1. Introduction
Wintertime orographic precipitation is important to the hydrological cycle and the main source of water in the interior western United States (IWUS), a relatively arid region (Roe 2005; Rasmussen et al. 2014). High-resolution regional climate models appear to be able to capture cold-season orographic precipitation in this region quite well (Ikeda et al. 2010; Rasmussen et al. 2011), in fact better than the typically sparse network of gauges or gauge-based gridded datasets (Jing et al. 2017), and thus such models can be used to gain understanding in the precipitation distribution across mountain ranges. Spatial distribution is important because precipitation falling on the opposite sides of a mountain crest affects water availability in different watersheds. Both numerical simulations and observations have been used to understand the control of ambient conditions over orographic precipitation amounts and spatial distribution (e.g., Smith 2003; Colle 2004; Zängl 2008; Yuter et al. 2011; Geerts et al. 2015).
To a first order, for a mountain barrier of a given height, the mountain-scale precipitation rate is proportional to the rate of vapor condensation on the windward side, and thus the water vapor flux across the barrier (Neiman et al. 2004; Colle 2004; Smith et al. 2005; Minder et al. 2008; Houze 2012). Key upstream factors thus are mountain-normal wind speed, orographic cloud-base height and temperature, and static stability. Wind speed and stability together impact the ability of the upstream low-level air mass to traverse the barrier or be blocked. Other factors that can be inferred from an upstream sounding matter too, such as the directional change of wind with height (Siler and Durran 2016), the ability of the terrain to generate vertically propagating waves (e.g., Reinking et al. 2000), the deep humidity profile, and factors affecting the ability of the mountain to trigger shallow or deep convection in otherwise stratified flow, especially through the release of potential instability (section 12.5.1 in Houze 2014). Finally, there are smaller-scale factors that affect orographic cloud processes and precipitation growth, such as secondary gravity waves (Garvert et al. 2007), shear-driven billows (Houze and Medina 2005; Medina and Houze 2015), cloud-top-generating cells (Kumjian et al. 2014), and boundary layer turbulence (Geerts et al. 2011).
Idealized simulations have been conducted to explore how upstream factors control the distribution of precipitation across an idealized terrain feature (e.g., Colle 2004, 2008; Zängl 2008; Watson and Lane 2012). Idealized simulations based on assumed mountain shapes are useful to tease out how terrain affects the sensitivity of orographic precipitation distribution to upstream conditions, but they cannot be used to build statistical relations that predict orographic precipitation for real mountain ranges. Smith (2003) and Smith and Barstad (2004) developed a linear theory that estimates the precipitation over a mountain according to the actual terrain shape, assuming simple wave dynamics and a microphysics scheme. This linear theory, supplied with average upstream wind and humidity conditions, reproduces average orographic precipitation amount and distribution reasonably well, at least for unblocked, stable flow (e.g., Smith 2006; Hughes et al. 2009). Siler and Durran (2016) suggest that more precipitation may fall in the lee if there is strong wind veering, since, at least for the Cascade Mountains in the northwestern United States, this is associated with a stagnant low-level cold air mass in the lee. Strong drying across the Cascades only occurs with a strong cross-mountain low-level wind.
A few observational studies have explored the upstream factors controlling the distribution of precipitation across a mountain range. For example, using ground-based radar data collected during 61 heavy precipitation events, James and Houze (2005) show that orographic precipitation enhancement is more significant when the cross-barrier wind is strong and humidity is high. Panziera and Germann (2010) show that wind speed has a larger influence on the precipitation intensity than static stability. Yuter et al. (2011), using three winters of ground-based radar data near the Cascade Mountains, also found that cross-barrier wind speed is the dominant driver of orographic precipitation intensity, rather than freezing level or stability. Ambient stability also affects the type of cloud (convective versus stratiform), which may impact where the resulting precipitation falls. Based on airborne dual-Doppler cloud radar data collected from 16 winter storms, Geerts et al. (2015) show that precipitation from shallow boundary layer convection and from stratiform clouds mostly falls on the upwind side, while precipitation from deeper convection mostly falls in the lee.
Observations are helpful to understand the orographic precipitation distribution across real mountains and to evaluate model simulations. However, observations have limitations; for example, low-level radar beams may be blocked by terrain, limiting the ability of ground-based radars to detect low-level precipitation growth (e.g., Fulton et al. 1998; Maddox et al. 2002; Lin and Hou 2012). Airborne profiling radar measurements are operationally expensive and cannot provide a long-term dataset. Precipitation gauges only provide single-point measurements and the gauge density is low over many mountains in the IWUS (Jing et al. 2017).
The objectives of this paper are to examine how upstream conditions (including macroscale cloud conditions) control the intensity and distribution of orographic precipitation, and to assess the ability of statistical relations based on upstream conditions to predict orographic precipitation. As mentioned above, properly configured high-resolution (<5 km) regional climate model (RCM) simulations can capture the seasonal amount and distribution of cold-season orographic precipitation, specifically in the IWUS (Rasmussen et al. 2011, 2014; Liu et al. 2011; Jing et al. 2017). At the same time, these simulations contain the dynamically consistent upstream conditions. Thus, RCM output serves as an excellent and rich resource for our purpose. To our knowledge, this is the first study using RCM simulations for this purpose. If their predictive power is high, then such statistical relationships are useful, for instance, to predict changes in finescale precipitation distributions across specific mountains in a changing climate, based solely on upstream conditions captured by coarse-resolution climate models. In fact, in a follow-up study (Jing et al. 2018, manuscript submitted to J. Appl. Meteor. Climatol., hereinafter Part II) we will diagnose the changes in wintertime orographic precipitation amount and distribution in a warming global climate, according to the upstream conditions captured in an array of climate model simulations. Both studies focus on the cold season only, because streamflow in the IWUS domain is controlled largely by cold-season orographic precipitation (mostly snowfall), and because warm-season precipitation mostly results from deep convection, whose behavior is more erratic (Jing et al. 2017).
This paper is organized as follows: Section 2 describes the analysis method. Sections 3 and 4 show the results. A discussion and the conclusions are given in sections 5 and 6, respectively.
