Application of multivariate statistics, trend- and cluster analysis to groundwater quality in the Tejo and Sado aquifer

A methodology based on multivariate statistics, classification and trend analysis techniques is applied to describe and classify the groundwater quality monitoring network for the confined aquifer of the Tejo and Sado system. Hydrochemical data consists of information on Ph, conductivity, Na, K, Ca, CI, HC03, Mg and S04 measured in 27 stations and annually sampled from 1980 to 1994. The proposed method encompasses the following steps. First, we use the Principal Component Analysis (a factorial method), to define the intercorrelation structures between the variables in different time horizons, in order to identify the differences and similarities of the most relevant parameters. The objective is to generate synthetical indicators (indexes) for a characterization of the hydrochemical changes. Second, the temporal variation of those indexes is analysed by the nonparametric Mann-Kendall test and the global trend is evaluated by means of tau coefficients and robust slopes. Finally, a hierarchical method (Cluster Analysis) is used to establish the groups of stations of similar temporal patterns. INTRODUCTION The relative magnitude of the hydrochemical changes (taking account the slow variation of groundwater quality) can be for instance a decisive guide for a correct identification of recharge/discharge areas or for evaluating the changes in the salt-fresh interface in coastal aquifers. To analyse the variation in the multivariate quality data we currently used graphical methods such as Piper or Stiff diagrams, which are very useful but cumbersome when we try to compare them for different time horizons. An alternative is not to use all the quality parameters themselves, but instead of them the indexes that synthesize the typical similarities and differences between the major ions in the groundwater environment. These new variables (indexes) can be easily identified by means of a factorial method. Then trends can be analysed by a robust technique. 40 Luis Ribeiro & Maria Emilia Macedo METHODOLOGY The methodology presented here consists of the application of three techniques, namely the Principal Component Analysis, Mann-Kendall test and Cluster Analysis. It is beyond the scope of this paper to consider in detail these three methods. Readers are invited to consult the literature suggested in the following chapters, where in short the principal procedures are presented. Principal Component Analysis This is a factorial technique (Jolliffe, 1985) providing the visualization and reduction of the data contained in tables of great dimension composed by sample stations (rows) and variables (columns). The method finds the factors which explain the opposition or similarity between the attributes by reducing the dimension of the initial cloud, while minimizing the loss of information. Graphically, a system of orthogonal axes is produced, where we can visualize in a plane the projections of the data matrix elements. Results are interpreted as follows. First, we assign a meaning to the factors based on the relative projection of the variables on the axes and, second, the similarities are given by a proximity criterium on the projections. After a clear interpretation of the factor in terms of a specific characteristic, synthetical indexes are generated from the projection of the variables onto the axes. Therefore, the coordinates along an axis identify the intensity of a studied property. The algorithm used here refers to standardized data and uses the Eigen vector decomposition of the correlation coefficient matrix of the variables. Mann-Kendall test This is a nonparametric statistical test (Mann, 1945; Kendall, 1975) to detect and assess the trends and the rate of change of variables in water quality. The technique is appropriate for data exhibiting one or more of the following characteristics: free distribution, missing values, outliers and seasonality. The method is applied to a sequence of observations ordered by time q, c2, • • •, cn. The statistic S is calculated as follows: S = E«c,-*> (1) • 0 f(jc) = 0 if x = 0 ftx) = 1 if x < 0 where the null hypothesis H of no trend is rejected or confirmed. To measure the strength of upward or downward trend, the Kendall's tau coefficient is calculated. Groundwater quality in the Tejo and Sado aquifer 41 Furthermore, in order to estimate the rates of change per unit time, an unbiased estimator due to Thiel (1950) and Sen (1968) is also calculated for the trend slope. This is the median of all the values dy defined by: for all (Cj,c^) pairs such that 1 < j < i < n. Cluster Analysis This is a classification method (Sneath & Sokal, 1973) which enables the grouping of similar stations on basis of a distance criteria and of a specific aggregative algorithm in order to create a typology which will characterize the elements to be classified. The method is a hierarchical one, providing a branching diagram with junction levels proportionate to the rate of inertia associated with each junction. Several distances can be used, such as the euclidean, x, etc. However, for this particular study the cos0 distance was selected due to good performance. This distance is defined by: d(a,b) i E x(aj)-m(a) x{bj)-m(b) (3) j a(a) a(a) where m(a) and m(b) are the means of rows a and b and o(a) and a{b) are their standard deviations. The aggregative criteria used here is the unweighed paired grouping using strategy arithmetic average. Application of the methods The methods are used in the following steps: (a) Principal Component Analysis is applied to a matrix containing the hydrochemical variables sampled at the available stations for all the time horizons. (b) The factorial axes are interpreted and synthetical indexes are calculated. (c) Trend analysis by Mann-Kendall test is carried out on these indexes and the magnitudes of the slopes are estimated. (d) Cluster Analysis is applied to a matrix generated with tau coefficients and trend slopes. From the resulting hierarchical tree, groups of stations with similar temporal patterns are identified. APPLICATION TO THE GROUNDWATER QUALITY IN THE TEJO AND SADO CONFINED AQUIFER Hydrogeology The groundwater system of Tejo and Sado covers an area of about 8000 km which includes, but extends beyond, the Setubal Peninsula, as shown in Fig. 1. The aquifer 42 Luis Ribeiro & Maria Emilia Macedo Fig. 1 Map of the Tejo and Sado groundwater system with the location of sampling stations on Setubal Peninsula. system is discussed in detail by Coma-Guillen (1978). The area corresponds to the MioPliocene detrital sedimentary basin of the Lower Tejo and the Lower Sado. In the northwest, the basin is bounded by Mesozoic limestones and sandstones, and in the east and south by Palaeozoic and Precambrian bedrock. In the west, the basin extends beyond the coastline under the Atlantic Ocean. It consists of an unconfined aquifer and an underlying confined aquifer. The latter is thicker than the upper aquifer. The two aquifers are separated by an aquitard (leaky hydraulic connection). Most of the past and the actual groundwater resource development is from the confined aquifer and is located in Setubal Peninsula. Some pumping wells for industrial purposes are located near the estuary. Within the peninsula, the aquifer system forms a sub-basin. Groundwater quality in the Tejo and Sado aquifer 43 Hydroctiemical data Data considered in this study are from 27 stations monitored in the confined aquifer of Setiibal peninsula region and irregularly annually sampled from 1980 to 1994. Due to the fact that the wells are connecting different aquifer levels, the final chemical composition of the water will be a contribution of various types of "waters" of the system. Their location can be seen in Fig. 1. It consists of measurements on pH, conductivity, Na, K, Ca, CI, HC03, Mg, and S04. There are numerous gaps as is shown on Fig. 2. This will condition the final results and justify the choice of an appropriate robust nonparametric method. The analysis will be performed on information on the major anions and cations. w E L L S W l W 2 W'3 W 4 WS W6 W 7 W 8 W'9 WTO W l l W I 2 W13 W14 W15 WX6 W17 W18 W19 W20 W21 W22 W23 W24 W25 W26 W27 1980