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  • View in gallery

    (a) The X–Y plot of the model domain used in the study. Inner model domain is indicated by right-angle markers. Topography is contoured at an interval of 100 m. (b) Three-dimensional depiction of the model topography viewed from the northeast [upper-right-hand corner of (a)].

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    The 500-hPa analysis at 1200 UTC for (a) 8 Apr 1995, (b) 9 Apr 1995, (c) 10 Apr 1995, and (d) 11 Apr 1995 (from the NWS daily weather map series).

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    Skew T–logp sounding for RAP at 1200 UTC on (a) 8 Apr 1995, (b) 9 Apr 1995, (c) 10 Apr 1995, and (d) 11 Apr 1995.

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    Isohyets for the 24-h precipitation (mm) for each of the 4 days, reported 0700 LT on the following day. Isohyet contours are heavy solid lines and the topography is shown by fine dashed lines: (a) 8 Apr 1995, (b) 9 Apr 1995, (c) 10 Apr 1995, and (d) 11 Apr 1995. The contours of the topography are every 300 m, starting at 900 m.

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    Map showing the locations of the precipitation stations used for this study.

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    (a) Surface wind vectors and vertical velocity contours for the inner domain for 8 Apr 1995. The scale vector is shown in the lower right corner. Thick dashed lines show the topography using a 200-m contour interval. Solid straight lines show where cross sections are taken. Thin dashed lines are downward velocities and thin solid lines are upward velocities. (b) Inner-domain Y–Z vertical velocity cross section at X = 152 km. The contour interval is 0.05 m s−1 for (a) and (b). (c) Inner-domain model cloud water field at the surface. (d) Inner-domain X–Z cloud water cross section at Y = 144 km. The contour interval is 0.01 g kg−1 for (c) and (d).

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    As in Fig. 6 but for 9 Apr 1995. (b) and (d) The Y–Z and X–Z cross sections are at X = 160 km and Y = 128 km, respectively.

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    (a) Inner-domain snow mixing ratio at the surface for 9 Apr 1995. Thick dashed lines are the topography with a 200-m contour interval. Thin solid lines are snow mixing ratio contours. (b) Inner-domain X–Z snow mixing ratio cross section at Y = 132 km. The contour interval is 0.001 g kg−1 for (a) and (b). (c) Snow accumulation at the surface for 9 Apr 1995. The contour interval is 0.02 mm.

  • View in gallery

    (a) Surface wind vectors and vertical velocity contours for the inner domain for 10 Apr 1995. (b) Inner-domain Y–Z vertical velocity cross section at X = 132 km. (c) The X–Y vertical velocity field at 2.5 km MSL. (d) Inner-domain X–Z vertical velocity cross section at Y = 124 km. The contour interval is 0.05 m s−1.

  • View in gallery

    (a) Inner-domain cloud water field at the surface at 180 min for 10 Apr 1995. (b) Inner-domain Y–Z cloud cross section at X = 132 km. (c) Inner-domain X–Z cloud cross section at Y = 200 km. The contour interval is 0.02 g kg−1.

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    As in Fig. 8 but at 180 min for 10 Apr 1995. (b) The Y–Z cross section is at X = 128 km. The contour interval is 0.01 g kg−1 for panels a and b, and 0.02 mm in panel c.

  • View in gallery

    (a) Inner-domain cloud water field at the surface at 360 min for 10 Apr 1995. (b) Inner-domain Y–Z total cloud cross section at X = 132 km. The contour interval is 0.01 g kg−1 for panels a and b. (c) Inner-domain Y–Z snow field cross section at X = 128 km. The contour interval is 0.01 g kg−1. (d) Inner-domain snow accumulation field at 360 min for 10 Apr 1995. The contour interval is 0.1 mm.

  • View in gallery

    As in Fig. 6 but for 11 Apr 1995. The Y–Z cross sections in panels b and d are at X = 128 km. The contour interval is 0.1 m s−1 for (a) and (b), 0.01 g kg−1 for (c), and 0.02 g kg−1 for (d).

  • View in gallery

    As in Fig. 8 but for 11 Apr 1995. The Y–Z cross section in (b) is at X = 128 km. The contour interval is 0.02 g kg−1 for (a) and (b), and 0.2 mm in (c).

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Numerical Simulation of a 4-Day Early Spring Storm Period in the Black Hills

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  • 1 Institute of Atmospheric Sciences, South Dakota School of Mines and Technology, Rapid City, South Dakota
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Abstract

This paper illustrates the potential for mesoscale models to depict the distribution of precipitation in orographic situations. The study covers a 4-day time period in April 1995. The domain of the numerical model covers much of western South Dakota and some of eastern Wyoming and is centered on the Black Hills of South Dakota. The 4-day storm period is characterized by changing atmospheric conditions, from primarily rain generation to snowfall production. Observations and climatic data of precipitation are analyzed to compare with model predictions. The model demonstrated the ability to respond appropriately to changing input conditions and produced reasonably accurate simulations of observed precipitation patterns. The model performed well for sufficiently cold, strongly forced conditions but seemed overly sensitive to the accuracy of model assumptions regarding ice initiation for warmer, weakly forced situations.

Corresponding author address: Richard D. Farley, Institute of Atmospheric Sciences, South Dakota School of Mines and Technology, 501 E. St. Joseph St., Rapid City, SD 57701-3995.

Abstract

This paper illustrates the potential for mesoscale models to depict the distribution of precipitation in orographic situations. The study covers a 4-day time period in April 1995. The domain of the numerical model covers much of western South Dakota and some of eastern Wyoming and is centered on the Black Hills of South Dakota. The 4-day storm period is characterized by changing atmospheric conditions, from primarily rain generation to snowfall production. Observations and climatic data of precipitation are analyzed to compare with model predictions. The model demonstrated the ability to respond appropriately to changing input conditions and produced reasonably accurate simulations of observed precipitation patterns. The model performed well for sufficiently cold, strongly forced conditions but seemed overly sensitive to the accuracy of model assumptions regarding ice initiation for warmer, weakly forced situations.

Corresponding author address: Richard D. Farley, Institute of Atmospheric Sciences, South Dakota School of Mines and Technology, 501 E. St. Joseph St., Rapid City, SD 57701-3995.

Introduction

Winter snowpack in mountainous regions provides water supplies for areas downstream. Many places in the western United States and around the world rely on spring runoff from this snowpack. However, most of these locales experience periodic drought caused by inadequate snowfall during wintertime. The snowpack of the Black Hills region of South Dakota and Wyoming is a valuable water resource for western South Dakota. Below-normal snowpack in this region in the late 1980s caused serious water shortages (Super 1990) and spawned interest in cloud seeding as a means of lessening the impact of droughts.

