collective and individual month-wise data management approach on the data collected in kalam (swat)...

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Sarhad J. Agric. Vol.25, No.4, 2009

COLLECTIVE AND INDIVIDUAL MONTH-WISE DATA MANAGEMENT

APPROACH ON THE DATA COLLECTED IN KALAM (SWAT) THROUGH

MULTIPLE REGRESSION ANALYSIS

AMJAD MASOOD*, SYED MUHAMMAD SAEED SHAH**, MANZOOR AHMAD MALIK*GUL DARAZ KHAN***, SAMAR GUL* and IKRAMUL HAQ****

* Pakistan Council of Research in Water Resources, Peshawar Pakistan.

** Center of Excellence in Water Resources Engineering, University of Engineering and Technology,

Lahore Pakistan.

*** Department of Water Management, NWFP Agricultural University, Peshawar Pakistan.

**** Department of Agricultural Extension Education and Communication, NWFP Agricultural University,

Peshawar Pakistan.

ABSTRACT

An understanding of hydrological regimes of mountain rivers is essential for water resources management

in Pakistan. As there are no proper estimates and relationships of river flow and climatic variables and especially

snow-melt stream flow relationships there is always a chance of floods which causes serious damages to crops,

human beings and other infrastructures. A proper study is therefore required to understand and analyze the runoff

regimes and its relation to the climatic variables to forecast the river flow. In this study different hydrological

regimes of River Swat Basin at Kalam are investigated by using inter-relationships of runoff with rainfall and

temperature. In regression analysis, two types of data management schemes are used in this study, first is Individual

Monthwise Regression in which 30 years monthly values of each parameter are regressed for each month

individually. The second is Collective Monthwise Regression in which normal value of each month is tabulated

against each parameter and then collectively flow values are regressed on precipitation, temperature and relative

humidity. In this collective monthwise technique encouraging results were obtained, which can be used for future

prediction of flow. Thirty years data was used to find out the linkages between river flows and climatic variables

(temperature, precipitation and relative humidity) in the study. Linkages in collective monthwise approach of

regression analysis came out quite better, especially for flow and temperature. This is due to the absence of gauging

stations at upper elevations, or it may be due to the reason that the station is not representative of the whole

catchment. In this study it is found that the Collective Month-wise Technique is a useful technique for Swat River

Basin at Kalam for predicting flow in River Swat.

Key Words: Water resources management, river flow, climatic variable, snowmelt, runoff regimes, regression analysis

Citation: Masood, A., S.M.S. Shah, M.A. Malik, G.D. Khan, S. Gul and I. Haq. 2009. Collective and individualmonth-wise data management approach on the data collected in Kalam (Swat) through multiple regression analysis.Sarhad J. Agric. 25(4): 557-561.

INTRODUCTION

Many of river catchments lie in the most northern part of Pakistan. The climate in Pakistan is mainly aridand semiarid. Having high altitudes, these catchments receive a considerable amount of snowfall during winterseason. The stream flow is mainly due to melting of the snow. The snowmelt stream flow is a valuable one becauseit occurs in the period of April, May and June before the monsoon rainfall. This early stream flow runoff is thereforeavailable for irrigation, power generation and water supply at the time when there is an extreme drought. The snow-

melt and glacier-melt continue in July and August, but meantime there is abundant water from the monsoon ofdamaging floods. But due to lack of proper estimates and relationships of river flow and climatic variables andsnow-melt stream flow relationships there is always a chance of floods which causes serious damage to crops,human beings and other infrastructures. A proper study therefore is required to understand and analyze the runoffregimes and its relation to the climatic variables to forecast the river flow at the proposed site.

One strategy for fitting a "best" line through the data would be to minimize the sum of the residual errorswhich is ei. This is an inadequate criterion; because best fit is a line connecting the points. Therefore, any straight-line passing through the mid point of connecting line (except a perfectly vertical line) results a minimum value ofei (Chapra and Canale, 1984). After fitting the best line, the second step in regression analysis is whether the datacan be adequately described by the regression line (Haan, 1973). Linear regression provides a powerful techniquefor fitting a "best" line to data. It is predicted on the fact that, relationship between dependent and independent


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Amjad Masood et al. Collective and individual month-wise data management approach 558

variables is linear (Chapra and Canale, 1984). Although these models fit into linear regression in order to evaluatethe coefficient as a best fit. They could then be transformed back to original state and used for predictive purposes.To test the accuracy of models, following three criteria (Haan, 1973; Pergram and Stretch, 1982; Chapra and Canale,1984) can be used. A useful extension of linear regression is the case where dependent variable Y is a linearfunction of two or more independent variables X1, X2, X3 etc.

