# Digital soil mapping of a coastal acid sulfate soil landscape.

Introduction

Globally, estuarine coastal floodplains are commonly underlain by sulfidic sediments and coastal acid sulfate soils (CASS). CASS typically display high spatial heterogeneity both laterally and with depth (Andriesse and van Mensvoort 2006). These soil types are characterised by high concentrations of acidity and chalcophilic metals such as iron (Fe). Oxidation of sulfides, predominantly pyrite (Fe[S.sub.2]), releases Fe (Sohlenius and Oborn 2004) and sulfate (S[O.sub.4.sup.2-]) and mobilises other trace metals, including aluminium (Al), which is released by weathering of aluminosilicates (Nordmyr et al. 2006). Oxidation of pyrite also releases acidity and mobilises trace metals, which can adversely affect adjacent waterways and impact on aquatic ecosystems (Sammut et al. 1995; Santos and Eyre 2011). Oxidation of these sediments and the resultant acidification of coastal floodplain sediments and waterways can occur as a result of artificial drainage (Sammut et al. 1996) or sea level lowering caused by eustatic or isostatic uplift (Boman et al. 2010).

An accurate understanding of the distribution of CASS is essential for developing targeted management strategies to reduce acidic discharges and associated trace metals from CASS floodplains to adjacent waterways. However, current knowledge of the spatial distribution and extent is limited to existing CASS risk maps (e.g. Tulau 1999). In Australia, the method of mapping has been based on traditional soil survey methods and techniques, whereby a limited number of locations were visited with morphological and geochemical properties of the soils measured and assessed. Subsequently, air-photo interpretation was used to interpolate the results across the landscape. Although large areas can be mapped quickly via this method (Fig. la), the overall approach is limited by the small-scale nature of the sampling interval and soil morphological description. Also, air-photo interpretation can be unreliable, especially in redox-dynamic, coastal floodplain wetlands. This is because when watertables are high, vegetation may be lush, surface expression of oxidised soil conditions can be minimal and scalded areas may not be recognisable. Figure 1 b (27 June 2011) shows where scalded areas are evident and are indicated by the dark shaded areas. Conversely, Fig. 1 c (21 June 2007) shows the same area with the CASS areas not as easily discerned.

[FIGURE 1 OMITTED]

In eastern Australia, CASS generally derive from marine or estuarine sediments in an environment with abundant organic matter and anaerobic conditions (Walker 1972; Lin et al. 1995). Therefore, the sediments are often of moderate to high salinity with shallow watertables, where the salts are derived from connate marine/estuarine sources or from increases in acidity due to sulfide oxidation. Decreasing pH and increasing acidity can increase mobilisation of pH-sensitive trace metals such as Al, manganese (Mn), zinc (Zn) and nickel (Ni) and release other major cations such as potassium ([K.sup.+]), sodium ([Na.sup.+]) and magnesium ([Mg.sup.2+]) due to hydrolysis of aluminosilicate clay minerals (Dent 1986). Sulfate salts are also produced in abundance.

Owing to the presence of a large amount of salts, electromagnetic (EM) instruments that measure apparent soil electrical conductivity ([EC.sub.a]) can be of potential use in mapping CASS in estuarine landscapes (Triantafilis et al. 2012; Huang et al. 2014). This is because EM instruments have been used successfully and extensively to map the spatial distribution of soil salinity in arid areas (Thomas et al. 2009), saline watertables (Buchanan et al. 2012), and salinity in coastal areas (Li et al. 2013). Johnston et al. (2005) demonstrated how an EM38 could be used to map changes in subsurface salinity as a function of opening floodgates in a coastal floodplain. There is thus potential to use proximal sensed EM induction instruments to map the spatial distribution of CASS (e.g. Johnston et al. 2003).

This study aims to evaluate the utility of EM surveys to determine the spatial distribution of CASS using [EC.sub.a] as a surrogate for acidity. Here, we use the fuzzy k-means (FKM) algorithm to identify soil management classes from two different sources of ancillary data: (i) proximal sensing EM data, and (ii) remotely sensed height above mean sea level (m) generated from a digital elevation model (DEM). The classes can then be mapped as potential CASS management zones. The resulting maps were validated and the numbers of classes tested by computing the mean prediction error variance of the class mean as a predictor for various soil properties, e.g. pH, titratable actual acidity (TAA) and exchangeable Al.

[FIGURE 2 OMITTED]

Materials and methods

Site description

Rocky Mouth Creek (29[degrees]6'S, 153[degrees]19'E) is south-west of Woodburn, New South Wales (NSW), in the subtropical region of eastern Australia (Fig. 2). The creek drains a floodplain wetland into the Richmond River. The study field is ~1.10 km by 0.25 km. At the northern end, it is defined by a well-developed, natural levee (i.e. >1 m), and the soil is characterised by Brown Dermosols (Isbell 1996) or Fluvaquentic Epiaquolls (Soil Survey Staff 1998). To the south, it grades into a backswamp wetland with elevations just above sea level, i.e. 0.25-1 m AHD (Australian Height Datum where 0 m is approximately sea level). This area has been mapped as the Dungarubba (dua) soil landscape unit by Morand (2001a). With decreasing elevation, the study area grades into the Everlasting (ev) soil landscape unit (Fig. la), which has local relief just above and below sea level (<0.25 m).

There is little distinction between the two soil landscape units, and they only vary with differences in soil moisture condition (Morand 2001a). The ev unit is significant because it is associated with open depressions that occur as backswamps in estuarine areas. The swamps vary in width from 500 to 1500 m and have concave cross-sections. Figure la shows the spatial extent in the broad study area. The subsoil is generally saturated and a shallow saline watertable is common, similar to many other CASS wetlands in NSW (Lin et al. 2001). The soil is Sulfuric/Sulfidic Oxyaquic Hydrosols (Isbell 1996) or Hydraquentic Sulfaquepts (Soil Survey Staff 1998).

The climate is subtropical with mean annual rainfall of 1343 mm. Rainfall is summer-autumn dominant with a mean maximum in March (188 mm) and minimum in September (50 mm). Mean temperature varies between 29.9[degrees]C (January) and 19.9[degrees]C (July). Vegetation is dominated by open pasture, including common couch (Cynodon dactylon), carpet grass (Axonopis fissifolius), kikuyu (Pennisetum clandestinum) and water couch (Paspalum distichum), with rushes such as Juncus and Eleocharis spp. found in the lower lying areas. The dominant land use is sugarcane farming and improved pastures for cattle grazing and dairying (Morand 2001a).

Electromagnetic induction survey

An EM induction survey was conducted using a Geonics EM38 (Geonics Ltd, Mississauga, Ontario, Canada) in both the horizontal (EM38h) and vertical (EM38v) dipole modes of operation. In the horizontal mode, the [EC.sub.a] (mS/m) has the greatest sensitivity of measurement at the soil surface (~0.75 m) and declines with depth. In the vertical mode, [EC.sub.a] is measured to an approximate depth of 1.5 m (McNeill 1990). Here, [EC.sub.a] was measured in both modes at 324 points. The measurements were made approximately every 20 m along parallel transects ~100m apart (Fig. 3b). Elevation data were derived at each point from a high-resolution DEM with a vertical accuracy of 256 mm and pixel size of 5 m. The EM surveying and soil sampling occurred during an extensive dry period with a low watertable and oxic surface soil conditions.

Data preparation and numerical clustering

The EM38h, EM38v and elevation data were first interpolated onto a common 10-m grid using ordinary kriging (OK), with a neighbourhood of 90-100 and a local variogram. The OK was carried out using Vesper (Minasny et al. 1999). The resulting EM38h, EM38v and elevation data were classified using FKM analysis. The FKM method is described elsewhere (e.g. Triantafilis et al. 2001). We used the FuzMe software (Minasny and McBratney 2002), described further in Triantafilis et al. (2003).

To determine classes (k), we clustered the ancillary data into k=2-10. To gauge a suitable degree of overlap between k, we generated clustering outcomes using fuzziness exponents ([phi])= 1.1-2.8. To elucidate a distance-dependent metric, we initially compared the results of k=3 using Mahalanobis, diagonal and Euclidean. We considered the different metrics because, while Euclidean gives equal weight to all data, diagonal accounts for different variances, with Mahalanobis additionally accounting for correlation between data.