Cloud seeding to increase winter snowpack over mountainous regions of the western United States has been investigated for more than 40 years (Reynolds 1988). There are remarkable similarities among the findings from the various field projects studying cold season orographic clouds and precipitation, which include Climax I and II (Mielke et al. 1970, 1971), the Colorado River Basin Pilot Project (Cooper and Saunders 1980; Cooper and Marwitz 1980), the Sierra Cooperative Pilot Project (Reynolds and Dennis 1986; Marwitz 1987a,b), and the Arizona Snowpack Augmentation Program (Super et al. 1989; Bruintjes et al. 1994; Klimowski et al. 1998). In general, supercooled liquid water (SLW) is available during at least some part of the storms, usually being concentrated in the lower portions of the clouds, and especially in shallow clouds with relatively warm tops. Average integrated SLW amounts are normally limited; this implies low cloud liquid water contents, as has been verified with aircraft observations (Super 1990). This indicates that, except in rare cases, only moderate snowfall rates can be produced by seeding. Radiometric measurements made during some of the more recent field projects suggest that considerable amounts of SLW pass overhead during the winter season, unused by nature. As Super suggests, a primary challenge to the weather modification community is to determine what fraction of this excess SLW can be brought to the surface by application of cloud seeding technology.

Greater understanding of the physical processes involved in natural and seeded clouds and the potential for increases in precipitation as a result of seeding continue to be subjects of scientific investigation, including numerical modeling efforts as reported here. One of the main purposes of a numerical modeling study of any complex physical phenomenon is to help gain further insight into how the processes involved in that phenomenon interact. Over the past several years, the numerical simulation of weather modification by cloud seeding has been a subject of increasing interest (Orville 1996). The successful numerical simulation of the evolution of mountain-induced clouds and cloud seeding should lead to a much better understanding of these interrelated subjects.

We have simulated the effects of cloud seeding for a number of years, concentrating primarily on cloud-scale models and summertime convective cloud situations. In the past few years, we have applied the Clark three-dimensional, time-dependent nested grid model to conditions in the Black Hills of South Dakota and Wyoming. A recent series of numerical simulations involved natural and seeded cases for a 4-day storm period in April 1995 (Farley et al. 1997). The results indicated that ground-based ice-phase seeding worked on only one of the four days and produced a redistribution of, as well as changes in, precipitation over the area.

The current study, which involves the same 4-day storm period, addresses issues related to the airflow and microphysical aspects of the natural cases for each of the four days simulated. Section 2 gives a brief description of the model used in this study. Section 3 describes the synoptic situation and observed precipitation patterns. The results of the primary model runs are presented and discussed in section 4. Section 5 provides a more general discussion, including some additional sensitivity tests and items relative to the seeded cases in Farley et al. (1997). This is followed by some general conclusions of these studies.

Model description

The dynamic framework for this study is the three-dimensional, time-dependent nonhydrostatic anelastic nested grid model developed by Clark and associates (Clark 1977; Clark and Farley 1984; Clark and Hall 1991). A terrain-following vertical coordinate transformation allows the treatment of realistic, complex topography. Subgrid-scale turbulent processes are parameterized using the first-order closure scheme of Lilly (1962) and Smagorinsky (1963). The finite-difference formulation of the model employs a second-order leapfrog scheme for momentum (Arakawa 1966; Lilly 1965). The positive-definite advective transport algorithm of Smolarkiewicz (1984) is used for heat and moisture variables.

Boundary conditions are specified only for the outermost model domain, with free-slip conditions assumed for the velocity components and zero-flux conditions applied to heat and moisture variables at the upper and lower surfaces of the model. A Rayleigh friction and Newtonian cooling absorber is applied in the upper regions of the outermost domain to prevent the reflection of vertically propagating gravity waves. An open-boundary extrapolation scheme, with a weak degree of specification applied to the velocity components and the potential temperature and water vapor fields, is used at the lateral boundaries.

The single-moment (mixing ratio) microphysical formulation employed is that of Lin et al. (1983) and uses bulk water equations for cloud water, cloud ice, snow, rain, and graupel/hail. Our extension of the microphysics of the 3D model to include the ice phase (described in Farley et al. 1992) was done independent of, but concurrent with, the formulation discussed in Bruintjes et al. (1994). The microphysical scheme of Lin et al. was specifically designed for summertime convective situations; one part of this study is an assessment of its applicability to orographically forced cold-season clouds and precipitation. A key aspect in this regard is the ice nuclei activity spectrum and the temperature at which pristine ice is initiated.

The model employs two domains in these simulations. The outer model domain has horizontal grid intervals of 8 km and a vertical resolution of 500 m. The inner model domain uses 4-km horizontal and 250-m vertical resolution. The orographic features providing low-level forcing are illustrated by the topography contours and 3D depiction of the Black Hills region shown in Fig. 1. The Bear Lodge Mountains, which are referred to frequently in the following sections, constitute the smaller-scale topographic feature just northwest of the main body of the Black Hills.

The model simulations were conducted using the morning sounding for Rapid City, South Dakota, for each of the 4 days and running the model until a quasi-steady solution1 was attained. The airflow was initialized with a three-dimensional potential flow solution; this solution captured the basic character of the airflow to a sufficient degree that temporal tendencies were relatively small even in the early stages of the integrations. Finescale features of the airflow, especially those associated with lee vortices and reverse flow (if present) continued to evolve weakly with time over the course of the integrations. Three hours of simulated time were adequate for our purposes for three of the days (days 1, 2, and 4). Day 3 displayed a more pronounced dependence on microphysical aspects and was run to 6 h.

Synoptic situation and observed precipitation patterns

The 8–11 April 1995 storm period was chosen to be modeled because of its variable airflow and precipitation characteristics. As the storm progressed, the low-level winds shifted from an east-southeasterly to northerly direction. Figures 2 and 3 show the 500-hPa-level winds and the 1200 UTC atmospheric soundings for the study period. The 4-day storm underwent a rather common progression characterized by the approach from the northwest, and passage to the south, of an upper-level cold trough. At the surface the Black Hills are under the influence of a stationary front to the west and a surface high pressure system to the north for the first 2 days, leading to easterly winds at the surface in Rapid City on the eastern slope of the Black Hills. As the upper trough moves through the area a surface low organizes and moves south and east of the Black Hills, leading to northerly winds at the surface for the last 2 days of the storm period.

The sounding data shown in Fig. 3 indicate a shallow fog and cloud layer for the first 500–1000 m above the surface on the first 2 days. The temperatures range from about +3° to 0°C in the cloud layer on the first day, surface winds are from the east. Cooling occurs so that the temperatures fall to −3° to −7°C in the cloud layer on 9 April (day 2), with surface winds shifting to the southeast. On 10 April (day 3), the cooling has continued and the cloud layer has deepened with the cloud top at about 680 hPa. The temperature at cloud top is about −13°C. The winds switch from northeast to south in the layer from 600 to 550 hPa. On 11 April (day 4), the midlevel of the cloud layer has cooled to about −15°C, with strong low-level winds from the north.

