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Accounting for measurement errors when harmonizing incongruent soil data--a case study.

Introduction

When collating soil data from different sources it is critical that the data are congruent, that is free of sampling or analytical artefacts, otherwise data from the different sources will need to be harmonised. Recently, the congruency of data on soil organic carbon content collated for calibrating near or mid infrared spectrometers has been questioned by Rayment et al. (2012). More generally, incongruent testing methods present a serious limitation to harmonising data from different soil monitoring networks (Arrouays et al. 2012). The question of congruency is also important for soil inventories and audits (e.g. National Land and Water Resources Audit 2001a) as soil data in these collections can span different epochs in analytical methodology, equipment performance and rigour in laboratory quality control. Indeed, the research reported here was prompted by difficulties in measuring differences in soil organic carbon at cereal and pasture trial sites first tested between 1968 and 1972 for the National Soil Fertility Project (Colwell 1977) and then again between 2011 and 2013, which led to the bigger question of how incongruent data can be harmonised.

Soil organic carbon content has been mostly determined using two approaches. Dry oxidation methods 6B2 and 6B3 in Rayment and Lyons (2011) are based on the Dumas method and are preferred as they consistently recover more soil organic carbon than the Walkley and Black method (Chatteijee et al. 2009), the most widely used wet oxidation method. The performance and details of any given version of the Walkley and Black method is seldom reported with soil organic carbon data; critical information that is needed to quantify incongruencies when collating and analysing data from different sources. Colwell (1969) reported that the Walkley and Black wet oxidation method was selected for the National Soil Fertility Project (NSFP) based on reproducibility rather than the recovery or concordance with accepted methods.

Correction factors have been applied to harmonise legacy soil organic carbon data, e.g. Skjemstad et al. (2000). However, the application of a correction factor is effectively a special case of simple linear regression (y = [alpha] + [beta] x + [epsilon]) where the intercept, a, is set to zero, i.e. the model becomes y = [beta] x + [epsilon]; a step justified if [alpha] is not significantly different (P > 0.05) to zero, e.g. Wang et al. (1996) and De Vos et al. (2007), so that the slope of the line, [beta], becomes the 'correction factor'. Lettens et al. (2007) and Karunaratne et al. (2014) applied a linear regression model in their attempts to harmonise soil organic carbon data and assumed that the errors in y, i.e. [epsilon], were random, had a normal distribution and were homoscedastic, and that x was measured without error.

The assumption that the explanatory variable, x, is measured without error is questionable. Webster (1997) suggests that errors in both variables be considered and an appropriate statistical method be chosen. A proposed solution to this errors-in-both-variables problem is to estimate the maximum likelihood functional relationship (MLFR: Ripley and Thompson 1987). The MLFR differs from ordinary linear regression (OLR) as it considers that both variables (x and y) are subject to error and accordingly determines weights by minimising the sum of variances for x and y. A variant of the MLFR commonly applied in clinical analytical chemistry is the Deming regression in which the errors for the two variables are assumed to be independent and normally distributed, e.g. Analytical Methods Committee (2002). Ripley and Thompson's solution could be applied to the harmonisation of soil data--in this paper soil organic carbon data.

In this study we pose the hypothesis that there are no differences between laboratories and methods of analysing soil organic carbon. If true, then there would be no need to harmonise data from different sources as the data would be congruent, i.e. the model: y [equivalent to] x, strictly applies. If not, then a first step is to investigate the differences between laboratories and methods. This then forms the basis for comparing models based on these two approaches. Ideally, researchers will have complete data on precision for structural analysis of the MLFR between y and x and such a scenario is explored. But not all researchers will have archived samples or legacy data that has information on precision. Therefore, data from analysis of archived samples from the NSFP, by the Dumas method were compared with data reported by Colwell (1977) based on the Walkley and Black method using precision data from currently operating laboratories; a scenario that will be faced by many users of legacy data and therefore worthy of examination.

Methodology

Rayment and Lyons (2011), the industry standard for the laboratory analysis of soil chemistry in Australasia, provides two wet oxidation methods for soil carbon: Method 6A1 based on the method of Walkley and Black (1934) and its variant with external heating; and Method 6B1 from Heanes (1984). Method 6B1 was developed by Heanes (1984) to improve the performance of the Walkley and Black method.

Different sources of soil organic carbon data for a range of soils were used for making comparisons between methods and laboratories, as well as data on the precision of their analyses. The data were selected to represent the two likely scenarios:

(1) Mean values from repeated determinations with the standard errors of each mean value as the information on precision,

(2) Single determinations of test samples with standard deviations from the repeated analysis of selected samples external to the test samples as the only source of information on precision. This scenario is more likely to be experienced by researchers working with legacy data.

