Sampling Optimization Trade-offs for Long-term Monitoring

of Gamma Dose Rates

S.J. Melles, G.B.M. Heuvelink, C.J.W. Twenhöfel, and U. Stöhlker

Presented at ICCSA, GEOG-AN-MODJuly 2, 2008, Perugia, Italy

Where do we go?

Motivation: why important, what can we gain, and current research needs?

Methods: Regression kriging context, mukv similar, can get a measure of uncertainty prior to sampling as long as you have complete info on predictors

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).

What have we learned? not related to sleeping

Motivation & motivating questions

1. Design of a sampling scheme important for the measure E.g.: Gamma radiation (minimize costs cant sample everywhere

Air pollution Environmental variables of interest

2. Need an objective assesment of the quality of a monitoring network

3 main things to consider: purpose, decision criteria, constraints

3. How to determine which approach to apply? Design-based DETERMINISTIC (probability), Model-based STOCHASTIC (simulation/interpolation in geostatistics) , Geometric (linear transects)

4. How to optimize? (Practical situations – have a decision problem:

Optimization problems are mathematical translations of decision problems, simulations)

Design-based vs. Model-baseddeterministic probability based, global vs. stochastic model-based, local

1. Target ‘design-unbiased’?2. Accuracy quantified objectively 3. Random sampling feasible?4. Reliable model available?5. Substantial spatial autocorrelations?

Part 2:

Methods to predict or describe spatial variability in

environmental variables

Spatial variability in geostats

z(s) = a realization of an underlying random function Z(s)

Spatial variability in Z(s) is related to natural, deterministic processes (e.g. gamma radiation is affected by soil type, altitude, etc.)

An exhaustive process description is not possible Stochastic methods are commonly used to describe

remaining spatial structure in the data (and map environmental variables for risk management)

Spatial variability in geostats – in order to do statistics and make inferences we assume

Second order stationarity E[Z(s)] = m Expected value of the random

variable C(h) = E[(Z(s + h) – m) (Z(s) - m] Covariance of two

random variables h distance apart Intrinsic stationarity allows us to make inferences in cases where the

mean γ(h) = ½ E[(Z(s + h) – Z(s))2]

Regression krigingoften 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)

Trends in the mean Hybrid spatial modelling technique

Regression Interpolation of regression residuals

Example: variogram & point cloud

Experimental variogram

distance

semivariance

0.2

0.4

0.6

500 1000 1500

0 500 1000 1500

01

23

4

distance

semivariance

Sem

ivar

ianc

e γ(

h)

Distance (h)

1500 1000 500

Distance (h)

1500 1000 500

0.6

0.4

0.2

Part 2:

Example: γ-dose rate radiation

Example: mean long term γ-dose rates

Self-effect of probe Anthropogenic

Hospitals, nuclear power plants, research

Natural Cosmic (atmospheric

pressure & altitude) Airborne (precipitation) RN, Bi,

Lb attached to aerosols

Terrestrial (soil type and soil moisture)

Spatially correlated residualsnotice directionality in residuals

0

frequ

ency

60

0 40-40

catsoilelevsZ )(

Modelled with aniso variogram spherical and linear component in all directions, but spherical is dominant in swesterly

and linear in ortho

Regression kriging prediction

30

80

nSv/hr

Kriging prediction error variance

65

85

nSv/hr

Part 3:

Optimization

How to optimize?

Minimize a CRITERION (the objective function) Prediction errors due to

REGRESSION MODEL PARAMETER ERRORSINADEQUATE SPATIAL COVERAGE

What about other decision criteria? E.g., dynamic and most important case???POPULATION DENSITYDISTANCE TO NPPS

ncCqqqCqcCqq

cCcCCsmeanRKSE

TTTT

nT

/))()()(

)(()((

01

011

01

0

10

10100

2

residual component

trend component

Optimization by simulated annealing

1. Start with current design2. Moving one device at a time3. Compute objective function

(criterion)

4. Compare criterion previous design

5. Accept if current is lower, but not always…

6. New sampling design constructed; loop back to step 1

Minimizing the objective function (RKSE)

Current design Optimized design

Examining the trade-offs?

Costs

Part 4:

What have we learned? Where to from here?

What have we learned?

Fairly minor changes to current network could be made

(improve quality of mapped predictions of gamma dose rate or remove stations w/ no decrease in ‘’quality’’, particularly at borders)

Most room for improvement in border regions

Examination of trade-offs useful to the extent that actual costs are evaluated and monitoring purpose is adequately captured by

objective function

Doesn’t that look like even spatial coverage sampling?

Current thinned design( 50% stations)

Optimized design(50% stations)

Npp

Where to from here:

Shortcomings I: Spatial correlation structure is an integral over

the whole range of values Does not deal well with extreme values Tends towards spatial coverage sampling with

larger sample sizes Assumes known trends and variogram

Where to from here:

Shortcomings II: Sensitive to boundary conditions Time consuming Dynamic case is primary purpose of monitoring…

As purposes differ, so do criteria. What to do with constraints (e.g. NPPs,

population centers)Next stage, multi-criteria optimization with

weights

6,)min(1

pwi

ppi

pi

THANK YOU!

Appendix

P of accepting a worsening design

T

feP

Delta f is the change in MUKV

Coming up with the costs

Ask the experts? But, no one wants to say… Are you an expert? Is anyone an expert? Consider the main purpose of the network…

Coming up with weights?

Ask the experts? Are you the expert? Is anyone an expert? Consider the main purpose of the network…

Dynamic case