Dealing with spatial outliers and mapping uncertainty ...

Geoderma 195–196 (2013) 220–233

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Dealing with spatial outliers and mapping uncertainty for evaluating the effects of urbanization on soil: A case study of soil pH and particle fractions in Hong Kong Xiao-Lin Sun a, b, c, e, Sheng-Chun Wu a, c, Hui-Li Wang d, Yu-Guo Zhao b, c, Gan-Lin Zhang b, c,⁎, Yu Bon Man a, Ming Hung Wong a, c,⁎⁎ a

Croucher Institute for Environmental Sciences, and Department of Biology, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong, China State Key Laboratory of Soil and Sustainable Agriculture, Institute of Soil Science, Chinese Academy of Sciences, 71 East Beijing Road, Nanjing 210008, China Joint Open Laboratory of Soil and Environment, Institute of Soil Science, Chinese Academy of Sciences and Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong, China d Guangxi Forest Academy, 23 Yongwu Road, Nanning 530002, China e College of Agriculture, Guangxi University, Nanning 530004, China b c

a r t i c l e

i n f o

Article history: Received 12 October 2010 Received in revised form 10 October 2011 Accepted 22 November 2012 Available online 9 January 2013 Keywords: Mapping uncertainty Spatial outliers Hong Kong Temporal variation of soil Urbanization

a b s t r a c t The effects of urbanization on soil have been accelerating around the globe and there is a need for these effects to be evaluated precisely. In order to do this, spatial outliers and mapping uncertainty should be handled properly. The present study aimed to deal with these two problems using a case study of soil pH and particle fractions (i.e., sand, silt and clay) in Hong Kong. Based on 133 topsoil samples collected in an urban and peri-urban mixed area of Hong Kong, robust estimators for spatial variogram were first adopted with a procedure for identifying spatial outliers to remove spatial outliers. Then, 1000 models were simulated for each soil property using the methods of maximum likelihood and Monte Carlo Markov Chain, in order to characterize parameter uncertainty. Finally, 100 of the 1000 simulated models were randomly selected to construct soil maps using kriging, and the interpolation uncertainty was characterized using Sequential Gaussian Simulation, generating 1000 simulations for each model. Based on the total 100,000 simulated values at each location for each soil property, temporal variation of the soil property at the location across the past half century was derived against the soil series map established in 1960s for this area. Probability that soil property value changed after urbanization was also computed, in order to show if soil property has changed with a significant confidence. Results showed that the situation of spatial outliers in the soil data of the present study was not serious and mapping uncertainties were large. Temporal variations of soil pH and particle fractions obtained through comparison between soil maps of pre-urbanization and post-urbanization were not completely attributed to the effects of urbanization, but partially to mapping uncertainties. Urbanization in Hong Kong during the past half century influenced soil pH slightly and influenced soil particle fractions relatively strongly. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Urbanization has developed very fast in recent decades over the globe (Duh et al., 2008; Madlener and Sunak, 2011). As the earth's living skin, soil has been greatly affected by this process (Cao et al., 2004; Chen, 2007; Zhao et al., 2007), and the effects have been attracting global attention (Darilek et al., 2009; De Kimpe and ⁎ Correspondence to: G.-L. Zhang, 71, Beijing East Road, Nanjing 210008, China. Tel.: +86 25 86881279; fax: +86 25 86881000. ⁎⁎ Correspondence to: M. H. Wong, Rm. 704, Cha Chi Ming Science Tower, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Kowloon, Hong Kong. Tel.: + 852-3411 7746; fax: + 852 3411 7743. E-mail addresses: [email protected] (X.-L. Sun), [email protected] (S.-C. Wu), [email protected] (H.-L. Wang), [email protected] (Y.-G. Zhao), glzhang@ issas.ac.cn (G.-L. Zhang), [email protected] (Y.B. Man), [email protected] (M.H. Wong). 0016-7061/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.geoderma.2012.11.017

Morel, 2000) due to fundamental functions of soil performed in agriculture, ecosystem, environment and hydrology. However, urbanization undoubtedly is an irreversible stage in human development and is expected to grow at an unprecedented rate for the coming half century (Kundu, 2009). Hence, proper evaluation of the effects of urbanization on soil is significantly important for soil sustainable development in the era of urbanization (Cao et al., 2004; Chen, 2007; Kalnay and Cai, 2003). To evaluate the effects of urbanization on soil, spatial variability of soil properties is essential (Darilek et al., 2009; Hu et al., 2007; Lee et al., 2006). The use of the kriging method to determine the spatial variability of a soil property is commonly as it provides the best linear unbiased estimation (BLUE) at un-sampled locations (Zhao et al., 2007). However, due to the intrinsic characteristics of the kriging method, a kriging prediction is unavoidably uncertain (Lark and Bolam, 1997). This uncertainty can then propagate in application of

