Function for plotting bivariate polar plots with smoothing.

Function for plotting pollutant concentration in polar coordinates showing concentration by wind speed (or another numeric variable) and direction. Mean concentrations are calculated for wind speed-direction ‘bins’ (e.g. 0-1, 1-2 m/s,... and 0-10, 10-20 degrees etc.). To aid interpretation, gam smoothing is carried out using mgcv.

Usage

polarPlot(
  mydata,
  pollutant = "nox",
  x = "ws",
  wd = "wd",
  type = "default",
  statistic = "mean",
  limits = NULL,
  exclude.missing = TRUE,
  uncertainty = FALSE,
  percentile = NA,
  cols = "default",
  weights = c(0.25, 0.5, 0.75),
  min.bin = 1,
  col.na = "grey",
  upper = NA,
  angle.scale = 315,
  units = x,
  force.positive = TRUE,
  k = 100,
  normalise = FALSE,
  breaks = NULL,
  labels = NULL,
  key.title = paste(statistic, pollutant, sep = " "),
  key.position = "right",
  strip.position = "top",
  auto.text = TRUE,
  ws_spread = 1.5,
  wd_spread = 5,
  x_error = NA,
  y_error = NA,
  kernel = "gaussian",
  formula.label = TRUE,
  tau = 0.5,
  plot = TRUE,
  key = NULL,
  ...
)

Arguments

mydata

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.

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). When pair-wise statistics such as Pearson correlation and regression techniques are to be plotted, pollutant takes two elements too. For example, pollutant = c("bc", "pm25") where "bc" is a function of "pm25".

x

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

wd

Name of wind direction field.

type

Character string(s) defining how data should be split/conditioned before plotting. "default" produces a single panel using the entire dataset. Any other options will split the plot into different panels - a roughly square grid of panels if one type is given, or a 2D matrix of panels if two types are given. type is always passed to cutData(), and can therefore be any of:

A built-in type defined in cutData() (e.g., "season", "year", "weekday", etc.). For example, type = "season" will split the plot into four panels, one for each season.
The name of a numeric column in mydata, which will be split into n.levels quantiles (defaulting to 4).
The name of a character or factor column in mydata, which will be used as-is. Commonly this could be a variable like "site" to ensure data from different monitoring sites are handled and presented separately. It could equally be any arbitrary column created by the user (e.g., whether a nearby possible pollutant source is active or not).

Most openair plotting functions can take two type arguments. If two are given, the first is used for the columns and the second for the rows.

statistic

The statistic that should be applied to each wind speed/direction bin. 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.Can be:

“mean” (default), “median”, “max” (maximum), “frequency”. “stdev” (standard deviation), “weighted.mean”.
statistic = "nwr" Implements the Non-parametric Wind Regression approach of Henry et al. (2009) that uses kernel smoothers. The openair implementation is not identical because Gaussian kernels are used for both wind direction and speed. The smoothing is controlled by ws_spread and wd_spread.
statistic = "cpf" the conditional probability function (CPF) is plotted and a single (usually high) percentile level is supplied. The CPF is defined as CPF = my/ny, where my is the number of samples in the y bin (by default a wind direction, wind speed interval) with mixing ratios greater than the overall percentile concentration, and ny is the total number of samples in the same wind sector (see Ashbaugh et al., 1985). Note that percentile intervals can also be considered; see percentile for details.
When statistic = "r" or statistic = "Pearson", the Pearson correlation coefficient is calculated for two pollutants. The calculation involves a weighted Pearson correlation coefficient, which is weighted by Gaussian kernels for wind direction an the radial variable (by default wind speed). More weight is assigned to values close to a wind speed-direction interval. Kernel weighting is used to ensure that all data are used rather than relying on the potentially small number of values in a wind speed-direction interval.
When statistic = "Spearman", the Spearman correlation coefficient is calculated for two pollutants. The calculation involves a weighted Spearman correlation coefficient, which is weighted by Gaussian kernels for wind direction an the radial variable (by default wind speed). More weight is assigned to values close to a wind speed-direction interval. Kernel weighting is used to ensure that all data are used rather than relying on the potentially small number of values in a wind speed-direction interval.
"robust_slope" is another option for pair-wise statistics and "quantile.slope", which uses quantile regression to estimate the slope for a particular quantile level (see also tau for setting the quantile level).
"york_slope" is another option for pair-wise statistics which uses the York regression method to estimate the slope. In this method the uncertainties in x and y are used in the determination of the slope. The uncertainties are provided by x_error and y_error — see below.

