Detecting subtle hydrochemical anomalies with multivariate statistics: an example from homogeneous groundwaters in the Great Artesian Basin, Australia

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1 HYDROLOGICAL PROCESSES Hydrol. Process., (06) Published online 22 September 06 in Wiley InterScience ( DOI: /hyp.6177 Detecting subtle hydrochemical anomalies with multivariate statistics: an example from homogeneous groundwaters in the Great Artesian Basin, Australia Bethany O Shea 1,2 * and Jerzy Jankowski 2,3 1 Department of Geology, Dickinson College, PO Box 1773, Carlisle, PA 17013, USA 2 School of Biological, Earth and Environmental Sciences, The University of New South Wales, Sydney NSW 52, Australia 3 Sydney Catchment Authority, PO Box 323, Penrith NSW 2751, Australia Abstract: The major ion composition of Great Artesian Basin groundwater in the lower Namoi River valley is relatively homogeneous in chemical composition. Traditional graphical techniques have been combined with multivariate statistical methods to determine whether subtle differences in the chemical composition of these waters can be delineated. Hierarchical cluster analysis and principal components analysis were successful in delineating minor variations within the groundwaters of the study area that were not visually identified in the graphical techniques applied. Hydrochemical interpretation allowed geochemical processes to be identified in each statistically defined water type and illustrated how these groundwaters differ from one another. Three main geochemical processes were identified in the groundwaters: ion exchange, precipitation, and mixing between waters from different sources. Both statistical methods delineated an anomalous sample suspected of being influenced by magmatic CO 2 input. The use of statistical methods to complement traditional graphical techniques for waters appearing homogeneous is emphasized for all investigations of this type. Copyright 06 John Wiley & Sons, Ltd. KEY WORDS multivariate statistics; homogeneous groundwaters; Great Artesian Basin; principal components analysis; hierarchical cluster analysis; major ions; Na HCO 3 -type waters INTRODUCTION Groundwater composition is influenced by several factors, including the chemistry of recharge waters, the mineralogy of the aquifer matrix, chemical processes during water rock interaction, the input of elements via pollution, and mixing of waters along the flow path. Hydrogeologists have long used traditional graphical techniques as an interpretative tool in the analysis of hydrogeochemical data. Various methods of hydrochemical representation include radial plots, Stiff pattern diagrams, semi-logarithmic graphs and Collins bar diagrams. Numerous texts give an explanation on the use of these diagrams, including Hem (199), Domenico and Schwartz (199), and Freeze and Cherry (1979). Guler et al. (02) provide an excellent review of the use of these graphical tools in hydrogeochemical investigations. The ionic strength of groundwaters is generally dominated by major cations (Na C,K C,Ca 2C and Mg 2C ) and major anions (HCO 3,Cl and SO 2 4 ). The concentrations of these major ions in groundwaters can indicate which geochemical processes are dominant in the system. If there are no known contaminants or elevated trace elements present in the groundwater then the major ions may be the only data available to determine mixing of waters or changes to system equilibrium. They thus have the advantage of providing * Correspondence to: Bethany O Shea, Department of Geology, Dickinson College, PO Box 1773, Carlisle, PA 17013, USA. osheab@dickinson.edu Received 16 September 04 Copyright 06 John Wiley & Sons, Ltd. Accepted 10 August 05

2 431 B. O SHEA AND J. JANKOWSKI geochemical information on the subsurface environment while employing a limited number of chemical analytes. Given their abundance in natural waters, most interpretation techniques utilize major ion data in isolation. Perhaps the most commonly used technique for finding hydrochemical patterns in major ion data are trilinear diagrams, such as the Piper diagram (Piper, 1944) and Durov diagram (Chilingar, 1956). Piper diagrams plot the percentage abundance of the major ions together for comparison of waters and interpretation of chemical evolution. These diagrams are useful for displaying large amounts of data and determining major trends visually. Yet, what if all waters plot in the same location on the Piper diagram? Does this mean their major ion composition is so similar that no variation in the data can be found? Piper (1944) recognized the fact that many waters differ only slightly in chemical composition and, as such, divided the diamond field into distinct categories dependent upon chemical composition. Back (1961) provided similar subdivisions on the diamond field and classified cations and anions according to their facies. Piper (1944) suggested plotting closely related waters at five times the standard scale in order to differentiate their chemical variability (a tool that is specifically recommended for differentiation of saline waters and brines). Additional differentiation can be obtained by scaling the symbol sizes to represent salinity or total dissolved solids (Domenico and Schwartz, 199). Another diagram was proposed by Chadha (1999). This utilizes much the same approach as a Piper diagram, with the main advantage of being easily constructed in common spreadsheet software packages. Chadha s diagram plots differences between ions in percentage milliequivalents onto a rectangular-shaped diagram with eight subdivisions. This diagram is suitable for the classification of natural waters and for analysing hydrochemical processes. For further graphical distinction of water types, the Durov diagram can be extended to include two additional parameters in conjunction with the major ion composition. These additional parameters can include ph, total dissolved solids (TDS), ionic strength, hardness, electrical conductivity (EC), total inorganic carbon or any minor elements of interest. By incorporating these additional parameters into the visual interpretation, homogeneous waters may be further differentiated with the aid of variation present in these two additional parameters. Thus, various graphical tools are available to examine major ion trends in groundwater. For a full comprehensive analysis of patterns present in the data, however, Piper (1944: 914) states many problems of interpretation can be answered only by intensive study of critical analytical data by other methods. The use of multivariate statistical methods in the analysis of hydrochemical data is not a new process. Many workers have used statistics to delineate groundwater mixing, zones of contamination, hydrochemical facies and other processes alike (Adams et al., 01; Meng and Maynard, 01). As discussed above, traditional graphical techniques have the disadvantage of incorporating a select few chemical constituents into the analysis. Thus, the use of statistics is often employed to include physical factors, such as well depth, rock type or distance from a contamination source, into the interpretation procedure. Often, a combination of graphical techniques and statistical methods are used to complement the results from each interpretative tool. Several studies have evaluated the use of statistical methods in comparison with traditional graphical techniques (Melloul and Collin, 1992; Guler et al., 02; Hussein, 04). However, many of these examples use data sets displaying distinct chemical variation, such as contamination versus background concentrations. Few studies address situations where major ion data are solely used and exhibit minor chemical differentiation. The aim of this paper is thus to examine statistically a data set with similar major ion groundwater compositions to determine whether subtle hydrochemical patterns can be distinguished. The findings of this investigation are expected to promote awareness of the need for statistical methods to be used in conjunction with traditional graphical techniques, and to reinforce the importance of critical analysis to be undertaken even when the data appear to exhibit minor variation.

