the range of ERA reanalysis and observed precipitation. The time evolution of QG in the simulation also matches the reanalysis reasonably well (). The precipitation comparisons between the control and perturbed cases show the sensitivity of the precipitation to the background climate. As an example, Fig. 2 shows daily precipitation from the control case (), the case, and the case. Each case includes six ensemble members with different realizations of small random noise in the initial conditions (). Precipitation increases with warming strongly and far above the variability within the ensemble. We focus on the 5-d mean precipitation between May 22 and May 26, 2015 (denoted ) hereafter. Precipitation totals on this timescale are relevant to impacts on larger scales (e.g., flooding in large river basins) and also relevant to interpretations of GCM results often used in the context of climate change studies. Many previous studies have used high-resolution regional simulations to examine changes with warming of convective-scale precipitation and updrafts (13, 15–19), which are of great societal relevance to local areas (39). Analyses of convective-scale responses to the surface warming are presented in as a complement to our primary focus on the larger space and timescale.

As increases from 293 K to 305 K, increases exponentially from 7.4 to 36.3 mm/d (Fig. 3). We calculate the exponential growth rate locally at each ( using centered differences, except for the first and last values, in which forward and backward differences are used) (Fig. 3). The precipitation sensitivity to surface temperature, , is not constant but increases from at to at ; then, it remains roughly constant as further increases. Overall, the extreme precipitation sensitivity substantially exceeds CC scaling, implying an important role for dynamic feedbacks. The results here are qualitatively consistent with the super-CC scaling of extreme precipitation found in observations on the interannual timescale (12) and in some numerical modeling studies (10, 14, 16).

Fig. 3.

(A) , , , and as functions of . B and C are the decompositions of based on Eqs. and , respectively. The black solid lines show the sum of the color lines. D and E show , , and . The changing of the line colors from blue to red corresponds to cases in which increases from 293 to 305 K. Note that the dashed lines in E almost all collapse to the same line.

We apply the conventional decomposition (10) to quantify the thermodynamic and dynamic components of the extreme precipitation sensitivity. This decomposition is based on the approximation that heavy precipitation comes primarily from the vertical advection of moisture: ( denotes pressure vertical integration), an approximation supported by our budget analysis (). is only slightly smaller than (Fig. 3), and is only slightly greater than (Fig. 3) (). Since the approximation holds well and at the same time, simplifies interpretation, from here on, we focus on . By separating the amplitudes and vertical structures of and , we havewhere is the absolute value of at 500 hPa, a metric of vertical motion amplitude in middle troposphere, and is column precipitable water. The parameter absorbs the covariances of the vertical structures of normalized vertical velocity () and normalized moisture stratification (). The percentage changes of can thus be written asThe RHS terms are the thermodynamic component, the dynamic component, and a component due to changes in the vertical structures of and , respectively.

The results of the decomposition in Eq. are shown in Fig. 3. varies little over all cases, with a mean value of . This value is slightly higher than the CC scaling, because the upper troposphere warms more than the surface does () and the precipitable water increases faster than the surface water vapor with (27, 40). The changes in covariance of vertical structure are small and negative (). The dynamic component, , is positive and contributes significantly to the super-CC scaling, consistent with the increases of with (Fig. 3). Interestingly, unlike the other two terms that are nearly independent of , increases from 2.5 to and then remains constant, explaining most of the dependence of on .

Next, we look into the dynamic component (). Given the linearity of the QG equation (Eq. ), we can separate as , in which is the part due to the imposed dry adiabatic dynamic forcing (), while is due to diabatic heating (Q). and can be calculated by solving Eq. , including the first two terms on the RHS and then, the third term on the RHS. The comparison of the components in the control case between results from the reanalysis and those from the simulation again shows reasonable agreement (). By examining the perturbed cases, we see that remains almost unchanged. This is largely due to the fact that the adiabatic dynamic forcing is prescribed to be fixed in experiment design. The increases of are mostly due to the increases of (Fig. 3).

In our calculations, is evaluated from the instantaneous horizontal-averaged temperature profile in the CRM simulations and increases with warming (the so-called lapse rate effect). However, the change of is relatively small here so that the resulting decreases in are similarly small. The increases in also partly compensate for increases in diabatic heating, but its changes are sufficiently small, and the heating changes dominate the response.

The extreme precipitation sensitivity can be decomposed based on the QG separation. Defining and as precipitation due to vertical moisture advection by and , respectively, we havewhere (the derivation is in ). The parameters , , , and are associated with the vertical shapes of vertical motion or QG forcing profiles. As will be seen below, their changes with warming are of secondary importance. The dependence of and with is shown in Fig. 3. The amplification parameter quantifies the diabatic heating feedback on precipitation due to QG adjustments (21). In general, depends on the horizontal length scale of the disturbance, the background state, and the adiabatic forcings (21, 22), with larger meaning stronger under the same . In the control case, , similar to the value found in the case of the 2010 Pakistan extreme precipitation event (22). As increases from the coldest to the warmest case, increases from 0.6 to 3.5, indicating that the diabatic heating feedback becomes stronger with warming.

Based on Eq. , we can decompose asThe terms in Eq. are shown in Fig. 3. The contributions from the changes of vertical shapes are generally small, except that (reflecting the change of the vertical structure of ) () becomes nonnegligible for large . One dominant term in Eq. is , which represents the change of due to increased precipitable water with approximately unchanged . The other dominant term is , meaning that the thermodynamic effect is amplified by the diabatic heating feedback by . Comparing Eq. with Eq. , we have , stating that the dynamic component of precipitation extremes is mainly due to the increased diabatic heating leading to increased , modified by a secondary term associated with the changes in the vertical structure of heating.

