Some spatial modelling examples

Marian Scott

SAGES March 2009

ECCOMAGS Project

• Funded by EC FPV – Nuclear Safety,

• Partners– BfS (Germany), CEA (France), DEMA/DTU (Denmark),

GBA (Austria), HSK (Switzerland), IGM (Portugal), SSI (Sweden), SGU (Sweden), STUK (Finland), SURRC (UK)

• Airborne Gamma-ray Spectrometry (AGS)• To assess comparability of the European AGS

systems• To assess comparability of AGS with ground-

based systems.

Exercise Survey Areas

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Dumfries

StranraerWigtownMerse

Inch Farm

CastleKennedy

ECCOMAGS Exercise : Survey Areas

Solway Firth

Dumfries and Galloway Region

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Ground sampling locations

Pre-Characterisation-sampling plan for in-situ measurement

• Expanding hexagonal sampling pattern showing the radial numbers and shell designations.

137Cs Map 6th June

Area X – 137Cs

137Cs regridded maps – Area Y

137Cs regridded maps – Area Z

Shape Analysis – Wigtown Merse

Team P (km) A (km2) P/A (km-1)

BFSA 10.20 2.68 3.81

BFSB 10.00 2.42 4.13

CEA 8.40 1.31 6.41

DEMA 8.60 2.57 3.35

SGU 7.80 1.04 7.50

SSI 9.40 1.56 6.03

SURRC 9.00 2.14 4.21

Mean 10.00 2.14 4.67

Map 12.00 1.46 8.22

Lochs in area Y

Example: Mapping SO2 over Europe and through time

How has SO2 levels changed over time as a result of international agreements?

How is SO2 distributed over Europe?

At each time point a plane across space was fitted and Gaussian Variograms of the residuals were computed. The average of the variogram parameters’ estimates were used to obtain the spatial

covariance matrix .

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observed values of SO2 May 1991

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estimated trend of SO2 May 1991

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observed values of SO2 September 1998

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estimated trend of SO2 September 1998

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Spatial Analysis Across TimeSpatial Analysis Across Time

Example: River quality over a river basin

How have nitrate levels changed over time as a result of changes in management and diffuse pollution control?

How are nitrate levels distributed over river basin?

network design-ECN

• try the Mururoa and Rosyth examples again and look at the map that is produced and compare it with the truth

Example: 60Co activity in sediment of an estuary

Suppose wanted to estimate the inventory of 60Co in the sediments of an estuary whose boundaries have been clearly defined. We know that 60Co is particle reactive and we have a map of sediment type in the estuary.

How would we make use of this information?

Stratified sampling chosen

Example: tritium in a South Pacific atoll

Suppose wanted to map the distribution of tritium inside and atoll (tritium in sea water). This will require us to collect water samples. How should we do this?

Transect sampling chosen

Summary

• Spatial modelling is an important skill, since much environmental data are spatially registered

• the complexities include describing the spatial correlation structure and considering if there is a temporal component how this can be modelled.