][....................3322110

^

aXBXBXBBY +++= Usually n observations are available for the variable and also n numbers of equations are formed one foreach observation. Therefore, we have to solve these n equations for the p unknown parameters (regressioncoefficients) then n must be greater than p (Haan, 1973).

There is a role of seasonal snow accumulation based on surface measurements (De Scally, 1994) or onremotely sensed assessments of snow covered area (Rango et al.1977; Dey et al.1989). De Scally (1994) studiedthe Jehlum Basin and obtained high correlation coefficients between annual maximum snow peak water storage ortotal winter precipitation and annual runoff, whilst summer precipitation was of little use in estimating annual flow.It is concluded that in the Kunhar basin low elevation snow courses were as useful for forecasting as data fromremote high elevation sites.

Salomonson et al. (1997) analyzed low-resolution meteorological satellite data and simple photo

interpretation techniques have been used to map snow-covered areas during early April over the Indus River andKabul River basin in Pakistan. The stream flow in the regression analyses for each watershed was estimated (IndusRiver, 1969-1973, R2 = 0.82 and Kabul River, 1967-1973 R2= 0.89). Predictions of 1974 seasonal stream flow usingthe regression equations were within 7% of the actual 1974 flow. Singh and Jain (2003) conducted studies on dailystream flow simulation for the Sutluj River basin located in the western Himalayan regions. The model wascalibrated using a data set of three years (1985/86-1987/88) and model parameters were optimized. Using theseoptimized parameters, simulations of daily stream flow were made for a period of six years (1988/89-1990/91 and1996/97-1998/99). Modeling of stream flow involves physical features of the basin, including its total area, itsaltitudinal distribution through elevation zones and the areas of these zones, and the altitude of precipitation andtemperature stations.

MATERIALS AND METHODS

Regression Analysis

The different data management schemes (individual and collective monthwise) for regression analysis havebeen used in this study. Regression is statistical technique, may be used to evaluate correlations inferred fromknowledge of the physical environment. The resulting equations are in the form:

1985,..]...1...[............................................3322110

Acremanbn

Xn

BXBXBXBBY ++++=

Evaluating the Regression

After fitting the best line, the second step in regression analysis is whether the data can be adequatelydescribed by the regression line (Haan, 1973). One approach is to determine, how much of the variability in thedependent variable is explained by the regression.

]2[)^

(2

)^

(2)(i

Yi

YYi

YYi

Y +=

The larger the sum of square due to regression the better data explained by regression equation. Ratio of the sum ofsquares due to regression to the total sum of squares corrected for the mean can be used as a measure of ability ofthe regression line to explain variations in the dependent variable. This ratio is commonly denoted by "r2" (Haan,1973). r2= sum of squares due to regression / sum of squares corrected for mean. Then:

]3[)(/2

)^

(2

Yi

YYi

Yr =

"r2" is called "coefficient of determination". The Equation (3) can also be written;

]4[/2

)(2

/[]/2

)(10

[2

ni

Yi

Yni

Yi

Yi

XBi

YBr +=

If the regression equation perfectly predicts every value of Yi then (Y^i - Y) would be zero. Therefore, Equation (2)could be;


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Sarhad J. Agric. Vol.25, No.4, 2009 559

]5[.......2

)(2

)^

( Yi

YYi

Y =

Under these condition, ratio of both sides of the equation would be one. On the other hand, if the regression equationis explaining none of the variation in "Y" then one side of the equation would be zero which makes the ratio equal tozero as well. Thus the range of coefficient of determination is from zero to one. Closer it is to one the betterregression equation fits the data.

Application of Linear Regression and Linearization of Non-Linear Relationship

Linear regression provides a powerful technique for fitting a "best" line to data. It is predicted on the factthat, relationship between dependent and independent variables is linear (Chapra and Canale, 1984). But this is notalways the case; in hydrology sometimes the parameters have non-linear relationship with each other. In such casestransformation (linearization) is essential to express the data in a form of linear regression. Therefore, bylinearization of non linear regression, we may be able to evaluate the constant and coefficients. Although thesemodels fit into linear regression in order to evaluate the coefficient as a best fit. They could then be transformed

back to original state and used for predictive purposes. To test the accuracy of models following three criteria (Haan,1973; Pergram and Stretch, 1982; Chapra and Canale, 1984) can be used.

