Analysis of Monthly Rainfall Data Prediction for Change of Economic Environment in Pampadumpara Using Gamma distribution

 

Sivajothi R¹, K. Karthikeyan^2*

¹Research Scholar, School of Advanced Sciences, VIT-University, Vellore, Tamil Nadu, India.

²Associate Professor, School of Advanced Sciences, VIT-University, Vellore, Tamil Nadu, India.

 

ABSTRACT:

The Gamma distribution model is well en suite to the monthly and annual rainfall estimate detection. The rainfall gauging station of Pampadumpara, Idukki district metrological station data is being used.  This study tests the goodness-of-fit using the Kolmogorov-simirnov (KS) test, and compare these results against gamma distribution which is commonly used during rainfall events. This distribution makes it feasible to estimate the likelihood of rainfall being within the specified range. In this paper, we consider the application of Gamma distribution in modelling intense rainfall. The distribution was applied to the monthly rainfall data from Pampadumpara station with the observation period from January 1978 to December 2013. The figures showed that the annual daily maximum rainfall received at any time ranged between 0.0 mm (Min) to 775.5 mm (Max) indicating a diverse range of fluctuation during the period of study. For this set of figures, Gamma distribution is opted for a better performance. The scientific results clearly established that the analytical procedure devised and tested in this study may be suitably applied for the identification of the best fit probability distribution of weather parameters. The distribution level is very good to predict the maximum monthly rainfall. The results showed that the Gamma distribution is very appropriate for extreme monthly rainfall. These models are used as decision making tools for food security, water management, agriculture, and hydroelectric power providing decision.

 

 

 

INTRODUCTION:

In India, rainfall variability is the central driver of the national economy as it is predominantly agricultural, food security, water management, energy productions are crucially dependent on the timely availability of adequate amount of water. The South West (SW) monsoon, which brings about 80% of the total precipitation in Pampadumpara, is critical for the availability of fresh water for drinking and irrigation.

 

The more concentration of rainfall in the monsoon months (June-September) results in scarcity of water in the state during the non-monsoon seasons. The changes in rainfall due to global warming will influence the hydrological cycle and uneven distribution of rainfall and the mismatch between water availability and demand.  Large irrigation structures are required to redistribute the natural flow in accordance with the requirements of the specific regions. Our investigation carried out to determine the spatial analysis of monthly and annual precipitation trends in Pampadumpara of Kerala state, using climatic variables data for 36 years collected from CRS (Cardamom research station), ICRI (Indian Cardamom Research Institute). This paper gives an exhaustive coverage of the studies dealing with rainfall variable which are critical in hydrologic studies. These statistics provide necessary information about accumulation amounts in both time and space for the region and from the basis for fitting and testing distribution models. In case, if the required data is improper or available data is incorrect or incomplete in a spatial or temporal sense, geophysical models can be used to fill in the missing values. The long term trends for the last 50 years indicate a significant decrease in the frequency of moderate to heavy rainfall events over most parts of India [1]. While the frequency of extreme rainfall events (100mm/day) have increased in certain parts of India [2], the statistical distribution of rainfall data highly built-in to gamma distribution during south west and north east monsoon season in India.  Bhargava et. al. [3] have studied the distribution of rainfall over the season has a great influence on the yield for a number of crops.  Fisher [4] has studied the influence of rainfall on the yield of wheat in Rothamasted.

 

The distribution of rainfall is determined during a season rather than its total amount which influence the crop yield. Biswas and Khambete [5] studied the minimum rainfall at different probability level by fitting gamma distribution probability model to week by week total rainfall of 82 stations in dry farming area of Maharashtra. Baskar et. al. [6] analysed the frequency analysis of consecutive days of maximum rainfall at Banswara, Rajasthan, India, and found gamma distribution as the premier rated type when compared by other distribution and tested by Chi-square value. Sen and Eljadid [7] evaluated the monthly rainfall in Arid regions, gamma probability distribution is well suited for the rainfall data. The theoretical expressions for the distribution function of the total amount of rainfall and the daily maximum rainfall is based on the gamma probability distribution. There are many probability distributions that could be successfully utilized to parameterize rainfall distributions. The distribution is commonly used for frequency analysis as well as for risk and reliability analysis of the lifetimes of systems in addition to their components. Its applications have been reported frequently in hydrology and meteorology.  Having fitted this distribution to the wet and dry sequences and obtained satisfactory results, it has been applied to short-time increment urban precipitation characteristics.  The gamma distribution is one of the most widely understood which best fits the probability distribution for the annual, monthly and seasonal periods in India.