X.-L. Sun et al. / Geoderma 195–196 (2013) 220–233

kriging prediction (Carré et al., 2007; Nol et al., 2010; Zhao et al., 2007), and may result in a useless output (Nelson et al., 2011). For urban and peri-urban areas, situation will be more serious because spatial outliers, which exhibit extreme values of a soil property in their spatial contexts, often exist due to stronger human activities (Rawlins et al., 2005; Zhang et al., 2009; Zhao et al., 2007). Spatial outliers can lead to poor predictions of soil and unreliable estimates of the uncertainty associated with predictions (Marchant et al., 2010; Saby et al., 2011). In this regard, kriging alone is not enough to properly assess the effects of urbanization on soil. In order to handle these problems, Zhao et al. (2007) used robust variogram estimators and sequential Gaussian simulation (SGS) to assess potential risk from heavy metal pollution. Robust variogram estimators were usually used to deal with spatial outliers, and Lark (2002) especially used them to develop a procedure for identifying spatial outliers, which was successfully used by Rawlins et al. (2005) and Zhao et al. (2007) to assess diffuse and point pollution in urban areas. Similar studies were conducted recently by Meklit et al. (2009), Marchant et al. (2010) and Saby et al. (2011), showing the usefulness of robust estimators in dealing with spatial outliers. Sequential Gaussian simulation (SGS) is a stochastic simulation method that has been widely used to tackle the problem of kriging uncertainty (Juang et al., 2004; Meirvenne and Meklit, 2010; Zhao et al., 2007). The remarkable advantage of using SGS is that it can provide the probability of a soil property value larger (or smaller) than a specific value (Nelson et al., 2011). For example, Meirvenne and Meklit (2010) used it to determine if concentrations of heavy metals in soil exceeded certain threshold levels. In addition to uncertainty generated by interpolation methods such as kriging, there are also other sources of uncertainty within soil mapping. According to Nelson et al. (2011), there are generally four sources of error within soil mapping, model error, covariate error, analytical error and positional error. Among the four sources, model error is always the dominant whereas the others account for only a small part (Minasny et al., 2011; Nelson et al., 2011). There are also other methods for dealing with uncertainty besides SGS, e.g., Monte Carlo simulation (Heuvelink et al., 2010; Nelson et al., 2011; Nol et al., 2010). Just recently, Minasny et al. (2011) proposed Markov Chain Monte Carlo (MCMC) simulation specifically for assessing parameter uncertainty in model-based geostatistics. Given the usefulness of robust variogram estimators and SGS respectively dealing with spatial outliers and kriging uncertainty, they could be explored further to assess the effects of urbanization on soil. For instance, by comparing a soil property value of preurbanization with a confidence interval derived from a set of Gaussian simulated realizations of post-urbanization, the effects of urbanization on soil can be statistically evaluated whether or not the effects are significant. Besides, it could be more appropriate to take into account of other sources of uncertainty when doing this, particularly the parameter uncertainty when several robust variogram estimators are applied simultaneously to construct variograms. However, as far as we know, spatial outliers and uncertainty so far have not been accounted for when evaluating the effects of urbanization on soil. The major aim of this study was to deal with spatial outliers and mapping uncertainty in evaluating the effects of urbanization on soil, based on a case study of soil pH and particle fractions (i.e., sand, silt and clay) in an urban and peri-urban mixed area of Hong Kong. The specific objectives of this study were to: (1) identify outliers in collected data of soil pH and particle fractions using robust kriging with a procedure of identifying outliers; (2) derive major uncertainty (parameter and interpolation uncertainties) in mapping soil pH and soil particle fractions using model-based geostatistics and MCMC; and (3) map the probabilities that soil pH and particle fractions at present exceed their values of pre-urbanization using SGS based on a conventional map produced before urbanization.

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2. Materials and methodologies 2.1. Study area The study area is located in the northern part of Hong Kong, southern tip of China (Fig. 1(a)). A rapid urbanization has occurred in this area during the past decades, with agricultural activities and arable lands shrinked dramatically by about two thirds (Zhang et al., 2007). The study area, not including mountainous areas and water surfacing areas (Fig. 1(b)), measures 110.6 km 2. The climate is subtropical, with air temperature between 13 and 31 °C and mean annual rainfall of 2214 mm. The local topography is rather complex, as shown by the digital elevation model (DEM) in Fig. 1(a). Steep hills and rugged mountains separate the study area into small flat patches where people inhabit (Fig. 1(b)). Thirty five percent of the study area, i.e., 38.7 km 2, is covered by buildings and constructions. Besides commercial and trade activities in the covered area, there are a number of car-dismantling factories, container storage factories and e-waste dismantling workshops (Man et al., 2010). The remaining area is uncovered, accounting for 65%, i.e., 71.9 km 2. Most uncovered areas are rather complexly intermixed with covered areas, while a few are well separated far from urban areas (Fig. 1(b)). Less than half of the uncovered areas are now cultivated with vegetables (major), flowers and scenic trees (minor), and fruits (very few), while others are left unused. However, before urbanization (1960s), most of this study area was cultivated with rice supplemented by vegetables and fruits (Grant, 1962). Soils of this study area were derived from seven kinds of parent materials: alluvial, alluvial and colluvial, boulder fan, boulder fan enriched by more recent alluvium, colluvium and alluvial fan, in situ, and mangrove swamp alluvial (Fig. 1(c)), according to Grant (1962). The soils are similar to Luviosls, Cambisols, Anthrosols and Acrisols of the World Reference Base for Soil Resources (Sun et al., 2011).

