Optimizing Spatio-Temporal Sampling Designs of Synchronous, Static, or Clustered Measurements

Helle Kristina B., Pebesma Edzer.

Abstract in Online-Sammlung (Konferenz)

Zusammenfassung

When sampling spatio-temporal random variables, the cost of a measurement may differ according to the setupof the whole sampling design: static measurements, i.e. repeated measurements at the same location, synchronousmeasurements or clustered measurements may be cheaper per measurement than completely individual sampling.Such "grouped" measurements may however not be as good as individually chosen ones because of redundancy.Often, the overall cost rather than the total number of measurements is fixed. A sampling design with groupedmeasurements may allow for a larger number of measurements thus outweighing the drawback of redundancy. Thefocus of this paper is to include the tradeoff between the number of measurements and the freedom of their locationin sampling design optimisation.For simple cases, optimal sampling designs may be fully determined. To predict e.g. the mean over a spatiotemporalfield having known covariance, the optimal sampling design often is a grid with density determined bythe sampling costs [1, Ch. 15]. For arbitrary objective functions sampling designs can be optimised relocatingsingle measurements, e.g. by Spatial Simulated Annealing [2]. However, this does not allow to take advantage oflower costs when using grouped measurements.We introduce a heuristic that optimises an arbitrary objective function of sampling designs, including static, synchronous,or clustered measurements, to obtain better results at a given sampling budget. Given the cost for ameasurement, either within a group or individually, the algorithm first computes affordable sampling design configurations.The number of individual measurements as well as kind and number of grouped measurements aredetermined. Random locations and dates are assigned to the measurements. Spatial Simulated Annealing is usedon each of these initial sampling designs (in parallel) to improve them. In grouped measurements either the wholegroup is moved or single measurements within the group, e.g. static measurements may be moved to another locationor the sampling times may be rearranged. After several optimisation steps, the objective functions of thesampling designs are compared. Only for the best ones optimisation is pursued. After several iterations the samplingdesigns are selected again. Thus more and more of the low performing sampling designs are deleted andcomputational effort is concentrated on the most promising candidates.The use case is optimisation of a monitoring sampling design for a river. We use a flow model to simulate thespread of a pollutant that enters the system at different locations with known, location-dependent probabilities andat random times. The objective function to be minimised is the amount of pollution that is not detected. [1] Jaap de Gruijter, Dick Brus, Marc Bierkens, and Martin Knotters. Sampling for Natural Ressource Monitoring.Springer, 2006. [2] J. W. van Groenigen. Spatial simulated annealing for optimizing sampling, In: GeoENV I Geostatistics forenvironmental applications, pages 351 - 361, 1997.

Details zur Publikation

Veröffentlichungsjahr: 2010
Sprache, in der die Publikation verfasst ist: Englisch
Link zum Volltext: http://meetingorganizer.copernicus.org/EGU2010/EGU2010-12462.pdf