Weakened Orographic Influence on Cool‐Season Precipitation in Simulations of Future Warming Over the Western US

High‐resolution regional climate model (RCM) simulations of global warming consistently predict larger percentage increases in precipitation in the lee of midlatitude mountain ranges than on their windward slopes, indicating a weakening of the orographic rain shadow. This redistribution of precipitation could have profound consequences for water resources and ecosystems, but its underlying mechanisms are unknown. Here we show that rain‐shadow weakening is just one manifestation of a more general decrease in the influence of orography on precipitation under global warming. We introduce a simple model of precipitation change based on this principle, and find that it agrees well with an ensemble of high‐resolution simulations performed over the western United States. We argue that diminished orographic influence can be explained by the unique vertical structure of orographically forced ascent, which tends to maximize in the lower atmosphere where condensation is thermodynamically less sensitive to warming.

winds and static stability will alter the vertical structure of mountain waves (Shi & Durran, 2014, 2016), and thus the magnitude and depth of orographically forced ascent and condensation.
Despite this complexity, however, a relatively simple picture has emerged from simulations of global warming in midlatitude mountain ranges performed with high-resolution regional climate models (RCMs) (Gergel et al., 2017;Leung et al., 2004;Michaelis et al., 2022;Musselman et al., 2018;Rasmussen et al., 2011).Over the western US, for example, simulated changes in precipitation patterns exhibit significant variability across different RCMs and emissions scenarios at large scales, but they are surprisingly consistent at smaller scales where orographic effects dominate.RCMs broadly agree that the largest percentage increases in precipitation will occur in the lee of mountain ranges, indicating a weakening of the climatological rain shadow (Diffenbaugh et al., 2005;Huang et al., 2020;Hughes et al., 2022;Mahoney et al., 2021;Rupp et al., 2017;Wehner, 2013).Notably, this result is found even in pseudo-global warming simulations that control for changes in large-scale variability (Ikeda et al., 2021;Li et al., 2019;Liu et al., 2017), suggesting that it is driven primarily by orographic mechanisms, and not by changes in synoptic-scale dynamics (Siler & Durran, 2016;Siler et al., 2013).However, it is not known why such rain-shadow weakening occurs in RCM simulations, or which mechanisms identified in other studies play a role.
In this paper, we present evidence that the pattern of rain-shadow weakening found in RCM simulations is just one manifestation of a more general weakening of the orographic influence on precipitation under global warming.Analyzing an ensemble of high-resolution PGW simulations over the western US, we show that the pattern of cool-season precipitation change is well represented by a simple model in which the orographic component of precipitation scales with warming at a consistently lower rate than the synoptic-scale component of precipitation.We argue that this result is likely not due to changes in orographic ascent, but rather to the fact that orographic ascent tends to be strongest in the lower troposphere where warming has a weaker effect on condensation than it does in the upper troposphere.

Projections of Cool-Season Precipitation Change Over the Western US
We begin by analyzing the patterns of precipitation change over the western US predicted by an ensemble of regional, storm-resolving simulations using the pseudo-global warming (PGW) method (Hara et al., 2008;Ikeda et al., 2021;Li et al., 2019;Liu et al., 2017;Michaelis et al., 2022;Rasmussen et al., 2011;Sandvik et al., 2018;Schär et al., 1996).The historical simulation spans a 30-year period from 1981 to 2010, and was downscaled to 6-km horizontal resolution using the Weather Research and Forecasting (WRF) model v3.8 (Skamarock et al., 2008) with boundary and initial conditions taken from the North American Regional Reanalysis (Chen, Duan, et al., 2019;Chen, Leung, et al., 2019;Chen et al., 2023;Mesinger et al., 2006).Five PGW simulations were performed with an identical configuration, except with boundary conditions modified by adding the long-term monthly mean difference between a future climate (2041-2070) and the historical climate , as simulated by five distinct GCMs under Representative Concentration Pathway 8.5 (van Vuuren et al., 2011): CESM1-CAM5, CanESM2, GFDL-ESM2M, HadGEM2-ES, and MPI-ESM-MR.See Text S1 in Supporting Information S1 for additional simulation details.
The left column of Figure 1 shows the mean total precipitation (P) during the cool season (October-March) of the historical simulation (Figure 1a) and the ensemble-mean precipitation sensitivity (α; Figure 1b), defined as the fractional change in P per degree of regional surface warming δT s (see Text S2 in Supporting Information S1): Examining the pattern of α in Figure 1b, we find the largest values to the east of the Sierra Nevada, Cascades, and northern Rockies, where precipitation is low, and smaller values at higher elevations where precipitation is high.This pattern indicates a weakening of the orographic rain shadow under warming, similar to what many other RCM and PGW simulations have also found (e.g., Diffenbaugh et al., 2005;Huang et al., 2020;Hughes et al., 2022;Ikeda et al., 2021;Li et al., 2019;Liu et al., 2017;Mahoney et al., 2021;Rupp et al., 2017;Wehner, 2013).

