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Spatial distribution of soil organic carbon concentrations in grassland of Ireland
Applied Geochemistry 18 (2003) 1629–1639 www.elsevier.com/locate/apgeochem
Spatial distribution of soil organic carbon concentrations in grassland of Ireland David McGratha, Chaosheng Zhangb,* a
Teagasc, Johnstown Castle Research Centre, Wexford, Ireland Department of Geography and Environmental Change Institute, National University of Ireland, Galway, Ireland
b
Received 30 August 2002; accepted 17 February 2003 Editorial handling by R. Fuge
Abstract Soil organic C (SOC) concentrations in topsoil samples taken at 678 sites in the grassland of Ireland were investigated using statistics and geostatistics. SOC concentrations (Walkley–Black method) follow a lognormal distribution, with a median and geometric mean of 5.0%, and an arithmetic mean of 5.3%. Statistically significant (P< 0.01) positive correlation between SOC and silt-plus-clay, and negative correlation between SOC and sand were observed, with lower correlation (P=0.17) between SOC and pH. Lower SOC concentrations were associated with higher percentages of land in tillage. In order to obtain a robust measurement of spatial structure, spatial outliers were detected, and subsequently eliminated, using the local Moran’s I index. The spatial distribution of SOC concentrations based on kriging interpolation showed coherent spatial patterns, with the highest values in the western coastal area, and relatively low values in the inland and southeastern coastal areas; soils at higher elevation were also found to contain higher SOC concentrations. These patterns are consistent with the distribution of rainfall within the country. # 2003 Elsevier Ltd. All rights reserved.
1. Introduction Soils play an important role in global C cycling and global warming. The global soil organic C (SOC) pool is estimated at 1500 Pg (Eswaran et al., 1995; Batjes, 1996), which is roughly equivalent to the sum of the atmospheric pool of 750 Pg and the biotic pool of 600 Pg (Schimel, 1995; Houghton, 1995; Lal, 2002). SOC levels are known to be influenced by a large number of factors, many of which are mutually interactive. These include: parent material, soil texture, climate, soil pH, landuse, management, topography and drainage. Manipulation of some of these factors, especially management-related ones, may be used to increase C sequestration in soils and thus mitigate national climate-change commitments (Smith et al., 2000). However,
* Corresponding author. Fax: +353-91-525700. E-mail addresses: [email protected] (D. McGrath), [email protected] (C. Zhang).
before changes can be evaluated, the baseline situation needs to be established and this is addressed here. Statistics and geostatistics have been used to study the relationships between SOC and these factors, and to quantify spatial distribution patterns and changes in SOC (e.g., Van Meirvenne et al., 1996; Saldan˜a et al., 1998; Chevallier et al., 2000; Frogbrook and Oliver, 2001). Geostatistics is based on the theory of a ‘‘regionalized variable’’ (Matheron, 1963), i.e., one which is distributed in space with spatial coordinates. The concepts of geostatistics are explained in several textbooks (e.g.: Cressie, 1993; Goovaerts, P., 1997; Clark and Harper, 2000; Webster and Oliver, 2001). In the past 20 a, geostatistics has become widely applied in soil sciences, and has provided advanced methodologies to quantify the spatial features of soil parameters and carry out spatial interpolation (Burgess and Webster, 1980; Webster, 1994; Dobermann et al., 1997; Stein et al., 1997; Zhang et al., 1998, 2000). Ireland is a country dominated by grassland, and SOC has primarily been investigated in these soils (Brogan, 1966; McGrath, 1980; McGrath and McCormack,
0883-2927/03/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0883-2927(03)00045-3
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1999). The data set from Brogan (1966) was obtained via a national soil survey, undertaken in 1964, which covers most parts of the Republic of Ireland. Despite the time-lag since the data was generated, it was considered to still provide a valuable base against which subsequent and future measurements could be evaluated. For this reason it has been used in this study.
2. Methods 2.1. Sampling and analysis of SOC About 59% of the land surface of the Republic of Ireland was recorded as being devoted to permanent pasture in 1964 (CSO, 1965). Soils (0–10 cm depth) were sampled from under permanent pasture (Brogan, 1966). A maximum of 2 sites were selected at random from each
1010 km2 sector of the national grid and sampled. Where land cover by lake, forest, bog and mountain was less than 25%, 2 sites were selected; when greater than 75%, no sample was taken. The 678 samples so obtained represent approximately 50% of the total that could be accommodated at a frequency of 2 samples for each 1010 km2 sector. The shortfall in the number of samples collected can be accounted for by the low sampling-density in some areas, e.g., in the west of the country, and in the Wicklow– south Dublin areas which, though largely mountainous, also included upland grassland sites. However, such sites were often peaty with SOC in excess of 18% and were excluded under the sampling protocol. The locations of the grassland sampling sites are shown in Fig. 1. SOC concentrations were determined by the Walkley-Black (Cwb) method (Metson, 1956). Sand, silt-plus-clay contents and pH values were also determined (Brogan, 1966).
Fig. 1. Soil sampling locations in Ireland (n=678).
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2.2. Geostatistics
2.3. Spatial outlier detection
Geostatistics (Matheron, 1963; Cressie, 1993; Webster and Oliver, 2001) uses the semi-variogram to measure the spatial variability of a regionalized variable, and provides the input parameters for the spatial interpolation method of kriging, a term introduced by Matheron in 1960 in honour of the work of the South African mining engineer D.G. Krige (1951). It relates the semivariogram, half the expected squared difference between paired data values z(x) and z(x+h) to the distance, lag h, by which locations are separated:
Outliers, and especially spatial outliers, in the data set can make the variogram exhibit erratic behaviour. Spatial outliers are those values that are obviously different from the values of their surrounding locations (Lalor and Zhang, 2001). In this work, such outliers are identified using an index, local Moran’s I (Anselin, 1995; Getis and Ord, 1996):
1 ðhÞ ¼ E ½zðxÞ zðx þ hÞ2 2
ð1Þ
For discrete sampling sites, such as those that had been sampled in this study, the function is written in the form: 1 X ½zðxi Þ zðxi þ hÞ2 2NðhÞ i¼1 NðhÞ
ðhÞ ¼
ð2Þ
where z(xi) is the value of the variable Z at location of xi, h is the lag, and N(h) is the number of pairs of sample points separated by h. For irregular sampling, it is rare for the distance between the sample pairs to be exactly equal to h. Therefore, h is often represented by a distance interval. A variogram plot is obtained by calculating values of the variogram at different lags. These values are then usually fitted with a theoretical model: spherical, exponential, or Gaussian (See Matheron, 1963; Cressie, 1993; or Webster and Oliver, 2001 for discussion). The models provide information about the spatial structure as well as the input parameters for the kriging interpolation. Kriging is regarded as an optimal spatial interpolation method, which is a type of weighted moving average: z^ðx0 Þ ¼
n X
li zðxi Þ
ð3Þ
i¼1
where z^ðx0 Þ is the value to be estimated at the location of x0; z(xi) is the known value at the sampling site xi, and li is a weight. There are n sites within the search neighbourhood around x0 used for the estimation, and the magnitude of n will depend on the size of the moving search window and user definition. Kriging differs from other methods (such as inverse distance weighted), in that the weight function li is no longer arbitrary, being calculated from the parameters of the fitted variogram model under the conditions of unbiasedness and minimized estimation variance for the interpolation. Thus, kriging is regarded as a best linear unbiased estimation (BLUE).
