Function for identifying clusters in bivariate polar plots (polarPlot); identifying clusters in the original data for subsequent processing.

polarCluster(mydata, pollutant = "nox", x = "ws", wd = "wd",
  n.clusters = 6, cols = "Paired", angle.scale = 315, units = x,
  auto.text = TRUE, ...)



A data frame minimally containing wd, another variable to plot in polar coordinates (the default is a column “ws” --- wind speed) and a pollutant. Should also contain date if plots by time period are required.


Mandatory. A pollutant name corresponding to a variable in a data frame should be supplied e.g. pollutant = "nox". Only one pollutant can be chosen.


Name of variable to plot against wind direction in polar coordinates, the default is wind speed, “ws”.


Name of wind direction field.


Number of clusters to use. If n.clusters is more than length 1, then a lattice panel plot will be output showing the clusters identified for each one of n.clusters.


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").


The wind speed scale is by default shown at a 315 degree angle. Sometimes the placement of the scale may interfere with an interesting feature. The user can therefore set angle.scale to another value (between 0 and 360 degrees) to mitigate such problems. For example angle.scale = 45 will draw the scale heading in a NE direction.


The units shown on the polar axis scale.


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 polarPlot, lattice:levelplot and cutData. Common axis and title labelling options (such as xlab, ylab, main) are passed via quickText to handle routine formatting.


As well as generating the plot itself, polarCluster also returns an object of class ``openair''. The object includes three main components: call, the command used to generate the plot; data, the original data frame with a new field cluster identifying the cluster; and plot, the plot itself. Note that any rows where the value of pollutant is NA are ignored so that the returned data frame may have fewer rows than the original.

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


Bivariate polar plots generated using the polarPlot function provide a very useful graphical technique for identifying and characterising different air pollution sources. While bivariate polar plots provide a useful graphical indication of potential sources, their location and wind-speed or other variable dependence, they do have several limitations. Often, a `feature' will be detected in a plot but the subsequent analysis of data meeting particular wind speed/direction criteria will be based only on the judgement of the investigator concerning the wind speed-direction intervals of interest. Furthermore, the identification of a feature can depend on the choice of the colour scale used, making the process somewhat arbitrary.

polarCluster applies Partition Around Medoids (PAM) clustering techniques to polarPlot surfaces to help identify potentially interesting features for further analysis. Details of PAM can be found in the cluster package (a core R package that will be pre-installed on all R systems). PAM clustering is similar to k-means but has several advantages e.g. is more robust to outliers. The clustering is based on the equal contribution assumed from the u and v wind components and the associated concentration. The data are standardized before clustering takes place.

The function works best by first trying different numbers of clusters and plotting them. This is achieved by setting n.clusters to be of length more than 1. For example, if n.clusters = 2:10 then a plot will be output showing the 9 cluster levels 2 to 10.

Note that clustering is computationally intensive and the function can take a long time to run --- particularly when the number of clusters is increased. For this reason it can be a good idea to run a few clusters first to get a feel for it e.g. n.clusters = 2:5.

Once the number of clusters has been decided, the user can then run polarCluster to return the original data frame together with a new column cluster, which gives the cluster number as a character (see example). Note that any rows where the value of pollutant is NA are ignored so that the returned data frame may have fewer rows than the original.

Note that there are no automatic ways in ensuring the most appropriate number of clusters as this is application dependent. However, there is often a-priori information available on what different features in polar plots correspond to. Nevertheless, the appropriateness of different clusters is best determined by post-processing the data. The Carslaw and Beevers (2012) paper discusses these issues in more detail.

Note that unlike most other openair functions only a single type “default” is allowed.


Carslaw, D.C., Beevers, S.D, Ropkins, K and M.C. Bell (2006). Detecting and quantifying aircraft and other on-airport contributions to ambient nitrogen oxides in the vicinity of a large international airport. Atmospheric Environment. 40/28 pp 5424-5434.

Carslaw, D.C., & Beevers, S.D. (2013). Characterising and understanding emission sources using bivariate polar plots and k-means clustering. Environmental Modelling & Software, 40, 325-329. doi:10.1016/j.envsoft.2012.09.005

See also


# NOT RUN { # load example data from package data(mydata) ## plot 2-8 clusters. Warning! This can take several minutes... polarCluster(mydata, pollutant = "nox", n.clusters = 2:8) # basic plot with 6 clusters results <- polarCluster(mydata, pollutant = "nox", n.clusters = 6) ## get results, could read into a new data frame to make it easier to refer to ## e.g. results <- results$data... head(results$data) ## how many points are there in each cluster? table(results$data$cluster) ## plot clusters 3 and 4 as a timeVariation plot using SAME colours as in ## cluster plot timeVariation(subset(results$data, cluster %in% c("3", "4")), pollutant = "nox", group = "cluster", col = openColours("Paired", 6)[c(3, 4)]) # }