Model of Precipitation Sensitivity in Complex Terrain
To explain the pattern of α found in Figure 1b, we introduce a simple model that is based on two assumptions.First, we assume that cool-season P can be decomposed into a synoptic-scale component (P SS ) and an orographic component (P OR ) (Smith & Barstad, 2004;Stoelinga et al., 2013): (2) 10.1029/2023GL107298 3 of 10 During the cool season, precipitation in the western US primarily occurs during synoptic-scale storms.Mountains modify the precipitation from these storms, but they rarely generate precipitation in isolation (e.g., Houze Jr, 2012).In Equation 2, P SS represents precipitation that is generated by synoptic-scale storms, including any orographic influence at synoptic and larger scales, while P OR represents the orographic modification of P SS at sub-synoptic scales.We estimate P SS by smoothing the pattern of P in the historical simulation using a 2D-Gaussian filter with a characteristic width of 2σ = 1,000 km, which is similar in scale to a typical midlatitude weather system (Figure 1c).We then subtract P SS from P to get P OR (Figure 1d).In contrast to P SS , P OR exhibits spatial variability only at sub-synoptic scales, with strongly positive values on windward slopes indicating orographic enhancement of precipitation and negative values in the lee of mountains indicating orographic suppression of precipitation (i.e., the rain shadow effect).
Second, we allow P SS and P OR to scale with warming at different rates.Let us define α SS and α OR as the fractional changes in P SS and P OR per degree of regional warming, consistent with α in Equation 1 (see Text S3 in Supporting Information S1).Differentiating both sides of Equation 2 with respect to T s and dividing through by P then gives where f OR = P OR /P represents the fraction of precipitation in the historical simulation that can be attributed to orographic effects.We estimate α SS (Figure 1e) based on changes in P SS and T s and compute f OR as the ratio of P OR to P in the historical climate.That leaves α OR as the only unknown variable in Equation 3. In principle, one can solve for α OR at each grid point by rearranging the terms in Equation 3: However, in regions where f OR is close to 0, Equation 4is not well behaved (Figure S3 in Supporting Information S1).We therefore take a different approach.First, we define a coarse grid consisting of 73 staggered grid points across the western US, spaced 200 km apart (Figure 2, inset).Then, at each of these points, we use least-squares regression to find the value of α OR that results in the best agreement with the true pattern of α within a radius of 115 km, using a standard bootstrapping procedure to quantify uncertainty (see Text S4 in Supporting Information S1).We repeat this procedure for each ensemble member using the model-specific patterns of α and α SS .
Figure 2 shows α OR that we estimate using this method, plotted against α SS at the same coarse grid points marked on the inset map.There are two aspects of Figure 2 that stand out.First, α OR is strongly correlated with α SS (r = 0.81), with a regression slope that is close to 1 when considering all ensemble members together (m = 0.93 ± 0.10, 95% confidence).Second, α OR is consistently lower than α SS , by an average of 3.25 ± 0.2% K −1 across all grid points and ensemble members (95% confidence level).Different grid resolutions produce similar results (Figure S4 in Supporting Information S1).The weaker sensitivity of P OR compared with P SS implies that the relative influence of orography on precipitation robustly weakens as the climate warms.
In light of this result, we propose a simple model of precipitation sensitivity (α) based on Equation 3, but assuming a constant difference between α SS and α OR of 3.25% K −1 : The performance of this simple model is evaluated in Figure 3, which shows the patterns of α in the ensemble mean and in each ensemble member alongside the approximate patterns of α predicted by Equation 5.The spatial correlations between the actual and approximate patterns of α are shown at the bottom of each panel.The correlations are strongly positive across all ensemble members, ranging from r = 0.76 (CanESM) to r = 0.93 (MPI).This shows that the simple model can successfully emulate the pattern of α in all cases, despite large differences in the patterns of α SS across the ensemble (Figure S2 in Supporting Information S1).
One of the most striking similarities between the actual and approximate patterns of α in Figure 3 is found in the Sierra Nevada and Cascades, where the simple model successfully predicts the relatively small changes in precipitation on windward slopes compared to the larger increases in the lee, indicative of a weaker rain shadow.
We can gain insight into this pattern of rain-shadow weakening from Equation 3: as the influence of orography diminishes in a warmer climate, α will be less than α SS wherever precipitation is enhanced by orography (i.e., where f OR > 0 in Figure 1f), and α will be greater than α SS wherever precipitation is suppressed by orography (i.e., where f OR < 0 in Figure 1f).A weaker rain shadow can therefore be understood as a specific manifestation of a more general decrease in the orographic influence on precipitation under global warming.