Ii ¼
n zi z X wij zj z 2 j¼1; j6¼i
ð5Þ
where zi is the value of the variable z at location i; z is the average value of z with the sample number of n; zj is the value of the variable z at all the other locations (where j6¼i); 2 is the variance of variable z; and wij is a weight, defined as the inverse of the distance dij between locations i and j: wij ¼
1 dij
ð6Þ
Local Moran’s I can be standardised so that its significance level can be tested based on the normal distribution (Levine, 1999), when the distribution of the raw data set is not too skewed. It should be noted that when the raw data are too skewed, the normal approximation of the local Moran’s I may fail. When the standardized value of local Moran’s I is higher than the critical value of 1.96, it is concluded (P=0.05) that the sample under test is clustered with (or similar to) the surrounding samples; if lower than 1.96, it is concluded (P=0.05) that the sample under test is significantly different from the surrounding samples and is considered to be a spatial outlier. 2.4. Data treatment with computer software The data sets were analysed using different software packages. The descriptive statistical parameters were calculated with Microsoft Excel# and SPSS# (version 10.0). Maps were produced with GIS software ArcView# (version 3.2) and its extension of Spatial Analyst# (version 2). The geostatistics analyses were carried out with GS+# (version 5.3) (Robertson, 2000) and Idrisi 32# (Release 2), and the local Moran’s I index was calculated with CrimeStat# (version 1.0) (Levine, 1999).
3. Descriptive statistics 3.1. Probability distribution Histograms of SOC concentrations determined by the Walkley–Black method are shown in Fig. 2. That for the raw data set has a long tail towards higher concentrations,
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Fig. 2. Histograms of Cwb concentrations in soils of Ireland (n=678): (a) raw data; (b) logarithmically transformed data.
whereas that for the logarithmically-transformed dataset can be satisfactorily modelled by a normal distribution. Table 1 shows the quantitative parameters of the probability distribution and significance level of the Kolmogorov–Smirnov test for conformance to a normal distribution for the variables. The probability distribution of Cwb is positively skewed and has a sharp peak (positive kurtoses). The log-transformed data show rather small skewnesses and kurtoses, and pass the K–S normality test at a significance level of higher than 0.05. On the other hand, contents of sand and silt-plus-clay follow a normal distribution, and log-transformation makes the fit to a normal distribution worse. pH values cannot pass either the normal or lognormal tests. However, its skewness and kurtosis are rather small. Therefore, the log-transformed data sets of Cwb, and the raw data sets of sand, silt-plus-clay and pH were used for the following multivariate analyses. 3.2. Mean values for SOC Percentiles and commonly used estimators of location and spread were calculated (Table 2). The range of Cwb varies from 2.0 to 17.8%, with the arithmetic mean of 5.3%. Both the geometric mean and median of Cwb are Table 1 Shape parameters of the probability distributions and significance level of Kolmogorov–Smirnov test (K–S p) (n=678)
Raw data
Log-transformed data
Statistics
Cwb
Skewness Kurtosis K–S p
1.66 4.77 0.00
Skewness Kurtosis K–S p
0.36 0.42 0.11
Sand
Silt+clay
pH
0.32 0.65 0.17
0.28 0.60 0.73
0.70 0.42 0.00
0.82 1.76 0.01
1.72 8.92 0.01
0.43 0.08 0.00
5.0%. Due to the lognormal feature of Cwb, the geometric mean and median are recommended as its representative mean value, while the arithmetic mean (average) should be discarded for this variable. 3.3. Relationships between SOC and other factors Pearson (linear) correlation coefficients between the 4 variables were calculated. These are given in Table 3, together with corresponding significance levels. Table 2 Basic statistic parameters of SOC concentrations and other related variables (%, except pH, n=678) Statistics
Cwb
Sand
Silt+clay
pH
Min 5% 25%
2.0 3.0 4.0
8 21 31
8 36 48
4.3 5.1 5.5
Median 75% 95%
5.0 6.1 9.1
37 44 56
55 63 71
5.8 6.2 7.0
87 37.7 36.1 10.5
88 54.9 53.7 10.7
7.8 5.9 5.8 0.6
Max Average GeoMean Stdev
17.8 5.3 5.0 1.9
Table 3 Correlation coefficients (lower-left side) and their significance levels (upper-right side) (n=678) LnCwb LnCwb Sand Silt+clay pH
Sand 0.00
0.43 0.22 0.05
0.91 0.14
Silt+clay 0.00 0.00 0.13
pH 0.17 0.00 0.00
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A positive correlation between SOC and silt-plus-clay and negative correlation between SOC and sand were also confirmed. It should be mentioned that the two variables of sand and silt-plus-clay sum up to almost 100%, which forms a constant sum proportion. In this case, the strong negative correlation between the two variables is expected. The correlation between SOC and pH is less pronounced. The causative relationship between SOC and pH is complex, with SOC being a progenitor of carbonic acid which then contributes to inhibiting organic matter degradation by soil microorganisms. To reveal the relationship between SOC concentrations and elevation of the sampling sites, the GIS software ArcView# was used to assign the samples to 4 elevation groups: 0 ( < 25), 50 (25–74), 100 (75–124), and 150 (> 124) m, based on which contour line the sampling location is close to. The box-plot (Fig. 3) shows the difference of SOC concentrations among these groups. In each box-plot, the lower boundary of the box shows the 25th percentile, and the upper boundary shows the 75th percentile. The whiskers are lines that extend from the box to the highest and lowest values, excluding outliers (here defined as the values that are outside 1.5 box lengths from the upper and lower edges of the box). The line across the box indicates the median. This plot shows that the SOC concentrations in the 0 (<24) m and 50 (25–74) m elevation groups are the lowest, and those in the 150 (> 124) m group are slightly higher. To better quantify the differences among the elevation groups, analysis of variance (ANOVA) was applied. The results show that the observed differences are significant at the level of 0.05. Further analysis of the post hoc test with Duncan’s test (Duncan, 1955) was carried out, and the results are shown in Table 4. The Kolmogorov– Smirnov test has shown that all the groups have passed the test for normality (P> 0.05). The Levene test has
Fig. 3. Box-plot of SOC in different elevation groups (n=50, 171, 301, 156 respectively).
