1. Introduction and background
One of the most fundamental aspects of mountain weather and climate is the snow line, loosely the boundary between low-elevation rainfall and high-elevation snowfall. The precise location that the snow line intersects the topography during storms is central in determining the navigability of mountain roadways and railways, the risk of landslides and avalanches, and the quality of mountain recreation. Additionally, the snow line modulates the effect of storms on mountain streamflow, since snow often accumulates on the ground whereas rainfall typically produces runoff much more quickly, potentially leading to flooding (White et al. 2002; Hamlet and Lettenmaier 2007; Lundquist et al. 2008). Furthermore, the distribution of snow line elevations among storms controls the seasonal accumulation of mountain snowpack (e.g., Minder 2010b), a crucial water resource for many communities (e.g., Barnett et al. 2005). Changes of just a few hundred meters in the snow line elevation have major impacts. For example, White et al. (2002) modeled that a rise in the snow line of about 2000 ft (610 m) during a storm would triple runoff for three mountainous river basins in northern California. Minder (2010b) modeled that the approximately 200-m rise in the average snow line elevation associated with 1°C of climate warming acts to reduce annual snowpack accumulation in the western Cascade Mountains of Washington by about 15%–18%.
Despite the large impacts of modest changes in the snow line, forecasters and researchers often estimate precipitation phase over mountains using methods that do not account for the myriad processes that control precipitation formation, phase change, and fallout over mountains. For instance, hydrological models often estimate precipitation phase based on surface temperature relationships, ignoring the impact of atmospheric processes aloft (e.g., Anderson 1976; Westrick and Mass 2001; Hamlet et al. 2005; Elsner et al. 2010). Furthermore, weather forecasts and climate studies often infer and predict mountain snow line elevations using vertical temperature profiles either from coarse-resolution models that poorly resolve mountainous topography and its effect on airflow (e.g., Diaz et al. 2003; Arendt et al. 2009; White et al. 2010) or from sounding observations taken tens to hundreds of kilometers away (e.g., Svoma 2011; Minder 2010b). The above, relatively crude, methodologies are used in part because the behavior of, and physical controls on, mountain snow lines are poorly characterized and understood. Motivated by the central role of the snow line in mountain weather and climate, this study aims to use modeling and theory to sharpen this understanding.
a. Terminology
To understand the snow line, a key variable is the 0°C isotherm elevation Z0C, since this is where frozen precipitation starts to melt as it falls. In this study Z0C is defined as the elevation where the atmospheric temperature profile T(z) crosses 0°C (e.g., Fig. 1a).1 The region below Z0C where melting is occurring is referred to as the melting layer.
Schematic illustration of how the main quantities considered in this study are defined. (a) Determination of Z0C from T(z). (b) Determination of ZS from a profile of qs,g(z). (c) Determination of δ0C, δS, and δ from upwind and mountainside values of Z0C (thick dashed line) and ZS (thick solid line). Thin horizontal lines are drawn at the elevation of the upwind Z0C and the mountainside ZS.
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
The snow line is not a sharp boundary since frozen, partially melted, and liquid precipitation may coexist, and thus it may be defined in various ways. This study focuses on the snow line elevation ZS, defined as the elevation where 50% of the frozen hydrometeor mass (quantified by the mixing ratio of snow and graupel: qs,g = qs + qg) falling through Z0C has been lost, presumably by melting into rain (e.g., Fig. 1b).2
Directly measuring ZS aloft is challenging and requires missions with specially equipped aircraft. Consequently, most observations of ZS are indirect, relying on remote measurements using radars. During stratiform precipitation, radar reflectivities often show a strong enhancement in the region of melting, referred to as the radar bright band (BB). This feature occurs as a result of aggregation of hydrometeors, changes in complex index of refraction, and changes in fall speed that occur during melting (e.g., Houze 1993). The BB typically begins just below Z0C and roughly coincides with the melting layer. The bright band elevation ZBB is defined as the elevation in the BB with maximum reflectivity (following, e.g., White et al. 2002, 2010) and is typically the best remotely sensed proxy for ZS available.
This study quantifies mesoscale orographic influences on the snow line by mapping out Z0C and ZS and comparing their values where they intersect the mountain to their upwind values (Fig. 1c). Orographic influences on temperature are quantified by δ0C, the displacement between the mountainside Z0C and its upwind value (Fig. 1c). Likewise, orographic influences on the snow line are quantified as δS, the displacement between the mountainside ZS and its upwind value (Fig. 1c). Understanding δS is relevant to the interpretation of radar datasets that measure ZBB upwind of and over mountains (e.g., White et al. 2002, 2010; Lundquist et al. 2008). Since orographic influences on Z0C may extend farther upwind than the precipitation region, the full orographic influence on the snow line is quantified as δ, the displacement between the mountainside ZS and the upwind Z0C (Fig. 1c). Understanding the behavior of δ is particularly important for relating temperature profiles from soundings and global models to mountain snow lines (e.g., Diaz et al. 2003; Arendt et al. 2009; Svoma 2011; Minder 2010b).
b. Previous work
Some of the earliest observational work to analyze the rain–snow transition over mountains was presented by Marwitz (1983, 1987). These studies examined orographic storms over the northern Sierra Nevada using ground-based C-band radar, special soundings, and in situ aircraft data. Over the windward slopes, during stratiform storms, Z0C was found to descend by at least 400 m (Fig. 2a; see Marwitz 1987), and the radar BB was found to increase several 100 m in depth as it approached the mountain (Fig. 2b; see Marwitz 1983).
