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Spatial interpolation comparison

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2 hour seminar within the Geostatistics training course at WUR

2 hour seminar within the Geostatistics training course at WUR

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Spatial interpolation comparison Spatial interpolation comparison Presentation Transcript

  • Spatial Interpolation ComparisonEvaluation of spatial prediction methodsTomislav HenglISRIC — World Soil Information, Wageningen University Geostatistics course, 25–29 October 2010, Wageningen
  • 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
  • Topic Geostatistics = a toolbox to generate maps from point data i.e.to interpolate; Geostatistics course, 25–29 October 2010, Wageningen View slide
  • 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 View slide
  • 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
  • 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
  • Have you heard of SIC? Geostatistics course, 25–29 October 2010, Wageningen
  • The spatial prediction gameParticipants were invited to estimate values located at 1000locations (right, crosses), using 200 observations (left, circles). Geostatistics course, 25–29 October 2010, Wageningen
  • 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 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
  • There are not as manyThere are roughly five main clusters of techniques: 1. splines (deterministic); Geostatistics course, 25–29 October 2010, Wageningen
  • There are not as manyThere are roughly five main clusters of techniques: 1. splines (deterministic); 2. kriging-based (plain geostatistics); Geostatistics course, 25–29 October 2010, Wageningen
  • There are not as manyThere 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
  • There are not as manyThere 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
  • There are not as manyThere 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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¨ predictor — ıve 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
  • Automated mappingIn 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
  • HypothesisWe need a single criteria to compare various prediction methods. Geostatistics course, 25–29 October 2010, Wageningen
  • Mapping accuracy and survey costsThe 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 frome.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 in2002). To map 1 ha of soil at 1:100,000 scale, for example, oneneeds (at least) 1.5 Euros. Geostatistics course, 25–29 October 2010, Wageningen
  • Survey costs and mapping scale q Minimum survey costs in EUR / ha (log−scale) 3 q 2 q 1 q 0 −1 q 9.5 10.0 10.5 11.0 11.5 12.0 12.5 Scale number (log−scale) Geostatistics course, 25–29 October 2010, Wageningen
  • Survey costs and mapping scaleTotal costs of a soil survey can be estimated by using the size ofarea and number of samples.The effective scale number (SN) is: A A SN = 4· · 102 ... SN = · 102 (3) N Nwhere A is the surface of the study area in m2 and N is the totalnumber of observations. Geostatistics course, 25–29 October 2010, Wageningen
