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Characterizing the spatio-temporal variability of relative sea level (RSL)and estimating local, regional, and global RSL trends requires statisticalanalysis of RSL data. Formal statistical treatments, needed to account for thespatially and temporally sparse distribution of data and for geochronologicaland elevational uncertainties, have advanced considerably over the last decade.Time-series models have adopted more flexible and physically-informedspecifications with more rigorous quantification of uncertainties.Spatio-temporal models have evolved from simple regional averaging toframeworks that more richly represent the correlation structure of RSL acrossspace and time. More complex statistical approaches enable rigorousquantification of spatial and temporal variability, the combination ofgeographically disparate data, and the separation of the RSL field into variouscomponents associated with different driving processes. We review the range ofstatistical modeling and analysis choices used in the literature, reformulatingthem for ease of comparison in a common hierarchical statistical framework. Thehierarchical framework separates each model into different levels, clearlypartitioning measurement and inferential uncertainty from process variability.Placing models in a hierarchical framework enables us to highlight both thesimilarities and differences among modeling and analysis choices. We illustratethe implications of some modeling and analysis choices currently used in theliterature by comparing the results of their application to common datasetswithin a hierarchical framework. In light of the complex patterns of spatialand temporal variability exhibited by RSL, we recommend non-parametricapproaches for modeling temporal and spatio-temporal RSL.

Statistical modeling of rates and trends in Holocene relative sea level