The standard deviations were from an inter-laboratory proficiency program which would be appropriate when collating and comparing data from different laboratories, and from a laboratory quality control program which would be appropriate when collating and comparing data from the one laboratory.

Soil organic carbon data

Data sources in this study included (a) reported results from an inter-laboratory proficiency program conducted by the Australasian Soil and Plant Analysis Council (ASPAC) to provide repeated analysis of samples, their mean values and the standard error of each mean, i.e. the ideal scenario; and (b) analytical results from several sources for the less than ideal scenario including new data collected from the analysis of archived samples originating from the NSFP for comparison to their corresponding values reported by Colwell (1977), i.e. legacy data, to provide individual results with data on precision from either the inter-laboratory proficiency program or from repeated analysis of soil samples used for quality control at the laboratories of the Department of Economic Development, Jobs, Transport and Resources (DEDJTR), Macleod, Victoria, Australia.

Inter-laboratory proficiency program (ILPP)

Soil organic carbon results from the ILPP were sourced from the ASPAC reports of the various rounds of this program run from 1997 to 2011 (Peverill and Johnstone 1997; Johnstone et al. 1999, 2001, 2002, 2003; Johnstone and Shelley 2000; Rayment et al. 2007; Lyons et al. 2008, 2010, 2011). Analytical results from five participating laboratories were used for this study as they had sufficient reported results. It was assumed that each datum in the ILPP data represents one determination of the sample received by the laboratory participating in any round, not the mean of multiple determinations. In summary, subsamples were sent to each of the participating laboratories in any round, from a finely ground homogenised bulk sample of soil, for soil organic carbon analysis using the Dumas method, without and with pretreatment to remove carbonates as needed, i.e. Method 6B2b and 6B3 in Rayment and Lyons (2011); and from the analysis of the same sub-samples by Method 6A1.

NSFP

Two sets of archived soil samples from the NSFP were prepared and analysed for the second scenario. Descriptions of soil type, summaries of sampling and analytical methods, and complete data were reported by Colwell (1977). The first set includes samples from seven sites covering major cropping soil types in Victoria, Australia (i.e. Vertosols and Sodosols) and were selected and made available from the National Soil Archive, CSIRO, Canberra. The samples from the cropping sites were formed by taking nine 1-m-deep cores, sectioning them into 10-cm depth increments and bulking the nine sections into composite samples representing the 0-10 cm, 10-20 cm and so on to the 90-100 cm depth increment. The second set were selected from archived pasture trial site soil samples, held in the Victorian Soil Archive located at DEDJTR Tatura. Samples from the pasture sites were formed by bulking 100 cores into a composite sample representing the 0-10 cm depth.

Laboratory analysis

Sub-samples from NSFP samples were analysed at DEDJTR Macleod by the Dumas method using a LECO TruMac instrument (LECO Co, St Joseph, USA) without and with pretreatment to remove carbonates, i.e. Methods 6B2b and 6B3 in Rayment and Lyons (2011), respectively. Soil was finely ground before analysis in a puck and ring mill. All data are reported on an air-dried basis as all samples were dried to constant weight in an oven at 40[degrees]C (Table 1) as reported by Colwell (1977).

Repeated analysis of homogenised soil samples from the laboratory quality control program at DEDJTR Macleod were collated to provide data on the variability of the Walkley and Black method and the Dumas method (Table 2). Some of these quality control samples were used in the analysis of the archived samples from the NSFP sites, and when this laboratory participated in the ILPP. The long-term mean of the standard deviations for the ILPP were also collated for comparison (Table 2).

Statistics

All statistical analyses were conducted using Genstat v13. For consistency, when comparing methods, the pro-numerals Y or y always represent variables containing means or individual results, respectively, of data from the Walkley and Black method, while X or x are corresponding variables containing data from the Dumas method. When comparing laboratories, data from the first laboratory is always represented by Y or y while that from the second is represented by X or x.

To analyse the ILPP data to construct the MLFR, mean values of soil organic carbon and their standard errors were calculated from unique combinations of sample, method and laboratory with the rounds of the program providing replicate determinations. For example, a comparison of two methods from the one laboratory would involve using determinations of soil organic carbon content in each of the n samples by the first method to calculate a mean soil organic carbon content and the standard error of that mean for each sample, and then compare these, i.e. [Y.sub.i] and [se.sub.Yi] for i = 1 ... n, to corresponding values of mean soil organic carbon content and its standard error for each of the same samples analysed by the second method at the same laboratory, i.e. [X.sub.i] and [se.sub.Xi] for i = 1 ... n. However, not all laboratories participated in each round, nor did a participating laboratory apply both methods to all samples in the rounds in which they participated. Consequently, the means and their standard errors were calculated from two to six determinations and not all samples were used in all comparisons of methods and laboratories. However, all data were included when analysing ILPP data using Kruskal-Wallis ranking.