  • Converges to: A X = exp 19.0825 − 1.6232 · log 0.0791 · · 102 (4) N Geostatistics course, 25–29 October 2010, Wageningen
  • Output map, from info perspectiveThe 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) theunexplained part of soil variation, and (2) the noise (measurementerror). The unexplained part of soil variation is the variation wesomehow failed to explain because we are not using all relevantcovariates and/or due to the limited sampling intensity. Geostatistics course, 25–29 October 2010, Wageningen
  • Prediction accuracyIn order to see how much of the global variation budget has beenexplained by the model we can use: RMSE RMSE r (%) = · 100 (6) szwhere sz is the sampled variation of the target variable.RMSE r (%) is a global estimate of the map accuracy, valid onlyunder the assumption that the validation points are spatiallyindependent from the calibration points, representative and largeenough ( 100). Geostatistics course, 25–29 October 2010, Wageningen
  • Kriging efficiency Geostatistics course, 25–29 October 2010, Wageningen
  • Mapping efficiencyWe propose two new measures of mapping success: (1) Mappingefficiency, defined as the amount of money needed to map an areaof standard size and explain each one percent of variation in thetarget variable: X θ= [EUR · km−2 · %−1 ] (7) A · RMSE rwhere X is the total costs of a survey, A is the size of area inkm−2 , and RMSE r is the amount of variation explained by thespatial prediction model. Geostatistics course, 25–29 October 2010, Wageningen
  • Information production efficiency(2) Equivalent measure of mapping efficiency is the informationproduction efficiency: X Υ= [EUR · B−1 ] (8) gzipwhere gzip is the size of data (in Bytes) left after compression andafter 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 onthe compression algorithm, fE is the extrapolation adjustmentfactor, cZ is the variable coding size, and M is the total number ofpixels. Geostatistics course, 25–29 October 2010, Wageningen
  • Effective precisionFollowing the Nyquist frequency concept from signal processing,which states that the original signal can be reconstructed ifsampling frequency is twice the maximum component frequency ofthe signal, we can derive the effective precision — also known asnumerical resolution — of a produced prediction map as: RMSE ∆z = (10) 2which means that there is no justification in saving the predictionswith better precision than half the average accuracy. Geostatistics course, 25–29 October 2010, Wageningen
  • Nyquist frequency concept q qq q qq q q q q qq q q q q q q qqq qq q q q q qq q q q q q q q q q qqq q q qq q q qFigure: The Nyquist rate is the optimal rate that can be used tocompress a signal (it equals twice the maximum component frequency ofthe signal) to allow perfect reconstruction of the signal from the samples. Geostatistics course, 25–29 October 2010, Wageningen
