A hybrid geoid for the U.S. using empirical Bayesian kriging

Abstract:

A corrector surface (also known as a hybrid geoid) relating U.S. gravimetric geoid USGG12 to the NAVD88 vertical datum is computed for the conterminous U.S. using empirical Bayesian krigng (EBK) in an ArcGIS environment. EBK is an interpolation method that accounts for uncertainty in the covariance function by using a weighted sum of many reasonable covariances (Krivoruchko and Gribov, 2014). This results in more realistic prediction uncertainty. EBK accounts for moderate data nonstationarity by building local models on subsets of the input data and then merging the models. In our EBK model, GPS on benchmark (GPSBM) data are transformed to a Gaussian distribution as described in Gribov and Krivoruchko, 2012 and a Mattern covariance model is simultaneously estimated using restricted maximum likelihood approach. Since our GPSBM dataset is large, the input data to EBK are first divided into overlapping subsets of 200 points. Each data subset uses models defined by nearby values, rather than being influenced by very distant factors. In each subset covariances are estimated, then, for each location, a prediction and prediction standard error are generated using weighted covariances from one or more subsets. We observed that the covariance model parameters are changing from region to region and we discuss this interesting feature of the USGG12 and GPSBM spatial data variation. We approximated ellipsoidal distances with chord distances to avoid distortion due to imperfect data projection. The EBK corrector surface is compared with a corrector surface computed by National Geodetic Survey (NGS) using least-squares collocation (LSC). Initial results show that the EBK corrector surface compares favorably with LSC. In particular, the EBK prediction error not only is lower than that of LSC but also is more representative because it accounts for both local data variation and sampling density.