Given the large number of classifications that we needed to consider, i.e. k=2-10 classes and [phi] = 1.1-2.8, validity functionals such as the fuzziness performance index (FPI) and the normalised classification entropy (NCE) are commonly employed to determine a suitable number of k and a value for 0. These functionals are provided as output from FuzME. Of these, the FPI is a measure of the continuity between classes. A value of 1 represents a very fuzzy classification, while 0 indicates distinct classes with little overlap. The NCE measures the degree of disorganisation created by partitioning the data into various classes. Values near 0 indicate well-structured classes. We also considered the plot of [phi] v. change in the FKM objective function (-dJ/d[phi]), which assists in determining a suitable value of [phi] (see McBratney and Moore 1985).

[FIGURE 3 OMITTED]

Soil sampling and laboratory analysis

To test the validity of our classes, soil data were collected at 24 soil sample locations (Fig. 3c). As indicated in Fig. 3c, these were selected across the study field to account for the variation in [EC.sub.a] and elevation. Soil sampling was undertaken using a hand auger. Two samples were obtained at each location. The first was collected from the topsoil (0-0.10 m) and the second from a subsoil horizon (0.70-0.80 m). In order to analyse these data and with reference to the CASS management zones identified, an average value was determined. At the time of sampling, the soil was placed into polyethylene bags and stored at 4[degrees]C before analysis.

Moisture content was determined by weight loss after drying at 105[degrees]C for 24h. Soil pH, [EC.sub.1:5] and soluble cations and metals were determined from a 1:5 soil: water extract (Rayment and Higginson 1992). Exchangeable cations and metals were extracted using Ba[Cl.sub.2]/N[H.sub.4]Cl (Rayment and Higginson 1992). Where the [EC.sub.1:5] [greater than or equal to] 0.3dS/m, soluble salts were removed by washing three times with an ethanol/glycerol solution as described in Rayment and Higginson (1992). The TAA (mol [H.sup.+]/t) was determined by titration with 0.1 m NaOH to pH 6.5 on 1:40 soil: 1 m KCl extracts after shaking for 4h (Ahem et al. 2004).

Data analyses

To analyse the results of the various clusters and compare, for example, the best distance metric, we proposed a linear mixed model for the data of the form:

y = X[beta] + [eta] + [epsilon] (1)

where y is an n x 1 vector of values of the target soil variable; X is an n x p design matrix; [beta] is a p x 1 vector of fixed effects coefficients; [eta] is an n x 1 vector, the elements of which are a realisation of a spatially correlated random variable; and [epsilon] is an n x 1 vector, the elements of which are a realisation of an independent and identically distributed random variable. The elements of the design matrix are the predictor variables and the fixed effects coefficients correspond.

There is, therefore, exactly one element equal to 1 in each row of the design matrix, where the elements of [beta] are the estimated mean values of the target soil variable in the respective classes. The correlated random variable [eta] is assumed to be normal and has mean zero and variance parameters. These are an overall variance ([[sigma].sup.2.sub.[eta]]) and a distance parameter for a selected variogram function (e.g. range of a spherical variogram). The error variable [epsilon] also has zero mean and a variance [[sigma].sup.2.sub.[epsilon]]. We fitted models of the form in Eqn 1 for target soil variables and with the fixed effects, either the class of maximum membership for the FKM clustering of the ancillary variables with k= 2-8 or a subset of the ancillary variables, in a regression-type model. The fitting was done using the LME procedure from the NLME library for the R platform (R Development Core Team 2010; Pinheiro et al. 2013). Under this procedure, variance parameters for the random effects were first estimated by residual maximum likelihood (REML) and the fixed effects coefficients were then estimated by weighted least-squares. The method used is described in Lark et al. (2006). After model fitting, summary statistics and histograms of the residuals were examined to confirm that these appeared consistent with an assumption of normality.

Expected prediction error variances

Another objective of this paper is to predict soil properties from the ancillary data, given that a relatively small set of direct measurements of the soil properties is available. To do this, we computed the expected value of the mean-squared prediction error for the alternative methods:

[[sigma].sup.2.sub.p] = E [[{y - [y.sup.*]}.sup.2]} (2)

where y denotes the value of the target variable at some unsampled location and [y.sup.*] denotes the predicted value.

When the predictor is the mean of a class (here obtained by cluster analysis of the ancillary data), then the mean-squared prediction error in class i is:

[[sigma].sup.2.sub.p,i] = [[sigma].sup.2.sub.i] (1 + 1/[n.sub.i]) (3)

where [[sigma].sup.2.sub.i] is the variance of the target property within class i and the mean of class i was estimated from [n.sup.i] independently and randomly selected observations in the class (Brus and Lark 2013). In this study, we used a pooled within-class variance, [[sigma].sup.2.sub.w]. If [[pi].sub.i], denotes the relative area of the ith class out of k and N is the total number of observations, then the expected value of the mean squared prediction error for classes is:

[chi] = [[summation].sub.i=1,k] [[sigma].sup.2.sub.w][[pi].sub.i](1 + l/N[[pi].sub.[iota]]) = [[sigma].sup.2.sub.w](1 + k/N) (4)

Here, we computed [[sigma].sup.2.sub.p,C] for each target soil property for k = 2-8. To do this we required a value of [[sigma].sup.2.sub.w]. We obtained this from the LMM, Eqn 1, fitted to the observed soil data for the corresponding classification. The sum of the variances of the random effects in the model for k classes as the random effects, [[sigma].sup.2.sub.[eta],[kappa]] + [[sigma].sup.2.sub.[epsilon],k], was treated as the expected value of the variance for the random variable (Cochran 1977; Lark 2011). The expected value of the mean-squared prediction error for our classification into k classes for some sample size N is therefore computed here as:

*[[sigma].sup.2.sub.p,C](N|k) = ([[sigma].sup.2.sub.[eta],k] + [[sigma].sup.2.sub.[epsilon],k]) A(1 + k/N) (5)

Results and discussion

Preliminary data analysis

Table 1 shows the basic summary statistics of the EM38h, EM38v and elevation data collected at the 324 EM survey locations. Table 1 shows that the minimum (19mS/m) and maximum (192mS/m) were measured by EM38h. However, the mean EM38v [EC.sub.a] (84mS/m) was higher than that of the EM38h (59mS/m), which suggests the subsoil has a higher conductivity than the topsoil. This is most likely attributable to the presence of a saline watertable associated with the underlying estuarine sulfidic sediments of the ev soil landscape unit. Given the positive skew in the EM data, and that the means are larger than the median values, this suggests that the ev landscape is not the predominant unit. The histogram (not shown) shows that [EC.sub.a] is bimodal.

The lower half of Table 1 shows that the EM38 data are highly correlated ([r.sup.2] = 0.95). This is also the case with respect to the correlation between the EM38h ([r.sup.2] = -0.61) and EM38v ([r.sup.2] = -0.69) with elevation. The slightly larger negative correlation between EM38v and elevation suggests that saline material is associated with the lower lying areas where there is less fluvial capping and underlying estuarine-derived sediments are closer to the ground surface. The lowest lying site is below sea level (i.e. minimum=-0.33 m). The median value (0.05 m) also indicates that most of the study field is at, or just above, sea level, with the large mean (0.16 m) indicating that some areas are comparatively elevated and represent the high points (i.e. 2.5 m) associated with the natural levee.

Table 1 also presents basic summary statistics of the ancillary data collected at the 24 soil sampling locations. Generally, the various statistics described above and for the various ancillary data to be used to identify CASS soil management zones are equivalent. This is the case for the mean and median values, as well as the correlation between ancillary data.

Table 2 shows the correlation between ancillary data and soil data. The largest correlation coefficient is achieved for EM38h ([r.sup.2] = 0.80) and EM38v ([r.sup.2] = 0.77) with [EC.sub.1:5]. The elevation data are most strongly correlated with pH ([r.sup.2] = 0.80) and TAA ([r.sup.2] = 0.68). Table 2 also shows that the study field soils are strongly acidic in nature with minimum pH (i.e. 3.81). The soil is also approaching a level of salinity that is becoming unfit for human consumption (i.e. 959 [micro]S/cm), with TAA also very high at some locations (i.e. 297 mol [H.sup.+]/t).

Spatial distribution of ancillary data

Figure 4 illustrates the contour plots of EM38h (Fig. 4a) and EM38v (Fig. 4b) data collected from the 324 sites. In both modes, a clear spatial trend in [EC.sub.a] is evident. Small [EC.sub.a] values (<70 mS/m) define the areas at the northern and southern end of the study area. As shown in Fig. 4c, the elevation is highest at the northern end and a pronounced and obvious levee is discernible. On the other side of the levee, Rocky Mouth Creek drains into the Richmond River a short distance to the north. Conversely, intermediate to large [EC.sub.a] (130-160 mS/m) characterises the central part of the field, with the largest [EC.sub.a] (>160mS/m) found within a relatively small area. As shown in Fig. 3c, in the general area ascribed by these intermediate to very large [EC.sub.a] values and between northings 6780100 and 6780550, the elevation is low and is either just above (0-0.25 m) or below (<0m) sea level. Given the basin-like morphology, and the larger [EC.sub.a], it is within this area that the estuarine sediments that are high in connate marine and sulfide-oxidation derived salts are most likely located.

