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Alexis B. Long

Abstract

Numerical solutions to the droplet collection equation, using certain polynomial approximations to the gravitational collection kernel, are examined to learn whether they usefully describe the evolution of a cloud droplet size distribution. The results for typical continental and maritime clouds show that the distribution is closely described if the kernel is replaced by
9x2y2R3xyR
or by
10x2R3xR
where R is the radius of the larger droplet, x its volume in cubic centimeters, and y the volume of the smaller droplet.

From the standpoint of including collision and coalescence of droplets in multi-dimensional cloud models an analytic solution to the collection equation is desirable. An attempt should be made to find such solutions based upon either of the above approximations. If these cannot be found because of the piecewise nature of the approximations, then solutions based on the portions for R≤50 μm would still describe the first few hundred seconds of droplet growth. A comparatively poor description of the droplet distribution comes from the most physically realistic analytic solution presently existing, based on the kernel approximation B(x+y)+Cxy.

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Alexis B. Long

Abstract

No abstract available.

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Alexis B. Long
and
Michael J. Manton

Abstract

Two anomalies are described which arise in the kernel for stochastic droplet collection when it is specified by the formula of Scott and Chen for the linear collision efficiency y(R,r) and by the formula of Wobus et al. for the droplet terminal velocity V(R). It is pointed out that if accurate values for y(R,r) are to be obtained for a given droplet pair by interpolation using data for specific droplet pairs, then for large droplet radii (R<30 μm) it is desirable that these data he tabulated for 2-μm intervals of R. It is shown that if the difference in terminal velocities of two droplets is computed from a formula approximating V(R) and composed of various functions V*(R) applicable over adjoining domains of R, then it is necessary that these functions be constructed so that the formula and its derivatives, at least up to second order, are everywhere continuous. An improved formula for V(R) satisfying this criterion is described.

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Alexis B. Long
,
Arlen W. Huggins
, and
Bernard A. Campistron

Abstract

A winter storm passing across the north–south-orientated Tushar Mountains in southwest Utah is investigated in this multipart paper. This Part I describes the evolving synoptic pattern, mesoscale kinematics, and calculated water release rates (condensation or deposition) in clouds over the western upstope part of the mountains. Horizontal mesoscale kinematic variables come from direct application of Volume Velocity Processing to single C-band Doppler radar data. Water release rates are computed from updrafts derived from the radar data and from the vertical gradient of saturation mixing ratio obtained from soundings.

In Stage I of the storm altostratus was present on the leading side of a long-wave trough. Weak updrafts occurred only at the higher altitudes within the clouds where there was convergence and large-scale synoptically forced lift. Downdrafts as great as −0.6 m s−1 occurred in the lower parts of the cloud where there was divergence. The downdrafts were induced in part by sublimation cooling of solid (ice) precipitation falling from the altostatus. Only virga was observed and the radar echoes did not reach the surface.

Stage II was initially dominated by passage of a short-wave aloft. Drier air associated with the short-wave led to complete evaporation of the altostratus of Stage I. The lower parts of this cloud (≤4.5 km MSL) eventually redeveloped into altocumulus.

Later in Stage II the wind veered more perpendicular to the mountains. Simultaneously, convergence developed in the lower 900–1200 m of the atmosphere, and mesoscale updrafts of 0.1–0.2 in m s−1 were calculated. Maxima in the water release rate were associated with the updrafts.

During Stage III a passing cold front influenced the kinematics and cloud and precipitation. From prior to frontal passage to a few hours afterward the wind beneath the frontal surface veered from southwesterly to northerly. There was strong convergence at low altitudes just upwind of the Tushar Mountains. It was accompanied by strong, deep mesoscale updrafts extending from near the ground up through the frontal surface and by water release maxima.

The storm changed character after the wind at low altitudes had veered to northerly and had become parallel to the Tushar Mountains. Convergence maxima continued to be present beneath the frontal surface but weaker. They preceded by ∼0.5 h maxima in the convergence above the frontal surface. Associated with these paired convergence features were updraft maxima located above the frontal surface. Water release rates were generally lower than earlier in Stage III. The decrease was greatest at low altitudes beneath the frontal surface where the wind had veered to northerly, where there was little uplift by the Tushar Mountains, and where updrafts were weak. Above the frontal surface the decrease in water release rate was not as great inasmuch as lift by the frontal surface was still occurring.