2. Model design, validation, and analysis method
a. Model design
The ability of a sufficiently resolved RCM to capture wintertime orographic precipitation, in particular in the IWUS, has been demonstrated in several previous papers (Ikeda et al. 2010; Rasmussen et al. 2011, 2014; Liu et al. 2011, 2017; Jing et al. 2017; Wang et al. 2018). The resolution needs to be no coarser than 4–6 km, at least in the Colorado Rockies (Ikeda et al. 2010; Rasmussen et al. 2011). In areas with a sparse precipitation gauge network, such as the Wind River Range, the RCM may actually produce a more refined and more accurate precipitation climatology than the gauge network or than observationally based gridded datasets such as the Parameter–Elevation Regressions on Independent Slopes Model (PRISM; Daly et al. 1994; Gutmann et al. 2012; Hughes et al. 2018; Jing et al. 2017).
In this study, the output from two convection-permitting RCM simulations using the Weather Research and Forecasting (WRF) Model is used to analyze the wintertime orographic precipitation in the IWUS (Fig. 1a). The first simulation is a continuous one, from October 2002 to February 2012, across a large domain, about 4 times as large as shown in Fig. 1a. The detailed model setup and physics choices of this IWUS RCM simulation are described in Wang et al. (2018), and the modeled precipitation has been evaluated in Wang et al. (2018) and in Jing et al. (2017). The Climate Forecast System Reanalysis (Saha et al. 2010) is used to provide the initial and lateral boundary conditions. The model domain has 420 × 410 grid points and 51 vertical levels, the horizontal resolution is 4 km. The key physics choices are the Thompson bulk cloud microphysics scheme (Thompson et al. 2008), the Noah-MP land surface scheme (Niu et al. 2011; Yang et al. 2011), the revised Monin–Obukhov surface-layer scheme (Jimenez et al. 2012), the Yonsei University planetary boundary layer (PBL) scheme (Hong and Pan 1996), and the Rapid Radiative Transfer Model for general circulation models (RRTMG) shortwave and longwave radiation scheme (Iacono et al. 2008). Except for a few differences, this model configuration is the same as that in the “CONUS” RCM (covering the entire continental United States) described in Liu et al. (2017). That configuration was subject to extensive sensitivity studies aimed to optimize precipitation simulation. We use the hourly output of the IWUS simulation for 10 winters [defined as December–February (DJF) in this study], that is, from December 2003 to February 2012.
Topography of (a) IWUS, (b) Park Range (label PR), (c) Wind River Range (label WRR), and (d) Teton Range (label TR). The black dashed box in (a) indicates the greater Yellowstone region. The red boxes in (a) show the locations of the domains of (b)–(d). The circles (red and blue) in (b)–(d) indicate the grid points used to plot the mean cross sections of precipitation. The red circles represent the grid points used to calculate the upwind ambient conditions. The grid resolution is 4 km in (b) and (c) and 1.33 km in (d).
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
The second simulation is a series of 10 separate DJF simulations covering the same 10 winters. This is a 1.33-km-resolution simulation, driven offline by the output of the IWUS simulation and focusing on the greater Yellowstone region. The physics choices of this 1.33-km-resolution simulation are the same as those of the IWUS simulation. The wintertime precipitation distribution from the 1.33-km-resolution simulation is similar to that from the 4-km-resolution simulation but has a finer texture, related to terrain (Fig. 7 in Jing et al. 2017).
b. Model validation
In comparing the IWUS simulation with SNOTEL gauge data in the mountains, it is seen that the mean bias of wintertime precipitation (IWUS − gauge) is −1.33 mm. This bias is less than 1% of the DJF precipitation. The root-mean-square error (RMSE) is 64 mm. The correlation coefficient is mostly greater than 0.8 over the various mountain ranges, and is as high as 0.95 for the entire domain of the IWUS simulation. The discrepancies of wintertime precipitation between the SNOTEL observation and the IWUS simulation are due to multiple reasons (Jing et al. 2017); for example, snow gauges may underestimate the snowfall when the wind is strong (Rasmussen et al. 2012), or the 4-km terrain resolution may not be adequate, especially for steep ranges like the Teton Range. The difference of wintertime precipitation between gauge observation and the IWUS simulation also increases with the increasing height difference between gauge sites and model terrain (Jing et al. 2017). The hourly and daily precipitation difference between gauge and IWUS simulation is larger than the monthly and seasonal precipitation difference because of larger random errors of both gauge observation and IWUS simulation, but statistically, the 4-km-resolution convection-permitting WRF simulation captures the finescale distribution of wintertime orographic precipitation fairly well (Jing et al. 2017; Wang et al. 2018). Sensitivity tests using WRF (Liu et al. 2017) showed that the performance of WRF on modeling orographic precipitation is sensitive to the choice of cloud microphysics parameterization; the Thompson microphysics scheme better captures the characteristics of wintertime orographic precipitation than do others. The choice of other physical processes, such as the PBL scheme, surface-layer scheme, and radiation scheme, has a minor impact on the performance of WRF. WRF simulations using different initial and lateral boundary conditions have only minor impact on the accuracy of the modeled wintertime orographic precipitation in the IWUS (Jing et al. 2017).
c. Analysis method
Three mountain ranges are selected in this study: Wind River Range, Park Range, and Teton Range (Figs. 1b–d). These mountains are selected because they are mostly linear, mostly normal to the prevailing southwesterly to westerly wind, and, in the upstream direction, there is a sufficiently broad basin or plain. The Wind River Range is the largest, while the Teton Range is the smallest of the three ranges. Model output from the 4 km-resolution IWUS simulation is used for Wind River Range and Park Range, the 4-km resolution can well resolve the terrain over these two ranges because of their relatively large size. Output from the 1.33-km-resolution simulation is used for Teton Range, because of its relatively small size and steep terrain. For each mountain range, we calculate the mean upwind conditions (e.g., temperature, wind speed, stability), and plot the mean cross sections of precipitation and parameters such as potential temperature and condensed water. The circles (red and blue) in Figs. 1b–d indicate the grid points used to calculate the mean precipitation rate and to plot composite values in cross sections. The red circles indicate the upwind grid points, which are used to calculate the mean upwind conditions. They are located about 25 km from the crest. Since the mountain crest is not a straight line, the red circles are not along a straight line. The distance from each upwind grid point to the mountain crest and the number of grid points in each individual transect are the same, however. Transects shown herein are based on an equal number of grid points on the windward and leeward sides for the Wind River and Park Ranges. There are proportionally more grid points on the windward side of the Teton Range, because of its asymmetry (steeper on the leeward side). The cross sections shown in this study are an along-mountain average of the individual transects. They are approximately along the prevailing wind, from southwest to northeast for the Wind River Range, from west to east for the Park Range, and from west-northwest to east-southeast for the Teton Range.
