Taylor Diagram for model evaluation with conditioning

Function to draw Taylor Diagrams for model evaluation. The function allows conditioning by any categorical or numeric variables, which makes the function very flexible.

Usage

TaylorDiagram(
  mydata,
  obs = "obs",
  mod = "mod",
  group = NULL,
  type = "default",
  normalise = FALSE,
  pos.cor = NULL,
  cols = "brewer1",
  rms.col = "darkgoldenrod",
  cor.col = "black",
  arrow.lwd = 3,
  annotate = "centred\nRMS error",
  text.obs = "observed",
  key.title = group,
  key.columns = 1,
  key.position = "right",
  strip.position = "top",
  auto.text = TRUE,
  plot = TRUE,
  key = NULL,
  ...
)

Arguments

mydata

A data frame minimally containing a column of observations and a column of predictions.

obs

A column of observations with which the predictions (mod) will be compared.

mod

A column of model predictions. Note, mod can be of length 2 i.e. two lots of model predictions. If two sets of predictions are are present e.g. mod = c("base", "revised"), then arrows are shown on the Taylor Diagram which show the change in model performance in going from the first to the second. This is useful where, for example, there is interest in comparing how one model run compares with another using different assumptions e.g. input data or model set up. See examples below.

group

The group column is used to differentiate between different models and can be a factor or character. The total number of models compared will be equal to the number of unique values of group.

group can also be of length two e.g. group = c("model", "site"). In this case all model-site combinations will be shown but they will only be differentiated by colour/symbol by the first grouping variable ("model" in this case). In essence the plot removes the differentiation by the second grouping variable. Because there will be different values of obs for each group, normalise = TRUE should be used.

type

Character string(s) defining how data should be split/conditioned before plotting. "default" produces a single panel using the entire dataset. Any other options will split the plot into different panels - a roughly square grid of panels if one type is given, or a 2D matrix of panels if two types are given. type is always passed to cutData(), and can therefore be any of:

A built-in type defined in cutData() (e.g., "season", "year", "weekday", etc.). For example, type = "season" will split the plot into four panels, one for each season.
The name of a numeric column in mydata, which will be split into n.levels quantiles (defaulting to 4).
The name of a character or factor column in mydata, which will be used as-is. Commonly this could be a variable like "site" to ensure data from different monitoring sites are handled and presented separately. It could equally be any arbitrary column created by the user (e.g., whether a nearby possible pollutant source is active or not).

Most openair plotting functions can take two type arguments. If two are given, the first is used for the columns and the second for the rows.

normalise

Should the data be normalised by dividing the standard deviation of the observations? The statistics can be normalised (and non-dimensionalised) by dividing both the RMS difference and the standard deviation of the mod values by the standard deviation of the observations (obs). In this case the “observed” point is plotted on the x-axis at unit distance from the origin. This makes it possible to plot statistics for different species (maybe with different units) on the same plot. The normalisation is done by each group/type combination.

pos.cor

Show only positive correlations (TRUE) or include negative correlations (FALSE). If negative correlations are shown, the Taylor Diagram will show two quadrants. The default, NULL, will use two quadrants if any negative correlations are present in the data and one quadrant if all correlations are positive.

cols

Colours to use for plotting. Can be a pre-set palette (e.g., "turbo", "viridis", "tol", "Dark2", etc.) or a user-defined vector of R colours (e.g., c("yellow", "green", "blue", "black") - see colours() for a full list) or hex-codes (e.g., c("#30123B", "#9CF649", "#7A0403")). Alternatively, can be a list of arguments to control the colour palette more closely (e.g., palette, direction, alpha, etc.). See openColours() and colourOpts() for more details.

rms.col

Colour for centred-RMS lines and text.

cor.col

Colour for correlation coefficient lines and text.

arrow.lwd

Width of arrow used when used for comparing two model outputs.

annotate

Annotation shown for RMS error.

text.obs

The plot annotation for observed values; default is "observed".

key.title

Used to set the title of the legend. The legend title is passed to quickText() if auto.text = TRUE.

key.columns

Number of columns to be used in a categorical legend. With many categories a single column can make to key too wide. The user can thus choose to use several columns by setting key.columns to be less than the number of categories.

key.position

Location where the legend is to be placed. Allowed arguments include "top", "right", "bottom", "left" and "none", the last of which removes the legend entirely.