Multiple Linear Regression Method

A useful extension of linear regression is the case where dependent variable Y is a linear function of two or moreindependent variables X1, X2, X3

]6....[........................................3322110

^++++= XBXBXBBY

Where B0 is constant coefficient or intercept and B1, B2 and B3 are coefficient for variables X1, X2, and X3 etc.Usually n observations are available for the variable also n numbers of equations are formed one for eachobservation. Therefore, we have to solve these n equations for the p unknown parameters (regressioncoefficients) then n must be greater than p (Haan, 1973). As an example of n equations can be:

]7........[,1

...........3,132,121,1101 p

Xp

BXBXBXBBY +++++=

]8....[,2

...........3,232,221,2102 p

Xp

BXBXBXBBY +++++=

]9....[,3

............3,332,321,3103 p

Xp

BXBXBXBBY +++++=

]10....[

,

..............

3,32,2110 pn

X

n

B

n

XB

n

XBXBB

n

Y +++++=

Individual Month-wise Approach (Multiple Regression)

In this Approach Multiple Regression Analysis has been performed for each month between river flow andclimatic variables (temperature, precipitation and relative humidity) to estimate the flows. The general regressionequation is as follows:

]11.......[.....................4min3max210

RHBTBTBPBBQ ++++=

Where Q= River flow in m3/s ,B0 = Constant coefficient or interceptB1 = Coefficient or intercept for the rainfall,B2= Coefficient for the Maximum temperatureB3= Coefficient for the minimum temperature

B4= Coefficient for the relative humidity

Collective Month-wise Approach (Multiple Regression)

In this approach Multiple Regression Analysis has been performed for the whole normal year (30 yearsaverage) between river flow and climatic variables (temperature, precipitation and relative humidity) to estimate theflows.

]12.......[..............................4

)2

(10

RHBmean

TBPBBQ +++=

Where Q= River flow in m3/s ,B0 = Constant coefficient or interceptB1 = Coefficient or intercept for the rainfall,B2

/= Coefficient for the Maximum and minimum temperatures (sayB2+ B3)B4= Coefficient for the relative humidity


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REFERENCES

Acreman, M.C. 1985. Predicting the mean annual flood from basin characteristics in Scotland. J. Hydrol.30(1)37-49.

Chapra, C.S. and R.P. Canale. 1984. Numerical methods for engineers. Mc Graw-Hill Co, London. pp.286-309.De Sacally, F.A. 1994. Relative importance of snow accumulation and monsoon rainfall for estimating the annual

runoff, Jehlum basin, Pakistan. Hydrol. Sci. J. 39: 199-216.

Dey, B., V.K. Sharma and A. Rango. 1989. A test of snowmelt-runoff model for a major river basin in the westernHimalayas. Nordic Hydrol. 20:167-178.

Haan, C.T. 1973. Statistical method in hydrology. McGraw-Hill, New York. pp.180-221.Pergram, G.G.S. and D.D. Stretch. 1982. Recursive integrated estimation of effective precipitation and continuous

stream flow model. Intl. Symp. Missipi, USA. pp.191-228.Rango, A., V.V. Salomonson and J.L. Foster. 1977. Seasonal stream-flow estimation in the Himalayan region

employing meteorological snow cover observations. Water Resources Res. 13,109-122.Salomonson, V.V. and A. Rango and J.L. Foster. 1997. Seasonal stream flow estimation in the Himalayan region

employing meteorological satellite snow cover observations. Water Resources Res. 27(7), 1541-1552.Singh, P. and S.K. Jain. 2003. Modeling of stream flow and its components for a large Himalayan basin with

predominant snowmelt yields. IAHS. 48(2)257-276.Vehvilainen, B. and J. Lohvansuu. 1991. The effects of climatic change on discharge and snow cover in Finland.

IAHS.36 (2) 109-121.

Yevjevich, Y. 1972. Probability and Statistics in Hydrology. Water Resource, Pub, Colorado, USA, pp. 232-275.

collective and individual month-wise data management approach on the data collected in kalam (swat)...

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