European Journal of Soil Science, June 2010, 61, 333–347 doi: 10.1111/j.1365-2389.2010.01232.x Pedometric mapping of soil organic matter using a soil map with quantified uncertainty B. Kempena,b , G. B. M. Heuvelinka,b ,D.J.Brusb & J. J. Stoorvogela aWageningen University, Land Dynamics Group, PO Box 47, 6700 AA Wageningen, the Netherlands, and bAlterra, Soil Science Centre, Wageningen University and Research Centre, PO Box 47, 6700 AA Wageningen, the Netherlands Summary This paper compares three models that use soil type information from point observations and a soil map to map the topsoil organic matter content for the province of Drenthe in the Netherlands. The models differ in how the information on soil type is obtained: model 1 uses soil type as depicted on the soil map for calibration and prediction; model 2 uses soil type as observed in the field for calibration and soil type as depicted on the map for prediction; and model 3 uses observed soil type for calibration and a pedometric soil map with quantified uncertainty for prediction. Calibration of the trend on observed soil type resulted in a much stronger predictive relationship between soil organic matter content and soil type than calibration on mapped soil type. Validation with an independent probability sample showed that model 3 out-performed models 1 and 2 in terms of the mean squared error. However, model 3 over-estimated the prediction error variance and so was too pessimistic about prediction accuracy. Model 2 performed the worst: it had the largest mean squared error and the prediction error variance was strongly under-estimated. Thus validation confirmed that calibration on observed soil type is only valid when the uncertainty about soil type at prediction sites is explicitly accounted for by the model. We conclude that whenever information about the uncertainty of the soil map is available and both soil property and soil type are observed at sampling sites, model 3 can be an improvement over the conventional model 1. Introduction Several studies showed that combining maps of soil type with soil property information from point observations can improve Although soil maps typically describe the spatial variation of soil spatial prediction of soil properties compared with prediction types, they are also an important source of information on spa- from a soil map only (Voltz & Webster, 1990; Heuvelink & tial variation of quantitative soil properties (Bregt & Beemster, Bierkens, 1992; Goovaerts & Journel, 1995; Brus et al., 1996; 1989; Van Meirvenne et al., 1994; Liu et al., 2006). A commonly Heuvelink, 1996; Oberthur¨ et al., 1999). Typically, a regression used method for spatial prediction of soil properties is to use a model is calibrated by using mapped soil type as predictor, ‘representative’ value for each map unit of the soil map (Leen- followed by kriging the residuals (Hengl et al., 2004; Liu et al., hardt et al., 1994; Brus et al., 1996; Voltz et al., 1997; Webster & 2006). However, the strength of the relationship between soil Oliver, 2007). These values are obtained from soil profile descrip- property and mapped soil type depends on the accuracy of the tions in soil survey reports or are provided by experienced soil soil type map. Large impurities in the map units might result surveyors. Goovaerts & Journel (1995) pointed out two weak- in a weak relationship, even when the relationship between soil nesses of this mapping approach: (i) it results in abrupt transitions property and the observed ‘true’ soil type is strong. in the predicted value from one soil type to another, which are When both soil property and soil type are observed at sampling unrealistic in landscapes where lateral changes in soil are gradual; sites, the regression model can be calibrated by using observed soil and (ii) it ignores spatial variation of the soil property within the type (e.g. Meersmans et al., 2009). This can improve the regres- map units. Marsman & De Gruijter (1986) found that within-map sion because the relationship between soil property and observed unit variation of soil properties ranged between 65 and 80% of soil type is not confounded by impurities in the soil map units. the total variation in a 1600 ha sandy area in the Netherlands. However, for spatial prediction the calibrated relationship has to be applied to the soil map because the true soil type is unknown Correspondence: B. Kempen. E-mail: [email protected] at unsampled prediction sites. Using hard information (observed Received 20 July 2009; revised version accepted 26 January 2010 soil type) for calibration and soft information (mapped soil type) © 2010 The Authors Journal compilation © 2010 British Society of Soil Science 333 334 B. Kempen et al. for