Figures from previous observational studies showing drops in Z0C and ZBB. All panels are vertical cross sections along the prevailing wind direction with winds impinging from the left. The terrain profiles are shown along the bottom. (a) Isotherms (°C, with Z0C in red) analyzed from aircraft in situ measurements (flight track shown with thin line) over the northern Sierra Nevada on 25 Feb 1983 (adapted from Marwitz 1987). (b) Radar reflectivity (dBZe, contoured) from RHI scans with the National Oceanic and Atmospheric Administration (NOAA) CP-3 radar over the northern Sierra Nevada on 15 Feb 1980 (from Marwitz 1983). (c) Reflectivity (dBZe, filled contours) from NOAA P-3 airborne radar analysis over the Lago Maggiore region of the Italian Alps on 21 Oct 1999 (from Medina et al. 2005). (d) Reflectivity (dBZe, filled contours) from RHI scans with the S-Pol radar over the Oregon Cascades on 28 Nov 2001 (from Medina et al. 2005). All panels copyright American Meteorological Society.
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
The features described by Marwitz (1983, 1987) are not unique to storms over the Sierra Nevada. This was made evident by Medina et al. (2005), who examined ground-based and airborne radar data from three stratiform storms: one over the Alps and two over the Oregon Cascades. As shown in Figs. 2c and 2d, they found a similar deepening of the BB and a drop in ZBB of several hundred meters over the windward slopes of both of these ranges.
The mesoscale modification of ZS also appears consistently in observations of many storms, distinguishing it as a climatological feature. Lundquist et al. (2008) and Kingsmill et al. (2008) used several years of radar profiler observations to characterize the spatial variability of ZS in the same region of the Sierra Nevada studied by Marwitz (1983, 1987). Lundquist et al. (2008) showed that on average ZBB drops by 73 m between a coastal radar profiler and a profiler at the base of the Sierra (although ZBB may drop even more between the radar and the windward slopes). Kingsmill et al. (2008) found that ZBB above the windward slopes is on average approximately 200 m lower than upwind of the terrain. Furthermore, large storm-to-storm variability was observed: the windward ZBB was found to range from 1 km lower to 200 m higher than the upwind ZBB (Kingsmill et al. 2008).
Few modeling studies have focused in detail on Z0C and ZS over mountains. Wei and Marwitz (1996) conducted 2D simulations of a single orographic blizzard over the Colorado Front Range, focusing on the impact of melting, while Colle (2004) showed a drop in ZS in a number of idealized simulations of flow over 2D ridges.
c. Possible mechanisms
A number of physical explanations have been proposed for the mesoscale structure of ZS observed over mountains. This study will focus on three possible mechanisms.
1) Latent cooling from melting precipitation
The first of these mechanisms relies on spatial variations in cooling of the air by the melting of precipitation Qmelt. During stratiform precipitation over flat terrain, the upper portion of the melting layer is often cooled to near-freezing temperatures by the uptake of latent heat during melting. This localized cooling can lead to an unstable stratification, which in turn induces convective overturning and a deepening of the layer of cooled air and melting (Findeisen 1940). In situ aircraft observations have shown near-isothermal 0°C layers, approximately 200 m thick, atop the melting layer and the radar BB, with unstable stratification below (Stewart et al. 1984). Simple analytic models—considering the energy balance and convective adjustment of a vertical column—have been used to understand how the depth of the 0°C isothermal layer increases with precipitation intensity and duration (Lin and Stewart 1986; Unterstrasser and Zängl 2006).
During storms over the Sierra, Marwitz (1983, 1987) observed soundings with deep near-0°C layers and cited these as evidence that the drop in ZBB (and ZS) over the windward slope is due to spatial variations in Qmelt; he argued that orographically enhanced precipitation rates over the mountain slopes lead to more Qmelt, deeper 0°C layers, and lower ZS than in the air upwind. The modeling studies of Wei and Marwitz (1996) and Colle (2004) also cited Qmelt as important in determining the mesoscale structure of ZS and Z0C.
2) Microphysical melting distance
Another hypothesis, not directly discussed in previous work, is that the drop in ZS can be explained, in part, by spatial variations in the vertical distance over which frozen hydrometeors melt (i.e., Z0C − ZS, hereafter Dmelt), which can vary widely. For instance, in northern California ZBB is on average displaced about 230–237 m below Z0C, but the displacement can range from 122 to 427 m (White et al. 2010). Controls on Dmelt include snowflake size, relative humidity, snow density, and atmospheric lapse rate (Matsuo and Sasyo 1981; Mitra et al. 1990). Mitra et al. (1990) modeled that a snowflake 10 mm in diameter would descend about 100 m farther below Z0C before melting than a 5-mm snowflake, demonstrating that snowflake size is a key control on Dmelt.
The upwind region of an orographic cloud—where vertical velocities and supersaturations are modest—may tend to have frozen hydrometeors that are smaller in diameter and less rimed than those found in the region just over the windward slope—where vertical velocities and supersaturation are larger (Rauber 1992; Garvert et al. 2005). If such an increase in hydrometeor size and riming occurs, it could cause Dmelt to increase toward the mountain by 1) increasing the mass of individual frozen hydrometeors, and thus the amount of time required for melting, and 2) increasing the fall speed of frozen hydrometeors, although this effect will depend on the crystal type and degree of riming (Locatelli and Hobbs 1974; Barthazy and Schefold 2006) as well as the horizontal variations in vertical wind speed.
3) Adiabatic cooling
Adiabatic cooling Qad, which occurs as air parcels are forced to rise over a topographic barrier and expand, could also play an important role (Bell and Bosart 1988; Medina et al. 2005; Kingsmill et al. 2008). If air parcels passing over a mountain have risen and cooled with respect to the air at the same elevation upwind, Z0C and ZS will drop.
