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Typically plots the concentration of a pollutant by wind direction and as a function of time as an annulus. The function is good for visualising how concentrations of pollutants vary by wind direction and a time period e.g. by month, day of week.


  pollutant = "nox",
  resolution = "fine", = NULL,
  period = "hour",
  type = "default",
  statistic = "mean",
  percentile = NA,
  limits = c(0, 100),
  cols = "default",
  width = "normal",
  min.bin = 1,
  exclude.missing = TRUE,
  date.pad = FALSE,
  force.positive = TRUE,
  k = c(20, 10),
  normalise = FALSE,
  key.header = "",
  key.footer = pollutant,
  key.position = "right",
  key = TRUE,
  auto.text = TRUE,



A data frame minimally containing date, wd and a pollutant.


Mandatory. A pollutant name corresponding to a variable in a data frame should be supplied e.g. pollutant = "nox". There can also be more than one pollutant specified e.g. pollutant = c("nox", "no2"). The main use of using two or more pollutants is for model evaluation where two species would be expected to have similar concentrations. This saves the user stacking the data and it is possible to work with columns of data directly. A typical use would be pollutant = c("obs", "mod") to compare two columns “obs” (the observations) and “mod” (modelled values).


Two plot resolutions can be set: “normal” and “fine” (the default).

Should the results be calculated in local time that includes a treatment of daylight savings time (DST)? The default is not to consider DST issues, provided the data were imported without a DST offset. Emissions activity tends to occur at local time e.g. rush hour is at 8 am every day. When the clocks go forward in spring, the emissions are effectively released into the atmosphere typically 1 hour earlier during the summertime i.e. when DST applies. When plotting diurnal profiles, this has the effect of “smearing-out” the concentrations. Sometimes, a useful approach is to express time as local time. This correction tends to produce better-defined diurnal profiles of concentration (or other variables) and allows a better comparison to be made with emissions/activity data. If set to FALSE then GMT is used. Examples of usage include = "Europe/London", = "America/New_York". See cutData and import for more details.


This determines the temporal period to consider. Options are “hour” (the default, to plot diurnal variations), “season” to plot variation throughout the year, “weekday” to plot day of the week variation and “trend” to plot the trend by wind direction.


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", "site") will produce a 2x2 plot split by season and site. The use of two types is mostly meant for situations where there are several sites. Note, when two types are provided the first forms the columns and the second the rows.

Also note that for the polarAnnulus function some type/period combinations are forbidden or make little sense. For example, type = "season" and period = "trend" (which would result in a plot with too many gaps in it for sensible smoothing), or type = "weekday" and period = "weekday".


The statistic that should be applied to each wind speed/direction bin. Can be “mean” (default), “median”, “max” (maximum), “frequency”. “stdev” (standard deviation), “weighted.mean” or “cpf” (Conditional Probability Function). Because of the smoothing involved, the colour scale for some of these statistics is only to provide an indication of overall pattern and should not be interpreted in concentration units e.g. for statistic = "weighted.mean" where the bin mean is multiplied by the bin frequency and divided by the total frequency. In many cases using polarFreq will be better. Setting statistic = "weighted.mean" can be useful because it provides an indication of the concentration * frequency of occurrence and will highlight the wind speed/direction conditions that dominate the overall mean.


If statistic = "percentile" or statistic = "cpf" then percentile is used, expressed from 0 to 100. Note that the percentile value is calculated in the wind speed, wind direction ‘bins’. For this reason it can also be useful to set min.bin to ensure there are a sufficient number of points available to estimate a percentile. See quantile for more details of how percentiles are calculated.


Limits for colour scale.


Colours to be used for plotting. Options include “default”, “increment”, “heat”, “jet” and user defined. 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")


The width of the annulus; can be “normal” (the default), “thin” or “fat”.


The minimum number of points allowed in a wind speed/wind direction bin. The default is 1. A value of two requires at least 2 valid records in each bin an so on; bins with less than 2 valid records are set to NA. Care should be taken when using a value > 1 because of the risk of removing real data points. It is recommended to consider your data with care. Also, the polarFreq function can be of use in such circumstances.