2.2. Soil sampling and chemical analyses Soil sampling was based on the soil series map established by Grant (1962), with totally 31 soil series. Parent materials and drainage classes, which were the only two criteria for classifying the soil series were displayed in place of soil series in Fig. 1(c). For sampling, the covered areas in Fig. 1(b) were excluded from the digitized soil series map using ArcGIS software. Twenty-five of the 31 soil series remained after exclusion, and therefore soil sampling was conducted in the 25 soil series. Sampling was conducted in two stages. In the first stage, 41 soil profile samples were collected (Fig. 2(a)), in order to represent the 25 soil series. The number of soil profiles for each soil series was depended on the area of this soil series. In general, sampling sites were located evenly in the patches of soil series in order to collect typical profile samples for each soil series which is used for soil quality evaluation (Sun et al., 2012). In the second stage, 92 topsoil samples were collected (Fig. 2(a)). For optimally selecting these sampling locations, the procedure for sampling with prior points, i.e., the 41 profile samples collected in the first stage, in SPCOSA package (Walvoort et al., 2010) for R software (R Development Core Team, 2010) was used to optimally locate a total of 150 sampling sites in this area. Besides the 41 prior points, 15 of the located 150 sampling sites were in the restricted area on the northern border of Hong Kong (Fig. 2) and another 2 did not possess any soil. At each of the remaining 92 sampling sites, topsoil samples were collected. Geographic coordinate data at each sampling site was recorded. For all collected soil samples, soil pH was determined using a pH meter (1: 2.5 soil to water ratio) and soil particle fractions were determined by the hydrometer method (Lu, 1999).

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Fig. 1. Information of the study area: (a) location (flat areas in the dashed rectangle) and digital elevation model, (b) land surface and (c) the soil series map (Grant, 1962).


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Fig. 2. (a) Sampling sites location and (b) soil series with soil properties data before urbanization.

2.3. Soil pH and soil particle fractions before urbanization

2.4. Spatial outlier identification

The soil survey conducted by Grant (1962) was the only survey completed before urbanization. Therefore, soil information from this survey is the only information available representing soil condition before urbanization, despite this information most certainly contain uncertainty. The digitized soil series map of the survey is displayed in terms of parent materials and drainage classes in Fig. 1(c). Unfortunately, not all of the soil series were analyzed for soil properties during this survey. Therefore, only the 13 soil series having soil data were used in the present study (Fig. 2(b)). Soil pH and soil particle fractions data for these soil series were retrieved from this survey.

The procedure proposed by Lark (2002) for identifying spatial outliers was employed in this study. This procedure first computed a ˜ for each variogram model estimated using four estimators, statistic, θ, i.e., Matheron's (1965) estimator and three robust estimators: Cressie and Hawkins's (1980), Dowd's (1984) and Genton's (1998) estimators (for detailed information about these estimators refer to Lark (2002)). A confidence interval for θ˜ was then estimated for determining which variogram model would be used for further analysis. The selected variogram model was finally used to calculate another statistic, O(xi), to determine whether soil data at a site was a spatial outlier

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or not, by testing whether this statistic was significantly different from zero or not (Lark, 2002). While implementing the procedure, we used the rule proposed by Rawlins et al. (2005) to determine if soil data needs to be transformed: transformation would be needed if octile skew (Rawlins et al., 2005) exceeded [− 0.2, 0.2]. Meanwhile, in order to show if a data (or a transformed data) was normally distributed, cumulative distribution function (cdf) of the data (or transformed data) was also compared with cdf of a standard Gaussian data with parameters of location and scale which were the median and Qn (Lark, 2002) of the data (or transformed data), respectively. The way for estimating the confidence interval for θ˜ was not the same to that used in Lark (2002), but a Monte Carlo simulation involving three steps: 1) randomly simulate a dataset based on the variogram model estimated using the Matheron's estimator, 2) compute θ˜ based on the simulated dataset using the same variogram model, and 3) repeat the two steps 1000 times and estimate the confidence ˜ Only the interval for θ˜ based on quantiles of the obtained 1000 θ. Matheron's estimator was considered because the other estimators would only be considered after the Matheron's estimator was rejected and then selected by comparing their θ˜ with 0.455 (Lark, 2002). The robust estimator with θ˜ closest to 0.455 would be selected. This was also used by Haskard et al. (2010) and Saby et al. (2011). A value with O(xi) larger than zero was only identified as a spatial outlier in Lark (2002), and this was reasonable for the simulation study of Lark (2002) as the contamination process was added to the background. However, soil property in an urban area may be either increased or decreased. Therefore, in this study, O(xi) significantly larger and smaller than zero were all identified as spatial outliers and was removed from the soil data. All of the above calculations were conducted using R (R Development Core Team, 2010), GeoR package (Ribeiro and Diggle, 2001) and qn package (Furrer and Genton, 1999) for R. 2.5. Soil mapping and uncertainty estimation After removing spatial outliers from the soil data, spatial variogram models were constructed for prediction. In order to comprehensively characterize model uncertainty, the Matérn correlation function that is flexible for modeling various spatial random processes (Minasny and McBratney, 2005) might be optimal for constructing a soil variogram, compared with other classical correlation functions such as spherical, exponential and linear correlation functions. However, this function could only be appropriately used with special spatial configuration of samples and required knowledge of variations at short distances or measurement variances (Minasny and McBratney, 2005; Marchant and Lark, 2007). Given the above sampling, it is obviously inappropriate to apply this function in this study. Thus, model functions for constructing soil variograms were inferred from empirical variograms based on the method of moments in this study since the classical variograms were useful to reflect spatial variations of soil in spite of the existing model uncertainty (Minasny et al., 2011). The spatial variogram models were calculated using the method of maximum likelihood (ML) which estimates parameters of a model directly from data using the following log-likelihood function (Minasny and McBratney, 2005): ‘ðθ; βÞ ¼ −

