Function to draw Taylor Diagrams for model evaluation. The function allows conditioning by any categorical or numeric variables, which makes the function very flexible.
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,
...
)As well as generating the plot itself, TaylorDiagram also
returns an object of class ``openair''. The object includes three main
components: call, the command used to generate the plot;
data, the data frame of summarised information used to make the
plot; and plot, the plot itself. 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.
An openair output can be manipulated using a number of generic operations,
including print, plot and summary.
A data frame minimally containing a column of observations and a column of predictions.
A column of observations with which the predictions (mod)
will be compared.
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.
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 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.
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.
Colours to be used for plotting. Useful options for
categorical data are avilable 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").
Colour for centred-RMS lines and text.
Colour for correlation coefficient lines and text.
Width of arrow used when used for comparing two model outputs.
Annotation shown for RMS error.
The plot annotation for observed values; default is "observed".
Should the key be shown?
Title for the key.
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.
Position of the key e.g. “top”,
“bottom”, “left” and “right”. See details in
lattice:xyplot for more details about finer control.
Should a strip be shown?
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.
David Carslaw
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").
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).
IPCC, 2001: Climate Change 2001: The Scientific Basis, Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change [Houghton, J.T., Y. Ding, D.J. Griggs, M. Noguer, P.J. van der Linden, X. Dai, K. Maskell, and C.A. Johnson (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 881 pp.
taylor.diagram from the plotrix package from which
some of the annotation code was used.
## 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"))
}
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