1. Introduction
Orographic precipitation replenishes a large fraction of the world’s freshwater supply. About 26% of the world’s population lives within mountains or their foothills, and over 40% live in river basins originating in mountainous regions (Beniston 2005). Heavy orographic precipitation on the other hand, can have less benign impacts, including triggering landslides and flash floods that produce significant loss of life and substantial disruption of the local economy (Maddox et al. 1978; Lin et al. 2001; Rasmussen and Houze 2012). Assessing how orographic precipitation may be altered in response to global warming is therefore an urgent problem.
Considerable progress has been made in understanding the change in global mean precipitation that will occur as the climate warms. Global climate models suggest that the relative humidity will remain roughly constant, implying through the Clausius–Clapeyron (CC) equation an increase in atmospheric water vapor of about 7% K−1 of surface warming. The strength of the hydrological cycle is constrained, however, not simply by the water vapor content of the air, but also by the need to balance the latent heating accompanying increased precipitation with additional longwave radiative cooling (Allen and Ingram 2002; Takahashi 2009; O’Gorman et al. 2012). Global climate models suggest that this energetic constraint will limit increases in global mean precipitation to roughly 2% K−1 of surface warming (Held and Soden 2006; Liepert and Previdi 2009).
Relatively few previous studies have focused on how global warming may influence the processes regulating stable orographic precipitation, such as that commonly generated by westerly flow across north–south mountain ranges such as the Rockies and the Andes. Moving beyond (1), Kirshbaum and Smith (2008) examined the influence of upstream temperature and moist stability on idealized simulations of precipitating cross-mountain flows representative of those impinging on midlatitude mountains. They found that the precipitation increased at rates well below the CC scaling in response to surface temperature increases when other environmental parameters (winds, static dry stability, and relative humidity) were held constant. They determined the most important factor producing the sub-CC scaling was the relatively slow rate at which the vertically averaged condensation increases in response to surface temperature increases. This finding is consistent with other studies showing that the sensitivity of dqs/dz to surface temperature provides a better scaling for precipitation and condensation occurring in a cloud layer of roughly constant depth than does the increase in total column water vapor in a warmer climate (Betts and Harshvardhan 1987; O’Gorman and Schneider 2009). A second important factor identified by Kirshbaum and Smith (2008) was that as the temperature increased, ice-phase precipitation growth was replaced by less efficient warm-rain processes. In an idealized study representative of the northern Alps, Zängl (2008) also found the temperature dependence of orographic precipitation was strongly influenced by changes in precipitation microphysics, particularly those associated with variations in the freezing level.
Both Kirshbaum and Smith (2008) and Zängl (2008) conducted process studies focused on the response of orographic precipitation to changes in temperature without considering the influence of circulation shifts that might lead to stronger or weaker cross-mountain winds and water vapor fluxes in a warmer climate—that is, without investigating changes in U, the other factor in the simple estimate (1). Most global climate models do, however, predict significant changes in the circulation in response to global warming, such as poleward shifts in the storm tracks (e.g., Yin 2005). To partially account for changes in the global mean climate, shifts in the mean atmospheric state have been incorporated in “pseudo-global warming” investigations of snow depth over the mountains of Japan (Hara et al. 2008) and Colorado (Rasmussen et al. 2011). Nevertheless, even pseudo-global warming simulations cannot account for changes in storminess, since they are based on regional model simulations driven at their upstream boundaries by weather perturbations whose strength and frequency match those in the current climate.
The goal of this study is to compare the roles played by thermodynamics and dynamics in regulating midlatitude orographic precipitation in a warmer climate. In particular we will examine the impacts of temperature and humidity changes, shifts in the mean circulation, and changes in the frequency of midlatitude cyclones. To isolate the most relevant variables and side-step uncertainties about the precise future changes in the midlatitude jets and storm tracks Ulbrich et al. (2008), we greatly simplify Earth’s actual topography and conduct general circulation model (GCM) simulations of an ocean-covered Earth pierced by simple idealized representations of major north–south midlatitude mountains.