Table 4 Results of post hoc tests in ANOVA with Duncan’s method (with mean values of LnCwb in each elevation group) Elevation group (m)
n
S.D.
Subset 1
0 50 100 150
50 171 301 156
0.365 0.306 0.340 0.304
1.557 1.559 1.622
Significance level
0.158
Subset 2
1.622 1.675 0.221
shown that the variances between the groups of the data set are homogenous at the significance level of 0.46, and thus Duncan’s test can be applied. The 4 groups of samples can be separated into 2 subsets. The first subset contains samples within the elevation groups of 0, 50, and 100 m; while the second subset consists of the 100 and 150 m elevation groups. The differences within either subset are not statistically significant, at the 0.05 level, with significance levels of 0.158 and 0.221, respectively. However, the difference between the subsets is significant at the level of 0.008 (with an F-value of 4.013). It can be concluded that statistically samples at the elevation group of 150 m have the highest SOC concentrations in this study. In explanation, it can be assumed that high elevation tends to result in increased precipitation and decreased temperature; both of these environmental factors tend to favour accumulation of humus (Jenny, 1980), and thus of SOC. Agricultural activities, especially tillage, play an important role on SOC concentrations. The proportion of agricultural land in tillage for each county in Ireland in 1964 was calculated based on data from the report of Central Statistics Office, Ireland (CSO, 1965). The average values of Cwb in each county were also calculated. A scatter plot of mean Cwb as a proportion of land in tillage shows a decreasing trend (Fig. 4). The correlation coefficient is 0.632, which is highly significant (P< 0.001).
Fig. 4. Average SOC concentrations in each county as a function of proportion of agricultural land in tillage (n=27).
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Fig. 5. SOC (Cwb) distribution in soils of Ireland and location of spatial outliers.
4. Spatial Distribution of SOC 4.1. Spatial symbol map and spatial outliers of SOC A point-symbol map of SOC concentrations in grassland of Ireland is shown in Fig. 5. Some possible spatial patterns are identifiable on this map. Western Ireland and the north-eastern part have relatively high SOC concentrations, while the southeastern part and north-western part generally have lower concentrations of SOC. However, it can be seen that some locations with high values have points with low values nearby; in some areas of low values, there are also some points with high values. This suggests the presence of spatial outliers which need to be eliminated prior to estimation of the spatial variogram.
Fig. 6. Variogram surface of LnCwb.
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Fig. 7. Isotropic variogram model of LnCwb: (a) spatial outliers excluded (n=639, exponential model: C0=0.05; C0+C=0.11; a=40 km); (b) all samples (n=678).
As described above, in order to avoid introducing bias, spatial outliers were detected using standardized local Moran’s I (Levine, 1999); Samples with values lower than 1.96 were defined as spatial outliers. The calculation was based on the log-transformed Cwb data set. Altogether, 39 spatial outliers were detected (Fig. 5). In the south-eastern part of the region, there are some outliers with abnormally higher values than the majority
of the samples. Some outliers with abnormally lower values than the majority of the samples occur in the western part, and two samples in the north-eastern part. In order to obtain a robust variogram, the spatial outliers were excluded in the variogram calculation. However, all values, including the detected spatial outliers, were included in the kriging calculation,
Fig. 8. Cross validation results showing the differences between the estimated and actual values.
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4.2. Spatial structure of SOC The variogram surface of LnCwb is illustrated in Fig. 6. It can be seen that the variogram is broadly isotropic, with the lowest values located in the centre, and it increases in all the directions with the increase of lag. Therefore, the experimental isotropic variogram for LnCwb was calculated (Fig. 7). For comparison, the variogram for all samples (spatial outliers included) is also shown in Fig. 7. The experimental variogram has been fitted with an exponential model. There is a significant nugget effect of 0.05, which accounts for 45% of the total sill of 0.11. This shows that the small-scale variances are quite strong. In this study, only grassland soils had been sampled. It is expected that the small-scale variances would be even stronger if all types of soils were sampled.
The range of 40 km in the model implies that the largescale spatial autocorrelation may extend to the effective range of 120 km. Hence the present sampling density is sufficient to reveal general patterns but short-range variations can only be disclosed by sampling at a higher spatial density. The optimum sampling-scale for SOC in Irish soils is not known but it will be a compromise between what is most effective and what is feasible. Clearly the mean sampling-interval used here, ca. 7 km, is too great. Van Meirvenne et al. (1996) found in an investigation in Belgium that most of the change occurred within about 4 km, so that the optimum sampling scale is almost certainly less than this. When compared with the variogram for all samples, significant improvement of the variogram is observed for the samples with the spatial outliers excluded. The variogram for all samples is close to a nugget effect, which is mainly attributed to these spatial outliers.
Fig. 9. Spatial distribution map of SOC concentrations in grassland of Ireland.