The five predictor upwind conditions retained in this study are mountain-normal wind speed U, Brunt–Väisälä (B-V) frequency N, cloud-base temperature CBT, mixed-layer lifted condensation level LCL, and cloud depth CD. We also examine total wind speed, wind direction, shear S, wind veering VEER, and Froude number Fr. The total wind speed, wind direction, U, and S are all averaged from the surface (~10 m) to the height of the mountaintop (defined here as the greatest height for each mountain in the WRF terrain) and averaged for all red grid points in Fig. 1. Shear S (unit: s−1) is the magnitude of the shear between the surface and mountaintop level. The S and U tend to be positively correlated, but if cold-air damming and a barrier jet do occur during some winter storms then S and U may be negatively correlated. VEER is the angular difference between the mean high-level (from mountaintop to 450 hPa) wind direction and the mean low-level (from surface to mountaintop) wind direction and is positive when the wind veers (turns clockwise) with height. Similar definitions of wind speed, wind direction, and wind veering have been used in previous studies (e.g., Jing et al. 2015; Siler and Durran 2016). The Fr is calculated using U, N, and the height H from the surface to mountain crest: Fr = U/(NH). Frequency N is a depth-weighted average of Ndry and Nmoist, where Ndry is the dry B-V frequency from the surface to the LCL and Nmoist is the moist B-V frequency from the LCL to the mountaintop.
We also examine cloud macroscale factors: the cloud-top temperature CTT and cloud-top height CTH are the mean temperature and height of the contiguous cloud top for the grid points where precipitation is found at the surface. A grid point is considered to be in “cloud” when the total condensed water (liquid plus ice) is greater than 0.001 g kg−1. The term “contiguous” implies that if there are multiple layers of unconnected clouds (i.e., containing one or more gaps where total condensed water is less than 10−3 g kg−1), only the lowest-level cloud is considered. If, however, the upper-level cloud is connected to the lower-level cloud, then CTT and CTH are determined using the upper-level cloud. The cloud-base height is estimated as the LCL, calculated using the mean potential temperature and specific humidity in the lowest 50 hPa (i.e., the mixed-layer LCL; Craven et al. 2002). CD is the height difference between CTH and LCL. CTT, CTH, and CD are computed for all grid points for specific mountain ranges shown in Fig. 1, unlike all other parameters, which are computed at the red points only.
The relations between upwind conditions and hourly precipitation are based on simultaneous (unlagged) model output. The typical advection time from the upwind sounding site to the crest (~30 km, at U ≈ 10 m s−1) is nearly 1 h. Also, the hourly precipitation represents the cumulative amount during the preceding hour. The resulting lag, ranging from 0 to 2 h or more, depending on wind speed and precipitation location, is not accounted for but is short relative to the typical storm duration (11 h on average for the three mountains).
As mentioned above, the IWUS wintertime precipitation over the mountains matches observations well (“validates”) and can be used to evaluate gauge-based gridded datasets (Jing et al. 2017). There are no observations to validate the modeled upstream and cloud conditions: the closest operational radiosonde sites upstream of the three ranges are well outside the red boxes in Fig. 1a. Because the IWUS simulation is contained within a small domain and is constrained by 6-hourly reanalysis data along the lateral boundaries, atmospheric conditions should be captured reasonably well. For the purpose of this study, the question of validity of upstream conditions is secondary because the objective is to relate orographic precipitation to dynamically consistent upstream conditions.
The upwind precipitation fraction (UPF) is defined as the ratio of windward precipitation to the total precipitation within the transect domains in Fig. 1. A similar parameter has been used in previous studies (e.g., Siler and Durran 2016). For each of the three mountains, data are composited for precipitation events only, defined as a time during which the mean hourly precipitation rate (at grid points with terrain above 2.6 km MSL) exceeds 0.1 mm h−1.
3. Precipitation distribution
a. Wintertime precipitation distribution climatology
The modeled DJF precipitation distribution is shown in Fig. 2. Figures 2a–c are plotted using the output from the 4 km-resolution IWUS simulation, and Fig. 2d is based on the output from the 1.33 km-resolution run. The 4-km-resolution simulation captures the mountain-scale precipitation over Teton Range adequately (Jing et al. 2017), but the 1.33-km-resolution simulation better resolves the terrain-related texture of precipitation, in particular the rapid drying across the steep eastern flanks of the Teton Range (Fig. 2d). Clearly mountains receive far more precipitation than the plains and basins; that is, the orographic precipitation enhancement (OPE; Neiman et al. 2004; Smith et al. 2005; Minder et al. 2008; Houze 2012) is substantial in the IWUS in winter. Overall, 64% of the simulation’s area-integrated wintertime precipitation falls over mountains (here defined as above 2 km MSL in elevation), yet the mountain area makes up only 45% of the domain in Fig. 2a. Defining the OPE as the precipitation above 2.6 km MSL divided by the precipitation in the upwind foothills (i.e., the red circles in Fig. 1), the 10-yr DJF mean OPE for the Wind River, Park, and Teton Ranges is 3.1, 2.1, and 2.4, respectively. These numbers would be higher if the OPE were to be defined relative to a plain region farther upwind than the foothills. Climatologically, the Wind River Range is the driest in winter, among the three ranges of interest (Fig. 2c), and Teton Range is wettest (Fig. 2d), which is consistent with PRISM data (Jing et al. 2017). For all the three mountains, the mountain crest receives the most precipitation, and more precipitation falls on the windward side (including the entire windward basin/plain) than on the leeward side. The 10-yr DJF mean UPF for Wind River, Park, and Teton Ranges is 0.58, 0.53, and 0.64, respectively, within the respective domains of grid points highlighted in Fig. 1.
Wintertime (DJF) precipitation maps modeled by WRF for (a) IWUS, (b) PR, (c) WRR, and (d) TR. The red boxes in (a) show the subdomain locations. Terrain height contours (km) are shown in (b)–(d).