Cause of Weakened Orographic Influence
Why might orographic precipitation scale with warming at a lower rate than synoptic-scale precipitation?One possibility, suggested by Shi and Durran (2014) and Shi and Durran (2016), is that orographic ascent is dampened The vertical offset between the solid and dashed lines represents the mean difference between α SS and α OR across all grid points and models, and the slope (m = 1) is close to that given by ordinary least-squares regression (m = 0.93 ± 0.10, 95% confidence).in a warmer climate due to changes in the vertical structure of static stability.However, in our analysis of strong orographic storms impacting the Cascades and Sierra Nevada, we find that vertical velocities over the two mountain ranges exhibit opposite changes in response to warming, likely as a result of different changes in mean horizontal winds (see Text S5, Figures S5 and S6c in Supporting Information S1).Considering that the orographic influence on precipitation robustly weakens in both mountain ranges (Figure 1b), it seems unlikely that changes in orographic ascent play more than a secondary role in modulating the pattern of α within the PGW simulations.
An alternative hypothesis involves thermodynamic changes in the vertical structure of condensation.Previous studies have shown that, for a given rate of ascent, the rate of condensation is less sensitive to warming in the lower troposphere than in the upper troposphere due to the temperature-dependence of the moist adiabatic lapse rate (Kirshbaum & Smith, 2008;O'Gorman & Schneider, 2009;Siler & Roe, 2014).Because orographic ascent tends to be strongest near the surface, Siler and Roe (2014) argued that this should result in a relatively modest increase in orographic precipitation under warming.While they did not consider synoptic-scale precipitation in their analysis, synoptic-scale ascent generally peaks in the mid-troposphere where condensation is more sensitive to warming (Holton & Hakim, 2013).Therefore, differences between α SS and α OR could also stem from differences in the altitude at which condensation occurs during synoptic-scale ascent versus orographic ascent.
To test this hypothesis, we focus on the thermodynamic change in column-integrated condensation, which is a primary control on surface precipitation even in mountain ranges where advection by the horizontal wind is significant (Smith & Barstad, 2004).We consider an idealized storm in which saturated conditions extend from the surface to the tropopause.In this case, the column-integrated rate of condensation is equal to where w is the vertical velocity, is the condensation per unit vertical displacement of saturated air, ρ is the air density, and dq/dz is the vertical gradient of specific humidity following a moist adiabat (i.e., holding equivalent potential temperature, θ e , constant) (Payne et al., 2020;Siler & Roe, 2014).
To isolate the thermodynamic sensitivity of C to warming, we assume a constant profile of w and differentiate Equation 6 with respect to T s .Dividing the result by C then yields the fractional change in column-integrated condensation per degree of surface warming: Equation 8 shows that the sensitivity of C to surface warming is equal to the vertical average of d ln S/dT s weighted by wS, which represents the vertical profile of the condensation rate in the historical climate.
To evaluate Equation 8, we assume a vertical temperature profile representative of typical conditions during strong orographic storms in the Cascades and Sierra Nevada (see Text S6 in Supporting Information S1).
Figure 4a shows the mean vertical structure of d ln S/dT s during these storms, which we computed from their average vertical profiles of temperature and temperature change (Figures S6a and S6b in Supporting Information S1).The result is qualitatively similar to what Siler and Roe (2014) found for a moist-adiabatic atmosphere, with d ln S/dT s increasing from about 1.8% K −1 near the surface to more than 16% K −1 at 10 km.This implies that the magnitude of d ln C/dT will depend on the vertical profile of ascent: if ascent is concentrated near the surface, C will increase by a smaller percentage than if ascent is concentrated aloft.
To determine whether this mechanism might explain the ∼3.25%K −1 difference between α SS and α OR , we assume that P is roughly proportional to C and evaluate Equation 8 using profiles of w that are representative of synoptic-scale and orographically driven ascent (w SS and w OR ).
Considering the complex terrain of the western US and the diversity of storms that contribute to cool-season precipitation there, we do not attempt to diagnose w SS and w OR directly from our numerical simulations.Instead, assuming a typical midlatitude tropopause height of z T = 10 km, we approximate w SS as a half-sine function, z = sin(πz/z T ), which satisfies the boundary conditions w SS = 0 at the surface and the tropopause (Figure 4b, dashed line), and we approximate w OR (Figure 4b, solid line) as a modified cosine function that represents the mean linear mountain-wave solution over the steepest upwind slope of an idealized ridge (Equation S7 in Supporting Information S1), where orographic enhancement of condensation is strongest (Siler & Durran, 2015).Note that we are only concerned with the shapes of w SS and w OR , since any scalar multiple of w will have no effect on d ln C/dT s (Equation 8).
These profiles of w SS and w OR exhibit very different vertical structures (Figure 4b).While w OR is largest near the surface, where d ln S/dT s is about 1.8% K −1 , w SS is largest in the mid-troposphere, where d ln S/dT s exceeds 6% K −1 (Figure 4a).Using these profiles of w SS and w OR , along with mean profiles of S and d ln S/dT s diagnosed from historical storms (Figure 4a), we find that α SS = 5.3% K −1 and α OR = 1.9%K −1 (Figure 4c).The difference between these values-3.4%K −1 -is close to the 3.25% K −1 difference found empirically in Figure 2, suggesting that thermodynamic changes alone can explain the difference in scaling between synoptic-scale and orographic precipitation.
In reality, α SS and α OR will not be spatially uniform, but will be further modulated by changes in the large-scale circulation and relative humidity.However, such changes are likely to impact α SS and α OR in similar ways: for example, because the magnitude of orographic ascent is roughly proportional to the cross-barrier wind speed (Smith, 1979), an intensification of the large-scale circulation or an increase in low-level humidity would likely result in larger values of both α SS and α OR .This would explain why, in our PGW simulations, the difference between α SS and α OR is relatively constant, even though both exhibit significant regional and inter-model variability (Figure 2).
Although our analysis has focused on changes in condensation, our results are equally relevant for understanding changes in evaporation caused by orographically driven descent, which dominates in regions where P OR is negative (Figure 1d).Over the lee slope of an idealized mountain range, the linear vertical velocity profile is equal and opposite to the profile of ascent that occurs over the windward slope (Siler & Durran, 2015).Assuming the atmosphere remains close to saturation where liquid water is present, the fractional change in lee-side evaporation should therefore be similar to the fractional change in windward condensation.This implies a similar value of α OR regardless of whether P OR is positive or negative.