Several other processes, not mentioned above, may also modify ZS. For instance, preexisting cold air that is blocked and unable to pass over a mountain could result in a lowering of Z0C and ZS (e.g., Bell and Bosart 1988; Bousquet and Smull 2003; Medina et al. 2005). Steenburgh et al. (1997) showed that cold continental air can be channeled through passes in the Cascade Mountains, in opposition to the synoptic-scale flow, resulting in a localized lowering of Z0C and ZS. Other studies have shown how the geometry of mountain valleys can amplify the tendency for Qmelt to lower ZS (e.g., Steinacker 1983; Unterstrasser and Zängl 2006). For simplicity this study focuses on unblocked flows and mechanisms responsible for determining ZS averaged along the length of a mountain, and thus the preceding mechanisms will be neglected despite their potential importance.
d. Questions
As described above, previous research has made it clear that mesoscale processes over the windward slopes of mountain ranges regularly act to lower ZS relative to the upwind value by several hundred meters. While a number of physical mechanisms have been suggested, no study has yet considered these mechanisms together and in depth, assessed their relative importance, examined their interactions, or used them to explain the storm-to-storm variability observed in the climatology.
This study uses a numerical model of mountain airflow and precipitation combined with theory to address the following:
How do Dmelt, Qmelt, and Qad interact to determine ZS on a mountainside?
How do upwind conditions and topographic form cause the mesoscale structure of ZS to vary storm to storm, with climate, and between mountains?
How robust are predictions of ZS to the choice of model configuration?
2. Numerical model
To represent the various dynamic, thermodynamic, and microphysical processes influencing ZS requires a full mesoscale numerical weather prediction model capable of simulating all these processes and their interactions. Accordingly, the Weather Research and Forecasting (WRF) model (version 3.0.1, Skamarock et al. 2008) is employed to conduct experiments. Since these experiments are focused on isolating and understanding the physical mechanisms that control ZS (as opposed to simulating ZS for a specific storm), the model is used in a semi-idealized configuration, with simplified topography and incoming flow characteristics.
Third-order Runge–Kutta time stepping is used, with fifth-order horizontal and third-order vertical advection. The boundary conditions are open in the x direction and periodic in the y direction. The time step is 5 s for advection and physics, and 
Setup for the WRF simulations. (a) Model domain showing the control terrain profile with a thick line. The location of the troposphere, stratosphere, and damping layer are denoted, as are the initial atmospheric conditions for the control simulation; (b) Skew T–logp plot showing soundings of temperature (solid) and dewpoint (dashed) used to initialize the control simulation.
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
The vertical discretization consists of 201 levels of terrain-following η coordinate, with spacing Δz varying from 17 m near the surface to about 450 m at the base of the damping layer, and up to 2 km at the model top at z = 25 km. The horizontal grid spacing Δx = Δy is 2 km, and there are 1250 grid points in x and 3 in y, yielding a domain 2500 km in x and 6 km in y (Fig. 3a).
The Coriolis force is applied to perturbations from the initial wind profile, which is assumed to be in geostrophic balance. This is equivalent to subtracting a geostrophically balanced reference state from the governing equations, and follows Colle (2004) and Kirshbaum and Smith (2008). The f-plane approximation is made, with f = 10−4 s−1. The Coriolis force is not applied to normal velocities at the open lateral boundaries.
For the control simulation, cloud and precipitation microphysics are parameterized with the Thompson et al. scheme (Thompson et al. 2008), a bulk mixed-phase scheme that predicts the number concentration of cloud ice and the mixing ratios of water vapor, cloud liquid water, cloud ice, rain, snow, and graupel. Unique features of the scheme include a nonspherical shape assumed for snow, a snow size distribution represented with the sum of exponential and gamma functions, and an acceleration of snow and graupel fall speeds in the melting layer to mimic partially melted hydrometeors. This scheme is used because it is one of the most sophisticated schemes available in WRF, its sensitivities have been extensively documented for the problem of orographic precipitation (e.g., Thompson et al. 2004, 2008; Lin and Colle 2009), and it has proved capable of accurately simulating mountain snowfall (Ikeda et al. 2009). A positive-definite limiter (Skamarock and Weisman 2009) is applied during the advection of microphysical variables to eliminate spurious moisture sources that can bias precipitation simulations (e.g., Hahn and Mass 2009; Lin and Colle 2009).
Turbulent mixing is parameterized using a prognostic equation for turbulent kinetic energy, which determines eddy viscosities. Cumulus convection is presumed to be resolved because of the fine grid used, and thus it is not parameterized. Parameterizations for boundary layer mixing, land surface processes, and radiation are all omitted.
Before analysis, hourly output from WRF is linearly interpolated from the model’s terrain-following coordinate onto a regularly spaced Cartesian grid. Results presented are 6-h averages beginning after the simulations reach an approximate steady state (at 42 h or later). Since the open upwind boundary condition does not mandate a steady incoming flow field, some modest drift occurs in the upwind conditions (e.g., |ΔU| ≤ 0.3 m s−1, |ΔTs| ≤ 0.3°C, |ΔNm| ≤ 0.0003 s−1). (This drift has only a modest influence on ZS; however, results in Figs. 13–18 reference the upwind conditions during the analysis period instead of the initial conditions to account for this drift.)
3. Results: Physical mechanisms
Results from a control simulation are now presented and analyzed in detail to diagnose and quantify the physical mechanisms that control ZS on the mesoscale.
a. Control simulation
For the control simulation, the initial sounding is characterized by a troposphere with vertically uniform wind U of 15 m s−1, Ts of 5°C, Nm of 0.005 s−1, and RH of 95% (Fig. 3a). A skew T–logp plot of the control sounding is shown in Fig. 3b. The upwind Z0C of this sounding is about 880 m. Sounding parameters were chosen such that the moist nondimensional mountain height (Nmhm)/U is 0.5, small enough that the flow should be unblocked and rise over the barrier (Pierrehumbert and Wyman 1985; Jiang 2003; Galewsky 2008). The Rossby number U/(fa) is 3.75, indicating that rotational effects will play a modest role. The Coriolis force will act to limit the upwind influence of the topography to roughly a deformation radius (Nmhm)/f = 75 km (Pierrehumbert and Wyman 1985).
Steady-state winds and cloud water fields from the control simulation are shown in Fig. 4. Cross-mountain winds u are decelerated as the flow approaches the barrier, and along-mountain flow υ develops as the winds are turned to the left because of the decreased Coriolis force (Fig. 4a). The u winds are everywhere positive, indicating that all flow passes over the ridge. The lack of surface friction allows strong near-surface winds (>20 m s−1 over the crest) to develop. Ascent over the mountain produces vertical winds w exceeding 35 cm s−1 (Fig. 4b).