Standard errors of zero were replaced with a value of 0.0045 where needed to facilitate statistical analysis of the MLFR, i.e. the worst-case scenario for rounding-off error when results are reported to two decimal places as is common for soil organic carbon analyses.

To analyse the data from the NSFP samples, statistical computations involved single determinations for each sample, i.e. [y.sub.i] and [x.sub.i] for i = 1 ... n samples. For the MLFR approach, information on precision, i.e. the standard deviation s in Table 2, was applied to the relevant variable.

Results

Analysis of data from the ILPP

Determinations of soil organic carbon using the Dumas method were in the range of 0.09-9.49% C with a mean of 2.37% C in the ILPP data. Determinations of soil organic carbon using the Walkley and Black method ranged within 0.08-10.00% C with a mean of 2.07% C. These ranges fall within the range found in data from surface soil samples from farm paddocks, collated from commercial and government laboratories for the National Land and Water Resources Audit (20016).

The Kruskal-Wallis ranking of the standard errors for each unique combination of laboratory and method are shown in Table 3 (as are the number of standard error observations and their mean). This shows that the precision of application of the two methods was not consistent between laboratories or between methods given that they were significantly different ([chi square] < 0.001).

Results in Table 3 illustrate how the comparison of one method or laboratory with another or the collation of different sources of data must consider the validity of the assumption that the explanatory variable, i.e. data from the 'benchmark', is measured without error when using OLR. These results also call into question the use of external sources of data on precision for harmonising incongruent data. These issues are explored using the following comparisons representing the different scenarios that would be faced by the soil scientist collating data from different sources.

The mean soil organic carbon content of samples from two sources were subjected to OLR to assess if Y was equivalent to X (Table 4) using the model Y = [alpha] + [beta] X + [epsilon], and testing the hypotheses that the intercept was zero, and the slope was unity, i.e. [alpha] = 0, and [beta] = 1, respectively. Comparisons were also made using the MLFR approach and testing the same hypotheses.

Initially, the data from one laboratory were compared with another for the same method, representing the analysis needed to harmonise data from different sources. Laboratories 1 and 2 were compared for the Dumas method, where the MLFR approach detected differences in intercept and slope to zero and one, respectively, but OLR did not. In contrast, comparing data for the Walkley and Black method from Laboratories 1 and 4 by either statistical approach was equally informative where the negative intercept of the model of the MLFR shows that Laboratory 4 recovered less soil organic carbon, i.e. 0.15% C. Using OLR, the difference was either 0.15 or 0.18% C depending upon which laboratory was selected as the explanatory variable. However, when comparing Laboratories 1 and 2 for the Walkley and Black method, it was evident from either statistical approach, that Laboratory 2 was not recovering the same amount of soil organic carbon as Laboratory 1.

Second, data from different methods from a participating laboratory were compared, a scenario that occurs when assessing the need for harmonising data from a laboratory using two different methods to determine the same soil property. Here we compared both methods for Laboratory 1 and then for Laboratory 2. Intercepts and slopes all significantly differed from zero and one, respectively. Also, the slope from the MLFR was much lower than in the equivalent OLR model, and the intercept was much higher.

Third, we compared Walkley and Black data from a laboratory against Dumas data from a different laboratory, a scenario that is likely to occur where data from different studies are collated into a large dataset where the datasets are from different laboratories using different methods. The intercept in the MLFR model significantly differed to zero at P<0.001, in contrast to the application of OLR where significant differences were inconsistent. Both statistical approaches highlighted that application of the Walkley and Black method by Laboratory 2 was not recovering as much soil organic carbon as the Dumas method as applied by Laboratory 1.

Data from archived NSFP samples

The determinations of Walkley and Black for cereals ranged within 0.07-1.50% C with a mean of 0.85% C. For pasture samples, organic carbon content ranged within 1.08-9.12% with mean of 2.10% C. Re-analysing these samples with the Dumas method showed that the total oxidisable carbon ranged within 0.17-1.83% C for cereals (mean of 0.49% C) and 1.06-9.83% C (mean of 3.63%) for pastures.

When regressing legacy data reported by Colwell (1977), y, on the new data by the Dumas method, x, using OLR, for all archived soils studied here, the intercept was not significantly different to zero, in contrast to the intercept from regressing x on y (Table 5). The slopes of both regression models were significantly different to one. Furthermore, the fitted models were not equivalent as the regression coefficients from fitting y on x and x on y, were not the same after algebraic re-arrangement, illustrating the problems when choosing a harmonisation model based on OLR, i.e. should y or x be the predictor?

