Spatial Interpolation Comparison
Evaluation of spatial prediction methods
Tomislav Hengl
ISRIC — World Soil Information, W...
Based on
Hengl, T., MacMillan, R.A., 2011? Mapping efficiency and
information content. submitted to International Journal of...
Topic
Geostatistics = a toolbox to generate maps from point data
i.e.to interpolate;
Geostatistics course, 25–29 October 2...
Topic
Geostatistics = a toolbox to generate maps from point data
i.e.to interpolate;
There are many possibilities;
Geostat...
Topic
Geostatistics = a toolbox to generate maps from point data
i.e.to interpolate;
There are many possibilities;
An inex...
Topic
Geostatistics = a toolbox to generate maps from point data
i.e.to interpolate;
There are many possibilities;
An inex...
Have you heard of SIC?
Geostatistics course, 25–29 October 2010, Wageningen
The spatial prediction game
Participants were invited to estimate values located at 1000
locations (right, crosses), using...
Lessons learned (from SIC)
Geostatistics course, 25–29 October 2010, Wageningen
Li and Heap (2008)
Geostatistics course, 25–29 October 2010, Wageningen
How many techniques are there?
Li and Heap (2008) list over 40 unique techniques.
1. Are all these equally valid?
2. How t...
There are not as many
There are roughly five main clusters of techniques:
1. splines (deterministic);
Geostatistics course,...
There are not as many
There are roughly five main clusters of techniques:
1. splines (deterministic);
2. kriging-based (pla...
There are not as many
There are roughly five main clusters of techniques:
1. splines (deterministic);
2. kriging-based (pla...
There are not as many
There are roughly five main clusters of techniques:
1. splines (deterministic);
2. kriging-based (pla...
There are not as many
There are roughly five main clusters of techniques:
1. splines (deterministic);
2. kriging-based (pla...
The 5 criteria
1. the overall mapping accuracy, e.g.standardized RMSE at
control points — the amount of variation explaine...
The 5 criteria
1. the overall mapping accuracy, e.g.standardized RMSE at
control points — the amount of variation explaine...
The 5 criteria
1. the overall mapping accuracy, e.g.standardized RMSE at
control points — the amount of variation explaine...
The 5 criteria
1. the overall mapping accuracy, e.g.standardized RMSE at
control points — the amount of variation explaine...
The 5 criteria
1. the overall mapping accuracy, e.g.standardized RMSE at
control points — the amount of variation explaine...
Can we simplify this?
1. In theory, we could derive a single composite measure that
would then allow you to select ‘the op...
Automated mapping
In the intamap package1 decides which method to pick for you:
> meuse$value <- log(meuse$zinc)
> output ...
Hypothesis
We need a single criteria to compare various prediction methods.
Geostatistics course, 25–29 October 2010, Wage...
Mapping accuracy and survey costs
The cost of a soil survey is also a function of mapping scale,
roughly:
log(X) = b0 + b1...
Survey costs and mapping scale
q
q
q
q
q
9.5 10.0 10.5 11.0 11.5 12.0 12.5
−10123
Scale number (log−scale)
Minimumsurveyco...
Survey costs and mapping scale
Total costs of a soil survey can be estimated by using the size of
area and number of sampl...
Converges to:
X = exp 19.0825 − 1.6232 · log 0.0791 ·
A
N
· 102
(4)
Geostatistics course, 25–29 October 2010, Wageningen
Output map, from info perspective
The resulting (predictions) map is a sum of two signals:
Z∗
(s) = Z(s) + ε(s) (5)
where ...
Prediction accuracy
In order to see how much of the global variation budget has been
explained by the model we can use:
RM...
Kriging efficiency
Geostatistics course, 25–29 October 2010, Wageningen
Mapping efficiency
We propose two new measures of mapping success: (1) Mapping
efficiency, defined as the amount of money neede...
Information production efficiency
(2) Equivalent measure of mapping efficiency is the information
production efficiency:
Υ =
X
g...
Effective precision
Following the Nyquist frequency concept from signal processing,
which states that the original signal c...
Nyquist frequency concept
q
q
qq
q
qq q
q
q
q
q q
qqq
q
q qq
q
qq q
q
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q
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q q
q
q
q q qqq q q
q
q
qq
Figure: Th...
