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,
mis.col = "grey",
upper = NA,
angle.scale = 315,
units = x,
force.positive = TRUE,
k = 100,
normalise = FALSE,
key.header = statistic,
key.footer = pollutant,
key.position = "right",
key = TRUE,
auto.text = TRUE,
ws_spread = 1.5,
wd_spread = 5,
x_error = NA,
y_error = NA,
kernel = "gaussian",
formula.label = TRUE,
tau = 0.5,
alpha = 1,
plot = TRUE,
...
)
```

## 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
`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.- 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 be used for plotting. Options include “default”, “increment”, “heat”, “jet” and

`RColorBrewer`

colours — see the`openair`

`openColours`

function for more details. 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")`

.`cols`

can also take the values`"viridis"`

,`"magma"`

,`"inferno"`

, or`"plasma"`

which are the viridis colour maps ported from Python's Matplotlib library.- 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.- mis.col
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`mis.col`

. To not highlight missing data when`min.bin`

> 1 choose`mis.col = "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
Sometimes the placement of the scale may interfere with an interesting feature. The user can therefore set

`angle.scale`

to any value between 0 and 360 degrees to mitigate such problems. For example`angle.scale = 45`

will draw the scale heading in a NE direction.- 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.- key.header
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.footer`

.- key.position
Location where the scale key is to plotted. Allowed arguments currently include

`"top"`

,`"right"`

,`"bottom"`

and`"left"`

.- key
Fine control of the scale key via

`drawOpenKey`

. See`drawOpenKey`

for further details.- 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.- 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.- alpha
The alpha transparency to use for the plotting surface (a value between 0 and 1 with zero being fully transparent and 1 fully opaque). Setting a value below 1 can be useful when plotting surfaces on a map using the package

`openairmaps`

.- plot
Should a plot be produced?

`FALSE`

can be useful when analysing data to extract plot components and plotting them in other ways.- ...
Other graphical parameters passed onto

`lattice:levelplot`

and`cutData`

. For example,`polarPlot`

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.

## 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.

Variants on `polarPlot`

include `polarAnnulus()`

and `polarFreq()`

.

## 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. http:// dx.doi.org/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. https://www.sciencedirect.com/science/article/pii/S1352231016307166

## See also

Other polar directional analysis functions:
`percentileRose()`

,
`polarAnnulus()`

,
`polarCluster()`

,
`polarDiff()`

,
`polarFreq()`

,
`pollutionRose()`

,
`windRose()`

## Examples

```
# Use openair 'mydata'
# basic plot
polarPlot(openair::mydata, pollutant = "nox")
if (FALSE) { # \dontrun{
# polarPlots by year on same scale
polarPlot(mydata, pollutant = "so2", type = "year", main = "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")
} # }
```