Wind and cloud for control simulation. (a) Cross-mountain winds (shaded, with thick gray line at u = U = 15 m s−1) and along-mountain winds (contoured every 1 m s−1, with thick line at υ = 0). (b) Vertical winds (contoured every 5 cm s−1, with thick line at w = 0) and cloud liquid water mixing ratio (qc, shaded).
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
This vertical motion leads to supersaturation and condensation of cloud through a 4-km-deep region, apparent in the cloud water mixing ratio qc plotted in Fig. 4b. Cloud ice qi is generated above z = 5 km and grows by deposition to form snow qs (Fig. 5a). Below about 2 km, high qc leads to riming of snow to form graupel qg. At low levels the snow and graupel melt to form rain qr. The surface precipitation rates, shown in Fig. 5b, reveal that the transition from rain to mostly snow with some graupel occurs over a few hundred meters of elevation and less than 20-km horizontal distance. The melting layer is detailed in Fig. 6, which shows that Z0C and ZS descend as the air approaches the terrain. Quantitatively, the mesoscale modifications of ZS and Z0C are δ0C = 142 m, δS = 221 m, and δ = 267 m.
(a) Mixing ratios of cloud and hydrometeor species for control simulation; qc is shaded every 0.05 g kg−1, starting at 1 × 10−5 g kg−1. Hydrometeor mixing ratios are contoured every 0.1 g kg−1, starting at 1 × 10−3 g kg−1: rain (qr, blue), snow (qs, green), graupel (qg, red), and cloud ice (qi, cyan). (b) Surface precipitation rates (at z = h) for total precipitation (pcp), rain (pcpr), snow (pcps), and graupel (pcpg). Also shown are the frozen precipitation rate (pcps,g) at z = Z0C and the terrain profile (h, gray).
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
Detail of melting region. Isotherms are contoured with thin lines every 1°C. Also shown are Z0C (thick dashed line), ZS (thick solid line), and qc (shaded, as in Fig. 5a). The mesoscale modification of Z0C and ZS are noted (δ0C, δS, and δ).
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
These basic results are only weakly sensitive to model horizontal and vertical resolution. For example, simulations with Δx = 6, 18, and 32 km (but maintaining the mountain’s full height) yield δ values within 15% of the control value, and a simulation with only 91 vertical levels (Δx ~ 40 m near the surface) yields a δ value within 8% of the control.
Figure 6 offers some initial insights into the mechanisms. Isotherms in a deep layer descend toward the mountain. Since this descent occurs well away from the melting region, where air parcels have not been cooled by Qmelt, it is clear that another process—such as Qad—is playing a role in lowering Z0C. Furthermore, the lack of a substantial modification of the temperature structure below Z0C (e.g., the lack of a near-isothermal layer) also suggests that Qmelt is not pronounced. Also of note is the much larger drop in ZS as compared to Z0C, indicating the importance of Dmelt variations.
Schematic diagram showing how the contributions of various physical processes to δ are quantified in the WRF simulation. Thick black lines represent Z0C (dashed) and ZS (solid) from a control simulation, while thick gray lines represent Z0C and ZS from a simulation where Qmelt is suppressed. Denoted on the right are contributions from Dmelt 
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
b. Effect of microphysical melting distance
The contribution of spatial variations in frozen hydrometeor melting distance 
Profiles of qs,g at x = −60 km from WRF control simulation (solid) and simplified column model (dashed) as a function of distance below Z0C. Horizontal lines show the ZS associated with the two qs,g profiles.
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
Let us hypothesize that, for a given environmental profile, the essential processes determining Dmelt are the rates of sedimentation and melting of hydrometeors as determined by the precipitation rate at Z0C and by the mean vertical wind and temperature lapse rate below. This implies that other microphysical tendencies (e.g., collection, sublimation/deposition) and other environmental conditions (e.g., the mixing ratios of cloud ice and liquid water) are only of secondary importance in setting Dmelt.
To test this hypothesis, a model of the precipitation in a single column of the melting layer is constructed. Hydrometeor mixing ratios qs, qg, and qr are stepped forward in time using a simplified version of the Thompson et al. (2008) scheme. This simplified scheme is formulated as described in Thompson et al. (2008) and configured in WRF V3.0.1, except that 1) all microphysical tendencies are ignored except sedimentation and melting; 2) an exponential size distribution for snow is assumed (as in Thompson et al. 2004) instead of the generalized gamma distribution (as in WRF and Thompson et al. 2008); and 3) the “boosting” of snow terminal velocity based on diagnosed degree of riming is omitted. The spatial domain ranges from Z0C to the surface, and the vertical grid spacing is 10 m. The temperature profile is assumed to be steady in time and is prescribed using the mean lapse rate from the output of the control WRF run at x = −60 m (Γ = 5.9°C km−1). The air is assumed to be saturated with respect to liquid water, and a uniform vertical velocity averaged from the WRF simulation (w = 0.24 m s−1) is prescribed. The initial condition is zero hydrometeor mixing ratios, except at the upper boundary where the values from the WRF simulation are prescribed and held constant. The model is run to a steady state.
Results are plotted in Fig. 8 (dashed lines). The column model and WRF profiles of qs,g match well, as do the predicted values of ZS. These results support the hypothesis that, at least over the middle of the windward slopes, Dmelt is determined mainly by the precipitation atop the melting layer and gross environmental characteristics within.