Rounding numbers
Original data
2.25 4.08 6.25 4.23 2.56 1.21 0.98 0.98 0.85 0.4
4.24 4.69 7.17 4.37 2.08 1.4 1.44 0.96 0.8...
Exercise
To follow this exercise, obtain the DSM_examples.R script.
Download it to your machine and then run step-by-step....
Meuse data
> data(meuse)
> coordinates(meuse) <- ~x+y
> proj4string(meuse) <- CRS("+init=epsg:28992")
> sel <- !is.na(meus...
Meuse
+
+ +
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++
+
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+ +++
+
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...
Eberg¨otzen (subset)
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...
Eberg¨otzen (subset)
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Eberg¨otzen (complete)
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OK vs RK
2.0 2.5 3.0 3.5
0.00.20.40.60.81.0
Sampling intensity (log)
Amountofvariationexplained
Ordinary kriging Regressio...
Prediction accuracy and survey costs
Geostatistics course, 25–29 October 2010, Wageningen
Summary results
For the two case studies there is a gain of 7% for mapping
organic matter (Meuse), and 13% and for mapping...
Summary results
For the two case studies there is a gain of 7% for mapping
organic matter (Meuse), and 13% and for mapping...
Summary results
For the two case studies there is a gain of 7% for mapping
organic matter (Meuse), and 13% and for mapping...
Conclusions
Mapping efficiency (cost / area / percent of variance
explained) is a possible universal criteria to compare pre...
Conclusions
Mapping efficiency (cost / area / percent of variance
explained) is a possible universal criteria to compare pre...
Conclusions
Mapping efficiency (cost / area / percent of variance
explained) is a possible universal criteria to compare pre...
Conclusions
Mapping efficiency (cost / area / percent of variance
explained) is a possible universal criteria to compare pre...
Conclusions
Mapping efficiency (cost / area / percent of variance
explained) is a possible universal criteria to compare pre...
Comparing methods
Geostatistics course, 25–29 October 2010, Wageningen
Literature
Dubois, G. (Ed.), 2005. Automatic mapping algorithms for routine
and emergency monitoring data. Report on the S...
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Spatial interpolation comparison

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Spatial interpolation comparison

  1. 1. Spatial Interpolation Comparison Evaluation of spatial prediction methods Tomislav Hengl ISRIC — World Soil Information, Wageningen University Geostatistics course, 25–29 October 2010, Wageningen
  2. 2. Based on Hengl, T., MacMillan, R.A., 2011? Mapping efficiency and information content. submitted to International Journal of Applied Earth Observation and Geoinformation, special issue Spatial Statistics Conference. Geostatistics course, 25–29 October 2010, Wageningen
  3. 3. Topic Geostatistics = a toolbox to generate maps from point data i.e.to interpolate; Geostatistics course, 25–29 October 2010, Wageningen
  4. 4. Topic Geostatistics = a toolbox to generate maps from point data i.e.to interpolate; There are many possibilities; Geostatistics course, 25–29 October 2010, Wageningen
  5. 5. Topic Geostatistics = a toolbox to generate maps from point data i.e.to interpolate; There are many possibilities; An inexperienced user will often be challenged by the amount of techniques to run spatial interpolation; Geostatistics course, 25–29 October 2010, Wageningen
  6. 6. Topic Geostatistics = a toolbox to generate maps from point data i.e.to interpolate; There are many possibilities; An inexperienced user will often be challenged by the amount of techniques to run spatial interpolation; . . .which method should we use? Geostatistics course, 25–29 October 2010, Wageningen
  7. 7. Have you heard of SIC? Geostatistics course, 25–29 October 2010, Wageningen
  8. 8. The spatial prediction game Participants were invited to estimate values located at 1000 locations (right, crosses), using 200 observations (left, circles). Geostatistics course, 25–29 October 2010, Wageningen
  9. 9. Lessons learned (from SIC) Geostatistics course, 25–29 October 2010, Wageningen
  10. 10. Li and Heap (2008) Geostatistics course, 25–29 October 2010, Wageningen