The application of MLFR does not lead to these problems. However, because the analyses were un-replicated, as would be ideal when using MLFR but typical of many scenarios, no data were available to ascertain the precision of the legacy data y. In such scenarios, the researcher must make a defendable choice from limited options when selecting information on precision. Hopefully, the researcher will at least have modern data on precision and it is applicable to the legacy data. The lack of replication means that the researcher must also assume that the errors in y and x are homoscedastic. For this case study, we chose to use data from ILPP and the DEDJTR Macleod quality control program (Table 2). The precision data from the former represents a situation when comparing analyses undertaken at different laboratories, the latter when comparing data from the same laboratory. We observed that the estimates of precision of the regression coefficients and the outcomes of the tests of hypotheses (Table 5) using either source of information on precision, were similar. These estimates of precision of the regression coefficients were also similar to those observed when using OLR, as were the outcomes of the hypotheses tests of the slope relative to unity. This contrasted with tests of the intercepts estimated by OLR, when comparing y on x and x on y.

We found contrasting estimates of the regression coefficients of models based on OLR and the MLFR approach when comparing the two methods (Table 5). The precision of the estimates for the regression coefficients using OLR on the data from crop sites was much lower compared with the model of the MLFR. But the tests of significant differences with zero and unity, were opposite in outcome. However, in data from the pasture sites the precision of the estimates was of similar magnitude for OLR and the MLFR approach and the outcomes of hypothesis testing were the same. Importantly, the Walkley and Black method recovered more carbon from pasture soil samples than from cropping soil samples, relative to the results from applying the Dumas method. It is not yet possible to analyse the effects of covariates when modelling the MFLR in contrast to modelling using OLR, hence separate statistical analyses would be needed for modelling of the MLFR.

Discussion

Variants of the method developed by Walkley and Black (1934) have long been used by different laboratories across the world, and so influence many legacy datasets available from surveys and field trials. For example, in Australia, the Australian Soil Resource Information System (Johnston et al. 2003) and the Victorian Soil Information System (Hunter Williams and Robinson 2010), contain data determined using this method since its publication. But, much new data on soil organic carbon is being generated based on the Dumas method which has become cheaper than the Walkley and Black method. The adoption of the Dumas method as the reference method for estimating soil carbon stocks (Sanderman et al. 2011) will also encourage scientists to discontinue the use of the different versions of the Walkley and Black method.

We hypothesised that there were no differences between laboratories or the methods of analysing soil organic carbon. Results from the study of the ILPP data showed that there were indeed differences between these two popular methods as they were applied in different laboratories and that each method was applied with different levels of precision in the different laboratories. Therefore, the results reported here supports both the call by Rayment et al. (2012) to examine the potential for different datasets to be incongruent, and the call by Webster (1997) to not ignore the errors-in-both-variables problem.

Assignment of which method is the benchmark and therefore which is represented by the explanatory variable, x, in regression analysis, is inconsistent across research reports. For example, Lowther et al. (1990) and Navarro et al. (1993) regressed data from the Dumas method on data from the Walkley and Black method, whereas recovery of the Walkley and Black method is nearly always calculated on the basis that the Dumas method is the benchmark. The precision of the different methods is of the same order of magnitude as seen here in the different laboratories (Table 3), in previous reports (Navarro et al. 1993; Meersmans et al. 2009), and as can be found by inspecting proficiency data or quality control data (as presented in Table 2). Therefore, assuming one method or the other is effectively measured without error is not valid. Furthermore, the error structure in OLR leads to biased estimates of the precision of predicted values of y where x is measured with error leading to limited utility of the statistical outputs. Future advances in environmental modelling may require estimates of the precision of harmonised data free of such bias.

If the regression intercept is not significantly different from zero then the analyst has justification for forcing the model through zero, e.g. Wang et al. (1996) and De Vos et al. (2007), and quoting a correction factor. However, there were variations in this test of significance when applying OLR to our data, depending on which analytical method was used as the reference (Table 4).

Usually comparison of outputs such as correction factors, are done assuming that there are no laboratory factors affecting the comparisons. This is not justified by the results of this study. The differences between the laboratories and methods presented here supports attempts to establish environment specific relationships between different methods within a study, e.g. Lowther et al. (1990), Navarro et al. (1993), Skjemstad et al. (2000) and Karunaratne et al. (2014), but confounds comparison of studies when attempting to assign environmental factors to differences in the performance of the different methods. The interaction effect of environmental factors such as soil type or vegetation, and laboratories on differences between methods must be addressed with an appropriate statistical design such as used by De Vos et al. (2007). It follows that harmonisation models will need a case-by-case development.