strip.position

Location where the facet 'strips' are located when using type. When one type is provided, can be one of "left", "right", "bottom" or "top". When two types are provided, this argument defines whether the strips are "switched" and can take either "x", "y", or "both". For example, "x" will switch the 'top' strip locations to the bottom of the plot.

auto.text

Either TRUE (default) or FALSE. If TRUE titles and axis labels will automatically try and format pollutant names and units properly, e.g., by subscripting the "2" in "NO2". Passed to quickText().

plot

When openair plots are created they are automatically printed to the active graphics device. plot = FALSE deactivates this behaviour. This may be useful when the plot data is of more interest, or the plot is required to appear later (e.g., later in a Quarto document, or to be saved to a file).

key

Deprecated; please use key.position. If FALSE, sets key.position to "none".

...

Addition options are passed on to cutData() for type handling. Some additional arguments are also available, varying somewhat in different plotting functions:

title, subtitle, caption, tag, xlab and ylab control the plot title, subtitle, caption, tag, x-axis label and y-axis label. All of these are passed through to quickText() if auto.text = TRUE.
xlim, ylim and limits control the limits of the x-axis, y-axis and colorbar scales.
ncol and nrow set the number of columns and rows in a faceted plot.
fontsize overrides the overall font size of the plot by setting the text argument of ggplot2::theme(). It may also be applied proportionately to any openair annotations (e.g., N/E/S/W labels on polar coordinate plots).
Various graphical parameters are also supported: linewidth, linetype, shape, size, border, and alpha. Not all parameters apply to all plots. These can take a single value, or a vector of multiple values - e.g., shape = c(1, 2) - which will be recycled to the length of values needed.
lineend, linejoin and linemitre tweak the appearance of line plots; see ggplot2::geom_line() for more information.
In polar coordinate plots, annotate = FALSE will remove the N/E/S/W labels and any other annotations.

Value

an openair object. If retained, e.g., using output <- TaylorDiagram(thedata, obs = "nox", mod = "mod"), this output can be used to recover the data, reproduce or rework the original plot or undertake further analysis. For example, output$data will be a data frame consisting of the group, type, correlation coefficient (R), the standard deviation of the observations and measurements.

Details

The Taylor Diagram is a very useful model evaluation tool. The diagram provides a way of showing how three complementary model performance statistics vary simultaneously. These statistics are the correlation coefficient R, the standard deviation (sigma) and the (centred) root-mean-square error. These three statistics can be plotted on one (2D) graph because of the way they are related to one another which can be represented through the Law of Cosines.

The openair version of the Taylor Diagram has several enhancements that increase its flexibility. In particular, the straightforward way of producing conditioning plots should prove valuable under many circumstances (using the type option). Many examples of Taylor Diagrams focus on model-observation comparisons for several models using all the available data. However, more insight can be gained into model performance by partitioning the data in various ways e.g. by season, daylight/nighttime, day of the week, by levels of a numeric variable e.g. wind speed or by land-use type etc.

To consider several pollutants on one plot, a column identifying the pollutant name can be used e.g. pollutant. Then the Taylor Diagram can be plotted as (assuming a data frame thedata):

TaylorDiagram(thedata, obs = "obs", mod = "mod", group = "model", type = "pollutant")

which will give the model performance by pollutant in each panel.

Note that it is important that each panel represents data with the same mean observed data across different groups. Therefore TaylorDiagram(mydata, group = "model", type = "season") is OK, whereas TaylorDiagram(mydata, group = "season", type = "model") is not because each panel (representing a model) will have four different mean values — one for each season. Generally, the option group is either missing (one model being evaluated) or represents a column giving the model name. However, the data can be normalised using the normalise option. Normalisation is carried out on a per group/type basis making it possible to compare data on different scales e.g. TaylorDiagram(mydata, group = "season", type = "model", normalise = TRUE). In this way it is possible to compare different pollutants, sites etc. in the same panel.

Also note that if multiple sites are present it makes sense to use type = "site" to ensure that each panel represents an individual site with its own specific standard deviation etc. If this is not the case then select a single site from the data first e.g. subset(mydata, site == "Harwell").

References

Taylor, K.E.: Summarizing multiple aspects of model performance in a single diagram. J. Geophys. Res., 106, 7183-7192, 2001 (also see PCMDI Report 55).

Author

David Carslaw

Jack Davison