Second-Phase Sampling Designs for Non-Stationary Spatial Variables.

Area of Science:

• Geostatistics
• Spatial Statistics
• Remote Sensing

Background:

• Second-phase sampling enhances spatial predictions after initial data collection.
• Kriging variance, a common criterion, assumes stationarity which is often violated.
• Existing methods may not fully capture spatial heterogeneity for optimal sampling.

Purpose of the Study:

• To develop an improved second-phase sampling strategy.
• To integrate spatial roughness with kriging variance for better sample allocation.
• To optimize sampling in spatial prediction using a novel objective function.

Main Methods:

• Weighted kriging variance using spatial moving average for roughness.
• Simulated annealing for non-linear objective function optimization.
• Application to remote sensing data with systematic and nested sampling designs.

Main Results:

• Second-phase sampling optimizing the proposed criterion yielded more accurate predictions than using kriging variance alone.
• The improvement in prediction accuracy was more pronounced with lower initial sampling densities.
• The method effectively updated semivariogram models and reconstructed images.

Conclusions:

• The proposed weighted criterion enhances second-phase sampling effectiveness in spatial prediction.
• Spatial roughness is a crucial factor to consider alongside kriging variance for optimal sampling.
• The method offers a robust approach for adaptive spatial sampling in various applications.