Collators of legacy data are unlikely to have information on precision when harmonising incongruent data. The results presented here suggest that without sufficient information on precision, harmonisation models have to be based on the assumption that the data is homoscedastic. Consequently, an MLFR approach will not have its full advantage over using OLR. A similar conclusion can be made from the work of De Vos et al. (2007) and Lettens et al. (2007). De Vos et al. (2007) constructed a functional relationship between data produced by the Walkley and Black method and the Dumas method. They compared the predictions from this relationship to those from a model based on OLR applied to the same data and found the absolute difference was only 0.075% soil organic carbon. However, they estimated the precision of their data from the variance of 30 replicate determinations of soil organic carbon in a single sample of soil using each method, i.e. their modelling was based on homoscedastic data.

Lettens et al. (2007) tested the ratio of the error variances from duplicate analyses of organic carbon in soil samples by the Dumas method and the Walkley and Black method. They reported that the average ratio was 0.046 but did not explain how the error variances were calculated. Furthermore, they reported that when the ratio, [[epsilon].sub.y.sup.2]/ [[epsilon].sub.x.sup.2], was less than 0.5, the effect on slope and intercept of the OLR of x on y was negligible which led them to regard the error in y to be sufficiently small to justify ignoring the errors-in-both-variables problem, i.e. their Walkley and Black method could be assumed to be measuring soil organic carbon without error in comparison to their Dumas method. This contrasts with the ILPP data where the application of the Dumas method was often more precise but its application was not more precise by a factor of the magnitude observed by Lettens et al. (2007). Importantly, this points to the need to further investigate in what circumstances is applying OLR acceptable or whether the errors-in-both-variables problem is sufficient to necessitate modelling the MLFR.

Conclusion

The research reported here supports the call of Rayment et al. (2012) for data on soil organic carbon content collated for calibrating infrared spectrometers to be examined in terms of congruency. More generally, research based on soil monitoring networks needs to consider measurement errors as does research based on legacy datasets, e.g. digital soil mapping and changes in carbon stock predictions.

The results reported here show how incongruent data, generated from different sources, can be harmonised while accounting for the measurement errors in the different sources. Importantly, it shows that not accounting for measurement errors by using OLR to construct harmonisation models, can lead to predictions that vary according to which method, analyst, laboratory or data source is designated as the reference, i.e. assumed to be without error.

We also illustrated why researchers need to ask questions about the universality of harmonisation models. This suggests that an onerous task awaits those collating incongruent soil organic carbon data, and by extension incongruent soil data in general.

For researchers to construct harmonisation models based on analysis of the MLFR, they will need archived soil samples and sufficient historical documentation to enable them to obtain data on precision and bias. Otherwise, OLR may be an easier option but only if the penalty is acceptably small.

Importantly, the research reported here highlights the value of soil sample archives. It also points to the need for further development of the MLFR approach to account for factors affecting differences between data, and for curvilinear relationships, if this is to be used as a source of harmonisation models.

Conflicts of interest

The authors declare no conflicts of interest.

https://doi.org/10.1071/SR17307

Acknowledgements

This research was funded by the Department of Economic Development, Transport, Jobs and Resources. Bruce Shelley provided advice on the history of soil organic carbon analysis. Murray Hannah wrote the Genstat procedure used to determine the maximum likelihood functional relationships and Kohleth Chia advised on their broader application to the errors-in-both variables problem. Linda Karsies and Peter Wilson (CSIRO) provided archived samples from the National Soil Archive, Canberra, Australian Capital Territory. These contributions are acknowledged.

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Handling Editor: Christian Walter

D. M. Crawford (A), S. Norng (B), M. Kitching (B), and N. Robinson (iD) (C,D,E)

(A) Department of Economic Development, Jobs, Transport and Resources, Ellinbank, Vic. 3821, Australia,

(B) Department of Economic Development, Jobs, Transport and Resources, Bundoora, Vic. 3083, Australia.

(C) Department of Economic Development, Jobs, Transport and Resources, Taylor Road, Epsom, Vic. 3551, Australia.

(D) School of Science, Engineering and Information Technology, Federation University, University Drive, Mt Helen, Vic. 3350, Australia.

