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Prediction of Cumulative Rainfall Deficits Using Growth Models

M.S.U. Talukder
Department of Irrigation and Water Management, Bangladesh Agricultural University, Mymensingh-2202, Bangladesh.

M.M. Ali
Department of Mathematics, Bangladesh Agricultural University, Mymensingh-2202, Bangladesh.

M.A. Hye
Department of Mathematics, Bangladesh Agricultural University, Mymensingh-2202, Bangladesh.

M.G. Hossain
Department of Physics, Bangladesh Agricultural University, Mymensingh-2202, Bangladesh.

Abstract/ Executive Summary:

Daily point rainfall and evaporation data of Mymensingh area for a period of 19 years (1975 -1993) were reviewed in this paper. The prediction of rainfall deficits in the form of mathematical expression were developed for week- 1 through 52nd at probability levels of 25%, 50% and 75% using two growth models viz. Gompertz model and the Logistic model. The results from two models were compared and found that the Gompertz model gave reliable prediction for this area and as such this model can safely be used for prediction of rainfall deficits where similar agroclimatic conditions exists.

Keywords: Rainfall deficit, Prediction, Growth models.

Location: BAU, Mymensingh

Start Date:

End Date:

Program Area: Socio-economic and Policy

Non-commodity: Performance

Objectives:

In this paper functional relationship have been established between cumulative rainfall deficits and time using two growth models viz. the Gompertz model and the Logistic model and their comparisons have been made at different probability levels.

Methodology:

Daily rainfall and evaporation data for a period of 19 years from 1975 to 1993 were collected from the Weather yard of the Department of Irrigation and Water Management, Bangladesh Agricultural University, Mymensingh (24°46' N Latitude and 90°56' E Longitude), Bangladesh. Daily rainfall and evaporation data were transformed into weekly data for prediction of rainfall deficits starting from 1st week to 52nd week. Data in the form of an MxN matrix with M = 1 ... 52 (weeks) and N = 1 ... 19 (years) were analyzed. Rainfall varies not only with time but also with geographical area and altitude in space and is a continuous random variable. The weekly values of rainfall and evaporation were arranged in descending order of magnitude. Probability analysis needs to define formulas for plotting positions of data points. The most commonly used Weibull's (1939) formula p = m/(n + 1), where n is the number of years of record and m is the rank of the event in order of magnitude, the largest event having m = 1, was used for determining plotting positions, For each standard week the rainfall and evaporation values were plotted against the corresponding computed probabilities. The best fitted line was obtained by using least square technique and the expected rainfall and evaporation magnitudes at different probability levels of 25, 50 and 75 were estimated. The rainfall deficits were calculated by subtracting the rainfall values from the evaporation values and cumulative rainfall deficits were determined for each week starting from 1st week through 52nd week for probability levels of 25%, 50% and 75%. The cumulative rainfall deficits at different probability levels were analyzed using two growth models for prediction.

Source of Information: Bangladesh J. Agril. Sci. 21 (2): 377-383, July, 1994

Article Link (Online Journal):

Funding Source:

Total Budget (Tk.) :

Achievement/Findings:

Higher values of coefficient of determination and lower percent average absolute deviation values give more reliable predictions. The results indicate that the Gompertz model produced closest fit for the rainfall deficits at 75% probability level followed by 50% and ~5% probability levels. Our findings do not agree with that of Malik and Agarwal (1982) who observed that the Logistic model gave the closest fit for the rainfall deficits at 75% probability level. The Logistic model also followed the similar trend with slightly lower values of coefficient of determination but with higher values of percent average absolute deviation at 75%, 50% and 25% probability levels. Comparison of rainfall deficits prediction by these models showed that at 75% probability level, the Gompertz model gave appreciably better prediction than the values predicted by Logistic model. However, the Gompertz model produced more reliable predictions at all the probability levels in comparison with Logistic model. Therefore, for prediction of rainfall deficits, for different periods, the Gompertz model may be suggested for obtaining better results. The Gompertz model can safely be used for prediction of rainfall deficits for most of the regions having similar agroclimatic conditions like Mymensingh.

Knowledge Management: Journal