To illustrate the sensitivity of Dmelt to precipitation rate, the column model is applied again, using the same environmental conditions (i.e., w, Γ) but various mixing ratios, and hence precipitation rates, prescribed at Z0C. Figure 9 shows that for very weak precipitation Dmelt is about 60 m, but, as precipitation increases, Dmelt reaches beyond 300 m. Where ZS intersects the terrain in the WRF simulation, Dmelt is 148 m (Fig. 6) and the frozen precipitation rate at Z0C is 3.5 mm h−1 (Fig. 5b). The column model predicts a very similar Dmelt (144 m) for the same precipitation rate (Fig. 9). In WRF, Dmelt approaches zero at the upwind edge of the snowfall, where precipitation is very weak (at about x = −90 km in Fig. 6). This contrasts with a 60-m Dmelt for weak precipitation in the column model (Fig. 9). This discrepancy may be due to the different size distribution assumptions in the column model and WRF.
Sensitivity of column model Dmelt to variations in pcps,g (=pcps + pcpg) at Z0C. All simulations use the same lapse rate and w as in Fig. 8.
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
The above comparisons of the column model and WRF suggest that, by modulating Dmelt, spatial variations in orographic precipitation enhancement may contribute significantly to lowering ZS over the windward slopes. The component of δ attributable to Dmelt variations is quantified as 
c. Effect of latent cooling
To quantify the role of melting-induced cooling 
(a) As in Fig. 6, but Z0C and ZS are also shown for the experiment in which Qmelt is suppressed (dashed), and δ0C, δS, and δ from the no-Qmelt experiment are denoted. (b) Back-trajectory analysis for the control simulation. One-hour air parcel back trajectories ending at Z0C are plotted (solid black lines, with circles every 10 min). Also shown are qs,g (shaded every 0.1 g kg−1, starting from 1 × 10−5 g kg−1) and Z0C (dashed black line).
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
The modest contribution of Qmelt is notable, since Qmelt has been suggested as the principal cause for the lowering of ZS by several previous studies (e.g., Marwitz 1983, 1987; Colle 2004). Why is Qmelt ineffective in substantially lowering Z0C and ZS in this simulation? An important time scale in the problem is the total time air parcels spend in the melting region, since this limits how much melting may cool the air. To characterize the residence time of air parcels in the melting region, 1-h back trajectories, calculated for air parcels ending at various locations along Z0C, are plotted in Fig. 10b. Also plotted are Z0C and qs,g, since only regions below Z0C with substantial qs,g should be associated with significant melting and cooling. The trajectories reveal that, because of the strong near-surface winds and the limited horizontal extent of the melting region, air parcels spend only about 10 min being cooled by melting. This is insufficient time for melting to cool the parcels substantially. Supporting this interpretation, application of the simple model of Lin and Stewart (1986) [as modified by Unterstrasser and Zängl (2006)], using the environmental lapse rate and precipitation rate from the WRF simulation, predicts a very shallow 0°C layer of only 15 m when a 10-min precipitation duration is used.
d. Effect of adiabatic cooling
The contribution from adiabatic cooling 
Schematics showing how δ0C is determined by Qad in the parcel model. (a) x–z section showing environmental temperature profile and flow along lowest streamline. (b) Idealized profiles of environmental temperature (with Γ) and parcel temperature (with Γd and Γm), showing how lapse rate differences lead to δ0C. (c) Profiles showing how a decrease in Ts decreases δ0C. (d) Profiles showing how an increase in Γ (and decrease in Nm) decreases δ0C.
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
This simple parcel model can be used to understand how upwind stratification and temperature affect δ0C. First, note that, as long as the environmental lapse rate Γ is less than Γm and Γd, a parcel rising over the mountain reaches Z0C at an elevation lower than the upwind sounding, and Qad acts to lower Z0C. For cooler temperatures, adiabatic cooling should lower Z0C less, since parcel and environmental temperatures diverge less before reaching 0°C (Fig. 11c). Likewise, larger Γ (smaller Nm) should lead to decreased lowering of Z0C, since parcel and environmental temperatures diverge less quickly (Fig. 11d).
Values of δ0C calculated with the parcel model are shown for a range of Ts and Nm in Fig. 12. This shows that δ0C is positive everywhere except at very low values of 
Results from idealized parcel model showing δ0C (contoured every 25 m) as a function of Ts and 
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
Revisiting the WRF results, the impact of Qad is apparent at all elevations in the isotherms shown in Fig. 6. Ascent of unsaturated air parcels, upwind of the orographic cloud, results in a downward slope of isotherms since Γd > Γ. As the air reaches saturation at the edge of the cloud, condensation occurs, releasing latent heat, and air parcels begin to rise with lapse rate of Γm. This change in parcel lapse rate results in an abrupt change in the isotherm slope, but since Γm is also greater than Γ, adiabatic cooling continues to force the isotherms to descend.
To relate the simple parcel model to the control WRF simulation, the δ0C from the no-Qmelt simulation is considered, since the parcel model does not attempt to account for Qmelt. For the upwind conditions associated with the WRF control simulation the parcel model predicts a δ0C of 107 m (see gray circle in Fig. 12). This agrees fairly well with the δ0C without Qmelt, 
4. Results: Sensitivity experiments
To understand how mesoscale controls on ZS vary among different storms, climates, and mountain ranges a series of sensitivity experiments are conducted. In each experiment the same setup as the control simulation is used, but a single aspect of either the incoming flow or the terrain geometry is altered. Since airflow and precipitation are most similar between 2D and 3D for unblocked flows (e.g., Epifanio and Durran 2001; Galewsky 2008), all but one of the following experiments are designed to keep (Nmhm)/U ≤ 1.
a. Temperature
To test sensitivity to temperature, additional simulations are made with warmer (7°C) and colder (3°C) values of Ts, with and without Qmelt. Figures 13a and 13b show cross sections with qc, Z0C, and ZS for these simulations. Since Nm is held constant, the Ts increase raises the upwind Z0C (from 0.50 to 1.24 km). Figure 13c shows the surface precipitation rates (pcp). As Ts is increased, pcp increases because of enhanced moisture flux, although this increase is moderated by microphysical effects (e.g., Kirshbaum and Smith 2008).
