Oblique coordinates as covariates for digital soil mapping

Activity: Talk or presentation typesLecture and oral contribution


• We generate sets of oblique geographic coordinates as covariates for Random Forest predictions.
• We test the method for predicting soil organic matter contents for an agricultural field in Denmark.
• The oblique coordinates effectively eliminate orthogonal artefacts from the map.
• They also increase the accuracy relative to maps generated with x- and y-coordinates.

The inclusion of an explicit spatial component into decision tree predictions for digital soil mapping remains a challenge. Studies have shown that x and y coordinates as covariates results in unrealistic orthogonal artefacts in the resulting maps (Hengl et al., 2018, Nussbaum et al., 2018). Hengl et al. (2018) instead proposed the use of buffer distances to the training points as covariates, referred to as Spatial Random Forest (RFsp). A disadvantage of RFsp is that it requires the calculation of buffer distances to every observation in the training data. RFsp therefore becomes computationally expensive with large datasets.
As an alternative, we propose several sets of coordinates at oblique angles as covariates for Random Forest predictions of soil properties. We test this approach for the prediction of soil organic matter (SOM) in a densely sampled agricultural field in Denmark. A previous study showed that kriging was the most accurate prediction technique for this field, yielding more accurate results than Random Forest and Cubist models with kriged residuals.
The use of oblique coordinates effectively eliminated orthogonal artefacts from the output maps. Moreover, even with a small number of oblique coordinates, the predictions were on par with the predictions previously obtained with kriging. Moreover, using the oblique coordinates in conjunction with covariates derived from a DEM and proximal and remote sensors further increased accuracy. In effect, the use of oblique coordinates makes Random Forest the most accurate method for predicting SOM in this field.
Oblique coordinates are a likely candidate for a generic implementation of a spatial component for Random Forest models in digital soil mapping. It eliminates orthogonal artefacts from the predictions, is computationally efficient and highly accurate. Furthermore, it may be useful for data with a high degree of anisotropy and variable spatial relationships.

Hengl, T., Nussbaum, M., Wright, M.N., Heuvelink, G.B. and Gräler, B., 2018. Random forest as a generic framework for predictive modeling of spatial and spatio-temporal variables. PeerJ 6, e5518. http://dx.doi.org/10.7717/peerj.5518.
Nussbaum, M., Spiess, K., Baltensweiler, A., Grob, U., Keller, A., Greiner, L., Schaepman, M.E. and Papritz, A., 2018. Evaluation of digital soil mapping approaches with large sets of environmental covariates. Soil 4(1), 1-22. http://dx.doi.org/10.5194/soil-4-1-2018.
Period3 Jun 2019
Event titlePedometrics
Event typeConference
LocationGuelph, Ontaria, CanadaShow on map
Degree of RecognitionInternational


  • Random Forest
  • RFsp
  • kriging
  • SOM
  • geographic space