In section 2 we describe the design of our numerical experiments. Section 3 presents the model climatology, with a focus on midlatitude orographic precipitation and its changes in response to doubling of the CO2 concentration. Important factors driving changes in local orographic precipitation are analyzed in sections 4 and 5 using a simple diagnostic model to better understand the stable (grid resolved) orographic precipitation predicted by the GCM. Section 6 contains the conclusions.
2. Experimental design
The GCM used in this study is the global atmosphere model developed by the Geophysical Fluid Dynamics Laboratory (GFDL) (Anderson et al. 2004). Standard physics packages and parameters of the GFDL Atmospheric Model, version 2.1 (AM2.1), are adopted in our simulations unless otherwise specified in the following text. Thus our description of the AM2.1 components is very brief. Readers interested in the details of the AM2.1 physics schemes or dynamics are referred to Anderson et al. (2004) and references therein.
The idealized topography for each island. Horizontal dimensions are in degrees of latitude and longitude; x0 = 45°, 135°, 225°, or 315° is the central longitude of an island.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00460.1
As detailed in Anderson et al. (2004), grid-resolved clouds and precipitation in AM2.1 are parameterized with the aid of prognostic variables for the cloud fraction and the specific humidities of cloud liquid water and cloud ice. Grid-scale fluxes of rain and snow are computed diagnostically from these prognostic fields using parameterizations that attempt to account for the subgrid-scale moisture distribution, the determination of liquid water fraction in mixed-phase clouds, and the dependence of the autoconversion threshold on subgrid-scale nonuniformities in the cloud distribution (Rotstayn 1997; Rotstayn et al. 2000). Cumulus convection is represented by the relaxed Arakawa–Schubert formulation of Moorthi and Suarez (1992).
Surface conditions at all island grid cells are computed by the GFDL land model (LM2), which includes soil sensible and latent heat storage, groundwater storage, and stomatal resistance. The surface vegetation is fixed as “broadleaf/needleleaf trees” and the soil type is “coarse/medium/fine mix.” Surface fluxes are computed using Monin–Obukhov similarity theory. We do not use the AM2.1 gravity wave drag and “orographic roughness” parameterizations because our numerical resolution is adequate to capture the simple smooth topography.
The concentrations of all greenhouse gases except CO2 are fixed at climatological means, and the radiative effects of aerosols are not considered in these simulations so as to avoid unnecessary complexity. Solar radiation is fixed at its annual mean value, with no seasonal or diurnal cycle. Such perpetual annual mean conditions facilitate the use of a single relatively shallow (2.4 m deep) mixed-layer ocean that comes rapidly into equilibrium with CO2-induced changes in the radiative forcing. Sea ice is neglected in these simulations for simplicity.
All simulations are run for 20 yr in total. The first 10 yr, which are more than adequate to spin up to the new climatic equilibrium, are discarded, and the last 10 yr of data are used for our analysis. Most of our investigation is focused on a pair of simulations with mountains between 40°–60°N. In one member of the pair, the concentration of CO2 in the atmosphere is 330 ppm, corresponding to the CO2 level of 1970s (referred to as experiment M1 hereafter), whereas in the other it is 660 ppm (referred to as M2). Results from a second pair of experiments, with mountains between 35° and 55°N (named M1′ and M2′) will also be discussed briefly. The third and final pair of 10-yr 330- and 660-ppm simulations are for pure aquaplanet conditions (without any islands) and will be referred to as A1 and A2, respectively.
3. Model climatology
a. Mean precipitation
The mean annual precipitation in experiment M1 is shown in Fig. 2; not surprisingly there is heavy precipitation on the western side of each mountain range and much drier conditions on the leeward side. The annual western-side precipitation in M1 ranges between 400 and 700 cm, which is roughly comparable to the 300–500 cm yr−1 observed on the windward side of the Olympic Mountains of Washington (Minder et al. 2008).
