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Weather Comparison of Monsoon Season for Four Cities of Sindh Province through Regression Model.

Byline: Ramzan Soomro Mir G.H Talpur and Saghir Pervaiz Ghauri

The monsoon rains is one of the source of water and is important consideration of Agricultural planning. In this paper multiple regression models were used which estimate the amount of rainfall in mm for monsoon season (June-Sep) for four cities of Sindh Sukkur Larkana Hyderabad and Karachi using previous data of 25 years (1987-2011). Goodness of fit test has been also used in this paper to identify the best fit models. These tests are based on the degree of similarity between the empirical distribution and the hypothesized distribution.

Key words: Rainfall Monsoon Prediction Multiple regression and Goodness of fit test.

IntroductionDue to increase of the population size the food and water is strongly needed to meet the challenges. The natural changes also take place to meet the situation in different ways. Where there is dearth of water and food it becomes in shape of dryness and on the other hand due to overflow of much water the situations turns to be natural calamity which destroys every thing in shape of flood loss of property and human lives will be evaluated. The rain caused massive destruction in Sindh province. These problems are closely linked with the behavior of the summer monsoon (Rajeevan 2011). Hasternrath (1988) discussed the usefulness of regression model in predicting Indian summer monsoon rainfall. Rain also plays an important role in growth of forests. Rains a natural boon for those who are cultivator of land a source of water for rivers and cleaner of all atmospheric impurities can become a natural catastrophe if received more than the earth's capacity to absorb it.

For analyzing rainfall data an appropriate approach is to fit the model for the probability of occurrence of rain. Multiple regression models are used to estimate the rainfall amount for monsoon season for four cities of Sindh Sukkur Larkana Hyderabad and Karachi using previous data of 25 years (1987-2011). The daily rainfall data was collected from Central Data Processing Centre (CDPC) Karachi. By using the previous data we will find the regression models for monsoon season for four cities of Sindh through these models we estimate the amount of rainfall for the model period of time. The estimated values were compared to the observed values to justify the difference. Goodness of fit through Chi-squire test will be used. Through these distributions we will find that our models lie or not in the critical region and how much these models are reliable for forecasting the amount of rainfall for future time period.

After justification of results we forecasted the amount of rainfall for further time periods (2012-2016) of the under studied four locations.

Literature Review

Regression model is good predictor for measuring rainfall (Masood 2009). Agriculture sector is the backbone of our economy which depends on the rainfall (Bhakar 2008). Rainfall is known to have considerable spatial variability (Jamaldin and Jemain 2007).

The precipitation amount is linked to temperature and surface air pressure (Jamal 2007). The monsoon precipitation plays very important role in the social and economic development of Pakistan rainfall occurs primarily due to different heating of land and sea (Muslehuddin and Faisal 2005). Agriculture is largely controlled by rainfall (Sahai and Grimm 2003). The agriculture economy of Pakistan is closely linked with rainfall that constitutes water resource for the country (Iqbal 2001).

Regression Models

The analysis has been carried out on precipitation in four cities of Sindh province. For rainfall amount unit is chosen mm. we consider wet day when precipitation is greater or equal to 0.1 mm. In this study Monsoon season is selected for four cities of Sindh province Sukkur Larkana Hyderabad and Karachi. The season consists four months June July August and September and months are used as variables.

The multiple linear regression model (MLR) isEquation

WhereY = The value of dependent variable (y) what is being predicted or explained. X1 = Rainfall amount for first month of year Y (June).

X2 = Rainfall amount for second month of year Y (July). X2 = Rainfall amount for third month of year Y(August).

X3 = Rainfall amount for fourth month of year Y(September). y = Median rainfall amount of X1 X2 and X3 X4 of year y.

a is the constant or intercept.

b1 b2 b3 and b4 are regression co-efficient

Now we determine the adequacy of a particular forecasting model which is based on judgment of how well the model has fit a given time series data goodness of fit test through Chi-squire is used.Equation

Results and Discussions

Monthly rainfall data for the period of 25 years1987 to 2011 for four cities of Sindh was used in the present study. Data was collected from Central Data Processing Centre (CDPC) Met Complex Karachi. In this paper the data of monsoon season was analyzed through Regression models and Chi squire distribution.

Table.1 Statistics of the rainfall amount in mm for four cities of Sindh.

###Sukkur###Larkana###Hyderabad###Karachi

###Minimum###1.5###0.9###0.3###0.2

###Maximum###209.60###278.40###316.0###270.40

###Mean###19.11###21.63###36.35###36.13

###Std. deviation###40.27###50.56###67.51###61.07

###Mean without zero entries###48.99###49.15###64.9###62.28

Table.2 Regression models for monsoon season for four cities of Sindh.

