CHAPTER INTRODUCTION:

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1 CHAPTER 6 THE IMPACT OF IRRIGATION THROUGH GROUND WATER AVAILABILITY: AN APPLICATION OF FACTOR ANALYSIS ON GROUND WATER DATA FROM CENTRAL WATER COMMISSION INDIA 6.1 INTRODUCTION: Factor analysis is by far the most often used multivariate technique of research studies, specially pertaining to social and behavioral sciences. It is a technique applicable when there is a systematic interdependence among a set of observed or manifest variables and the researcher is interested in finding out something more fundamental or latent which creates this commonality. For instance, we might have data, say, about an individual s income, education, occupation and dwelling area and want to infer from these some factor (such as social class) which summarizes the commonality of all the said four variables. The technique used for such purpose is generally described as factor analysis. Factor analysis, thus, seeks to resolve a large set of measured variables in terms of relatively few categories, known as factors. This technique allows the researcher to group variables into factors (based on correlation between variables) and the factors so derived may be treated as new variables (often termed as latent variables) and their value derived by summing the values of the original variables which have been grouped into the factor. Since the factors happen to be linear combination of data, the coordination of each observation or variable is measured to obtain what are called factor loadings. Such factor loadings represent the correlation between the particular variable and the factor, and are usually placed in a matrix of correlations between the variable and the factors. M.C. Garg and AnjuVerma had done an empirical factor analysis of Marketing Mixture in the Life Insurance Industry in India. They have created nine dimensions and converted them into four factors after applying factor analysis 1 P a g e

2 through principal component analysis. D. P. Chaudhri had also applied factor analysis to child labor in India with Pervasive Gender and Urban Bias in School Education. They had tried to present the role of community factor in important individual and household decisions that generate social outcomes like incidence of child labor, non-participation in school education and household s fertility decisions. 6.2 METHODOLOGY: The mathematical basis of factor analysis concerns a data matrix (also termed as score matrix), symbolized as S. The matrix contains the scores of N persons of k measures. Thus a 1 is the score of person 1 on measure a, a 2 is the score of person 2 on measure a, and k N is the score of person N on measure k. The score matrixes then take the form as shown following: The mathematical basis of factor analysis concerns a data matrix (also termed as score matrix), symbolized as S. The matrix contains the scores of N persons of k measures. Thus a 1 is the score of person 1 on measure a, a 2 is the score ofperson 2 on measure a, and k N is the score of person N on measure k. The score matrix then takes the form as shown following: SCORE MATRIX (OR MATRIX S) Measures (variables) a B c k 1 a 1 b 1 c 1.. k 1 2 a 2 b 2 c 2.. k 2 3 a 3 b 3 c 3.. k 3 N a N b N c N.. k N Persons(objects) It is assumed that scores on each measure are standardized. This being so, the sum of scores in any column of the matrix, S, is zero and the variance of scores 2 P a g e

3 in any column is 1. Then factors (a factor is any linear combination of the variables in a data matrix and can be stated in general way like: A = W a a + W b b + + W k k) are obtained (by any method of factoring). After this, we work out factor loadings (i.e., factor variable correlations). Then communality, symbolized as h 2, the eigenvalue and the total sum of squares are obtained and the results interpreted. For realistic results, we resort to the technique of rotation, because such rotation reveals different structures in the data. Finally, factor scores are obtained which help in explaining what the factors mean. They also facilitate comparison among groups of items as groups. With factor scores, one can also perform severalas multiple regressions, cluster analysis, multiple discriminate analyses, etc. 6.3 IMPORTANT TERMS AND METHODS OF FACTOR ANALYSIS:- There are several methods of factor analysis, but they do not necessarily give same results. As such factor analysis is not a single unique method but a set of techniques. Important methods of factor analysis are: The centroid method; The principal components method; The maximum likelihood method. Following are some basic terms relating to factor analysis: FACTOR: A factor is an underlying dimension that account for several observed variables. There can be one or more factors, depending upon the nature of the study and the number of variables involved in it. FACTOR-LOADINGS: Factor-loadings are those values which explain how closely the variables are related to each one of the factors discovered. They are also known as factor-variable correlations. In fact, factor-loadings work as key to underlying what the factors mean. It is the absolute size (rather than the signs, plus or minus) of the loadings that is important in the interpretation of a factor. COMMUNALITY (h 2 ): Communality, symbolized as h 2, shows how much of each variable is accounted for by the underlying factor taken together. A high value of communality means that not much of the variable is left over after 3 P a g e

