Create a Taylor diagram

Creates a Taylor diagram comparing one or more quantitative prediction models with an observation vector. The radial coordinate is the model standard deviation divided by the observation standard deviation and the polar angle represents the Pearson correlation. Optional centred root-mean-square distance (RMSD) contours are drawn around the observation reference point.

Usage

gg_taylor(
  mods,
  obs,
  label = FALSE,
  legend = FALSE,
  point_size = 6,
  label_size = 4,
  na.rm = TRUE,
  half = FALSE,
  rmsd = TRUE,
  rmsd_colour = "red3",
  rmsd_breaks = NULL
)

Arguments

mods: Numeric vector, list of numeric vectors, or numeric matrix/data frame with one model per column. Rows match obs in order. Supplied model names must be unique; missing names are generated.
obs: A numeric observation vector.
label: Logical; draw model names directly on the diagram using ggrepel?
legend: Logical; colour model points by model and display a legend? The standard ggplot2 discrete colour palette is used by default.
point_size: Numeric size of model points.
label_size: Numeric text size for model labels.
na.rm: Logical; remove incomplete observation-prediction pairs separately for each model? If FALSE, missing pairs cause an error because diagram coordinates cannot be calculated. The default is TRUE.
half: Logical; if TRUE, draw only the positive-correlation portion of the Taylor diagram (r = 0 to r = 1). If FALSE, draw the full Taylor diagram (r = -1 to r = 1).
rmsd: Logical; show centred RMSD contours and their labels?
rmsd_colour: Character string giving the colour of the RMSD contours and labels.
rmsd_breaks: Optional numeric vector giving the RMSD contour values. If NULL, contours are drawn every 0.5 units.

Value

A ggplot2 plot object. It can be extended with ordinary ggplot2 layers, scales, labels, and themes.

Details

The geometry and default styling follow Wadoux, Walvoort, and Brus (2022) and the original implementation in the accompanying repository.

Missing pairs are removed separately per model when na.rm = TRUE. Two complete pairs with non-zero observation SD are required. All plotted statistics can be retrieved with diagram_stats().

Model names can be displayed either directly on the diagram with label = TRUE or through a colour legend with legend = TRUE.

With legend = TRUE, model points use the standard ggplot2 discrete colour palette. Because the returned object is a regular ggplot2 object, the model colour scale, legend, theme, titles, fonts, and other graphical elements can subsequently be customised with ordinary ggplot2 layers.

RMSD contours can be removed with rmsd = FALSE, recoloured with rmsd_colour, or placed at user-defined values with rmsd_breaks.

Interpretation

Let sigma-star denote the prediction standard deviation divided by the observation standard deviation, and let r be Pearson correlation. The Taylor geometry follows $$\mathrm{SDE}^{*} = \sqrt{1 + \sigma_{\mathrm{star}}^2 - 2\sigma_{\mathrm{star}}r},$$ where SDE* is the centred (unbiased) root mean square difference divided by the observation standard deviation. Radial distance gives sigma_star; the polar angle is acos(r); and the reference point has a standard-deviation ratio of one and correlation of one. Points nearer the reference point have smaller unbiased error.

A point inside the unit-radius arc has less variation than the observations (a smoother prediction), while a point outside it has greater variation. Points nearer the horizontal positive-correlation axis have stronger pattern agreement. The diagram does not show mean error: a model can be close to the reference point but systematically biased. Use gg_solar() or gg_target() together with bias() when mean error is important.

References

Wadoux, A. M. J.-C., Walvoort, D. J. J., and Brus, D. J. (2022). An integrated approach for the evaluation of quantitative soil maps through Taylor and solar diagrams. Geoderma, 405, 115332. doi:10.1016/j.geoderma.2021.115332

Taylor, K. E. (2001). Summarizing multiple aspects of model performance in a single diagram. Journal of Geophysical Research, 106, 7183-7192. doi:10.1029/2000JD900719

Examples

obs <- c(1, 2, 3, 4, 5)

mods <- list(
  perfect = obs,
  biased = obs + 1,
  smooth = c(2, 2, 3, 4, 4)
)

# Positive-correlation Taylor diagram with model names
gg_taylor(mods, obs, label = TRUE, half = TRUE)