Behavoir of a Very Large Number of Constant-Volume Trajectories

Abstract

A numerical experiment is performed with the purpose of investigating the behavior of the trajectories of a very large number of constant-volume particles. Practical significance is given to this problem by the possibility of using superpressured, constant-volume balloons for routine upper air observations. The computational scheme of the experiment is described with emphasis on some aspects of trajectory computations. Thirty-day diagnostic trajectories are computed for two levels using the total velocity components, and for one level using only the nondivergent ones, and the resulting spacing of the trajectory points is discussed. Theory of the distances to the nearest among a large number of points is developed and applied for the statistical description of the results. Histograms of distances from the constant-volume particles as well as from random points in space to the nearest neighboring constant-volume particle are computed, and compared with the frequency function of those distances for the case of a random distribution of particles. It is shown that the nondivergent part of the atmospheric motions gives rise to a random distribution of initially regularly spaced particles. Departures from the random distribution are therefore produced by the divergent part of the atmospheric motions. In the experiment they resulted in the increase in distances from random points in space to the nearest constant-volume particle of about 12 and 4 per cent, at the levels corresponding to 800 and 300 mb, respectively. The computational region was approximately equal to the area north of 15N; a somewhat larger effect of the divergent part of the wind should be expected in the case of the global constant-volume trajectories.