4 whatever the factors represent is taken into consideration. It is worked out in respect of each variable as under: h 2 of the i th variable = (i th factor loading of factor A) 2 + (i th factor loading of factor B) 2 + EIGEN VALUE (OR LATENT ROOT): When we take the sum of squared values of factor loadings relating to a factor, then such sum is referred to as Eigen Value or latent root. Eigen value indicates the relative importance of each factor in accounting for the particular set of variables being analyzed. TOTAL SUM OF SQUARES: When Eigen values of all factors are totaled, the resulting value is termed as the total sum of squares. This value, when divided by the number of variables (involved in a study), results in an index that shows how the particular solution accounts for what all the variables taken together represent. If the variables are all very different from each other, this index will below. If they fall into one or more highly redundant groups, and if the extracted factors account for all the groups, the index will then approach unity. ROTATION: Rotation, in the context of factor analysis, is something like staining a microscope slide. Just as different stains on it reveal different structures in the tissue, different rotations reveal different structures in the data. Though different rotations give results that appear to be entirely different, but from a statistical point of view, all results are taken as equal, none superior or inferior to others. However, from the standpoint of making sense of the results of factor analysis, one must select the right rotation. If the factors are independent orthogonal rotation is done and if the factors are correlated, an oblique rotation is made. Communality for each variable will remain undisturbed regardless of rotation but the Eigen values will change as a result of rotation. FACTOR SCORES: Factor score represents the degree to which each respondent gets high scores on the group of items that load high on each factor. Factor scores can help explain what the factors mean. With such scores, several other multivariate analyses can be performed. 4 P a g e

5 Let s take up the most famous and important method under our study of Factor analysis. 6.4 PRINCIPAL-COMPONENTS METHOD OF FACTOR ANALYSIS: Principal-components method (or simply P.C. method) of factor analysis, developed by H. Hotelling, seeks to maximize the sum of squared loadings of each factor extracted in turn. Accordingly PC factor explains more variance than would the loadings obtained from any other method of factoring. The aim of the principal components method is the construction out of a given set of variables X j s (j = 1, 2 k) of new variables (p i ), called principal components which are linear combinations of the X s P 1 = a 11 X 1 +a 12 X a 1k X k P 2 = a 21 X 1 +a 22 X a 2k X k P k = a k1 X 1 +a k2 X a kk X k The method is being applied mostly by the using the standardized variables, i.e., z j = ( X j - X j ) 2 / σ j. The a ij s are called loadings and are worked out in such a way that the extracted principal components satisfy two conditions: (i) principal components are uncorrelated (orthogonal) and (ii) the first principal component (p 1 ) has the maximum variance, the second principal component (p 2 ) has the next maximum variance and so on. Following steps are usually involved in principal components method: Estimates of a ij s are obtained with which X s are transformed into orthogonal variables i.e., the principal components. A decision is also taken with regard to the question: how many of the components to retain into the analysis? We then proceed with the regression of Y on these principal components i.e., Y= y p 1 +y p y m p m (m < k) From thea ij s and y ij, we may find b ij of the original model, transferring back from the p s into the standardized X s. 5 P a g e