limits

The function does its best to choose sensible limits automatically. However, there are circumstances when the user will wish to set different ones. An example would be a series of plots showing each year of data separately. The limits are set in the form c(lower, upper), so limits = c(0, 100) would force the plot limits to span 0-100.

exclude.missing

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.

uncertainty

Should the uncertainty in the calculated surface be shown? If TRUE three plots are produced on the same scale showing the predicted surface together with the estimated lower and upper uncertainties at the 95% confidence interval. Calculating the uncertainties is useful to understand whether features are real or not. For example, at high wind speeds where there are few data there is greater uncertainty over the predicted values. The uncertainties are calculated using the GAM and weighting is done by the frequency of measurements in each wind speed-direction bin. Note that if uncertainties are calculated then the type is set to "default".

percentile

If statistic = "percentile" 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.

percentile is also used for the Conditional Probability Function (CPF) plots. percentile can be of length two, in which case the percentile interval is considered for use with CPF. For example, percentile = c(90, 100) will plot the CPF for concentrations between the 90 and 100th percentiles. Percentile intervals can be useful for identifying specific sources. In addition, percentile can also be of length 3. The third value is the ‘trim’ value to be applied. When calculating percentile intervals many can cover very low values where there is no useful information. The trim value ensures that values greater than or equal to the trim * mean value are considered before the percentile intervals are calculated. The effect is to extract more detail from many source signatures. See the manual for examples. Finally, if the trim value is less than zero the percentile range is interpreted as absolute concentration values and subsetting is carried out directly.

cols

Colours to use for plotting. Can be a pre-set palette (e.g., "turbo", "viridis", "tol", "Dark2", etc.) or a user-defined vector of R colours (e.g., c("yellow", "green", "blue", "black") - see colours() for a full list) or hex-codes (e.g., c("#30123B", "#9CF649", "#7A0403")). Alternatively, can be a list of arguments to control the colour palette more closely (e.g., palette, direction, alpha, etc.). See openColours() and colourOpts() for more details.

weights

At the edges of the plot there may only be a few data points in each wind speed-direction interval, which could in some situations distort the plot if the concentrations are high. weights applies a weighting to reduce their influence. For example and by default if only a single data point exists then the weighting factor is 0.25 and for two points 0.5. To not apply any weighting and use the data as is, use weights = c(1, 1, 1).

An alternative to down-weighting these points they can be removed altogether using min.bin.

min.bin

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.

col.na

When min.bin is > 1 it can be useful to show where data are removed on the plots. This is done by shading the missing data in col.na. To not highlight missing data when min.bin > 1 choose col.na = "transparent".

upper

This sets the upper limit wind speed to be used. Often there are only a relatively few data points at very high wind speeds and plotting all of them can reduce the useful information in the plot.

angle.scale

In radial plots (e.g., polarPlot()), the radial scale is drawn directly on the plot itself. While suitable defaults have been chosen, sometimes the placement of the scale may interfere with an interesting feature. angle.scale can take any value between 0 and 360 to place the scale at a different angle, or FALSE to move it to the side of the plots.

units

The units shown on the polar axis scale.

force.positive

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 positive. This is useful for several reasons. First, with lots of missing data more interpolation is needed and this can result in artefacts because the predictions are too far from the original data. Second, if it is known beforehand that the data are all positive, 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.

k

This is the smoothing parameter used by the gam function in package mgcv. Typically, value of around 100 (the default) seems to be suitable and will resolve important features in the plot. The most appropriate choice of k is problem-dependent; but extensive testing of polar plots for many different problems suggests a value of k of about 100 is suitable. Setting k to higher values will not tend to affect the surface predictions by much but will add to the computation time. Lower values of k will increase smoothing. Sometimes with few data to plot polarPlot will fail. Under these circumstances it can be worth lowering the value of k.

normalise

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.