[FIGURE 4 OMITTED]

Fuzzy k-means clustering

To determine the number of potential classes in the ancillary data and to numerically discern classes that we can map, we considered the results of the FKM clustering of the EM38h, EM38v and DEM data into k = 2-10 classes using [phi] = 1.1-2.8. Given the strong correlation between EM38h and EM38v, as well as with elevation, we presumed the Mahalanobis metric would be best able to account for this. Nevertheless, we also clustered the data using diagonal and Euclidean metrics. In addition, and in order to account for the large differences in variance of the EM38 and elevation data, we standardised the variables to a common variance and conducted our FKM analysis for the Mahalanobis and Euclidean metrics using the standardised data.

[FIGURE 5 OMITTED]

Figure 5 shows the FPI (Fig. 5a) and NCE (Fig. 5b) plotted against k, and the relationship between the change in the FKM objective function (-dJ/d[phi]) and [phi] (Fig. 5c). This function has been shown to be a good indicator of a suitable value for 0 (see Triantafilis and Monteiro Santos 2009). In order to reduce the complexity in Fig. 5c, we plot only values of -dJ/d[phi] for k= 3, because this is how many soil landscape units we anticipate and because the results for k=4 and 5 are equivalent. When choosing [phi], the value considered most suitable is when (--dJ/d[phi]) is a maximum. For Mahalanobis, this occurs when [phi] = 1.6, whereas for diagonal and Euclidean it is when [phi] = 2.0 and 2.1, respectively. The results shown in Fig. 5a and b are for these values of 0.

In terms of the FPI, the Mahalanobis metric produces a minimum when k = 3 with a local minimum apparent at k = 9. Equivalent results are evident when considering NCE. The diagonal metric shows minima from k= 3 to 4 for the FPI and k = 4 for the NCE. The Euclidean metric shows local minima for k = 4 and 7 for both the FPI and NCE.

Comparison of metrics

To determine which metric is most appropriate to identify the CASS management zones, we first plotted the results of the FKM analysis for k = 3. Figure 6 shows the spatial distribution achieved using Mahalanobis ([phi] = 1.6), diagonal ([phi] = 2.1) and Euclidean ([phi] = 2.0). In all cases, membership (m) is considered when m >0.5

In general, the study field is divided in essentially the same way. For example, when we consider the results derived using Mahalanobis, which is the most popularly used metric, class 3A defines the elevated north-west comer, which is associated with the Rocky Mouth Creek levee. Here, and as shown in Table 3, the EM38h (33mS/m) and EM38v (48mS/m) centroid values are smallest and the elevation (1.12m) highest. Conversely, class 3C represents the bowl-shaped depression that characterises the centre. It is defined by centroids which show that the EM38h (91 mS/m) and EM38v (123mS/m) are largest and elevation lowest (-0.14 m). In between these areas, and to the south of class 3C, intermediate values of [EC.sub.a] (e.g. EM38h = 42mS/m) and elevation (0.21m) define class 3B. These three areas are consistent with the approximate locations of the various soil-landscape units identified by Morand (2001a), whereby classes 3A and 3B represent the dua and du soil landscapes, respectively, and 3C the ev soil landscape unit (see Fig. la).

Figure 6b shows the map achieved using the non-standardised data and the diagonal metric. The main difference between this map and Mahalanobis is that class 3A is a little larger in its areal extent. From a numerical perspective, Table 3 shows that the centroid values of the classes, for example Class 3B, achieved by the diagonal metric are also smaller in terms of [EC.sub.a] (e.g. EM38h = 44 mS/m) with elevation slightly higher (i.e. 0.16 m). The reason for this is due to the elevation data having more weight in the clustering when using the diagonal metric. This is also the case with regard to class 3C and in terms of [EC.sub.a]; however, the elevation is the same. The Euclidean metric yields a very similar result to the diagonal and in terms of the spatial extent of the classes (Fig. 6c). The reason for this is that by standardising the EM38 and elevation data, the Euclidean metric is able to account for the large difference in scale apparent between these two ancillary data (see Table 2). The main difference is the centroid values (Table 3), which are, in general, larger in terms of EM38 and lower in terms of elevation.

[FIGURE 6 OMITTED]

To ascertain which metric to pursue, we looked at the expected value of the mean-squared prediction error of the class means for sample size of 24 and k=3 (i.e. [[sigma].sup.2.sub.p,C] (24 | 3)). Table 4 shows the value of [[sigma].sup.2.sub.p,C]C (24 | 3) and for each of the soil properties measured. From the wide array of properties that would be indicative of alluvial and estuarine (i.e. CASS) sediments and soil, the variances are minimised to the greatest extent via the use of the standardised data and the Mahalanobis metric. This includes pH (0.11), TAA (924), exchangeable A1 (1931) and Fe (1.05), and soluble A1 (166) and Fe (36.8). The only exceptions to this were [EC.sub.1:5] (7837), which was smaller for the Euclidean metric, and Al/effective cation exchange capacity (Al/ECEC: 0.05) (0.24) for the diagonal metrics. Similar results were achieved when k=4 was considered. Given [[sigma].sup.2.sub.p,C] (24 | 3) is minimised for Mahalanobis, and across a wide range of independently derived soil properties, we proceeded using this metric.

[FIGURE 7 OMITTED]

Comparison of the number of classes

Figure 7 shows the class maps obtained when using the Mahalanobis metric and when k = 4-6. Figure la shows the map for k = 4. For the most part, classes 4A and 4B are the same as classes 3A and 3B. Table 5 shows that the centroids are also equivalent. The major difference is that the depression in the centre of the field is divided into two approximately equal areas. For the most part, class 4C has the same centroid values as class 3C, except that the EM38h is slightly larger (101 mS/m) and represents the northern end of the depressed area, and is associated with the artificial drain along the western side of the field. The class is also associated with most of the eastern margin. Class 4D covers the remaining area and represents measurements with slightly smaller [EC.sub.a].

The result achieved when k=5 is near identical to k=4. The difference is that class 4B is divided into two relatively equal parts for k = 5, where one half defines the area to the north (class 5B) and the other the south (class 5E) of the bowl-shaped depression (Fig. 7b). While both areas are associated with the du soil landscape, the southern part is characterised by slightly larger EM38h and EM38v (respectively, 49 and 72 mS/m). This is most likely a function of the centroid elevation for class 5E being much lower (i.e. 0.04 m), and as such this end of the field is more likely to be susceptible to fluctuating watertables that are saline. Figure 7c shows the result when k= 6 is considered. Flere a small class (i.e. class 6F) is recognised and associated with the south-west corner of class 5D.

Statistical comparison of digital soil maps of soil landscapes

The results are akin to a keying out of the study field, whereby when we consider an increase in k, the classes are systematically partitioned into subclasses. The question, therefore, is whether this partitioning into smaller classes represents an improvement in terms of mapping of either soil types, or whether it realistically improves our understanding of individual soil property variations? Both of these issues are relevant to improving the natural resource management outcomes in this area. To answer this question an analysis of the results in terms of measured soil properties is required.

We did this by evaluating which of the k=3-8 maps produces the greatest discrimination in terms of measured soil properties of interest. In CASS landscapes, this includes soil properties such as pH, TAA and exchangeable Al. The pH is important because increasing acidity (i.e. decreasing pH) can increase mobilisation of pH-sensitive trace metals, including Al, Zn and Ni. This is because of the hydrolysis of aluminosilicate clay minerals (Dent 1986). Figure 8a shows that the [[sigma].sup.2.sub.p,C] (24 | k) of soil pH is at a minimum when k= 5, with local minima and k = 2 and 8.

Titratable actual acidity also measures exchangeable acidity held in acidic metal cations, such as Fe and Al, because additional hydrolysis and oxidation (of Fe) can further add to acidity. The TAA is therefore a better functional measure of soil acidity than pH alone, as pH only measures highly soluble acidity (i.e. the activity of [H.sup.+] ions). As indicated in Fig. 8b, a global minimum in [[sigma].sup.2.sub.p,C] (24 | k) is achieved when k = 4, with a local minimum apparent when k = 6.