Mean annual precipitation in simulation M1.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00460.1
Figure 3a plots the zonal-mean precipitation as a function of latitude for simulations M1, M2, A1, and A2. Comparing A1 with M1 and A2 with M2, it is apparent that the mountains make only a modest change in the zonally averaged precipitation, slightly increasing the maximum and shifting the entire distribution a little toward the equator. Doubling the CO2 concentration causes a 2.56-K increase in the global mean surface temperature between M1 and M2, and a 2.35-K increase between A1 and A2. In both pairs of simulations, the increase in CO2 produces a 2°–3° northward shift and a very slight increase in the magnitude of the zonal-mean midlatitude rain maximum. This shift is due to a poleward shift in the midlatitude storm tracks, which is a robust feature of circulation changes in most twenty-first-century climate simulations (Yin 2005).
Latitudinal dependence of the (a) zonal mean annual precipitation for the mountainous and aquaplanet simulations and (b) annual precipitation averaged over just the cells in north–south bands along the western sides of the four mountains. Blue bars along the abscissa indicate the latitudinal span of the mountains.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00460.1
In contrast to the behavior of the zonal mean, doubling the CO2 leads to a substantial increase in precipitation over the western side of the mountains (Fig. 3b), increasing the maximum annually averaged precipitation by as much as 140 cm yr−1 at 52°N. The local increases are particularly pronounced between 48° and 58°N, whereas they are small or even negative along the southern part of the ridge between 40° and 45°N.
The global mean hydrological sensitivity, defined as the percentage change in precipitation per degree of global-mean surface warming, is 1.6% and 1.5% K−1 for the M and A simulations, respectively; these values are similar to those obtained in many other climate models (Held and Soden 2006). The latitudinal variation in the zonal-mean hydrological sensitivity (again defined with respect to the global-mean surface warming) is plotted for the band occupied by the mountains in Fig. 4. The presence of mountains has only a small impact on the zonal mean hydrological sensitivity, which increases with latitude from −3% to 7% K−1, but the local response over the western slopes of the ridges is much larger, ranging from −6% to 14% K−1, between 40° and 58°N. Precipitation near the northern end of the mountains increases at twice the CC scaling, which given that the global-mean surface temperature rises by 2.56 K, corresponds to a very substantial 36% increase in the precipitation between M1 and M2. Some care must be taken when interpreting the values obtained for hydrological sensitivity south of 45°N since, as shown in Fig. 3b, there is a very strong north–south gradient in precipitation in this region and large sensitivities are produced by small latitudinal shifts in the precipitation pattern.
Latitudinal dependence of the hydrological sensitivity of the annual precipitation averaged around the full latitude band in simulations M1 (red) and A1 (black), or averaged only over the western side of the mountains in simulation M1 (blue).
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00460.1
The western-side hydrological sensitivity for simulations M1′ and M2′, with mountains between 35° and 55°N, is compared in Fig. 5 with the sensitivity for M1 and M2, which have ridges between 40° and 60°N. In both cases there is a reduction in sensitivity and in total precipitation within 2° of the northern end of the mountains as the flow experiences less orographic ascent and more lateral deflection around the end of the mountain. The north–south gradient in the western-side hydrological sensitivity as a function of distance from the northern end of the mountain is similar in both cases, suggesting that the processes responsible for this gradient are not sensitive to the precise location of the barrier. The hydrological sensitivities averaged over the entire western side are nevertheless quite different for these two cases; for the 35°–55°N mountain this sensitivity is 1.6% K−1, but it is 5% K−1 in the 40°–60°N case.
Latitudinal dependence of the hydrological sensitivity of the annual precipitation averaged over the western side of the mountains from simulations M1′ and M2′ (red dashed) or M1 and M2 (blue solid).