n 1 1 T −1 logð2πÞ− logjCj− ðz−βÞ C ðz−βÞ 2 2 2

where θ denotes the vector of parameters, β is the estimated mean, n is the number of samples, C is the covariance matrix, and z is the vector of observed values. Variogram models estimated using such kind of method was termed as model-based geostatistics (Minasny et al., 2011). For this study, there is an advantage of using ML over the

classical method of moments, i.e., avoiding the selection between different variogram estimators in the above, despite that Lark (2002) has provided a simple method for selection. Other advantages of using this method include uncertainty reduction in prediction (Minasny and McBratney, 2005), no decision need to be made about how point estimates of the variogram are to be binned (Saby et al., 2011), etc. For model-based geostatistics, Minasny et al. (2011) proposed a method for parameter uncertainty evaluation, i.e., a Bayesian approach based on MCMC simulation. MCMC is a method that successively uses the most recent sample value to randomly generate the next sample value directly from a parameter space, resulting in a Markov chain walk through the parameter space after a long run. According to Minasny et al. (2011), MCMC has been often used in geostatistics and a new algorithm of this method recently developed by Vrugt et al. (2009), DiffeRential Evolution Adaptive Metropolis (DREAM), is very efficient and easy to be used for estimating parameter uncertainty in model-based geostatistics. Thus, the DREAM package for R was used in this study to obtain the last 10,000 posterior sets of parameters of the above soil variogram models from prior defined uniform distributions of these parameters. Parameters for running DREAM were set as the same to those in Minasny et al. (2011) except the number of pairs that was set to be 1 because Vrugt et al. (2009) showed results from DREAM were fairly insensitive to this parameter. After establishing the variogram models, ordinary kriging was applied to make prediction at unsampled locations, and associated interpolation variances were calculated accordingly. However, exploring the obtained 10,000 posterior sets of parameters into mapping may not be necessary and it also demands sophisticated computer hardware. Thus, 100 models were randomly sampled from the 10,000 sets, and used for mapping. Parameter uncertainty at each location was then calculated as the variance of the 100 predictions at the site, while the associated interpolation uncertainty was the mean prediction variance. 2.6. Dealing with uncertainty for assessing the effects of urbanization on soil Due to mapping uncertainties, a predicted value generated using any mapping technique could be insufficiently believable for considering whether soil properties has really changed during urbanization. Therefore, uncertainties should be properly handled for accurately assessing the effects of urbanization on soil. A common method for this problem is generating a sufficient number of random independent simulations based on uncertainties, which would result in an entire probability and a confidence interval for a prediction (Heuvelink et al., 2010; Nelson et al., 2011; Nol et al., 2010). In this study, two uncertainty sources, interpolation and variogram parameters, were considered. This is because these two sources accounted for the majority of the overall error in a soil mapping based on linear mixed model, while other uncertainty sources due to covariate, analysis and position were considerably smaller (e.g., in Nelson et al. (2011), total 67–72% of the former compared with total 2–7% of the later). Among a lot of methods for dealing with mapping uncertainty, SGS was frequently used to deal with interpolation uncertainty through generating a large number of realizations which are random, Gaussian and equiprobable, e.g., Zhao et al. (2007), Meirvenne and Meklit (2010) and Nol et al. (2010). Thus, it was used in this study and implemented using the Gstat package (Pebesma, 2004) for R. In order to incorporate parameter uncertainty, SGS was repeatedly implemented based on the above sampled 100 variogram models for each soil property. For each variogram model, SGS generated 1000 simulations, resulting in a total of 100,000 realizations at each location for each soil property. Then, for each location and each soil


3. Results

Table 1 Summary statistics for soil properties. pH

Mean Min Max Std.c Skew Octile skew Kurtosis Median Qn

Sand (%)

Silt (%)

Prea

Postb

Pre

Post

5.32 4.90 6.70 0.47 2.30

5.65 3.71 8.36 0.89 0.66 0.17 0.55 5.52 0.79

61.44 45.10 76.40 11.71 −0.08

57.57 27.40 93.01 13.48 −0.03 0.09 −0.46 57.22 13.83

6.39

−1.70

Pre 14.55 5.90 28.90 7.67 0.63 −0.77

3.1. Exploratory data analysis

Clay (%) Post

Pre

Post

34.12 6.12 59.00 10.59 0.07 0.10 −0.41 33.08 10.89

21.12 11.80 37.40 7.98 0.85

8.31 0.87 20.87 4.74 0.73 0.27 −0.15 6.93 4.15

0.16

a Pre: pre-urbanization and statistics were calculated based on digitized soil series map. b Post: post-urbanization. c Std.: standard deviation.