3 HYDROCHEMICAL ANOMALY DETECTION WITH MULTIVARIATE STATISTICS 4319 SITE DESCRIPTION The Great Artesian Basin (GAB) is one of Australia s most important water resources. It covers approximately one-fifth (22%) of Australia s landmass and geographically underlies parts of Queensland, New South Wales, South Australia and the Northern Territory (Figure 1). The GAB is a confined multilayered aquifer system consisting of alternating layers of permeable quartzose sandstone and impermeable marine siltstone and mudstone of Cretaceous Triassic age. The hydrostatic pressure placed on the confined aquifers raises the potentiometric pressure to above ground level in most parts of the GAB, allowing bores that are drilled into the water-bearing units to flow freely along the ground surface. Sodium, bicarbonate and chloride contribute to greater than 90% of the groundwater s total ionic strength, with little variation in chemistry observed between the recharge zone in the east and the main basin area (Habermehl, 193, 196). A small section in the southeast of the GAB was chosen for this study. This section covers an approximate area of 5100 km 2 and extends along the Namoi River between Narrabri and Walgett in northern New South Wales (Figure 1). Geologically, the study area is situated in the Coonamble Embayment, a subsection of one of the three main GAB depression-filled sub-basins, the Surat Basin. During the early Cretaceous, a marine transgression covered the eastern section of the study area, providing stratigraphic differences between sediments in the east and sediments in the west. A schematic geological cross-section is provided in Figure 2; a full account of these stratigraphic differences can be found in O Shea (00). The main water-bearing aquifer in this area is the Jurassic Pilliga Sandstone unit, in parts underlain by bedrock granite and overlain by the confining Rolling Downs Group. Inferred regional groundwater flow direction is from east to west in the study area; however, distinct subsystems can occur, with Radke et al. (00) implying that southern, northeastern and western subflows may occur in this area. The chemical compositions of groundwaters in the GAB have been discussed by several workers. Habermehl (19) discussed the geology, hydrogeology and exploitation of the GAB, identifying the eastern groundwaters as largely Na HCO 3 in composition with minor chloride and sulphate present. In 193 he furthered his WESTERN AUSTRALIA NORTHERN TERRITORY SOUTH AUSTRALIA GREAT ARTESIAN BASIN NAMOI STUDY AREA ARTESIAN BORE QUEENSLAND NEW SOUTH WALES VICTORIA TAS N RIVER BOGAN WALGETT MACQUARIE BARWON CASTLEREAGH RIVER NAMOI GWYDIR COONAMBLE RIVER MOREE RIVER NARRABRI INVERELL GUNNEDAH RIVER NYNGAN RIVER RIVER DUBBO GOULBURN 0 km RIVER SINGLETON Figure 1. Extent of the GAB in Australia, with the location of bores in the lower Namoi River valley study area enlarged

