In addition to mapping predicted concentrations for 1990 and 2015, the change in As, Pb and Zn concentrations between the two years (2015-1990) was calculated using back-transformed predictions. To determine the statistical significance of the change in each metal, the z-statistic was calculated for each grid point using predictions of metal concentrations on the log scale (Filippi et al., 2016):
y V y y z ˆ ˆ ˆ ˆ2015 1990 , (2)where
V ˆˆ y
is the contrast variance,ˆy
2015is the log- metal concentration at the grid point in 2015, andˆy
1990is the log- metal concentration at the grid point in the year 1990. The contrastChapter 5: Using bivariate linear mixed models to predict the change in spatial distribution of heavy metals at the site of a historic landfill
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variance is calculated based upon prediction variance on the log scale for each year and the covariance between each (Filippi et al., 2016):
ˆ
ˆ(ˆ
)
ˆ(ˆ
)
2(ˆ(ˆ
))
ˆ
2015 , 1990 2015 1990V
y
V
y
y
V
y
V
, (3)where
Vˆ(yˆ
1990)
is the prediction variance at time 1 (1990),Vˆ(yˆ
2015)
is the log-predictionvariance at time 2 (2015), and
Vˆ(yˆ
1990,2015)
is the associated covariance between the two surveys. It should be noted that we performed hypothesis testing on the log-transformed data as this is the scale on which we modelled to meet the modelling assumptions.Following calculation of change in concentration and z-statistics, the results were also mapped for comparison with predictions of metal concentrations in each year.
5.3 Results
5.3.1 Exploratory data analysis
Mean values for As, Pb and Zn did not exceed the associated NEPC (1999) guide values for parks and open spaces (Table 5.2), except in 1990 for Pb. For Pb in 1990 the maximum value and 7.8% of sample points did exceed the guide of 600 mg kg-1 (1215 mg kg-1), with 13.6% of sample points exceeding the most conservative NEPC (1999) guide value of 300 mg kg-1. Pb
concentrations were much lower in 2015 with the maximum dropping to 120mg kg-1. Concentrations of Zn were elevated but did not exceed guidelines in both 1990 and 2015 whereas As concentrations were very low for both years.
The data were highly skewed for all years and metals, evident in the smallest skewness being 1.0 and evident in the notable difference between median and mean values for each variable. Due to the high level of skew, all variables were log-transformed and summary statistics also presented in Table 5.2.
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Table 5.2. Summary statistics for Pb, Zn and As in 1990 and 2015.
Variable Mean Median Min Max SD Skewness Guide
1990 dataset n = 144 As (mg kg-1) 3.810 1.400 0.160 41.000 6.632 3.483 300 log-transformed As 0.495 0.337 -1.832 3.714 0.500 0.494 Pb (mg kg-1) 120.400 64.500 0.000 1215.000 161.608 3.956 600 log-transformed Pb 4.216 4.182 0.000 7.103 1.164 -0.701 Zn (mg kg-1) 183.500 93.500 1.000 2850.000 290.167 5.959 30,000 log-transformed Zn 4.614 4.538 0.001 7.955 1.109 -0.305 2015 dataset n = 60 As (mg kg-1) 5.217 5.000 1.000 14.000 2.637 1.419 300 log-transformed As 1.534 1.609 0.000 2.639 0.500 -0.335 Pb (mg kg-1) 46.880 43.000 11.000 120.000 28.913 1.000 600 log-transformed Pb 3.691 3.784 2.485 4.796 0.613 -0.087 Zn (mg kg-1) 123.700 94.500 36.000 1100.000 138.723 5.971 30,000 log-transformed Zn 4.602 4.549 3.584 7.003 0.570 1.159
Note: SD = Standard Deviation; Guide refers to the Health Investigation Level (mg/kg) stated in NEPC (1999) for recreational areas.