The observed precipitation patterns and amounts are shown in Fig. 4. Data from 57 stations were used to construct the figures. The first 41 of these are National Oceanic and Atmospheric Administration stations in western South Dakota and eastern Wyoming, which are augmented by 16 stations from the Black Hills Hydrology Study conducted by the U.S. Geological Survey. The station locations are shown in Fig. 5. Coverage is better in the northern and southeastern hills than in other portions of the region. There were reports of light rain and snow on 8 April at the Rapid City airport. The isohyetal pattern for the first 2 days indicates precipitation maxima on the eastern and northern hills (Figs. 4a,b), in response to the easterly airflow. The change to northerly flow on the third day shows a characteristic snowfall pattern of a maximum in the northern hills, with an unexpected maximum to the south of the hills extending slightly to the southwest (Fig. 4c). This maximum is thought to occur in a leeside convergence region. The final-day precipitation pattern in Fig. 4d shows the effects of the storm moving out of the area.

Overall, the estimated total precipitation for the April storm was 320 × 106 metric tons (for the area shown in Fig. 4). This amount of precipitation is significantly larger than an average localized summertime convective storm (of order 2 million metric tons). In general, the April and spring precipitation climate datasets of DeGaetano and French (1991) compare well to the observed April 1995 storm precipitation for the different wind regimes. Areas of precipitation maxima in the climate data and for the storm under study generally shift toward the north as the winds shift to the north.

Results

The model results for each of the 4 days will be presented in chronological order in this section. Additional sensitivity tests are reported and discussed in section 5. Discussion of the model results includes comparison to theory and the results of other studies in addition to the observed cloud cover and precipitation characteristics. The simulated airflow for each of the days is discussed in terms of the dimensionless Froude number. The Froude number was calculated from the sounding data using the layer from the surface to the first sounding point above the crest of the hills. The stability was determined over the depth of this layer; potential temperature and wind speed were layer averages. The barrier height was set at 1150 m for easterly and southeasterly flow (days 1 and 2) and 1300 m for northerly flow (days 3 and 4). Values of the Froude number derived using the layer from the surface to 700 hPa were consistent.

The drag coefficient was set to zero in these simulations to avoid nonphysical effects induced by the model grid nesting scheme. With surface friction active, the simulations were plagued by weak, but not insignificant, artificial convergence zones along the projection of the inner model domain boundaries onto the outer domain. Neglecting surface friction causes the winds at the surface and the lowest layers to be overestimated somewhat, but is not crucial to this study. Other studies of a similar nature have also neglected the effects of surface friction (e.g., Bruintjes et al. 1994; Smolarkiewicz and Rotunno 1989, 1990).

Model results for 8 April 1995 (day 1)

General flow and vertical motion

Figure 6a displays the inner-domain surface wind vectors for the 8 April 1995 simulation. The flow is from the east at low levels at about 6 m s−1 with a maximum of about 11 m s−1 from the south over the central hills. A wind component of about 6 m s−1 from the east slows to about 2 m s−1 as it encounters the eastern slopes of the hills. The low-level winds from the southeast and east split and flow around the Black Hills and then converge in the northern region of the hills. The winds veer around to predominantly westerly above 3 km mean sea level (MSL).

Because of the relatively weak surface winds, the vertical velocity fields were also relatively small (less than 0.1 m s−1) near the surface of the central hills as shown by the contours in Fig. 6a. At the northern region of the hills the descending airflow produced a maximum downward motion of about 0.25 m s−1, while the converging winds above this point produced an upward vertical motion of about 0.15 m s−1 at about 2 km MSL (shown more clearly in Fig. 6b). Also indicated in Figs. 6a,b is a gravity wave at about X = 152 km with a south-to-north orientation (aligned with southerly flow over the hills). This gravity wave has a wavelength of about 40 km and maximum upward and downward velocities of about 0.45 m s−1. The cross section of the vertical velocity field in Fig. 6b shows very weak upward motion near the surface.

The Froude number calculated using the sounding data was 0.26, suggesting complex airflow over and around the hills. The model representation of the flow fits the calculated Froude number well; airflow originating at low levels is diverted around the hills after undergoing limited ascent, whereas airflow originating at levels within about 400 m of the crest flows over the hills and is responsible for the gravity wave.

Cloud fields

The cloud water field in Fig. 6c shows that the bulk of the cloud water is produced by orographic lifting along the eastern slope of the hills. The maximum mixing ratio of the cloud water field was about 0.05 g kg−1 at the eastern region of the hills southwest of the Rapid City National Weather Service (NWS) indicator (hereinafter, RAP) A more extensive area of cloud is indicated above the surface extending eastward. Another weak maximum, associated with converging winds, occurred in the northern region of the hills just east of the Bear Lodge Mountains. It should be noted that earlier in the simulation the cloud cover was more extensive in the east and that the Bear Lodge area did not develop cloud until about 2 h into the simulation. The vertical cross section of the cloud field at Y = 144 km given in Fig. 6d shows that the thickness of the cloud southwest of Rapid City is about 1 km. The observed synoptic condition at RAP had a layer of shallow fog at the surface, which resembled the model representation of the cloud field.

The observed precipitation pattern for 8 April shown in Fig. 4a was due to rain or a mix of snow and rain at the surface, with maxima (>4 mm) in the northern Bear Lodge Mountains and to the east of the southern hills. This is in rough agreement with the precipitation climate dataset of the Black Hills region (DeGaetano and French 1991), which shows a secondary maximum in the northern hills under east wind conditions in April. The model, however, failed to produce precipitation in this case. This is due to the fact that the 0°C isotherm was above the simulated cloud top and the model is currently restricted to form precipitation via an ice path (for the low cloud water contents characteristic of these cases). The representativeness of the morning sounding was also called into question because snow was observed on this day. The issue of the representativeness of the input conditions and possible microphysical defects of the model in terms of both the formulations themselves and assumed values of some parameters are discussed below in section 5.

Model results for 9 April 1995 (day 2)

General flow and vertical motion

The 1200 UTC sounding for Rapid City for 9 April 1995 (Fig. 3b) shows southeasterly flow at the surface veering to predominantly southwesterly flow above 3 km MSL. Figure 7a shows the inner-domain representation of the surface airflow around the Black Hills on this day. The simulated airflow is generally from the southeast and splits at the southeastern part of the hills and converges to the north of the hills. The maximum surface wind vector over the central area of the hills is about 14 m s−1 from the south. A moderate surface wind of about 8 m s−1 to the southeast of the hills slows to about 3 m s−1 as it approaches the southeast quadrant of the hills. An area of convergence is indicated north of the hills, just east of the Bear Lodge Mountains. This convergence zone and downward motion in the northern hills is essentially the same as the simulation of the first day; near the surface the flow is downward, whereas at about 500 m above the convergence point, the flow is upward.

