The abanico plot: Visualising chronometric data with individual standard errors
Introduction
Many geoscientific dating communities, such as luminescence (optically stimulated luminescence; OSL, thermoluminescence, TL), fission track (FT) and cosmogenic nuclides (CN), including radiocarbon (14C) generate data that consist of age estimates with individual standard errors.1 There are several plot types for such chronometric data. Among them are rather simple representations of age estimates, without focus on errors (e.g., histograms or kernel density estimates). More insight into the data is possible when plotting standard errors explicitly in some relation to ages (e.g., plots of ages with error bars in ranked order or the radial plot). However, there is always a trade-off between adequate visualisation and straightforward interpretation of variability in ages and variability in errors. Galbraith and Roberts (2012) provide a thorough overview and discussion of currently available plot types for chronometric data with individual standard errors, focused on OSL data.
In this article, we argue for an enhancement of the radial plot (Galbraith, 1988). A radial plot is a scatter plot, showing data precision (reciprocal standard error) on the x-axis and a standardised estimate of age on the y-axis. Thereby, data precision increases along the x-axis and data variation around a given central value (e.g., the weighted mean) manifests as dispersion along the y-axis. Hence, these two sources of variability are geometrically separated. The radial plot further allows projecting each measured value on a z-axis depicting a scale of ages, and thereby in principle gives a sense of the corresponding ages and their distribution. Nevertheless, this view on age distributions is not really intuitive. Each age needs to be mapped by mentally drawing a line from the origin of the scatter plot (zero at the x- and y-axis), through the data point, to the z-axis. This drawback might be reduced by adding rugs, short lines perpendicular to the z-axis at the projected position of each data point, to the z-axis (e.g., as in Galbraith, 1988). But still, the radial plot is no intuitive tool to put emphasis on age frequency distributions. It therefore seems useful to combine the advantages of the radial plot with those of age frequency distribution plots, such as kernel density estimate plots, histograms or dot plots. The abanico plot explicitly focuses on the display of age frequency distributions. Accordingly, it is not intended to replace the radial plot, which provides an excellent approach to illustrating distribution of standardised estimates and precision. A radial plot (also available as function plot_RadialPlot() in the R package “Luminescence”, R Luminescence Developer Team, 2015) can be a sufficient or even more appropriate solution, for example when individual standard errors vary significantly or are high in general.
Typically, the above mentioned plots can be produced by specific software, such as Radial Plotter (Vermeesch, 2009), Analyst (e.g., Duller, 2007a, Duller, 2007b, Duller, 2015), S-scripts, SigmaPlot™ and so on. In any case, it requires to prepare, import and modify the age data, create the plot and export/save it for potential further modification steps. Usually, this involves dealing with several programs, although it might be reasonable to work with just one software. Kreutzer et al. (2012) introduced a collection of functions for the statistical programming language R (R Development Core Team, 2015): the package “Luminescence” (current version 0.5.0). The primary goals of the package are to provide a free, open, transparent, modifiable and comprehensive tool for luminescence data analysis. Specifically, the package supports nearly all published age models and plot types to handle luminescence data. However, its applicability is not restricted to luminescence data. Other dating communities share a considerable portion of data analysis and might also benefit from the package.
The scope of this article is to introduce the abanico plot, a plot type that merges a radial plot with a kernel density estimate plot (or other univariate plot types if the user decides so). Thus, it combines the benefits of both plot types to provide a comprehensive view on chronometric data. The contribution shows options to modify the abanico plot for different display purposes. Several examples highlight the overall applicability of the abanico plot to different dating disciplines. A Supplementary document provides a tutorial-like, step-by-step introduction to data import and how to create and customise the abanico plot.
Section snippets
Philosophy and construction
The abanico plot is named after its fan-like appearance (el abanico [span.] – the fan, [aβa'niko]). The initial concept of this plot emerged during the revision of an S-script by Rex Galbraith to create radial plots and is based on the combination of a radial plot and a kernel density estimate curve as suggested by Galbraith and Green 1990, Fig. 4, p. 204. Such aligned plots have been already adopted by fission track dating groups (e.g., Clift et al., 2013). However, a comprehensive view on
Applications
Like the radial plot (Galbraith, 1988, Galbraith, 1994), the abanico plot is devoted to a broad scientific community to display data adequately and straightforward, but also to maintain the possibility to adjust the plot layout for specific purposes. In the following paragraphs we show selected examples of possible applications in chronometric disciplines without any intention to re-interpret the published data but rather to highlight which aspects might be revealed by data visualisation using
Conclusion
The abanico plot overcomes most of the limitations of existing plot types for showing chronometric data with individual standard errors. Thereby, it does not represent a fundamentally new invention, but rather the combination of established plot types, each with own strengths and limitations. The abanico plot can be used to separate two sources of uncertainty: individual data precision and deviation from a common value. At the same time it allows for inspection of the data in their original age
Acknowledgements
First, we are grateful to the work of Rex Galbraith, especially for pointing at the idea to append further plots to the z-scale of a radial plot, for discussions about the meaningful implementation of plot parameters and for providing the original S-script, which the radial plot function is based on. The initial version of the abanico plot and earlier versions of this manuscript benefited significantly from his elaborated and critical input. We also thank the reviewer and editor team for their
References (26)
- et al.
Cosmogenic nuclide surface exposure dating of boulders on last-glacial and late-glacial moraines, Lago Buenos Aires, Argentina: Interpretive strategies and paleoclimate implications
Quat. Geochronol.
(2006) - et al.
Estimating the component ages in a finite mixture
Nucl. Tracks Radiat. Meas.
(1990) - et al.
Statistical aspects of equivalent dose and error calculation and display in OSL dating: an overview and some recommendations
Quat. Geochronol.
(2012) RadialPlotter: a Java application for fission track, luminescence and other radial plots
Radiat. Meas.
(2009)R in a Nutshell
(2012)- et al.
R by Example
(2012) - et al.
Zircon and apatite thermochronology of the Nankai Trough accretionary prism and trench, Japan: sediment transport in an active and collisional margin setting
Tectonics
(2013) - et al.
A practical guide to the R package Luminescence
Anc. TL
(2013) Analyst
(2007)Assessing the error on equivalent dose estimates derived from single aliquot regenerative dose measurements
Anc. TL
(2007)