Results from Ts simulations. (a) Cross section for Ts = 3°C: qc (shaded every 0.05 g kg−1), Z0C (dashed line), and ZS (solid line). (b) As in (a), but for Ts = 7°C. (c) Surface precipitation rates (see key) and terrain profile (gray). (d) Values of δS, δ0C, and δ as a function of Ts (see key). (e) Contributions of 
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
Figure 13d shows that δ0C, δS, and δ all increase with increasing Ts, and Fig. 13e quantifies the contributions to δ of 
If a similar dependency of δ on Ts exists in nature it could have important consequences for regional climate change in mountainous areas. As Ts is warmed in these simulations, Z0C rises by 742 m upwind of the mountains. However, because of the increase in δ, ZS only rises by 530 m on the mountainside. Thus, mesoscale processes over the mountain act to buffer the impact of warming on ZS, reducing by 29% the rise in ZS that would be expected by only considering the effects of warming on the upwind Z0C.
b. Stratification
To test the effect of stratification, simulations are made with smaller (Nm = 0.002 s−1) and larger (Nm = 0.007 s−1) moist stabilities (Fig. 14). As Nm is increased, the upwind Z0C is increased since Γ is decreased (Figs. 14a,b). Changes in Nm affect both the upwind water vapor flux profile and the pattern of vertical motion over the mountain, and the effect on the precipitation pattern is complex (Fig. 14c). For instance, surface precipitation shifts upwind as Nm increases from = 0.002 to 0.005 s−1, due to a greater upwind tilt with height of the gravity wave vertical velocities (e.g., Smith and Barstad 2004; Colle 2004). However, further increases in Nm, from 0.005 to 0.007 s−1, result in gravity wave descent aloft that suppresses the formation of qi above the windward slope (not shown) and drastically reduces pcp over much of the mountain (Fig. 14c).
(a) As in Fig. 13a, but for Nm = 0.002 s−1 simulation. (b) As in (a), but for Nm = 0.007 s−1. (c) As in Fig. 13c, but for Nm simulations. (d),(e) As in Figs. 13d,e, but for Nm experiments.
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
Figure 14d shows that δ increases with Nm. This is largely attributable to increases in δ0C due to 
c. Wind speed
To test the effect of wind speed, simulations are made with slower (U = 10 m s−1) and faster (U = 20 m s−1) cross-mountain winds (Fig. 15). Since the moisture flux scales with U, changes in wind speed have a large impact on precipitation intensity, with stronger winds yielding heavier precipitation rates (Fig. 15c). Increasing U from 10 to 15 m s−1 increases pcp everywhere. In contrast, as U is increased further, to 20 m s−1, the time scale associated with cross-mountain advection becomes comparable with the microphysical time scales required for precipitation formation and fallout, resulting in a downwind shift of the pcp pattern (e.g., Jiang and Smith 2003; Smith and Barstad 2004; Colle 2004).
(a) As in Fig. 13a, but for U = 10 m s−1 simulation. (b) As in (a), but for U = 20 m s−1. (c) As in Fig. 13c, but for U simulations. (d),(e) As in Figs. 13d,e, but for U experiments.
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
Increasing U from 10 to 15 m s−1 increases δ0C, δS, and δ, while increasing U from 15 to 20 m s−1 leads to declines (Figs. 15a,b,d). For U = 20 m s−1, ZS is not defined at some points near the mountain because strong updrafts keep all snow above Z0C (Fig. 15b).
The initial increase in δ, from U = 10 to 15 m s−1 is due to increases in 
d. Relative humidity
To test the effect of humidity, simulations are made with RH ranging from 85% to 98% (Fig. 16). As RH is increased, both the intensity and extent of precipitation increase, since the moisture flux is increased and less lifting is required to cool the air to saturation (Fig. 16c).
(a) As in Fig. 13a, but for RH = 85% simulation. (b) As in (a), but for RH = 98%. (c) As in Fig. 13c, but for RH simulations. (d),(e) As in Figs. 13d,e, but for RH experiments.
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
Increasing RH leads to strong decreases in δ0C and δ, whereas δS is more weakly affected (Figs. 16a,b,d). Variations in 
e. Mountain width
To test the effect of mountain width, simulations are made with a ranging from 15 to 65 km (Fig. 17). As a increases, precipitation becomes more broadly distributed and less intense (Fig. 17c). Although intensity decreases, the total precipitation over the windward slopes increases by about 50% as a varies from 15 to 65 km. This occurs because the increased time scale for cross-mountain advection (relative to microphysical conversion and sedimentation time scales) allows more water vapor to condense and fallout before being advected into the lee (e.g., Jiang and Smith 2003; Smith and Barstad 2004; Colle 2004).
(a) As in Fig. 13a, but for the a = 15 km simulation. (b) As in (a), but for a = 65 km. (c) As in Fig. 13c, but for a simulations. (d),(e) As in Figs. 13d,e, but for a experiments.
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
Figures 17a, 17b, and 17d show that δS, δ0C, and δ all increase with a. This behavior comes from variations in 
f. Mountain height
To test the effect of mountain height, simulations are made with hm ranging from 1.2 to 3 km (Fig. 18). As the mountain becomes taller, precipitation becomes more intense because of increased lifting of the incoming flow (Fig. 18c).
(a) As in Fig. 13a, but for hm = 1.2 km. (b) As in (a), but for hm = 3 km. (c) As in Fig. 13c, but for hm simulations. (d),(e) As in Figs. 13d,e, but for hm experiments.
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
As hm is increased there is surprisingly little coherent change in δS, δ0C, or δ (Fig. 18d). None of the three mechanisms shows a strong hm dependence (Fig. 18e). While increased precipitation rates should act to increase 
g. A preliminary look at the effects of blocking
The above experiments have avoided the blocked regime, where 2D simulations produce airflow and precipitation distinct from 3D simulations, even for very long ridges (Epifanio and Durran 2001; Galewsky 2008). As (Nmhm)/U increases, low-level flow deflection around mountains becomes substantial in 3D flows. This deflection reduces ascent over the terrain, moderates precipitation rates, and spreads precipitation upwind (e.g., Jiang 2003; Galewsky 2008). Since this flow deflection can only be properly represented in 3D simulations, the generalizability of 2D results in the blocked regime is questionable at best.
