Rain shadow development during the growth of mountain ranges: An atmospheric dynamics perspective

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114,, doi: /2008jf001085, 2009 Rain shadow development during the growth of mountain ranges: An atmospheric dynamics perspective Joseph Galewsky 1 Received 28 May 2008; revised 7 September 2008; accepted 14 November 2008; published 17 February [1] An idealized atmospheric model is used to explore the links between climate and topography in the development of orographic rain shadows during orogenesis. The atmospheric dynamics theory of density stratified fluid flow over topography is used to interpret the results. The controlling nondimensional parameter is Nh/U, where N is the Brunt-Vaisala frequency, a measure of atmospheric stability, h is the terrain relief, and U is the initial horizontal wind speed. Rain shadow development is found to be a nonlinear and nonunique function of both topography and atmospheric state, indicating that geological records of orographic aridity cannot be interpreted in terms of relief alone. When upstream topography exceeds Nh/U 1 during surface uplift, downstream orographic precipitation vanishes, and downstream orographic cloud mass decreases by as much as 90%. Upstream blocking of air flow can generate a forward projecting rain shadow in which a relatively low ridge (Nh/U < 1) situated upstream of a relatively high ridge (Nh/U > 1) may be decoupled from the atmospheric flow by a zone of flow stagnation extending upstream of the high terrain. Such an effect may occur if the valley separating the two ranges is narrower than the length scale of flow stagnation. In the model configuration used here, lateral widening of a relatively low (Nh/U < 1) range changes downstream orographic cloud mass by only a few percent, while lateral growth of a relatively high (Nh/U > 1) range increases downstream cloud mass by up to a factor of 3. These results help to refine interpretations of climate-tectonic interactions in shaping the geological record of the Sierra Nevada and Andes. Citation: Galewsky, J. (2009), Rain shadow development during the growth of mountain ranges: An atmospheric dynamics perspective, J. Geophys. Res., 114,, doi: /2008jf Introduction [2] Orographic rain shadows are a primary feature of Earth s surface climatology and are thought to influence the erosion and landscape evolution of mountain belts [Sobel et al., 2003; Strecker et al., 2007; Biswas et al., 2007; Grujic et al., 2006]. Geological records of aridification recorded in soils and sediment have been interpreted in terms of the growth of topographic barriers and used to constrain models of orogenesis [Kleinert and Strecker, 2001; Ruskin and Jordan, 2007; Rech et al., 2006; Poage and Chamberlain, 2002; Amit et al., 2006; Mulch et al., 2008], but the relative roles played by tectonics and climate in controlling these records remain enigmatic [Hartley and Chong, 2002; Hartley, 2003]. [3] Disentangling the effects of tectonics and climate in the evolution of mountain belts remains a primary goal of the geosciences, but progress has been hampered by the lack of theories for their interactions. The theoretical framework 1 Department of Earth and Planetary Sciences, University of New Mexico, Albuquerque, New Mexico, USA. Copyright 2009 by the American Geophysical Union /09/2008JF of stratified fluid flow over topography [Baines, 1995] has been used successfully to understand the atmospheric response to topography in the meteorological context [Pierrehumbert and Wyman, 1985; Rotunno and Ferretti, 2001; Smolarkiewicz and Rotunno, 1989, 1990], but has not been applied to problems in orogenesis. The goal of this study is to use this framework to better understand the processes that control the development of orographic rain shadows during the growth of mountain ranges. The aim of this paper is not to predict specific precipitation patterns or erosional outcomes for any particular mountain belt, but is instead to determine the controlling fluid dynamical parameters and length scales of the problem and to relate such parameters to the general geological problem of orographically induced aridification. 2. Stratified Flow Over Topography [4] The theory of density stratified fluid flow over topography is described in detail by Baines [1995], but the main results are summarized here. The controlling nondimensional parameter for atmospheric flow over topography is Nh/U, sometimes called the Froude number or the nondimensional mountain height, where N (s 1 ) is the Brunt-Vaisala fre- 1of17

