Information Retrieval & Data Mining

Rainfall Estimation in India

By:Akrita Agrawal

INTRODUCTION

India is basically an agricultural country and the success or failure of the harvest and water scarcity in any year is always considered with the greatest concern. These problems are closely linked with the behavior of the summer monsoon rains in India.

In this research paper, a multiple linear regression (MLR) method is adopted to predict the average summer monsoon rainfall in a given year using the monthly rainfall data of the summer-monsoon of the previous year.

What is LINEAR REGRESSION MODEL

Linear Regression includes any approach to modeling a predictive relationship for one set of variables based on another set of variables, in such a way that unknown parameters appear linearly.

TYPES of LINEAR REGRESSION MODEL

Simple linear Regression is the simplest type of regression, involving only one explanatory variable.

Multiple linear regression the case of involving more than only one explanatory variable. And in our project we are using this model to predict the rainfall.Multivariate Linear Regression is where multiple correlated dependent variables are predicted rather than a single scalar variable.

General Linear Model considers the situation when the response variable Y is not a scalar but a vector.

Multiple Linear Regression Model (MLR)

MLR is often used to determine how many specific factors such as the price of a commodity, interest rates, and particular industries or sectors, influence the price movement of an asset. For example, the current price of oil, lending rates, and the price movement of oil futures, can all have an effect on the price of an oil company's stock price. MLR could be used to model the impact that each of these variables has on stock's price.

MLR takes a group of random variables and tries to find a mathematical relationship between them. The model creates a relationship in the form of a straight line (linear) that best approximates all the individual data points.

Yi = B0 + B1xi1 + B2xi2 + ... + Bpxip + Ei where i = 1,2, ..., n

LIMITATIONOnly Looks at Linear Relationshipsit assumes there is a straight-line relationship between them. Sometimes this is incorrect. For example, the relationship between income and age is curved.

Only Looks at the Mean of the Dependent VariableJust as the mean is not a complete description of a single variable, linear regression is not a complete description of relationships among variables.

Data Must Be IndependentLinear regression assumes that the data are independent. That means that the scores of one subject (such as a person) have nothing to do with those of another. This is often, but not always, sensible.

IMPLIMENTATION

Required Data: Data used in the present study are collected from the website http://www.tropmet.res.in published by Indian Institute of Tropical Meteorology. In this project only six months’ data (June-November) are explored because these six months are the Indian monsoon months.Rainfall Data used in our project for the North Central Indian region.

Train Data years : 1842-1959 Test Data years : 1960-2005Predict year : 2006

EQUATION

Coefficients predictedB0 = 99.86319 (Intercept) B1 = 4.704049 (June)B2 = 5.343824 (July)B3 = 5.119389 (August)B4 = 3.870940 (September)B5 = 3.524525 (October)B6 = 0.660939 (November)

Yi = B0 + B1xi1 + B2xi2 + ... + B6xi6 where i = 1,2, ..., 6

RESULT

Schematic of the actual and predicted average monthly rainfall of Indian summer monsoon during 1960-2005

COMPARISION

Overall prediction error is to be found 1.426458 %

As from the final graph predicted and actual graph are fairly equal and prediction for every next year is fairly good.

At the end prediction for year 2006 is also shown in the graph.

CONCLUSION

Multiple Linear regression implements a statistical model that, when relationships between the independent variables and the dependent variable are almost linear, shows optimal results. In MLR predicted variables can be treated as fixed values.

With the help of Multiple Linear Regression model we have predicted the estimated rainfall for 45 years (i.e. 1960-2005) and the results are optimally equal to the actual rainfall occurred.

This project illustrates, that almost all of the months is a good predictor of average monsoon rainfall of a given year.

CONCLUSION cont..

The topic of monsoon-rainfall data series is complex; the role that multiple linear regression might play in this topic is one for future research—it appears, from the evidence here, modal to be fairly usable as a predictive model. Whether it might be useful for offering an approximate value of future monsoon rainfall remains to be seen.

REFERENCES

• The Prediction of Indian Monsoon Rainfall: A Regression Approach: Goutami Bandyopadhyay (pdf)

• Data: http://www.tropmet.res.in/static_page.php?page_id=52#data

ftp://www.tropmet.res.in/pub/data/rain-series/3-nci.txt

• Linear regression with multiple variables (pdf)