4 43 B. O SHEA AND J. JANKOWSKI Drildool Beds Keelendi Beds W Non-marine Western Section Marine-influenced Eastern Section E Rolling Downs Group Approx. Depth (m) Pilliga Sandstone Orallo Formation Approx. Scale 3km Kanimblan Granite Figure 2. Generalized geological cross-section in the Namoi River valley study area. The extent of marine transgression in the Cretaceous resulted in depositional differences between the east and west in the study area interpretation by identifying two dominant water types in the GAB: Na HCO 3 Cl in the main basin area, and Na Cl SO 4 type in the southwest (Habermehl, 193). Habermehl (196) deduced that the increase in HCO 3 and decrease in SO 2 4 might be the result of biochemical reduction of sulphate, producing H 2 S and CO 2. Herczeg et al. (1991) discussed the evolution of chemistry along a flow path, suggesting that Na C and K C were removed by reactions involving kaolinite, a sodium smectite and illite. They also came to the conclusion that the addition of CO 2 to the system drives carbonate dissolution reactions. Habermehl (1996) found that Ca 2C,Mg 2C and SO 2 4 concentrations were higher in the recharge areas and decreased basinwards. Ion-exchange reactions contribute Na C to the system at the expense of Ca 2C and Mg 2C. Habermehl (1996) also suggested that high Cl values in the centre of the basin may indicate very low to semi-stagnant flow conditions. The origin of Na HCO 3 waters in the GAB has been the focus of some recent work on GAB hydrochemistry. Several workers suggest that soil-generated CO 2 dissolves carbonates and silicates, releasing HCO 3 into the system followed by ion exchange on clay sites to release Na C (Habermehl, 196; Herczeg et al., 1991). The suggestion that CO 2 is biogenically produced is in contrast to Schofield (199) and Schofield and Jankowski (04), who studied Na HCO 3 waters in the Ballimore region in the eastern recharge area of the GAB. The Na HCO 3 -rich groundwaters in Ballimore were found to be derived from magmatic CO 2. Lavitt (1999) also found that CO 2 was coming from mantle degassing in the Mooki River catchment in a separate recharge area in the east of the GAB. Most recently, Jankowski and McLean (01) analysed GAB waters from the lower Namoi River valley study area using 13 C and found that these waters experienced an enrichment of υ 13 C compared with waters in other parts of the basin, where carbon influx was thought to be derived from biogenic CO 2. Cainozoic volcanic activity in the eastern part of the GAB was found to modify the υ 13 C signature due to the possible influx of heavy 13 C from magmatic activity. Studies using other isotopes ( 7 Sr/ 6 Sr and 3 He) have deduced that mantle-derived gases associated with Cainozoic volcanic activity may influence GAB waters (Torgersen et al., 197, 1992; Collerson et al., 19). Previous studies by O Shea (00) suggested that two different groundwater types were present in the Namoi River valley study area, with each water type being characterized by slight differences in water chemistry with respect to chloride concentration. A geological boundary between marine sediments in the east of the study area and non-marine sediments in the west was postulated to be a plausible control on differences between

5 HYDROCHEMICAL ANOMALY DETECTION WITH MULTIVARIATE STATISTICS 4321 the two water types. Each type of water plotted together in discrete groups on various chemical bivariate plots (O Shea, 00). No statistical methods were applied during this previous study; the author suggested these trends based purely on familiarity with the data set. McLean (03) subsequently applied Q-mode cluster analysis to the Namoi River valley GAB waters and agreed that two distinct water types were indeed present: the east and the west. No further statistical analysis was carried out on the GAB waters; hence, further analysis is conducted herein to confirm or dismiss these trends. METHODOLOGY Collection of groundwaters and analysis of major ions Twenty-five artesian water bores were sampled in either March or August 00. No temporal variation between summer or winter samples was observed, due to the lengthy flow paths encountered at great depths in the basin. Most bores were installed within the past century and have detailed logs available from state geological departments. These logs indicate that the Pilliga Sandstone unit is the most commonly encountered aquifer in the study area. All GAB bores were flowing, so sampling could begin immediately, in contrast to non-flowing bores that require purging before sampling can begin. A flowing bore was the sole requirement for sampling, regardless of the depth of the aquifer penetrated. General parameters (temperature T, EC, redox (Eh), dissolved oxygen and ph) were recorded at the head of the bore once readings stabilized to within š5%. Samples were field filtered through a 0Ð45 µm cellulose acetate membrane filter to remove any suspended matter. Alkalinity (as HCO 3 ) was determined in the field by titration with 0Ð01 M HCl against bromocresol green indicator (Greenberg et al., 1992). Two measurements were taken and the results were averaged. Chloride was determined by argentometric titration with AgNO 3 (Greenberg et al., 1992). The remaining ions were preserved with nitric acid in the field and analysed by inductively coupled plasma atomic emission spectrometry in the laboratory at the University of New South Wales (Table I). Sampling and analyses were carried out under strict quality control regimes that included the collection of duplicates, blanks and calculation of solution electroneutrality to within š5%. This sampling programme was part of a larger study where several hundred water samples were repeatedly collected and analysed under the same stringent quality control procedures (McLean, 03). Statistical analysis Assessment of normality. Prior to commencing statistical analyses, the data set should be assessed for normality and completeness of data. Results of the data screening process determine whether the data are suitable for statistical tests in raw form, or whether they require manipulation to achieve more accurate results from the statistical procedures employed. The data screening process for the GAB chemical data is described below. All statistical analyses were conducted using the SPSS (version 12Ð0) statistical software package. Data producing a bell-shaped frequency distribution, with values clustered around a central point and the frequency of occurrence declining away from this point, are said to be normally distributed (Davis, 196). It is often assumed that variables are normally distributed, and many statistical tests are based on this assumption. Principal components analysis (PCA) is an exception to this rule, as it is based solely on eigenanalysis of the correlation/covariance matrix (Meglin, 1991). However, hierarchical cluster analysis (HCA) assumes that the data are either normal or log normal (Guler et al., 02); therefore, an assessment of normality was required before HCA could be undertaken. Histograms of the GAB data showed that major ion concentrations were skewed both positively and negatively. Most naturally occurring element distributions follow a positively skewed pattern (Miesch, 1976) rather than an asymmetrical normal distribution. The log 10 -transformed data appeared to approximate normality better for the GAB major ions. There are advantages and disadvantages to transforming data sets. Dreher (03) debated the use of transformation techniques on positively skewed data owing to the possibility of

