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,
  cols = "brewer1",
  rms.col = "darkgoldenrod",
  cor.col = "black",
  arrow.lwd = 3,
  annotate = "centred\nRMS error",
  text.obs = "observed",
  key = TRUE,
  key.title = group,
  key.columns = 1,
  key.pos = "right",
  strip = TRUE,
  auto.text = TRUE,
  ...
)

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

type determines how the data are split i.e. conditioned, and then plotted. The default is will produce a single plot using the entire data. Type can be one of the built-in types as detailed in cutData e.g. “season”, “year”, “weekday” and so on. For example, type = "season" will produce four plots --- one for each season.

It is also possible to choose type as another variable in the data frame. If that variable is numeric, then the data will be split into four quantiles (if possible) and labelled accordingly. If type is an existing character or factor variable, then those categories/levels will be used directly. This offers great flexibility for understanding the variation of different variables and how they depend on one another.

Type can be up length two e.g. type = c("season", "weekday") will produce a 2x2 plot split by season and day of the week. Note, when two types are provided the first forms the columns and the second the rows.

Note that often it will make sense to use type = "site" when multiple sites are available. This will ensure that each panel contains data specific to an individual site.

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.

cols

Colours to be used for plotting. Useful options for categorical data are available from RColorBrewer colours --- see the openair openColours function for more details. Useful schemes include “Accent”, “Dark2”, “Paired”, “Pastel1”, “Pastel2”, “Set1”, “Set2”, “Set3” --- but see ?brewer.pal for the maximum useful colours in each. For user defined the user can supply a list of colour names recognised by R (type colours() to see the full list). An example would be cols = c("yellow", "green", "blue").

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

Should the key be shown?

key.title

Title for the key.

key.columns

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

key.pos

Position of the key e.g. “top”, “bottom”, “left” and “right”. See details in lattice:xyplot for more details about finer control.

strip

Should a strip be shown?

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.

...

Other graphical parameters are passed onto cutData and lattice:xyplot. For example, TaylorDiagram passes the option hemisphere = "southern" on to cutData to provide southern (rather than default northern) hemisphere handling of type = "season". Similarly, common graphical parameters, such as layout for panel arrangement and pch and cex for plot symbol type and size, are passed on to xyplot. Most are passed unmodified, although there are some special cases where openair may locally manage this process. For example, common axis and title labelling options (such as xlab, ylab, main) are passed via quickText to handle routine formatting.

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

Examples

## in the examples below, most effort goes into making some artificial data
## the function itself can be run very simply
if (FALSE) {
## dummy model data for 2003
dat <- selectByDate(mydata, year = 2003)
dat <- data.frame(date = mydata$date, obs = mydata$nox, mod = mydata$nox)

## now make mod worse by adding bias and noise according to the month
## do this for 3 different models
dat <- transform(dat, month = as.numeric(format(date, "%m")))
mod1 <- transform(dat, mod = mod + 10 * month + 10 * month * rnorm(nrow(dat)),
model = "model 1")
## lag the results for mod1 to make the correlation coefficient worse
## without affecting the sd
mod1 <- transform(mod1, mod = c(mod[5:length(mod)], mod[(length(mod) - 3) :
length(mod)]))

## model 2
mod2 <- transform(dat, mod = mod + 7 * month + 7 * month * rnorm(nrow(dat)),
model = "model 2")
## model 3
mod3 <- transform(dat, mod = mod + 3 * month + 3 * month * rnorm(nrow(dat)),
model = "model 3")

mod.dat <- rbind(mod1, mod2, mod3)

## basic Taylor plot

TaylorDiagram(mod.dat, obs = "obs", mod = "mod", group = "model")

## Taylor plot by season
TaylorDiagram(mod.dat, obs = "obs", mod = "mod", group = "model", type = "season")

## now show how to evaluate model improvement (or otherwise)
mod1a <- transform(dat, mod = mod + 2 * month + 2 * month * rnorm(nrow(dat)),
model = "model 1")
mod2a <- transform(mod2, mod = mod * 1.3)
mod3a <- transform(dat, mod = mod + 10 * month + 10 * month * rnorm(nrow(dat)),
model = "model 3")
mod.dat2 <- rbind(mod1a, mod2a, mod3a)
mod.dat$mod2 <- mod.dat2$mod

## now we have a data frame with 3 models, 1 set of observations
## and TWO sets of model predictions (mod and mod2)

## do for all models
TaylorDiagram(mod.dat, obs = "obs", mod = c("mod", "mod2"), group = "model")
}
if (FALSE) {
## all models, by season
TaylorDiagram(mod.dat, obs = "obs", mod = c("mod", "mod2"), group = "model",
type = "season")

## consider two groups (model/month). In this case all months are shown by model
## but are only differentiated by model.

TaylorDiagram(mod.dat, obs = "obs", mod = "mod", group = c("model", "month"))
}