6 Alternative method for finding the factor loadings is as under Correlation coefficients (by the product moment method) between the pairs of k variables are worked out and may be arranged in the form of a correlation matrix, R, as under: CORRELATION MATRIX, R Variables X 1 X 2 X 3.. X k X 1 X 2 X 3. r 11 r 12 r 13.. r 1k r 21 r 22 r 23.. r 3k r 31 r 32 r 33.. r 3k X k r k1 r k2 r k3.. r kk The main diagonal spaces include unities since such elements are selfcorrelations. The correlation matrix happens to be a symmetrical matrix. Presuming the correlation matrix to be positive manifold, the first step is to obtain the sum of coefficients in each column, including the diagonal element. The vector of column sums is referred to as U a1 and when U a1 is normalized, we call it V a1.this is done by squaring and summing the column sums in U a1 and then dividingeach element in U a1 by the square root of the sum of squares (which may be termed as normalizing factor). Then elements in V a1 are accumulatively multiplied by the first row of R to obtain the first element in a new vector U a2. For instance, in multiplying V a1 by the first row of R, the first element in V a1 would be multiplied by the r 11 value and this would be added to the product of the second element in V a1 multiplied by the r 12 value, which would be added to 6 P a g e

7 the product of third element in V a1 multiplied by the r 13 value, and so on for all the corresponding elements in V a1 and the first row of R. To obtain the second element of U a2, the same process would be repeated i.e., the elements in V a1 are accumulatively multiplied by the second row of R. The same process would be repeated for each row of R and the result would be a new vector U a2. Then U a2 would be normalized to obtain V a2. One would then compare V a1 and V a2. If they are nearly identical, then convergence is said to have occurred (If convergence does not occur, one should go on using these trial vectors again and again till convergence occurs). Suppose the convergence occurs when we work out V a8 in which case V a7 will be taken as V a (the characteristic vector) which can be converted into loadings on the first principal component when we multiply the said vector (i.e., each element of V a ) by the square root of the number we obtain for normalizing U a8. To obtain factor B, one seek solutions for V b, and the actual factor loadings for second component factor, B. The same procedures are used as we had adopted for finding the first factor, except that one operates off the first residual matrix, R 1 rather than the original correlation matrix R. This very procedure is repeated over and over again to obtain the successive PC factors (viz. C, D, etc.) 6.5 OTHER STEPS INVOLVED IN FACTOR ANALYSIS: Next the question is: How many principal components to retain in a particular study? Various criteria for this purpose have been suggested, but one often used is Kaiser s criterion. According to this criterion only the principal components, having latent root greater than one, are considered as essential and should be retained. The principal components so extracted and retained are then rotated from their beginning position to enhance the interpretability of the factors. Communality, symbolized, h 2, is then worked out which shows how much of each variable is accounted for by the underlying factors taken together. A high communality figure means that not much of the variable is left over after whatever the factors represent is taken into consideration. It is worked out in respect of each variable as under: 7 P a g e

8 h 2 of the i th variable = (i th factor loading of factor A) 2 + (i th factor loading of factor B) 2 + Then it follows the task of interpretation. The amount of variance explained (sum of squared loadings) by each PC factor is equal to the corresponding characteristic root. When these roots are divided by the number of variables, they show the characteristic roots as proportions of total variance explained. The variables are then regressed against each factor loading and the resulting regression coefficients are used to generate what are known as factor scores which are then used in further analysis and can also be used as inputs in several other multivariate analyses. 6.6 RELATED TESTS: KMO-TEST Before performing the factor analysis, it is important to investigate whether a particular data set is suitable for the analysis or not. This can be done by Kaiser-Meyer-Olkin (KMO) statistics. BARTLETT S TEST Bartlett s measure tests the null hypothesis that the original correlation matrix is an identity matrix. For factor analysis to work we need some relationships between variables and if the R-matrix were an identity matrix then all correlation coefficients would be zero. Therefore, we want this test to be significant.(i.e. have a significance value less than 0.05). A significant test tells us that the R-matrix is not an identity matrix; therefore, there are some relationships between the variables we hope to include in the analysis. 8 P a g e