  • Rounding numbers Original data Coded data 1.18 1.48 1.35 2.13 2.11 3.64 7.56 6.92 2.97 1.96 1 1 2 2 4 8 7 3 2 0.67 1 1.23 1.53 2.04 3.12 5.74 3.71 1.53 0.92 1 1 2 2 3 6 4 2 1 0.86 1.22 1.39 2.71 2.17 1.61 2.37 1.56 0.66 0.47 1 3 2 2 2 1.19 2.69 3.76 3.63 1.86 0.97 1.24 0.64 0.37 0.26 1 3 4 4 2 1 0 2.87 5.45 10.34 5.01 2.42 1.88 1.5 0.61 0.3 0.23 3 5 10 5 2 2 1 2.83 10.55 14.45 5.79 3.13 2.95 2.85 0.89 0.34 0.22 3 11 14 6 3 3 3 2.72 8.75 7.77 4.63 2.88 2.34 2.93 1.49 0.57 0.25 3 9 8 5 3 2 3 1 1 3.62 5.39 5.27 3.11 2.04 1.57 1.67 1.43 0.61 0.28 4 5 5 2 2 2 1 1 4.24 4.69 7.17 4.37 2.08 1.4 1.44 0.96 0.89 0.31 5 7 4 2 1 1 0 2.25 4.08 6.25 4.23 2.56 1.21 0.98 0.98 0.85 0.4 2 4 6 4 3 1 1 0 Geostatistics course, 25–29 October 2010, Wageningen
  • ExerciseTo 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
  • Meuse data> data(meuse)> coordinates(meuse) <- ~x+y> proj4string(meuse) <- CRS("+init=epsg:28992")> sel <- !is.na(meuse$om)> bubble(meuse[sel,], "om") om q qqq qqqq qq qq q q q qq q q qqq q q q qq q q q q qq q q q q qq q q qqq q q q q q q qq q q q q qq q q q qq q qq q q q q 1 qq q q q q q 5.3 q q q 6.9 qq q qq q q q q 9 17 q q q qq q q q q q qq q q q q qq q q qqqq q qq q qqq q q qq qq q qq qqq q q q q q qq q q q qq qq q q q q q q q q q q q q Geostatistics course, 25–29 October 2010, Wageningen
  • Meuse om.ok om.rk + + 14 + + + + + + + + + + + + + + + + ++ + + + ++ + + + + + + + + + + + 12 + + + + + + + + ++ + + ++ + + + + + + + + + +++ + + +++ + ++ + ++ + + + ++ + + ++ 10 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 8 + + + + + + + + + + + ++ + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 6 + + + + + + + + + + + + + + + + + + + + ++ + + + ++ + ++ + ++ + ++ + + + + + + ++ + + + + + + + + + + + + 4 ++ ++ + + ++ + + + + ++ + + + + + + + + + + + + ++ + + + + ++ + + + + + + + + + + + + + + + + 2 + + + + + + + + + + + + + + + + + + 0 Geostatistics course, 25–29 October 2010, Wageningen
  • Eberg¨tzen (subset) o + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + ++ + + + + + ++ + SAND.ok.1 + + + + + + + + ++ + + + + + ++ + SAND.rk.1 + + + + + + + + ++ + 90 + + ++ + + ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 80 + +++ + +++ + + + + + + + + ++ + ++ ++ + + ++ + ++ ++ + + + + + + + ++ + + + + + + + + + + + + + + + + + 70 + + + + + ++ + ++ + + + + + + + ++ + ++ + + ++ + ++ ++ + ++ + ++ + + + ++ ++++ ++ ++++ + + + + + + + ++ + + ++ + ++ + + ++ 60 + + + + + + + + + + + + + + + + + + + + + ++ + ++ + + ++ + ++ + + + ++ + + + + ++ + + + + + + + + + + + + + + + + 50 + + + + + + + + + + + + + + + + + + + + + ++ + + ++ + + + + + + + + + + + + + + + + + + + + + 40 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + ++ + + + + + + + + 30 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + ++ + + + + + 20 + ++ + + ++ + + + + + + + + + + + + + + + + + + + + + ++ + + ++ ++ + + + + + ++ ++ + + + + + ++ + + + + + + + + + + + + + + + + 10 ++ + + ++ + + + + + + + + + + + + ++ ++ + + + + + + + + ++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 0 Geostatistics course, 25–29 October 2010, Wageningen