Discussion and Conclusions
In this study, we have shown that the pattern of precipitation change in the western US predicted by PGW simulations is well represented by a simple model in which the orographic component of precipitation scales with temperature at a smaller rate than the synoptic-scale component.This difference in scaling explains the weakening of the orographic rain shadow in the Cascades and Sierra Nevada identified in previous RCM studies.It likely stems from differences in the profiles of synoptic-scale and orographic ascent, with orographic ascent occurring lower in the atmosphere where condensation is thermodynamically less sensitive to warming.
Although our analysis has focused on the western United States, our results are likely relevant to other midlatitude mountain ranges where cool-season precipitation is associated with similar large-scale weather patterns.Indeed, RCM simulations over the southern Andes (Pabón-Caicedo et al., 2020) and Scandinavia (Jacob et al., 2018) also indicate a weaker rain shadow under global warming, consistent with a general weakening of orographic influence across the midlatitudes.
An open question is what our results might mean for regions or seasons in which orographic precipitation is primarily convective rather than stratiform.This includes many tropical islands, as well as mountainous parts of East Asia, South Asia, and Southwestern North America, where orographic convection acts to enhance precipitation during the summer monsoon.In these cases, our framework suggests that the patterns of precipitation change will depend on how the vertical structure of orographic convection might differ from that of non-orographic convection, and how each might respond to future warming.Answering these questions is an important avenue of future research.