The vertical velocity field shown in Fig. 7a indicates downward motion of about 0.4 m s−1 near the surface in the northern hills. An upward-propagating gravity wave is produced over the northern hills above the region where the downward airflow and converging airflow occurs. The Y–Z cross section of the vertical velocity field at X = 160 km in Fig. 7b shows the gravity wave formed over the northern hills. This gravity wave has an upward velocity of about 0.8 m s−1 in Fig. 7b. The windward side of the Bear Lodge Mountains has an upward velocity of approximately 0.1 m s−1. There are weak surface updrafts on the order of 0.05 m s−1 in the southeastern region of the hills; this is the area where cloud is formed (Figs. 7c,d).

A Froude number of 0.49 was calculated using the sounding data. This suggests that air originating within about 650 m of the crest flows over the hills and air at lower levels goes around the hills. The airflow at the northern part of the hills shows an area of convergence and turning of the winds with a hint of reversal of the airflow. This turning of the wind and airflow reversal is consistent with expectations for the calculated Froude number based on other studies such as Hunt and Snyder (1980).

Cloud and precipitation fields

Figures 7c,d show the main cloud formation is in the southeastern region of the hills (as expected) because of orographic lifting. A weak maximum is just northwest of RAP while the primary maximum is near Wind Cave (27 in Fig. 5). The weak upward motion produced a maximum mixing ratio of about 0.13 g kg−1 of SLW. The X–Z cross section at Y = 128 km (Fig. 7d) indicates the depth of the orographic cloud is about 1 km, which agrees with the sounding at RAP for this day (Fig. 3b). An interesting point to be made is that there was no cloud formed in the areas associated with higher vertical velocities (i.e., near the Bear Lodge Mountains and where the gravity wave was located) because of the lack of moisture (see sounding in Fig. 3b). As in the day 1 simulated case, there was a larger areal extent of cloud cover above the surface and at earlier times in the simulation.

The snow mixing ratio at the surface is shown in Fig. 8a. The areal extent of the snow field is slightly larger than the cloud field. However, the amount of the snow is very small compared to that of the cloud water. The primary maximum in the southeastern region of the hills has a mixing ratio of about 0.01 g kg−1, the other northwest of RAP is 0.006 g kg−1. The X–Z cross section at Y = 132 km (Fig. 8b), shows that the thickness of the snow mixing ratio field extends to about 1 km above the surface. The simulated snow flux at the surface (not shown), has a maximum rate of about 0.04 mm h−1. The simulated snow accumulation at 180 min indicates a maximum value of about 0.12 mm as shown in Fig. 8c. A calculated 24-h accumulation would be about 1 mm if steady-state assumptions were used. The observed precipitation pattern (Fig. 4b) indicates a primary maximum (>5 mm) northeast of the Bear Lodge Mountains with a broad secondary maximum (>3 mm) over the central Black Hills region. The simulation greatly underestimated precipitation amounts in comparison with the observed values, and the pattern was shifted southeastward.

Model results for 10 April 1995 (day 3)

Day 3 results of the 4-day storm period are described next. During the course of the model run, the cloud water field decreased markedly with time after the snow field developed. The total simulated time for this run was 360 min and the subsections discuss the microphysical fields at both 180 and 360 min.

General flow and vertical motion

On this day the low-level airflow switched to be from the north-northeast. The winds reverse directions aloft (see Fig. 3c). This reversal of flow from the north to the south occurs near 4 km MSL. It causes precipitation content at upper levels of the cloud to be spread to the north (as discussed in more detail later).

Figure 9a shows the surface wind vectors of the airflow around the Black Hills, with a maximum value of about 13 m s−1 from the northeast over the central region of the Black Hills. As the airflow approaches the hills, the flow splits at the northern tip of the hills and converges in the southwestern region of the hills. Some lee flow reversal is also seen in this region of convergence. The airflow is very complex and two locations in the Black Hills are discussed in more detail; the northern tip where there is orographic lifting, and the region of convergence over the southwestern sector of the hills.

For the northern location, Fig. 9a indicates the northerly component of the low-level winds slows from about 6 m s−1 to almost 2 m s−1 as they impinge on the northern slope of the hills. The more peripheral northerly flow slows slightly before accelerating after being diverted around the hills. The contours of vertical motion at the surface in Fig. 9a show that the northern hills and the Bear Lodge Mountains each have upward motion of about 0.1–0.15 m s−1. Figure 9b, the Y–Z cross-sectional view of the vertical velocity field at X = 132 km, also shows this upward motion in the northern hills.

Figure 9a also shows much of the low-level northerly airflow is diverted around the hills and converges southwest of the hills. Air that is forced up and over the hills switches to downward motion (on the order of 0.3 m s−1) downstream of the crest of the hills. Slightly farther to the south, lee-side reversal of the flow is evident. This induces weak upslope flow, which provides a low-level connection to the gravity wave formed aloft. Figures 9b–d show details of this gravity wave formed over the southwestern hills, which has maximum upward motion of about 0.45 m s−1. The upward air motion in the southwestern hills protrudes up to about 4 km MSL (above the region where the winds shift from northerly to southerly) and is tilted to the north. Although the mechanism is not understood, the reversal of the airflow above 4 km MSL appears to absorb the gravity wave energy in this case. Figure 9c, the horizontal cross section of the vertical velocity field at Z = 2.5 km MSL, shows another perspective of the gravity wave, which is aligned with the northeasterly flow over the central Black Hills.

A Froude number of 0.42 was calculated using the sounding data. This number suggests complex nonlinear airflow with low-level airflow mainly around the barrier and higher level (within about 500 m of the crest) airflow over the barrier. This number also agrees with the complexity of the winds generated in the central area of the Black Hills. Results from other studies with Froude numbers similar to the calculated value confirm that lee flow reversal should occur as indicated in the model results.

Cloud and precipitation fields at 180 min

The northerly flow produces a moderate amount of cloud water over the northern hills even though the upward motion is relatively weak. Figure 10a is the surface plot of the cloud field and shows a maximum area of cloud water in the northern hills, a second over the Bear Lodge Mountains and a third maximum near Harney Peak in the south central hills. The maximum mixing ratio value in the northern hills is about 0.25 g kg−1, about 0.18 g kg−1 for the Bear Lodge Mountains, and about 0.13 g kg−1 for Harney Peak. Figures 10b,c show Y–Z and X–Z cross sections of the cloud field at X = 132 km and Y = 200 km, respectively. A cloud thickness of about 2 km is shown in these cross sections for the northern hills. The entire northern portion of the model domain is overcast as a result of the spreading of the low-level cloud aloft. Another area of cloud formation is associated with the convergence region and gravity wave in the southwestern hills. The Y–Z cross section given in Fig. 10b shows the cloud in this region, with a maximum of 0.14 g kg−1, extends beyond 4 km MSL.