  11. 11. How many techniques are there? Li and Heap (2008) list over 40 unique techniques. 1. Are all these equally valid? 2. How to objectively compare various methods (which criteria to use)? 3. Which method to pick for your own case study? Geostatistics course, 25–29 October 2010, Wageningen
  12. 12. There are not as many There are roughly five main clusters of techniques: 1. splines (deterministic); Geostatistics course, 25–29 October 2010, Wageningen
  13. 13. There are not as many There are roughly five main clusters of techniques: 1. splines (deterministic); 2. kriging-based (plain geostatistics); Geostatistics course, 25–29 October 2010, Wageningen
  14. 14. There are not as many There are roughly five main clusters of techniques: 1. splines (deterministic); 2. kriging-based (plain geostatistics); 3. regression-based; Geostatistics course, 25–29 October 2010, Wageningen
  15. 15. There are not as many There are roughly five main clusters of techniques: 1. splines (deterministic); 2. kriging-based (plain geostatistics); 3. regression-based; 4. bayesian methods; Geostatistics course, 25–29 October 2010, Wageningen
  16. 16. There are not as many There are roughly five main clusters of techniques: 1. splines (deterministic); 2. kriging-based (plain geostatistics); 3. regression-based; 4. bayesian methods; 5. expert systems / machine learning; Geostatistics course, 25–29 October 2010, Wageningen
  17. 17. The 5 criteria 1. the overall mapping accuracy, e.g.standardized RMSE at control points — the amount of variation explained by the predictor expressed in %; Geostatistics course, 25–29 October 2010, Wageningen
  18. 18. The 5 criteria 1. the overall mapping accuracy, e.g.standardized RMSE at control points — the amount of variation explained by the predictor expressed in %; 2. the bias, e.g.mean error — the accuracy of estimating the central population parameters; Geostatistics course, 25–29 October 2010, Wageningen
  19. 19. The 5 criteria 1. the overall mapping accuracy, e.g.standardized RMSE at control points — the amount of variation explained by the predictor expressed in %; 2. the bias, e.g.mean error — the accuracy of estimating the central population parameters; 3. the model robustness, also known as model sensitivity — in how many situations would the algorithm completely fail / how much artifacts does it produces?; Geostatistics course, 25–29 October 2010, Wageningen
  20. 20. The 5 criteria 1. the overall mapping accuracy, e.g.standardized RMSE at control points — the amount of variation explained by the predictor expressed in %; 2. the bias, e.g.mean error — the accuracy of estimating the central population parameters; 3. the model robustness, also known as model sensitivity — in how many situations would the algorithm completely fail / how much artifacts does it produces?; 4. the model reliability — how good is the model in estimating the prediction error (how accurate is the prediction variance considering the true mapping accuracy)?; Geostatistics course, 25–29 October 2010, Wageningen
  21. 21. The 5 criteria 1. the overall mapping accuracy, e.g.standardized RMSE at control points — the amount of variation explained by the predictor expressed in %; 2. the bias, e.g.mean error — the accuracy of estimating the central population parameters; 3. the model robustness, also known as model sensitivity — in how many situations would the algorithm completely fail / how much artifacts does it produces?; 4. the model reliability — how good is the model in estimating the prediction error (how accurate is the prediction variance considering the true mapping accuracy)?; 5. the computational burden — the time needed to complete predictions; Geostatistics course, 25–29 October 2010, Wageningen
  22. 22. Can we simplify this? 1. In theory, we could derive a single composite measure that would then allow you to select ‘the optimal’ predictor for any given data set (but this is not trivial!) 2. But how to assign weights to different criteria? 3. In many cases we simply finish using some na¨ıve predictor — that is predictor that we know has a statistically more optimal alternative, but this alternative is not feasible. Geostatistics course, 25–29 October 2010, Wageningen