The storm dissipated in Stage IV. The axis of the longwave trough passed through the area, winds at higher altitudes beneath the frontal surface veered more northerly, and there was substantial drying at all altitudes above and below the frontal surface. The winds beneath the frontal surface were divergent, indicative of subsidence, and mesoscale downdrafts were present.

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Bernard Campistron
,
Arlen W. Huggins
, and
Alexis B. Long

Abstract

This Part III of a multipart paper deals with the analysis of turbulent motion in a winter storm, which occurred over the mountains of southwest Utah. The storm was documented with a long duration single Doppler radar dataset (∼21 h) comprised of volume scan observations acquired at 10-min intervals. Turbulence parameters were determined using a new technique of volume processing of single Doppler radar data.

Physical analysis of turbulence is restricted to three particular storm regions: a prefrontal region far removed from a cold frontal discontinuity, a frontal zone aloft, and a low layer in the post-frontal region where a long lasting (∼6 h) wind-maximum existed. The prefrontal period showed enhancement of turbulent parameters near 2.6 km height, apparently due to disturbed flow caused by an upwind mountain range. Turbulence parameters in this prefrontal region showed good agreement with K-mixing length theory. Within the frontal zone most turbulence parameters reached peak values, but were generally less than orographically induced turbulence values in the prefrontal period.

Turbulence in the low-level postfrontal period experienced periodic oscillations consistent with precipitation and kinematic variables described in Parts I and II, and associated with mesoscale precipitation bands. Acceleration of the valley-parallel wind component was apparent in prefrontal and postfrontal periods and was related to the specific valley configuration through a Venturi effect.

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Kenneth Sassen
,
Arlen W. Huggins
,
Alexis B. Long
,
Jack B. Snider
, and
Rebecca J. Meitín

Abstract

A comprehensive analysis of a deep winter storm system during its passage over the Tushar Mountains of southwestern Utah is reported. The case study, drawn from the 1985 Utah/NOAA cooperative weather modification experiment, is divided into descriptions of the synoptic and kinematic properties in Part I, and storm structure and composition here in Part II. In future parts of this series, the turbulence structure and indicated cloud seeding potential will be evaluated. The analysis presented here in Part II focuses on multiple remote sensor and surface microphysical observations collected from a midbarrier (2.57 km MSL) field site. The collocated remote sensors were a dual-channel microwave radiometer, a polarization lidar, and a Ka-band Doppler radar. These data are supplemented by upwind, valley-based C-band Doppler radar observations, which provided a considerably larger-scale view of the storm.

In general, storm properties above the barrier were either dominated by barrier-level orographic clouds or propagating mesoscale cloud systems. The orographic cloud component consisted of weakly (−3° to −10°C) supercooled liquid water (SLW) clouds in the form of an extended barrier-wide cap cloud that contained localized SLW concentrations. The spatial SLW distribution was linked to topographical features surrounding the midbarrier site, such as abrupt terrain rises and nearby ridges. This orographic cloud contributed to precipitation primarily through the riming of particles sedimenting from aloft, and also to some extent through an ice multiplication process involving graupel growth. In contrast, mesoscale precipitation bands associated with a slowly moving cold front generated much more significant amounts of snowfall. These precipitation bands periodically disrupted the shallow orographic SLW clouds. Mesoscale vertical circulations appear to have been particularly important in SLW and precipitation production along the leading edges of the bands. Since the SLW clouds during the latter part of the storm were based at the frontal boundary, SLW and precipitation gradually diminished as the barrier became submerged under the cold front.

Based on a winter storm conceptual model, we conclude that low-level orographic SLW clouds, when decoupled from the overlying ice cloud layers of the storm, are generally inefficient producers of precipitation due to the typically warm temperatures at these altitudes in our region.

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