The entire cloud formed in the northern hills region is supercooled, but does not have cloud ice present because the cloud top is just below the assumed ice initiation temperature of −15°C at about 3.75 km MSL (see Fig. 3c). A cirrus cloud shield with a maximum ice content of 0.015 g kg−1 is indicated between 8 and 10 km MSL, in Figs. 10b,c. This simulated cirrus cloud covers the entire Black Hills region in agreement with cloud cover in the synoptic observations.

The surface plot of the snow field in Fig. 11a shows that the northern hills region has not experienced any snow at 180 min into the simulation. However, the southwestern hills region has a maximum snow mixing ratio at the surface of about 0.05 g kg−1. Figure 11b, the Y–Z cross section of the snow field at X = 128 km, shows that the snow field produced in the cloud associated with the gravity wave is about 3 km thick with a maximum mixing ratio of about 0.13 g kg−1. The maximum snow accumulation shown in Fig. 11c for the southwestern region is about 0.12 mm. The corresponding maximum snow flux at this time is 0.22 mm h−1; comparing accumulation and flux values, it is clear the snow process has been active for less than 1 h.

Cloud and precipitation fields at 360 min

From Fig. 12a, the cloud water in the northern hills region is seen almost to disappear 6 h into the simulation. The maximum mixing ratio at this time is less than 0.01 g kg−1. Ice and snow are initiated at about 240 min over the northern hills. The snow grows rapidly, consuming most of the cloud water in that region. However, the location and character of the cloud associated with the gravity wave have not changed although the maximum mixing ratio has decreased to less than 0.1 g kg−1 (Fig. 12b). The upper-level cirrus deck noted in the 180-min results has become slightly thicker and the maximum ice content has increased to about 0.04 g kg−1.

The Y–Z cross section of the snow field at X = 128 km in Fig. 12c shows that the northern hills region now has a maximum snow mixing ratio of about 0.04 g kg−1. In the vicinity of the gravity wave over the southern hills, an increase of the snow field mixing ratio to about 0.23 g kg−1 is seen.

The maximum snow flux associated with the gravity wave has now increased to about 0.52 mm h−1 (not shown) in the southwestern region of the hills and to about 0.14 mm h−1 over the northern hills. The snow accumulation at 360 min, shown in Fig. 12d, indicates that the maximum depth for the southwestern region has increased to nearly 1.4 mm, whereas the maximum for the northern hills is 0.5 mm. It should be stressed that there is only weak observational support for the model-produced precipitation maximum in the southwestern hills. The observed precipitation pattern (Fig. 4c) indicates a primary maximum in excess of 10 mm, in the northern hills near Lead (16 in Fig. 5) and secondary maxima in excess of 6 mm for RAP, the higher regions of the Bear Lodge Mountains and a relatively broad area at the southern extremity of the Black Hills. The observed hourly winds at RAP shifted to a more northerly direction a couple of hours after the 1200 UTC sounding; this wind shift may be responsible for the difference between the model results and observations regarding the positioning of the southern precipitation maximum.

Model results for 11 April 1995 (day 4)

General flow and vertical motion

From the inner-domain representation of the wind vectors shown in Fig. 13a, the general surface flow around the Black Hills on 11 April 1995 can be seen as northerly. The flow is split slightly as it impinges on the northern part of the hills and converges about 40 km south of the southern boundary of the inner model domain. Most of the flow is over the hills, with the maximum wind vector depicted over the central hills of about 31 m s−1. The northerly component of the winds is strong up to a height of about 3 km MSL, but winds are primarily easterly between 4 and 12 km MSL (Fig. 3d).

Figure 13a also shows the vertical velocity at the surface indicating upward motion of about 0.5 m s−1 in the northern hills, whereas vertical velocity of about 0.3 m s−1 is indicated on the northern slope of the Bear Lodge Mountains. Descending motion of corresponding magnitude is seen to the lee of each updraft area. A propagating gravity wave with upward motion of about 0.7 m s−1 is seen at about 6 km MSL in Fig. 13b and was probably induced by the northerly flow over the hills.

A Froude number of 1.27 was calculated using the RAP sounding data, which suggests that the airflow is over the hills and little, if any, flows around the hills. The simulated wind fields and the basic character of the flow agree with theory, as well as studies done by Hjelmfelt and Farley (1992) and Hunt and Snyder (1980). Froude numbers in this range confirm that large-amplitude gravity waves could be present as depicted by the model.

Cloud and precipitation fields

Figure 13c shows a plot of the cloud field at the surface and Figure 13d displays the Y–Z cross section at X = 128 km. As would be expected for a northerly flow over the hills, cloud is formed on the northern slopes. Two main areas of SLW are found, a small region on the northern portion of the Bear Lodge Mountains, and a larger one on the northern slope of the Black Hills. The SLW region is about 2.5 km in depth over the northern hills, and about 1 km in depth over the Bear Lodge Mountains. This agrees well with the estimated cloud depth from the sounding on 11 April 1995 (see Fig. 3d). The maximum mixing ratio of SLW produced over the northern hills is 0.13 g kg−1 and just over 0.07 g kg−1 over the Bear Lodge Mountains. This agrees with theory on where SLW should form for this flow regime, although the mixing ratio amounts generally are small for orographic clouds.

In addition to the upslope-induced low clouds just noted, the model also indicates ice cloud formation associated with the gravity wave. This ice cloud is indicated between 6 and 9 km MSL in Fig. 13d. It is formed just above the updraft maximum of the dominant mode of the gravity wave. The horizontal extent of upper- and lower-level clouds indicates about 70% coverage whereas the surface synoptic chart shows the entire Black Hills region as being cloudy on that day.

The snow mixing ratio at the surface depicted in Fig. 14a shows a maximum of about 0.32 g kg−1 over the northern hills and a secondary maximum of about 0.18 g kg−1 over the Bear Lodge Mountains. Figure 14b, the Y–Z cross section of the snow field at X = 128 km, shows that the depth of the snow content over the northern hills is about 2.5 km.

The snow accumulation at the surface, shown in Fig. 14c, gives the northern hills a maximum accumulation of about 2.6 mm for the 180-min simulation. It can be seen that the snow accumulation over the northern hills is about twice that over the Bear Lodge Mountains. Assuming steady-state conditions for a 24-h period yields a maximum liquid equivalent of nearly 21 mm. The observed maximum value in the northern hills was about 6-mm liquid equivalent (Fig. 4d) with a broad area in excess of 6 mm along the eastern slope of the hills and plains south of Rapid City.

