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DIWAKAR A. MOOLEY

Abstract

Using data from 39 well-distributed and long-record stations over the area, we found gamma distribution to be the most suitable probability model from among the Pearsonian models that show good fit to monthly rainfall in the Asian summer monsoon. We show that the monthly rainfall distribution is not Gaussian and the simple square-root, cube-root, and logarithmic transformations are of limited utility for normalizing the rainfall distribution.

A Craig type chart indicates that the rainfall distribution is a Type I distribution or a special or limiting case of this distribution; these distributions are fitted to monthly rainfall, and the goodness-of-fit is tested by the chi-square test. The gamma distribution (Pearson's Type III), which is a limiting case of Type I distribution and next, to the Gaussian distribution in simplicity, gives a good fit to monthly rainfall at all the stations in each of the summer monsoon months; the Kolmogorov-Smirnov test and the variance ratio test confirm this good fit. The Type I distribution shows good fit to June rainfall at 26 stations, July rainfall at 31 stations, August rainfall at 24 stations, and September rainfall at 23 stations. Type IX, a special case of Type I, shows good fit to June rainfall at four stations, July rainfall at two stations, August rainfall at four stations, and September rainfall at three stations.

In cases where the gamma and other Pearsonian distributions show good fit, the gamma distribution is found to be the most suitable. The spatial distribution of the scale and shape parameters of the gamma distribution applied to monthly rainfall over the area is examined and the chief features of the distribution are indicated and explained. Deciles of the mixed gamma distribution applied to monthly rainfall are tabulated; these can be used to obtain the monthly rainfall probabilities required by any user.

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DIWAKAR A. MOOLEY

Abstract

This study is based on all the monsoon depressions that moved westward across India between Calcutta, Allahabad, and Delhi on the right and Gopalpur, Nagpur, and Ahmadabad on the left during July and August for the period 1891–1960. Statistical distribution, of 24-hr motion and of the intensity of the depression, the relation between 24-hr motion and concurrent 24-hr rainfall, and the relation between the intensity of the depression and subsequent 24-hr rainfall are examined. In addition, the average rainfall per depression day and its standard deviation, the contribution of depression rainfall to the total rainfall, and the efficiency of the depression as a rain giver are computed. Mean patterns of 24-hr rainfall within 500 km of the center of the depression along longitudes 87°E, 80°E, and 75°E are obtained, and the main points of difference between them are discussed.

In the quadrants to the right of the depression track, the rainfall field is flat. In the quadrants to the left, however, large gradients of rainfall exists, particularly along and west of 80°E; the maximum rainfall is located in the left front quadrant, about 150 km from the center and 50–150 km from the depression track. Heavy rainfall extends about 250 km from the depression track in the left sector. Reasons for maximum rainfall in the left front quadrant were sought. We examined statistical distributions 24-hr rainfall in the four quadrants of depression along the three longitudes and found that the gamma probability model gives a good fit to 24-hr rainfall in each of the four quadrants of depression. Using the gamma model, we computed probabilities of rainfall of different intensities in the four quadrants. In this study, orography within the sector is kept constant by considering the rainfall from the same set of rain gage stations along each of the three longitudes.

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DIWAKAR A. MOOLEY

Abstract

Following the Monte Carlo technique, we have obtained an estimate of the period of monthly rainfall that would provide approximate normality for the marginal distributions of the shape and scale parameters of the gamma model applied to monthly rainfall and an estimate of the stability period of these parameters. The long rainfall records (exceeding 130 yr) of Bombay, Calcutta, and Madras have been utilized. These three stations in India are from three distinctly different rainfall regimes during the summer monsoon. The marginal distributions of the shape and scale parameters appear to attain approximate normality when the period of monthly data approaches 75 yr. The stability period of the gamma model parameters (based on the specific criterion adopted) appears to be from 50 to 65 yr.

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