  • Eberg¨tzen (subset) o + + + + + ++ + + + + + ++ + ++ + + + + +++ + ++ + + + + + + + + ++ + + + + +++ + ++ + + + + + + + + + + + + + ++ + +++ + + + + + ++ + +++ + + + + + ++ + + + ++ + + ++ + + ++ + ++ SAND.ok.3 ++ + + ++ ++ + + + + + ++ + + + ++ + + ++ + + ++ + ++ SAND.rk.3 ++ + + ++ ++ + + + 90 + ++ + + +++ + + + + + + ++ + + +++ + + + + + ++ + + + +++ + + ++++ ++ + + + ++ + + + +++ + + ++++ ++ + + + + + + + + + + + + + ++ + + ++ ++ + ++ + + + ++ ++ + + ++ ++ + ++ + + + ++ + + + ++ ++ + + + + + + ++ ++ + + + + ++ + + ++ +++ + + ++ ++ + + ++ + + ++ +++ + + ++ ++ + 80 + + + ++ + + + + ++ ++ + + + + ++ + + + + ++ ++ + + + + + ++ + + + + + + + + + + ++ + + + + + + + + + + ++ + + + + + ++ + + + + + + + + + + + + + ++ + + + + + ++ + + + + + + + + ++ ++ ++ + + + + + + ++ ++ ++ + + + + + + + ++ + ++ + + + ++ + + + + + + + ++ + + ++ + ++ ++ + ++ + + + ++ + + + + + + + ++ + ++ + ++ + 70 + + + + ++ + + + + + + ++ + ++ + + + + + + ++ + + + + + + + ++ + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + ++ + + + + + ++ + ++ ++ + + + + + ++ + + + + + ++ + ++ ++ + + + + + ++ + + + + + + + ++ ++ ++ + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + ++ ++ +++ ++ ++++ ++ ++ + + + + + + + + ++ + + + + ++ +++ ++ ++++ ++ ++ + + + + 60 + ++ ++ + + ++ + + + + ++ + ++ ++ ++ + + ++ + + + + ++ + + + ++ ++ ++ + + ++ + + + + + ++ + ++ ++ + + ++ + + + + + + ++ + ++ + + + ++ + + ++ + + + + + + ++ + + + + + + + + + + + + ++ + + + ++ + + + + + + ++ + + + + + + + + + + + + ++ ++ ++ + + + ++ ++ + ++ ++++ ++ + + + ++ ++ + + ++++ + ++++ + ++ + + ++++ + ++++ + ++ + + ++ + + + + +++ + + + + + + ++ + + + ++ + + + + ++ + + + + +++ + + + + + + ++ + + + +++ + + 50 + + ++ + + ++ + + + ++ + + ++ + + + + + ++ + + + + + + + + + ++ + + + + + + + + + + + + + + + ++ + + + + + +++ + ++ + + + + + + + +++ + + + + ++ + ++ + + + + ++ + + ++ + + + + + ++ + + + + ++ + ++ + + + + ++ + + +++ + ++ ++ + + + +++ + ++ + + + + ++ + + + +++ ++ + + ++ + + + + + ++ + + + +++ ++ + + ++ + + 40 ++ + + + ++ + + ++ + + + +++ +++ + ++ + + + + + + ++ + + + + ++ ++ + + + + + + + + ++ + ++ + ++ + + ++ ++ + + ++ + +++ ++ + + + ++ + + ++ + + +++ ++ + + + ++ + + ++ + + + + ++ + + ++ + + + ++ + + ++ + + ++ + + + + ++ + + + ++ + + +++ ++ + + + + + ++ + + + ++ + + +++ ++ + + + + + + + + + + + + + + + 30 ++ ++ + ++ + + + ++ + ++ + + ++ ++ + + + + ++ ++ + ++ + + + ++ + ++ + + ++ ++ + + + + + + + + + + +++ + + + ++ ++ + + + + +++ + + + ++ ++ + + + + ++ + + ++ + + ++ + + ++ ++ ++ + + ++ ++ ++ + + ++ + + + + + + + + + + + + + + + ++ +++ + + ++ + + + + ++ +++ + + ++ + ++ ++ + ++ + + + ++ ++ + ++ + + + 20 + ++ + + + + ++ + + + + + ++ + + + ++++ ++ + + + + + ++ + + + ++++ ++ + + + + + + ++ + ++ + + + + ++ + ++ + + + + ++ + ++ + + + + + + + + ++ + ++ + + + + + + + + ++ + + + + + + ++ + + + + + + ++ + + + + + ++ + + + + ++ + + + + + ++ + + + + + + + + + + + + +++ + + + + + + + + + + + + + +++ + + 10 + ++ + + + + + + + + + + + ++ + + + + + + + + + + ++ + ++ + + ++ + ++ + ++ + ++ + + ++ +++ ++ + + + + + + + +++ + + ++ ++ + + + + + + + + + +++ + + ++ ++ + + + + + + + ++ + + + + + + + + ++ + + + ++ + + + + + ++ ++ ++ ++ + ++ ++ + + + + + + + + ++ + + + + + + ++ ++ ++ ++ + ++ ++ + + + ++ + ++ + + + + + + + ++ + + + ++ + ++ ++ + + ++ + + + + + + + + + + + + + + + + + ++ + + + + + ++ + ++ ++ + + ++ + + + + + + + + + + + ++ + 0 ++ + ++ + + + ++ + + ++ + ++ + + + ++ + + Geostatistics course, 25–29 October 2010, Wageningen