6 4322 B. O SHEA AND J. JANKOWSKI Table I. Groundwater chemical data, lower Namoi River valley GAB samples Sample ID ph Eh (mv) Temperature ( C) EC (µs cm 1 ) DO Ca 2C Mg 2C Na C K C HCO 3 Cl SO Ð Ð Ð00 3Ð 0Ð59 292Ð72 2Ð50 647Ð39 77Ð3 0Ð00 2 7Ð Ð Ð00 2Ð5 0Ð43 2Ð27 2Ð1 734Ð04 63Ð36 0Ð00 3 7Ð Ð Ð00 2Ð90 0Ð49 302Ð36 2Ð40 73Ð31 64Ð52 0Ð00 4 7Ð Ð Ð00 2Ð34 0Ð54 306Ð51 2Ð09 72Ð54 61Ð53 0Ð00 5 7Ð Ð Ð00 3Ð64 0Ð53 29Ð29 2Ð65 709Ð02 73Ð91 0Ð00 6 7Ð Ð Ð00 3Ð39 0Ð52 30Ð75 2Ð54 727Ð32 6Ð15 0Ð00 7 7Ð Ð Ð00 3Ð49 0Ð69 304Ð52 2Ð30 730Ð9 72Ð52 0Ð00 7Ð66 41Ð Ð00 4Ð11 0Ð9 29Ð95 2Ð7 673Ð02 70Ð67 0Ð00 9 7Ð Ð Ð00 2Ð59 0Ð63 26Ð5 2Ð14 67Ð66 56Ð64 0Ð Ð Ð Ð00 3Ð50 0Ð34 263Ð5 2Ð53 609Ð56 75Ð56 0Ð Ð Ð 105 0Ð00 2Ð94 0Ð0 249Ð75 1Ð90 577Ð22 74Ð6 0Ð Ð Ð Ð00 2Ð50 0Ð4 30Ð00 2Ð14 699Ð26 59Ð56 0Ð Ð Ð Ð00 2Ð3 0Ð70 316Ð2 2Ð36 73Ð92 63Ð62 0Ð Ð Ð Ð00 3Ð39 0Ð65 27Ð55 2Ð5 666Ð31 69Ð75 0Ð Ð Ð Ð00 3Ð33 0Ð34 291Ð56 2Ð69 713Ð29 69Ð55 0Ð Ð Ð Ð00 3Ð32 0Ð 250Ð01 2Ð 633Ð57 74Ð06 0Ð Ð Ð Ð00 3Ð4 0Ð55 269Ð72 2Ð25 622Ð37 72Ð6 0Ð00 1 Ð Ð Ð00 2Ð1 0Ð24 262Ð77 1Ð90 569Ð90 72Ð71 0Ð Ð Ð Ð00 2Ð62 0Ð46 245Ð13 1Ð64 594Ð14 73Ð66 0Ð00 7Ð Ð Ð00 3Ð40 0Ð75 272Ð4 2Ð3 636Ð41 69Ð2 0Ð Ð Ð Ð00 3Ð13 0Ð60 2Ð00 1Ð97 725Ð53 76Ð94 0Ð Ð Ð Ð00 6Ð13 1Ð47 266Ð00 6Ð5 7Ð04 44Ð46 0Ð Ð Ð Ð00 3Ð49 0Ð53 2Ð00 2Ð67 7Ð65 69Ð43 0Ð Ð Ð Ð00 3Ð46 0Ð66 333Ð00 3Ð10 7Ð36 6Ð26 0Ð Ð Ð Ð00 2Ð96 0Ð59 313Ð70 0Ð69 66Ð44 50Ð34 0Ð00 information (specifically anomalies) becoming lost. Guler and Thyne (03) responded to Dreher s comment by stating that transformation is required to produce maximum results from parametric (normal) statistical methods. Given the debate on this subject, the raw major ion data were used for PCA (which does not require the assumption of normality) and the log 10 -transformed data were used for HCA (which does require the assumption of normality). Standardization. In order for each variable to have an equal weight in the statistical analyses, the data can be standardized to a range of š3 standard deviations, centred about a mean of zero (Guler et al., 02). Dreher (03) disputed the use of standardization, saying it shifts the relationships between the ions and neglects information derived from relative abundances, such as supply and demand on the air, soil, unsaturated and saturated zones. Guler and Thyne (03) responded to this comment saying they used standardization to avoid misclassifications arising from the inappropriate weighting of parameters with large magnitudes. A number of other workers have standardized their geochemical data (Ruiz et al., 1990; Farnham et al., 00; Swanson et al., 01). Standardization is necessary when data vary over wide ranges, as is generally the case with concentrations of major ions in the GAB data set (<1 mgl 1 to >700 mg l 1 ). Standardization was employed herein to ensure each analyte was equally weighted during the statistical analyses. Cluster analysis. HCA was performed on the major ions Na C,K C,Mg 2C,Ca 2C,HCO 3 and Cl. Sulphate was not included, as it was not detected in any of the samples analysed. Q-mode HCA classified each case (sample), measured by variable (major ion), into statistically defined groups. Ward s (1963) linkage method was chosen to iteratively link nearby points of similarity. Euclidean distance measure assessed the similarity