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
The instantaneous (hourly) precipitation rate also is generally lowest over the Wind River Range, and highest over the Teton Range, as shown by the histograms in Fig. 3. The histograms in Fig. 3 do not show the frequency of events, but rather the normalized contribution to the total precipitation. The normalized precipitation in any bin is the total precipitation in the given bin divided by the total precipitation in all bins. The distribution is broadest for the Wind River Range, and narrowest for the Teton Range. We define light, moderate, and heavy precipitation events based on the hourly precipitation rate (computed as the average at all grid points above 2.6 km MSL) as follows: a light precipitation event has a precipitation rate between 0.1 and 1 mm h−1, a moderate precipitation event falls between 1 and 2.5 mm h−1, and a heavy precipitation event has a precipitation rate exceeding 2.5 mm h−1. Cases with a precipitation rate of less than 0.1 mm h−1 are ignored. Over the Wind River and Park Ranges, light precipitation events contribute the most precipitation, and heavy precipitation events contribute just ~10% of the total precipitation. Over the Teton Range, moderate precipitation events contribute the most to overall wintertime precipitation. The total hours of precipitation events (>0.1 mm h−1) during the 10 winters over the Wind River, Park, and Teton Ranges are 4821, 6181, and 6318, respectively. These precipitation events will be used in the following sections to study the factors controlling the precipitation distribution, using hourly model output.
Histograms of the normalized precipitation at elevations above 2.6 km as a function of precipitation rate for (a) WRR, (b) PR, and (c) TR. The vertical dashed lines represent the precipitation rates of 0.1, 1, and 2.5 mm h−1. The percentiles of the precipitation for very light (<0.1 mm h−1), light (0.1–1.0 mm h−1), moderate (1.0–2.5 mm h−1), and heavy (>2.5 mm h−1) precipitation events are given in (a)–(c).
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
b. Dependence on wind
Orographic precipitation amount and distribution are strongly influenced by the wind field (e.g., Colle 2004). Figure 4 shows the histogram of normalized precipitation and normalized precipitation accumulation as a function of total wind speed, S, wind direction, VEER, and Fr calculated at the upstream points (Fig. 1). The precipitation rate is mostly weak in cases with a wind direction parallel to the orientation of mountain crest; for the Wind River Range, that is 135° and 315°. In a few cases precipitation occurs when the low-level wind blows from <140° (Fig. 4a3), essentially reversing the definition of windward and leeward sides. Thus, only the cases whose wind direction falls between the dashed lines in Figs. 4a3–c3 are used in the remainder of this study, that is, those with a significant mountain-normal wind component. For the Wind River Range, cases with a wind direction between 160° and 290° are used; for the Park and Teton Ranges, the angular wind ranges are 205°–335° and 225°–355°, respectively. These exclude about 17%, 11%, and 19% of total precipitation for the Wind River, Park, and Teton Ranges, respectively, mostly corresponding to northwesterly wind cases over the Wind River Range and southerly wind cases over the Park and Teton Range.
Histograms of normalized precipitation (black) and normalized precipitation accumulation (red) as functions of (top) upstream wind speed, (top middle) wind shear, (middle) wind direction, (bottom middle) wind veering, and (bottom) Fr. The vertical dashed lines in (a3), (b3), and (c3) represent the range of wind directions that are used as threshold in the selection of precipitation events. Cases with imaginary values of Fr are not included in (a5), (b5), and (c5).
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
For all three mountains, a large fraction of the precipitation is associated with wind veering (Figs. 4a4–c4). Veering may be due to warm-air advection, the effects of surface friction, and cold-air damming resulting in along-barrier flow. About 80%, 60%, and 50% of the Fr values are smaller than 1 for the three mountains, respectively (Figs. 4a5–c5), indicating that the low-level flow is at least partially blocked during these precipitation events. The Wind River Range experiences the most blocked flow (80% with Fr < 1).
This raises the question of occurrence of cold-air damming, whereby, under highly stratified conditions, the low-level cross-barrier wind speed U is reduced, an along-barrier wind V develops (V > 0 in a frame in which the y axis is aligned with the mountain barrier), and cold air pools along the foothills (e.g., chapter 13.2 in Markowski and Richardson 2010). Barrier jets have been documented along the more significant barriers such as the Sierra Nevada (Parish 1982), the northern California coastal mountains (e.g., Valenzuela and Kingsmill 2015), the Oregon Cascades, and (under easterly prevailing flow) the Colorado Front Range (e.g., Dunn 1992), but they have not been documented along the shorter mountain ranges examined here. An upstream barrier jet from the southeast is relatively rare along the Wind River Range (Fig. 4a3).
To further examine the occurrence of cold-air damming and flow deflection to the left of the cross-mountain flow, we compare conditions at our default upstream array (near mountain foot; Fig. 1) with those at an array of points farther upstream (~85 km from the crest) during these precipitation events. In the presence of cold-air damming, we expect ΔU = Ufoot − U85km < 0 (cross-flow deceleration), ΔV = Vfoot − V85km > 0 (along-barrier deflection), and Δθ = θfoot − θ85km < 0 (cold-air pooling) on a constant pressure surface midway between the surface and the mountain crest (we chose 770 hPa) (θ is potential temperature). For the Wind River Range, we find that ΔU = −1.9 m s−1, ΔV = 0.9 m s−1, and Δθ = −0.7 K, on average, with a significant negative correlation between ΔV and Δθ (Fig. 5). So cold-air-damming dynamics are somewhat active in the Wind River Range, but, except for a few cases, the damming strength is generally weak. It is even less prominent in the Teton Range and is absent in the Park Range (Fig. 5).
Scatterplot of along-barrier deflection ΔV against cold-air-pooling strength Δθ at 770 hPa for DJF precipitation events with westerly prevailing flow. The ΔV is the difference between V at the mountain foot and V at ~85 km upstream of the mountain crest (Vfoot − V85km), Δθ is the difference between θ at the mountain foot and θ at ~85 km upstream of mountain crest (θfoot − θ85km). The gray dots represent hourly data from RCM simulations, the red dots and bars represent the means and standard deviations, and the black solid lines are the linear regressions.
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
Blocked flow conditions tend to displace precipitation toward the upstream valley (Rotunno and Houze 2007). Yet over the Wind River Range, with the highest frequency of blocked flow (Fr < 1), the UPF is only 58%, and there is no marked enhancement in the plains to the southwest of this range (Fig. 2c). The likely explanation is the presence of another mountain range west of the Wind River Range (Fig. 1a). Thus, there is no uplift over the stable, cold air mass trapped in the basin upwind of the Wind River Range and no precipitation enhancement.