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4.3. Spatial distribution of SOC concentrations The parameters of the exponential model were used for kriging to produce the spatial distribution map of SOC concentrations in soils of Ireland. A search region of 32 nearest-neighbours was applied in order to offset the relatively high nugget effect. To test the effectiveness of the model, cross validation (i.e., back-calculation of the observed values) was carried out with all the samples including spatial outliers. The results are shown in Fig. 8. It can be seen that the under-estimated and overestimated points are irregularly distributed over the study area. The spatial outliers detected using local Moran’s I in the eastern part tend to be under-estimated, while those in the western and northeast parts are over-estimated, which reconfirms that they are outliers. For the log-transformed data, the median of the relative absolute errors (the difference between the estimated and
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actual values regardless of sign) of LnCwb is 11.9%, and the average of relative absolute errors is 15.6%. When the data are back-transformed to Cwb, the median and average value of the relative absolute errors are 18.8 and 24.2% respectively. For the spatial interpolation, a cell size of 500500 m was chosen to divide the study area into a grid system containing 707 rows and 625 columns. Ordinary kriging was used with a block size of 22 and a search neighbourhood of 32 nearest-neighbours. The interpolated values were then back transformed according lognormal kriging. Fig. 9 shows the final result of this spatial interpolation process. The data range of the interpolated values is from 3.3 to 8.2% Cwb. This is narrower than that of the raw data set (Table 2), but is to be expected because of the smoothing effect of the spatial interpolation. However, this smoothing effect helps to identify the general spatial
Fig. 10. Hillshade map showing topography of Ireland.
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patterns and reduces both the local variations and the negative effect of random errors. The spatial distribution of SOC is generally consistent with elevation (Fig. 10) and precipitation (Rohan, 1975; Collins and Cummins, 1996) in Ireland. The highest SOC concentrations are located in the western coastal area, where elevation and precipitation are the highest. In the northern part, there is a relatively highconcentration area between counties Cavan, Roscommon, Leitrim and Monaghan. On the eastern side, a small area of high concentrations is located in counties Dublin and Wicklow. These areas also have relatively high elevation and precipitation. On the other hand, SOC concentrations are rather low in the southeastern part, which is consistent with the relatively low precipitation. Even though the elevation is not low, the southeastern part of Ireland is a rain-shadow area caused by the mountains on the west side. Another area with obviously low values is located in east Galway, south Roscommon, west Longford and Westmeath. This area has low precipitation and low elevation. In west Kerry, the SOC concentration is not as high as expected, which may be related to the low sampling density in this area. Finally, western Ireland generally has higher SOC concentrations than eastern Ireland. More detailed quantitative comparison between SOC and precipitation and elevation may be carried out when more detailed sampling is available in the future.
5. Conclusions The SOC concentration (measured by the Walkley– Black method) in grassland of Ireland follows a lognormal distribution, with a median value of 5.0%, arithmetic mean of 5.3%, and geometric mean of 5.0%. Statistically significant positive correlation exists between SOC and silt-plus-clay; negative correlation between SOC and sand, and lower correlation between SOC and pH were found. Low SOC concentrations are consistent with higher proportions of land in tillage. The local Moran’s I index has been effective in this study in detecting spatial outliers. The spatial distribution of SOC concentrations in Ireland show a broad regional pattern, with the highest values in the west coastal areas, and relatively low values in the inland and south-eastern coastal areas. This is generally consistent with the spatial distribution of precipitation and elevation in the country.
Acknowledgements This study was sponsored by the Research Development Fund of TEAGASC (Agriculture and Food Development Authority, Ireland) and the Millennium
Research Fund 2002 of National University of Ireland, Galway. The raw data sets were provided by TEAGASC. Helpful discussions with Prof. Mı´chea´l O´ Cinne´ide are acknowledged. The authors are grateful to Dr. Richard Howarth, Dr. Nils Gustavsson, and an anonymous reviewer for their helpful comments and suggestions to improve this paper. References Anselin, L., 1995. Local indicators of spatial association— LISA. Geog. Anal. 27, 93–115. Batjes, N.H., 1996. The total C and N in soils of the world. Eur. J. Soil Sci. 47, 151–163. Brogan, J.C., 1966. Organic carbon in Irish pasture soils. Irish J. Agric. Res. 5, 169–176. Burgess, T.M., Webster, R., 1980. Optimal interpolation and isarithmic mapping of soil properties: II. Block kriging. J. Soil Sci. 31, 333–341. Chevallier, T., Voltz, M., Blanchart, E., Chotte, J.L., Eschenbrenner, V., Mahieu, M., Albrecht, A., 2000. Spatial and temporal changes of soil C after establishment of a pasture on a long-term cultivated vertisol (Martinique). Geoderma 94, 43–58. Clark, I., Harper, W.V., 2000. Practical Geostatistics 2000. Ecosse North America Llc, Columbus OH, USA. Collins, J.F., Cummins, T., 1996. Agroclimatic Atlas of Ireland. AGMET—Joint Working Group on Applied Agricultural Meteorology, Dublin. Cressie, N.A.C., 1993. Statistics for Spatial Data, second ed. John Wiley & Sons, New York. CSO, 1965. Statistical Abstract of Ireland. Central Statistics Office, Dublin. Dobermann, A., Goovaerts, P., Neue, H.U., 1997. Scaledependent correlations among soil properties in two tropical lowland rice fields. Soil Sci. Soc. Am. J. 61, 1483–1496. Duncan, D.B., 1955. Multiple range and multiple F tests. Biometrika 11, 1–42. Eswaran, H., Van den Berg, E., Reich, P., Kimble, J., 1995. Global soil carbon resources. In: Lal, R., Kimble, J., Levine, E., Stewwart, B.A (Eds.), Soils and Global Change. CRC Lewis Publishers, Boca Raton, FL, pp. 27–43. Frogbrook, Z.L., Oliver, M.A., 2001. Comparing the spatial predictions of soil organic matter determined by two laboratory methods. Soil Use Manag. 17, 235–244. Getis, A., Ord, J.K., 1996. Local spatial statistics: an overview. In: Longley, P., Batty, M. (Eds.), Spatial Analysis: Modelling in a GIS Environment. GeoInformation International, Cambridge, UK, pp. 261–277. Goovaerts, P., 1997. Geostatistics for Natural Resources Evaluation. Oxford University Press, New York. Houghton, R.A., 1995. Changes in the storage of terrestrial carbon since 1850. In: Lal, R., Kimble, J., Levine, E., Stewwart, B.A. (Eds.), Soils and Global Change. CRC Lewis Publishers, Boca Raton, FL, pp. 45–65. Jenny, H., 1980. The Soil Resource, Origin and Behavior. Springer-Verlag, New York. Krige, D.G., 1951. A statistical approach to some basic mine valuation problems on the Witwatersrand. J. Chem. Metall. Min. Soc. S. Africa 52, 119–139.