property, the cumulative frequency of this soil property value before urbanization in the 100,000 realizations was computed by Fðx0 Þ ¼

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nðx≤x0 Þ nT

where Fðx0 Þ denotes the cumulative frequency, x is the realization of the soil property at the location, x0 is the soil property value before urbanization at the location, n(x ≤ x0) denotes the number of soil property realization x less than or equal to x0, nT denotes the total number of realizations (i.e., 100 000). The computed cumulative frequency Fðx0 Þ was then compared with four critical probabilities: 0.05, 0.1, 0.90 and 0.95. Fðx0 Þ at a location less than 0.1/0.05 or bigger than 0.90/0.95 would suggest that the soil property on this location has possibly increased or decreased during urbanization with a confidence probability of 0.90/0.95. Otherwise, soil property on this location may not change during urbanization.

Table 1 summarizes the results of soil pH and soil particle fractions measured before urbanization and after urbanization. The results show that after urbanization soil pH increased slightly, i.e., 0.33, and soil particle fraction contents changed more considerably: 3.87% decrease for sand content, 19.57% increase for silt content, and 12.81% decrease for clay content. Based on the standard deviations, variations of soil pH, sand content and silt content became larger, whereas variation of clay content became smaller after urbanization. Since the data from pre-urbanization will not be used in spatial interpolation, octile skew and other indexes were not computed for this data. The octile skew values of the post-urbanization data indicated that only clay content data needed to be transformed. Therefore, clay content data was transformed by calculating their natural logarithms. Octile skew of the transformed clay content data decreased to − 0.08. Fig. 3 shows the cdf of each soil property data along with a standard Gaussian cdf with parameters of median and Qn estimated from the data. Comparison between cdf of soil pH data and the Gaussian counterpart reflected that soil pH data had a longer right tail, indicating that some marginal outliers with relatively larger soil pH existed in the data. Similarly, some marginal outliers with relatively smaller values were observed in silt content data and transformed clay content data. cdf of sand content data was relatively symmetrical. 3.2. Identification of spatial outliers Fig. 4 shows that the isotropic variograms obtained by Matheron's estimator and the three robust estimators. Fitted variogram models were also shown, except the variogram model for clay content based on Dowd's estimator because this variogram demonstrated marked discontinuities (Fig. 4(d)). For every soil property, the

Fig. 3. Cumulative distribution frequency for soil property data. The solid line on each plot is the Gaussian cdf parameterized with parameters of median and Qn estimated from the soil properties data.

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nuggets obtained by robust estimators were smaller than that by Matheron's estimator. However, differences between them were very small. In the case of soil pH, the sill estimated using Matheron's estimator was larger than the others. Ranges obtained by Matheron's estimator for sand and silt content model were smaller than those by robust estimators, whereas all estimated ranges for soil pH model and for clay content models were equal. These suggested that the situation of spatial outliers in the present soil data was not serious. This

was further proved by the results listed in Table 2, showing that all θ˜ were in their 95% confidence intervals. In the following process of identifying spatial outliers, it should be noted that the variogram model estimated for clay content based on Cressie–Hawkins's estimator was used instead of the estimate based on Matheron's estimator. This is because the spatial dependence indicated by the later was very weak (the ratio of partial sill to sum of partial sill and nugget was small). Fig. 5 shows that

Fig. 4. Variograms and fitted models for: (a) soil pH, (b) sand content, (c) silt content and (d) clay content estimated using the four estimators. The lower red, middle blue and upper red dashed lines within each plot for Matheron model are the 2.5, 50 and 97.5 percentiles of models estimated using MCMC (lines of 2.5 percentiles for pH and clay have a very short range). The circles in the plot for Matheron model of clay (d) represent the variogram estimated based on the non-transformed clay data.


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Fig. 4 (continued).

there were four spatial outliers with higher soil pH, one spatial outlier with a higher sand content, one spatial outlier with lower silt content and three spatial outliers with lower clay contents. Positions of these spatial outliers are shown in Fig. 6. Three of the four soil pH spatial outliers were on vegetable lands, and the other was on a wasteland. The only sand content spatial outlier and the only one silt content spatial outlier were the same one, which was also one of the three clay content spatial outliers. This spatial outlier was on a wasteland. The other two low clay spatial outliers were also on wastelands.

3.3. Mapping uncertainties and temporal variations of the soil properties In Fig. 4, the conventional variograms based on the method of moments are constructed using a spherical function. Therefore, MCMC analysis was conducted to simulate spherical variograms for all the soil properties. Based on the last 10,000 posterior variogram generated from the MCMC analysis on each soil property data, associated 95% confidence interval (2.5 and 97.5 percentiles) and median (50 percentile) variograms were estimated and presented in Fig. 4, indicating general distributions of variogram parameters. With the exception of pH,

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Table 2 The statistic θ˜ and its estimated 95% confidence intervals estimated using the variogram models estimated based on the four estimators.

pH Sand Silt Clay

Matheron (1965)

Cressie and Hawkins (1980)

Dowd (1984)

Genton (1998)