(E) Corresponding author. Email: n.robinson@federation.edu.au
Table 1. Total organic carbon content (TOC, g C. 100 [g.sup.-1]
air-dried soil) in archived soil samples from the National Soil
Fertility Project (Colwell 1977) from analysis using the
Dumas method

Site      Depth (m)    TOC      Site    Depth (m)

V69W03      0-0.1     1.053    V72W17     0-0.1
V69W03     0.1-0.2    0.540    V72W17    0.1-0.2
V69W03     0.2-0.3    0.425    V72W17    0.2-0.3
V69W03     0.3-0.4    0.462    V72W17    0.3-0.4
V69W03     0.4-0.5    0.347    V72W17    0.4-0.5
V69W03     0.5-0.6    0.242    V72W17    0.5-0.6
V69W03     0.6-0.7    0.204    V72W17    0.6-0.7
V69W03     0.7-0.8    0.218    V72W17    0.7-0.8
V69W03     0.8-0.9    0.231    V72W17    0.8-0.9
V69W03     0.9-1.0    0.349    V72W17    0.9-1.0
V70W05      0-0.1     1.832    V70P1      0-0.1
V70W05     0.1-0.2    0.732    V70P2      0-0.1
V70W05     0.2-0.3    0.481    V70P4      0-0.1
V70W05     0.4-0.5    0.3007   V70P5      0-0.1
V70W05     0.5-0.6    0.3057   V70P6      0-0.1
V70W05     0.6-0.7    0.243    V70P7      0-0.1
V70W05     0.7-0.8    0.190    V70P12     0-0.1
V70W05     0.8-0.9    0.184    V70P9      0-0.1
V70W05     0.9-1.0    0.168    V70P10     O-O.l
V70W06     0.8-0.9    0.217    V70P13     0-0.1
V70W06     0.9-1.0    0.247    V70P14     0-0.1
V71W20      0-0.1     1.323    V70P15     0-0.1
V71W20     0.1-0.2    0.814    V70P19     0-0.1
V71W20     0.2-0.3    0.684    V70P21     0-0.1
V71W20     0.3-0.4    0.545    V70P22     0-0.1
V71W20     0.4-0.5    0.463    V70P23     0-0.1
V71W20     0.5-0.6    0.426    V70P26     0-0.1
V71W20     0.6-0.7    0.383    V70P28     0-0.1
V71W20     0.7-0.8    0.327    V70P29     0-0.1
V71W20     0.8-0.9    0.293    V70P30     0-0.1
V71W20     0.9-1.0    0.306    V71P30     0-0.1
V72W15      0-0.1     1.107    V71P31     0-0.1
V72W15     0.1-0.2    0.801    V71P15     0-0.1
V72W15     0.2-0.3    0.726    V71P13     0-0.1
V72W15     0.3-0.4    0.713    V71P2      0-0.1
V72W15     0.4-0.5    0.652    V71P3      0-0.1
V72W15     0.5-0.6    0.606    V71P1      0-0.1
V72W15     0.6-0.7    0.556    V71P5      0-0.1
V72W15     0.7-0.8    0.502    V71P4      0-0.1
V72W15     0.8-0.9    0.450
V72W15     0.9-1.0    0.380

Site       TOC     Site    Depth (m)    TOC

V69W03    0.836   V71P6      0-0.1     3.204
V69W03    0.488   V71P8      0-0.1     2.905
V69W03    0.462   V71P7      0-0.1     3.077
V69W03    0.440   V71P9      0-0.1     3.832
V69W03    0.354   V71P10     0-0.1     4.018
V69W03    0.332   V71P11     0-0.1     4.293
V69W03    0.359   V71P16     0-0.1     2.970
V69W03    0.262   V72P1      0-0.1     1.729
V69W03    0.222   V72P2      0-0.1     1.710
V69W03    0.210   V72P3      0-0.1     1.579
V70W05    1.328   V72P4      0-0.1     4.389
V70W05    1.771   V72P5      0-0.1     5.275
V70W05    4.737   V72P6      0-0.1     4.403
V70W05    4.348   V72P7      0-0.1     6.248
V70W05    4.167   V72P8      0-0.1     3.771
V70W05    5.662   V72P9      0-0.1     2.928
V70W05    2.335   V72P10     0-0.1     2.367
V70W05    3.731   V72P11     0-0.1     2.204
V70W05    3.825   V72P12     0-0.1     2.506
V70W06    1.954   V72P13     0-0.1     3.546
V70W06    2.197   V72P14     0-0.1     4.177
V71W20    1.847   V72P15     0-0.1     3.841
V71W20    4.718   V72P16     0-0.1     6.956
V71W20    4.618   V72P19     0-0.1     2.228
V71W20    2.748   V72P20     0-0.1     1.942
V71W20    3.586   V72P21     0-0.1     2.162
V71W20    3.107   V72P22     0-0.1     3.364
V71W20    1.664   V72P23     0-0.1     4.095
V71W20    2.120   V72P24     0-0.1     4.474
V71W20    1.063   V72P26     0-0.1     4.399
V71W20    2.098   V72P37     0-0.1     7.088
V72W15    3.391   V72P38     0-0.1     6.050
V72W15    1.521   V72P39     0-0.1     9.834
V72W15    1.734   V72P40     0-0.1     6.607
V72W15    1.415   V72P41     0-0.1     8.618
V72W15    2.347   V72P42     0-0.1     8.527
V72W15    1.147
V72W15    4.171
V72W15    5.432
V72W15
V72W15

