Disaggregation of legacy soil data using area to point kriging for mapping soil organic carbon at the regional scale
Highlights
► Determining ways to disaggregate and use legacy data in regression kriging (RK). ► Area to point kriging (AtoP) is used to disaggregate legacy data from polygon maps. ► Using legacy data disaggregated by simple rasterization in RK reduces errors. ► Using AtoP disaggregated legacy data in RK reduces errors further. ► As few as 300 samples can be used to map soil organic matter for all Northern Ireland.
Introduction
In traditional soil survey, surveyors use their knowledge of soil forming factors combined with aerial photographs and field-based soil observations to delineate soil classes as polygons on a map. Typical soil profiles of these classes are often described and published as a memoir which may include values of key soil properties at various depths. This traditional approach gives no indication of variability in these soil properties within or between classes and it has no statistical basis which can lead to bias (Carré et al., 2007a). In the last 10–15 years the need for raster based digital soil maps has been emphasized and a digital soil mapping (DSM) approach has been developed (McBratney et al., 2003). Such maps have pixels of different sizes depending on the scale of interest and have values of key soil properties, such as soil organic carbon (SOC) concentration, available at several depths (McBratney et al., 2003). More specifically, DSM has been defined as the creation and population of spatial soil information by the use of field and laboratory observational methods coupled with spatial and non-spatial soil inference systems (Carré et al., 2007b, Lagacherie and McBratney, 2007).
Polygon maps representing soil classes at various levels of national or international classification systems exist in many locations. Effective methods are required for the disaggregation and incorporation of such a wealth of ‘legacy soil data’ into DSM at national and regional scales. Appropriate use of this historical data could ensure that additional sampling effort associated with modern digital soil mapping is minimized. De Bruin et al., 1999, Eagleson et al., 1999 proposed approaches that use hierarchical spatial reasoning for disaggregation of soil polygons. Bui and Moran (2001) investigated some such methods empirically along with other methods for spatial disaggregation of soil polygon maps in the Murray–Darling basin, Australia.
The theoretical merits of several forms of spatial disaggregation were investigated by McBratney (1998); the author suggested transfer functions and pycnophylactic interpolation should be applied. Mass preservation in pycnophylactic methods (Tobler, 1979) means that the mass or values over all the finer pixels contained within a polygon is preserved; in other words the average of the values in the finer pixels gives the polygon value. McBratney (1998) noted that the mass preservation property of pycnophylactic splines is a useful feature for disaggregating soil data as it could make transitions between scales in DSM more sensible. This could mean that intense sampling at each scale is not essential. Mass preservation is also a feature of the recently developed geostatistical approach of area to point kriging (Kyriakidis, 2004). The typical centroid-based approach to kriging from areas to points assumes that the spatial support of units is constant (Goovaerts, 2006). Hence it is not appropriate for use with polygon data of varying shape and size (Gotway and Young, 2002). The advantage of AtoP kriging is that it incorporates the variable size and shape of polygons in variogram deconvolution and kriging. Recently, Goovaerts, 2010, Goovaerts, 2011 used AtoP and regression kriging (RK) to incorporate both point field measurements and areal data (calibration of geological map) in the spatial interpolation of heavy metals in the Swiss Jura. Sensitivity analysis indicated that these new kriging procedures improve prediction over ordinary kriging and traditional RK based on the assumption that the local mean is constant within each mapping unit. To our knowledge, the advantages associated with AtoP kriging have not been used for disaggregating legacy soil maps and for optimizing DSM or compared to current state-of-the-art methods in DSM.
Current DSM methods in more data-rich settings include RK (McBratney et al., 2003) to map variation in important soil properties such as organic carbon based on ancillary data. Soil organic carbon is arguably one of the most important soil properties due to the benefits it confers such as enhancing soil structure through aggregation, improved water holding and cation-exchange capacities and also acting as a store of terrestrial carbon. In a recent study, two types of ancillary data (altitude and airborne radiometric measurements of potassium) were shown to be effective for improved mapping of soil organic carbon across all of Northern Ireland within a RK framework (Rawlins et al., 2009). However, the authors did not incorporate disaggregated legacy data into their procedure.