Discussion

This section provides additional discussion of the impact of various microphysical assumptions as well as the basic procedure chosen for the conduct of these numerical experiments. Questionable microphysical parameterizations of particular relevance to this study are reviewed and additional simulations testing the sensitivity to ice initiation are presented and discussed. This is followed by a discussion of how well the morning sounding for each day of this study represents the environmental conditions responsible for the clouds and precipitation observed on that day.

Microphysical aspects and sensitivity tests

The bulk water microphysical scheme employed in the model was designed for convective clouds in the northern Great Plains and is currently set up to produce precipitation via ice processes for the low liquid water contents typical of cold season situations. Based on our experience in modeling warm season convection, the liquid precipitation formation process in the model requires relatively high water contents not present in these type of storms. The inclusion of a drizzle formation process seems warranted for certain situations, but would probably be ineffective for the low liquid water contents of the current study (rarely greater than 0.2 g kg−1). This supposition is based on the findings of the Winter Icing and Storms Project. Rasmussen et al. (1995) report that drizzle drops tend to form in regions of the cloud with SLW greater than 0.25 g m−3, although low concentrations of smaller drizzle drops are also found in portions of the cloud containing lower values of SLW. Pobanz et al. (1994) note similar findings for a large number of cases; their Table 1 indicates that large drops are present in all cases with SLW values greater than 0.3 g m−3. Even though a drizzle formation process may not have played a significant role in the current study, such a process should be included in future model formulations, especially when applied to long-lived clouds such as marine stratocumulus and upslope situations. Efforts along these lines are ongoing.

The ice nuclei activity spectrum and the initiation temperature of pristine natural ice crystals are more critical parameters in this study. Typical values for the ice initiation temperature in the range of −15° to −20°C had observational support for our work with convective clouds but lack that observational basis for the cold-season, orographically forced clouds of this study. Simulations of the first 2 days were run with an ice initiation temperature of −10°C instead of the normal value of −15°C because of the fact that shallow clouds with relatively warm cloud-top temperatures were anticipated based on the soundings.

For the simulation of day 1, the shallow (∼1-km depth) cloud deck formed in the upslope flow along the eastern edge of the Black Hills had tops warmer than 0°C. Therefore, the simulation, which was restricted to an ice path, did not produce precipitation. The pattern of the simulated cloud over the eastern hills, however, was similar to that of the observed precipitation in that region. The simulation also indicated limited cloud formation along the eastern slopes of the Bear Lodge Mountains in contrast to the primary precipitation maximum observed over the northern portion of the Bear Lodge Mountains.

The simulation of day 2 produced a shallow cloud deck similar to that of day 1 although the atmosphere had cooled sufficiently that the −10°C initiation temperature for ice triggered a small amount of precipitation. The Fletcher ice nuclei activity spectrum employed in the model is generally conceded to underestimate ice nuclei at relatively warm temperatures. An alternative form of the ice nuclei spectrum based on supersaturation with respect to ice developed by Meyers et al. (1992) (hereinafter referred to as Meyers form) predicts much higher concentrations of pristine ice at relatively low supercoolings. Although the Meyers and Fletcher forms predict roughly equivalent concentrations of ice nuclei at −20°C, the Meyers form predicts more than a hundred-fold increase at −10°C.

Two sensitivity test simulations have been conducted for day 2 using the Meyers formulation. The first of these continued to use −10°C as the initiation temperature for cloud ice crystals, whereas the second increased the threshold temperature to −5°C. The Meyers form indicates about a factor-of-500 increase in active ice nuclei at −10°C in comparison with the Fletcher curve used for the case described in section 4b. Both sensitivity cases produce cloud and precipitation patterns very similar to the base case, but quantitative differences are quite pronounced. Cloud liquid water amounts are markedly decreased while cloud ice and snow contents are increased significantly for the Meyers cases. Maximum precipitation accumulations increased from 0.14 mm in the base case to 0.32 mm for the −10°C Meyers case and 0.35 mm for the −5°C Meyers case. It is also worth noting here that the Meyers cases exhibited a less steady microphysical character than the base case during the later stages of each simulation. This increased unsteadiness in the later stages of the Meyers cases is due to the fact that the locations of maximum values are more variable than in the Fletcher case. Increased ice production in the Meyers cases depletes the SLW locally resulting in new maxima developing in other regions of the extensive cloud deck along the eastern slopes of the Black Hills. Although the Meyers cases increased the surface precipitation amounts in better agreement with the observed precipitation, there was no significant improvement in the prediction of the precipitation pattern.

The results for day 3 presented in section 4 apply through a 6-h simulation, starting from the morning sounding for the day. The actual winds switched more to the northwest as the day progressed, but the model was not updated accordingly. The observed precipitation for the day is given in Fig. 4c. The northern maximum is picked up by the model, but the maximum is misplaced slightly in the south. Other modeling studies (Hjelmfelt et al. 1994) show that the winds at Rapid City change little as the winds in the northern Black Hills shift from northeast to northwest. The northwest winds would tend to move the convergence zone over the southwestern hills more to the southeast.

The microphysical evolution of the base case simulation for day 3 displayed a much stronger time-dependent character (and also a much more dramatic response to cloud seeding) than the other 3 days. This is the reason for the longer-term integrations applied to the day-3 cases. The strong time-dependent character of the base case simulation is a direct result of the fact that the cloud-top temperature for the cloud deck formed in the upslope flow over the northern hills is marginally warmer than the assumed ice initiation temperature of −15°C for the first 3 h of the simulation. An extensive cloud deck forms during this time period. Shortly before the fourth hour, the ice process is initiated in the northern stratiform deck and precipitation develops rapidly, quickly eroding the cloud deck away. The cloud seeding applied to this case initiated precipitation in the early stages for the cloud deck formed over the northern hills, leading to a markedly different evolution.

As a test of model sensitivity, the day-3 simulation was repeated, but with the ice initiation temperature increased to −10°C (as had been done for the first 2 days). This sensitivity case produced a solution that was very similar to the seeded case reported in Farley et al. (1997) with regard to the cloud formed over the northern hills. The cloud formed over the southwestern region of the hills was not modified appreciably by the choice of ice initiation temperature. Seeding applied to day-3 with natural ice initiated at −10°C proved to be ineffective. These results indicate that the model displays a very strong dependence on the presence of ice but much less sensitivity to details of how this ice is initiated.

The model response to the ice nuclei activity spectrum and the ice initiation temperature in the sensitivity tests reported above seemingly invalidate the positive day-3 seeding results reported in Farley et al. (1997). This is not necessarily true. Positive effects of cloud seeding (in the real world, was well as in numerical simulations) require that natural ice initiation occur at colder temperatures than ice produced by seeding. The previously reported day-3 results merely illustrate an example of what could happen in a case naturally deficient in producing ice. The actual ice initiation temperature for day 3 is unknown.

