4. Development of downdrafts

A  one-dimensional  modeling  study  by  Srivastava  (1985)  showed  how  downdraft production is related to evaporation of raindrops (ice was neglected in the model). The speed of the downdraft is a function of the liquid water content, sub-cloud lapse rate, and the distance the downdraft descends. In the absence of dynamic forcing, it is assumed that the surface outflow wind speeds are equal to the downdraft speed. This section describes how the model is applied to "dry" microbursts using observation from Utah. First we describe various thermodynamic and microphysical processes that govern downdraft production.

Following is a brief overview of how to convert reflectivity values to liquid water content: The water mass is obtained by manipulating the radar equation such that,

where:

M = liquid water content (kg m^-3)
Z_e = equivalent reflectivity (mm⁶ m^-3) assuming Rayleigh scattering.
 
Although equation [1] appears to be fairly simple, it is considerably more complex when using it operationally owing to the fact that Z_e is not a linear term. The equation for reflectivity per cubic meter is

, [2]

where:

Z_e = reflectivity factor (mm⁶ m^-3),
D = drop diameter (mm).

Since Z_e is related to the 6th power of D, then just a slight increase in the drop diameter can result in a large increase in reflectivity values. Hail contamination, even by small hailstones (e.g., D = 13 mm or 0.5 in), can lead to fictitiously high estimates of Z_e and, therefore, unrealistically high values of liquid water content. As an example, one-hundred 4-mm diameter rain drops contribute more total mass (3.351 g) than one 13-mm diameter water-coated hailstone (1.767 g). However, the equivalent reflectivity computations indicate that Z_e = 409,600 mm⁶m^-3 (or 56.1 dBZ) for the one-hundred 4-mm diameter drops, whereas Z_e = 4,826,809 mm⁶ m^-3 (or 66.8 dBZ) for the one 13-mm diameter "drop." Obviously, the equivalent reflectivity of a single 13 mm diameter hailstone will be less than 66.8 dBZ since a "drop" that size is not a true Rayleigh scatterer which further exacerbates the problem when dealing with hail contamination.

Once M, the liquid water content is obtained, it must be converted from units of g m^-3 to units of g kg^-1 for use in Srivastava's modeling results. This conversion is approximated by assuming 1 cubic meter of dry air has a specific mass of 1 kg. For additional information on obtaining  radar-derived  liquid  water  estimates,  see  Greene  and  Clark  (1972)  or  Stewart (1991a,b;1996).

While estimates of liquid water concentrations can be obtained from reflectivity values and use of the radar equation, this process is fraught with errors owing to unknowns in particle type, density, and concentration. Recall that our downdraft model consists of the negative buoyancy production from melting, evaporation and/or sublimation. Ice particles have a greater contribution than water drops to the downdraft process through cooling from sublimation (melting plus evaporation). In most of the cases that comprise this data set, cloud base temperatures  were  typically near -5° C.   Since ice  forms at  temperatures  between -10° and -20° C, the actual presence of ice in a storm depends on the vertical extent of the updraft. It is safe to assume that radar echoes above -10° C contain some amount of ice. If ice is present, the actual downdraft speed will be greater than the predicted speed.

Another factor is the drop size distribution. Srivastava showed how downdraft production is related to evaporation of a mix of small and large raindrops (he neglected ice.) Most of the smaller drop sizes cannot survive the large fall distances before evaporating completely, whereas large drops can usually survive most fall distances and will break up into smaller drops (D < 2 mm) that evaporate more efficiently (Srivastava, 1985; Tuttle et al, 1989). The result is that a deeper, stronger downdraft is produced by spreading the cooling rapidly over a greater vertical depth.

After a thorough analysis of several case studies from the Salt Lake City, Utah area, the authors modified Srivastava's results to fit the mean terrain elevation of (approx. 4,300 ft ASL) for the Great Salt Lake basin mainly west of the Wasatch Range. Table 1 is a nomogram of predicted peak wind gusts in kt (mph) as a function of (a) reflectivity values at or just above cloud base, and (b) sub-cloud lapse rates that occur over a depth of 3,800 m. Note that strong wind gusts of 40 to 50 kt can be achieved with just modest reflectivity values (~30 dBZ) when the sub-cloud lapse rates are near or exceed the dry adiabatic lapse rate (-9.8° C km^-1).

It is also important to remember that the nomogram does not apply to peak reflectivity at any altitude within the storm. For example, results of the 1978 NIMROD and 1982 JAWS experiments showed little or no correlation between peak radar echo intensity observed anywhere in the column and microburst-induced wind gusts (Fujita, 1979; Fujita and Wakimoto, 1983; Fujita, 1985). On the other hand, the authors of this module have found a good correlation between observed wind speeds and the peak reflectivity value observed at or above cloud base when the cloud base is nearly in juxtaposition with the freezing/melting level. However, we again emphasize that, due to the unknown variables involved in predicting gusts in a real world environment, a range of possible gust values should be considered rather than focusing on a specific predicted gust value obtained from Table 1.