The numerical results are summarized in Fig. 4 together with another group of experiments performed as sensitivity tests (). increases about two times faster than , indicating a nearly double CC scaling in these simulations on average. The scatter points are above the linear fit line, consistent with the fact that increases as increases (Fig. 3). In experiment group 2, the CRM is subject to time-constant and forcings to better match the CRM background profiles with those of CMIP5 (). The results of experiment group 2 are qualitatively similar to those of group 1 shown in the text; the diabatic heating feedback is weaker but still significantly contributes to the super-CC sensitivity of extreme precipitation ().

Fig. 4.

Changes in extreme precipitation () vs. changes in column water vapor () from experiment group 1 (blue circles) and experiment group 2 (red triangles) (). The black dashed line is the one-to-one line. Blue and red lines are the linear fit lines to the two experiment groups.

Fig. 5 summarizes the feedbacks in the CQG system and how it amplifies the sensitivity of precipitation extremes to warming. Under the current climate, the adiabatic QG forcing () induces vertical motion (), which on its own, would produce precipitation . The feedback due to the latent heating release on QG leads to vertical motion of , providing an additional component of precipitation, . The strength of the feedback is quantified as , so that the total precipitation is the adiabatic QG component multiplied by . In a warmer climate, while there is little change in (due to the assumed constancy of here as well as the smallness of the changes in ), the increased water vapor leads to increasing at the rate . This thermodynamic contribution is further amplified by the diabatic feedback by and expressed largely as the dynamic contribution. At the same time, the vertical structures of and may change, leading to secondary terms , , , and ; here, these terms are negative and reduce the magnitude of the positive sensitivity. Because the total diabatic heating feedback is positive and becomes larger in a warmer climate, the sensitivity of precipitation extremes with surface temperature exceeds CC scaling.

Fig. 5.

A schematic of the scaling of precipitation extremes with temperature in a CQG system. A is under the current climate. Upper shows an upper level synoptic wave, lower level fronts, and a low-pressure center. Lower shows the side view of the convecting and precipitating region over the low-pressure center. B is in a warmer climate: the fractional changes of vertical motion and precipitation if the large-scale adiabatic QG forcing (and ) is unchanged. The darker color of the cloud cartoon indicates that the convective system is stronger in a warmer climate.

Conclusions and Discussion

We have investigated the sensitivity of precipitation extremes to temperature using the extreme precipitation event of May 2015 in Texas and Oklahoma as an example and studied it with idealized CRM simulations on a small domain under the CQG method. The 2015 event was simulated under different climatic background conditions with varying under the same adiabatic QG forcing. In the control case, under the actual climatic conditions in 2015, the model results reproduce the precipitation in observations reasonably well, while perturbed cases show that the extreme precipitation increases exponentially as increases. The exponential growth rate exceeds CC scaling due to the positive contribution from the dynamic response due to increased large-scale ascent driven by increased diabatic heating. It is approximately equal to the relative changes of atmospheric moisture multiplying a diabatic heating amplification factor , modified by a secondary term associated with the changes in the vertical structure of heating. While the thermodynamic contribution is nearly constant with warming, the diabatic heating feedback becomes stronger, leading to increasing extreme precipitation sensitivity.

The super-CC scaling for extreme precipitation that we find here is consistent with some observational and GCM modeling studies (10, 12). Our results are strictly for a single event, but we view them as relevant to a larger set of events with a strong convective component as well as strong large-scale PV dynamics. Particularly interesting examples may include precipitation extremes in the subtropics during the summer half-year, including those caused by tropical–extratropical interaction (41), as well as monsoon depressions (42) and similar disturbances. Similar considerations may apply to a wider range of midlatitude precipitation systems accompanied by convection as well, although since the dynamic amplification that we find is greatest for the warmest climates, we might expect it to be smaller for winter storms.

The CQG method allows us to analyze in detail the mechanisms by which the super-CC scaling comes about, providing perspective relevant to interpreting the different extreme precipitation sensitivities found in GCM simulations. Climate models with stronger diabatic heating feedback in simulations of the current climate are likely to produce greater sensitivity of extreme precipitation to climate change, such as has been found for the response of the North Atlantic storm track to warming in a regional model sensitivity study (43). The CQG method could be used to diagnose in more detail the mechanisms leading to different results in different climate models.

A significant limitation of this study is that we assume that the adiabatic QG forcing and the horizontal length scale associated with the disturbance remain constant as climate changes, so that all changes are driven directly by the changing thermodynamic environment. We view this as a reasonable starting point given the greater uncertainty in dynamic compared with thermodynamic components of climate change (30–32, 34). Other factors not considered here include, for instance, the effects of large-scale circulation pattern changes on local regions (44), the possible changes of eddy length scale (45), and the possible changes of frequencies of strong synoptic perturbations (46). All of these factors may also modify the sensitivity of extreme precipitation. Studies with comprehensive climate models suggest, in fact, that warming may lead to a reduction in the dynamic component of extreme precipitation in the region and season of interest here (11, 45). If so, our results suggest that this reduction is due to these other effects, with dynamic amplification due to increased heating (for a given and wave number ) still relevant and perhaps dominant in other regions. Efforts to analyze all of these effects more broadly using a hierarchy of numerical models would be valuable.