Exchangeable Al is also of interest in CASS landscapes, as Al has serious impacts on aquatic ecosystems. It is highly toxic when it is soluble and is often associated with fish kills in the estuaries surrounding the study area. In the case of the Al/CEC (Fig. 8c), the [[sigma].sup.2.sub.p,C] (24 | k) is at a minimum when k = 5, with k = 8 and 4 the next best. In terms of exchangeable Al as a function of the total CEC (results not shown), a minimum in [[sigma].sup.2.sub.p,C] (24 | k) is achieved for k=5 and 3. The ratio [Cl.sup.-]/S[O.sub.4.sup.2] is at a minimum at k = 4, with the next best achieved at k =3 (Fig. 8d).

[FIGURE 8 OMITTED]

REML analysis

Despite the equivocal nature of these results, they are what could be reasonably expected in such a landscape, since there is little distinction between the du and ev soil landscape units, given that they vary with differences in soil moisture condition (Morand 2001a). Here we interpret the mean values of soil properties for classes obtained by FKM analysis of the ancillary data when k=4. This is because the spatial distribution of these classes closely reflects the soil-landscape units identified by Morand (20016), albeit the ev soil landscape is characterised by two subclasses (i.e. classes 4C and 4D). We employ this k value also because the [[sigma].sup.2.sub.p,C] (24 | k) suggests that k=4 minimises the variation in soil properties (e.g. TAA and [Cl.sup.-]/S[O.sub.4.sup.2-]) that typically characterise CASS landscapes.

Figure 9 presents the mean value of the soil properties and the standard error for each of the k=4 classes obtained from the linear mixed model estimated by REML. Figure 9a shows that all of the classes have low pH. This is particularly the case for classes 4C (3.8) and 4D (3.6), both of which have average pH values close to 3.5. More significant is that pH of the subsoil samples (0.7-0.8 m) in class 4D is <3.5. The importance of these results is that when soil pH is <3.5, it is indicative of the presence of a strong acid, commonly associated with the oxidation of pyrite (Fe[S.sub.2]), iron sulfides (FeS) and elemental sulfur (S).

[FIGURE 9 OMITTED]

These results and those described above confirm that the two classes represent the ev soil-landscape unit, which characterise the open bowl-shaped depression in the middle of the field. The properties associated with these results represent characteristics of acid sulfate soils. As indicated previously, further decrease in pH will result in increasing acidity, which can increase mobilisation of pH-sensitive trace metals. The elevated TAA (Fig. 9b) and exchangeable Fe (Fig. 9c) in classes 4C and 4D, relative to 4A and 4B, indicate that this has most likely already occurred.

Mobilisation of metals, cations and anions also result in an increase in salinity. Salinity in acid sulfate soils occurs as a function of primary or secondary processes (Lin et al. 2001; Rosicky et al. 2006). In the former, and under natural conditions, CASS are deposited in estuarine or marine environments and contain connate salts that reflect their depositional setting (Rosicky et al. 2006). Typically, CASS are characterised by higher salt contents. Previously they were known as potential acid sulfate soils. If these sediments are drained artificially to lower the saline watertable, secondary salinisation occurs as a result of release of S042 from pyrite oxidation and an increase in trace metal concentrations (e.g. Fe, Al, Mn, Zn, Cu, Ni), owing to formation of sulfuric sediments. This is apparent in class 4C (Fig. 9d), which is characterised by the largest mean average [EC.sub.1:5] (863.0 [micro]S/cm). This result is consistent with the high correlation between EM38h and EM38v [EC.sub.a] with [EC.sub.1:5] but also because the centroid value for class 4C is defined by the largest [EC.sub.a] for both EM38h (101 mS/m) and EM38v (125 mS/m) and the lowest elevation (i.e. -0.14 m).

Conclusions

A CASS wetland toposequence in a coastal alluvial-estuarine landscape near the junction of Rocky Mouth Creek and the Richmond River in far north NSW was divided into soil-landscape units using FKM analysis of proximally sensed [EC.sub.a] and DEM data. Using various indices (e.g. FPI, MPE) and employing the mean prediction error variance of various soil properties, we determined that Mahalanobis produced the best predictive results. Taking into account various soil properties (e.g. TAA and CE/S[O.sub.4.sup.2-]) that would best discriminate CASS or estuarine soil from alluvial sediments, the best solution was achieved for k=4 classes. Derived classes were shown to differ in soil properties such as pH, TAA, exchangeable Fe and [EC.sub.1:5].

From a management standpoint, classes 4C and 4D indicate the spatial extent of the CASS, otherwise known as the Everlasting (ev) soil landscape unit. Here the EM38 [EC.sub.a] and elevation data clearly delineated the extent of a saline subsoil layer subject to fluctuating water levels. The significance of this is that the CASS sediments are subject to drying and wetting cycles, whereby in the drying phase, the Fe[S.sub.2] inherent in the sediment is oxidised, resulting in generation of sulfuric acid.

The approach used indicates a potential method to augment existing mapping and to map in greater detail the spatial distribution of the ev soil-landscape unit across the broader landscape. Other ancillary data might also be appropriate in this regard and may include LANDS AT TM data and DEM data acquired from remote platforms. However, EM data would still be necessary to characterise the interface between the root-zone and the saline watertable. In order to understand the hydrological processes, EM inversion of the EM38 data could be useful (Triantafilis and Monteiro Santos 2010). Alternatively, mapping salinity in three dimensions might be possible using a DUALEM-421 (Triantafilis et al. 2013).

http://dx.doi.org/10.1071/SR13314

Acknowledgements

This project was funded by the New South Wales Government Environmental Trust Seeding Grant Program. Salary support for VNLW was provided by the Australian Research Council (LP0882141). Salary support for Scott Johnston was provided by the Australian Research Council Future Fellowship (grant no. FT110100130). We acknowledge the Environmental Analysis Laboratory for assistance with sample analysis and Paul Cheeseman for assistance with fieldwork.

Received 28 October 2013, accepted 13 February 2014, published online 1 May 2014

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Jingyi Huang (A), Terence Nhan (A), Vanessa N. L. Wong (B), Scott G. Johnston (C), R. Murray Lark (D), and John Triantafilis (A,E)

(A) School of Biological, Earth and Environmental Science, The University of New South Wales, Sydney, NSW 2052, Australia.

(B) School of Geography and Environmental Science, Monash University, Wellington Road, Clayton, Vic. 3800, Australia.

(C) Southern Cross Geoscience, Southern Cross University, Lismore, NSW 2480, Australia.

(D) British Geological Survey, Keyworth, Nottingham, NG12 5GG, UK.

(E) Corresponding author. Email: j.triantafilis@unsw.edu.au

Globally, estuarine coastal floodplains are commonly underlain by sulfidic sediments and coastal acid sulfate soils (CASS). CASS typically display high spatial heterogeneity both laterally and with depth (Andriesse and van Mensvoort 2006). These soil types are characterised by high concentrations of acidity and chalcophilic metals such as iron (Fe). Oxidation of sulfides, predominantly pyrite (Fe[S.sub.2]), releases Fe (Sohlenius and Oborn 2004) and sulfate (S[O.sub.4.sup.2-]) and mobilises other trace metals, including aluminium (Al), which is released by weathering of aluminosilicates (Nordmyr et al. 2006). Oxidation of pyrite also releases acidity and mobilises trace metals, which can adversely affect adjacent waterways and impact on aquatic ecosystems (Sammut et al. 1995; Santos and Eyre 2011). Oxidation of these sediments and the resultant acidification of coastal floodplain sediments and waterways can occur as a result of artificial drainage (Sammut et al. 1996) or sea level lowering caused by eustatic or isostatic uplift (Boman et al. 2010).

An accurate understanding of the distribution of CASS is essential for developing targeted management strategies to reduce acidic discharges and associated trace metals from CASS floodplains to adjacent waterways. However, current knowledge of the spatial distribution and extent is limited to existing CASS risk maps (e.g. Tulau 1999). In Australia, the method of mapping has been based on traditional soil survey methods and techniques, whereby a limited number of locations were visited with morphological and geochemical properties of the soils measured and assessed. Subsequently, air-photo interpretation was used to interpolate the results across the landscape. Although large areas can be mapped quickly via this method (Fig. la), the overall approach is limited by the small-scale nature of the sampling interval and soil morphological description. Also, air-photo interpretation can be unreliable, especially in redox-dynamic, coastal floodplain wetlands. This is because when watertables are high, vegetation may be lush, surface expression of oxidised soil conditions can be minimal and scalded areas may not be recognisable. Figure 1 b (27 June 2011) shows where scalded areas are evident and are indicated by the dark shaded areas. Conversely, Fig. 1 c (21 June 2007) shows the same area with the CASS areas not as easily discerned.