  23. 23. Automated mapping In the intamap package1 decides which method to pick for you: > meuse$value <- log(meuse$zinc) > output <- interpolate(data=meuse, newdata=meuse.grid) R 2009-11-11 17:09:14 interpolating 155 observations, 3103 prediction locations [Time models loaded...] [1] "estimated time for copula 133.479866956255" Checking object ... OK 1 http://cran.r-project.org/web/packages/intamap/ Geostatistics course, 25–29 October 2010, Wageningen
  24. 24. Hypothesis We need a single criteria to compare various prediction methods. Geostatistics course, 25–29 October 2010, Wageningen
  25. 25. Mapping accuracy and survey costs The cost of a soil survey is also a function of mapping scale, roughly: log(X) = b0 + b1 · log(SN) (1) We can fit a linear model to the empirical table data from e.g.Legros (2006; p.75), and hence we get: X = exp (19.0825 − 1.6232 · log(SN)) (2) where X is the minimum cost/ha in Euros (based on estimates in 2002). To map 1 ha of soil at 1:100,000 scale, for example, one needs (at least) 1.5 Euros. Geostatistics course, 25–29 October 2010, Wageningen
  26. 26. Survey costs and mapping scale q q q q q 9.5 10.0 10.5 11.0 11.5 12.0 12.5 −10123 Scale number (log−scale) MinimumsurveycostsinEUR/ha(log−scale) Geostatistics course, 25–29 October 2010, Wageningen
  27. 27. Survey costs and mapping scale Total costs of a soil survey can be estimated by using the size of area and number of samples. The effective scale number (SN) is: SN = 4 · A N · 102 . . . SN = A N · 102 (3) where A is the surface of the study area in m2 and N is the total number of observations. Geostatistics course, 25–29 October 2010, Wageningen
  28. 28. Converges to: X = exp 19.0825 − 1.6232 · log 0.0791 · A N · 102 (4) Geostatistics course, 25–29 October 2010, Wageningen
  29. 29. Output map, from info perspective The resulting (predictions) map is a sum of two signals: Z∗ (s) = Z(s) + ε(s) (5) where Z(s) is the true variation, and ε(s) is the error component. The error component consists, in fact, of two parts: (1) the unexplained part of soil variation, and (2) the noise (measurement error). The unexplained part of soil variation is the variation we somehow failed to explain because we are not using all relevant covariates and/or due to the limited sampling intensity. Geostatistics course, 25–29 October 2010, Wageningen
  30. 30. Prediction accuracy In order to see how much of the global variation budget has been explained by the model we can use: RMSEr (%) = RMSE sz · 100 (6) where sz is the sampled variation of the target variable. RMSEr (%) is a global estimate of the map accuracy, valid only under the assumption that the validation points are spatially independent from the calibration points, representative and large enough ( 100). Geostatistics course, 25–29 October 2010, Wageningen
  31. 31. Kriging efficiency Geostatistics course, 25–29 October 2010, Wageningen
  32. 32. Mapping efficiency We propose two new measures of mapping success: (1) Mapping efficiency, defined as the amount of money needed to map an area of standard size and explain each one percent of variation in the target variable: θ = X A · RMSEr [EUR · km−2 · %−1 ] (7) where X is the total costs of a survey, A is the size of area in km−2, and RMSEr is the amount of variation explained by the spatial prediction model. Geostatistics course, 25–29 October 2010, Wageningen
  33. 33. Information production efficiency (2) Equivalent measure of mapping efficiency is the information production efficiency: Υ = X gzip [EUR · B−1 ] (8) where gzip is the size of data (in Bytes) left after compression and after reformatting the values to match the effective precision (based on Eq.10). This can be estimated as: gzip = fc · (fE · M ) · cZ [B] (9) where fc is the loss-less data compression factor that depends on the compression algorithm, fE is the extrapolation adjustment factor, cZ is the variable coding size, and M is the total number of pixels. Geostatistics course, 25–29 October 2010, Wageningen
  34. 34. Effective precision Following the Nyquist frequency concept from signal processing, which states that the original signal can be reconstructed if sampling frequency is twice the maximum component frequency of the signal, we can derive the effective precision — also known as numerical resolution — of a produced prediction map as: ∆z = RMSE 2 (10) which means that there is no justification in saving the predictions with better precision than half the average accuracy. Geostatistics course, 25–29 October 2010, Wageningen
