A flexible approach to assessing synchroneity of past events using Bayesian reconstructions of sedimentation history

Abstract

The dating of depths in two or more cores is frequently followed by a study of the synchroneity or otherwise of events reflected in the cores. The difficulties most frequently encountered are: (a) determining precisely the depths associated with the events; and (b) determining the ages associated with the depths. There has been much progress in recent years in developing tools for the study of uncertainties in establishing chronologies. This has not yet been matched by similar progress in modelling event/depth relationships. This paper proposes a simple and flexible approach, showing how uncertain events can be married to uncertain chronologies.

Difficulties in studying event/depth/age relationships typically involve a confounding of two different problems. First, what exactly do we mean by an ‘event’ – a point in history, a single depth in the core corresponding to a single time, or a depth/time range? Sometimes ‘event’ is in fact a shorthand for a space-time process. Do the data reflect more than one type of event/process? This can reflect vagueness in definition. Second, what are the sources and implications of the uncertainties?

Here we illustrate the issues involved by examination of several features seen in north European Holocene pollen records. The Alnus rise is regarded as a diachronous early Holocene event; in contrast the Ulmus decline is widely seen as a near synchronous event in the mid-Holocene. The third feature we examine is the interval between the Ulmus decline and the first occurrence of Cerealia-type pollen. The evidence for these events lies in cores of lake sediment from which are determined: (a) the proportions of pollen at many depths; and (b) radiocarbon age estimates from, usually, fewer depths. For this illustration we focus on six sites.

We draw attention to a new and flexible method (implemented in the free R software package Bchron; [Haslett, J., Parnell, A., 2008. A simple monotone process with application to radiocarbon dated depth chronologies. Journal of the Royal Statistical Society: Series C 57 (4), 399–418]) for the establishment of the uncertainties surrounding the dating of samples in such cores. We illustrate its flexibility by assessing the synchroneity of past events.

Introduction

An issue of considerable importance to our understanding of Quaternary palaeoenvironmental history is that of establishing synchroneity in events recognised in two or more stratigraphic records. Where the event appears asynchronous, an important second issue is that of establishing the extent of the asynchrony (see e.g. Davis, 1983, Birks, 1989, Alley et al., 1997, Haas et al., 1998, Bennett and Fuller, 2002, Blaauw et al., 2007). A common challenge is the uncertainty in establishing the age of the event in each of those records, as well as the identification of the event itself. This paper proposes a new and flexible approach to modelling such uncertainties and thus to the drawing of appropriately qualified scientific conclusions.

We illustrate this new approach using three events apparent in palynological data in northern Europe from six sites at each of which there is partial ¹⁴C dating information. These events are: (1) the early- to mid-Holocene increase in abundance of Alnus (alder) pollen (‘the alder rise’); (2) the mid-Holocene decline in abundance of Ulmus (elm) pollen (‘the elm decline’); and (3) the first mid- to late-Holocene occurrence of Cerealia-type pollen. We assess the degree of synchroneity across a number of sites of the first two events, and also compare the intervals between the last two events at the same sites. We suggest, however, that the overall approach is of wide relevance.

Notwithstanding its central importance in many aspects of Quaternary science, the problems associated with making such assessments of synchroneity have received remarkably little attention. For example, while a web search readily finds dozens of papers using the term “degree of synchroneity/synchronicity of an event” in the context of the Holocene, neither the terms synchroneity nor event are typically defined. Yet precise formal definitions are vital for the discussion of uncertainty. As discussed in this paper, we define an ‘event’ to be a unique point in time at a precise location in space. We study the time differences between pairs of such events each measured with uncertainty. Technically these are measures of the degree of diachroneity, in the presence of statistical noise. Typically events, as so defined, reflect unobserved space-time processes, such as the Ulmus decline, and study focusses on spatial structure in the degree of diachroneity.

From a much wider spatio-temporal perspective, the Ulmus decline across NW Europe is itself an ‘event’; indeed this is the sense in which we use it in the previous paragraph. It would be pedantic to insist always on separate terms for both the ‘unique in time and space’ event and the ‘spatiotemporal process’ event. Thus in general discussion below we will sometimes use the term in both senses, leaving the context to make it clear to the reader. Nevertheless, in our discussion of synchroneity in the presence of uncertainty, events are as defined above and as elaborated and illustrated below.

We identify three general aspects of the problem. First, there are problems associated with characterising the event itself, and hence in determining the depth at which the event occurred in a given stratigraphic sequence. If we are to associate an event with a point in history, a single depth in the core, what are the implications? Closely related to this is the establishment of the uncertainty about this depth, given the data available. Finally, there are challenges in assigning an age to this depth, with an associated statement of uncertainty. The latter are issues of statistical inference.

The structure of the paper is as follows. In Section 2 we discuss approaches to event definition, chronology modelling and synchroneity. Section 3 presents the data and proposes depth intervals for the events. Section 4 presents an illustration of various approaches applied to six selected sites around north western Europe. Finally, in Section 5, we discuss the potential of the new approach with further illustrations.