[FIGURE 1 OMITTED]

In eastern Australia, CASS generally derive from marine or estuarine sediments in an environment with abundant organic matter and anaerobic conditions (Walker 1972; Lin et al. 1995). Therefore, the sediments are often of moderate to high salinity with shallow watertables, where the salts are derived from connate marine/estuarine sources or from increases in acidity due to sulfide oxidation. Decreasing pH and increasing acidity can increase mobilisation of pH-sensitive trace metals such as Al, manganese (Mn), zinc (Zn) and nickel (Ni) and release other major cations such as potassium ([K.sup.+]), sodium ([Na.sup.+]) and magnesium ([Mg.sup.2+]) due to hydrolysis of aluminosilicate clay minerals (Dent 1986). Sulfate salts are also produced in abundance.

Owing to the presence of a large amount of salts, electromagnetic (EM) instruments that measure apparent soil electrical conductivity ([EC.sub.a]) can be of potential use in mapping CASS in estuarine landscapes (Triantafilis et al. 2012; Huang et al. 2014). This is because EM instruments have been used successfully and extensively to map the spatial distribution of soil salinity in arid areas (Thomas et al. 2009), saline watertables (Buchanan et al. 2012), and salinity in coastal areas (Li et al. 2013). Johnston et al. (2005) demonstrated how an EM38 could be used to map changes in subsurface salinity as a function of opening floodgates in a coastal floodplain. There is thus potential to use proximal sensed EM induction instruments to map the spatial distribution of CASS (e.g. Johnston et al. 2003).

This study aims to evaluate the utility of EM surveys to determine the spatial distribution of CASS using [EC.sub.a] as a surrogate for acidity. Here, we use the fuzzy k-means (FKM) algorithm to identify soil management classes from two different sources of ancillary data: (i) proximal sensing EM data, and (ii) remotely sensed height above mean sea level (m) generated from a digital elevation model (DEM). The classes can then be mapped as potential CASS management zones. The resulting maps were validated and the numbers of classes tested by computing the mean prediction error variance of the class mean as a predictor for various soil properties, e.g. pH, titratable actual acidity (TAA) and exchangeable Al.

[FIGURE 2 OMITTED]

Materials and methods

Site description

Rocky Mouth Creek (29[degrees]6'S, 153[degrees]19'E) is south-west of Woodburn, New South Wales (NSW), in the subtropical region of eastern Australia (Fig. 2). The creek drains a floodplain wetland into the Richmond River. The study field is ~1.10 km by 0.25 km. At the northern end, it is defined by a well-developed, natural levee (i.e. >1 m), and the soil is characterised by Brown Dermosols (Isbell 1996) or Fluvaquentic Epiaquolls (Soil Survey Staff 1998). To the south, it grades into a backswamp wetland with elevations just above sea level, i.e. 0.25-1 m AHD (Australian Height Datum where 0 m is approximately sea level). This area has been mapped as the Dungarubba (dua) soil landscape unit by Morand (2001a). With decreasing elevation, the study area grades into the Everlasting (ev) soil landscape unit (Fig. la), which has local relief just above and below sea level (<0.25 m).

There is little distinction between the two soil landscape units, and they only vary with differences in soil moisture condition (Morand 2001a). The ev unit is significant because it is associated with open depressions that occur as backswamps in estuarine areas. The swamps vary in width from 500 to 1500 m and have concave cross-sections. Figure la shows the spatial extent in the broad study area. The subsoil is generally saturated and a shallow saline watertable is common, similar to many other CASS wetlands in NSW (Lin et al. 2001). The soil is Sulfuric/Sulfidic Oxyaquic Hydrosols (Isbell 1996) or Hydraquentic Sulfaquepts (Soil Survey Staff 1998).

The climate is subtropical with mean annual rainfall of 1343 mm. Rainfall is summer-autumn dominant with a mean maximum in March (188 mm) and minimum in September (50 mm). Mean temperature varies between 29.9[degrees]C (January) and 19.9[degrees]C (July). Vegetation is dominated by open pasture, including common couch (Cynodon dactylon), carpet grass (Axonopis fissifolius), kikuyu (Pennisetum clandestinum) and water couch (Paspalum distichum), with rushes such as Juncus and Eleocharis spp. found in the lower lying areas. The dominant land use is sugarcane farming and improved pastures for cattle grazing and dairying (Morand 2001a).

Electromagnetic induction survey

An EM induction survey was conducted using a Geonics EM38 (Geonics Ltd, Mississauga, Ontario, Canada) in both the horizontal (EM38h) and vertical (EM38v) dipole modes of operation. In the horizontal mode, the [EC.sub.a] (mS/m) has the greatest sensitivity of measurement at the soil surface (~0.75 m) and declines with depth. In the vertical mode, [EC.sub.a] is measured to an approximate depth of 1.5 m (McNeill 1990). Here, [EC.sub.a] was measured in both modes at 324 points. The measurements were made approximately every 20 m along parallel transects ~100m apart (Fig. 3b). Elevation data were derived at each point from a high-resolution DEM with a vertical accuracy of 256 mm and pixel size of 5 m. The EM surveying and soil sampling occurred during an extensive dry period with a low watertable and oxic surface soil conditions.

Data preparation and numerical clustering

The EM38h, EM38v and elevation data were first interpolated onto a common 10-m grid using ordinary kriging (OK), with a neighbourhood of 90-100 and a local variogram. The OK was carried out using Vesper (Minasny et al. 1999). The resulting EM38h, EM38v and elevation data were classified using FKM analysis. The FKM method is described elsewhere (e.g. Triantafilis et al. 2001). We used the FuzMe software (Minasny and McBratney 2002), described further in Triantafilis et al. (2003).

To determine classes (k), we clustered the ancillary data into k=2-10. To gauge a suitable degree of overlap between k, we generated clustering outcomes using fuzziness exponents ([phi])= 1.1-2.8. To elucidate a distance-dependent metric, we initially compared the results of k=3 using Mahalanobis, diagonal and Euclidean. We considered the different metrics because, while Euclidean gives equal weight to all data, diagonal accounts for different variances, with Mahalanobis additionally accounting for correlation between data.

Given the large number of classifications that we needed to consider, i.e. k=2-10 classes and [phi] = 1.1-2.8, validity functionals such as the fuzziness performance index (FPI) and the normalised classification entropy (NCE) are commonly employed to determine a suitable number of k and a value for 0. These functionals are provided as output from FuzME. Of these, the FPI is a measure of the continuity between classes. A value of 1 represents a very fuzzy classification, while 0 indicates distinct classes with little overlap. The NCE measures the degree of disorganisation created by partitioning the data into various classes. Values near 0 indicate well-structured classes. We also considered the plot of [phi] v. change in the FKM objective function (-dJ/d[phi]), which assists in determining a suitable value of [phi] (see McBratney and Moore 1985).

[FIGURE 3 OMITTED]

Soil sampling and laboratory analysis

To test the validity of our classes, soil data were collected at 24 soil sample locations (Fig. 3c). As indicated in Fig. 3c, these were selected across the study field to account for the variation in [EC.sub.a] and elevation. Soil sampling was undertaken using a hand auger. Two samples were obtained at each location. The first was collected from the topsoil (0-0.10 m) and the second from a subsoil horizon (0.70-0.80 m). In order to analyse these data and with reference to the CASS management zones identified, an average value was determined. At the time of sampling, the soil was placed into polyethylene bags and stored at 4[degrees]C before analysis.

Moisture content was determined by weight loss after drying at 105[degrees]C for 24h. Soil pH, [EC.sub.1:5] and soluble cations and metals were determined from a 1:5 soil: water extract (Rayment and Higginson 1992). Exchangeable cations and metals were extracted using Ba[Cl.sub.2]/N[H.sub.4]Cl (Rayment and Higginson 1992). Where the [EC.sub.1:5] [greater than or equal to] 0.3dS/m, soluble salts were removed by washing three times with an ethanol/glycerol solution as described in Rayment and Higginson (1992). The TAA (mol [H.sup.+]/t) was determined by titration with 0.1 m NaOH to pH 6.5 on 1:40 soil: 1 m KCl extracts after shaking for 4h (Ahem et al. 2004).

Data analyses

To analyse the results of the various clusters and compare, for example, the best distance metric, we proposed a linear mixed model for the data of the form:

y = X[beta] + [eta] + [epsilon] (1)

where y is an n x 1 vector of values of the target soil variable; X is an n x p design matrix; [beta] is a p x 1 vector of fixed effects coefficients; [eta] is an n x 1 vector, the elements of which are a realisation of a spatially correlated random variable; and [epsilon] is an n x 1 vector, the elements of which are a realisation of an independent and identically distributed random variable. The elements of the design matrix are the predictor variables and the fixed effects coefficients correspond.