2 quency (a measure of atmospheric stability, described in more detail shortly), h is the orogen-scale topographic relief (m), and U is the average wind speed (m s 1 ) perpendicular to the strike of the orogen. When Nh/U is much less than unity, air can flow directly over topography without deflection, resulting in the familiar coupling of orographic precipitation to topography. When Nh/U is much greater than unity, however, the air cannot flow over the terrain and more complex orographic precipitation regimes develop. The impact of low Nh/U flows has been explored in several geomorphic studies [Roe et al., 2002, 2003; Kessler et al., 2006], but the geomorphic effects of high Nh/U flows are largely unknown, despite the fact that such flows are common [Marwitz, 1980; Parish, 1982; Galewsky and Sobel, 2005; Reeves et al., 2008; Cox et al., 2005; Rotunno and Ferretti, 2001; Reeves and Lin, 2006]. One of the goals of this study is to introduce the principles of high Nh/U atmospheric flows to the geomorphology community with the hope of spurring further research into the significance of these atmospheric conditions for landscape dynamics Components of Nh/U [5] In this study, as in most idealized studies of flow over topography, h is simply the maximum relief of a smooth ridge relative to the surrounding plain. In case studies from more complex (and realistic) terrain [Galewsky and Sobel, 2005; Mass and Ferber, 1990], h is estimated from the average relief of the terrain crest relative to the surrounding plain. Because this theory is primarily applicable to largescale rather than valley-scale atmospheric flows, it is most appropriate to think of h in terms of orogen-scale relief rather than the local relief of individual valleys. Terrain asymmetry can certainly impact the details of precipitation distributions, but the large-scale atmospheric flow patterns that are the focus of this study do not depend much on the terrain profile [Baines and Hoinka, 1985]. Thus the results obtained here should apply to a variety of geologically relevant orogen geometries, including critical wedge and normal fault-bounded ranges. [6] The Brunt-Vaisala frequency, N, is a fundamental parameter in atmospheric sciences and is derived in detail by Holton [2004], and an outline of the key concepts is presented here. The potential temperature, q, is the temperature that a parcel of dry air at pressure p and temperature T would have if it were expanded or compressed adiabatically to a standard pressure p s. It is given by q = T(p s /p) R/c p, where R is the gas constant and c p is the specific heat at constant pressure. Outside of regions of active precipitation, q is nearly conserved in midlatitude weather systems. For the idealized case in which the potential temperature is constant with altitude, the lapse rate of temperature is given by: dt dz ¼ g c p ¼ G d where G d is the dry adiabatic lapse rate. In general, the potential temperature is a function of height and the temperature lapse rate will differ from the adiabatic lapse rate: ¼ G d G ð1þ ð2þ If G < G d, q increases with height, and an air parcel that is adiabatically displaced from its equilibrium level will be negatively buoyant when displaced upward so that it will return to its equilibrium level. In this case, the atmosphere is said to be statically stable, and this study is restricted to such cases. [7] Adiabatic oscillations of an air parcel around its equilibrium level in a stably stratified atmosphere are called buoyancy oscillations, and the characteristic frequency of such oscillations is N, the buoyancy frequency or Brunt- Vaisala frequency and is given by: N 2 ¼ g d ln q 0 dz [8] The above formulation only applies to an atmosphere without water vapor. The presence of water vapor adds substantial complexity to the problem [e.g., Barcilon et al., 1979]. The latent heat released during the condensation of water vapor into cloud water or ice decreases the stability of an air parcel by about a factor of three and requires a different (and more complex) formulation for N [Durran and Klemp, 1982]. Furthermore, upon saturation, N switches abruptly from its dry to its moist value, producing a significant nonlinearity into orographic flows and precipitation. Previous studies [Jiang, 2003; Colle, 2004] have shown that the flow response in a saturated atmosphere can still be understood using Nh/U, with the moist formulation of the Brunt-Vaisala frequency used instead of the dry formulation, an approach used here. [9] The processes that control the static stability are still the subject of active research in the atmospheric sciences. In the tropics, the stability is reasonably well understood and is controlled by moist convection [Xu and Emanuel, 1989]. The stability of the midlatitude atmosphere is much less well understood, but is thought to scale with the meridional (north south) gradient in the equivalent potential temperature (q e ) which is the potential temperature that an air parcel would reach if all of the water vapor in it were to condense [Juckes, 2000; Frierson, 2006]. The meridional gradient of q e is strongly controlled by the land surface, especially soil moisture availability [Frierson, 2006]. The value of N can change on time scales as short as a few hours, during the passage of a storm system [Marwitz, 1980], to time scales of centuries or longer as a result of global climate change. [10] Finally, the wind speed U is just the average horizontal wind speed sufficiently far upstream of the terrain to be unaffected by the presence of the terrain itself. In regions of complex topography, it can be difficult to estimate U; furthermore, during the course of individual storms U may vary by a factor of 2 or more. [11] The nondimensional parameter Nh/U is not fixed for a given orogen but changes on a wide range of time scales. As will be shown in the numerical experiments below, any process that affects N, h, oru can impact orographic air flow, precipitation, and rain shadows. The geological record must therefore be interpreted with this nonuniqueness in mind Using Nh/U to Predict Atmospheric Flows [12] Having introduced the nondimensional parameter for flow over topography, its utility in predicting atmospheric ð3þ 2of17