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Spatial distribution of soil organic carbon concentrations in grassland of Ireland David McGratha, Chaosheng Zhangb,* a
Teagasc, Johnstown Castle Research Centre, Wexford, Ireland Department of Geography and Environmental Change Institute, National University of Ireland, Galway, Ireland
b
Received 30 August 2002; accepted 17 February 2003 Editorial handling by R. Fuge
Abstract Soil organic C (SOC) concentrations in topsoil samples taken at 678 sites in the grassland of Ireland were investigated using statistics and geostatistics. SOC concentrations (Walkley–Black method) follow a lognormal distribution, with a median and geometric mean of 5.0%, and an arithmetic mean of 5.3%. Statistically significant (P< 0.01) positive correlation between SOC and silt-plus-clay, and negative correlation between SOC and sand were observed, with lower correlation (P=0.17) between SOC and pH. Lower SOC concentrations were associated with higher percentages of land in tillage. In order to obtain a robust measurement of spatial structure, spatial outliers were detected, and subsequently eliminated, using the local Moran’s I index. The spatial distribution of SOC concentrations based on kriging interpolation showed coherent spatial patterns, with the highest values in the western coastal area, and relatively low values in the inland and southeastern coastal areas; soils at higher elevation were also found to contain higher SOC concentrations. These patterns are consistent with the distribution of rainfall within the country. # 2003 Elsevier Ltd. All rights reserved.
1. Introduction Soils play an important role in global C cycling and global warming. The global soil organic C (SOC) pool is estimated at 1500 Pg (Eswaran et al., 1995; Batjes, 1996), which is roughly equivalent to the sum of the atmospheric pool of 750 Pg and the biotic pool of 600 Pg (Schimel, 1995; Houghton, 1995; Lal, 2002). SOC levels are known to be influenced by a large number of factors, many of which are mutually interactive. These include: parent material, soil texture, climate, soil pH, landuse, management, topography and drainage. Manipulation of some of these factors, especially management-related ones, may be used to increase C sequestration in soils and thus mitigate national climate-change commitments (Smith et al., 2000). However,
* Corresponding author. Fax: +353-91-525700. E-mail addresses: [email protected] (D. McGrath), [email protected] (C. Zhang).
before changes can be evaluated, the baseline situation needs to be established and this is addressed here. Statistics and geostatistics have been used to study the relationships between SOC and these factors, and to quantify spatial distribution patterns and changes in SOC (e.g., Van Meirvenne et al., 1996; Saldan˜a et al., 1998; Chevallier et al., 2000; Frogbrook and Oliver, 2001). Geostatistics is based on the theory of a ‘‘regionalized variable’’ (Matheron, 1963), i.e., one which is distributed in space with spatial coordinates. The concepts of geostatistics are explained in several textbooks (e.g.: Cressie, 1993; Goovaerts, P., 1997; Clark and Harper, 2000; Webster and Oliver, 2001). In the past 20 a, geostatistics has become widely applied in soil sciences, and has provided advanced methodologies to quantify the spatial features of soil parameters and carry out spatial interpolation (Burgess and Webster, 1980; Webster, 1994; Dobermann et al., 1997; Stein et al., 1997; Zhang et al., 1998, 2000). Ireland is a country dominated by grassland, and SOC has primarily been investigated in these soils (Brogan, 1966; McGrath, 1980; McGrath and McCormack,
0883-2927/03/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0883-2927(03)00045-3
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1999). The data set from Brogan (1966) was obtained via a national soil survey, undertaken in 1964, which covers most parts of the Republic of Ireland. Despite the time-lag since the data was generated, it was considered to still provide a valuable base against which subsequent and future measurements could be evaluated. For this reason it has been used in this study.
2. Methods 2.1. Sampling and analysis of SOC About 59% of the land surface of the Republic of Ireland was recorded as being devoted to permanent pasture in 1964 (CSO, 1965). Soils (0–10 cm depth) were sampled from under permanent pasture (Brogan, 1966). A maximum of 2 sites were selected at random from each
1010 km2 sector of the national grid and sampled. Where land cover by lake, forest, bog and mountain was less than 25%, 2 sites were selected; when greater than 75%, no sample was taken. The 678 samples so obtained represent approximately 50% of the total that could be accommodated at a frequency of 2 samples for each 1010 km2 sector. The shortfall in the number of samples collected can be accounted for by the low sampling-density in some areas, e.g., in the west of the country, and in the Wicklow– south Dublin areas which, though largely mountainous, also included upland grassland sites. However, such sites were often peaty with SOC in excess of 18% and were excluded under the sampling protocol. The locations of the grassland sampling sites are shown in Fig. 1. SOC concentrations were determined by the Walkley-Black (Cwb) method (Metson, 1956). Sand, silt-plus-clay contents and pH values were also determined (Brogan, 1966).
Fig. 1. Soil sampling locations in Ireland (n=678).
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2.2. Geostatistics
2.3. Spatial outlier detection
Geostatistics (Matheron, 1963; Cressie, 1993; Webster and Oliver, 2001) uses the semi-variogram to measure the spatial variability of a regionalized variable, and provides the input parameters for the spatial interpolation method of kriging, a term introduced by Matheron in 1960 in honour of the work of the South African mining engineer D.G. Krige (1951). It relates the semivariogram, half the expected squared difference between paired data values z(x) and z(x+h) to the distance, lag h, by which locations are separated:
Outliers, and especially spatial outliers, in the data set can make the variogram exhibit erratic behaviour. Spatial outliers are those values that are obviously different from the values of their surrounding locations (Lalor and Zhang, 2001). In this work, such outliers are identified using an index, local Moran’s I (Anselin, 1995; Getis and Ord, 1996):
1 ðhÞ ¼ E ½zðxÞ zðx þ hÞ2 2
ð1Þ
For discrete sampling sites, such as those that had been sampled in this study, the function is written in the form: 1 X ½zðxi Þ zðxi þ hÞ2 2NðhÞ i¼1 NðhÞ
ðhÞ ¼
ð2Þ
where z(xi) is the value of the variable Z at location of xi, h is the lag, and N(h) is the number of pairs of sample points separated by h. For irregular sampling, it is rare for the distance between the sample pairs to be exactly equal to h. Therefore, h is often represented by a distance interval. A variogram plot is obtained by calculating values of the variogram at different lags. These values are then usually fitted with a theoretical model: spherical, exponential, or Gaussian (See Matheron, 1963; Cressie, 1993; or Webster and Oliver, 2001 for discussion). The models provide information about the spatial structure as well as the input parameters for the kriging interpolation. Kriging is regarded as an optimal spatial interpolation method, which is a type of weighted moving average: z^ðx0 Þ ¼
n X
li zðxi Þ
ð3Þ
i¼1
where z^ðx0 Þ is the value to be estimated at the location of x0; z(xi) is the known value at the sampling site xi, and li is a weight. There are n sites within the search neighbourhood around x0 used for the estimation, and the magnitude of n will depend on the size of the moving search window and user definition. Kriging differs from other methods (such as inverse distance weighted), in that the weight function li is no longer arbitrary, being calculated from the parameters of the fitted variogram model under the conditions of unbiasedness and minimized estimation variance for the interpolation. Thus, kriging is regarded as a best linear unbiased estimation (BLUE).
