openair (version 1.0)

TaylorDiagram: Taylor Diagram for model evaluation with conditioning

Description

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", 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 th

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.

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

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

cols

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, <

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.

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 def

Value

• 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.

Details

The Taylor Diagram is a very useful model evaluation tool. Details of the diagram can be found at http://www-pcmdi.llnl.gov/about/staff/Taylor/CV/Taylor_diagram_primer.pdf. 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, http://wwwpcmdi. llnl.gov/publications/ab55.html)

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. (see http://www.grida.no/climate/ipcc_tar/wg1/317.htm#fig84)

See Also

taylor.diagram from the plotrix package from which some of the annotation code was used.

Examples

## in the examples below, most effort goes into making some artificial data
## the function itself can be run very simply
## 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")
## all models, by season
TaylorDiagram(mod.dat, obs = "obs", mod = c("mod", "mod2"), group = "model",
type = "season")