3 Figure 1. Cartoon illustrating the relationship between flow over 2-D topography and the nondimensional parameter Nh/U, where N is the atmospheric stability, h is the terrain relief, and U is the initial horizontal wind speed perpendicular to the orogen. Profile view of flow. Arrows indicate direction of air flow. Dashed line in Figure 1b indicates the upstream zone of flow stagnation associated with high Nh/U flow. flows is now described in terms of previous studies on the subject. A common simplification in fluid mechanics is to consider two-dimensional flow over topography. In this case, the air can flow either upward or in the cross-strike direction, but cannot flow parallel to the strike of the orogen. In 2-D flows with Nh/U 1 (Figure 1a), the terrain is considered hydrodynamically low and the winds can flow directly over the topography with little deflection or deceleration. In these cases, a vertically propagating gravity wave consisting of alternating updrafts and downdrafts develops over the topography and can produce orographic clouds that serve as feeder condensate for orographic enhancement of precipitation [Carruthers and Choulartan, 1983]. The seeder-feeder mechanism of orographic precipitation enhancement has been shown to contribute as much as 80 percent of the total precipitation at high elevations [Reinking et al., 2000]. [13] For Nh/U 1 (Figure 1b), the topography is considered hydrodynamically high and the winds are blocked by the topography. A zone of decelerated air (shown by the dashed line in Figure 1b) forms upstream of the topography acting, in effect, as an extension of the topography over which a secondary vertically propagating gravity wave can form and in which additional clouds form [Smolarkiewicz et al., 1988; Galewsky, 2008]. In these cases, orographic enhancement of precipitation can occur well upstream of the topographic barrier. In 2-D flows in the absence of Coriolis forces, the zone of deceleration and associated secondary wave formation extends far upstream [Baines and Hoinka, 1985; Pierrehumbert and Wyman, 1985] and is not representative of real atmospheric flows. [14] In 2-D orographic flows, the winds must flow either over the topography, stagnate upstream of the terrain, or reverse direction. In 3-D, the winds can flow around the topography, over it, or stagnate upstream, depending on the conditions. In 3-D flow over topography, an additional parameter is the ratio of the along-strike orogen length to the across-strike orogen length, referred to as b, where b =1 represents a bell-shaped mountain, and b = 10 represents a long linear mountain belt. For Nh/U 1, the winds flow over the topography and yield cloud patterns similar to that in 2-D flows (Figure 2a), but for large Nh/U (Figure 2b), a significant fraction of the flow is directed around the terrain, yielding weaker lifting of air parcels and associated condensation, and an upstream shift in condensation and precipitation. For Nh/U > 1 and b = 1 (Figure 2c), the flow splits around the terrain with lifting and cloud development limited to a narrow region near the mountain crest. Even for long 3-D mountain ranges (b 12), however, the magnitude of lifting and condensation of air parcels is less than half that in 2-D flows [Galewsky, 2008]. For 3-D flows with large Nh/U, a pair of vortices develop downstream of the terrain [Smolarkiewicz and Rotunno, 1989] rotating around a vertical axis of rotation. These lee vortices are associated with the development of severe storms that produce hail, flooding, and tornadoes, and, via interaction with larger weather systems, large lee cyclones [e.g., Epifanio, 2003; Lin and Jao, 1995; Crook et al., 1990]. [15] For atmospheric flows in the midlatitudes that persist for more than a few hours, the Coriolis force can be significant. Owing to the atmospheric pressure perturbation that can develop on the upstream side of high Nh/U terrain, the winds can turn and flow parallel to the topographic front (Figure 2d), a feature known as a barrier jet [e.g., Parish, 1982]. In addition, atmospheric lifting is greater on one side of such flows, yielding a marked asymmetry in condensation and precipitation fields [Galewsky, 2008]. In 2-D flows affected by the Coriolis force, the upstream extent of flow deceleration and associated condensation and precipitation is limited to a characteristic scale of Nh/f, where f is the Coriolis parameter (about 10 4 s 1 for midlatitudes). This length scale is called the Rossby radius of deformation [Pierrehumbert and Wyman, 1985]. In 3-D flows affected Figure 2. Cartoon illustrating the relationship between flow over 3-D topography, the nondimensional parameter Nh/U, and the streamwise-to-spanwise terrain aspect ratio b. Map view of flow. 3of17

4 Figure 3. Idealized model configuration used in this study. by the Coriolis force, the upstream extent of flow deceleration and associated upstream condensation is limited by the smaller of either the Rossby radius of deformation or the horizontal dispersion of gravity waves associated with the flow over the terrain, a distance that scales roughly with the along-strike length of the orogen [Epifanio and Durran, 2001]. [16] The nondimensional parameter Nh/U thus encapsulates properties of both the atmosphere and topography. The flow regime, and associated precipitation processes, can switch from the flow over style of small Nh/U to the flow around style of large Nh/U by changing the topography, the atmospheric conditions, or by a combination of the two. This framework has been used for understanding orographic atmospheric flows during individual storms [Marwitz, 1980; Rotunno and Ferretti, 2001; Galewsky and Sobel, 2005] and for understanding climatologically persistent features in the atmosphere [Smolarkiewicz et al., 1988], but has not previously been used for studies in orogenesis. [17] The remainder of the paper is organized as follows: In section 3, a detailed description of the model configuration is presented. In section 4, numerical results are presented, first for two ridges with varying relief. Then the impacts of changing valley and orogen width and rotation are explored. The results are discussed in section 5 and summarized in section Model Configuration [18] Several geological studies [Roe et al., 2002, 2003; Anders et al., 2008] have used linear orographic precipitation models [e.g., Smith and Barstad, 2004] to explore the coupling between climate and landscape evolution. Such models parsimoniously and accurately capture many of the effects of 2-D, low Nh/U conditions on orographic precipitation, but they do not capture the more complex atmospheric flows associated with three-dimensional topography or the effects associated with high Nh/U atmospheric flows. Therefore, in this study, a fully nonlinear atmospheric model is used. [19] The numerical model used in this study is the Advanced Research Weather Research and Forecast Model (WRF-ARW) version 2.2, a numerical weather prediction model which integrates the fully compressible, nonhydrostatic Euler equations for atmospheric motions [Skamarock et al., 2005]. Numerical weather prediction models can be run in real data configurations in order to simulate or forecast specific meteorological events, or they can be run in idealized configurations with prescribed terrain and atmospheric states in order to study orographic flows and precipitation under controlled conditions [e.g., Pierrehumbert and Wyman, 1985; Rotunno and Ferretti, 2001; Colle, 2004]. In the idealized configuration used here, cloud and precipitation processes are parameterized using the WRF Single Moment 6-Phase (WSM6) cloud microphysics scheme [Hong et al., 2004], a relatively complex scheme that accounts for the phase transformations of water vapor, cloud liquid water, ice, snow, graupel, and rain. In line with other idealized studies, no planetary boundary layer, convective, or radiative schemes are used. The 3-D simulations are run on a domain of 450x450 points in the horizontal with a 2-km grid spacing, and 64 unevenly spaced vertical points, with greater resolution near the surface, in a 30 km high domain with open lateral boundaries. [20] The idealized topography for all of the experiments takes the form of two smooth ridges, separated by a valley, oriented with their long axes perpendicular to the x direction (Figure 3). The topography for a single ridge is given by: where hðx; yþ ¼ h0 16 ½1 þ cosðprþš4 ; r 1; 0; otherwise 8 < r 2 x 2þ jyj ðb 1Þa 2; ¼ 4a 4a jyj > ðb 1Þa; : x 2; 4a otherwise where h 0 and b are the mountain height and horizontal aspect ratio, respectively, and a is the length scale for the terrain width. In this study, the maximum terrain height in the different experiments varies between 250 m and 6 km with a = 6 30 km, corresponding to a ridge width of km. The valley width varies from 50 km to 300 km. N is initialized to be uniform throughout the domain and is defined relative to a moist static stability of N m =0.01s 1 or, for some simulations N m = s 1, using the technique described by Miglietta and Rotunno [2005], with an initial relative humidity of 98% and a surface temperature of 16 C. Additional simulations (not shown here) were conducted with a surface temperature below freezing. In these cases, all of the condensate is in the solid phase. Snow can be advected further downstream than rain, an effect that may impact landscape evolution [Anders et al., 2008], but the basic atmospheric flow characteristics described here were found to be consistent in terms of the nondimensional parameter Nh/U. [21] The flow is initialized by gradually accelerating the basic wind from rest over the first hour of integration. Simulations with rotation use a Coriolis parameter f = 10 4 s 1, and rotational effects are introduced after the first ð4þ ð5þ 4of17