There is, therefore, exactly one element equal to 1 in each row of the design matrix, where the elements of [beta] are the estimated mean values of the target soil variable in the respective classes. The correlated random variable [eta] is assumed to be normal and has mean zero and variance parameters. These are an overall variance ([[sigma].sup.2.sub.[eta]]) and a distance parameter for a selected variogram function (e.g. range of a spherical variogram). The error variable [epsilon] also has zero mean and a variance [[sigma].sup.2.sub.[epsilon]]. We fitted models of the form in Eqn 1 for target soil variables and with the fixed effects, either the class of maximum membership for the FKM clustering of the ancillary variables with k= 2-8 or a subset of the ancillary variables, in a regression-type model. The fitting was done using the LME procedure from the NLME library for the R platform (R Development Core Team 2010; Pinheiro et al. 2013). Under this procedure, variance parameters for the random effects were first estimated by residual maximum likelihood (REML) and the fixed effects coefficients were then estimated by weighted least-squares. The method used is described in Lark et al. (2006). After model fitting, summary statistics and histograms of the residuals were examined to confirm that these appeared consistent with an assumption of normality.

Expected prediction error variances

Another objective of this paper is to predict soil properties from the ancillary data, given that a relatively small set of direct measurements of the soil properties is available. To do this, we computed the expected value of the mean-squared prediction error for the alternative methods:

[[sigma].sup.2.sub.p] = E [[{y - [y.sup.*]}.sup.2]} (2)

where y denotes the value of the target variable at some unsampled location and [y.sup.*] denotes the predicted value.

When the predictor is the mean of a class (here obtained by cluster analysis of the ancillary data), then the mean-squared prediction error in class i is:

[[sigma].sup.2.sub.p,i] = [[sigma].sup.2.sub.i] (1 + 1/[n.sub.i]) (3)

where [[sigma].sup.2.sub.i] is the variance of the target property within class i and the mean of class i was estimated from [n.sup.i] independently and randomly selected observations in the class (Brus and Lark 2013). In this study, we used a pooled within-class variance, [[sigma].sup.2.sub.w]. If [[pi].sub.i], denotes the relative area of the ith class out of k and N is the total number of observations, then the expected value of the mean squared prediction error for classes is:

[chi] = [[summation].sub.i=1,k] [[sigma].sup.2.sub.w][[pi].sub.i](1 + l/N[[pi].sub.[iota]]) = [[sigma].sup.2.sub.w](1 + k/N) (4)

Here, we computed [[sigma].sup.2.sub.p,C] for each target soil property for k = 2-8. To do this we required a value of [[sigma].sup.2.sub.w]. We obtained this from the LMM, Eqn 1, fitted to the observed soil data for the corresponding classification. The sum of the variances of the random effects in the model for k classes as the random effects, [[sigma].sup.2.sub.[eta],[kappa]] + [[sigma].sup.2.sub.[epsilon],k], was treated as the expected value of the variance for the random variable (Cochran 1977; Lark 2011). The expected value of the mean-squared prediction error for our classification into k classes for some sample size N is therefore computed here as:

*[[sigma].sup.2.sub.p,C](N|k) = ([[sigma].sup.2.sub.[eta],k] + [[sigma].sup.2.sub.[epsilon],k]) A(1 + k/N) (5)

Results and discussion

Preliminary data analysis

Table 1 shows the basic summary statistics of the EM38h, EM38v and elevation data collected at the 324 EM survey locations. Table 1 shows that the minimum (19mS/m) and maximum (192mS/m) were measured by EM38h. However, the mean EM38v [EC.sub.a] (84mS/m) was higher than that of the EM38h (59mS/m), which suggests the subsoil has a higher conductivity than the topsoil. This is most likely attributable to the presence of a saline watertable associated with the underlying estuarine sulfidic sediments of the ev soil landscape unit. Given the positive skew in the EM data, and that the means are larger than the median values, this suggests that the ev landscape is not the predominant unit. The histogram (not shown) shows that [EC.sub.a] is bimodal.

The lower half of Table 1 shows that the EM38 data are highly correlated ([r.sup.2] = 0.95). This is also the case with respect to the correlation between the EM38h ([r.sup.2] = -0.61) and EM38v ([r.sup.2] = -0.69) with elevation. The slightly larger negative correlation between EM38v and elevation suggests that saline material is associated with the lower lying areas where there is less fluvial capping and underlying estuarine-derived sediments are closer to the ground surface. The lowest lying site is below sea level (i.e. minimum=-0.33 m). The median value (0.05 m) also indicates that most of the study field is at, or just above, sea level, with the large mean (0.16 m) indicating that some areas are comparatively elevated and represent the high points (i.e. 2.5 m) associated with the natural levee.

Table 1 also presents basic summary statistics of the ancillary data collected at the 24 soil sampling locations. Generally, the various statistics described above and for the various ancillary data to be used to identify CASS soil management zones are equivalent. This is the case for the mean and median values, as well as the correlation between ancillary data.

Table 2 shows the correlation between ancillary data and soil data. The largest correlation coefficient is achieved for EM38h ([r.sup.2] = 0.80) and EM38v ([r.sup.2] = 0.77) with [EC.sub.1:5]. The elevation data are most strongly correlated with pH ([r.sup.2] = 0.80) and TAA ([r.sup.2] = 0.68). Table 2 also shows that the study field soils are strongly acidic in nature with minimum pH (i.e. 3.81). The soil is also approaching a level of salinity that is becoming unfit for human consumption (i.e. 959 [micro]S/cm), with TAA also very high at some locations (i.e. 297 mol [H.sup.+]/t).

Spatial distribution of ancillary data

Figure 4 illustrates the contour plots of EM38h (Fig. 4a) and EM38v (Fig. 4b) data collected from the 324 sites. In both modes, a clear spatial trend in [EC.sub.a] is evident. Small [EC.sub.a] values (<70 mS/m) define the areas at the northern and southern end of the study area. As shown in Fig. 4c, the elevation is highest at the northern end and a pronounced and obvious levee is discernible. On the other side of the levee, Rocky Mouth Creek drains into the Richmond River a short distance to the north. Conversely, intermediate to large [EC.sub.a] (130-160 mS/m) characterises the central part of the field, with the largest [EC.sub.a] (>160mS/m) found within a relatively small area. As shown in Fig. 3c, in the general area ascribed by these intermediate to very large [EC.sub.a] values and between northings 6780100 and 6780550, the elevation is low and is either just above (0-0.25 m) or below (<0m) sea level. Given the basin-like morphology, and the larger [EC.sub.a], it is within this area that the estuarine sediments that are high in connate marine and sulfide-oxidation derived salts are most likely located.

[FIGURE 4 OMITTED]

Fuzzy k-means clustering

To determine the number of potential classes in the ancillary data and to numerically discern classes that we can map, we considered the results of the FKM clustering of the EM38h, EM38v and DEM data into k = 2-10 classes using [phi] = 1.1-2.8. Given the strong correlation between EM38h and EM38v, as well as with elevation, we presumed the Mahalanobis metric would be best able to account for this. Nevertheless, we also clustered the data using diagonal and Euclidean metrics. In addition, and in order to account for the large differences in variance of the EM38 and elevation data, we standardised the variables to a common variance and conducted our FKM analysis for the Mahalanobis and Euclidean metrics using the standardised data.

[FIGURE 5 OMITTED]

Figure 5 shows the FPI (Fig. 5a) and NCE (Fig. 5b) plotted against k, and the relationship between the change in the FKM objective function (-dJ/d[phi]) and [phi] (Fig. 5c). This function has been shown to be a good indicator of a suitable value for 0 (see Triantafilis and Monteiro Santos 2009). In order to reduce the complexity in Fig. 5c, we plot only values of -dJ/d[phi] for k= 3, because this is how many soil landscape units we anticipate and because the results for k=4 and 5 are equivalent. When choosing [phi], the value considered most suitable is when (--dJ/d[phi]) is a maximum. For Mahalanobis, this occurs when [phi] = 1.6, whereas for diagonal and Euclidean it is when [phi] = 2.0 and 2.1, respectively. The results shown in Fig. 5a and b are for these values of 0.

In terms of the FPI, the Mahalanobis metric produces a minimum when k = 3 with a local minimum apparent at k = 9. Equivalent results are evident when considering NCE. The diagonal metric shows minima from k= 3 to 4 for the FPI and k = 4 for the NCE. The Euclidean metric shows local minima for k = 4 and 7 for both the FPI and NCE.