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00460.1
b. Precipitation intensity
To estimate changes in the intensity of orographic precipitation, all precipitation events over the western slopes were sorted into four classes based on the precipitation accumulated over each hour: negligible events (<0.02 mm h−1), light events (0.02–1.0 mm h−1), moderate events (1.0–4.0 mm h−1), and heavy/extreme events (≥4.0 mm h−1). The 4.0 mm h−1 threshold for the heavy/extreme events approximates the 99th percentile of the orographic precipitation intensity in the M1 simulation. To reveal the substantial north–south variations in precipitation intensity, the western side of each mountain was divided to five east–west bands, each of which spans 4° in latitude. The frequency and average intensity for each precipitation class in each band is compared for simulations M1 and M2 in Fig. 6.
Frequency as a function of latitude for (a) negligible, (b) light, (c) moderate, and (d) heavy/extreme precipitation events over the western slopes of the mountains. Values for simulations M1 and M2 are shown in light and dark blue, respectively. The mean intensity (mm h−1) for each class appears in the corresponding vertical bar.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00460.1
Figure 6a shows the percentage of time during which negligible or no precipitation occurred. Clearly there were significant changes in this quantity in the warmer climate, with the percentage of dry days increasing from 15% to 20% in the southernmost band but decreasing from 29% to 22% in the northernmost band. Comparing all four panels in Fig. 6, it is apparent that the warmer climate skews toward heavier precipitation events. In particular, the frequency of heavy/extreme events is doubled in the three northern bands. The mean intensities of the heavy/extreme events also increase at all latitudes.
Most of the accumulated precipitation (reflecting the product of intensity and frequency) in each of the five bands is produced by events in either the light or the moderate precipitation classes, each of which provides roughly 45% of the total. The rest is contributed by heavy/extreme events. As the climate warms, the portion from the moderate and the heavy/extreme classes increases, while that from light precipitation decreases.
(a) Latitudinal dependence of the sensitivity (% K−1) in the annual accumulated precipitation δAp/Ap, the averaged precipitation rate 
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00460.1
Further verification of a northward shift in storminess is provided by examining the sensitivity of the zonally averaged vertical velocity variance δω′2/ω′2 (in units of percent per kelvin of surface warming). The values of ω′2 are mass-weighted vertical averages between 850 and 600 hPa and 2–8-day bandpass filtered; they reveal the influence of transient synoptic-scale disturbances on vertical velocities in the layer typically occupied by orographic clouds. As shown in Fig. 7b, δω′2/ω′2 decreases by 2% K−1 over the southern end of the mountains; it drops to zero around 47°N, and it increases by 5% K−1 over the northern end of the range. These variations are similar to those in δτ/τ, supporting the interpretation that the change in the annually averaged frequency of rainy hours is driven by changes in synoptic-scale storminess.
c. Water vapor transport
Let 〈⋅〉 denote the annual mean averaged over all hours, including those with no rain. The difference between the annual mean precipitation rate 〈P〉 and the annual mean evaporation rate 〈E〉 averaged over the latitude band between 40° and 60°N is given by the annual mean convergence of water flux into the band. In AM2.1, the total water flux is the sum of the fluxes of water vapor, cloud liquid water, and cloud ice (there are no prognostic precipitation fields). The cloud water fluxes are much smaller than the water vapor fluxes and have only a trivial influence on the water balance in the band. The terms in the annual average water budget for this band are listed in Table 1 for simulations M1, M2, A1, and A2. The values of 〈P〉 and 〈E〉 are accumulated at every model time step, whereas the water vapor fluxes are available only once per day. As a consequence of the coarse time resolution in the water vapor flux calculation (and the neglect of cloud water fluxes), the budget does not close perfectly, but the residual is less than 1% of the largest term 〈P〉.1 In the doubled CO2 cases, water vapor transport from the tropics increases by about 12% and becomes almost equal to the second-largest term: evaporation within the band. Aside from a tendency to modestly reduce the evaporative fluxes, the mountains have little influence on the individual terms in the zonally averaged water budget. The average hydrological sensitivity in the band between 40° and 60°N is 2.6% K−1 for the cases with mountains and 2.2% K−1 for the aquaplanet simulations.