5 Figure 4. Surface wind streamlines (thin lines) and column-integrated cloud water (thick lines; contour interval 0.25 mm) at t = 12 h for Nh/U of upstream and downstream ridges, respectively of (a) (0.75, 0.75), (b) (2.25, 0.75), (c) (0.75, 3.0), and (d) (2.25, 3.0), with N = 0.01 s 1 and U = 10 m s 1. hour spin-up. In the simulations presented here, all cloud processes are active from t = 0, and we focus on the period between t = 6 h and t = 12 h. While there is some long-term transience in the flow fields, the basic flow response is established by t = 5 h. [22] This analysis will focus on model output of winds, clouds, and precipitation, with the aim of relating changes in these fields to changes in Nh/U of the upstream and downstream ridges and to the width of the valley between them. As found in previous studies [Jiang, 2003; Galewsky, 2008], the modeled precipitation in 3-D idealized simulations may be very light and is not necessarily representative of the overall potential for orographic enhancement of precipitation during the passage of large-scale weather systems. Therefore, the quantity tracked is the vertically integrated condensate, which is the depth of precipitation that would collect at the surface if all of the cloud water, cloud ice, rain drops, snow, and graupel above that point immediately fell to the surface. This quantity provides a convenient way of visualizing the map view structure of the cloud formations and how they relate to the terrain and the near-surface winds. Furthermore, these orographic clouds can act as feeder condensate for orographic enhancement of precipitation in large-scale weather systems, so this quantity illustrates the potential patterns of orographically enhanced precipitation. 4. Numerical Results 4.1. Fixed Valley and Orogen Width [23] The first set of experiments focuses on the impact of varying the elevation of the two ridges while keeping the valley and orogen widths constant. Figure 4 shows the terrain (in gray scale), the surface wind streamlines, and contours of the column-integrated condensate at t = 12 h after the initialization of the flow. Figure 5 shows profiles across the two ridges and intervening valley of the vertical wind speed (gray scale, cm s 1, where light colors indicate updrafts and dark colors indicate downdrafts) and the horizontal wind speed deficit (contours, m s 1), u0 u, where u0 is the wind speed far upstream of the terrain and u is the local horizontal wind speed at t = 6 h. The horizontal wind speed deficit shows the deceleration that occurs as wind passes over topography from left to right in Figure 5. Figure 6 shows a profile of the cloud liquid water, cloud ice, snow, and graupel mixing ratios (kg of condensate per kg of air) at t = 12 h. In the simulations presented here, most of the condensate consists of cloud liquid water, and the other 5 of 17

6 Figure 5. Profile of vertical winds (gray scale; light colors indicate updrafts, and dark colors indicate downdrafts) and horizontal wind deficit (contours of U U 0,whereUis local wind speed and U 0 =10ms 1 is initial wind speed; contour interval 1 m s 1 )att=6hfornh/u of upstream and downstream ridges, respectively of (a) (0.75, 0.75), (b) (2.25, 0.75), (c) (0.75, 3.0), and (d) (2.25, 3.0). microphysical species are relatively minor. In simulations where the surface temperature is below freezing (not shown), cloud snow and ice are dominant. [24] Figures 4a, 4b, 5a, 5b, 6a, and 6b show the results for a low downstream ridge, with Nh/U =0.75(N =0.01s 1, U = 10 m s 1, and h = 750 m). Figures 4c, 4d, 5c, 5d, 6c, and 6d show the results for a high downstream ridge, with Nh/U = 3.0 (N =0.01s 1, U =10ms 1, and h = 3 km). [25] Figure 4a is the only case in which both ridges have Nh/U < 1. In this case, where both ridges have Nh/U = 0.75, the winds can flow over the terrain with little lateral deflection, setting up a well-developed gravity wave structure over the ridges with an alternating series of updrafts (in light colors) and downdrafts (in dark colors; Figure 5a), with an associated series of clouds in the updrafts (Figure 6a). Relatively low-relief terrain can have a large influence on the atmosphere when the atmosphere is strongly stratified, as it is in these simulations. [26] All of the other cases involve at least one ridge where Nh/U > 1. A prominent feature of these cases is the pair of horizontally oriented vortices that form downstream of the terrain (Figures 4b 4d), a characteristic of high Nh/U flows. For the case with an upstream ridge of Nh/U = 2.25 and a downstream ridge of Nh/U = 0.75, the winds over the valley are nearly stagnant (Figure 5b) with vertical motion and cloud formation restricted to the region upstream of and directly above the high upstream ridge (Figure 6b). [27] With an upstream ridge of Nh/U = 0.75 and a downstream ridge of Nh/U = 3, the winds over the upstream ridge are dominated by flow deceleration associated with the high downstream ridge (Figure 4c). Vertical air motion (Figure 5c) and cloud formation (Figure 6c) here are almost completely controlled by the high downstream ridge, with clouds developing near the top of that ridge and in a zone of lifting upstream of both ridges. [28] Finally, when both ridges are relatively high (upstream Nh/U = 2.25, downstream Nh/U = 3), the large-scale flow is similar to that for a single high ridge, with flow deflection upstream and nearly stagnant winds in the intervening valley (Figure 4d). There is a region of lifting near the downstream ridge crest (Figure 5d) producing clouds along the upper slopes (Figure 6d). [29] These results illustrate how winds can flow over or around the terrain, and how this basic flow response can 6of17

