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Surface Water Monitoring And Evaluation of Indravati Reservoir using the application of Principal Component Analysis using Satellite Remote Sensing Technology
The climate of the study area is humid and tropical. It is characterized by a hot and dry summer from March to May, and monsoon or rainy season from June to September and a good pleasant winter from October to February. However, climatologically, four seasons viz., summer (pre-monsoon), monsoon, post-monsoon and winter could be deciphered as comprising the following months:
Data Used Surface water monitoring and evaluation of Indravati reservoir using the application of Principal Component Analysis (PCA), multi-year (April, 1999 and January, 2000) IRS-LISS-III satellite remote sensing data has been used. After the acquisition of the satellite data in the form of a CD-ROM, it was subjected to various preprocessing techniques in order to obtain geographically referenced data. The data was utilized for the digital classification for identification the surface water monitoring. Methodology The study area is covered by the Survey of India (SOI) toposheets number 65 I/16 and 65 M/4 on 1:50,000 scale. The SOI sheets pertaining to the study area were digitally scanned and projected. Common Ground Control Points (GCPs) were selected on the raw satellite data (IRS LISS-III) as well as on the SOI maps with proper spatial distribution covering the entire study area. The coordinates of the GCPs on the reference image and the corresponding coordinates of the similar GCPs on the raw satellite data were used for the geometric correction of the uncorrected satellite data. This was achieved using a first order polynomial transformation fit. The geometric correction of the satellite data with reference to the SOI topo sheets has been evaluated by superimposing the geometrically corrected satellite data over mosaiced SOI sheets in the digital domain. Using the swipe procedure co-registration of the spatial features on the rectified image with that of the SOI maps was verified. Such geometric rectification of the satellite data facilitates overlaying different administrative (district, taluk etc.) and infrastructure (forest block/compartment) boundaries to extract and analyze the information at different functional units/levels. Various steps followed for land use/land cover mapping are given below.
Principal component analysis (often called PCA, or Karhunen- Loeve analysis) has proved to be of value in the analysis of multispectral remotely sensed data (Press et al., 1992; Wang, 1993). The transformation of the raw remote sensor data using PCA can result in new principal component images that may be more interpretable than the original data (Singh and Harrison, 1985). PCA analysis may also be used to compress the information content of a number of bands of imagery (e.g., seven Thematic Mapper bands) into just two or three transformed principal component images. The ability to reduce the dimensionality (i.e., the number of bands in the data set that must be analyzed to produce usable results) from n to two or three bands in an Important economic consideration, especially if the potential information recoverable from the transformed data is just as good as the original remote sensor data. A form of PCA may also be useful for reducing the dimensionality of the hyperspectral data set. Satellite remote sensing data sets of the future may be hyperspectral; containing hundred of bands (e.g., MODIS). For example, Lee et al. (1990) used a modified PCA transformation (i.e., the maximum noise fraction, or MNF) for data compression and noise deduction of 64-channel hyper spectral scanner data in Australia. Noise was removed from the multispectral data by transforming to the MNF space, smoothing or rejecting the most noisy components, and then retransforming to the original space. To perform principal component analysis we apply a transformation to a correlated set of multispectral data. The application of the transformation to the correlated remote sensor data will result in another correlated multispectral dataset that has certain ordered variance properties (Singh and Harrison, 1985). This transformation is conceptualized by considering the two-dimensional distribution of pixel values obtained in two TM bands, which we will label simply X1 and X2. A scatter plot of all the brightness values associated with each pixel in each band is shown in figure- 1a, along with the location of the respective means, m1 and m2. The spread or variance of the distribution of points is an indication of the correlation and quality of information associated with both bands. If all the data points clustered in an extremely tight zone in the two-dimensional space, these data would probably provide very little information. The initial measurement coordinates axes (X1 and X2 may not be the best arrangement in multispectral feature space to analyze the remote sensor data associated with these two bands. The goal is to use PCA to translate and lor rotate the original axes so that the original brightness values on axes X1 and X2 are redistributed (reprojected) into a new set of axes or dimensions, X'1 and X'2 (Wang, 1993). For example, the best translation for the original data points from X1 to X'1 and from X2 to X'2 coordinate systems might be the simple relationship X'1=X1 -m1 and X'2 =X2 -m2.Thus, the origin of the new coordinate system (X'1 and X'2) now lies at the location of both means in the original scatter of the points (fig 1b). Figure 1 Diagrammatic representation of the spatial resolution ship between the first two principal component: (a) Scatterplot of data points collected from two remotely bands labeled X1 and X2 with the means of the distribution labeled m1 and m2. (b) A new coordinate system is created by shifting the axes to an X' system. The values for the new data points are found by the relationship X'1 = X1 -m1 and X'2 = X2 -m2. (c) The X' axis system is then rotated about its origin (m1, m2) so that PC1 is projected through the semimajor axis of the distribution of points and the variance of PC1 is a maximum. PC2 must be perpendicular to PC1. The PC axes are the principal component of this two-dimensional data space. Component 1 usually accounts for approximately 90% of the variance, with component 2 accounting for approximately 50%. The X' coordinate system might then be rotated about its new origin (m1, m2) in the new coordinate system some F degree so that the first axis X'1 is associated with the maximum amount of variance in the scatter of point (figure 1c). This new axis is called the first principal component (PC1=l1). The second principal component (PC1=l1) is perpendicular (orthogonal) to PC1. Thus, the major and minor axes of the ellipsoid of points in bands X1 and X2 are called the principal components. The third, fourth, fifth and so on, components contain decreasing amounts of the variance found in the data set. To transform (reproject) the original data on the X1 and X2 axes onto the PC1 and PC2 axes, we must obtain certain transformation coefficients that we can apply in a linear fashion to the original pixel values. The linear transformation required is derived from the covariance matrix of the original data set. Thus, this is a data-dependent process with each new data set yielding different transformation coefficients. The transformation is computed from the original spectral statistics as follows (Short, 1982).
Where EVT is the transpose of the eigenvector matrix, EV, and E is a diagonal covariance matrix whose elements lii , called eigenvalues, are the variance of the pth principal components, where p= 1 to n components. The nondiagonal eigenvalues, lij are equal to zero and therefore can be ignored. The number of nonzero eigenvalues in an n x n covariance matrix always equals n, the number of bands examined. The eigenvalues are often called components (i.e., eigenvalue 1 may be referred to s principal component 1). |