Water budget for the latitude band 40°–60°N for simulations M1, M2, A1, and A2. Entries are the annual-averaged area-integrated precipitation rate 〈P〉, evaporation rate 〈E〉, and water vapor fluxes across the southern and northern boundaries (units are 109 kg s−1).
The mountains do reduce the annual averaged eastward moisture fluxes impinging on their windward slopes. Table 2 compares the frequency with which zonal winds averaged between the surface and the height of the mountain at the upstream edge of the topography (i.e., 2.5° west of the ridgeline) were at least 2 m s−1 in simulations A1 and M1.2 Also listed are the average eastward moisture fluxes through a meridional cross section above the western foot of the mountains and the mean vertically integrated humidity for simulations M1 and A1 (again restricted to those cases with low-level eastward winds stronger than the 2 m s−1 threshold). The frequency and the strength of the eastward moisture flux increases greatly from north to south in both simulations A1 and M1. The mountains do not significantly influence the frequency of eastward flow, but they have a strong impact on the moisture fluxes, which are reduced between simulations A1 and M1 by roughly 30% in the middle and southern sections of the mountain. This reduction is entirely a result of a reduction in the strength of the eastward flow, because the upstream humidity is generally greater in simulation M1, as indicated in the last two columns of Table 2.3
Comparison of the water vapor flux at western boundaries of the five bands of the mountains in M1 and that of the corresponding areas in A1. The first two columns are the frequency (%) of the occurrence of eastward flux with low-level wind speeds greater than 2 m s−1 in A1 (fA1) and M1 (fM1). The middle two columns are the mean integrated eastward flux (kg s−1) through vertical surface bounding the western sides of each latitude band (FA1 and FM1 for A1 and M1 respectively). The last two columns are the mean water vapor integrated over the same vertical boundaries (kg m−2) (QA1 and QM1).
Figure 8 illustrates how the water budget for the windward slopes changes between simulations M1 and M2. As in Table 2, these values are broken into latitude bands for cases where the average low-level winds at the western edge of each band exceed 2 m s−1. The cases making up the average therefore vary among the latitude bands and, thus, the north–south water vapor fluxes do not match across the band boundaries. In both simulations, the largest term is the eastward flux impinging on the mountains; this flux increases substantially from north to south and also increases with increasing CO2. The incoming fluxes are primarily balanced by outgoing eastward fluxes at the ridge crest, whose latitudinal variation is also substantial. The north–south water vapor flux divergence removes a modest amount of water from each band, except in the southernmost band where it matches (M1) or exceeds (M2) the precipitation. Evaporation makes an almost negligible contribution to the total budget. The water budgets diagrammed in Fig. 8 are not annual means, and therefore need not close exactly. All the residuals are negative, ranging between −7% and −1% of the eastward flux into the band. The residual water balances for the remaining cases not included in Fig. 8 are all positive; the mountains act as a sink of water during the rainy periods and as a water source through evaporation when it is not raining.
Schematic illustration of the terms in the water balance for the five bands on the windward slope for simulations (a) M1 and (b) M2. Dashed lines show the extent of each budget volume; the latitude bands match those in Tables 2–4. Shading shows the topography. Blue numbers are precipitation, and red are evaporation. Black numbers are water vapor fluxes through the adjacent boundary. All values are averages for times with band-averaged eastward winds between the surface and 2 km greater than 2 m s−1. North–south fluxes are not continuous across the band boundaries because different sets of cases make up the average in each band.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00460.1
The “drying ratio” (DR) is a measure of the efficiency with which mountains remove moisture from the air. It is defined by Smith et al. (2003) as the precipitation divided by the water vapor flux into some control volume, or equivalently one minus the ratio of outgoing to incoming water vapor flux. Kirshbaum and Smith (2008) evaluated the drying ratio in idealized horizontally uniform flows impinging on an isolated mountain, but because nontrivial eastward moisture fluxes strike our mountains almost twice as often in the south as in the north (Table 2), it is difficult to define a meaningful drying ratio for the entire ridge. Instead we compute DR as a function of latitude band for simulations M1 and M2 in Table 3 using the same >2 m s−1 low-level wind speed criterion imposed on the data in Fig. 8. The incoming and outgoing water vapor fluxes used to determine these DR include both the zonal and meridional components.