7 Figure 6. As in Figure 5 but for cloud mixing ratio. Cloud liquid water (heavy solid line, contour interval (c.i.) = kg kg 1 ), cloud ice (thin solid line, c.i. = kg kg 1 ), snow (dashed line, c.i. = g kg kg 1 ), and graupel (dotted line, c.i. = kg kg 1 ) mixing ratios at t = 12 h. impact cloud formation. This response is not controlled by relief alone, but by the nondimensional flow parameter Nh/U, which encapsulates aspects of both climate and topography. This point is further illustrated in Figures 7 and 8. The upstream and downstream elevation of the ridges in these simulations is 1.25 km and 1.5 km, respectively, but varying the stability and wind speed changes the flow conditions from low Nh/U conditions (Figures 7a and 8a) to high Nh/U conditions (Figures 7b, 7c, 8b, and 8c) with an associated upstream shift in the condensate and reduction in condensate over the valley. As the flow switches from the flow-over (Figures 7a and 8a) to the flow-around (Figures 7c and 8c) regimes, the total mass of cloud across the valley drops by a factor of 40. This example illustrates how changes in the atmospheric state alone, in the absence of changes in relief, can substantially alter the presence of a rain shadow. [30] Having illustrated some of the basic links between the atmosphere, topography, and cloud formation in this idealized modeling framework, we now consider how these fields change within the valley during uplift of the upstream ridge (Figure 9) while keeping the downstream ridge fixed. We consider two sets of cases: one in which the downstream ridge is fixed at a low Nh/U and another in which the downstream ridge is fixed at a high Nh/U. We perform these calculations for two different values of N in order to illustrate the nondimensional aspects of the problem. Note that halving the stability requires doubling the ridge elevation to maintain the same Nh/U. [31] Figure 10 shows the 6 12 h accumulated precipitation averaged along the valley centerline for a relatively low downstream ridge (Figure 10a; Nh/U = 0.75) and a relatively high downstream ridge (Figure 10b; Nh/U = 3) as a function of the Nh/U value of the upstream ridge for static stability of N =.01 s 1 (solid lines) and N =.005 s 1 (dashed lines). In Figures 10a and 10b, Nh/U = 0 of the upstream ridge means that there is no upstream ridge. In general, the orographic precipitation rates in the valley are low; this is to be expected as orographic effects alone are often unable to produce heavy rain. Nevertheless, the results are illustrative. When the upstream ridge exceeds a threshold of Nh/U 1, the precipitation rates in the valley nearly vanish for both choices of atmospheric stability. This threshold corresponds to the transition in the upstream flow from one in which the winds can travel over the upstream ridge when it is below Nh/U = 1 to one in which the winds are deflected when the upstream ridge exceeds Nh/U = 1. [32] For the low-stability cases (dashed lines), the precipitation amounts are substantially higher than for the highstability cases (solid lines) owing, in part, to the higher 7of17

8 [33] A complementary viewpoint can be obtained by quantifying relative changes in the mass of orographic cloud that forms over the valley as the upstream ridge rises. Because of its potential to serve as feeder condensate in a Figure 7. Surface wind streamlines and column-integrated cloud water (contour interval 0.25 mm) at 12 h for fixed terrain elevations of 1250 m and 1500 m upstream and downstream, respectively, but with varying atmospheric state as labeled. elevation in the low-stability cases. For example, Nh/U = 0.75 at N =0.01s 1 requires a ridge elevation of 750 m, while the same Nh/U value with a stability of N = s 1 requires a ridge elevation of 1500 m. Lifting occurs through a deeper zone for the higher ridge elevation, thereby producing more precipitation and indicating some of the limits to the nondimensionalization of the problem when applied to quantitative precipitation amounts. Figure 8. As in Figure 7 but for profile of cloud mixing ratios at t = 12 h. Cloud liquid water (heavy solid line, c.i. = kg kg 1 ), cloud ice (thin solid line, c.i. = kg kg 1 ). Because of enhanced snow and graupel in Figure 8a, snow contour interval (dashed line) is kg kg 1, and graupel contour interval (dotted line) is kg kg 1. 8of17