  35. 35. Nyquist frequency concept q q qq q qq q q q q q q qqq q q qq q qq q q q q q q qq q q q q q q q q qqq q q q q qq Figure: The Nyquist rate is the optimal rate that can be used to compress a signal (it equals twice the maximum component frequency of the signal) to allow perfect reconstruction of the signal from the samples. Geostatistics course, 25–29 October 2010, Wageningen
  36. 36. Rounding numbers Original data 2.25 4.08 6.25 4.23 2.56 1.21 0.98 0.98 0.85 0.4 4.24 4.69 7.17 4.37 2.08 1.4 1.44 0.96 0.89 0.31 3.62 5.39 5.27 3.11 2.04 1.57 1.67 1.43 0.61 0.28 2.72 8.75 7.77 4.63 2.88 2.34 2.93 1.49 0.57 0.25 2.83 10.55 14.45 5.79 3.13 2.95 2.85 0.89 0.34 0.22 2.87 5.45 10.34 5.01 2.42 1.88 1.5 0.61 0.3 0.23 1.19 2.69 3.76 3.63 1.86 0.97 1.24 0.64 0.37 0.26 0.86 1.22 1.39 2.71 2.17 1.61 2.37 1.56 0.66 0.47 0.67 1 1.23 1.53 2.04 3.12 5.74 3.71 1.53 0.92 1.18 1.48 1.35 2.13 2.11 3.64 7.56 6.92 2.97 1.96 Coded data 2 4 6 4 3 1 1 0 5 7 4 2 1 1 0 4 5 5 2 2 2 1 1 3 9 8 5 3 2 3 1 1 3 11 14 6 3 3 3 3 5 10 5 2 2 1 1 3 4 4 2 1 0 1 3 2 2 2 1 1 2 2 3 6 4 2 1 1 1 2 2 4 8 7 3 2 Geostatistics course, 25–29 October 2010, Wageningen
  37. 37. Exercise To follow this exercise, obtain the DSM_examples.R script. Download it to your machine and then run step-by-step. Geostatistics course, 25–29 October 2010, Wageningen
  38. 38. Meuse data > data(meuse) > coordinates(meuse) <- ~x+y > proj4string(meuse) <- CRS("+init=epsg:28992") > sel <- !is.na(meuse$om) > bubble(meuse[sel,], "om") om qqqq qq qq q qq q qq qq q q q qqqq q qqq q q q q q q q qq q qq q q q q q q q q qq qqqqq q q q q q q q q qq q q q q qq qq qq q q q qq q q q q q q q q q qq q qq q qq q q q q q q q q q q q qq q q qq q q q q q qq q q q q q q q q q q q q q q q qq q q q q qq qq q q q q qq q q q q q q q 1 5.3 6.9 9 17 Geostatistics course, 25–29 October 2010, Wageningen
  39. 39. Meuse + + + + + + ++ + + + + + + + + + + + + +++ + +++ + + + + ++ + ++ + ++ + + ++ + + + + + + ++ + +++ + + + + + + + + + + + + + + + ++ + + ++ + + + + + + + + + + + + + + ++ + + + + ++ + + + + + + + + + + + ++ + + ++ + + + + + ++ + + + + + + + + + + + + + + + ++ + + + + + + ++ + + + + ++ + + om.ok + + + + + + ++ + + + + + + + + + + + + +++ + +++ + + + + ++ + ++ + ++ + + ++ + + + + + + ++ + +++ + + + + + + + + + + + + + + + ++ + + ++ + + + + + + + + + + + + + + ++ + + + + ++ + + + + + + + + + + + ++ + + ++ + + + + + ++ + + + + + + + + + + + + + + + ++ + + + + + + ++ + + + + ++ + + om.rk 0 2 4 6 8 10 12 14 Geostatistics course, 25–29 October 2010, Wageningen
  40. 40. Eberg¨otzen (subset) + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + ++ + + + +++ + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + ++ + +++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + ++ + ++ + + + + + + ++ + + + + + + + + + + + + + + + + + SAND.ok.1 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + ++ + + + +++ + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + ++ + +++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + ++ + ++ + + + + + + ++ + + + + + + + + + + + + + + + + + SAND.rk.1 0 10 20 30 40 50 60 70 80 90 Geostatistics course, 25–29 October 2010, Wageningen
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+ + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + ++ + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++ + + + + + + + + + + + ++ + ++ + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ ++ ++ +++ + + ++ + + + ++ + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + ++ + + ++ + + ++ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + ++ + + + + ++ + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + ++ + + + + + ++ + + + + + ++ + + + + + + + + + + + + + + + ++ + + + ++ + + + + + + + + + ++ + + + + + + + + + ++ + ++ + + + + + + + + + + + + + + + ++ + + + + + + + ++ + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + ++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + ++ + +++ + + + ++ + + + + + + + + + + + + + + + + + + + + + + + SAND.rk.5 0 10 20 30 40 50 60 70 80 90 Geostatistics course, 25–29 October 2010, Wageningen