The last simulated day, 11 April 1995 (day 4), was characterized by much stronger low-level winds, which produced a deeper and more persistent orographic cloud. Details of ice initiation are not particularly important in simulations of this case. Significant amounts of precipitation were observed in the northern half of the hills and to the east of the Black Hills as the storm moved east on day 4. This movement was not captured in the model simulation, as changing conditions were not modeled. The simulation did a good job of picking up the precipitation maximum observed over the northern hills. This is consistent with results from another case with strong north-northwest flow and a deep upslope cloud formation (Li 1996).

The model appears to perform well for sufficiently cold strongly forced (high wind) situations, but is much less reliable for the more marginal cases characterized by warmer, weakly forced conditions. The degree of realism obtained in simulations of these marginal cases is very dependent on the accuracy of key microphysical assumptions relative to ice initiation. Once sufficient ice has formed, the model microphysics seem reasonable. The vast majority of the growth of snow is due to depositional growth from the vapor. Riming exerts a significant influence only in regions of relatively high SLW (>0.1 g kg−1). The treatment of pristine cloud ice crystals, and the conversion of ice crystals to snow, would probably be improved by incorporating a prognostic equation for ice crystal number concentration in the microphysical scheme.

Retrospective

Some of the problems encountered in this study were due to the fact that the 1200 UTC soundings for Rapid City used to initialize the model for each of the 4 days were not representative of each 24-h storm period. The 0000 UTC soundings may have been more representative of conditions that produced the observed precipitation patterns and would probably have been a better choice for the simulations because they generally indicated more moisture aloft. However, the decision to use the morning sounding as representative of each of the 4 days was made early on in the course of this work.

In particular, for day 1, observations at RAP show that as the day progressed the surface temperature cooled to about 0°C and the depth of stratiform cloud extended to about 1.5 km above the ground whereas the winds at the surface and aloft did not change appreciably. For day 2, the 0000 UTC sounding for RAP again indicated a slightly cooler surface temperature and more moisture resulting in a deeper cloud. The surface wind also shifted to more easterly flow although the wind speed was not changed from 1200 UTC. As was noted earlier, the surface wind at RAP became more northerly 2 h after the 1200 UTC sounding for day 3, which may explain the mislocated precipitation maximum in the southern hills. For day 4, the surface wind direction became more northwesterly about an hour after the 1200 UTC sounding. Snowfall was also heavier at RAP after the wind shifted to the northwest. This may account for the differences in the precipitation patterns between the simulation and the observations for day 4 although it is obvious that the observed storm was moving away from the Black Hills later in the day, producing heavy snow to the east of the hills.

A related issue is the ability of a single sounding location to represent conditions adequately for a mesoscale area the size of the outer model domain, especially if the sounding location is downwind of a topographic feature such as the Black Hills. The Clark model has the capability of incorporating larger-scale model or observational data to provide time-varying boundary conditions and heterogeneous initial conditions. This is no doubt preferable to the single sounding initialization and static boundary tendencies used in this study, and should result in better numerical simulations and provide a stronger link between simulated and real time. Unfortunately, it would have required nearly an order of magnitude more computer time for a continuous simulation of the 4-day storm period versus the snapshot approach for each of the 4 days used in the current study. It also would have made the cloud-seeding simulations, which were originally a primary focus of this study, more difficult in that the various generator locations would have been limited to a predetermined specific set of locations, which would then be turned on and off as the low-level winds changed.

Conclusions and final remarks

The model simulated the dynamics of the 4 days reasonably well when compared with theory, physical experiments, and numerical studies. The general cloud and precipitation patterns were also simulated reasonably well by the model in that as the wind regime changed, the pattern of cloud cover and/or precipitation fairly well represented the observations. Notable exceptions were the region of observed precipitation maximum in the vicinity of the Bear Lodge Mountains for the easterly wind regime where the model indicated limited cloud formation and the improper positioning of the southern precipitation maximum for day 3. The total precipitation amounts for each of the four simulated days were also generally underestimated in this study, although comparisons of observed and modeled precipitation amounts are somewhat dubious due to differences in appropriate time periods and extrapolations that must be made. Comparisons of precipitation patterns are much more meaningful.

Some general conclusions are the following.

  • The model performs well for cold strongly forced conditions but has trouble simulating warmer weakly forced situations that tend to be inordinately sensitive to the accuracy of microphysical assumptions, especially those relative to ice initiation.

  • Accurate representation of the environmental conditions responsible for the observed clouds and precipitation is a necessary, but not sufficient, condition for realistic simulations. The general cloud and precipitation patterns and the dynamics of the airflow would probably have been simulated better by the Clark model if we had taken into account the changing synoptic conditions. In general, the precipitation amounts were underestimated for environmental conditions based on the morning soundings.

  • The ice microphysics processes, developed for convective storms, need some improvements and/or modifications to simulate cold season stratiform precipitation properly. One such improvement to the microphysics would be to incorporate a more realistic ice nuclei activity curve at low supercoolings, which would produce more ice at relatively warm temperatures. Improved treatment of ice should also result from incorporating cloud ice number concentration as a prognostic variable. A drizzle process parameterization would also be appropriate in some situations.

  • Winds near the surface at Rapid City may not be representative of the winds in the northern Black Hills.

  • The positive seeding results reported for day 3 in Farley et al. (1997) are probably overstated somewhat given the model sensitivity to ice initiation. Although seeding proved to be effective for day 3 with natural ice initiation at −15°C, it was shown to be ineffective for ice initiation at −10°C. This attests to the fact that clouds (real or simulated) must be deficient in natural ice production for seeding to be effective.

As a concluding remark, the numerical simulations from this study suggest that numerically modeling precipitation patterns for different wind regimes (i.e., a“numerical precipitation climatology”) may prove to be a useful forecasting aid.

Acknowledgments

We gratefully acknowledge the assistance of Dan Driscoll and Jim Winter of the U.S. Geological Survey for providing precipitation data from the Black Hills Hydrology Study and Fred Kopp for performing the objective analysis of the precipitation data. We also thank Ms. Connie Crandall and Mrs. Carol Hirsch for their help in preparing this manuscript, and the reviewers for their comments and criticisms, which have resulted in an improved presentation. The work was supported by Grant ATM 9630008 and Grant ATM 9206919 from the National Science Foundation. The computations were performed using the facilities of the Scientific Computing Division of the National Center for Atmospheric Research, which is operated by the University Corporation for Atmospheric Research and is sponsored by the National Science Foundation.

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Fig. 1.
Fig. 1.