7 HYDROCHEMICAL ANOMALY DETECTION WITH MULTIVARIATE STATISTICS 4323 combined with linkage. R-mode HCA was useful in establishing relationships between the variables (analytes) rather than the cases (samples), as is the situation in Q-mode HCA. A dendrogram was produced for each cluster analysis undertaken, with the phenon line set to five to show statistical similarity. PCA. A second geostatistical tool was used on the GAB data, namely PCA, which is a mathematical technique used for reducing data and deciphering patterns within large data sets (Hull, 194; Joliffe, 196; Wold et al., 197; Stetzenbach et al., 1999). Principal components (PCs) are based on eigenanalysis of the correlation or covariance matrix; therefore, data do not need to be normally distributed (Meglin, 1991). PCA was thus conducted on raw standardized data using the correlation matrix. PCs are the result of strong correlations between variables. PCs may result from the correlation of suites of variables (such as marine elements) representing the same geological origin or geochemical source. The first PC is that component which has the greatest possible variance, the second PC has the second greatest variance, and so on. All PCs are uncorrelated (i.e. orthogonal) to one another. Eigenvalues describe the amount of variance explained by each PC, and thus decrease with each successive PC extracted. Eigenvectors (or PC loadings) indicate the relative contribution that each element makes to that PC score. The larger the score (in absolute value), the stronger the influence of that element (Webster, 01). RESULTS Major ion composition was similar for all water samples, resulting in a classification of Na HCO 3 -type groundwater. The Piper diagram shows homogeneity in major ion composition due to the close proximity of all plotted points (Figure 3a). According to Piper s (1944) classification, all waters are generalized as >50% carbonate alkali-type groundwaters. A second Piper diagram was constructed where the scale of the plotted area was enlarged to distinguish any subtle patterns present in the data (Figure 3b). Magnification of the data in this way revealed two distinct populations; both were Na HCO 3 -type waters, but one was slightly more influenced by chloride with respect to the other. In comparison, the Durov diagram (Figure 4) shows the same major ion similarity yet variability is illustrated via differences in TDS and ph. These differences are minor; however, one sample (number 22) exhibits a slight, yet distinctive, variation in ph. Durov s classification (as presented in Chilingar (1956)) characterizes the GAB waters as alkaline bicarbonate commonly devoid of sulphates. (a) Mg SO Ca Na HCO Piper (1944) Classification Group 5 - carbonate hardness > 50% Group 6 - non-carbonate hardness > 50% Group 7 - non-carbonate alkali > 50% Group - carbonate alkali > 50% Group 9 - no single cation-anion pair > 50% Cl Na-HCO 3 waters Na-HCO 3 with Cl influence Mg SO Ca Na HCO 3 Cl Figure 3. (a) Piper diagram showing Na HCO 3 GAB sample composition and the area magnified in (b) which distinguishes two separate groups in the data due to Cl variability (b)

8 4324 B. O SHEA AND J. JANKOWSKI 100% SO Cl HCO % Mg 50 TDS (mg/l) Na+K ph Figure 4. Durov diagram showing ph and TDS with major ion plots enabling variability in the groundwater composition to be illustrated. TDS values vary marginally among samples, and sample 22 is identified as an anomaly when differentiated by ph (CO HCO3 - ) - (Cl - +SO4 2- ) % meq (Ca 2+ +Mg 2+ ) - (Na + +K + ) % meq 22 (CO HCO3 - ) - (Cl - +SO4 2- ) % meq (Ca 2+ +Mg 2+ ) - (Na + +K + ) % meq Figure 5. Chadha (1999) classifies the GAB waters as Na HCO 3 dominant (group ). Magnification of the scale is successful in delineating different water types and two subtle anomalies (samples 22 and 25) Chadha s (1999) diagram was also useful in establishing water type as Na HCO 3 dominant with the further classification of subdivision representing alkali metals (Na C K) exceeding alkaline earths (CaC Mg) and weak acidic anions (HCO 3 ) exceeding strong acidic anions (Cl ). Division of the water samples into two different groups is not apparent at small scales; however, magnification of the scale successfully delineated two different water types (Figure 5). In addition, two individual samples have successfully been defined as subtle anomalies in Chadha s diagram that were not previously visible in the Piper and Durov diagrams (with the exception of one sample in the Durov diagram that was delineated by a difference in ph).