9 Figure 9. Cartoon illustrating the geometry of the experiments shown in Figures 10 and 11. larger-scale weather system, cloud mass may be a useful indicator of the potential for orographic enhancement of precipitation. These results are shown in Figure 11, which shows the total condensate mass across the valley, measured from the upstream peak to the downstream peak, along the entire strike of the valley, normalized by the condensate mass upstream of a single ridge over the same upstream distance, plotted as a function of Nh/U of the upstream ridge for a fixed downstream ridge of Nh/U = 0.75 (Figure 11a) and Nh/U = 3 (Figure 11b), with static stabilities of N =.01 s 1 (solid lines) and N =.005 s 1 (dashed lines). This measure provides a means for quantitatively comparing the valley cloud response for different topographic and atmospheric configurations at a given value of Nh/U. [34] For the case with a relatively low downstream ridge (Figure 11a), a break in the slope occurs around Nh/U =1, indicating the effects of the different flow regimes for Nh/U 1 and Nh/U 1 illustrated above. The sharpest decay in downstream cloud mass occurs during uplift of the upstream ridge to Nh/U = 1, corresponding to a ridge elevation of 1 km and 2 km for N =.01 s 1 and N =.005 s 1, respectively. As Nh/U of the upstream ridge rises to 3 (corresponding to a ridge elevation of 3 km and 6kmforN =.01 s 1 and N =.005 s 1, respectively), the change in cloud mass is much less pronounced. This result suggests a potentially important nonlinearity in the development of rain shadows, with most of the aridification occurring during the early stages of surface uplift. [35] The results for the downstream ridge with Nh/U > 1 are shown in Figure 11b, which shows the normalized valley cloud mass versus Nh/U, for a downstream ridge Figure 10. Average 6 12 h accumulated rainfall (mm) in the center of the valley, versus Nh/U of the upstream ridge, for a downstream ridge of (a) Nh/U = 0.75 and (b) Nh/U =3 for an initial atmospheric state of N =0.01s 1 (solid line) and N = s 1 (dashed line). Note that the y axis in Figure 10a spans an tenfold greater range in precipitation than Figure 10b. Figure 11. Normalized valley-integrated cloud mass versus Nh/U of the upstream ridge, for a downstream ridge of (a) Nh/U = 0.75 and (b) Nh/U = 3 for an initial atmospheric state of N =0.01s 1 (solid line) and N = s 1 (dashed line). 9of17

10 Figure 12. Summary cartoon illustrating the different flow regimes explored in this study. Dashed lines indicate regions of flow stagnation. (a) Both ridges have low Nh/U; (b) upstream ridge has high Nh/U, and downstream ridge has low Nh/U; (c) upstream ridge has low Nh/U, and downstream ridge has high Nh/U; and (d) both ridges have high Nh/U. with Nh/U = 3. For Nh/U < 1, there is little change in the cross-valley cloud mass during uplift to Nh/U 1, owing to the upstream stagnation induced by the high downstream ridge. As the upstream ridge rises above Nh/U = 1, it induces more flow deflection and sharply reduced cloud production over the valley. This case will be explored in more detail in the next section. [36] These results are summarized in a cartoon illustrating the different flow regimes (Figure 12). When both ridges have a low Nh/U (Figure 12a), the winds flow over them both with little deflection or deceleration, and condensation is controlled by gravity waves over both ridges. During uplift of the upstream ridge, cloud formation over the valley decreases sharply with increasing Nh/U of the upstream ridge, until Nh/U exceeds 1, (Figure 12b) when the upstream flow switches nonlinearly from a flow-over to a flow-around regime and a zone of decelerated air and precipitation develops upstream of the orogen. The winds in the valley and over the downstream ridge become nearly stagnant and orographic precipitation vanishes within the valley. [37] In the case with a downstream ridge with Nh/U > 1 and an upstream ridge with Nh/U < 1 (Figure 12c), the winds over the upstream ridge and within the valley are controlled by the zone of air stagnation and deflection that form in front of the high downstream ridge. This phenomenon is further explored in the next section. When both ridges have Nh/U > 1 (Figure 12d) winds over the valley are nearly stagnant, and clouds are limited, at most, to a region near the crest of the ridges. When Nh/U of the upstream ridge exceeds 1 and equals or exceeds Nh/U of the down- Figure 13. Surface wind streamlines and column-integrated cloud water (contour interval 0.25 mm) at 12 h for Nh/U of upstream and downstream ridges of (a) (0.25, 0.25), valley width 100 km; (b) (0.25, 0.25), valley width of 200 km; (c) (3, 3), valley width 100 km; and (d) (3, 3), valley width 200 km. 10 of 17

11 Figure 14. As in Figure 13 but for profile of cloud mixing ratio cloud liquid water (heavy solid line, c.i. = kg kg 1 ), cloud ice (thin solid line, c.i. = kg kg 1 ), snow (dashed line, c.i. = g kg kg 1 ), and graupel (dotted line, c.i. = kg kg 1 ) mixing ratios at t = 12 h. stream ridge (not shown), no condensate develops over the valley or the downstream ridge Impacts of Varying Valley Width [38] We now consider some of the impacts of the valley width on the flow and cloud processes. We first focus on two scenarios that are different from the above terrain configurations, one in which both ridges are characterized by Nh/U = 0.25 (Figures 13a, 13b, 14a, and 14b) and another in which both ridges are Nh/U = 3 (Figures 13c, 13d, 14c, and 14d). [39] For low ridges (Nh/U < 1) the condensation is controlled by the primary gravity wave over each ridge (Figures 14a and 14b). When the ridges are relatively close, the primary gravity waves apparently may interact, but not in a way that substantially alters the condensate amounts over the valley. When the Nh/U values of the ridges exceeds 1, the processes of flow blocking and deflection predominate. For valleys narrower than 150 km, the low-level winds in the valley are weak, with some flow reversal. For broader valleys, two sets of lee vortices are seen to develop, one in the valley, and the other downstream of the second ridge. In this case, additional cloud develops over the valley in association with enhanced primary gravity wave development over the first ridge. [40] Although the lee vortices do not impact the precipitation in these idealized simulations, their potential to enhance severe weather when linked with larger-scale weather systems [Epifanio, 2003] makes them important for the current study. As seen in these simulations, when the valley width exceeds the horizontal scale of the vortices, they may develop within the valley (Figures 13d) rather than downstream of the orogen (Figure 13c) and may thus influence precipitation within the valley. [41] Finally, we explore the impact of valley width on the upstream flow stagnation phenomenon illustrated in Figure 12c by varying the width of the valley between the low upstream and high downstream ridges. The results are shown in Figures 15 and 16. When the valley width is less than the width of the zone of upstream flow stagnation (e.g., Figures 15a, 15b, 16a, and 16b), the low upstream ridge is nearly isolated from the larger-scale flow. In these cases, the upstream condensation maximum is not associated with flow over the upstream ridge but is instead related to the lifting and condensation over the upstream decelerated zone. When the valley width exceeds the width of the upstream zone of deceleration (Figures 15c and 16c), however, the flow and cloud processes are more directly coupled to the topography of the upstream ridge. Thus, if the valley width is less than the horizontal scale of flow deceleration, then the valley may be nearly isolated from the 11 of 17