To examine the effect of U, S, Fr, and VEER on precipitation amount and distribution across our mountain ranges, we partition all events in three groups, according to the magnitude of these parameters and then plot the mean cross-range precipitation distribution (for the grid points shown in Fig. 1) for each category (Fig. 6). The variables U, S, and VEER are partitioned into three equal groups, respectively, and Fr is partitioned according to physically meaningful thresholds (Fr < 0.5, 0.5 ≤ Fr < 1, and Fr ≥ 1). Higher U results in heavier precipitation and a lower UPF (Figs. 6a1–c1), consistent with Colle (2004) and other studies. Increasing S (Figs. 6a2–c2) or Fr (Figs. 6a3–c3) has an effect that is similar to that of increasing U. This is because U and S are well correlated: the correlation coefficients between U and S are 0.84, 0.72, and 0.74; this implies that the barrier jet is very weak, as we found to be the case for the mountain ranges studied here. A barrier-jet-prone mountain could reveal a negative correlation between U and S (weak wind allows cold-air damming, barrier flow, and thus a large shear vector S). Using an idealized simulation, Colle (2004) showed that S has a smaller impact on the orographic precipitation distribution, as compared with U. A larger Fr value also results in heavier precipitation rate and a lower UPF. The Fr incorporates the impacts of both U and N2. The correlation coefficients between U and Fr are 0.57, 0.55, and 0.51 for the three mountain ranges. These values are not very large, indicating that U and N2 are not strongly correlated. The influence of N2 on the precipitation rate and UPF will be explored later.
Cross sections of precipitation rate over WRR, PR, and TR under various ambient conditions, related to (top) U, (top middle) S, (bottom middle) Fr, and (bottom) VEER. The upwind precipitation fractions are given in each panel for each condition. The terrain profiles are gray shaded.
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
Wind veering has no obvious impact on the precipitation distribution across a mountain range (Figs. 6a4–c4). On the basis of an observational case study and idealized simulations for the Cascade Range, Siler and Durran (2016) suggested that strong wind veering is associated with trapped cold air in the leeside basin (Washington’s Columbia basin). Such trapping is common in winter under southerly low-level flow, in part also because of higher terrain to the north, and because the westerly maritime flow crossing the Cascades is potentially warmer than more continental air parcels trapped in the Columbia basin. In such cases of strong veering, the leeward precipitation fraction in the Cascades often is larger than in cases with weaker wind veering (Siler and Durran 2016). This phenomenon is not found in the composite results for any of the three mountains analyzed here (Figs. 6a4–c4). The reason is evident in Figs. 7c and 7d, which show cross sections of composite total condensed water, potential temperature, wind vectors, and vertical moisture flux over the Wind River Range, for the two extreme groups of VEER values. Stronger wind veering (Fig. 7d) results in slightly deeper clouds than weaker wind veering (Fig. 7c). Cases with stronger wind veering typically are more stable (as indicated by the potential temperature contours), consistent with the stronger warm-air advection above mountaintop, but the lee stability is not high enough to generate stagnant air conditions in the lee and to inhibit deep subsidence. In both VEER groups, the wind accelerates across the crest and plunges into the lee valley. Thus, the veering amount has no significant impact on the precipitation distribution for the cold-season events in this study.
Cross sections of condensed water (colored), potential temperature (K; black contours), vertical moisture flux (g s−1 m−2; blue contours, positive only) and wind vectors over WRR for the 33% of cases with the (a) weakest and (b) strongest mountain-normal wind speed and the 33% of cases with the (c) weakest and (d) strongest wind veering.
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
Mountain-normal wind speed, on the other hand, has a pronounced effect: stronger U (Fig. 7b) results in deeper upwind ascent and a far larger upwind vertical moisture flux, leading to deeper clouds, more precipitation, and also more hydrometeor transport into the lee. The latter is significant because almost all DJF precipitation falls as snow, which has a small fall speed relative to rain. (A small fraction falls as graupel in the IWUS simulation, but none as rain.) Thus, the lower UPF under higher U (Fig. 6a1) is in part explained by the precipitation type, and in warmer conditions this fraction probably will depend on freezing level. The vertical wavelength (λz = 2πU/N) of the main terrain-induced vertically propagating gravity wave is larger for higher wind speed U (and lower stability N), which allows for stronger ascent and vertical transport of moisture over the upwind slope (Colle 2004).
c. Dependence on stability and cloud vertical extent
We now evaluate the impact of stability and cloud vertical extent on orographic precipitation distribution. Histograms of normalized precipitation and normalized precipitation accumulation for N2, CBT, CTT, LCL, and CD are shown in Fig. 8. Only the cases in which wind direction falls between the dashed lines in Figs. 4a3–c3 are considered in this figure. The Wind River Range has the highest frequency of highly stratified upstream conditions (large N2; Figs. 8a1–c1), and its mountain crest is higher than the two others relative to the upwind plains, resulting in typically small Fr (Fig. 4a5). Unstable cases (N2 < 0) are very rare in winter, but especially upwind of the Teton Range the low-level lapse rate often is close to moist adiabatic (not shown). Histograms for CBT, CTT, and CD are relatively broad. Not surprising is that CTT and CD are well correlated (correlation coefficient > 0.85 for all three mountains). The cloud base (mixed-layer LCL) generally is close to the ground (Figs. 8a4–c4), but occasionally it is much higher—as high as mountaintop level. The cases with high LCL typically have a low CBT and light precipitation, mostly over the high terrain only.
Histograms of normalized precipitation (black) and normalized precipitation accumulation (red) as functions of N2, CBT, CTT, cloud-base height, and CD for cases with wind direction that falls between the dashed lines in Figs. 4a3, 4b3, and 4c3.
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
Cross sections of the precipitation across the three mountain ranges for different stability and cloud-macroscale properties are shown in Fig. 9. Here, N2 is grouped into N2 < 10−6 s−2, 10−6 s−2 ≤ N2 < 10−4 s−2, and N2 ≥ 10−4 s−2; the other factors are partitioned into three equal groups. Larger N2 (i.e., higher stability) generally results in a slightly larger UPF (Figs. 9a1–c1), on account of the stronger lee subsidence and hydrometeor evaporation under stratified flow (Figs. 10a,b). As mentioned above, the vertical wavelength of orographic gravity waves is larger for lower N2, which may result in deeper ascent and thus more precipitation, but the opposite applies (less precipitation for the lowest stability group) in all three mountain ranges.
Cross sections of precipitation rate over WRR, PR, and TR for different N2, CBT, LCL, and CD. The UPFs are shown in each panel for each condition.
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
As in Fig. 7, but for the following ambient or storm conditions: the cases with (a) N2 > 10−4 s−2 and (b) N2 < 10−6 s−2, the 33% of cases with the (c) coldest (d) and warmest CBT, the 33% of cases with the (e) highest and (f) lowest LCL, and the 33% of cases with the (g) shallowest and (h) deepest clouds.