  43. 43. OK vs RK 2.0 2.5 3.0 3.5 0.00.20.40.60.81.0 Sampling intensity (log) Amountofvariationexplained Ordinary kriging Regression−kriging Geostatistics course, 25–29 October 2010, Wageningen
  44. 44. Prediction accuracy and survey costs Geostatistics course, 25–29 October 2010, Wageningen
  45. 45. Summary results For the two case studies there is a gain of 7% for mapping organic matter (Meuse), and 13% and for mapping sand content (Eberg¨otzen) using regression-kriging vs ordinary kriging. Geostatistics course, 25–29 October 2010, Wageningen
  46. 46. Summary results For the two case studies there is a gain of 7% for mapping organic matter (Meuse), and 13% and for mapping sand content (Eberg¨otzen) using regression-kriging vs ordinary kriging. to map organic carbon for the Meuse case study, one would need to spend 13.1 EUR km−2 %−1 (1.13 EUR B−1); to map sand content for the Eberg¨otzen case study would costs 11.1 EUR km−2 %−1 (5.88 EUR B−1). Geostatistics course, 25–29 October 2010, Wageningen
  47. 47. Summary results For the two case studies there is a gain of 7% for mapping organic matter (Meuse), and 13% and for mapping sand content (Eberg¨otzen) using regression-kriging vs ordinary kriging. to map organic carbon for the Meuse case study, one would need to spend 13.1 EUR km−2 %−1 (1.13 EUR B−1); to map sand content for the Eberg¨otzen case study would costs 11.1 EUR km−2 %−1 (5.88 EUR B−1). Information production efficiency is possibly a more robust measure of mapping quality than mapping efficiency because it is scale-independent and because it accounts for extrapolation effects. Geostatistics course, 25–29 October 2010, Wageningen
  48. 48. Conclusions Mapping efficiency (cost / area / percent of variance explained) is a possible universal criteria to compare prediction methods. Geostatistics course, 25–29 October 2010, Wageningen
  49. 49. Conclusions Mapping efficiency (cost / area / percent of variance explained) is a possible universal criteria to compare prediction methods. Maps are not what they seem. Geostatistics course, 25–29 October 2010, Wageningen
  50. 50. Conclusions Mapping efficiency (cost / area / percent of variance explained) is a possible universal criteria to compare prediction methods. Maps are not what they seem. Geostatistics really outperforms non-statistical methods (but this is area/data dependent). Geostatistics course, 25–29 October 2010, Wageningen
  51. 51. Conclusions Mapping efficiency (cost / area / percent of variance explained) is a possible universal criteria to compare prediction methods. Maps are not what they seem. Geostatistics really outperforms non-statistical methods (but this is area/data dependent). It’s not about the making beautiful maps, it’s about understanding what they mean. Geostatistics course, 25–29 October 2010, Wageningen
  52. 52. Conclusions Mapping efficiency (cost / area / percent of variance explained) is a possible universal criteria to compare prediction methods. Maps are not what they seem. Geostatistics really outperforms non-statistical methods (but this is area/data dependent). It’s not about the making beautiful maps, it’s about understanding what they mean. If you deal with several equally valid (independent) methods, maybe you should consider combining them? Geostatistics course, 25–29 October 2010, Wageningen
  53. 53. Comparing methods Geostatistics course, 25–29 October 2010, Wageningen
  54. 54. Literature Dubois, G. (Ed.), 2005. Automatic mapping algorithms for routine and emergency monitoring data. Report on the Spatial Interpolation Comparison (SIC2004) exercise. EUR 21595 EN. Office for Official Publications of the European Communities, Luxembourg, p. 150. Hengl, T., 2009. A Practical Guide to Geostatistical Mapping, 2nd edition. University of Amsterdam, 291 p. ISBN 978-90-9024981-0. Li, J., Heap, A., 2008. A review of spatial interpolation methods for environmental scientists. Record 2008/23. Geoscience Australia, Canberra, p. 137. Pebesma, E., Cornford, D., Dubois, D., Heuvelink, G.B.M., Hristopoulos, D., Pilz, J., Stohlker, U., Morin, G., Skoien, J.O., 2010. INTAMAP: The design and implementation of an interoperable automated interpolation web service. Computers & Geosciences, In Press, Corrected Proof. Geostatistics course, 25–29 October 2010, Wageningen
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