Nevertheless, a single 2D simulation in the blocked regime is conducted. This is used only as a tool to investigate qualitatively the effects of airflow deceleration and blocking on ZS. The simulation is conducted with hm = 3 km, Nm = 0.005 s−1, and U = 10 m s−1. This gives (Nmhm)/U = 1.5, indicating favorable conditions for flow deceleration and splitting. Since the flow is more transient in this regime, results presented are averaged only over a 2-h period: t = 86–87 h.
Results show that cross-mountain flow is severely decelerated over the lower windward slopes to less than 2 m s−1 (Fig. 19a). The flow deceleration is much stronger than that found in the hm = 3 km case from the previous section (not shown) because of the decreased U and consequently increased (Nmhm)/U. The weak low-level winds lead to large residence times for air parcels in the melting region, allowing for substantial Qmelt that destroys the low-level stratification, and produces convective cells at the foot of the mountain with their tops in the melting layer (Findeisen 1940; Szyrmer and Zawadzki 1999). The role of melting in producing these cells is confirmed by examining a simulation without Qmelt, which exhibits no convection (Fig. 19b). Low-level flow deceleration also results in lifting, cloud, and precipitation far upwind of the mountain, and the convective overturning leads to localized maxima in the microphysical fields (Fig. 19c).
(a) Results from simulation with hm = 3 km, Nm = 0.005 s−1, U = 10 m s−1, and (Nmhm)/U = 1.5 averaged from t = 86 to 87 h, with u winds (shaded, with thick line at U = 10 m s−1), and w winds (contoured every 5 cm s−1, with thick line at w = 0, and negative values contoured in red). (b) As in (a), but for simulation with Qmelt suppressed. (c) Microphysical mixing ratios, as in Fig. 5a. (d) Detail of melting region with qc, ZS, and Z0C, for simulations with and without Qmelt, as in Fig. 10a.
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
Figure 19d shows that ZS and Z0C descend sharply in this simulation, dropping by about 50% more than in any of the previous experiments (δ = 603 m). Much of this descent is eliminated when Qmelt is suppressed (Fig. 19d). Thus, cooling from melting, and the subsequent downward mixing of the cooled air by the induced convection, plays a crucial role in producing the large δ found in this case. While these results suggest that flow blocking and deceleration may enhance 
5. Results: Microphysical uncertainties
An array of studies have documented how the simulated amount, pattern, and phase of orographic precipitation depends on the microphysical parameterization chosen and how it is applied (e.g., Colle and Zeng 2004a,b; Thompson et al. 2004; Colle et al. 2005; Grubišić et al. 2005; Lin and Colle 2009; Jankov et al. 2009). The impact of the microphysical scheme on these results is explored by repeating the control simulation using four other microphysical parameterizations available in WRF. All are bulk schemes—with assumed size distributions for precipitation and cloud particles—that predict cloud liquid water, cloud ice, rain, snow, and graupel separately. These include the default WRF v3.0.1 configurations of the following schemes: Purdue–Lin (Chen and Sun 2002), WRF single-moment six-phase (WSM6) (Hong et al. 2004; Hong and Lim 2006), the Goddard Cumulus Ensemble (Tao et al. 2003), and Morrison et al. (Morrison et al. 2005, 2009). Detailed discussions of the differences between these are found in Skamarock et al. (2008), Lin and Colle (2009), and Jankov et al. (2009).
The top panels in Fig. 20 show how the predicted mixing ratios vary among the schemes. All of these schemes simulate more qi aloft as compared to Thompson et al. In the WSM6 simulation, qc is confined to much lower levels and shows a strong enhancement near Z0C. Like Thompson et al., Goddard and WSM6 produce a mixture of snow and graupel, whereas Purdue–Lin produces nearly all graupel and Morrison et al. produces all snow. These differences in the relative abundance of qs and qg are consistent with the results of previous studies (e.g., Lin and Colle 2009; Jankov et al. 2009).
Results from simulations with different microphysical parameterizations. (top) Mixing ratios (qc, qr, qs, qg, and qi) as in Fig. 5a, except qi is contoured every 0.025 g kg−1. (bottom) Detail of melting region showing Z0C (dashed), ZS (solid), and qc as in Fig. 6.
Citation: Journal of the Atmospheric Sciences 68, 9; 10.1175/JAS-D-10-05006.1
All the simulations exhibit a drop in both Z0C and ZS over the windward slopes (see bottom panels of Fig. 20). They produce a fairly similar δ0C (all δ0C values are within 27% of the mean δ0C across the five schemes). Thus, it appears that 
The structure of ZS is much less consistent across the various runs. The Purdue–Lin and WSM6 simulations give substantially larger δ than the control simulation, but show a similar ZS structures to the control, with Dmelt increasing as the mountain is approached. In contrast, for both the Goddard and the Morrison et al. simulations ZS does not diverge from Z0C as the mountain is approached.6 Accordingly, in these cases 
Observations (e.g., Stewart et al. 1984; Mitra et al. 1990; White et al. 2010) broadly suggest that the very small Dmelt found in the Goddard and the Morrison simulations are unrealistic. However, other limitations may be common to all of the schemes. For instance, melting snowflakes have shapes, fall speeds, and other characteristics that are distinct from those of rain or snow (e.g., Mitra et al. 1990), yet none of these schemes treats melting snow as a separate microphysical species. Furthermore, the process of melting tends to convert the smallest snowflakes into rain first, eliminating the lower end of the snow size spectrum, yet these schemes all have size distribution assumptions that do not allow this to occur. Extensive comparisons with observations (e.g., Stewart et al. 1984; Jankov et al. 2009) and more sophisticated models of melting microphysics (Szyrmer and Zawadzki 1999; Theriault et al. 2006) are required to identify which schemes most faithfully represent ZS. Until such work is completed 
6. Discussion
a. Limitations
While the semi-idealized WRF simulations produce mesoscale drops in ZS similar to the climatological mean values observed in the Sierra (e.g., Kingsmill et al. 2008), only the preliminary blocked flow simulation produces a lowering of ZS that approaches the extremely large drops (~1 km) occasionally found in the climatology (Kingsmill et al. 2008) and in case studies (e.g., Marwitz 1987; Medina et al. 2005). This suggests that an important process responsible for the behavior of ZS has been neglected in this study. This could be an effect of blocking but also could relate to other omitted aspects of real orographic storms including boundary layer fluxes, 3D airflow, transient forcing of vertical motion by fronts and synoptic-scale lifting, and small-scale terrain variability.
