AN UNCERTAINTY ANALYSIS PROCEDURE FOR SPATIALLY JOINT SIMULATIONS OF MULTIPLE ATTRIBUTES

In this study, an uncertainty analysis procedure for joint sequential simulation of multiple attributes of spatially explicit models was developed based on regression analysis. This procedure utilizes information obtained from joint sequential simulation to establish the relationship between model uncertainty and variation of model inputs. Using this procedure, model variance can be partitioned by model input parameters on a pixel by pixel basis. In the partitioning, the correlation of neighboring pixels is accounted for. With traditional uncertainty analysis methods, this is not possible. In a case study, spatial variation of soil erodibility from a joint sequential simulation of soil properties was analyzed. The results showed that the regression approach is a very effective method in the analysis of the relationship between variation of the model and model input parameters. It was also shown for the case study that (1) uncertainty of soil erodibility of a pixel is mainly propagated from its own soil properties, (2) soil properties of neighboring pixels contribute negative uncertainty to soil erodibility, (3) it is sufficient for uncertainty analysis to include the nearest three neighboring pixel groups, and (4) the largest uncertainty contributors vary by soil properties and location

A multi-resolution approximation for massive spatial datasets

Automated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high-resolution observations of spatial fields over large spatial regions. If these datasets can be efficiently exploited, they can provide new insights on a wide variety of issues. However, traditional spatial-statistical techniques such as kriging are not computationally feasible for big datasets. We propose a multi-resolution approximation (M-RA) of Gaussian processes observed at irregular locations in space. The M-RA process is specified as a linear combination of basis functions at multiple levels of spatial resolution, which can capture spatial structure from very fine to very large scales. The basis functions are automatically chosen to approximate a given covariance function, which can be nonstationary. All computations involving the M-RA, including parameter inference and prediction, are highly scalable for massive datasets. Crucially, the inference algorithms can also be parallelized to take full advantage of large distributed-memory computing environments. In comparisons using simulated data and a large satellite dataset, the M-RA outperforms a related state-of-the-art method.Comment: 23 pages; to be published in Journal of the American Statistical Associatio