breaks, labels

If a categorical colour scale is required then breaks should be specified. These should be provided as a numeric vector, e.g., breaks = c(0, 50, 100, 1000). Users should set the maximum value of breaks to exceed the maximum data value to ensure it is within the maximum final range, e.g., 100–1000 in this case. Labels will automatically be generated, but can be customised by passing a character vector to labels, e.g., labels = c("good", "bad", "very bad"). In this example, 0 - 50 will be "good" and so on. Note there is one less label than break.

key.title

Used to set the title of the legend. The legend title is passed to quickText() if auto.text = TRUE.

key.position

Location where the legend is to be placed. Allowed arguments include "top", "right", "bottom", "left" and "none", the last of which removes the legend entirely.

strip.position

Location where the facet 'strips' are located when using type. When one type is provided, can be one of "left", "right", "bottom" or "top". When two types are provided, this argument defines whether the strips are "switched" and can take either "x", "y", or "both". For example, "x" will switch the 'top' strip locations to the bottom of the plot.

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". Passed to quickText().

ws_spread

The value of sigma used for Gaussian kernel weighting of wind speed when statistic = "nwr" or when correlation and regression statistics are used such as r. Default is 0.5.

wd_spread

The value of sigma used for Gaussian kernel weighting of wind direction when statistic = "nwr" or when correlation and regression statistics are used such as r. Default is 4.

x_error

The x error / uncertainty used when statistic = "york_slope".

y_error

The y error / uncertainty used when statistic = "york_slope".

kernel

Type of kernel used for the weighting procedure for when correlation or regression techniques are used. Only "gaussian" is supported but this may be enhanced in the future.

formula.label

When pair-wise statistics such as regression slopes are calculated and plotted, should a formula label be displayed? formula.label will also determine whether concentration information is printed when statistic = "cpf".

tau

The quantile to be estimated when statistic is set to "quantile.slope". Default is 0.5 which is equal to the median and will be ignored if "quantile.slope" is not used.

plot

When openair plots are created they are automatically printed to the active graphics device. plot = FALSE deactivates this behaviour. This may be useful when the plot data is of more interest, or the plot is required to appear later (e.g., later in a Quarto document, or to be saved to a file).

key

Deprecated; please use key.position. If FALSE, sets key.position to "none".

...

Addition options are passed on to cutData() for type handling. Some additional arguments are also available, varying somewhat in different plotting functions:

title, subtitle, caption, tag, xlab and ylab control the plot title, subtitle, caption, tag, x-axis label and y-axis label. All of these are passed through to quickText() if auto.text = TRUE.
xlim, ylim and limits control the limits of the x-axis, y-axis and colorbar scales.
ncol and nrow set the number of columns and rows in a faceted plot.
fontsize overrides the overall font size of the plot by setting the text argument of ggplot2::theme(). It may also be applied proportionately to any openair annotations (e.g., N/E/S/W labels on polar coordinate plots).
Various graphical parameters are also supported: linewidth, linetype, shape, size, border, and alpha. Not all parameters apply to all plots. These can take a single value, or a vector of multiple values - e.g., shape = c(1, 2) - which will be recycled to the length of values needed.
lineend, linejoin and linemitre tweak the appearance of line plots; see ggplot2::geom_line() for more information.
In polar coordinate plots, annotate = FALSE will remove the N/E/S/W labels and any other annotations.

Value

an openair object. data contains four set columns: cond, conditioning based on type; u and v, the translational vectors based on ws and wd; and the local pollutant estimate.

Details

The bivariate polar plot is a useful diagnostic tool for quickly gaining an idea of potential sources. Wind speed is one of the most useful variables to use to separate source types (see references). For example, ground-level concentrations resulting from buoyant plumes from chimney stacks tend to peak under higher wind speed conditions. Conversely, ground-level, non-buoyant plumes such as from road traffic, tend to have highest concentrations under low wind speed conditions. Other sources such as from aircraft engines also show differing characteristics by wind speed.

The function has been developed to allow variables other than wind speed to be plotted with wind direction in polar coordinates. The key issue is that the other variable plotted against wind direction should be discriminating in some way. For example, temperature can help reveal high-level sources brought down to ground level in unstable atmospheric conditions, or show the effect a source emission dependent on temperature e.g. biogenic isoprene.