prediction has the undesirable consequence that the prediction sampling site the residual is computed by subtracting the mean error variance will be under-estimated because the uncertainty in a(sk) from the measured soil property value z(sk). The residual is the map units of the soil map is not accounted for by the model. standardized by division with the standard deviation b(sk). Next Furthermore, a strong, informative, relationship between soil prop- the spatial structure of the standardized residuals is modelled with erty and soil type is applied to a soil map that is less informative a variogram. The sill of the variogram is known to be 1, and the about the soil property. Thus to take advantage of a calibration on remaining variogram parameters are estimated from the sample true soil type for spatial prediction, the true soil type at the predic- of residuals. Residuals at unsampled sites can then be predicted tion sites must be used. The true soil type is typically unknown but using simple kriging. Next the soil property Z at a prediction site it can be represented with a probability model. When a probability s0 is predicted by back-transformation of the kriged residual using model is available, this may be used for spatial prediction of the b(s0) and a(s0) (Goovaerts, 1997): soil property. Probability distributions of soil type can be obtained from soil maps produced using pedometric methods such as indi- n ˆ = · · + cator kriging (Goovaerts & Journel, 1995; Oberthur¨ et al., 1999), z(s0) b(s0) λk ε(sk) a(s0), (2) = Bayesian maximum entropy (Brus et al., 2008) or multinomial k 1 logistic regression (Debella-Gilo & Etzelmuller,¨ 2009; Kempen where z(ˆ s ) is the predicted soil property value at s , ε(s ) is the et al., 2009). Soil survey reports accompanying traditional soil 0 0 k observed residual at sampling site s and λ is the simple kriging maps often provide areal estimates of the soil types occurring k k weight assigned to the residual at s . The prediction error variance within the map units (Soil Survey Staff, 1993). Such information k at s is calculated as: may be used to define a frequency distribution for each map unit 0 that can serve as a probability distribution at any location within = · ˆ − that map unit. V(s0) var(b(s0) [ε(s0) ε(s0)]) In the present paper we present a model for spatial prediction 2 = b (s0)var[ε(ˆ s0) − ε(s0)], (3) of quantitative soil properties that uses a soil type map with quan- tified uncertainty (i.e. a map that represents true soil type at each where var[ε(ˆ s0) − ε(s0)] is the simple kriging variance. location with a probability distribution). We illustrate the model Prediction of soil property Z at each site s0 requires estimates for spatial prediction of the organic matter content of the topsoil of a(s0)andb(s0). We will now discuss three models for (0–30 cm) in the province of Drenthe in the Netherlands. For prediction of Z where these model parameters are a function of this province a pedometric soil map is available with location- the categorical explanatory variable ‘soil type’. The models differ specific probability distributions of 10 major soil types (Kempen in the source from which the soil type information is obtained to et al., 2009), as well as a large data set with point observations estimate a(s ) and b(s ). on soil organic matter (SOM) and soil type. The prediction model 0 0 In this paper we assume that a(s ), b(s ) and the variogram is calibrated with soil type information from these point observa- 0 0 are estimated without error: a(ˆ s ) and b(ˆ s ) are substituted into tions and is subsequently applied to the pedometric soil type map 0 0 Equations (2) and (3) as if these are the true values to obtain the for spatial prediction of the SOM content. Model performance is prediction of soil property Z and the prediction error variance. validated with an independent probability sample and compared Ignoring the estimation error of the model parameters simplifies with results from (i) the conventional model that uses mapped soil modelling dramatically but is generally unrealistic and affects the type (i.e. the soil type with the largest probability) for calibration model outcome. We will return to this assumption in the results and prediction and (ii) the theoretically flawed model that uses and discussion section. observed soil type at sampling sites for calibration and the soil type as depicted on the map for prediction. Model 1: Parameter estimation and prediction using soil type Theory information from a soil map We assume the following model of spatial variation of a soil Suppose that a soil map is available that distinguishes M soil property Z: types, m = 1, 2,...,M, and that specifies the soil type cmap(s) at each site s ∈ D.