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
A higher CBT results in heavier precipitation (Figs. 9a2–c2), because a warmer cloud base is typically associated with a higher low-level water vapor mixing ratio and thus a higher vertical moisture flux and hydrometeor production (Fig. 10d). The warmer cases tend to be more stratified also (cf. Fig. 10c and Fig. 10d). The UPF appears to be immune to CBT (Figs. 9a2–c2)), probably because of conflicting contributions: warm cases have stronger wind U (and thus more leeward precipitation) but higher stability (and thus more windward precipitation) (cf. Fig. 10c and Fig. 10d). Only the Wind River Range is examined in Fig. 10, but the cross sections for the Park and Teton Ranges (not shown) reveal the same general patterns.
A lower cloud base (LCL) typically results in heavier precipitation and a larger UPF (Figs. 9a3–c3) for all three mountains, even when the impact of the wind field is neutralized (not shown), indicating that cloud-base height has a considerable impact on the orographic precipitation distribution. This is because cases with a lower cloud base have a larger upwind upward moisture flux and deeper clouds (Figs. 10e,f). When the cloud base is lower, hydrometeors tend to grow at lower levels, and a larger fraction of the hydrometeors reach the ground on the windward side.
The CD has a strong impact on the precipitation intensity but not on spatial distribution, as shown in Figs. 9a4–c4. The same applies to CTT (not shown). Deep clouds produce far more precipitation, and the precipitation tends to be more uniformly distributed. The heavier precipitation in deep clouds is due in part to stronger low-level winds (U) and thus larger vertical moisture flux, compared to shallow clouds (Figs. 10g,h). To some extent, it is due also to large-scale forcing such as frontal/baroclinic wave dynamics that are responsible for deep ascent and precipitation growth over great depth, irrespective of the underlying terrain.
In short, U has a strong impact on orographic precipitation amount and distribution; other factors such as N2, CBT, LCL, and CD also influence the orographic precipitation amount and distribution, but, in the analysis of these parameters, the effect of variable U is not teased out, and therefore their independent impact is not clear. The impact of those parameters for given U values will be discussed later, in section 4.
d. Dependence on cloud type: Stratiform versus convective
Airborne radar data have shown that cold-season deep (sometimes elevated) convection tends to result in a leeward shift in precipitation, compared to stratiform clouds and shallow boundary layer convection, at least for a mountain range in Wyoming, where most storms are unblocked (Fr > 1) (Geerts et al. 2015). In this section, we examine whether the same applies to nearby mountain ranges. The challenge is to distinguish convective precipitation in a 4-km-resolution convection-permitting simulation, which is unable to capture the finescale cold-season orographic convection such as that depicted in Kumjian et al. (2014), Geerts et al. (2015), or Jing and Geerts (2015).
The modeled convective precipitation events are identified using two simple methods. In the first method, following Churchill and Houze (1984), a convective core is defined as a grid point in which the precipitation rate is twice the background average. Here, the background average is calculated over a 20 km × 20 km area. The second method, following Xu (1995), is similar to the first one, but uses the maximum vertical velocity instead of surface precipitation rate for each grid column. Both methods can identify convective cores fairly well, as evaluated in Lang et al. (2003). A grid point that meets the requirement of either method is identified as a convective core. In this paper, a precipitation event is defined as convective if the following three conditions are satisfied: 1) there are at least 0.2% of the grid points (among all grid points in Figs. 1b–d) identified as convective cores, 2) N2 < 3 × 10−5 s−2 to ensure that the lower troposphere is moist neutral and convection is possible, and 3) the precipitation rate exceeds 2.5 mm h−1 at ≥1 grid point to exclude relatively shallow or weak isolated convection. An event in which one of the three criteria fails is identified as a mixed case. This may occur when convective cells are embedded in stratiform precipitation. The remaining cases are regarded as stratiform events. Given these restrictive criteria, the fraction of convective precipitation events in DJF is 2.2%, 2.9%, and 5.6%, and the fraction of stratiform events with mixed precipitation is 8.5%, 14.0%, and 23.2% for the Wind River, Park, and Teton Ranges, respectively. The real convective precipitation fraction over these mountains (and elsewhere in the IWUS), including from shallow convection and from convective cells embedded in stratiform precipitation, probably is considerably higher in winter, although this is unknown.
Transects of the normalized precipitation from stratiform, mixed, and convective events are shown in Fig. 11 for the three mountain ranges. Mixed or convective precipitation events generally are more intense (even area averaged) and are associated with lower UPF than stratiform precipitation for all three mountains, consistent with Geerts et al. (2015). Select sequences of precipitation maps (not shown) reveal that small (often single gridpoint) convective cores with a relatively short lifetime occur mostly on the upwind side and dissipate mostly before they reach the lee side, whereas larger, longer-lived convective cells often persist into the lee. Convective precipitation is just as orographically focused as stratiform precipitation in winter (Fig. 11), unlike in summer, when thunderstorms may occur almost as commonly over the plains as the mountains of the IWUS (Jing et al. 2017).
Cross sections of normalized precipitation from stratiform, mixed, and convective cases over (a) WRR, (b) PR, and (c) TR.
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
Cross sections of total condensed water, potential temperature, vertical moisture flux, and wind vectors for convective and stratiform events over Wind River Range are shown in Fig. 12. In general, the pattern for stratiform clouds (Fig. 12a) is similar to that with relatively large N2 (Fig. 10a), and the pattern for convective clouds (Fig. 12b) is similar to that for relatively small N2 (Fig. 10b). The vertical moisture flux and cloud depth tend to be larger in convective events. For stratiform clouds, the maximum upward moisture flux is found near the mountain crest, but for convective clouds it is displaced upwind, probably on account of more common convective updrafts on the windward slope. Stratiform clouds tend to dry out rapidly in the lee because of the more intense lee subsidence, whereas in the convective events more condensed water is advected into the lee. These contrasts between stratiform and convective precipitation events are present in cross sections across the Park and Teton Ranges as well.
As in Fig. 7, but for (a) stratiform and (b) convective cases.
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
4. Statistical analysis
a. Precipitation intensity
According to the preceding analysis, the intensity of orographic precipitation is controlled by at least four factors: CD (or CTT), U, CBT, and LCL. The dependency of precipitation intensity (averaged across all grid points in Fig. 1) on these four factors is further examined in scatterplots in Fig. 13. Cloud depth (or CTT) has been widely used to estimate the precipitation intensity (e.g., Joyce et al. 2004). In general, the precipitation rate increases with increasing CD (Figs. 13a1–a3). For similar CD, the precipitation rate increases with increasing U, increasing CBT, and decreasing LCL (Figs. 13b–d) for all three mountains. The impact of U, CBT, and LCL on precipitation rate are more pronounced for deeper clouds (green dots) than shallower clouds (black dots). Other ambient factors such as wind veering, stability, and precipitation type have minor impacts on the mean precipitation rate, as compared with CD, U, CBT, and LCL.