(a) The X–Y plot of the model domain used in the study. Inner model domain is indicated by right-angle markers. Topography is contoured at an interval of 100 m. (b) Three-dimensional depiction of the model topography viewed from the northeast [upper-right-hand corner of (a)].

Citation: Journal of Applied Meteorology 39, 8; 10.1175/1520-0450(2000)039<1299:NSOADE>2.0.CO;2

Fig. 2.
Fig. 2.

The 500-hPa analysis at 1200 UTC for (a) 8 Apr 1995, (b) 9 Apr 1995, (c) 10 Apr 1995, and (d) 11 Apr 1995 (from the NWS daily weather map series).

Citation: Journal of Applied Meteorology 39, 8; 10.1175/1520-0450(2000)039<1299:NSOADE>2.0.CO;2

Fig. 3.
Fig. 3.

Skew T–logp sounding for RAP at 1200 UTC on (a) 8 Apr 1995, (b) 9 Apr 1995, (c) 10 Apr 1995, and (d) 11 Apr 1995.

Citation: Journal of Applied Meteorology 39, 8; 10.1175/1520-0450(2000)039<1299:NSOADE>2.0.CO;2

Fig. 4.
Fig. 4.

Isohyets for the 24-h precipitation (mm) for each of the 4 days, reported 0700 LT on the following day. Isohyet contours are heavy solid lines and the topography is shown by fine dashed lines: (a) 8 Apr 1995, (b) 9 Apr 1995, (c) 10 Apr 1995, and (d) 11 Apr 1995. The contours of the topography are every 300 m, starting at 900 m.

Citation: Journal of Applied Meteorology 39, 8; 10.1175/1520-0450(2000)039<1299:NSOADE>2.0.CO;2

Fig. 5.
Fig. 5.

Map showing the locations of the precipitation stations used for this study.

Citation: Journal of Applied Meteorology 39, 8; 10.1175/1520-0450(2000)039<1299:NSOADE>2.0.CO;2

Fig. 6.
Fig. 6.

(a) Surface wind vectors and vertical velocity contours for the inner domain for 8 Apr 1995. The scale vector is shown in the lower right corner. Thick dashed lines show the topography using a 200-m contour interval. Solid straight lines show where cross sections are taken. Thin dashed lines are downward velocities and thin solid lines are upward velocities. (b) Inner-domain Y–Z vertical velocity cross section at X = 152 km. The contour interval is 0.05 m s−1 for (a) and (b). (c) Inner-domain model cloud water field at the surface. (d) Inner-domain X–Z cloud water cross section at Y = 144 km. The contour interval is 0.01 g kg−1 for (c) and (d).

Citation: Journal of Applied Meteorology 39, 8; 10.1175/1520-0450(2000)039<1299:NSOADE>2.0.CO;2

Fig. 7.
Fig. 7.

As in Fig. 6 but for 9 Apr 1995. (b) and (d) The Y–Z and X–Z cross sections are at X = 160 km and Y = 128 km, respectively.

Citation: Journal of Applied Meteorology 39, 8; 10.1175/1520-0450(2000)039<1299:NSOADE>2.0.CO;2

Fig. 8.
Fig. 8.

(a) Inner-domain snow mixing ratio at the surface for 9 Apr 1995. Thick dashed lines are the topography with a 200-m contour interval. Thin solid lines are snow mixing ratio contours. (b) Inner-domain X–Z snow mixing ratio cross section at Y = 132 km. The contour interval is 0.001 g kg−1 for (a) and (b). (c) Snow accumulation at the surface for 9 Apr 1995. The contour interval is 0.02 mm.

Citation: Journal of Applied Meteorology 39, 8; 10.1175/1520-0450(2000)039<1299:NSOADE>2.0.CO;2

Fig. 9.
Fig. 9.

(a) Surface wind vectors and vertical velocity contours for the inner domain for 10 Apr 1995. (b) Inner-domain Y–Z vertical velocity cross section at X = 132 km. (c) The X–Y vertical velocity field at 2.5 km MSL. (d) Inner-domain X–Z vertical velocity cross section at Y = 124 km. The contour interval is 0.05 m s−1.

Citation: Journal of Applied Meteorology 39, 8; 10.1175/1520-0450(2000)039<1299:NSOADE>2.0.CO;2

Fig. 10.
Fig. 10.

(a) Inner-domain cloud water field at the surface at 180 min for 10 Apr 1995. (b) Inner-domain Y–Z cloud cross section at X = 132 km. (c) Inner-domain X–Z cloud cross section at Y = 200 km. The contour interval is 0.02 g kg−1.

Citation: Journal of Applied Meteorology 39, 8; 10.1175/1520-0450(2000)039<1299:NSOADE>2.0.CO;2

Fig. 11.
Fig. 11.

As in Fig. 8 but at 180 min for 10 Apr 1995. (b) The Y–Z cross section is at X = 128 km. The contour interval is 0.01 g kg−1 for panels a and b, and 0.02 mm in panel c.

Citation: Journal of Applied Meteorology 39, 8; 10.1175/1520-0450(2000)039<1299:NSOADE>2.0.CO;2

Fig. 12.
Fig. 12.

(a) Inner-domain cloud water field at the surface at 360 min for 10 Apr 1995. (b) Inner-domain Y–Z total cloud cross section at X = 132 km. The contour interval is 0.01 g kg−1 for panels a and b. (c) Inner-domain Y–Z snow field cross section at X = 128 km. The contour interval is 0.01 g kg−1. (d) Inner-domain snow accumulation field at 360 min for 10 Apr 1995. The contour interval is 0.1 mm.

Citation: Journal of Applied Meteorology 39, 8; 10.1175/1520-0450(2000)039<1299:NSOADE>2.0.CO;2

Fig. 13.
Fig. 13.

As in Fig. 6 but for 11 Apr 1995. The Y–Z cross sections in panels b and d are at X = 128 km. The contour interval is 0.1 m s−1 for (a) and (b), 0.01 g kg−1 for (c), and 0.02 g kg−1 for (d).

Citation: Journal of Applied Meteorology 39, 8; 10.1175/1520-0450(2000)039<1299:NSOADE>2.0.CO;2

Fig. 14.
Fig. 14.

As in Fig. 8 but for 11 Apr 1995. The Y–Z cross section in (b) is at X = 128 km. The contour interval is 0.02 g kg−1 for (a) and (b), and 0.2 mm in (c).

Citation: Journal of Applied Meteorology 39, 8; 10.1175/1520-0450(2000)039<1299:NSOADE>2.0.CO;2

1

The quasi-steady state in these cases is based on a subjective determination rather than any statistical consideration. In a qualitative sense, dynamic aspects become steady early on. Microphysical aspects display more pronounced temporal variations for longer periods. Extreme and mean values of dynamic quantities and the various hydrometeor mixing ratios typically change by 10% or less over the last hour of the simulation.

* Deceased.

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