Mean surface temperature (K) and drying ratio for the western slopes of the mountains averaged over the indicated latitude bands in simulations M1 and M2.
Table 3 lists these drying ratios together with the mean upwind surface temperature in each band. The drying ratios are smallest near the northern and southern ends of the ridge, where the flow can easily deflect around the ends of the mountain. The drying ratios in the central three latitude bands are roughly 75% as large as the values obtained by Kirshbaum and Smith (2008) for flows at the same surface temperature impinging on a 3D Gaussian ridge about half the width of our mountain. Given the substantial differences in the details of our precipitation events and those simulated in Kirshbaum and Smith (2008), there is no reason to expect better quantitative agreement. As in both Kirshbaum and Smith (2008) and Cannon et al. (2012), DR in the central part of the range decreases with increasing temperature, both north to south along the ridge and within each latitude band when CO2 is doubled. Of course temperature is not the only determinant of DR; the temperature between 44° and 48°N in M1 is greater than that between 52° and 56°N in M2, but DR is smaller in the colder northern band.
One way to appreciate the importance of circulation changes in regulating the precipitation along each ridge is to contrast the actual changes in water vapor flux convergence with what would be expected if the circulation remained unchanged in a warmer world. Consider the same 4°-wide bands on the upwind slope identified in Fig. 8. The difference between the annual mean precipitation rate 〈P〉 and the annual mean evaporation rate 〈E〉 in each band is given by the annual mean total water flux convergence across the band. As argued in the “dry get drier” theory of precipitation changes in response to global warming (Held and Soden 2006; Scheff and Frierson 2012), if the velocities that define the circulation are unchanged, then the fractional changes in total water flux convergence must be equal to the fractional changes in the water content of the air, which should follow the CC scaling.
Table 4 gives the sensitivities to the change in global mean surface temperature of 〈P〉, 〈E〉, and 〈P〉 − 〈E〉 averaged over the western slope of the ridge within each latitude band. As previously illustrated in Fig. 3, the systematic south–north increase in δ〈P〉/〈P〉 is quite substantial. The south–north increase in δ(〈P〉 − 〈E〉)/(〈P〉 − 〈E〉) is, however, even larger; it ranges from −5.7% K−1 in the south to 15.4% K−1 in the north, and it must be balanced by identical changes in total water flux convergence. But the sensitivity of the annual mean column-integrated water vapor4 above the western slope in each latitude band 
Sensitivities with respect to the global mean surface temperature in the annual mean: precipitation 〈P〉, evaporation 〈E〉, their difference, the column-integrated water vapor 
4. A simple diagnostic model for orographic precipitation
It is difficult to develop a simple conceptual understanding of the key factors responsible for the changes in orographic precipitation by directly examining every term in the diagnostic parameterizations of precipitation in the AM2.1 simulations. The parameterization of convective precipitation is highly idealized and not tuned to describe the convection triggered by mountains. The grid-resolved (hereafter referred to as “stratiform”) precipitation parameterization also includes many elements (such as a parameterization of the autoconversion threshold to account for subgrid-scale variations in cloudiness) that are not typically present in mesoscale atmospheric models with prognostic equations for the precipitating microphysical variables. The physical processes responsible for the stratiform orographic precipitation in these simulations can, therefore, be more clearly understood using the prognostic wind, temperature, and moisture fields from the AM2.1 simulations to drive a physically motivated diagnostic model. As will be demonstrated, the precipitation from this diagnostic model gives a good approximation to the actual stratiform orographic precipitation generated by the AM2.1 simulations.