Table 2. Mean standard deviations for total organic carbon
(Dumas method) and oxidisable organic carbon (Walkley and
Black method)

Source                               Method          Mean standard
                                                    deviation (cg C
                                                    [g.sup.-1] soil)

Intra-laboratory quality              Dumas              0.076
control data from repeated
analysis of standard soil       Walkley and Black        0.101
samples used at DEDJTR
Macleod

Inter-Laboratory Proficiency          Dumas              0.122
Program reported by the
Australian Soil and Plant
Analysis Council from 1997      Walkley and Black        0.271
to 2011

Table 3. Kruskal-Wallis ranking of the precision of the analyses of 50
soil samples reported by Australasian Soil and Plant Analysis Council's
inter-laboratory proficiency program conducted from 1997 to 2011 by
five laboratories using two methods of analysing soil organic carbon

Treatment                     Rank      Mean of the       n
                                      standard errors
                                      (cg C [g.sup.-1]
                                           soil)

Walkley and Black method     107.42        0.053         42
  Laboratory 4
Dumas method Laboratory 1    112.02        0.050         49
Dumas method Laboratory 5    124.50        0.043          7
Walkley and Black method     130.52        0.049         33
  Laboratory 5
Dumas method Laboratory 4    147.70        0.065         10
Walkley and Black method     149.45        0.124         41
  Laboratory 3
Dumas method Laboratory 2    160.17        0.089         21
Walkley and Black method     176.36        0.124         40
  Laboratory 2
Walkley and Black method     193.43        0.100         48
  Laboratory 1

Table 4. Ordinary linear regression (OLR) of y on x or maximum
likelihood functional relationship (MLFR) between y on x, using the
model y = [alpha] + [beta] x with standard errors of the
coefficients ([se.sub.[alpha]] and and the probability (P) that
[alpha] = 0 or [beta] = 1, for h pairs of j and x All values of y
or x were means of two or more raw data with data on precision from
the standard error of each mean. Data were from the Australasian
Soil and Plant Analysis Council's inter-laboratory proficiency
program 1997 to 2011. TOC = Dumas method, WB = Walkley and Black
method

                                [alpha]   [se.sub.   [P.sub.
                                          [alpha]]   [alpha]]

Comparing laboratories that
were using the Dumas method
  OLR of Laboratory 2 on         0.016     0.036      0.674
  Laboratory 1 for TOC

  OLR of Laboratory 1 on        -0.010     0.036      0.795
  Laboratory 2 for TOC

  MLFR between Laboratory 2      0.037     0.008      <0.001
  and Laboratory 1 for TOC

Comparing laboratories that
were using the Walkley and
Black method
  OLR of Laboratory 4 on        -0.152     0.054      0.007
  Laboratory 1 for WB

  OLR of Laboratory 1 on         0.187     0.052      0.001
  Laboratory 4 for WB

  MLFR between Laboratory 4     -0.158     0.017      <0.001
  and Laboratory 1 for WB

  OLR of Laboratory 2 on        -0.003     0.073      0.963
  Laboratory 1 for WB

  OLR of Laboratory 1 on         0.069     0.078      0.385
  Laboratory 2 for WB

  MLFR between Laboratory 2     -0.014     0.017      0.394
  and Laboratory 1 for WB

Comparing methods in
selected laboratories
  OLR of WB on TOC for           0.194     0.043      <0.001
  Laboratory 1

  OLR of TOC on WB for          -0.192     0.052      <0.001
  Laboratory 1

  MLFR between WB and TOC        0.317     0.010      <0.001
  for Laboratory 1

  OLR of WB on TOC for           0.179     0.071      0.023
  Laboratory 2

  OLR of TOC on WB for          -0.196     0.097      0.059
  Laboratory 2

  MLFR between WB and TOC        0.230     0.017      <0.001
  for Laboratory 2

Comparing methods
and laboratories
  OLR of WB for Laboratory 2     0.146     0.063      0.026
  on TOC for Laboratory 1

  OLR of TOC for Laboratory 1   -0.120     0.081      0.149
  on WB for Laboratory 2

  MLFR between WB for            0.260     0.008      <0.001
  Laboratory 2 and TOC for
  Laboratory 1

                                [beta]    [se.sub.   [P.sub.   n
                                          [beta]]    [beta]]

