OCR Text |
Show discrepancy between the computed and observed precipitation distribution indicates a need for further refinement and calibration of the model. 5. 2 Spectrum Analysis Procedures For most of the experimental period the periodic seeding input was applied at one cycle per hour from a point about 18 kilometers from the target area. If the local wind field were stable, the precipitation primarily orographic, and the nucleation process essentially linear, seeding agent would be expected to arrive in the clouds as pulses, and any resulting precipitation would arrive at the ground sensors as a modified pulse. The basic tenet of the evaluation scheme as outlined in the experimental plan was to measure a high resolution time series of precipitation rate, and to isolate the periods with a definite seeding effect by performing a power spectral analysis on the records of precipitation rate. If there were no naturally occurring frequency component at the frequency of the input, evaluation of the periodic seeding would be simple. However, the natural component at frequencies around one cycle per hour is not negligible. As in other evaluation schemes, the problem was in picking out a forced effect from a natural background. The scheme does have the advantage that the forced effect is a known frequency, rather than just a variation in the average value. A brief description of the spectral analysis technique will be presented here for the sake of completeness. The spectrum of a time series is analogous to an optical spectrum in that it shows the contributions of oscillations with various frequencies to the total variance of a time series. Power spectral analyses start with the autocorrelation function of a stationary random process, which is defined as (/) (T) = lim (1 /n) or(/) ('T) = X l x. 1 (t) X (t) x. (t 1 + T) (t +T) As the name implies , the autocorrelation function is a measure of how well the function x (t) is correlated with itself after an elapsed time of T • If x (t) contains a periodic component, (/) ( T) will also contain a periodic component of the same frequency. The power spectral d e nsity function is simply th e Fourier transform of the autocorrelation function. G ( w) 267 = J. [ Q) ( T) ] |