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Third International Workshop on "Geographical Analysis, Urban Modeling, Spatial Statistics"

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  • I’d like to thank the organizers for allowing me to present our work on sampling design optimization and thank you to the audience for coming. I realize that this is actually siesta time after lunch, so I won’t be offended if you power nap at optimal moments. My talk is about the design of a monitoring network for the measurement of an environmental variable of interest. In this case, we look at the sampling design of radiation monitoring networks in the Netherlands and the two neighbouring German states of Niedersachen and Noord westfalen. The environmental variable of interest here is natural background radiation levels.
  • Melles

    1. 1. Sampling Optimization Trade-offs for Long-term Monitoring of Gamma Dose Rates S.J. Melles, G.B.M. Heuvelink, C.J.W. Twenh ö fel, and U. St ö hlker Presented at ICCSA, GEOG-AN-MOD July 2, 2008, Perugia, Italy
    2. 2. Where do we go? <ul><li>Motivation: why important, what can we gain, and current research needs? </li></ul><ul><li>Methods: Regression kriging context, mukv similar, can get a measure of uncertainty prior to sampling as long as you have complete info on predictors </li></ul><ul><li>Optimization: Simulated annealing (algorithm to min. Obj. Function developed in the field of condensed matter physics and based on the analogy of controlled cooling of a metal in order to achieve optimal overall strength, avoiding local weakness). </li></ul><ul><li>What have we learned? not related to sleeping </li></ul>
    3. 3. Motivation & motivating questions <ul><li>Design of a sampling scheme important for the measure E.g.: </li></ul><ul><ul><li>Gamma radiation (minimize costs cant sample everywhere </li></ul></ul><ul><ul><li>Air pollution </li></ul></ul><ul><ul><li>Environmental variables of interest </li></ul></ul><ul><li>Need an objective assesment of the quality of a monitoring network </li></ul><ul><li>3 main things to consider: purpose, decision criteria, constraints </li></ul><ul><li>How to determine which approach to apply? Design-based DETERMINISTIC (probability), Model-based STOCHASTIC (simulation/ interpolation in geostatistics ) , Geometric (linear transects) </li></ul><ul><li>How to optimize? ( Practical situations – have a decision problem: Optimization problems are mathematical translations of decision problems, simulations ) </li></ul>
    4. 4. Design-based vs. Model-based deterministic probability based, global vs. stochastic model-based, local <ul><li>Target ‘design-unbiased’? </li></ul><ul><li>Accuracy quantified objectively </li></ul><ul><li>Random sampling feasible? </li></ul><ul><li>Reliable model available? </li></ul><ul><li>Substantial spatial autocorrelations? </li></ul>
    5. 5. Part 2: Methods to predict or describe spatial variability in environmental variables
    6. 6. Spatial variability in geostats <ul><li>z (s) = a realization of an underlying random function Z (s) </li></ul><ul><li>Spatial variability in Z (s) is related to natural, deterministic processes (e.g. gamma radiation is affected by soil type, altitude, etc.) </li></ul><ul><li>An exhaustive process description is not possible </li></ul><ul><ul><li>Stochastic methods are commonly used to describe remaining spatial structure in the data (and map environmental variables for risk management) </li></ul></ul>
    7. 7. Spatial variability in geostats – in order to do statistics and make inferences we assume <ul><li>Second order stationarity </li></ul><ul><ul><li>E [ Z (s)] = m Expected value of the random variable </li></ul></ul><ul><ul><li>C (h) = E [( Z (s + h) – m ) ( Z (s) - m ] Covariance of two random variables h distance apart </li></ul></ul><ul><li>Intrinsic stationarity allows us to make inferences in cases where the mean </li></ul><ul><ul><li>γ (h) = ½ E[( Z (s + h) – Z (s)) 2 ] </li></ul></ul>
    8. 8. Regression kriging often w/ enviro data, we have known deterministic trends that influence our var of interest, and for which the parameters are unknown (a spatial regression technique) <ul><li>Trends in the mean </li></ul><ul><ul><li>Hybrid spatial modelling technique </li></ul></ul><ul><ul><ul><li>Regression </li></ul></ul></ul><ul><ul><ul><li>Interpolation of regression residuals </li></ul></ul></ul>