Comparing laboratories that
were using the Dumas method
  OLR of Laboratory 2 on         1.010     0.011      0.375    21
  Laboratory 1 for TOC

  OLR of Laboratory 1 on         0.988     0.011      0.274    21
  Laboratory 2 for TOC

  MLFR between Laboratory 2      0.986     0.004      0.002    21
  and Laboratory 1 for TOC

Comparing laboratories that
were using the Walkley and
Black method
  OLR of Laboratory 4 on         0.980     0.019      0.301    42
  Laboratory 1 for WB

  OLR of Laboratory 1 on         1.006     0.019      0.767    42
  Laboratory 4 for WB

  MLFR between Laboratory 4      1.019     0.010      0.065    42
  and Laboratory 1 for WB

  OLR of Laboratory 2 on         0.911     0.025      0.001    39
  Laboratory 1 for WB

  OLR of Laboratory 1 on         1.069     0.029      0.021    39
  Laboratory 2 for WB

  MLFR between Laboratory 2      0.899     0.011     <0.001    39
  and Laboratory 1 for WB

Comparing methods in
selected laboratories
  OLR of WB on TOC for           0.867     0.014     <0.001    48
  Laboratory 1

  OLR of TOC on WB for           1.140     0.019     <0.001    48
  Laboratory 1

  MLFR between WB and TOC        0.777     0.004     <0.001    48
  for Laboratory 1

  OLR of WB on TOC for           0.769     0.021     <0.001    19
  Laboratory 2

  OLR of TOC on WB for           1.285     0.034     <0.001    19
  Laboratory 2

  MLFR between WB and TOC        0.746     0.010     <0.001    19
  for Laboratory 2

Comparing methods
and laboratories
  OLR of WB for Laboratory 2    0.7960     0.020     <0.001    40
  on TOC for Laboratory 1

  OLR of TOC for Laboratory 1   1.2281     0.030     <0.001    40
  on WB for Laboratory 2

  MLFR between WB for           0.76635    0.004     <0.001    40
  Laboratory 2 and TOC for
  Laboratory 1

Table 5. Regression using ordinary linear regression (OLR) or
maximum likelihood functional relationship (MLFR) of y (Walkley and
Black method) on x (Dumas method) using the model y = [alpha] +
[beta] x with standard errors of the coefficients ([se.sub.[alpha]]
and [se.sub.[beta]]) and the probability (P) that [alpha] = 0 or
that [beta] = 1, with different sources of data on precision as
shown in Table 2

                                      [alpha]   [se.sub.   [P.sub.
                                                [alpha]]   [alpha]]

OLR of v on x for both land uses      -0.064     0.040      0.119

OLR of x on y for both land uses       0.112     0.041      0.007

MLFR between y and x with             -0.071     0.040      0.080
precision data from ILPP for both
land uses

MLFR between y and x with             -0.067     0.038      0.082
precision data from DEDJTR MacLeod
for both land uses

OLR of y on x for data from           -0.047     0.013      <0.001
crop soils only

MLFR between y and x for crop          0.126     0.075      0.515
soils only with precision data
from ILPP

MLFR between y and x for crop         -0.048     0.0720     0.508
soils with precision data from
DEDJTR MacLeod

OLR of y on x for soils under          0.126     0.103      0.227
pasture

MLFR between y and x for soils         0.102     0.0793     0.202
under pasture with precision data
from ILPP

MLFR between y and x for soils         0.116     0.0754     0.130
under pasture with precision data
from DEDJTR MacLeod

                                      [beta]   [se.sub.   [P.sub.
                                               [beta]]    [beta]]

OLR of v on x for both land uses      0.960     0.013     <0.001

OLR of x on y for both land uses      1.020     0.014     <0.001

MLFR between y and x with             0.964     0.013      0.006
precision data from ILPP for both
land uses

MLFR between y and x with             0.962     0.012      0.002
precision data from DEDJTR MacLeod
for both land uses

OLR of y on x for data from           0.803     0.023     <0.001
crop soils only

MLFR between y and x for crop         0.806     0.129      0.138
soils only with precision data
from ILPP

MLFR between y and x for crop         0.804     0.124      0.120
soils with precision data from
DEDJTR MacLeod

OLR of y on x for soils under         0.921     0.025      0.003
pasture

MLFR between y and x for soils        0.928     0.019     <0.001
under pasture with precision data
from ILPP

MLFR between y and x for soils        0.924     0.018     <0.001
under pasture with precision data
from DEDJTR MacLeod
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Author:Crawford, D.M.; Norng, S.; Kitching, M.; Robinson, N.
Publication:Soil Research
Article Type:Case study
Geographic Code:8AUST
Date:Nov 1, 2018
Words:7670
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