The complete dynamical fields were output from the full simulations only once per day. As a consequence, our diagnostic evaluation of the annual accumulated rainfall 
Latitudinal dependence of (a) the accumulated western-side stratiform precipitation, the total (stratiform plus convective, Ap) and 
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00460.1
5. Understanding the changes in stratiform orographic precipitation
a. Use of annual averaged values
Hydrological sensitivity of the western-side precipitation rate for the GCM large scale cloud scheme Pst, the full diagnostic precipitation model 
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00460.1
Individual contributions to the change in mean stratiform orographic precipitation intensities from changes in westerly wind speed δ
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00460.1
b. Lapse rate of saturation specific humidity
According to Fig. 11, δΓs/M contributes about 4% K−1 toward the total hydrological sensitivity at all latitudes occupied by the mountains. From (6), 
The dependence of γs and qs on temperature. The blue curve is δ ln(qs)/∂T, while other curves are values of δ ln(γs)/∂T at different pressure levels. The discontinuities are produced by our simple treatment of the transition between condensation and deposition.
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00460.1
c. Westerly wind speed
As evident in Fig. 11, the changes in cross-mountain wind speed δ
To quantify the poleward shift of the storm track, we define the latitude of the eddy-driven jet following Ceppi and Hartmann (2013) as the latitude of the maximum zonal-mean zonal wind at the 850-hPa pressure level. Using this definition, the Northern Hemisphere jet shifts poleward by 1.65° as global mean surface temperature increases from M1 to M2. Interestingly, our Northern Hemisphere mountains produce an even larger 2.62° poleward shift in the mountain-free Southern Hemisphere. In contrast, in both hemispheres of the aquaplanet the poleward shift of the jet between simulations A1 and A2 is 2.16°. The shifts in the jet are sensitive to the position of mountains. In simulations M1′ and M2′, in which the mountains lie between 35° and 55°N, the jets shift poleward 2.24° and 2.53° in the Northern and Southern Hemisphere, respectively.
d. Saturated vertical displacement
The preceding is verified in Figs. 13a–c, which show meridional cross sections along the topography above the second-from-the-west grid cell (i.e., 1.56° west of the ridgeline); 
Meridional cross sections above the second cell east of the base of the mountain showing the mean rainy-time difference M2 − M1 of (a) 
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00460.1
The change in LCL is primarily as a result of changes in relative humidity, as is evident from a comparison of Figs. 13c and 13d; there is drying between the heights of 1.5 and 4 km superimposed on a substantial meridional gradient with dryness increasing to the south at all heights above the southern half of the mountain. The north–south gradient in δRH is associated with the north–south shifts in the storm track.5 The large north–south gradient in the sensitivity of the saturated vertical displacement (δ
6. Conclusions
It is difficult to untangle all the factors regulating the changes in precipitation forced by Earth’s topography in realistic GCM simulations of warmer climates. As a first step, we compared the relative influence of thermodynamics and dynamics on the hydrological sensitivity of midlatitude orographic precipitation over the western slopes of four major north–south barriers equally spaced around the Northern Hemisphere of a planet otherwise covered by ocean. Our mountains are smooth and wide enough to be reasonably represented on the numerical mesh, allowing the dynamics of stratiform precipitation to be simulated with minimal parameterization. Interestingly, the latitudinal (along the ridgeline) hydrological sensitivity in the GCM simulations turns out to be similar for both stratiform and convective precipitation. Nevertheless, because of uncertainties in the accuracy of convective parameterizations (particularly over mountains), our detailed analysis focuses on the stratiform precipitation.
In our simulations, the changes in midlatitude orographic precipitation due to global warming show a strong north–south asymmetry. The water vapor fluxes impinging on the ridges strengthen at all latitudes even as precipitation decreases near the southern ends of the mountains and increases in the north. For mountains stretching from 40° to 60°N, the hydrological sensitivity exceeds the CC scaling over the entire northern half of the range. A maximum in the hydrological sensitivity of 14% K−1 occurs near the northern end of the range, which given the 2.56-K increase in global-mean surface temperature obtained when CO2 is increased from 330 to 660 ppm, corresponds to a substantial 36% increase in the north. Conversely, near the southern end of the range, precipitation decreases as a slight shift in a region of steep precipitation gradients produces a sensitivity of −6% K−1. In contrast to the total annual precipitation, the frequency of extreme events does increase at all latitudes. The greatest increase in these extremes, exceeding a factor of 2, is in the north.