9 HYDROCHEMICAL ANOMALY DETECTION WITH MULTIVARIATE STATISTICS 4325 An analysis of the descriptive statistics (Table II) supports the homogeneous character of the waters. Descriptive statistics provide an indication of abundance and elemental outliers. The mean and standard deviation for Ca 2C,Mg 2C,K C and Cl are clearly lower than the results reported for Na C and HCO 3. Similarly, the range of concentration values reported for these major ions are small when compared with the larger range and concentrations of Na C and HCO 3. For comparison with other studies conducted in the GAB, mean concentrations reported by Habermehl (193) for the southeastern part of the GAB are similar to those reported herein and are also listed in Table II. In comparison, the multivariate statistical analysis identifies distinct patterns in the data. Q-mode HCA was conducted to determine similarity between samples. The dendrogram produced (Figure 6) shows four main clusters (phenon line set to 5). Two samples stand alone, i.e. samples 22 and 25. These waters are most dissimilar to other waters given their distance from the phenon line to the closest cluster; as such, they Table II. Descriptive statistics for the GAB groundwater samples (n D 25). Comparison with mean ion concentrations from a separate study shows groundwater composition has not changed dramatically over time Statistical parameter Ca 2C Mg 2C Na C K C HCO 3 Cl SO 4 2 Range 3Ð 1Ð40 7Ð9 5Ð Ð4 0Ð00 Minimum 2Ð30 0Ð Ð Ð5 0Ð00 Maximum 6Ð10 1Ð Ð Ð 0Ð00 Standard deviation 0Ð70 0Ð30 22Ð7 1Ð00 54Ð0 Ð 0Ð00 Mean a 3Ð30 0Ð Ð Ð 0Ð00 Comparative mean b 2Ð00 0Ð Ð Ð7 0Ð96 a Means calculated from data collected for this study. b Means taken from Habermehl s (193) study of the southeast section of the GAB. SAMPLE Phenon Line = 5 CLUSTER 1 CLUSTER 3 CLUSTER 2 CLUSTER 4 Anomaly Anomaly Figure 6. Dendrogram from the Q-mode HCA procedure identifying four main clusters and two distinct anomalies

10 4326 B. O SHEA AND J. JANKOWSKI are designated anomalous. The originally defined (non-statistical) water types proposed by O Shea (00) were again separated into two distinct groups (clusters 1 and 2 representing the eastern divide and clusters 3 and 4 the western divide), with further subdivision of these original groups based on more subtle numerical differences present in the data. This geographical separation is responsible for the non-consecutive ordering of the clusters on the dendrogram. Figure 7 shows the original groundwater types proposed, compared with the clusters defined by multivariate statistical techniques. To determine which ions were responsible for influencing each cluster, R-mode HCA was conducted to assess the similarity between ions in each cluster group. The R-mode dendrograms are presented in Figure. From the results of the R-mode HCA it can be seen that Na C and HCO 3 are generally not closely related, except for a minor relationship observed in cluster 3. Subtle changes in the relationships between cations in different clusters may indicate ion-exchange processes occurring at different sections along the flow path. These processes may contribute to the dominance of sodium cations, since it is unlikely that both Na C and HCO 3 are derived from the same geochemical source given their lack of similarity. However, dissolution of a sodium clay should not be discounted should ion exchange be dominating the HCA results. Cluster 4 shows a particularly interesting non-relationship between Cl and the other ions, perhaps indicative of an additional Cl input in this part of the aquifer, such as upwards leakage from the underlying Palaeozoic granite bedrock. PCA was conducted to show variability in the data rather than similarity, as is the case with HCA. Six PCs were responsible for 99Ð99% of the variation present in the data (Table III). PCs with eigenvalues less than one (mostly representing noise) were discarded, leaving the first two PCs for further analysis. PCs 1 and 2 represent 50% and 30% of variance respectively, and their object scores are plotted graphically in Figure 9 to show variance and illustrate the relationship between these two main components. Samples with similar groundwater chemistry will plot as clusters on bivariate plots. For comparison, the cluster groups deduced from HCA have also been plotted on the PC bivariate plot. Absolute loadings (eigenvectors) for PCs 1 and 2 were evaluated to determine the elements that contribute most strongly to variance in the data (Table IV). For each PC retained (1 and 2), the eigenvectors were matched with corresponding PC scores (Table V) as explained below. Cluster 1 is represented by intermediate (mid) positive loadings on PC1 and high positive loadings on PC2. Table IV shows mid positive loadings on PC1 are represented by Na C and HCO 3, with high positive loadings on PC2 also represented by Na C and HCO 3. Thus, cluster 1 on the PC bivariate plot is characterized by variability in Na C and HCO 3 concentrations. A similar classification can be made for cluster 2. Cluster 3 remains characterized by Na C and HCO 3 for PC1, but is also influenced by variability in Mg 2C in PC2. Cluster 4 differs from the previous three clusters, in that high negative PC1 scores distinctly represent variability in Cl, in addition to high negative PC2 scores represented by variability in Ca 2C. An anomalous sample from cluster 2 (identified as sample 22) exhibits high positive PC1 scores representing variability in Non-statistical divide proposed by O Shea (00) Cluster 1 Cluster 2 Cluster 3 Cluster 4 Anomaly Barwon River WALGETT Castlereagh River Gwydir River WEST MOREE 25 NARRABRI EAST Figure 7. Spatial view of assigned cluster membership to the Namoi River valley GAB groundwater samples. Note that the position of the non-statistical divide previously proposed coincides with current statistical boundaries

11 HYDROCHEMICAL ANOMALY DETECTION WITH MULTIVARIATE STATISTICS CLUSTER K Cl HCO 3 Mg Na Ca CLUSTER 2 Ca K Mg Na Cl HCO 3 CLUSTER 3 Mg K Na HCO 3 Ca Cl CLUSTER 4 Ca K HCO 3 Mg Na Cl Phenon Line = 5 Figure. Dendrograms from R-mode HCA showing the relationship between ions in each cluster Table III. PCs, eigenvalues and variance accounted for in the GAB groundwaters PC Eigenvalue Variance (%) Cumulative variance (%) 1 3Ð019 50Ð32 50Ð32 2 1Ð12 30Ð19 Ð52 3 0Ð654 10Ð90 91Ð42 4 0Ð259 4Ð32 95Ð74 5 0Ð157 2Ð61 9Ð35 6 0Ð099 1Ð65 99Ð99 Total 6Ð000 99Ð99 99Ð99 Ca 2C,Mg 2C and K C. This same sample was not grouped tightly with the other cluster-2 samples, indicating it is least similar to these and other samples used in the analysis. DISCUSSION The dominance of Na HCO 3 -type groundwaters can be seen in the original Piper diagram and the complementary descriptive statistics. However, the magnification of the original Piper diagram and inclusion of the Durov diagram shows that graphical techniques can be successful in distinguishing subtle patterns in