Scatterplots of the mean precipitation rate as functions of CD, U, CBT, and LCL over (top) WRR, (middle) PR, and (bottom) TR. The small gray dots are from the hourly model output. Red lines in (a1)–(a3) are fitted curves using the exponential function shown in the first term of Eq. (1). The black, blue, and green dots the remaining panels represent different cloud depths, as labeled. The big dots and bars are mean and standard deviation of precipitation rate for different ranges of each variable and condition.
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
Scatterplots of the fitted and RCM hourly precipitation rate over (a) WRR, (b) PR, and (c) TR. The black dots represent the precipitation rate fitted using the first term in Eq. (1) (i.e., CD only), and the blue dots represent the precipitation rate fitted using the complete Eq. (1). The black solid lines are the 1:1 line and the factor-of-2 lines. Correlation coefficient r, mean error (label “me”), and RMSE are shown in each panel. Also shown for (d) WRR, (e) PR, and (f) TR is the correlation coefficient between the fitted and RCM precipitation as a function of increasing number of ambient factors used to fit the precipitation rate: subscripts 1, 2, 3, and 4 on the “f” labels on the x axis represent CD, U, CBT, and LCL, respectively.
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
b. Upwind precipitation fraction
Scatterplots of UPF as a function of different ambient conditions are shown in Fig. 15. Wind U is the dominant factor controlling the orographic precipitation distribution. The UPF tends to decrease with increasing U (Figs. 15a1–a3). The UPF is fitted best using an exponential function of U over all three mountains. The relations between the UPF and other ambient factors vary with different values of U. As shown in Figs. 15b1–b3, the rate of decrease of UPF with increasing LCL depends on U. The mean UPF (big dots) can be fitted using a linear regression of a similar slope for different U. CBT has a benign impact on the UPF (Figs. 15c1–c3). For the Wind River and Park Ranges, the UPF increases with increasing CBT, consistent with Figs. 9a2 and 9b2. For the Teton Range, however, there is no correlation between the UPF and CBT. CD has a variable impact on the UPF, depending on U. As shown in Figs. 15d1–d3, for weaker wind, the UPF decreases with increasing CD (black dots), maybe because under weak wind the orographic forcing is weak, yet a deeper storm implies strong large-scale forcing, which is neutral to the windward/leeward distinction. Under stronger wind, the UPF increases slightly with increasing CD (green dots). The UPF generally increases with increasing N2 (Figs. 15e1–e3), but the trend is relatively weak in comparison with other factors such as U and LCL, especially for weak U.
Scatterplots of the UPF as functions of U, LCL, CBT, CD, and N2 over (top) WRR, (middle) PR, and (bottom) TR. The small gray dots are from the hourly model output, and the big dots are the mean values. Red curves in (a1), (a2), and (a3) are fitted lines using the exponential function shown in the first term of Eq. (2). The black, blue, and green dots in the remaining panels represent different U values as labeled, and the corresponding solid lines are the linear regressions.
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
(a1)–(a3) Scatterplots of the fitted and modeled hourly UPF over the WRR, PR, and TR, respectively. The black dots represent the UPF fitted using the first term in Eq. (2) (i.e., U only), and the blue dots represent the UPF fitted using the full Eq. (2) (i.e., all five factors). The black solid lines are the 1:1 line and the factor-of-2 lines; r, mean error, and RMSE are shown in each panel. (b1)–(b3) Correlation coefficient between the fitted and RCM precipitation as a function of increasing number of ambient factors used to fit the UPF; subscripts 1, 2, 3, 4, and 5 on the “f” labels on the x axis represent U, LCL, CBT, CD, and N2, respectively. (c1)–(c3) Scatterplots of the fitted and RCM upwind precipitation volume. The fitted upwind precipitation volume is calculated as a cross product of the fitted UPF, RCM precipitation rate, and upwind area.
Citation: Journal of Applied Meteorology and Climatology 57, 8; 10.1175/JAMC-D-17-0291.1
Other than the UPF, water managers may be interested in the upwind precipitation volume, which is defined as the product of the upwind precipitation rate and the upwind area (all grid points west of the crest, for the three mountain ranges in Fig. 1). The scatterplots of the fitted and actual hourly upwind precipitation volume are shown in Figs. 16c1–c3. The fitted hourly upwind precipitation volume is calculated using the fitted UPF and the precipitation rate from the IWUS simulation. The scatterplots show that the fitted and actual upwind precipitation volumes are quite consistent. This consistency is better for heavy and moderate precipitation events than for light precipitation events: the scatter shown in Figs. 16a1–a3) is mostly due to light precipitation. In short, if the mean precipitation rate, U, LCL, CBT, CD, and N2 can be obtained, the upwind precipitation fraction and volume can be statistically predicted on the basis of Eq. (2).
5. Discussion
Several studies have used idealized model simulations (e.g., Colle 2004) or observations (e.g., Yuter et al. 2011) to examine how upstream conditions or cloud vertical structure control the intensity and distribution of orographic precipitation. Such studies have recognized limitations in that idealized terrain simulations are not representative of actual mountain ranges, and observations typically are quite limited in terms of proximity radiosonde data, density of the gauge network, accuracy of precipitation (especially snowfall) measurements (Rasmussen et al. 2012; Martinaitis et al. 2015), and number of well-sampled events. Long-term high-resolution regional climate model simulations, such as the IWUS simulation used here, have the advantages of allowing numerous samples, a dense network of data (at each grid point), and dynamically consistent, time-synchronized profiles of wind, stability, moisture, and cloud conditions. In addition, such simulations have been shown to capture cold-season orographic precipitation very well, possibly better than gauge-driven or gauge/radar-driven gridded precipitation datasets, some of which use terrain-dependent regression techniques (Jing et al. 2017). Such datasets may have systematic biases under certain ambient conditions; for instance, they appear to underestimate cold-season orographic precipitation under strong winds (Jing et al. 2017).