9 6.7 APPLICATION TO STATE-WISE GROUND WATER RESOURCE AVAILABILITY, UTILIZATION AND STAGE OF DEVELOPMENT In this section, we discuss the incidence of the ground water resource availability or other indicators related to it. Our study here deals with the incidence of ground water resource availability in India for the period GROUND WATER RESOURCE AVAILABILITY AND DEVELOPMENT STATUS (A) DYNAMIC FRESH GROUND WATER RESOURCE: The ground water resource of the country has been estimated based on the reports of all the states as per the technical guidance of R & D Advisory Committee on ground water estimation. Ground water resources have been estimated for fresh water as per GEC 97 methodology. The year of assessment is different for different states varying from 1998 to The ground water draft figures were projected to March, 2004 to bring ground water estimation figures of different states on a common datum. The GEC 97 recommends that the assessment unit for alluvium could be Block, but for hard rock, it should be Watershed. However, except for the three states of Maharashtra, Andhra Pradesh and Karnataka, other states do not have watershed-wise data, hence computations were done on Block/ Taluka-wise basis in case of most of the states. The Annual Replenishable Ground Water Resource for the entire country is 433 billion cubic metres (bcm). Plate XIV presents the over-all scenario of ground water resource utilization and availability of the country. The ground water assessed is the dynamic resource which is replenished each year. The Annual Replenishable Ground Water Resource is contributed by two major sources rainfall and other sources that include canal seepage return flow from irrigation, seepage from water bodies and artificial recharge due to water conservation structures. The overall contribution of rainfall to country s Annual Replenishable Ground Water Resource is 67% and the share of other sources taken together is 33%. State-wise Ground Water Resources of India as 9 P a g e

10 on March, 2004 is given in Table. The contribution from other sources such as canal seepage, return flow from irrigation, seepage from water bodies etc in annual Replenishable resources is more than of 33% in the states of Andhra Pradesh, Delhi, Haryana, Jammu & Kashmir, Jharkhand, Punjab, Tamil Nadu, Uttar Pradesh, Uttaranchal and UT of Pondicherry. South-West monsoon being the most prevalent contributor of rainfall in the country, about 73% of country s Annual Replenishable Ground Water Recharge takes place during the Kharif period of cultivation. Keeping 34 bcm for natural discharge, the Net Ground Water Available for utilization for the entire country is 399 bcm. The Annual Ground Water Draft is 231 bcm, out of which 213 bcm is for Irrigation use and 18 bcm for Domestic & Industrial use. An analysis of ground water draft figures indicates that in the states of Himachal Pradesh, Jammu & Kashmir, Kerala, north eastern Orissa ground water draft for domestic & industrial purposes are more than 15% which is comparatively higher than the national average of 8%. In general, the irrigation sector remains the main consumer of ground water (92% of total annual ground water draft for all uses).aterrio Monitoring of ground water regime is an effort to obtain information on ground water levels and chemical quality through representative sampling. The important attributes of ground water regime monitoring are ground water level, ground water quality and temperature. The primary objective of establishing the ground water monitoring network stations is to record the response of ground regime to the natural and anthropogenic stresses of recharge and discharge parameters with reference to geology, climate, physiographic, land use pattern and hydrologic characteristics. The natural conditions affecting the regime involve climatic parameters like rainfall, evapotranspiration etc., whereas anthropogenic influences include pump age from the aquifer, recharge due to irrigation systems and other practices like waste disposal etc. Ground water levels are being measured four times a year during January, April/ May, August and November. The regime monitoring started in the year 1969 by Central Ground Water Board. At present a network of P a g e

11 observation wells located all over the country is being monitored. Ground water samples are collected from these observation wells once a year during the month of April/ May to obtain background information of ground water quality changes on regional scale. The database thus generated forms the basis for planning the ground water development and management program. The ground water level and quality monitoring is of particular importance in coastal as well inland saline environment to assess the changes in salt water/fresh water interface as also the gradual quality changes in the fresh ground water regime. This data is used for assessment of ground water resources and changes in the regime consequent to various development and management activities. The State-wise distribution of the ground water observation wells is given in table 6.1. Table 6.1: STATEWISE DISTRIBUTION OF OBSERVATION WELLS S. No. Name of the State Total No. of Observation Wells (as on ) 1 AP Arunachal 19 3 Assam Bihar Gujarat Haryana Himachal 85 8 J & K Karnataka Kerala MP Maharashtra Orissa Punjab Rajasthan Tamil Uttar Pradesh 1218 Total P a g e

