Function for plotting bivariate polar plots with smoothing.
polar_plot.Rd
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
polar_plot(
data,
pollutant,
x = "ws",
wd = "wd",
facet = NULL,
statistic = "mean",
exclude_missing = TRUE,
uncertainty = FALSE,
percentile = NA,
weights = c(0.25, 0.5, 0.75),
min_bin = 1,
force_positive = TRUE,
k = 100,
normalise = FALSE,
ws_spread = 1.5,
wd_spread = 5,
x_error = NA,
y_error = NA,
kernel = "gaussian",
tau = 0.5,
alpha = 1
)
Arguments
- data
A data frame containing wind direction, wind speed, and pollutant concentrations.
- pollutant
One or more column names identifying pollutant concentrations. When multiple pollutants are specified for a single-pollutant
statistic
(e.g., "mean"), a faceted plot will be returned. Two pollutants must be provided for certainstatistic
options (e.g., "Pearson" inpolar_plot()
).- x
Name of variable to plot against wind direction in polar coordinates, the default is wind speed, “ws”.
- wd
Name of wind direction field.
- facet
One or two faceting columns.
facet
determines how the data are split and then plotted. Whenfacet
is length 1 it is passed toggplot2::facet_wrap()
, and when it is length 2 it is passed toggplot2::facet_grid()
with the first element being used as columns and the second rows. Some other options (e.g., multiplepollutant
columns) can limit the the number of faceting columns to 1.- statistic
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”.
statistic = "nwr"
Implements the Non-parametric Wind Regression approach of Henry et al. (2009) that uses kernel smoothers. Theopenair
implementation is not identical because Gaussian kernels are used for both wind direction and speed. The smoothing is controlled byws_spread
andwd_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; seepercentile
for details.When
statistic = "r"
orstatistic = "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 alsotau
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 inx
andy
are used in the determination of the slope. The uncertainties are provided byx_error
andy_error
--- see below.
- 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 toFALSE
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"
thenpercentile
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 setmin_bin
to ensure there are a sufficient number of points available to estimate a percentile. Seequantile
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.- 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, useweights = c(1, 1, 1)
. An alternative to down-weighting these points they can be removed altogether usingmin_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.
- 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 artifacts 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 settingforce_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 packagemgcv
. Typically, value of around 100 (the default) seems to be suitable and will resolve important features in the plot. The most appropriate choice ofk
is problem-dependent; but extensive testing of polar plots for many different problems suggests a value ofk
of about 100 is suitable. Settingk
to higher values will not tend to affect the surface predictions by much but will add to the computation time. Lower values ofk
will increase smoothing. Sometimes with few data to plotpolarPlot
will fail. Under these circumstances it can be worth lowering the value ofk
.- 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 onepollutant
is chosen.- 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 is0.5
.- 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 is4
.- x_error
The
x
error / uncertainty used whenstatistic = "york_slope"
.- y_error
The
y
error / uncertainty used whenstatistic = "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.- tau
The quantile to be estimated when
statistic
is set to"quantile.slope"
. Default is0.5
which is equal to the median and will be ignored if"quantile.slope"
is not used.- alpha
The transparency of the plot. This is mainly useful to overlay it on a map.
Value
A ggplot2::ggplot2 figure
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.
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.
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
in the package
openair
. 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. 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:
polar_annulus()
,
polar_cluster()
,
polar_diff()
,
polar_freq()
,
rose_metbias()
,
rose_percentile()
,
rose_pollution()
,
rose_wind()