95% confidence interval

0.41 0.43 0.51 0.47

0.43 0.46 0.55 0.47

0.48 0.50 0.59 –

0.44 0.47 0.56 0.48

0.307–0.654 0.305–0.652 0.310–0.641 0.302–0.671

median variograms for the three particle fractions were very close to their corresponding conventional ones. The 2.5 percentile variograms for pH and clay content were almost horizontal lines, due to the very short ranges of the two variograms (i.e., 354 m and 234 m, respectively). In addition, with relatively smaller nuggets of the two 2.5 percentile variograms, the 95% confidence intervals of variograms for pH and clay content were apparently asymmetric with respect to corresponding median models. Comparatively, symmetries of the 95% confidence intervals of variograms for sand and silt contents were much better. Fig. 6 shows the kriged maps of the four soil properties and associated mapping uncertainties due to interpolation and variogram parameters (measured as standard deviation). For each soil property, the maps were derived based on randomly selected 100 of the last 10,000 posterior variograms generated from the MCMC analysis. At each location, the mapped value, mapping uncertainties due to interpolation and variogram parameters were respectively the mean kriging value, mean kriging variance and variance of kriging values over the output generated using the 100 randomly selected variograms. The mapped value and two uncertainties for each soil property were compared with each other to show importance of uncertainties in mapping. Table 3 summarized the comparison and showed that uncertainty due to interpolation were many times more important than uncertainty due to variogram

parameters. Averagely, standard deviations of the mapped pH, sand, silt and clay contents due to interpolation uncertainty accounted for 14%, 20%, 27% and 54% of the mapped values, respectively, while standard deviations of the mapped four soil properties due to parameter uncertainty accounted for only 2%, 1%, 2% and 7%, respectively. The uncertainties due to interpolation were many times of those due to parameters, i.e., 8, 15, 13 and 8 times for pH, sand, silt and clay contents. Fig. 6 also shows the temporal variations of the soil properties, which were computed by subtracting soil property values indicated on the soil series map of Fig. 2(b) from the soil property values of Fig. 6. Soil pH variation ranged from − 1.3 to 1, with the mean of 0.19 and standard deviation of 0.60. In summary, 66% of the depicted area registered an increase in soil pH while the remaining 34% with a decrease in soil pH. Fig. 6(a) shows that soil pH increased in the central area while decreased on the fringe areas in general. Temporal variations of the contents of soil particle fractions were dramatic (Fig. 6(b), (c) and (d)). The variation of sand contents ranged from − 16 to 9%, with the mean of − 3.8% and standard deviation of 4.7%. The sand content decreased in 79% of the depicted areas shown in Fig. 6(b) and increased in the remaining 21%. However, spatial distribution of sand contents temporal variation was rather complex to be summarized. The variation of silt contents ranged from 1 to 20%, with the mean of 10.7% and standard deviation of 3.5%. All the depicted areas in Fig. 6(c) had increases in silt contents. In contrast, clay contents decreased all over the depicted area (Fig. 6(d)). The temporal variation ranged from − 15 to − 0.1%, with the mean of − 5.5% and standard deviation of 2.8%. 3.4. Confidence probability of soil property change during urbanization Fig. 7 displays the maps of probabilities that the four soil properties at present exceed their values of pre-urbanization, which were derived using SGS. Table 4 summarizes percentages of areas with four probabilities, i.e. 0.05, 0.10, 0.90 and 0.95, for each soil property.

Fig. 5. Plots of standardized data against the statistics of O for: (a) soil pH, (b) sand content, (c) silt content and (d) clay content. Dash horizontal lines represent the 99% threshold values for O.


In Fig. 7(a), only soil pH decrease on 9.99% of the area was possible with a confidence probability of 0.90 (i.e., Fðx0 Þ ≥0.90). In Fig. 7(b), sand content increase on 0.69% of the area was possible with a confidence probability of 0.9, and sand content decrease on 22.01% and 8.87% of the area was possible with a confidence probability of 0.90

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and 0.95, respectively. In Fig. 7(c), silt increase was possible with a confidence probability of 0.90 and 0.95 on 86.04% and 67.30% of the area, respectively. In Fig. 7(d), clay content increase was possible with a confidence probability of 0.90 and 0.95 on 79.78% and 66.91%, respectively.

Fig. 6. Predicted map uncertainties due to interpolation and parameters and temporal variations: (a) soil pH, (b) sand content, (c) silt content and (d) clay content. Crossings on the maps are identified spatial outliers.

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Fig. 6 (continued).

