Space-time Kalman filtering of soil redistribution

G.B.M. Heuvelink, J.M. Schoorl, A. Veldkamp, D.J. Pennock

Research output: Contribution to journalArticleAcademicpeer-review

23 Citations (Scopus)


Soil redistribution is the net result of erosion and sedimentation. Assessment of soil redistribution in a given landscape over a given period of time may be done using process-based and empirical approaches. Process-based approaches rely on knowledge of how environmental processes acting in the landscape cause soil to move from one place to another. Empirical approaches rely on measurements of soil redistribution, which may be interpolated in space and time using (geo)statistical methods. In this paper we use space¿time Kalman filtering to combine these two basic approaches. The Kalman filter operates recursively to predict forward one step at a time the soil redistribution from the predicted soil redistribution at the previous time and the measurements at the current time. The methodology is illustrated with a case study from a seven hectare segment site, located on the hummocky till plains of Saskatchewan, Canada. Tillage erosion causes soil to move downward along the steepest gradient, whereby the amount of soil loss per year is assumed linearly related to slope angle. Measurements of cumulative soil redistribution from 1963 to 2000 were derived using Cesium-137 as a tracer. In total 99 measurements were taken, using a regular sampling design with a grid mesh of 25 m. The soil redistribution measurements differed meaningfully from the deterministic model predictions (R2 = 0.389), causing the Kalman filter to make a marked adjustment to the soil redistribution map. The adjustment was particularly strong along the transportation route near the measurement locations. Use of the space¿time Kalman filter to predict soil redistribution is attractive because it makes optimum use of process knowledge and measurements, but routine use of the technique is hampered by the computational load and by parameterisation problems. Sensitivity analyses showed that the model results are most sensitive to the system noise. Future research must therefore be directed to realistic assessment of the errors inflicted by the assumptions and simplifications of the soil redistribution model
Original languageEnglish
Pages (from-to)124-137
Issue number1-2
Publication statusPublished - 2006


  • landscape evolution
  • elevation models
  • tillage erosion
  • cesium-137
  • geostatistics
  • water
  • assimilation
  • movement
  • patterns
  • moisture

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