The lack of surface fluxes and the effects of boundary layer mixing may have important implications, since they may strongly alter the low-level winds and stratification. In particular, very strong surface winds occur in the above simulations because of the use of a free-slip bottom boundary condition. Slower, more realistic low-level winds could increase the residence time of air parcels in the melting layer and produce large 
Additionally, this study has not explored the effects of fully 3D airflow patterns. A 3D version of the control simulation with a finite-length ridge (not shown) yields similar results in terms of the magnitude of δ and the responsible processes (Minder 2010a). Still, further work is required to accurately represent the 3D effects of airflow blocking for (Nmhm)/U ≥ 1.
b. Implications
The simulation by WRF of δS values comparable with observations (e.g., Lundquist et al. 2008; Kingsmill et al. 2008) suggests that current mesoscale models are capable of capturing the dominant mesoscale controls on ZS. In particular, 
The temperature dependence of δ indicated in Figs. 13d and 13e suggests that mesoscale processes may play an important role in shaping the impacts of climate warming on mountain snowfall. The important role of various mesoscale processes in controlling ZS argues for the use of high-resolution dynamical models in investigations of regional climate. For instance, hydrological models that investigate changes in snowpack by assuming regionally uniform warming and surface temperature thresholds for snow accumulation (e.g., Hamlet and Lettenmaier 1999; Casola et al. 2009; Elsner et al. 2010) may miss important mesoscale influences on mountain snowfall.
7. Summary and conclusions
Observations show that a mesoscale lowering of the 0°C isotherm Z0C and the snow line ZS over the windward slopes is a pervasive feature of mountain weather and climate (Marwitz 1987; Medina et al. 2005; Lundquist et al. 2008; Kingsmill et al. 2008) and is large enough to have important implications for mountain hydroclimate. Three physical mechanisms appear to be responsible for this behavior: 1) under stable stratification, adiabatic cooling of rising air results in colder temperatures, and lower Z0C, over the mountain than upwind; 2) orographic enhancement of precipitation over the windward slopes results in a localized cooling of the air by melting of frozen hydrometeors that lowers Z0C relative to the upwind; and 3) orographic enhancement of precipitation over the windward slopes results in frozen hydrometeors that descend farther below Z0C before melting into rain than in the upwind.
This study has used semi-idealized simulations with a mesoscale numerical atmospheric model to diagnose the processes responsible for determining ZS on the mesoscale, to quantify their relative importance, and to investigate their sensitivities to atmospheric conditions and terrain geometry. These simulations have reproduced a mesoscale lowering of ZS similar to that found in observations. Results reveal that all three of the above processes may play an important role in determining δ.
Contributions from the various processes change depending on the mountain, storm, or climate. For long ridges, large drops of ZS are favored by flows with strong stratification, warm temperatures, and moderate relative humidities, and by mountains that are wide. Taken together, the simulated sensitivities help to explain the large variability in δS found in observations. Of particular interest is the simulated increase in δ with temperature, since such an effect could act to buffer mountain hydroclimates against the impacts of climate warming. The microphysical parameterization chosen has a large impact on the simulation of ZS over topography, representing an important source of uncertainty in simulations of mountain snowfall.
Additional aspects of mountain precipitation neglected in this study, such as boundary layer fluxes and fully 3D airflow, are probably required to represent the full range of behavior found in real orographic storms (such as kilometer-scale drops in ZS) and will be investigated in future work. For instance, initial results suggest that low-level flow deceleration associated with blocking may greatly amplify the impact of latent cooling from melting and help produce large drops in ZS. Nevertheless, this study presents a framework for how the various mesoscale controls on ZS can be quantified and understood, even in more complex scenarios. Using this as a foundation, future work will add additional layers of realism to the simulations and synthesize model results with field observations to give a more complete understanding of the rain–snow transition over mountains.
Acknowledgments
Mark Stoelinga and Jessica Lundquist provided comments that improved the manuscript. This work also benefited from discussions with researchers from NOAA-ESRL’s HMT-west group. The authors acknowledge support from NSF Grants EAR-0642835 and ATM-0836316.
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In general, isothermal layers or temperature inversions may complicate the definition of Z0C, but such features are absent from the simulations presented here.
Other valuable measures of the snow–rain transition are possible. One alternative is the elevation at which the vertical flux of hydrometeors is half-frozen and half-liquid. Results from section 3 are qualitatively similar if this measure is used instead (see Minder 2010a).
This also assumes that the mountain is tall enough to lift and cool parcels to 0°C.
Note that the parcel model neglects blocking of the incoming airflow, which could prevent surface streamlines from following the topography, particularly for high mountains and strong stability. Therefore, the regime corresponding to the upper right of Fig. 12, where stabilities are high, a tall mountain is required to lift and cool parcels to 0°C, and blocking is favored, is likely poorly represented by this model.
This and subsequent (δ)parcel calculations use the upwind Nm and Ts at the time of analysis to account for the modest drift that occurs in the upwind conditions.
However, a temporary increase in Dmelt is found at the cloud edge in the Morrison et al. simulation. This anomalous feature is not steady in time and its cause is unclear.