Ii ¼
n zi z X wij zj z 2 j¼1; j6¼i
ð5Þ
where zi is the value of the variable z at location i; z is the average value of z with the sample number of n; zj is the value of the variable z at all the other locations (where j6¼i); 2 is the variance of variable z; and wij is a weight, defined as the inverse of the distance dij between locations i and j: wij ¼
1 dij
ð6Þ
Local Moran’s I can be standardised so that its significance level can be tested based on the normal distribution (Levine, 1999), when the distribution of the raw data set is not too skewed. It should be noted that when the raw data are too skewed, the normal approximation of the local Moran’s I may fail. When the standardized value of local Moran’s I is higher than the critical value of 1.96, it is concluded (P=0.05) that the sample under test is clustered with (or similar to) the surrounding samples; if lower than 1.96, it is concluded (P=0.05) that the sample under test is significantly different from the surrounding samples and is considered to be a spatial outlier. 2.4. Data treatment with computer software The data sets were analysed using different software packages. The descriptive statistical parameters were calculated with Microsoft Excel# and SPSS# (version 10.0). Maps were produced with GIS software ArcView# (version 3.2) and its extension of Spatial Analyst# (version 2). The geostatistics analyses were carried out with GS+# (version 5.3) (Robertson, 2000) and Idrisi 32# (Release 2), and the local Moran’s I index was calculated with CrimeStat# (version 1.0) (Levine, 1999).
3. Descriptive statistics 3.1. Probability distribution Histograms of SOC concentrations determined by the Walkley–Black method are shown in Fig. 2. That for the raw data set has a long tail towards higher concentrations,
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Fig. 2. Histograms of Cwb concentrations in soils of Ireland (n=678): (a) raw data; (b) logarithmically transformed data.
whereas that for the logarithmically-transformed dataset can be satisfactorily modelled by a normal distribution. Table 1 shows the quantitative parameters of the probability distribution and significance level of the Kolmogorov–Smirnov test for conformance to a normal distribution for the variables. The probability distribution of Cwb is positively skewed and has a sharp peak (positive kurtoses). The log-transformed data show rather small skewnesses and kurtoses, and pass the K–S normality test at a significance level of higher than 0.05. On the other hand, contents of sand and silt-plus-clay follow a normal distribution, and log-transformation makes the fit to a normal distribution worse. pH values cannot pass either the normal or lognormal tests. However, its skewness and kurtosis are rather small. Therefore, the log-transformed data sets of Cwb, and the raw data sets of sand, silt-plus-clay and pH were used for the following multivariate analyses. 3.2. Mean values for SOC Percentiles and commonly used estimators of location and spread were calculated (Table 2). The range of Cwb varies from 2.0 to 17.8%, with the arithmetic mean of 5.3%. Both the geometric mean and median of Cwb are Table 1 Shape parameters of the probability distributions and significance level of Kolmogorov–Smirnov test (K–S p) (n=678)
Raw data
Log-transformed data
Statistics
Cwb
Skewness Kurtosis K–S p
1.66 4.77 0.00
Skewness Kurtosis K–S p
0.36 0.42 0.11
Sand
Silt+clay
pH
0.32 0.65 0.17
0.28 0.60 0.73
0.70 0.42 0.00
0.82 1.76 0.01
1.72 8.92 0.01
0.43 0.08 0.00
5.0%. Due to the lognormal feature of Cwb, the geometric mean and median are recommended as its representative mean value, while the arithmetic mean (average) should be discarded for this variable. 3.3. Relationships between SOC and other factors Pearson (linear) correlation coefficients between the 4 variables were calculated. These are given in Table 3, together with corresponding significance levels. Table 2 Basic statistic parameters of SOC concentrations and other related variables (%, except pH, n=678) Statistics
Cwb
Sand
Silt+clay
pH
Min 5% 25%
2.0 3.0 4.0
8 21 31
8 36 48
4.3 5.1 5.5
Median 75% 95%
5.0 6.1 9.1
37 44 56
55 63 71
5.8 6.2 7.0
87 37.7 36.1 10.5
88 54.9 53.7 10.7
7.8 5.9 5.8 0.6
Max Average GeoMean Stdev
17.8 5.3 5.0 1.9
Table 3 Correlation coefficients (lower-left side) and their significance levels (upper-right side) (n=678) LnCwb LnCwb Sand Silt+clay pH
Sand 0.00
0.43 0.22 0.05
0.91 0.14
Silt+clay 0.00 0.00 0.13
pH 0.17 0.00 0.00
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A positive correlation between SOC and silt-plus-clay and negative correlation between SOC and sand were also confirmed. It should be mentioned that the two variables of sand and silt-plus-clay sum up to almost 100%, which forms a constant sum proportion. In this case, the strong negative correlation between the two variables is expected. The correlation between SOC and pH is less pronounced. The causative relationship between SOC and pH is complex, with SOC being a progenitor of carbonic acid which then contributes to inhibiting organic matter degradation by soil microorganisms. To reveal the relationship between SOC concentrations and elevation of the sampling sites, the GIS software ArcView# was used to assign the samples to 4 elevation groups: 0 ( < 25), 50 (25–74), 100 (75–124), and 150 (> 124) m, based on which contour line the sampling location is close to. The box-plot (Fig. 3) shows the difference of SOC concentrations among these groups. In each box-plot, the lower boundary of the box shows the 25th percentile, and the upper boundary shows the 75th percentile. The whiskers are lines that extend from the box to the highest and lowest values, excluding outliers (here defined as the values that are outside 1.5 box lengths from the upper and lower edges of the box). The line across the box indicates the median. This plot shows that the SOC concentrations in the 0 (<24) m and 50 (25–74) m elevation groups are the lowest, and those in the 150 (> 124) m group are slightly higher. To better quantify the differences among the elevation groups, analysis of variance (ANOVA) was applied. The results show that the observed differences are significant at the level of 0.05. Further analysis of the post hoc test with Duncan’s test (Duncan, 1955) was carried out, and the results are shown in Table 4. The Kolmogorov– Smirnov test has shown that all the groups have passed the test for normality (P> 0.05). The Levene test has
Fig. 3. Box-plot of SOC in different elevation groups (n=50, 171, 301, 156 respectively).