Figure 1 .
Figure 1.(a) Mean total precipitation during the cool season (October-March) of the historical simulation (1981-2010).(b) Precipitation sensitivity (α; % K −1 ) defined as the percent change of precipitation divided by the change in synoptic-scale surface temperature between the historical simulation and the ensemble mean of the PGW simulations (2041-2070).(c) Synoptic-scale component of precipitation (P SS ), found by smoothing the spatial pattern of P in (a) using a 2D Gaussian filter with a standard deviation of σ = 500 km.(d) Orographic component of precipitation (P OR ), found by subtracting P SS from P. (e) The ensemble-mean synoptic-scale precipitation sensitivity (α SS ), representing the fractional change in P SS per degree of regional surface warming.(f) f OR in the historical simulation, representing the ratio of orographic-to-total precipitation (P OR /P).Positive values of f OR signify orographic enhancement of precipitation, while negative values signify orographic suppression of precipitation.

Figure 2 .
Figure2.A scatter plot of α OR versus α SS at each of the red grid points shown in the inset map.Colors represent specific PGW simulations, with error bars indicating 95% confidence.The grid is staggered such that each grid point is 200 km away from the six nearest grid points.Values of α OR are found at each grid point by minimizing the error in Equation 3 within a radius of 115 km.For example, the central red circle in the inset map encloses an area within 115 km of a grid point in southern Idaho and is surrounded by six equally spaced circles.The solid line in the main panel represents the 1-1 line (α OR = α SS ).More than 97% of data points fall below this line, indicating that α OR is robustly weaker than α SS , despite significant spatial and inter-model variability in both α OR and α SS .Across all ensemble members, α OR and α SS are correlated at r = 0.81.The dashed line represents α OR = α SS − 3.25%K −1 .The vertical offset between the solid and dashed lines represents the mean difference between α SS and α OR across all grid points and models, and the slope (m = 1) is close to that given by ordinary least-squares regression (m = 0.93 ± 0.10, 95% confidence).

Figure 3 .
Figure 3.A comparison between the actual patterns of α predicted by the PGW simulations (rows 1 and 3) and the approximate patterns of α computed from Equation 5 (rows 2 and 4).Results are shown for the ensemble mean (a, b), and for individual PGW simulations forced with output from the following GCMs: (c, d) CESM1-CAM5; (e, f) CanESM2; (g, h) GFDL-ESM2M; (i, j) HadGEM2-ES; and (k, l) MPI-ESM-MR.The spatial correlation coefficient between the actual and approximate patterns is given in the lower left of each panel in rows 2 and 4.

Figure 4 .
Figure 4. (a) The sensitivity of condensation to warming per unit of vertical displacement (d ln S/dT s ), based on the mean upstream temperature profile during strong orographic storms in both the Washington Cascades and the Sierra Nevada.(b)Representative profiles of w associated with synoptic ascent (w SS , dashed) and orographic ascent (w OR , solid).w SS represents a half-sine wave, w SS = (sin πz/z T ), with an assumed tropopause height of z T = 10 km.w OR is determined from linear mountainwave theory, based on the mean upstream temperature profile during the storms.(c) Vertical profiles of d ln S/dT s weighted by wS, assuming w = w OR and w SS from (b).Vertically integrating these profiles gives d ln C/dT s = 5.3% for w SS and 1.9% for w OR .