by Bas Kempen

SUMMARY: A two-day workshop on “Spatial Uncertainty Propagation” was held before the start of the biennial Pedometrics conference in Tübingen, Germany. The workshop gathered 18 participants from various universities and research institutes from four continents. The tutors Gerard Heuvelink and James Brown had compiled a varied program with lectures, pen-and-paper exercises and computer practicals. The workshop focused on uncertainty propagation of continuous variables in a simple environmental model. Software packages DUE and R were used to build probability models of the data and to perform uncertainty propagation analyses. In this short report you can find more information on the workshop program, some examples of the output and some pictures.

1. Backgrounds

It has become tradition to organize a two-day workshop before the start of the biennial Pedometrics conference. The aim of the pre-conference workshop is to introduce one topic from the broad pedometric spectrum on a basic level. The topic of the workshop of Pedometrics 2007 was “Spatial Uncertainty Propagation” and was held at the Institute of Geography of the University of Tübingen in Germany. Eighteen participants gathered and were introduced to uncertainty propagation analysis by Gerard Heuvelink of Wageningen University and Research Centre and James Brown of the National Oceanic and Atmospheric Administration in Washington D.C.

The workshop started with a lecture on the definition of uncertainty, ways to represent uncertainty in spatial data and Taylor series approximation for uncertainty propagation analysis. The lecture was illustrated by pen-and-paper exercises and a computer practical in R on uncertainty propagation through a very simple model of lead ingestion by children:

I = PB * S,

where I is the lead ingestion, PB the soil lead concentration, and S the soil ingestion of a child. A small dataset from the southern part of the Netherlands was used for the exercises. The soil lead concentration was mapped by kriging point observations in R. Taylor series approximation was used to analyze how uncertainty in soil lead concentration, represented by the kriging variance, propagates to lead ingestion. The results are shown in Figure 1. The first day of the workshop ended with an introduction of DUE, the Data Uncertainty Engine software tool developed by James and Gerard. DUE is designed to help users define, assess, store and simulate uncertain spatio-temporal environmental data.

Figure 1. Results of uncertainty propagation analysis with Taylor series approximation. The left figure shows the lead ingestion by children (µg/day). The right figure shows the standard deviation of the lead ingestion.

During the second day of the workshop uncertainty propagation was analyzed with the Monte Carlo method. DUE was used to build probability models of uncertain variables S and PB of the lead ingestion model, and to generate realizations of the uncertain variables. The simulated soil ingestion and soil lead concentration values were used in R in a Monte Carlo uncertainty propagation analysis. The results are shown in Figures 2 and 3.

Figure 2. Results of uncertainty propagation analysis with the Monte Carlo method. The left figure shows the lead ingestion by children (µg/day). The right figure shows the standard deviation of the lead ingestion.

Figure 3. Left: Probability of exceeding the acceptable lead intake (50 µg/day). Right: Probability that lead intake is larger than the acceptable daily intake = 5% (yellow area).

2. Final notes

The workshop was concluded with an exercise on terrain uncertainty. A DEM and dataset with sampled elevation errors from the Baranja Hills in Eastern Croatia was used to simulate uncertainty in elevation. Again DUE was used to build a probability model of the elevation using the sampled errors, and to generate realizations of the DEM.

Gerard and James gave an excellent introduction of spatial uncertainty propagation to enthusiastic participants. The program contained a well-balanced mix of lectures, powerful pen-and-paper exercises and computer practicals. The workshop provided the participants with enough knowledge to carry out basic uncertainty propagation analyses on their own spatial data. On behalf of the workshop participants I would like to thank Gerard, James and the organizing committee of Pedometrics 2007 for the successful start of Pedometrics 2007.

Finally, some pictures of the workshop!

References:

1. Brown, J.D. and Heuvelink, G.B.M. 2007. The Data Uncertainty Engine (DUE): A software tool for assessing and simulating uncertain environmental variables. Computers & Geosciences, 33(2): 172-190.
2. Heuvelink, G.B.M. 1998. Error Propagation in Environmental Modelling with GIS. Taylor and Francis, London (1998) 144 pp.
3. Heuvelink, G.B.M. 2002. Analysing uncertainty propagation in GIS: why is it not that simple?. In: G.M. Foody and P.M. Atkinson, Editors, Uncertainty in Remote Sensing and GIS, Wiley, Chichester (2002), pp. 155–165.
4. Heuvelink, G.B.M., Brown, J.D., Van Loon, E.E., 2006a. A Probabilistic framework for representing and simulating uncertain environmental variables. International Journal of Geographic Information Science, in press.