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Relationships between calibrated ages and depth in stratigraphical sequences: an estimation procedure by mixed-effect regression

Bjerknes Centre for Climate Research, University of Bergen, All6gaten 55, 5007 Bergen, Norway; Biological Institute, University of Bergen, Allegaten 41, 5007 Bergen, Norway einar.heegaard{at}bio.uib.no

H. J.B. Birks

Bjerknes Centre for Climate Research, University of Bergen, All6gaten 55, 5007 Bergen, Norway; Biological Institute, University of Bergen, Allegaten 41, 5007 Bergen, Norway; Environmental Change Research Centre, University College London, 26 Bedford Way, London WCIH OAP, UK

Richard J. Telford

Bjerknes Centre for Climate Research, University of Bergen, All6gaten 55, 5007 Bergen, Norway

We present a procedure for estimating age-depth relationships in stratigraphical sequences by means of a generalized mixed-effect regression using an ancillary function for the partitioning of the fixed effect and the random effect corresponding to the degree of representativity of the individual calibrated dates for a particular section of the sedimentary sequence. The procedure uses mid-point estimates of the calibrated ages in combination with the central distributional range as the basis for estimating the fixed relationship between age and depth. Further, it combines the variability of the calibrated age at individual layers (within-object variance) with estimation of the variability of the calibrated age distribution as a whole between the layers standardized by the fixed effect (between-object variance). These components of random variability can be considered independent, and hence the uncertainty of the estimated fixed relationship between age and depth can be estimated by combining the two random variables. The procedure follows the logic of mixed-effects models, but with prior information about the expected variance within each dated object.

Key Words: Sediment sequences • age-depth relationships • GAM • mixed effects • calibrated ages

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