4. Discussion 4.1. Spatial outliers Spatial outliers arise due to local anomalous processes (Marchant et al., 2010), such as industrial pollutions (Rawlins et al., 2005),

deposition of facet and urine by grazing livestock (Lark, 2002), fertilizer application and geological anomalies (Saby et al., 2011). Only several spatial outliers existed in the data of soil pH and particle fractions. A reason for this is that it is generally not so easy to alter soil pH and particle fractions drastically as heavy metals which can be strongly affected by widely existing industrial pollutions (Meklit

X.-L. Sun et al. / Geoderma 195–196 (2013) 220–233 Table 3 Summary statistics on ratios of interpolation uncertainty to mapping value, parameter uncertainty to mapping value and interpolation uncertainty to parameter uncertainty. Interpolation to map

pH Sand Silt Clay

Parameter to map

Interpolation to parameter

Mean

Min

Max

Mean

Min

Max

Mean

Min

Max

0.14 0.20 0.27 0.54

0.13 0.17 0.20 0.39

0.15 0.26 0.39 0.72

0.02 0.01 0.02 0.07

0.01 0.002 0.004 0.02

0.07 0.05 0.07 0.24

8.18 15.41 13.05 8.13

1.82 4.53 4.56 1.79

19.72 77.52 74.63 24.10

et al., 2009; Rawlins et al., 2005; Zhao et al., 2007). In this study area, there are also no apparent evidences of local anomalous processes that could change soil pH and particle fractions abruptly in a local area. This indicates that spatial variations of soil pH and particle fractions in this study area were dominated by geologic variations and continuous variations (Lark, 2002; Marchant et al., 2010). The procedure used in this study to identify spatial outliers is not able to find all outliers, which might be another reason for so few identified outliers being observed. The simulation study of Lark (2002) demonstrated that this technique found 20 of 30 contaminated points at the confidence level of 99%. However, there is no universally agreed best method so far and different methods give relatively different answers (Zhang et al., 2009). More studies were recently devoted to this issue, such as Meklit et al. (2009), Marchant et al. (2010) and Saby et al. (2011). For example, Meklit et al. (2009) proposed an integrated method of fuzzy and robust means to identify both marginal and spatial outliers. Saby et al. (2011) simplified the method proposed by Marchant et al. (2010). Future works require a comparison of the different methods to establish a standard method.

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Table 4 Percentage (%) of areas where soil properties possibly changed with a confidence probability during urbanization. Significant level

pH

Sand (%)

Silt (%)

Clay (%)

Fðx0 Þ ≤ 0.05 Fðx0 Þ ≤ 0.1 Fðx0 Þ ≥ 0.90 Fðx0 Þ ≥ 0.95

0 0 9.99 0a

0 0.69 22.01 8.87

67.30 86.04 0 0

0 0 79.78 66.91

The identified spatial outliers were therefore removed from the soil data for further analysis in this study. However, Marchant et al. (2010) criticized this and believed that outliers also contain information about the continuous variation. In contrast, an identified outlier might be statistical artifacts (Saby et al., 2011). Therefore, proper handling spatial outliers deserves careful attention. For this, some approaches have been proposed in literature. Zhang et al. (2009) suggested that identified outliers should be confirmed and justified using scientific knowledge. Marchant et al. (2010) and Saby et al. (2011) demonstrated using robust kriging to make the best use of identified outliers, which may improve soil prediction and help soil scientists determine relationship between soil properties and covariates such as geological classes. 4.2. Mapping uncertainty Mapping uncertainty is inevitable in soil mapping. Thus, it is important to derive mapping uncertainty to indicate reliability of a soil map for further application (Carré et al., 2007). This issue is attracting more and more attention (Heuvelink et al., 2010; Minasny et al., 2011; Nol et al., 2010). Results of this study also demonstrated the

Fig. 7. Probabilities that the four soil properties at present exceed their values of pre-urbanization: (a) soil pH, (b) sand content, (c) silt content and (d) clay content.

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importance of this issue as mapping uncertainties of soil pH and particle fractions (Fig. 6) were relatively large, for example, clay content had an average mapping standard deviation accounting for about 60% of mapped values. Comparatively, the interpolation uncertainties were often many times more than parameter uncertainties (Table 3). This has already been justified in Minasny et al. (2011). Few studies focusing on spatial–temporal variation of soil have dealt with mapping uncertainty, for example, Sun et al. (2003), Hu et al. (2007), Darilek et al. (2009). However, given the confidence probabilities derived based on mapping uncertainty in this study, the obtained temporal variations of soil pH and particle fractions based on soil maps for pre-urbanization and post-urbanization cannot be totally attributed to urbanization, but partially to mapping uncertainties. For example, soil pH change was detected over the whole area in Fig. 6(a), but on only 9.99% of the area, soil pH change can be trusted at the confidence level of 0.90 (Table 4). Hence, dealing with mapping uncertainty can substantially avoid the chance of wrongly attributing the soil change to urbanization. It is also worthy to mention that the temporal variations of soil pH and particle fractions may also be due to other factors, for example, uncertainty in generating soil information of pre-urbanization based on the map of soil series (Fig. 1(c)) and differences between soil analysis methods used in this study and Grant (1962). Without proper methods and enough data available, these two factors were not dealt with in this study. However, they could be dealt with in other studies having soil data of two periods, for example, Sun et al. (2003), Hu et al. (2007), Darilek et al. (2009). 4.3. The effect of urbanization on soil pH in Hong Kong The influence of urbanization on soil pH has been frequently reported (Cao et al., 2004; Chen, 2007; Darilek et al., 2009). For example, Cao et al. (2004) and Darilek et al. (2009) reported that soil pH was averagely reduced by 0.9 and 1.02, respectively, under the influence of urbanization in several decades. In the present study, soil pH averagely decreased 0.12 with a probability of 0.9 on about 9.99% of the study area in Fig. 7(a), while no soil pH increase was detected with a probability of 0.9 or above. Thus, the effects of urbanization on soil pH in Hong Kong were relatively slighter than other areas. Many factors could have caused soil pH changes during urbanization of the present study. The primary factor was probably land use alteration (Cao et al., 2004 and Darilek et al., 2009). Before urbanization, rice cultivation was common here (Grant, 1962), but it was totally vanished three decades ago (Man et al., 2010). This conversion substantially reduces leaching of basic cations (Darilek et al., 2009). A lot of lands in this study area were left fallow after urbanization. Plants growing in the soil of the lands returned bases into the soil when they die (Darilek et al., 2009). In addition, acid deposition also played a role in the soil pH change of this study area (Ayers and Yeung, 1996). 4.4. The effects of urbanization on soil particle fractions in Hong Kong The influence of urbanization on soil particle fractions in Hong Kong was relatively strong, verified by the larger temporal variations of soil particle fractions in the present study than those found in other studies such as Lal (1997) and Doichinova et al. (2006). For instance, the largest temporal variation of sand content in the present study, i.e., 17% (with a confidence probability of 0.99), was nearly one and a half time of the largest one indicated by Lal (1997), which occurred after 3 years of plowing. The great temporal variations in soil particle fractions were first contributed by the altered land use during urbanization (Wang et al., 2008). Lal (1997) revealed that different tillage methods could redistribute soil particle fractions. Cheng et al. (2009) found that non-paddy soil has a significantly lower clay contents when compared with paddy soil