12 432 B. O SHEA AND J. JANKOWSKI High positive PC1 Ca, Mg, K Sample Cluster 1 Cluster 2 Cluster 3 Cluster 4 Mid positive PC1 Na, HCO Sample 25 PC High negative PC1 Cl PC2 High negative PC2 Ca Low negative PC2 Mg High positive PC2 Na, HCO 3 Figure 9. PC1 versus PC2. Clusters 1 and 2 are characterized by variability in Na and HCO 3. Cluster 3 is dominated by variability in Mg, whereas Cl and Ca variability characterizes cluster 4 Table IV. Component loadings for PC1 and PC2 Ion PC1 PC2 Ca 2C 2Ð19 2Ð064 Mg 2C 2Ð63 0Ð394 Na C 0Ð992 3Ð3 K C 2Ð411 1Ð607 HCO 3 1Ð693 2Ð597 Cl 1Ð3 0Ð997 hydrochemical data. The two separate waters defined in Figure 3b are consistent with the original division proposed by O Shea (00) in Figure 7. The Durov diagram again plots samples in close relationship to each other before dividing them further based on the use of the additional parameters TDS and ph. This graphical technique establishes sample 22 as a subtle anomaly based on the inclusion of ph into the major ion analysis. The enlarged Chadha diagram provides the clearest graphical representation of two separate water types and also delineates the presence of two subtle anomalies: samples 22 and 25. With the added benefit of easily being constructed in a standard spreadsheet software package, the Chadha diagram provided the most suitable graphical representation of the GAB data set. The classification of waters in the Chadha diagram includes a description that such waters deposit residual sodium carbonate in irrigation use and cause foaming problems.

13 HYDROCHEMICAL ANOMALY DETECTION WITH MULTIVARIATE STATISTICS 4329 Table V. Object scores for each sample in PC1 and PC2 Sample ID PC1 PC2 1 0Ð04 0Ð Ð026 0Ð Ð037 0Ð Ð00 0Ð Ð045 0Ð Ð097 0Ð9 7 0Ð113 0Ð162 0Ð261 0Ð Ð026 0Ð Ð253 0Ð Ð55 0Ð Ð021 0Ð Ð153 0Ð Ð014 0Ð Ð033 0Ð Ð367 0Ð Ð146 0Ð Ð479 0Ð Ð446 0Ð299 0Ð023 0Ð Ð07 0Ð Ð365 0Ð5 23 0Ð061 0Ð Ð256 0Ð Ð011 0Ð405 McLean and Jankowski (02) have identified that Na HCO 3 groundwaters in the lower Namoi River valley pose a threat to the future sustainability of groundwater quality and use for irrigation. The use of descriptive statistics supports the homogeneity of groundwaters, as shown by the Piper and Durov diagrams, but does not provide any further geochemical patterns. Given that the graphical representations base their comparisons on abundance of major ions, the descriptive statistics are useful in expressing the actual concentrations and range of concentrations of the major ions present in the groundwater. Both multivariate statistical methods applied were successful in defining distinct water types (HCA), with the added benefit of providing some additional information on the ions most likely to be responsible for delineating those water types (PCA). To support the results of the statistical analysis, hydrochemical graphs were constructed with each separate cluster group identified separately on each graph. The graphs in Figure 10 show the successful delineation of the cluster groups and the geochemical trends evident in the groundwaters examined. Figure 10a shows that concentrations of Na C and HCO 3 are higher in clusters 1 and 2 (the eastern section). The PCA results indicated that these two clusters were influenced by variability in Na C and HCO 3. There is more Na C in the system than HCO 3, suggesting ion-exchange reactions may be occurring to increase Na C concentrations and/or HCO 3 is decreasing due to precipitation with Ca 2C and other carbonates (Figure 10b). Ca 2C and Mg 2C are increasing along flowpath in the eastern section, whereas HCO 3 remains constant. It is suggested, therefore, that ion-exchange processes are controlling Na C concentrations in the eastern section (clusters 1 and 2). This trend reverses in clusters 3 and 4 (the western section), as Ca 2C and Mg 2C concentrations begin to decrease along the flow path in conjunction with HCO 3. Precipitation of carbonates is thus suggested for the western section. PCA supports this conclusion by representing cluster 3 due to variability in Mg 2C,Na C