Comparison of metrics

To determine which metric is most appropriate to identify the CASS management zones, we first plotted the results of the FKM analysis for k = 3. Figure 6 shows the spatial distribution achieved using Mahalanobis ([phi] = 1.6), diagonal ([phi] = 2.1) and Euclidean ([phi] = 2.0). In all cases, membership (m) is considered when m >0.5

In general, the study field is divided in essentially the same way. For example, when we consider the results derived using Mahalanobis, which is the most popularly used metric, class 3A defines the elevated north-west comer, which is associated with the Rocky Mouth Creek levee. Here, and as shown in Table 3, the EM38h (33mS/m) and EM38v (48mS/m) centroid values are smallest and the elevation (1.12m) highest. Conversely, class 3C represents the bowl-shaped depression that characterises the centre. It is defined by centroids which show that the EM38h (91 mS/m) and EM38v (123mS/m) are largest and elevation lowest (-0.14 m). In between these areas, and to the south of class 3C, intermediate values of [EC.sub.a] (e.g. EM38h = 42mS/m) and elevation (0.21m) define class 3B. These three areas are consistent with the approximate locations of the various soil-landscape units identified by Morand (2001a), whereby classes 3A and 3B represent the dua and du soil landscapes, respectively, and 3C the ev soil landscape unit (see Fig. la).

Figure 6b shows the map achieved using the non-standardised data and the diagonal metric. The main difference between this map and Mahalanobis is that class 3A is a little larger in its areal extent. From a numerical perspective, Table 3 shows that the centroid values of the classes, for example Class 3B, achieved by the diagonal metric are also smaller in terms of [EC.sub.a] (e.g. EM38h = 44 mS/m) with elevation slightly higher (i.e. 0.16 m). The reason for this is due to the elevation data having more weight in the clustering when using the diagonal metric. This is also the case with regard to class 3C and in terms of [EC.sub.a]; however, the elevation is the same. The Euclidean metric yields a very similar result to the diagonal and in terms of the spatial extent of the classes (Fig. 6c). The reason for this is that by standardising the EM38 and elevation data, the Euclidean metric is able to account for the large difference in scale apparent between these two ancillary data (see Table 2). The main difference is the centroid values (Table 3), which are, in general, larger in terms of EM38 and lower in terms of elevation.

[FIGURE 6 OMITTED]

To ascertain which metric to pursue, we looked at the expected value of the mean-squared prediction error of the class means for sample size of 24 and k=3 (i.e. [[sigma].sup.2.sub.p,C] (24 | 3)). Table 4 shows the value of [[sigma].sup.2.sub.p,C]C (24 | 3) and for each of the soil properties measured. From the wide array of properties that would be indicative of alluvial and estuarine (i.e. CASS) sediments and soil, the variances are minimised to the greatest extent via the use of the standardised data and the Mahalanobis metric. This includes pH (0.11), TAA (924), exchangeable A1 (1931) and Fe (1.05), and soluble A1 (166) and Fe (36.8). The only exceptions to this were [EC.sub.1:5] (7837), which was smaller for the Euclidean metric, and Al/effective cation exchange capacity (Al/ECEC: 0.05) (0.24) for the diagonal metrics. Similar results were achieved when k=4 was considered. Given [[sigma].sup.2.sub.p,C] (24 | 3) is minimised for Mahalanobis, and across a wide range of independently derived soil properties, we proceeded using this metric.

[FIGURE 7 OMITTED]

Comparison of the number of classes

Figure 7 shows the class maps obtained when using the Mahalanobis metric and when k = 4-6. Figure la shows the map for k = 4. For the most part, classes 4A and 4B are the same as classes 3A and 3B. Table 5 shows that the centroids are also equivalent. The major difference is that the depression in the centre of the field is divided into two approximately equal areas. For the most part, class 4C has the same centroid values as class 3C, except that the EM38h is slightly larger (101 mS/m) and represents the northern end of the depressed area, and is associated with the artificial drain along the western side of the field. The class is also associated with most of the eastern margin. Class 4D covers the remaining area and represents measurements with slightly smaller [EC.sub.a].

The result achieved when k=5 is near identical to k=4. The difference is that class 4B is divided into two relatively equal parts for k = 5, where one half defines the area to the north (class 5B) and the other the south (class 5E) of the bowl-shaped depression (Fig. 7b). While both areas are associated with the du soil landscape, the southern part is characterised by slightly larger EM38h and EM38v (respectively, 49 and 72 mS/m). This is most likely a function of the centroid elevation for class 5E being much lower (i.e. 0.04 m), and as such this end of the field is more likely to be susceptible to fluctuating watertables that are saline. Figure 7c shows the result when k= 6 is considered. Flere a small class (i.e. class 6F) is recognised and associated with the south-west corner of class 5D.

Statistical comparison of digital soil maps of soil landscapes

The results are akin to a keying out of the study field, whereby when we consider an increase in k, the classes are systematically partitioned into subclasses. The question, therefore, is whether this partitioning into smaller classes represents an improvement in terms of mapping of either soil types, or whether it realistically improves our understanding of individual soil property variations? Both of these issues are relevant to improving the natural resource management outcomes in this area. To answer this question an analysis of the results in terms of measured soil properties is required.

We did this by evaluating which of the k=3-8 maps produces the greatest discrimination in terms of measured soil properties of interest. In CASS landscapes, this includes soil properties such as pH, TAA and exchangeable Al. The pH is important because increasing acidity (i.e. decreasing pH) can increase mobilisation of pH-sensitive trace metals, including Al, Zn and Ni. This is because of the hydrolysis of aluminosilicate clay minerals (Dent 1986). Figure 8a shows that the [[sigma].sup.2.sub.p,C] (24 | k) of soil pH is at a minimum when k= 5, with local minima and k = 2 and 8.

Titratable actual acidity also measures exchangeable acidity held in acidic metal cations, such as Fe and Al, because additional hydrolysis and oxidation (of Fe) can further add to acidity. The TAA is therefore a better functional measure of soil acidity than pH alone, as pH only measures highly soluble acidity (i.e. the activity of [H.sup.+] ions). As indicated in Fig. 8b, a global minimum in [[sigma].sup.2.sub.p,C] (24 | k) is achieved when k = 4, with a local minimum apparent when k = 6.

Exchangeable Al is also of interest in CASS landscapes, as Al has serious impacts on aquatic ecosystems. It is highly toxic when it is soluble and is often associated with fish kills in the estuaries surrounding the study area. In the case of the Al/CEC (Fig. 8c), the [[sigma].sup.2.sub.p,C] (24 | k) is at a minimum when k = 5, with k = 8 and 4 the next best. In terms of exchangeable Al as a function of the total CEC (results not shown), a minimum in [[sigma].sup.2.sub.p,C] (24 | k) is achieved for k=5 and 3. The ratio [Cl.sup.-]/S[O.sub.4.sup.2] is at a minimum at k = 4, with the next best achieved at k =3 (Fig. 8d).

[FIGURE 8 OMITTED]

REML analysis

Despite the equivocal nature of these results, they are what could be reasonably expected in such a landscape, since there is little distinction between the du and ev soil landscape units, given that they vary with differences in soil moisture condition (Morand 2001a). Here we interpret the mean values of soil properties for classes obtained by FKM analysis of the ancillary data when k=4. This is because the spatial distribution of these classes closely reflects the soil-landscape units identified by Morand (20016), albeit the ev soil landscape is characterised by two subclasses (i.e. classes 4C and 4D). We employ this k value also because the [[sigma].sup.2.sub.p,C] (24 | k) suggests that k=4 minimises the variation in soil properties (e.g. TAA and [Cl.sup.-]/S[O.sub.4.sup.2-]) that typically characterise CASS landscapes.

Figure 9 presents the mean value of the soil properties and the standard error for each of the k=4 classes obtained from the linear mixed model estimated by REML. Figure 9a shows that all of the classes have low pH. This is particularly the case for classes 4C (3.8) and 4D (3.6), both of which have average pH values close to 3.5. More significant is that pH of the subsoil samples (0.7-0.8 m) in class 4D is <3.5. The importance of these results is that when soil pH is <3.5, it is indicative of the presence of a strong acid, commonly associated with the oxidation of pyrite (Fe[S.sub.2]), iron sulfides (FeS) and elemental sulfur (S).

[FIGURE 9 OMITTED]

These results and those described above confirm that the two classes represent the ev soil-landscape unit, which characterise the open bowl-shaped depression in the middle of the field. The properties associated with these results represent characteristics of acid sulfate soils. As indicated previously, further decrease in pH will result in increasing acidity, which can increase mobilisation of pH-sensitive trace metals. The elevated TAA (Fig. 9b) and exchangeable Fe (Fig. 9c) in classes 4C and 4D, relative to 4A and 4B, indicate that this has most likely already occurred.

