BACKGROUND INFORMATION 



BLACKADAR JET-WIND THEORY 



Several low-level jet-wind mechanisms have been 

 proposed (Blackadar 1957; Wexler 1961; Lettau 1967), 

 but only one of these applies over any continental surface, 

 whether it be level or mountainous. According to 

 Blackadar (1957), the low-level wind maxima is best 

 developed on the Great Plains at night; however, examples 

 may be found almost anywhere in the United States 

 during any season of the year. The phenomenon results 

 from rapid relaxation of friction drag at about the time of 

 sunset. During the day, convective mixing produces a 

 relatively deep friction layer above the earth's surface. 

 Air movement in this layer is retarded by frictional drag. 

 At night, thermal convection ceases and the earth's friction 

 layer decreases in vertical extent. Air just above the 

 nighttime friction layer, free of the daytime frictional drag, 

 responds by accelerating under the influence of the 

 unbalanced Coriolisand pressure-gradient forces. During 

 the course of the night the air accelerates beyond the 

 geostrophic value (supergeostrophic) before decreasing 

 again. 



The formation of a nocturnal temperature inversion will 

 further damp out vertical mixing and enhance the buildup 

 of a low-level jet wind. It has been observed that 

 temperature inversions occur in mountainous regions at 

 all times of the year. For example, detailed measurements 

 by Hayes (1941) revealed that nocturnal inversions are 

 common during the summer months in the Priest River 

 Valley of northern Idaho. Schroeder and Buck (1970) 

 point out that inversion layers are more common and more 

 intense in mountain valleys than over flat areas and that 

 the height of the inversions is usually below the main 

 ridges. The land surface above the inversions is subject 

 to increased windspeeds. 



Blackadar (1957) derived a theory that explained the 

 low-level jet in terms of a mechanism that can produce a 

 diurnal variation of wind velocity in the boundary layer over 

 any continental land surface. He assumed the motion just 

 above the temperature inversion layer is completely 

 horizontal and frictionless, and the horizontal pressure 

 gradient is constant with time. An equation was derived 

 that describes the deviation from the geostrophic wind. 

 The solution is 



W = Wq e-i^^ (1) 

 where W is the deviation from the geostrophic wind at time 

 t and Wq represents the deviation at an initial time, which 

 may be taken to be the time of sunset (fig. 1). The letter 

 i is the imaginary unit of a complex number and f is the 

 Coriolis parameter. 



The flow is one of inertia oscillation. After release of 

 friction, the flow of air accelerates under the unbalanced 

 Coriolis and pressure-gradient forces. The deviation from 

 the geostrophic wind remains constant in magnitude, 

 but is driven constantly to the right by the Coriolis force 

 during the night at a constant angular speed of f radians 

 per second. If continued, the motion would perform a 

 complete revolution. The circle of inertia marks the loci 

 of the end positions of the wind vector as a function of 

 time. The period of a complete revolution is one-half 

 pendulum day (Hess 1959). A supergeostrophic maximum 

 windspeed is reached about t = 7r/f hours after sunset 

 (about 8.5 hours at 45° latitude). 



Blackadar's theory permits prediction of the wind dis- 

 tribution during the entire night from initial conditions. 

 Field observations show that the locus of points (head of 

 the wind arrows) actually stretches out into an elliptical 

 form instead of a perfect circle as given by figure 1 (Buajitti 

 and Blackadar 1957). The elliptical path results from 

 gradual relaxation of friction. 



Figure 1.— Development of supergeostrophic winds in the low-level jet 

 (after Blackadar 1957). Vg is the geostrophic wind, Vq the initial 

 wind, and V the true wind. W and Wq are defined in equation 1. 



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