12 Table 6.2: STATE-WISE GROUND WATER RESOURCES AVAILABILITY, UTILIZATION AND STAGE OF DEVELOPMENT, INDIA States A B C D E F G H I J K L M AP Arunachal Assam Bihar Gujarat Haryana Himachal J & K Karnataka Kerala MP Maharashtra Orissa Punjab Rajasthan Tamil UP WB SOURCE: Ground water year data book GOI 12 P a g e

13 TABLE 6.3: INDICATORS FOR AVAILABILITY OF GROUND WATER AND RECHARGE & UTILIZATION OF GROUND WATER SOME CO-RELATES OF ( ) A B C D E F G H I J K L M Recharge from rainfall during monsoon season Recharge from other sources during the monsoon season Recherché from rainfall during non-monsoon season Recharge from other sources during the non-monsoon season Total of Monsoon and non-monsoon Natural Discharge during non-monsoon season Net Annual ground water availability Irrigation Domestic and Industrial uses Projected Demand for Domestic and industrial uses Total annual ground water draft Ground water Availability for future irrigation Stage ground water development SOURCE: Ground water year data book CWC, GOI (B) STAGE OF GROUND WATER DEVELOPMENT The stage of ground water development for the country as a whole is 58%. The status of ground water development is comparatively high in the states of Haryana, Punjab and Rajasthan where the Stage of Ground Water Development is more than 100%, which implies that in these states the average annual ground water consumption is more than average annual ground water recharge. In the states of Gujarat, Karnataka, Tamil Nadu and Uttar Pradesh the average stage of ground water development is 70% and above. In rest of the the stage of ground water development is below 70%. 13 P a g e

14 6.7.1 (C) CATEGORIZATION OF ASSESSMENT UNITS Out of 5723 assessed administrative units (Blocks/ Taluks/ Mandals/ Districts), 4078 units are Safe, 550 units are Semi-critical, 226 units are Critical, 839 units are Over-exploited and 30 units are Saline. Number of Over-Exploited and Critical administrative units are significantly higher (more than 15% of the total assessed units) in Andhra Pradesh (where categorization was done up to subunit level i.e. within Mandals command and non-command- wise), Gujarat, Haryana, Karnataka, Punjab, Rajasthan and Tamil Nadu. 6.8 STATISTICAL INFERENCE: RELATIONSHIP BETWEEN VARIABLES OF AVAILABILITY OF GROUND WATER AND RECHARGE & UTILIZATION OF GROUND WATER: In order to understand the relationship between availability of ground water and recharge & utilization of ground water in , correlation is calculated. Table 6.4 shows the correlation between various factors availability of ground water. This correction matrix is used to check the pattern of relationships. The result suggest positive correlation between recharge from rainfall during monsoon and natural discharge during non monsoon (A and E correlation is 0.899), recharge from rainfall during monsoon and ground water availability for future irrigation (A and L correlation is 0.91),recharge form other resources during non- monsoon and total availability of ground water during monsoon and non- monsoon season ( D and E correlation is 0.812), total availability of ground water during monsoon and non-monsoon and natural discharge during non-monsoon season ( E and F correlation is 0.918), total availability of ground water during monsoon and nonmonsoon and net annual ground water availability ( E and G correlations is 0.99), total availability of ground water during monsoon and non-monsoon and ground water availability for future irrigation (E and L correlation is 0.901), natural discharge during non-monsoon season and net annual ground water availability (F 14 P a g e

15 and G correlations is 0.905), natural discharge during non-monsoon season and ground water availability for future irrigation (G and L correlations is 0.90), Irrigation and projected demand for industrial uses (H and J correlation is 0.996) and Domestic and industrial uses verses total annual draft of ground water (I and K correlations 0.84) are notice highly correlated. The remaining variables have least correlation with availability of ground water. In general, it may be concluded that increase in one least correlated variable would lead to a decrease in the incidence of availability of ground water. The determinant is listed at the bottom of the matrix. For this data its value is which is greater than the necessary value of Therefore, multi-co-linearity is not a problem for this data. The values of P for all the variables are significant. 15 P a g e