For these reasons, high-resolution regional climate model simulations can provide insight into the dependence of orographic precipitation on upstream conditions and cloud vertical structure. This study finds that both the amounts and detailed spatial distribution of cold-season precipitation across three select mountain ranges in the IWUS can be predicted reasonably well using a simple array of parameters describing upstream conditions and cloud vertical structure, as demonstrated by the introduction of regression equations. While these statistical relations are specific to the select mountain ranges, the technique developed herein can be applied elsewhere using the IWUS simulation or other well-validated regional climate simulations.
This study is also potentially helpful to estimate the amount of orographic precipitation and its distribution across watersheds in a changing climate, using the statistical relations presented herein between precipitation intensity/UPF and ambient factors predicted by coarse-resolution climate model output, for various models and various climate change scenarios, at least for the three particular mountains analyzed in this paper. For example, precipitation intensity may decline in an environment with weaker cross-mountain winds (Luce et al. 2013). The same technique can be applied over any mountain for which faithful regional climate simulations are available. In fact, in a follow-up study (Part II), we plan to use this technique to estimate changes in precipitation intensity and UPF in the next few decades, using the WRF Model with a pseudo-global-warming approach (Liu et al. 2017), in which the climate perturbations predicted by the CMIP5 climate models are applied.
This study certainly has its limitations. First, the ambient conditions obtained from the IWUS simulation have not been independently validated, for lack of good observations. The modeled wintertime precipitation distribution, snowpack, and surface temperature have been evaluated in detail (Liu et al. 2017; Jing et al. 2017; Wang et al. 2018), but more observations are needed to evaluate ambient conditions such as low-level wind, CTT, CBT, and stability.
Second, regarding the convective/stratiform separation, uncertainties exist about the ability of a 4-km-resolution simulation to capture convection, especially wintertime orographic convection, which usually is small scale, shallow, and/or embedded in stratiform precipitation. Also, convective precipitation events as defined herein are less common than the stratiform precipitation events during winter, so its composite structure is statistically not as robust. Therefore, further work is recommended on this front.
Third, while the technique presented here can be applied elsewhere, the results of this study apply to three specific mountains only. While the analysis of three mountain ranges reveals consistent, general patterns about the influence of ambient factors on precipitation amounts and distribution, the statistical relations between the precipitation intensity/UPF and ambient conditions are mountain specific, as related to the unique orientation and geometries of the mountains (Watson and Lane 2012) and neighboring mountains.
Fourthly, the location where “upstream” conditions are sampled is dynamically close to the mountain crest. The Rossby radius of deformation (LR = NH/f, where f is the Coriolis parameter) is often larger than the distance upstream used herein. For the largest range, the Wind River Range, LR = 67.5 km on average during winter storms. Thus the “upstream” conditions may in fact be modified by the proximity to the mountain range. Yet, as discussed in section 3b, significant cold-air damming and flow deflection are rare, and conditions farther upstream (~85 km from the crest) are generally similar to those near mountain foot. The correlation coefficients between the fitted and RCM precipitation rate and UPF are not better when using upstream locations ~85 km from the crest, even after adjusting for the additional time of advection (not shown).
Last, this analysis is confined to the cold season because regional climate simulations of precipitation in the warm season are not as good in the IWUS domain (Jing et al. 2017) and across the continental United States (Liu et al. 2017), probably because a 4-km resolution is not high enough to adequately resolve deep convection (which dominates warm-season precipitation), and cloud microphysics schemes are more challenged for convective precipitation (Khain et al. 2015; Yang et al. 2016, 2018).
In short, high-resolution regional climate simulations form a good tool to study the orographic precipitation over complex terrain. Further model improvements will make the approach presented herein more appealing.
6. Conclusions
This study analyzes the ambient factors controlling the amount and distribution of wintertime orographic precipitation across select mountain ranges, using a high-resolution (4 km) regional climate simulation over the interior western United States. Three mountain ranges are analyzed: the Wind River, Park, and Teton Ranges. The latter is smaller and steeper, thus it is analyzed using 1.33-km-resolution model output, driven by the 4-km-resolution simulation. The main findings of this study are as follows:
The low-level mountain-normal wind speed is the dominant factor that controls orographic precipitation. Statistically, stronger wind results in heavier precipitation that is distributed more evenly across leeward and windward sides. This is because stronger winds produce deeper upwind moist ascent, which leads to deeper clouds. The precipitation patterns for different values of deep shear and of the bulk Froude number are similar to those for different wind speeds, because these parameters are well correlated. Wind veering has a minor impact on the precipitation distribution, at least for the three mountains analyzed in this study.
Low-level static stability and cloud vertical structure affect orographic precipitation as well. Statistically, precipitation falls more on the windward side if the upwind lower troposphere is more stratified, but this stratification has no obvious impact on the precipitation intensity. A higher cloud-base temperature (or lower cloud-base height) is typically associated with heavier precipitation but does not consistently affect precipitation distribution. The overall depth of the precipitating cloud has a strong positive impact on the precipitation intensity, but its impact on precipitation distribution is wind speed dependent.
Convective precipitation falls more on the lee side, as compared to stratiform precipitation. The vertical moisture flux is greater in convective cases than stratiform cases. For stratiform clouds, the vertical moisture flux peaks near the mountain crest, while for convective clouds, it peaks on the windward slope. Because of the larger midlevel stability and stronger subsidence, stratiform clouds tend to dry out rapidly in the lee, whereas in convective cases clouds can propagate farther into the lee.
The mountain-scale precipitation intensity can be fitted very well by a CD-dependent multivariate regression of four parameters: mountain-normal wind speed, cloud depth, cloud-base temperature, and lifting condensation level.
The upwind precipitation fraction can be fitted very well by a U-dependent multivariate regression of the same four parameters plus the low-level static stability. The upwind precipitation volume also can be predicted well by multiplying the fitted upwind precipitation fraction, the modeled mean precipitation rate, and the upwind area.
This result indicates that upstream conditions and cloud vertical structure strongly influence the wintertime orographic precipitation amount and distribution, at least for the three select mountains in this study. The different statistical equations for the three sample mountains may suggest a complex geographical variability in response to climatic changes.
Since the wintertime orographic precipitation is highly dependent on ambient factors, future changes in ambient conditions may lead to changes in the amount and watershed-specific distribution of orographic precipitation. Changes in wintertime orographic precipitation in the IWUS in a warmer climate will be explored in a follow-up study.
Acknowledgments
This work was funded by the Wyoming Water Development Commission and the U.S. Geological Survey, under the auspices of the University of Wyoming Water Research Program. The lead author was funded by a Wyoming Engineering Initiative Doctoral Fellowship. We appreciate the three anonymous reviewers for their constructive comments and suggestions.
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