14 4330 B. O SHEA AND J. JANKOWSKI (a) Na (meq/l) Sample 22 NaHCO 3 concentrations are higher in the eastern section (b) HCO 3 (meq/l) Ca + Mg increase in east Ca + Mg decrease in west Sample HCO 3 (meq/l) Ca + Mg (meq/l) (c) Sample 22 Cl increasing in east (d) Sample 22 HCO 3 (meq/l) Cluster 1 Cluster 2 Cluster 3 Cluster Cl (meq/l) Stable and higher Cl concentrations in west Na/Cl ratio 6 4 Decreased Na/Cl ratio in the west, 2 possibly due to additional Cl source with decrease in EC attributed to decrease in other ionic species EC (us/cm) Figure 10. Bivariate scatter plots showing patterns in data successfully differentiated by HCA. (a) Na HCO 3 water dominance; (b) ion-exchange processes; (c) Cl is higher in the west, yet increasing in the east; (d) additional source of Cl proposed and HCO 3. Cluster 4 is also influenced by variability in Ca 2C on the PC plot. The PCA is thus successful in delineating changes in groundwater types due to the dominance of carbonate precipitation in the west and ion exchange processes in the east. Elevated Cl in the western section (Figure 10c) distinguishes the same subtle differences detected in the magnified Piper diagram (Figure 3b). This elevated Cl may be due to Cl leakage from the Palaeozoic bedrock below. Figure 10d illustrates the drop in Na/Cl ratio and the decrease in EC potentially from loss of HCO 3 and TDS due to precipitation. It appears that the statistically defined water types within this investigation may indicate areas where Cl input is supplementary and, therefore, possibly derived from upward leakage of Cl groundwaters from below. Changes to geochemical processes spatially throughout the lower Namoi River valley study area may be due to a number of factors. These potentially include: ž The chemical evolution along the flow path is not a singular factor dominating reactions in the system, given that a number of different flow paths have previously been inferred for this study area (Radke et al., 00). Mixing between flow paths may contribute to differences between the eastern and western sections. ž The east west divide has also been suggested to be a factor of the partial (eastern) extent of marine transgression over the study area during the Cretaceous (O Shea, 00). Herczeg et al. (1991) suggested that the effects of saline waters from Cretaceous marine mudstones leaking into the Jurassic aquifer would be slight. The homogeneity of the major ion composition shown within supports this suggestion. However the slight increase in Cl along the flow path in the east may indicate marine mudstones contributing to

15 HYDROCHEMICAL ANOMALY DETECTION WITH MULTIVARIATE STATISTICS 4331 chemical contribution of groundwaters in this area. The use of indicator trace elements by O Shea (00) and McLean and Jankowski (01) suggest that groundwaters of the study area may be influenced by marine geology. ž Vertical upwards leakage of Cl from Palaeozoic basement granites may be more pronounced in the western section of the study area where the main GAB aquifer is inferred to overlie bedrock directly. Bentley et al. (196) proposed that a contribution of dead Cl was being added in some GAB flow regimes, possibly from an underlying aquifer containing connate water. ž Alternatively, Airey et al. (1979) suggested that variations in Cl,Na C and HCO 3 concentrations in water samples with distance from the recharge area may reflect variations in the annual rainfall and the rate of infiltration of recycled salt throughout the late Quaternary. Samples 22 and 25 were identified as anomalies in several interpretation methods applied: the Chadha diagram, Durov diagram, HCA and PCA. Sample 25, located close to the town of Narrabri, is distinguished by its relatively shallow depth (172 m b.g.s.) compared with the other bores (ranging from approximately 600 to 0 m b.g.s.). Thus, sample 25 can be differentiated based on its depth, which determines the geological unit screened and lower water temperature (due to geothermal gradients), which may influence some chemical reactions. Sample 22 was first distinguished based on its lower ph value in the Durov diagram. HCA subsequently showed its dissimilarity to other clusters, whereas PCA indicated it was the only water sample to be represented by variability in Ca 2C,Mg 2C and K C. Figure 10b shows a cluster-2 sample separate from the rest of the cluster that exhibits the highest Ca 2C and Mg 2C concentrations, i.e. sample 22. Isotopic investigations (McLean, 03; Jankowski and McLean, 01) show that one GAB sample exhibits different characteristics to the rest of the population. This sample suggested an influx of magmatic CO 2 and is likely to be sample 22. CONCLUSIONS Of the traditional graphical techniques used in this assessment, the Chadha diagram provided the clearest trends in the major ion data by successfully identifying two distinct water types and two subtle anomalies. Further distinction between water types was made by HCA, with PCA contributing information on potential geochemical processes occurring in, and differing between, each water group. Thus, the use of multivariate statistics has enabled subtle trends in otherwise homogeneous groundwaters to be defined using major ion data only. Both interpretative tools (graphical and statistical) aided in the chemical interpretation of the groundwaters and identified three main geochemical processes occurring in the study area: ion-exchange reactions, carbonate precipitation, and addition of Cl. Differences in the spatial occurrence of these processes may be due to a number of factors, including upwards vertical leakage, mixing of flow paths, original recharge water composition, extent of marine transgression in the Cretaceous, and input of CO 2 from varying sources. The multivariate statistics also successfully delineated two subtle anomalies representing minor differentiation in the data set. Many previous investigations have supported the use of statistical analysis in conjunction with traditional graphical techniques. This study shows the importance of combining the two methods for homogeneous groundwaters that, on first presentation, appear to be chemically similar. Application of both techniques should be emphasized to people with limited training in hydrochemistry who may simply plot waters on a trilinear diagram and conclude there are no trends evident in the data, without further investigation.

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