Multi-event universal kriging (MEUK)

• A novel extension to universal kriging (UK) for use with multi-event data sets is described, referred to as MEUK
• MEUK enables the inclusion of physically-derived trends in the evaluation of spatio-temporal data
• Trend terms can be global (apply to ALL data events) or local (apply to individual or subsets of data events)
• The applications are to water level mapping, but any spatio-temporal data could be evaluated using MEUK

Multi-event universal kriging (MEUK) is a method of interpolation that creates a series of maps, each corresponding to a specific sampling “event”, which exhibit spatial relationships that persist over time. MEUK is computed using minimum-variance unbiased linear prediction from data obtained via a sequence of events. MEUK assumes multi-event data can be described by a sum of (a) spatial trends that vary over time, (b) spatial trends that are invariant over time, and (c) spatially- and temporally-stationary correlation among the residuals from the combination of these trends. The fundamental advance made by MEUK versus traditional universal kriging (UK) lies with the generalized least squares (GLS) model and the multi-event capability it facilitates, rather than in the geostatistics, although it is shown how use of MEUK can greatly reduce predictive variances versus UK. For expediency, MEUK assumes a spatial covariance that does not change over time – although it does not have to – which is an advantage over space-time methods that employ a full space-time covariance function. MEUK can be implemented with large multi-event datasets, as demonstrated by application to a large water level dataset. Often, MEUK enables the stable solution of multiple events for similar computational effort as for a single event. MEUK provides an efficient basis for developing “wheel-and-axle” monitoring strategies [32] that combines frequently sampled locations used monitor changes over time with many more locations sampled periodically to provide synoptic depictions. MEUK can aid in the identification of the core monitoring locations, allowing for reduced sampling frequency elsewhere. Although MEUK can incorporate longitudinal variograms as in other space-time methods, doing so reduces the computational advantages of MEUK.