 

BACKGROUND OF THE STUDY:

In this section, we explain the study area, data and methods about the rainfall in South Indian states of Kerala and Tamil Nadu.

 

 

STUDY AREA:

The study is carried out for Indian Cardamom Hills (9 15’-10 0’N, 76 45’-77 25’E). Cardamom hills are the part of the Western Ghats located in the south Indian states of Kerala and Tamil Nadu. The average elevation of the Cardamom Hills is 2637 meters or 8652 feet. The Cardamom hills produce cardamom, tea, coffee, teak and bamboo.

 

Figure.1: Location of study station (Pampadumpara, Kerala)

 

Data

Observed daily rainfall data collected from the following governmental organizations

1. The cardamom Research stations (CRS)

2. Indian cardamom research institute (ICRI)

3. United Planters Association of South India (UPASI)

 

These are functioning under Kerala agricultural university, Kerala. Data for 36 years (January 1978 to December 2013) have been verified and used for our Research. Since the data collected from research station is no conflict about the originality of the data. The daily observed data were summed up to arrive at an average values depending on the temporal scale (Monthly and Annual average data). The cross verified and checked data were used for our analysis.

 

Gamma distribution function

The gamma distribution is often used to model the distribution of wet-day rainfall amounts. The gamma distribution is distinctly skewed to the right, which suits the distribution of daily rainfall and accommodates the lower limit of zero which constrains rainfall values [8]. It is obvious that no single distribution consistently suits all regions, seasons and climates better than others. For example, it has been found that the gamma distribution generally fits the least well for daily rainfall in the United States and the mixed exponential was more appropriate. Tested a similar range of models for UK rainfall and found that the gamma distribution performed best for most regions and seasons in India.

 

 

RESULTS AND DISCUSSION:

This research describes important findings of understanding of the rainfall in Pampadumpara. This study relies heavily on modelled data for the results, a note about this would be appropriate. Any use of the rainfall dataset (Fig. 3) must acknowledge the limitations of the model, which should be used to guide the application of the dataset. This model is designed to estimate precipitation by combining various inputs to create an output representing a synergism of the positive characteristics of the input datasets. It is not designed to be spatially explicit, and therefore quantitative analysis should be performed for areas rather than at individual points. The rainfall data has been shown to approximate precipitation with reasonable accuracy. With these limitations in mind, caution must be used in the interpretation of the outputs presented. The gamma distribution parameters require some understanding of the distribution properties. Unlike the normal distribution where a single parameter, such as the mean or standard deviation can directly provide an intuitive understanding of some aspect of the distribution, the gamma distribution requires that both the shape and scale parameters be interpreted together. Areas with similar shape values, but different scale values, have very different probability density functions describing the rainfall.

 

 

Fig. 3: Year wise monthly rainfall (mm)

 

 

 

Table 1: summary of statistical and KS test results

 

 

 

 

(a)

 

 

(b)

Figure 4 (a) and (b): Mean Ks stat and Mean p-value of rainfall for 36 years

 

The KS test was run using all points in the monthly rainfall data that contained more than one rainfall value in the climatological history. The results from this are displayed in Table 1. A rejection level of 0.1 was used to test the rejection of the gamma distribution as suitable for parameterising the rain fall data record in Pampadumpara.  For this data, including the points from all months, approximately 3.8% of points with at least two non-zero rainfall events in the 36-year history had a calculated p-value smaller than the 0.1 threshold (Column 6 of Table 1).