12 Figure 15. Cloud mixing ratio at t = 12 h for upstream and downstream ridges with Nh/U of 0.75 and 3.0, respectively, for valley widths of (a) 75 km, (b) 100 km, and (c) 150 km. Contour interval as in Figure 6. Figure 16. As in Figure 15 but for profile of vertical winds and horizontal wind speed deficit. Contours as in Figure of 17

13 Figure 17. Cartoon illustrating the experimental geometry of the terrain during lateral growth of the orogen for the results shown in Figure 18. larger-scale flow in a kind of forward projecting rain shadow that apparently has not been recognized previously. Conversely, if the valley width is much larger than this horizontal deceleration scale, or if climatic conditions change so that Nh/U of the downstream ridge decreases below unity, then the low upstream ridge and valley respond to the larger-scale flow, and precipitation may be controlled by both ridges. [42] The horizontal scale of flow deceleration has been explored by Pierrehumbert and Wyman [1985] and Epifanio and Durran [2001] and is dependent on the effects of planetary rotation, which can be understood in terms of the Rossby number Ro = U/fL, where U is the horizontal wind speed, f is the Coriolis parameter, and L is the streamwise length scale of the topography. When Ro 1, which can occur for mountain ranges near the equator or for very narrow mountain ranges, rotational effects are not significant and the maximum upstream scale of flow deceleration is roughly b a, or the along-strike mountain width. When Ro 1, rotational effects may be significant, and the maximum upstream scale is given by the smaller of b a or the deformation radius Nh/f Orogen Width [43] Mountain ranges grow in width as well as in relief, and understanding the impact changes in width on airflow and condensation is the goal of this section. Two scenarios are addressed, one in which both ridges have Nh/U < 1 and the other in which both ridges have Nh/U > 1. A cartoon illustrating this configuration is shown in Figure 17. When both ridges are relatively low (i.e., Nh/U < 1, Figure 18, dashed line), widening of the ridges only changes the cloud mass across the valley by a few percent. In contrast, when both ridges are relatively high (Nh/U > 1, Figure 18, solid line), the cloud mass across the valley increases by nearly a factor of three as the upstream range increases in width from 50 km to 250 km, an increase in the width that may be too large for some geological settings, but serves to illustrate the physical process involved. [44] The reasons for this marked difference are illustrated in Figure 19. For the situation with two relatively low ridges (Figures 19a and 19b), the cloud mass over the valley is controlled by the gravity wave associated with the downstream ridge, and while the structure of this wave and associated cloud changes as the upstream ridge widens, the overall amount of cloud across the valley does not change much. For the situation with two relatively high ridges (Figures 19c and 19d), the sharp increase in cloud mass over the valley is due to broadening of the lee wave cloud associated with the upstream ridge. [45] The important result is that, at least for the idealized configuration considered here, increasing the width of a relatively low orogen does not significantly influence the rain shadow, but increasing the width of a relatively high orogen is associated with a marked orographic enhancement of downstream clouds, potentially corresponding to a weakening of the rain shadow via increased seeder-feeder precipitation enhancement in the valley between the two ranges Impacts of Rotation [46] In midlatitude atmospheric flows that persist for more than a few hours, the Coriolis effect can exert an important influence on the wind and associated condensation patterns. Understanding the impact of rotation on the results presented above is the goal of this section. As described above, the controlling nondimensional parameter for rotating flows is the Rossby number, Ro = U/Lf, where U is the horizontal wind speed, L is the width of the mountain range, and f is the Coriolis parameter. For the simulations presented here, we use a typical midlatitude value of f =110 4 s 1. When Ro 1, rotational effects are negligible, but when Ro 1, the flow fields are strongly affected by the Coriolis force. In the simulations presented here, Ro 1, indicating that rotational effects cannot be neglected. [47] Figure 20 shows the surface streamlines and columnintegrated condensate at t = 12 h. Even for Nh/U = 0.75 (Figure 20a), rotational effects induce an asymmetry into the flow and cloud fields. The winds are able to traverse the relatively low ridges, but there is more flow deflection over the northern part of the ridge than in the south, and more cloud develops over the northern flanks of the ridges. When the upstream flow is blocked, the low-level winds are more strongly deflected to the north, with a maximum cloud mass over the northern end of the valley (Figures 20b and 20d). [48] Despite these influences of rotation, the cloud and precipitation fields for the simulations with rotation exhibit Figure 18. Normalized valley-integrated cloud mass versus width of the upstream ridge, for upstream and downstream Nh/U of 0.5 and 0.75, respectively, shown as the dashed line, and 2.5 and 3.0, shown as the solid line. Initial N =0.01s 1 and U = 10 m s of 17