  • Eberg¨tzen (complete) o + + + + + + + + + + ++++ + + ++ + + + + + + + + + + + +++ + + + + + ++ + + ++ + + + + ++ + ++ + +++ + + + + ++ + +++ + + ++ + + + + + + + + +++ + + + + +++ + + + +++++ +++ + ++++ ++ +++ +++ ++++ + +++ + + + + + ++ + + + + + + + + ++ + +++ + + + + +++ + + + + ++ ++ + + + ++ + ++ ++ + +++ ++++++ + + +++ + + ++ + + + + + + + ++++ + ++ ++ + + ++ + + + + + ++ + + + + ++ + + + + + + ++ + + + + ++ ++ + + + + + + + + +++ + +++ + + + ++ +++ +++++++++ + ++ + ++ ++ +++ ++ +++ + + + + ++ + + + + + ++ ++ + + + + + + + ++ + ++ + +++ ++ ++ + +++ + + ++ + + + + + ++ + + + + + + + + ++ + + + ++ +++ ++ + + + + ++ + + ++ + + ++ + ++ +++ + + SAND.ok.5 + + ++ ++ +++ + ++++++ ++ ++ + + ++ + + ++ ++ ++++++ + + + ++ ++ + ++ + + + + ++ + + +++ +++ +++ + + + + + ++++ ++ +++ + ++ + ++ +++ + + + SAND.rk.5 + + ++ ++ +++ + ++++++ ++ ++ + + + + + + + ++ ++ ++++++ + + + +++ ++ + +++ + + ++ + + + + ++ + + + + + + ++ 90 +++ ++++++ + + ++ + ++ + + + + + ++++++ + ++++ ++ + + + ++ + + + ++ + + + + ++ + ++++++++ +++ + + ++ + + + + + +++ + + + ++ + + + + + ++ + + + + ++ + + ++ + + ++ ++ ++++ + ++ ++++ + + + + + + ++++++ + ++ + ++ + + + + +++ + +++ ++ + + ++ + ++ ++++ + + + + + ++ + + + + + +++ + + + ++ ++++ + + + + +++ + +++ ++ + + ++ + + ++ ++ + ++ ++++ + + + ++ + + + + +++ ++ + + ++ + + + ++ ++ + ++ ++++ + + + ++ + + + + +++ ++ + + ++ + + + +++ + + + + + ++ + + + ++ + + + + + ++ + ++ + + + + +++ + + + + + ++ + + + ++ + + + + + ++ + + + + + + +++ + ++ + + + + + + + + + + + + + + +++ + ++ + + + + + + + + + +++++ ++ ++ ++++ ++ + + + + + + ++ ++ + + +++++ ++ ++ ++++ ++ + + + + + + ++ ++ + + 80 + + + + +++ ++ ++++ + ++++ + + ++ + + + + + +++ ++ + + + + + ++++++ ++ + + + + +++ ++ + ++++ ++ ++++ + + ++ + + + + + +++ ++ + + + + + ++++++ ++ + + ++ +++ ++ + + + + + ++ + + ++ ++ ++ + + + + + ++ +++ + + ++ + + + + + + + + ++ ++ + + + + + + ++ ++ + ++ ++ +++ + + ++ + + + + + + + + ++ ++ + + + + + + ++ ++ + ++ ++ + + + +++ +++ + + + ++ + +++++++++ + + ++ + + + + + + + + + + +++ +++ + + + 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+ + ++ + + ++ + + +++++ +++ + +++ + + + + ++ + ++ + ++ + + ++ + + + +++ ++ + + ++ + + ++ ++ ++ + ++ + + ++ + ++++ + + ++++++ ++ + + ++ ++ + + + ++ + +++++ +++ + +++ + + + + ++ + ++ + ++ + + ++ + ++ + + ++ + + ++ ++ + + +++ + + + +++ + + +++ +++ + + + +++++ ++++ + + + ++ + + ++ ++ + + + + ++ + ++ + + + + + + ++ + + + + + ++ ++ ++ + + +++ Geostatistics course, 25–29 October 2010, Wageningen
  • OK vs RK 1.0 0.8 Amount of variation explained 0.6 0.4 0.2 Ordinary kriging Regression−kriging 0.0 2.0 2.5 3.0 3.5 Sampling intensity (log) Geostatistics course, 25–29 October 2010, Wageningen
  • 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 sand content (Eberg¨tzen) using regression-kriging vs ordinary o kriging. 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 sand content (Eberg¨tzen) using regression-kriging vs ordinary o 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¨tzen case study would costs o 11.1 EUR km−2 %−1 (5.88 EUR B−1 ). 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 sand content (Eberg¨tzen) using regression-kriging vs ordinary o 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¨tzen case study would costs o 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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 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