The changes in accumulated precipitation are due to differences in both intensity and frequency. Except in the extreme south, the change in precipitation intensity makes the larger contribution. Nevertheless, the changes in the number of hours with precipitation are also quite significant. In the north, for example, more frequent precipitation contributes 5% K−1 toward a total sensitivity of 14% K−1. The latitudinal dependence of the sensitivity to surface warming in the annual average number of hours during which precipitation occurs closely tracks that of the 2–8-day bandpass-filtered vertical velocity variance, suggesting that changes in the frequency of precipitation are primarily driven by changes in the frequency of midlatitude storms. Such changes in storminess are not captured in pseudoglobal warming experiments (Hara et al. 2008; Rasmussen et al. 2011), in which the climatological means are shifted to match those in warmer-world GCM simulations, but the day-to-day weather is driven by perturbations at the lateral boundaries whose frequencies and intensities match those in the current climate.
The stratiform precipitation intensity in the full AM2.1 depends on many variables via a complex parameterization. The changes in the average stratiform precipitation intensity can, however, be well approximated using a simple diagnostic model involving three factors: the moist adiabatic lapse rate of saturation specific humidity δΓs, the westerly wind speed δ
In summary, stratiform midlatitude orographic precipitation responds in different ways to the changes in thermodynamics and dynamics simulated by the GCM in response to doubled CO2. Thermodynamic changes (warmer temperatures and higher specific humidities) are responsible for an almost uniform positive hydrological sensitivity of 4%–5% K−1 on the windward slopes of the mountains. Yet the actual hydrological sensitivity is far different and is largely driven by dynamical changes resulting from shifts in the storm tracks and storm frequency. The strong north–south gradients in the actual hydrological sensitivity (see Fig. 5) suggest that attempts to simulate finescale global warming–induced changes in orographic precipitation with regional climate models will be highly dependent on the accuracy of the large-scale flows used to force the regional circulations.
Many additional physical processes and much higher numerical resolution would need to be included in the model before attempting to make predictions for specific real-world locations. Convection is a key physical process that is crudely parameterized in the GCM and not included in our diagnostic model. Cannon et al. (2012) suggest that changes in embedded convection owing to warmer less stable upstream flows might significantly modify orographic precipitation over narrow mountain ridges, but would generate only a modest 6%–12% increase over wide ridges such as those considered in this study. There are also a wide variety of possible terrain configurations that might be explored through similar numerical experiments. We briefly considered identical ridges located 5° farther south (35°–55°N) and found latitudinal gradients in the hydrological sensitivity similar to those in the 40°–60°N case.
Acknowledgments
The authors have benefited from conversations with Dargan Frierson, David Battisti, and the comments of two anonymous reviewers. This research was supported by National Science Foundation (NSF) Grant AGS-1138977 and used computing resources provided by the University of Washington eScience Institute and the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF Grant OCI-1053575.
APPENDIX A
The Moist Lapse Rate of Saturation Specific Humidity and the Lifting Condensation Level
APPENDIX B
Changes in the Frequency of Lifting Parcels to their LCL
Latitudinal variations in the sensitivities with respect to surface temperature in the saturated vertical displacement δDz/M, its approximation 
Citation: Journal of Climate 27, 11; 10.1175/JCLI-D-13-00460.1
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Computed with four decimal places of precision.
The 2 m s−1 threshold was imposed to avoid counting weak thermally driven upslope flows.
The zonally averaged evaporation rates are similar in A1 and M1 because the decreases in the surface westerlies in M1 are compensated by increased meridional winds that keep the zonally averaged surface wind speed roughly constant.
The column-integrated total water was not archived in these simulations and is not available, but simulations of similar cases show that 
The reason for the vertical gradients in δRH is a subject of continued study.