Comparison between corresponding points collected in 1990 and 2015 indicate some change had occurred, with both increases and decreases in concentrations, depending on the location (Table 5.3). The difference was calculated by subtracting values in 1990 from corresponding values in 2015 and summary statistics calculated. The largest increase was 447 mg kg-1 for Zn, followed by Pb (80 mg kg-1) and As, which showed only a relatively small maximum increase of 11.9 mg kg-1. The greatest decrease in concentrations was Pb (971 mg kg -1), followed by Zn (650 mg kg-1) and As (25 mg kg-1). Mean Pb across the study area possessed the greatest amount of change overall at a decrease of 60.2 mg kg-1, followed by Zn which was much
smaller (decrease of 12.06 mg kg-1) and As which showed very little change overall, with an
overall increase in 2.03 mg kg-1. Correlation analysis between each year further suggested
there was some change in the spatial pattern of metal concentrations (r = 0.193 for As, r = 0.317 for Pb and r = 0.364 for Zn; Table 5.3).
Table 5.3. Change in metal concentrations between 1990 and 2015.
2015-1990 Mean Median Min Max Pearson correlation
As 2.028 2.50 -25.00 11.90 0.193
Pb -60.20 -19.50 -971.00 80.00 0.317
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Correlations between log-transformed metals and numerical predictors may show likely relationships and potential predictors in the subsequent modelling process. No correlations exceeded 0.4, meaning at best moderate relationships between metals and predictors overall (Table 5.4). The highest correlation existed between Zn (2015) which possessed a correlation of 0.390. Other notable correlations with Zn from 2015 was with elevation (r = 0.220) and log- distance to all roads (r = 0.254). Remaining correlations >|0.20| were between metals for 1990, such as Zn and log-distance to all roads (r = 0.224), Pb and distance to main roads (r = 0.218), and As and plan curvature (r = -0.204) which also happened to be the only negative correlation (greater than |0.2|). Despite the weak correlations with individual predictors, relationships may be found in the modelling stage through the combination of predictors.
Table 5.4. Correlation matrix between numerical predictors and log-transformed response variables for each time point*.
As-1990 As-2015 Pb-1990 Pb-2015 Zn-1990 Zn-2015 Elevation -0.023 0.197 0.136 0.089 0.062 0.220 Square-root slope 0.027 -0.063 0.039 -0.085 0.124 0.104 Aspect -0.014 0.050 -0.039 -0.015 -0.074 0.167 Plan curvature -0.204 -0.142 -0.001 0.057 -0.033 -0.022 Profile curvature -0.073 -0.043 0.067 -0.013 -0.014 0.034 MRVBF 0.019 0.028 -0.062 0.030 -0.085 -0.101 MRRTF -0.138 -0.003 -0.043 -0.041 -0.116 -0.035 TWI 0.104 0.176 -0.041 -0.017 0.101 0.025
Distance to main road -0.055 0.075 0.218 0.028 0.196 0.390
Log- distance to all roads 0.025 0.137 -0.006 0.026 0.224 0.254
* Values in bold have a Pearson correlation coefficient > |0.2|, indicating possible relationships between covariate and response variable.
Many studies have found heavy metal concentrations to be correlated with each other (Hu et al., 2013; Lu et al., 2003), which is further supported by the findings of this study (Table 5.5). Strong correlations existed between log-transformed Pb and Zn (r = 0.705 for 2015; 0.654 for 1990), Pb and As in 2015 (r = 0.696), and As and Zn in 2015 (r = 0.559). Weaker relationships existed between log-transformed As and Pb in 1990 (r = 0.364), with the correlation between As and Zn in 1990 being the weakest (r = 0.151).
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Table 5.5. Pearson correlations between each tested (log-transformed) metal for each year*.
1990 2015
As-Pb 0.364 0.696
As-Zn 0.151 0.559
Pb-Zn 0.654 0.704
* Values in bold have a Pearson correlation coefficient > |0.2|