16 TABLE 6.4: CORRELATION ANALYSIS BETWEEN THE VARIABLES MATRIX TO BE FACTORED A B C D E F G H I J K L M A 1.00 B C D E F G H I J K L M Determinant = INTERPRETATION OF FACTOR ANALYSIS: After calculating the relationship between the selected indicators and availability of ground water, factor analysis is carried out to investigate the linear relationship of some underlying factors. Requesting principal component analysis & specifying varimax rotation, the output of the factor analysis is obtained. Table 6.5 presents the output of the factor analysis for this problem, the rotated factor matrix comprising all the twelve variables, the percent of variance, the cumulative percent of variance and the eigenvalue of all the factors having eigenvalue of 1 or more than 1. It is seen from the cumulative percent of the variable column that three factors extracted together account for % of the total variance this is pretty good bargain because from all the twelve variables, 16 P a g e

17 three underlying factors are extracted. The total 87% of information is retained by the three factors extracted- only 13% of information is lost out of twelve original variables. The factor loadings are in the expected direction. Variables with first factor have a highest loading, which explains availability of ground water more than next two factors (0.971).While, factor two and three explains minor effects than first factors (0.037 and 0.055). So we ve concentrated on first factor. Table 6.5: ROTATED FACTOR MATRIX Factors Variables A L G E K F I D M J H B C Eigenvalue Percentage of variance Cumulative percentage P a g e

18 The Rotated factor matrix draw attention to affecting indicators on factor one. Recharge from rainfall during monsoon season (0.971), Ground water availability for future irrigations (0.914), Net Annual ground water availability (0.872), Total of Monsoon and non-monsoon (0.865), Total annual ground water draft (0.747), Natural Discharge during non monsoon season (0.701), Domestic and Industrial uses (0.655), Recharge from other sources during the non-monsoon season (0.651). Stage ground water development loaded negative value ( ), which focus on lacking of infrastructure development. Similarly, Projected demand for domestic and industrial uses, Irrigation, Recharge from other sources during the monsoon season, Recherché from rainfall during non-monsoon season have been loading least values in compare of second and third factor. We derived that irrigation is also one major indicator of infrastructure development and found poor. The overall recharge of ground water is not fulfilled due to the runoff of rain water as it is indicating by indicator B with factor one recharge from other sources during the monsoon season. It is also noticeable here that during the season of monsoon if the infrastructure cannot be utilized, it may be not look ahead to recharge from rainfall during non-monsoon season. Table 6.6: KMO AND BARTLETT S TEST Test Value Kaiser-Meyer-Olkin Measure of Sampling Adequacy Bartlett s Test of Sphericity Approx. Chi-Square Df 78 Significance The value of Kaiser-meyer-olkin measure of sampling adequacy is which tells us that we should be confident that factor analysis is appropriate for these data. Kaiser (1974) recommends accepting values greater than 0.5. While, Barllett s test is highly significant (0<0.001) which also shows factor analysis is 18 P a g e

19 quite suitable for data. As described in the early section, a significant test tells us that the R-matrix is not an identity matrix; therefore, there are some relationships between the viable we have included in the analysis. 6.9 CONCLUSIONS: Though the water book data on availability of groundwater shows a nurture trend, it has not automatically resulted to execute the level of ground water in India. Due to the system cannot have proper coverage, affects the ground water potential. The unconsolidated formations alluvial system of Indo-Gangetic& Brahmaputra plains has Enormous reserves down to 600 m depth. High rain fall and hence recharge is ensured, which can support large-scale development through deep tube wells. The Coastal Areas can reasonably extensive aquifers but risk of saline water intrusion. The parts of desert areas Rajasthan and Gujarat have scanty rainfall it is negligible recharge it have salinity hazards and the availability at great depths. The semi consolidated formations and sedimentary-basalts and crystalline rocks system have coverage peninsular areas and the Availability depends on secondary porosity developed due to weathering, fracturing etc. the scope for ground water availability at shallow depths (20-40 m) in some areas and deeper depths ( m) in other areas. The systems of hilly areas (coverage of hilly states) have low storage capacity due to quick runoff. The discussed indicators for availability of ground water focus to develop the infrastructure in India. 19 P a g e