2.1) Regression Model for Sukkur is###2.2) Regression Model for Larkana is

Y = -3.793+0.607X1+ 0.065 X2+0.058X3+ 0.916X4 Y= -1.965+0.076X1+0.071 X2+0.156X3+0.665X4

Predictor Co-eff St.Error###95%###t-ratio P-value###Pred:###Co-eff###St.Error###95%###t-ratio###P-value

Constants -3.793###1.022###-5.926 -3.711###0.002###Const:###-1.965###2.419###-7.012###-0.812###0.426

###X1###0.607###0.071###0.460###8.626###0.000###X1###0.076###0.127###-0.190###0.600###0.556

###X2###0.065###0.013###0.037###4.867###0.000###X2###0.071###0.025###0.019###2.820###0.010

###X3###0.058###0.024###0.009###2.449###0.024###X3###0.156###0.041###0.071###3.854###0.001

###X###4###0.916###0.072###0.765###12.663###0.000###X###4###0.665###0.103###0.450###6.462###0.000

###Using t-statistic X1 X2 X3 X4 are significant###ii) Using t-statistic X2 X3 X4 are significant

Table.3###Goodness of fit test for four cities of Sindh

Location###Observed Expected Weighted value###Table value###Conclusion

###D

Sukkur###210.1###210.1###6.636###36.415###2 (cal) less than 2 (tab)

Larkana###271.9###271.9###35.518###36.415###2 (cal) less than 2 (tab)

Hyderabad###637.55###637.50###20.0###36.415###2 (cal) less than 2 (tab)

Karachi###581.85###581.85###31.542###36.415###2 (cal) less than 2 (tab)

The expected amount of rainfall in mm for model period 1987-2011 was obtained by applying the multiple regression models (2.1-2.4). The observed and expected amount of rainfall was tested by goodness of fit test shown in figures (1-4). We tested H0 against H1 by applying Chi squire test for monsoon seasons for four cities of Sindh are 6.636 35.518 20.0 and 31.542 for Sukkur Larkana Hyderabad and Karachi respectively shown in table (3). The tabulated values of Chi squire at 5% level of significance at k-1 d.f are 36.415. According to Chi squire test it is clear that null hypothesis of independence of rainfall on consecutive month is rejected. The predicted values for four cities for further time period 2012-2016 are shown in figure (5-8).

Conclusion

In this paper we used multiple regression models to forecast the rainfall in four locations of Sindh province namely Sukkur Larkana Hyderabad and Karachi. The results of multiple regression models is checked by Goodness of fit test which resulted that all regression models passed the test and conclude that the given set of data follows the specific distribution then we forecast the rainfall amount for all four locations shown in figures (5-8) and concluded that rainfall declined in three locations and one of four only Hyderabad location value of rainfall increased after 2011.

It is required to meet the shortage of water in these locations small reservoirs should be constructed for storage of water.

References

Bhakar S.R (2008). Probability analysis of rainfall at Kota Indian Journal of Agricultural. Research 42 (3) 201-206.

Delsole T and Shukla J. (2002). Linear prediction of Indian monsoon rainfall Journal of climate (15) 3645-3658.

Iqbal M.J. (2001). Modeling of monsoon rainfall of Pakistan and its impact on food grain production Proc ICCS-vii Lahore Pakistan 12 419-425

Jamaldin S. and Jemain A.A. (2007). Fitting the Statistical distribution to the daily rainfall amount in Peninsula Malaysia. Journal Technology 46(c) 33-48.

Jamal N. (2007). Ridge regression A tool to forecast wheat area and production Pak JR of Stat: Operation Research 8(2) 125-134.

Muslehuddin M. and Faisal N. (2005). Sindh Summer (June-Sep) monsoon rainfall predictions Journal of Metrology 2(4) 110.

Masood A. (2009). Collective and Individual month wise data management approach on data collected in Kalam (Sawat) through multiple regression analysis Sarhad Journal of Agriculture 25(4) 557-561.

Sahai A.K and Grimm A.M. (2003). Long lead prediction of Indian summer monsoon rainfall from global SST evolution Climate Dynamics (20) 855-863.

Singhrattna N. (2005). Seasonal forecasting of Thailand Summer monsoon rainfall International Journal of Climatology 25 649-664.

Thompson S. and Peter J. T. (2007). Fitting a multisite daily rainfall model to New Zealand data. Journal of Hydrology 340(1-2) .25-39.
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Publication:New Horizons
Article Type:Report
Geographic Code:9PAKI
Date:Jun 30, 2014
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