 

This test includes the points with very few rainfall values that tend to have a very high KS-statistic associated with them. However, this reduction in the KS-statistic did not translate into a large increase in the average p-value. This is due to the fact that more samples are included in the empirical dataset, so the acceptable value of the KS-statistic becomes smaller. There was a notable improvement in the percentage of points with a p-value greater than 0.1. Of all points meeting the testing criteria, approximately 98.5% had a p-value greater than 0.1, meaning that we do not reject. The gamma distribution for 98.5% of the test sites that if more common threshold of 0.05 is used, the level of acceptance improves to 99.5% of all points with non-zero rainfall values. This test shows that, overall, the gamma distribution appears to do an adequate job of approximating the historical rainfall distributions. Results show that at 0.1 rejection level, the performance of the gamma estimation techniques is quite comparable.

 

CONCLUSIONS:

This work has described the calculation of rainfall data for change of economic environment in Pampadumpara using gamma distribution. Though the commonly used 2-parameter gamma distribution performs fairly well on the basis of traditional goodness of fit tests,  here the result shows p-value has more than 0.1. The joint interpretation of monthly shape and scale parameters conveys the distribution of values in the model rainfall data at Pampadumpara allowing the interpreter, a qualitative assessment on the amount and stability of rainfall throughout the season. If we consider only points that received rainfall for 36 years, the percentage of points that were acceptable at the 0.10 level increased slightly. This hypothesis testing indicates that the gamma distribution provides a reasonable description of the empirical rainfall probability distribution. The ability to represent the rainfall using the gamma distribution parameters allows for interpretation of the parameter estimates as a compact summary of the full rainfall distribution.  From this observation, there is no notable change in rainfall and economical as well, in the future of Pampadumpara scenario. This research could prove precious to a wide range of groups from scientists studying precipitation to policy makers in assessing forecast information to local farmers estimating their crop yields.

 

 

REFERENCES:

1.     Dash, S. K., Kulkarni, M. A., Mohanty, U. C., and Prasad, K. (2009). Changes in the characteristics of rain events in India. Journal of Geophysical Research: Atmospheres, 114(D10).

2.     Goswami, B. N., Venugopal, V., Sengupta, D., Madhusoodanan, M. S., and Xavier, P. K. (2006). Increasing trend of extreme rain events over India in a warming environment. Science, 314(5804), 1442-1445.

3.     Bhargava, P.N. The influence of rainfall on crop production. Research Journal of Jawahar Lal Nehru Krishi Vishwavidyalaya. 1974; 32, No. 1 and 2.

4.     Fisher, R. A. (1925). The influence of rainfall on the yield of wheat at Rothamsted. Philosophical Transactions of the Royal Society of London. Series B, Containing Papers of a Biological Character, 213, 89-142.

5.     Biswas, B. C., and Khambete, N. N. (1979). Distribution of short period rainfall over dry farming tract of Maharashtra. Journal of Maharashtra Agricultural Universities, 4(2).

6.     Bhakar, S. R., Bansal, A. K., Chhajed, N., and Purohit, R. C. (2006). Frequency analysis of consecutive days maximum rainfall at Banswara, Rajasthan, India. ARPN Journal of Engineering and Applied Sciences, 1(3), 64-67.

7.     ŞEN, Z., and Eljadid, A. G. (1999). Rainfall distribution function for Libya and rainfall prediction. Hydrological sciences journal, 44(5), 665-680.

8.     Wilks, D. S. (1999). Multisite downscaling of daily precipitation with a stochastic weather generator. Climate Research, 11(2), 125-136.

9.     Wilks, D. S. (1990). Maximum likelihood estimation for the gamma distribution using data containing zeros. Journal of Climate, 3(12), 1495-1501.

10.   Crutcher, H. L. (1975). A note on the possible misuse of the Kolmogorov-Smirnov test. Journal of Applied Meteorology, 14(8), 1600-1603.

11.   Wilks, D. S. (2011). Statistical methods in the atmospheric sciences (Vol. 100). Academic press.

 

 

 

 

Accepted on 30.07.2016        © RJPT All right reserved

Research J. Pharm. and Tech 2016; 9(9):1477-1482.