which was generated from the same parent material and for the same period of time to non-paddy soil. In this study, puddling soil commonly used for rice cultivation before urbanization (Grant, 1962), was replaced by tillage methods for cultivating vegetables, or became abandoned. The second reason for the large variation of soil particle fractions was soil erosion in urban areas. Anthropogenically induced soil erosion in urban areas is reported to be severe in Sun et al. (2001). This is particularly true for Hong Kong due to its intensive rainfall climate (Zhang et al., 2007) and rugged mountains (Fig. 1). Another reason for redistributing soil particle fractions is that clay formation in urban soils appeared to be reduced, as pointed out by Doichinova et al. (2006). This is much related to the intrinsic soil properties of the local soil series. 5. Conclusions Studies focusing on the effects of urbanization on soil have not paid enough attention to spatial outliers and mapping uncertainty. The present study dealt with these two problems using a case study of soil pH and particle fractions in Hong Kong. Results showed that the situation of spatial outliers in the soil data of the present study was not serious. Only several spatial outliers existed in the data of soil pH and particle fractions. Mapping uncertainties in the present study were large. Therefore, the temporal variations of soil pH and particle fractions obtained through comparison between soil maps of pre-urbanization and posturbanization were not totally attributed to the effects of urbanization, but partially to mapping uncertainties. With mapping uncertainty considered, urbanization in Hong Kong during the past half century influenced soil pH slightly while relatively strongly for soil particle fractions. However, the obtained temporal variation may also be attributed to other uncertainties contained in the soil map made before urbanization and soil analysis methods. Unfortunately, these factors were not dealt with in the present study due to lack of data. For other studies with available data of both pre-urbanization and post-urbanization, the effects of urbanization on soil, as well as spatial–temporal variation of soil, could be quantified more precisely. Acknowledgment The authors thank the financial support from the Public Policy Research (2002-PPR-3) of Research Grants Council of Hong Kong, the Knowledge Innovation Program Foundation of Chinese Academy of Sciences (KZCX2-YW-409) and Natural Science Foundation of China (41201216, 40625001 and 40771092). We gratefully thank Dr Murray Lark (Rothamsted Research) for the provision of a method used in the present study. References Ayers, G.P., Yeung, K.K., 1996. Acid deposition in Hong Kong. Atmospheric Environment 30, 1581–1587. Cao, Z.H., Huang, J.F., Zhang, C.S., Li, A.F., 2004. Soil quality evolution after land use change from paddy soil to vegetable land. Environmental Geochemistry and Health 26, 97–103. Carré, F., McBratney, A.B., Mayr, T., Montanarella, L., 2007. Digital soil assessments: beyond DSM. Geoderma 142, 69–79. Chen, J., 2007. Rapid urbanization in China: a real challenge to soil protection and food security. Catena 69, 1–15. Cheng, Y.Q., Yang, L.Z., Cao, Z.H., Ci, E., Yin, S., 2009. Chronosequential changes of selected pedogenic properties in paddy soils as compared with non-paddy soils. Geoderma 151, 31–41. Cressie, N., Hawkins, D., 1980. Robust estimation of the variogram. Mathematical Geology 12, 115–125. Darilek, J.L., Huang, B., Wang, Z., Qi, Y., Zhao, Y., Sun, W., Gu, Z., Shi, X., 2009. Changes in soil fertility parameters and the environmental effects in a rapidly developing region of China. Agriculture, Ecosystems & Environment 129, 286–292. De Kimpe, C.R., Morel, J.L., 2000. Urban soil management: a growing concern. Soil Science 165, 31–40. Doichinova, V., Zhiyanski, M., Hursthouse, A., 2006. Impact of urbanisation on soil characteristics. Environmental Chemistry Letters 3, 160–163.

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