The plots can vary considerably depending on how much smoothing is done. The approach adopted here is based on the very flexible and capable mgcv package that uses Generalized Additive Models. While methods do exist to find an optimum level of smoothness, they are not necessarily useful. The principal aim of polarPlot is as a graphical analysis rather than for quantitative purposes. In this respect the smoothing aims to strike a balance between revealing interesting (real) features and overly noisy data. The defaults used in polarPlot() are based on the analysis of data from many different sources. More advanced users may wish to modify the code and adopt other smoothing approaches.

Various statistics are possible to consider e.g. mean, maximum, median. statistic = "max" is often useful for revealing sources. Pair-wise statistics between two pollutants can also be calculated.

The function can also be used to compare two pollutant species through a range of pair-wise statistics (see help on statistic) and Grange et al. (2016) (open-access publication link below).

Wind direction is split up into 10 degree intervals and the other variable (e.g. wind speed) 30 intervals. These 2D bins are then used to calculate the statistics.

These plots often show interesting features at higher wind speeds (see references below). For these conditions there can be very few measurements and therefore greater uncertainty in the calculation of the surface. There are several ways in which this issue can be tackled. First, it is possible to avoid smoothing altogether and use polarFreq(). Second, the effect of setting a minimum number of measurements in each wind speed-direction bin can be examined through min.bin. It is possible that a single point at high wind speed conditions can strongly affect the surface prediction. Therefore, setting min.bin = 3, for example, will remove all wind speed-direction bins with fewer than 3 measurements before fitting the surface. Third, consider setting uncertainty = TRUE. This option will show the predicted surface together with upper and lower 95% confidence intervals, which take account of the frequency of measurements.

References

Ashbaugh, L.L., Malm, W.C., Sadeh, W.Z., 1985. A residence time probability analysis of sulfur concentrations at ground canyon national park. Atmospheric Environment 19 (8), 1263-1270.

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.

Henry, R.C., Chang, Y.S., Spiegelman, C.H., 2002. Locating nearby sources of air pollution by nonparametric regression of atmospheric concentrations on wind direction. Atmospheric Environment 36 (13), 2237-2244.

Henry, R., Norris, G.A., Vedantham, R., Turner, J.R., 2009. Source region identification using Kernel smoothing. Environ. Sci. Technol. 43 (11), 4090e4097. DOI: 10.1021/es8011723.

Uria-Tellaetxe, I. and D.C. Carslaw (2014). Source identification using a conditional bivariate Probability function. Environmental Modelling & Software, Vol. 59, 1-9.

Westmoreland, E.J., N. Carslaw, D.C. Carslaw, A. Gillah and E. Bates (2007). Analysis of air quality within a street canyon using statistical and dispersion modelling techniques. Atmospheric Environment. Vol. 41(39), pp. 9195-9205.

Yu, K.N., Cheung, Y.P., Cheung, T., Henry, R.C., 2004. Identifying the impact of large urban airports on local air quality by nonparametric regression. Atmospheric Environment 38 (27), 4501-4507.

Grange, S. K., Carslaw, D. C., & Lewis, A. C. 2016. Source apportionment advances with bivariate polar plots, correlation, and regression techniques. Atmospheric Environment. 145, 128-134. DOI: 10.1016/j.atmosenv.2016.09.016.

Author

David Carslaw

Examples


# basic plot
polarPlot(mydata, pollutant = "nox")

if (FALSE) { # \dontrun{

# polarPlots by year on same scale
polarPlot(mydata, pollutant = "so2", type = "year", title = "polarPlot of so2")

# set minimum number of bins to be used to see if pattern remains similar
polarPlot(mydata, pollutant = "nox", min.bin = 3)

# plot by day of the week
polarPlot(mydata, pollutant = "pm10", type = "weekday")

# show the 95% confidence intervals in the surface fitting
polarPlot(mydata, pollutant = "so2", uncertainty = TRUE)


# Pair-wise statistics
# Pearson correlation
polarPlot(mydata, pollutant = c("pm25", "pm10"), statistic = "r")

# Robust regression slope, takes a bit of time
polarPlot(mydata, pollutant = c("pm25", "pm10"), statistic = "robust.slope")

# Least squares regression works too but it is not recommended, use robust
# regression
# polarPlot(mydata, pollutant = c("pm25", "pm10"), statistic = "slope")
} # }