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Predicting water table depth using Remotely sensed data

Om Prakash Dubey
Department of Civil Engg. University of Roorkee, Roorkee, India.

Sriniwas, A. K. Awasthi
Department of E.sc., University of Roorkee, Roorkee, India.


Abstract
In the present study a simple method for delineating ground water source areas has been presented. Aerial photographs at 1:50,000 scale, Landsat MSS band 5 and 7 blow up at 1:250,000 scale, Landsat CCT and ground truth has been utilized for preparation of base map land cover map, slope map, grain size map and water table map. Multi-vitiate optimization technique in form of PCA considering Rainfall, elevation above mean sea level ground slope, vegetal cover , drainage density and texture of surface material has been carried out. It has been found that PCI accounts for about 928 of total variation. Bivariate plot of PCI and depth of water table clearly brings out clusters for different land uses. This bivariate plot can be utilized for predicting ground water table.

Introduction
If today we are suffering from problems associated with provision of suitable supply of oil at a price we can afford. We are moving towards a state when we shall be suffering from comparable problems associated with provision of water. Several surface and subsurface methods are available for exploration of ground water resources. These methods require large data set making them very costly and time consuming. For optimal exploration of ground water, it is essential to delineate promising areas.

Keeping above in view a study has been carried out in a part of Genetics plain to develop a simple methodology for delineating the promising areas.

Development of Methodology
It is a established fact that ground water availability depends upon several factors viz. Rainfall, elevation above mean sea level, vegetal cover, drainage density, texture of surface material, ground slope etc. The techniques commonly adopted for the analysis of multivariate data are cluster analysis, discriminate analysis, multivariate regression and principal component analysis (PCA) etc. (Dunteman, 1984).

PCA involves the selection of a set of weights to the variance. The problem is to find

b' = [b11, b12, ......... bip] such that the variance of b', x= b11 x1+b12x+............maximized subject to the constraints that


The problem can be stated as: y= b' v b-(b'b-1)

Where y is the function to be maximized, V is the pxp covariance (correlation) matrix of the original variable, and b' vb is the variance of the composite to be maximized. l is largance multiplier. b'b-1 =10.

The next step is to find b' and l such that the y is maximised.

(y/b) = 2vb-2 l b =0

or, (v-lI)b= 0; since b¹0;

The matrix V-lI must be singular (V-lI) b=0; If we premultiply by b' b' (V-lI) b=0

or, b'Vb = l b'b or, b'Vb = l

i.e. we want to maximize b'Vb= l (that is the variance of the composite)

We can then find the vector b associated with the largest root. The stepwise procedure can be summarized as under
  1. The first step in the iterative procedure is to compute successive powers of the correlation matrix. We start with R, then compute R2, R4 and so on, until we find the elements of a'Ri and a'R2i are proportional to each other. The vector a' can be any arbitrary vector at this stage we say that solution has converged and that a'Ri is proportional to the largest latent root vector b.

  2. Latent vectors are evaluated. This latent vector is also the weighting vector for the largest component.

  3. The residual correlation matrix is computed and the next largest principal component is evaluated. This process continues till the correlation matrix is completely exhausted.
Data Base
For the above study Rainfall, percentage vegetal cover, Drainage density, elevation above mean sea land, slope percentage and grain size data is required.

For evaluation of these data following map has been compiled.
  1. Basemap-Location, spot height and contours, Drainage network.

  2. Landcover map-Barren land, cultivation, moderately dense forest, dense forest.

  3. Slope map

  4. Grain size map

  5. Depth of water table map.
Followinfg data set has been used.
  1. Aerial photographs at 1:50,000 scale

  2. B &W landsat MSS band 5 and band 7 blow up at 1:250,000 scale

  3. Dand sat MSS CCT

  4. Water table data

  5. Grain size analysis data
For evaluation of the required information following stepwise procedure has been followed.
  1. Preliminary Analysis

    1. Analysis of landsat blow up for preparation of base map, land cover map.

    2. For some selected areas on the basis of stratified sampling, aerial photographs were analysed for obtaining the required information.

    3. For some selected areas ground surveys has been conducted.

    Based on step 1(b) and 1(c) above maps prepared in step 1 data base has been generated for training sets to be used in digital analysis.

  2. Final analysis

    1. Supervised classification of the CCT was carried out using parrelopiped piped classifier on MIDAS (multi Interactive Data analysis System) for preparation of map.

    2. Based on spot heights and contours slope analysis has been carried out and map has been prepared.

    3. From the observed ground water table data and land use map. Depth of water table in other areas has been evaluated using the developed model (Dubey, et.al. 1984).

    4. Observed grain size data and CCT (When surface covers was minimum has been found to be correlated. The relationship was used to predict the grain size at various locations.
Organization of the Data
The data were grouped according to the four different landuse categories. In each category fifteen sample points were used.

Results
  1. Bivarate plot of PC1 and PC2 brings out the difference between the land use categories. The plot may be used for landuse classification of any area.

  2. Bivarate plot of PC1 and depth of water table brings out clusters for different landuse categories. The plot can be used to predict the depth of water table in any area.

Acknowledgements
The authors are very thankful to the IIRS Dehradun, Ground Water Investigations for providing the necessary data for the study.

References
  1. Dunteman, G.H., 1984, Introduction to Multivariate Analysis. Sage publications, Beverly Hills, London.

  2. Dubey, O.P., Sriniwas, A.K., Awasthi, 1984, Analysis of Remote sensed Data for Ground Water Studies of Piedmout zone. Proc. V Asian Conference on Remote sensing.