Setting this option to TRUE (the default) removes points from the plot that are too far from the original data. The smoothing routines will produce predictions at points where no data exist i.e. they predict. By removing the points too far from the original data produces a plot where it is clear where the original data lie. If set to FALSE missing data will be interpolated.


For type = "trend" (default), date.pad = TRUE will pad-out missing data to the beginning of the first year and the end of the last year. The purpose is to ensure that the trend plot begins and ends at the beginning or end of year.


The default is TRUE. Sometimes if smoothing data with steep gradients it is possible for predicted values to be negative. force.positive = TRUE ensures that predictions remain postive. This is useful for several reasons. First, with lots of missing data more interpolation is needed and this can result in artifacts because the predictions are too far from the original data. Second, if it is known beforehand that the data are all postive, then this option carries that assumption through to the prediction. The only likely time where setting force.positive = FALSE would be if background concentrations were first subtracted resulting in data that is legitimately negative. For the vast majority of situations it is expected that the user will not need to alter the default option.


The smoothing value supplied to gam for the temporal and wind direction components, respectively. In some cases e.g. a trend plot with less than 1-year of data the smoothing with the default values may become too noisy and affected more by outliers. Choosing a lower value of k (say 10) may help produce a better plot.


If TRUE concentrations are normalised by dividing by their mean value. This is done after fitting the smooth surface. This option is particularly useful if one is interested in the patterns of concentrations for several pollutants on different scales e.g. NOx and CO. Often useful if more than one pollutant is chosen.


Adds additional text/labels to the scale key. For example, passing the options key.header = "header", key.footer = "footer1" adds addition text above and below the scale key. These arguments are passed to drawOpenKey via quickText, applying the auto.text argument, to handle formatting.


see key.header.


Location where the scale key is to plotted. Allowed arguments currently include “top”, “right”, “bottom” and “left”.


Fine control of the scale key via drawOpenKey. See drawOpenKey for further details.


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 passed onto lattice:levelplot and cutData. For example, polarAnnulus passes the option hemisphere = "southern" on to cutData to provide southern (rather than default northern) hemisphere handling of type = "season". Similarly, common axis and title labelling options (such as xlab, ylab, main) are passed to levelplot via quickText to handle routine formatting.


As well as generating the plot itself, polarAnnulus 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 <- polarAnnulus(mydata, "nox"), this output can be used to recover the data, reproduce or rework the original plot or undertake further analysis.

An openair output can be manipulated using a number of generic operations, including print, plot and summary.


The polarAnnulus function shares many of the properties of the polarPlot. However, polarAnnulus is focussed on displaying information on how concentrations of a pollutant (values of another variable) vary with wind direction and time. Plotting as an annulus helps to reduce compression of information towards the centre of the plot. The circular plot is easy to interpret because wind direction is most easily understood in polar rather than Cartesian coordinates.

The inner part of the annulus represents the earliest time and the outer part of the annulus the latest time. The time dimension can be shown in many ways including "trend", "hour" (hour or day), "season" (month of the year) and "weekday" (day of the week). Taking hour as an example, the plot will show how concentrations vary by hour of the day and wind direction. Such plots can be very useful for understanding how different source influences affect a location.

For type = "trend" the amount of smoothing does not vary linearly with the length of the time series i.e. a certain amount of smoothing per unit interval in time. This is a deliberate choice because should one be interested in a subset (in time) of data, more detail will be provided for the subset compared with the full data set. This allows users to investigate specific periods in more detail. Full flexibility is given through the smoothing parameter k.


David Carslaw


# load example data from package

# diurnal plot for PM10 at Marylebone Rd
if (FALSE) polarAnnulus(mydata, pollutant = "pm10",
main = "diurnal variation in pm10 at Marylebone Road")

# seasonal plot for PM10 at Marylebone Rd
if (FALSE) polarAnnulus(mydata, poll="pm10", period = "season")

# trend in coarse particles (PMc = PM10 - PM2.5), calculate PMc first

mydata$pmc <- mydata$pm10 - mydata$pm25
if (FALSE) polarAnnulus(mydata, poll="pmc", period = "trend",
main = "trend in pmc at Marylebone Road")