In this study we use area to point (AtoP) kriging to disaggregate soil organic carbon (SOC) data from a polygon map and compare it with disaggregation by simple rasterization of the same data. We also compare these methods with AtoP regression kriging (AtoP RK) which includes some hierarchical spatial reasoning in the disaggregation process (Liu et al., 2008, Yoo and Kyriakidis, 2009). In this approach, ancillary data are used to inform on within-class variation in key scorpan factors (McBratney et al., 2003) such as relief and parent material, i.e. they provide a local mean and the residuals are AtoP kriged. The errors involved with each disaggregation approach are investigated. We then use the same regression models and data as Rawlins et al. (2009), but we add legacy map SOC data disaggregated by simple rasterization (polygon SOC) and AtoP kriging (AtoP SOC) as extra fixed effects in RK. This two-step approach (Liu et al., 2008) to incorporating legacy data into RK was used to allow direct comparison with the results of Rawlins et al. (2009), however, there is no guarantee that the pycnophylactic or mass preserving property of AtoP kriging is preserved with a two-step AtoP RK procedure. Goovaerts, 2010, Goovaerts, 2011 introduced an approach where point and areal data are incorporated in one-step (i.e. one kriging system solved) instead of the two-step approaches (AtoP kriging followed by RK kriging) used here. Although this methodology, coined area-and-point (AAP) kriging, is theoretically more efficient than a two-step approach, and is pycnophylactic, it is not currently available in commercial software.
The errors associated with incorporating polygon SOC and AtoP SOC into RK using the six models of Rawlins et al. (2009) are investigated and a suitable number of samples for mapping SOC across Northern Ireland based on the available covariates is suggested. We comment on the benefits for DSM of disaggregating data from legacy soil polygon maps using simple rasterization, AtoP kriging and AtoP RK and incorporating the former two types of disaggregated legacy data into RK.
Section snippets
Area to point kriging
Consider the problem of estimating the value of a soil property z at any location us within a study area A from a set of B areal data {z(vβ); β = 1,…,B}. These areal or legacy soil polygon map data are typically measured on spatial supports (mapping units) vβ of various sizes and shapes. Area to point (AtoP) kriging can be viewed as the counterpart of block kriging in that point estimates zAtoP*(us) are obtained as the following linear combination of areal (block) measurements:
Soil sampling
The soil sampling was undertaken between July 2004 and March 2006 comprising the collection of a sample of topsoil from a site in every other square kilometer of the Irish National Grid, by simple random selection within each square, subject to the avoidance of roads, tracks, railways, urban areas and other seriously disturbed ground. This was part of the Tellus survey of Northern Ireland http://www.bgs.ac.uk/gsni/tellus/. There were 6862 sample sites in total. At each site soil was taken with
Disaggregation of legacy soil polygon map data
Table 2 shows the MAEs based on disaggregation of the SOC data from the legacy soil polygon map. When all soil types are considered, simple rasterization (polygon SOC) has slightly smaller MAEs than AtoP SOC. However, while the MAEs are similar for mineral and peat soils for AtoP SOC and polygon SOC (around 4 and 18%, respectively), the AtoP disaggregation method has substantially smaller MAEs (13.0%) for organo-mineral soils than the polygon SOC approach (15.2%). The lowest MAEs in each soil
Conclusions
Our analysis shows that for disaggregating legacy SOC data from a polygon map, an AtoP RK approach is more effective than simple rasterization. An AtoP RK approach is theoretically sound because it allows for within class variability, spatial autocorrelation and scorpan factors as represented by ancillary data. In the case of estimating SOC concentrations across Northern Ireland, the AtoP RK approach does not require the collection and use of new soil measurements, but could produce overall
Acknowledgements
We thank Michael Young of the Geological Survey of Northern Ireland for arranging access to the Tellus data. The Tellus project was funded by the Department of Enterprise, Trade and Investment and by the Building Sustainable Prosperity Scheme of the Rural Development Programme (Department of Agriculture and Rural Development of Northern Ireland). Topographic data are based upon Ordnance Survey of Northern Ireland's data with the permission of the Controller of Her Majesty's Stationery Office, ©
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2021, GeodermaCitation Excerpt :For instance, variation in soil carbon at the farm-scale is largely driven by texture and micro-organisms while these factors are less important at continental scale, where climate and vegetation are dominant (Wiesmeier et al., 2019). Geostatistics has since long developed block kriging to aggregate from fine to coarse support (e.g. Burgess and Webster, 1980), while spatial disaggregation using area-to-point kriging developed much later (e.g. Kerry et al., 2012). Techniques to spatially disaggregate polygon soil type maps were also developed (e.g. Odgers et al., 2014).