Table 4 Results of post hoc tests in ANOVA with Duncan’s method (with mean values of LnCwb in each elevation group) Elevation group (m)
n
S.D.
Subset 1
0 50 100 150
50 171 301 156
0.365 0.306 0.340 0.304
1.557 1.559 1.622
Significance level
0.158
Subset 2
1.622 1.675 0.221
shown that the variances between the groups of the data set are homogenous at the significance level of 0.46, and thus Duncan’s test can be applied. The 4 groups of samples can be separated into 2 subsets. The first subset contains samples within the elevation groups of 0, 50, and 100 m; while the second subset consists of the 100 and 150 m elevation groups. The differences within either subset are not statistically significant, at the 0.05 level, with significance levels of 0.158 and 0.221, respectively. However, the difference between the subsets is significant at the level of 0.008 (with an F-value of 4.013). It can be concluded that statistically samples at the elevation group of 150 m have the highest SOC concentrations in this study. In explanation, it can be assumed that high elevation tends to result in increased precipitation and decreased temperature; both of these environmental factors tend to favour accumulation of humus (Jenny, 1980), and thus of SOC. Agricultural activities, especially tillage, play an important role on SOC concentrations. The proportion of agricultural land in tillage for each county in Ireland in 1964 was calculated based on data from the report of Central Statistics Office, Ireland (CSO, 1965). The average values of Cwb in each county were also calculated. A scatter plot of mean Cwb as a proportion of land in tillage shows a decreasing trend (Fig. 4). The correlation coefficient is 0.632, which is highly significant (P< 0.001).
Fig. 4. Average SOC concentrations in each county as a function of proportion of agricultural land in tillage (n=27).
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Fig. 5. SOC (Cwb) distribution in soils of Ireland and location of spatial outliers.
4. Spatial Distribution of SOC 4.1. Spatial symbol map and spatial outliers of SOC A point-symbol map of SOC concentrations in grassland of Ireland is shown in Fig. 5. Some possible spatial patterns are identifiable on this map. Western Ireland and the north-eastern part have relatively high SOC concentrations, while the southeastern part and north-western part generally have lower concentrations of SOC. However, it can be seen that some locations with high values have points with low values nearby; in some areas of low values, there are also some points with high values. This suggests the presence of spatial outliers which need to be eliminated prior to estimation of the spatial variogram.
Fig. 6. Variogram surface of LnCwb.
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Fig. 7. Isotropic variogram model of LnCwb: (a) spatial outliers excluded (n=639, exponential model: C0=0.05; C0+C=0.11; a=40 km); (b) all samples (n=678).
As described above, in order to avoid introducing bias, spatial outliers were detected using standardized local Moran’s I (Levine, 1999); Samples with values lower than 1.96 were defined as spatial outliers. The calculation was based on the log-transformed Cwb data set. Altogether, 39 spatial outliers were detected (Fig. 5). In the south-eastern part of the region, there are some outliers with abnormally higher values than the majority
of the samples. Some outliers with abnormally lower values than the majority of the samples occur in the western part, and two samples in the north-eastern part. In order to obtain a robust variogram, the spatial outliers were excluded in the variogram calculation. However, all values, including the detected spatial outliers, were included in the kriging calculation,
Fig. 8. Cross validation results showing the differences between the estimated and actual values.
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4.2. Spatial structure of SOC The variogram surface of LnCwb is illustrated in Fig. 6. It can be seen that the variogram is broadly isotropic, with the lowest values located in the centre, and it increases in all the directions with the increase of lag. Therefore, the experimental isotropic variogram for LnCwb was calculated (Fig. 7). For comparison, the variogram for all samples (spatial outliers included) is also shown in Fig. 7. The experimental variogram has been fitted with an exponential model. There is a significant nugget effect of 0.05, which accounts for 45% of the total sill of 0.11. This shows that the small-scale variances are quite strong. In this study, only grassland soils had been sampled. It is expected that the small-scale variances would be even stronger if all types of soils were sampled.
The range of 40 km in the model implies that the largescale spatial autocorrelation may extend to the effective range of 120 km. Hence the present sampling density is sufficient to reveal general patterns but short-range variations can only be disclosed by sampling at a higher spatial density. The optimum sampling-scale for SOC in Irish soils is not known but it will be a compromise between what is most effective and what is feasible. Clearly the mean sampling-interval used here, ca. 7 km, is too great. Van Meirvenne et al. (1996) found in an investigation in Belgium that most of the change occurred within about 4 km, so that the optimum sampling scale is almost certainly less than this. When compared with the variogram for all samples, significant improvement of the variogram is observed for the samples with the spatial outliers excluded. The variogram for all samples is close to a nugget effect, which is mainly attributed to these spatial outliers.
Fig. 9. Spatial distribution map of SOC concentrations in grassland of Ireland.
