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.
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,
...
)an openair object. data contians four set
columns: cond, conditioning based on type; u and
v, the translational vectors based on ws and wd; and
the local pollutant estimate.
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". 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".
Name of variable to plot against wind direction in polar coordinates, the default is wind speed, “ws”.
Name of wind direction field.
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.
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.
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.
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.
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".
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.
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.
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.
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.
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".
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.
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.
The units shown on the polar axis scale.
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.
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.
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.footer.
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.
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.
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.
The x error / uncertainty used when statistic =
"york_slope".
The y error / uncertainty used when statistic =
"york_slope".
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.
When pair-wise statistics such as regression slopes are calculated and plotted, should a formula label be displayed?
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.
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.
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.
David Carslaw
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().
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
Other polar directional analysis functions:
percentileRose(),
polarAnnulus(),
polarCluster(),
polarDiff(),
polarFreq(),
pollutionRose(),
windRose()
# Use openair 'mydata'
# basic plot
polarPlot(openair::mydata, pollutant = "nox")
if (FALSE) {
# 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")
}
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