14 Figure 19. Cloud mixing ratio at t = 12 h for simulations with lateral growth of the upstream ridge. Contour interval as in Figure 6. similar relative changes during uplift of the upstream ridge to the nonrotating cases. As in the nonrotating case, the midvalley orographic precipitation vanishes when Nh/U of the upstream ridge exceeds 1 (not shown). The changes in slope in the cloud mass versus upstream Nh/U is similar as well (Figure 21), suggesting that the basic relationships between flow deflection, Nh/U of the downstream ridge, and cloud formation are similar despite the effects of rotation. For the case of a high downstream ridge and a low upstream ridge, the weak decay in cloud mass with uplift of the upstream ridge (Figure 21, solid line for Nh/U < 1) is similar to the nonrotating case (Figure 12c), except that rotation alters the horizontal scale of the decelerated zone as described above. 5. Discussion [49] The motivation for this study was to better understand the links between climate and topography in the development of rain shadows during the growth of mountain ranges, with the aim of providing a better meteorological foundation for the interpretation of geological records. The results of the idealized models show that orographic aridification is not linearly related to changes in relief, but is a nonlinear and nonunique function of topography and atmospheric state. Geological evidence of aridity thus cannot be interpreted in terms of relief alone and cannot by itself provide meaningful quantitative constraints on paleoelevation. Two examples illustrate some of the geological applications of these results. [50] First, in California s Sierra Nevada mountains, [Mulch et al., 2008] used hydrogen isotopes in volcanic glass to argue that the rain shadow associated with the Sierras has persisted since at least 12 Ma and that the Sierras must therefore have existed as a topographic feature with mean elevations comparable to the modern since the Late Miocene. Their results appear to be incompatible with studies suggesting large magnitude surface uplift in the last 3 4Ma[Jones et al., 2004]. The argument of Mulch et al. [2008] is based on a model of orographic precipitation in which isotopic depletion of precipitation scales directly with mountain elevation. In their model, moist air parcels pass directly over the Sierran topographic barrier and become progressively more depleted in heavy isotopes as a result of condensation and rainout. Because air parcels can be deflected around the topographic barrier under high Nh/U conditions, the model of Mulch et al. [2008] is only applicable to low Nh/U conditions. Figures 10a and 11a show that rain shadow strength does not scale directly with mountain elevation; once Nh/U of the upstream ridge exceeds 1, additional increases in Nh/U do not lead to substantially greater aridity downstream. Although the timing of the onset of high Nh/U conditions in the Sierras is not known, such conditions are common in the Sierra Nevada 14 of 17

15 Figure 20. As in Figure 4 but for simulations with rotational effects. today [Parish, 1982; Galewsky and Sobel, 2005; Reeves et al., 2008] and are associated with significant lateral flow deflection. Once the Sierra Nevada were uplifted high enough for Nh/U conditions to develop, additional surface uplift, even in excess of 1 km, may not have had a significant impact on the downstream rain shadow or on the isotopic ratios of precipitation. Therefore, evidence of persistent rain shadow conditions in the lee of the Sierras over the last 12 Ma does not rule out late Cenozoic uplift of the Sierra Nevada. [51] A second example is from the Atacama Desert of northern Chile. The relative roles of global and regional climate change and surface uplift of the Andes in controlling the hyperaridity of the Atacama desert remain unresolved. Rech et al. [2006] interpreted paleosols from the Atacama Desert as recording a change in precipitation from semiarid to hyperarid conditions between 19 and 13 Ma. They linked this aridification to a rain shadow induced by uplift of the Central Andes to elevations in excess of 2 km. Their paleoaltitude estimate was based on modern records that show a significant decrease in precipitation at around 2 km in the Central Andes. Given the variable climate of the middle Miocene [Flower and Kennett, 1993], it is far from clear that modern conditions can be applied to interpreting the ancient record. Indeed, the results shown in Figures 7 and 8 suggest that little or no Andean uplift is required to explain the onset of increased aridity between 19 and 13 Ma. Instead, an enhanced rain shadow at this time could have been caused by the climate changing from a less stable (low Nh/U) to a more stable (high Nh/U) regime, modulated by preexisting Andean topography. Hartley and Chong [2002] and Hartley [2003] dated the onset of hyperaridity in the Atacama to the late Pliocene, about 10 Ma after uplift of the Andes had established a rain shadow, and attributed hyperaridification to enhanced upwelling of the Humboldt current or to global climate cooling rather than to the uplift of topographic barriers. The results of the present study suggest that Pliocene climate change to drier, more stable conditions could have enhanced the Andean rain shadow and that climate variability cannot be easily separated from orographic effects: climate change alone can substantially affect rain shadow strength, even in the absence of surface uplift, and ongoing surface uplift need not produce progressively stronger rain shadows. [52] Case studies of modern mountain storm systems [e.g., Marwitz, 1980] indicate that flow conditions can change from high Nh/U (terrain blocked conditions) to low Nh/U (unblocked conditions) over just a few hours during the passage of a single storm over a mountain range. A statistical description of the stability and winds of storms, and an understanding of how these statistics change with large-scale climate variability, is necessary for extending the highly idealized simulations presented here to geological problems. [53] One of the few studies of the climatology of topographic blocking [Hughes et al., 2009] indicates that about half of the rainfall in Southern California between 1995 and 2006 fell during high Nh/U conditions. The extent to which 15 of 17