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4.3. Spatial distribution of SOC concentrations The parameters of the exponential model were used for kriging to produce the spatial distribution map of SOC concentrations in soils of Ireland. A search region of 32 nearest-neighbours was applied in order to offset the relatively high nugget effect. To test the effectiveness of the model, cross validation (i.e., back-calculation of the observed values) was carried out with all the samples including spatial outliers. The results are shown in Fig. 8. It can be seen that the under-estimated and overestimated points are irregularly distributed over the study area. The spatial outliers detected using local Moran’s I in the eastern part tend to be under-estimated, while those in the western and northeast parts are over-estimated, which reconfirms that they are outliers. For the log-transformed data, the median of the relative absolute errors (the difference between the estimated and
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actual values regardless of sign) of LnCwb is 11.9%, and the average of relative absolute errors is 15.6%. When the data are back-transformed to Cwb, the median and average value of the relative absolute errors are 18.8 and 24.2% respectively. For the spatial interpolation, a cell size of 500500 m was chosen to divide the study area into a grid system containing 707 rows and 625 columns. Ordinary kriging was used with a block size of 22 and a search neighbourhood of 32 nearest-neighbours. The interpolated values were then back transformed according lognormal kriging. Fig. 9 shows the final result of this spatial interpolation process. The data range of the interpolated values is from 3.3 to 8.2% Cwb. This is narrower than that of the raw data set (Table 2), but is to be expected because of the smoothing effect of the spatial interpolation. However, this smoothing effect helps to identify the general spatial
Fig. 10. Hillshade map showing topography of Ireland.
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patterns and reduces both the local variations and the negative effect of random errors. The spatial distribution of SOC is generally consistent with elevation (Fig. 10) and precipitation (Rohan, 1975; Collins and Cummins, 1996) in Ireland. The highest SOC concentrations are located in the western coastal area, where elevation and precipitation are the highest. In the northern part, there is a relatively highconcentration area between counties Cavan, Roscommon, Leitrim and Monaghan. On the eastern side, a small area of high concentrations is located in counties Dublin and Wicklow. These areas also have relatively high elevation and precipitation. On the other hand, SOC concentrations are rather low in the southeastern part, which is consistent with the relatively low precipitation. Even though the elevation is not low, the southeastern part of Ireland is a rain-shadow area caused by the mountains on the west side. Another area with obviously low values is located in east Galway, south Roscommon, west Longford and Westmeath. This area has low precipitation and low elevation. In west Kerry, the SOC concentration is not as high as expected, which may be related to the low sampling density in this area. Finally, western Ireland generally has higher SOC concentrations than eastern Ireland. More detailed quantitative comparison between SOC and precipitation and elevation may be carried out when more detailed sampling is available in the future.
5. Conclusions The SOC concentration (measured by the Walkley– Black method) in grassland of Ireland follows a lognormal distribution, with a median value of 5.0%, arithmetic mean of 5.3%, and geometric mean of 5.0%. Statistically significant positive correlation exists between SOC and silt-plus-clay; negative correlation between SOC and sand, and lower correlation between SOC and pH were found. Low SOC concentrations are consistent with higher proportions of land in tillage. The local Moran’s I index has been effective in this study in detecting spatial outliers. The spatial distribution of SOC concentrations in Ireland show a broad regional pattern, with the highest values in the west coastal areas, and relatively low values in the inland and south-eastern coastal areas. This is generally consistent with the spatial distribution of precipitation and elevation in the country.
Acknowledgements This study was sponsored by the Research Development Fund of TEAGASC (Agriculture and Food Development Authority, Ireland) and the Millennium
Research Fund 2002 of National University of Ireland, Galway. The raw data sets were provided by TEAGASC. Helpful discussions with Prof. Mı´chea´l O´ Cinne´ide are acknowledged. The authors are grateful to Dr. Richard Howarth, Dr. Nils Gustavsson, and an anonymous reviewer for their helpful comments and suggestions to improve this paper. References Anselin, L., 1995. Local indicators of spatial association— LISA. Geog. Anal. 27, 93–115. Batjes, N.H., 1996. The total C and N in soils of the world. Eur. J. Soil Sci. 47, 151–163. Brogan, J.C., 1966. Organic carbon in Irish pasture soils. Irish J. Agric. Res. 5, 169–176. Burgess, T.M., Webster, R., 1980. Optimal interpolation and isarithmic mapping of soil properties: II. Block kriging. J. Soil Sci. 31, 333–341. Chevallier, T., Voltz, M., Blanchart, E., Chotte, J.L., Eschenbrenner, V., Mahieu, M., Albrecht, A., 2000. Spatial and temporal changes of soil C after establishment of a pasture on a long-term cultivated vertisol (Martinique). Geoderma 94, 43–58. Clark, I., Harper, W.V., 2000. Practical Geostatistics 2000. Ecosse North America Llc, Columbus OH, USA. Collins, J.F., Cummins, T., 1996. Agroclimatic Atlas of Ireland. AGMET—Joint Working Group on Applied Agricultural Meteorology, Dublin. Cressie, N.A.C., 1993. Statistics for Spatial Data, second ed. John Wiley & Sons, New York. CSO, 1965. Statistical Abstract of Ireland. Central Statistics Office, Dublin. Dobermann, A., Goovaerts, P., Neue, H.U., 1997. Scaledependent correlations among soil properties in two tropical lowland rice fields. Soil Sci. Soc. Am. J. 61, 1483–1496. Duncan, D.B., 1955. Multiple range and multiple F tests. Biometrika 11, 1–42. Eswaran, H., Van den Berg, E., Reich, P., Kimble, J., 1995. Global soil carbon resources. In: Lal, R., Kimble, J., Levine, E., Stewwart, B.A (Eds.), Soils and Global Change. CRC Lewis Publishers, Boca Raton, FL, pp. 27–43. Frogbrook, Z.L., Oliver, M.A., 2001. Comparing the spatial predictions of soil organic matter determined by two laboratory methods. Soil Use Manag. 17, 235–244. Getis, A., Ord, J.K., 1996. Local spatial statistics: an overview. In: Longley, P., Batty, M. (Eds.), Spatial Analysis: Modelling in a GIS Environment. GeoInformation International, Cambridge, UK, pp. 261–277. Goovaerts, P., 1997. Geostatistics for Natural Resources Evaluation. Oxford University Press, New York. Houghton, R.A., 1995. Changes in the storage of terrestrial carbon since 1850. In: Lal, R., Kimble, J., Levine, E., Stewwart, B.A. (Eds.), Soils and Global Change. CRC Lewis Publishers, Boca Raton, FL, pp. 45–65. Jenny, H., 1980. The Soil Resource, Origin and Behavior. Springer-Verlag, New York. Krige, D.G., 1951. A statistical approach to some basic mine valuation problems on the Witwatersrand. J. Chem. Metall. Min. Soc. S. Africa 52, 119–139.
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