    9. 9. Example: variogram & point cloud <ul><li>Experimental variogram </li></ul>Semivariance γ (h) 0.6 0.4 0.2 Distance (h) 1500 1000 500 Distance (h) 1500 1000 500
    10. 10. Part 2: Example: γ - dose rate radiation
    11. 11. Example: mean long term γ -dose rates <ul><li>Self-effect of probe </li></ul><ul><li>Anthropogenic </li></ul><ul><ul><li>Hospitals, nuclear power plants, research </li></ul></ul><ul><li>Natural </li></ul><ul><ul><li>Cosmic (atmospheric pressure & altitude) </li></ul></ul><ul><ul><li>Airborne (precipitation) RN, Bi, Lb attached to aerosols </li></ul></ul><ul><ul><li>Terrestrial (soil type and soil moisture) </li></ul></ul>
    12. 12. Spatially correlated residuals notice directionality in residuals 0 frequency 60 0 40 -40
    13. 13. Modelled with aniso variogram spherical and linear component in all directions, but spherical is dominant in swesterly and linear in ortho
    14. 14. Regression kriging prediction 30 80 nSv/hr
    15. 15. Kriging prediction error variance 65 85 nSv/hr
    16. 16. Part 3: Optimization
    17. 17. How to optimize? <ul><li>Minimize a CRITERION (the objective function) </li></ul><ul><ul><li>Prediction errors due to </li></ul></ul><ul><ul><ul><li>REGRESSION MODEL PARAMETER ERRORS </li></ul></ul></ul><ul><ul><ul><li>INADEQUATE SPATIAL COVERAGE </li></ul></ul></ul><ul><ul><li>What about other decision criteria? E.g., dynamic and most important case??? </li></ul></ul><ul><ul><ul><li>POPULATION DENSITY </li></ul></ul></ul><ul><ul><ul><li>DISTANCE TO NPPS </li></ul></ul></ul>residual component trend component
    18. 18. Optimization by simulated annealing <ul><li>Start with current design </li></ul><ul><li>Moving one device at a time </li></ul><ul><li>Compute objective function (criterion) </li></ul><ul><li>Compare criterion previous design </li></ul><ul><li>Accept if current is lower, but not always… </li></ul><ul><li>New sampling design constructed; loop back to step 1 </li></ul>
    19. 19. Minimizing the objective function (RKSE) Current design Optimized design
    20. 20. Examining the trade-offs? Costs
    21. 21. Part 4: What have we learned? Where to from here?
    22. 22. What have we learned? <ul><li>Fairly minor changes to current network could be made </li></ul><ul><li>(improve quality of mapped predictions of gamma dose rate or remove stations w/ no decrease in ‘’quality’’, particularly at borders) </li></ul><ul><li>Most room for improvement in border regions </li></ul><ul><li>Examination of trade-offs useful </li></ul><ul><ul><ul><li>to the extent that actual costs are evaluated </li></ul></ul></ul><ul><ul><ul><li>and monitoring purpose is adequately captured by objective function </li></ul></ul></ul>
    23. 23. Doesn’t that look like even spatial coverage sampling? Current thinned design ( 50% stations) Optimized design (50% stations) Npp
    24. 24. Where to from here: <ul><li>Shortcomings I: </li></ul><ul><ul><li>Spatial correlation structure is an integral over the whole range of values </li></ul></ul><ul><ul><li>Does not deal well with extreme values </li></ul></ul><ul><ul><li>Tends towards spatial coverage sampling with larger sample sizes </li></ul></ul><ul><ul><li>Assumes known trends and variogram </li></ul></ul>
    25. 25. Where to from here: <ul><li>Shortcomings II: </li></ul><ul><ul><li>Sensitive to boundary conditions </li></ul></ul><ul><ul><li>Time consuming </li></ul></ul><ul><ul><li>Dynamic case is primary purpose of monitoring… </li></ul></ul><ul><ul><ul><li>As purposes differ, so do criteria. </li></ul></ul></ul><ul><ul><ul><li>What to do with constraints (e.g. NPPs, population centers) </li></ul></ul></ul><ul><ul><ul><li>Next stage, multi-criteria optimization with weights </li></ul></ul></ul>
    26. 26. THANK YOU!
    27. 27. Appendix
    28. 28. P of accepting a worsening design Delta f is the change in MUKV
    29. 29. Coming up with the costs <ul><li>Ask the experts? </li></ul><ul><li>But, no one wants to say… </li></ul><ul><li>Are you an expert? </li></ul><ul><li>Is anyone an expert? </li></ul><ul><li>Consider the main purpose of the network… </li></ul>
    30. 30. Coming up with weights? <ul><li>Ask the experts? </li></ul><ul><li>Are you the expert? </li></ul><ul><li>Is anyone an expert? </li></ul><ul><li>Consider the main purpose of the network… </li></ul>
    31. 31. Dynamic case