Mobilisation of metals, cations and anions also result in an increase in salinity. Salinity in acid sulfate soils occurs as a function of primary or secondary processes (Lin et al. 2001; Rosicky et al. 2006). In the former, and under natural conditions, CASS are deposited in estuarine or marine environments and contain connate salts that reflect their depositional setting (Rosicky et al. 2006). Typically, CASS are characterised by higher salt contents. Previously they were known as potential acid sulfate soils. If these sediments are drained artificially to lower the saline watertable, secondary salinisation occurs as a result of release of S042 from pyrite oxidation and an increase in trace metal concentrations (e.g. Fe, Al, Mn, Zn, Cu, Ni), owing to formation of sulfuric sediments. This is apparent in class 4C (Fig. 9d), which is characterised by the largest mean average [EC.sub.1:5] (863.0 [micro]S/cm). This result is consistent with the high correlation between EM38h and EM38v [EC.sub.a] with [EC.sub.1:5] but also because the centroid value for class 4C is defined by the largest [EC.sub.a] for both EM38h (101 mS/m) and EM38v (125 mS/m) and the lowest elevation (i.e. -0.14 m).

Conclusions

A CASS wetland toposequence in a coastal alluvial-estuarine landscape near the junction of Rocky Mouth Creek and the Richmond River in far north NSW was divided into soil-landscape units using FKM analysis of proximally sensed [EC.sub.a] and DEM data. Using various indices (e.g. FPI, MPE) and employing the mean prediction error variance of various soil properties, we determined that Mahalanobis produced the best predictive results. Taking into account various soil properties (e.g. TAA and CE/S[O.sub.4.sup.2-]) that would best discriminate CASS or estuarine soil from alluvial sediments, the best solution was achieved for k=4 classes. Derived classes were shown to differ in soil properties such as pH, TAA, exchangeable Fe and [EC.sub.1:5].

From a management standpoint, classes 4C and 4D indicate the spatial extent of the CASS, otherwise known as the Everlasting (ev) soil landscape unit. Here the EM38 [EC.sub.a] and elevation data clearly delineated the extent of a saline subsoil layer subject to fluctuating water levels. The significance of this is that the CASS sediments are subject to drying and wetting cycles, whereby in the drying phase, the Fe[S.sub.2] inherent in the sediment is oxidised, resulting in generation of sulfuric acid.

The approach used indicates a potential method to augment existing mapping and to map in greater detail the spatial distribution of the ev soil-landscape unit across the broader landscape. Other ancillary data might also be appropriate in this regard and may include LANDS AT TM data and DEM data acquired from remote platforms. However, EM data would still be necessary to characterise the interface between the root-zone and the saline watertable. In order to understand the hydrological processes, EM inversion of the EM38 data could be useful (Triantafilis and Monteiro Santos 2010). Alternatively, mapping salinity in three dimensions might be possible using a DUALEM-421 (Triantafilis et al. 2013).

http://dx.doi.org/10.1071/SR13314

Acknowledgements

This project was funded by the New South Wales Government Environmental Trust Seeding Grant Program. Salary support for VNLW was provided by the Australian Research Council (LP0882141). Salary support for Scott Johnston was provided by the Australian Research Council Future Fellowship (grant no. FT110100130). We acknowledge the Environmental Analysis Laboratory for assistance with sample analysis and Paul Cheeseman for assistance with fieldwork.

Received 28 October 2013, accepted 13 February 2014, published online 1 May 2014

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Jingyi Huang (A), Terence Nhan (A), Vanessa N. L. Wong (B), Scott G. Johnston (C), R. Murray Lark (D), and John Triantafilis (A,E)

(A) School of Biological, Earth and Environmental Science, The University of New South Wales, Sydney, NSW 2052, Australia.

(B) School of Geography and Environmental Science, Monash University, Wellington Road, Clayton, Vic. 3800, Australia.

(C) Southern Cross Geoscience, Southern Cross University, Lismore, NSW 2480, Australia.

(D) British Geological Survey, Keyworth, Nottingham, NG12 5GG, UK.

(E) Corresponding author. Email: j.triantafilis@unsw.edu.au

Table 1. Summary statistics of ancillary data collected at the 324 survey locations and 24 soil-sampling sites Survey locations EM38h EM38v Elevation (mS/m) (m) Mean 59 84 0.16 Median 49 73 0.05 s.d. 30 34 0.41 Minimum 19 30 -0.33 Maximum 192 170 2.35 Skewness 1.03 0.43 1.85 Kurtosis 1.25 -1.02 4.35 Pearson correlation coefficients EM38h 1 0.95 -0.61 EM38v 1 -0.69 DEM 1 Sampling locations EM38h EM38v Elevation (mS/m) (m) Mean 58 84 0.21 Median 47 66 0.07 s.d. 26 35 0.47 Minimum 23 41 -0.22 Maximum 128 170 1.45 Skewness 0.9 0.79 1.54 Kurtosis 0.26 -0.33 1.79 Pearson correlation coefficients EM38h 1 0.98 -0.62 EM38v 1 -0.69 DEM 1 Table 2. Summary statistics of soil data collected at the 24 soil sampling sites ECEC, Effective cation exchange capacity pH TAA Cl /S[O.sub.4.sup.2] Al/ECEC (mol [H.sup.+]/t) Mean 4.01 210 0.14 0.56 Median 3.81 231 0.12 0.67 s.d. 0.52 71.3 0.08 0.27 Minimum 3.41 63.5 0.04 0.05 Maximum 5.18 297 0.33 0.85 Skewness 0.93 -0.61 0.95 -0.58 Kurtosis -0.30 -0.67 0.13 -1.11 Pearson correlation coefficients EM38h 0.31 0.18 0.01 0.20 EM38v 0.37 0.25 0.03 0.26 DEM 0.80 0.68 0.30 0.65 [EC.sub.l:5] ([micro]S/cm) Mean 474 Median 433 s.d. 289 Minimum 117 Maximum 959 Skewness 0.40 Kurtosis -1.32 Pearson correlation coefficients EM38h 0.80 EM38v 0.77 DEM 0.55 Table 3. Centroid values of ancillary data clustered using FuzME for class k = 3 and for Mahalanobis, diagonal and Euclidean Centroids shown for EM38h and EM38v (mS/m) and elevation (m), respectively Class Mahalanobis Diagonal Euclidean ([phi] = 1-6) ([phi] = 2.0) ([phi] = 2.1) A 33, 48, 1.12 30, 45, 0.87 35, 53, 0.47 B 42, 64, 0.21 44, 66, 0.16 59, 87, -0.02 C 91, 123, -0.14 90, 122, -0.14 95, 127, -0.15 Table 4. Expected value of the mean-squared prediction error of the class means for sample size of 24 and k=3, i.e. [sigma].sup.2.sub.p,C] (24 | 3), of different soil properties using Mahalanobis, diagonal and Euclidean metrics TAA, Titratable actual acidity; ECEC, effective cation exchange capacity. Fuzziness exponents ([phi]) vary for each metric Soil property Mahalanobis Diagonal Euclidean ([phi] = 1.6) (9 = 2.0) (9 = 2.1) PH 0.11 0.19 0.12 [EC.sub.1:5] 12 322 26 451 7837 Cl /S[O.sub.4.sup.2] 0.002 0.01 0.002 TAA 924 4575 1355 Al/ECEC 0.24 0.05 0.21 Exchangeable A1 1931 6919 2050 Soluble Al 166 563 166 Exchangeable Fe 1.05 5.94 1.17 Soluble Fe 36.8 125.8 37.3 Table 5. Mahalanobis centroid values of ancillary data clustered using FuzME and for classes k = 4, 5 and 6 Centroids shown for EM38h and EM38v (mS/m) and elevation (m), respectively Class k = 4 k = 5 k = 6 A 34, 48, 1.14 34, 49, 1.19 34, 49, 1.19 B 40, 61, 0.24 32, 51, 0.45 32, 51, 0.46 C 101, 125, -0.14 101, 125, -0.14 101, 124, -0.14 D 79, 115, -0.13 81, 118, -0.13 91, 129, -0.13 E 49, 72, 0.04 47, 68, 0.07 F 63, 96, -0.09

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Author: | Huang, Jingyi; Nhan, Terence; Wong, Vanessa N.L.; Johnston, Scott G.; Lark, R. Murray; Triantafilis, |
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Publication: | Soil Research |

Article Type: | Report |

Geographic Code: | 8AUST |

Date: | Jun 22, 2014 |

Words: | 7762 |

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