This function provides a way of showing the differences in concentrations between two time periods as a polar plot. There are several uses of this function, but the most common will be to see how source(s) may have changed between two periods.
polarDiff(
before,
after,
pollutant = "nox",
type = "default",
x = "ws",
limits = NULL,
auto.text = TRUE,
plot = TRUE,
...
)an openair plot.
Data frames representing the "before" and "after" cases.
See polarPlot() for details of different input requirements.
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".
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.
Name of variable to plot against wind direction in polar coordinates, the default is wind speed, “ws”.
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.
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.
Should a plot be produced? FALSE can be useful when analysing
data to extract plot components and plotting them in other ways.
Arguments passed on to polarPlot
wdName of wind direction field.
statisticThe 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.
exclude.missingSetting 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.
uncertaintyShould 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".
percentileIf 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.
colsColours 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.
weightsAt 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.binThe 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.colWhen 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".
alphaThe 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.
upperThis 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.scaleSometimes 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.
unitsThe units shown on the polar axis scale.
force.positiveThe 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.
kThis 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.
normaliseIf 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.headerAdds 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.
key.footersee key.footer.
key.positionLocation where the scale key is to plotted. Allowed
arguments currently include "top", "right", "bottom" and "left".
keyFine control of the scale key via drawOpenKey. See drawOpenKey
for further details.
ws_spreadThe 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_spreadThe 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_errorThe x error / uncertainty used when statistic = "york_slope".
y_errorThe y error / uncertainty used when statistic = "york_slope".
kernelType 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.labelWhen 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".
tauThe 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.
While the function is primarily intended to compare two time periods at the same location, it can be used for any two data sets that contain the same pollutant. For example, data from two sites that are close to one another, or two co-located instruments.
The analysis works by calculating the polar plot surface for the before and
after periods and then subtracting the before surface from the after
surface.
Other polar directional analysis functions:
percentileRose(),
polarAnnulus(),
polarCluster(),
polarFreq(),
polarPlot(),
pollutionRose(),
windRose()
if (FALSE) {
before_data <- selectByDate(mydata, year = 2002)
after_data <- selectByDate(mydata, year = 2003)
polarDiff(before_data, after_data, pollutant = "no2")
# with some options
polarDiff(before_data, after_data, pollutant = "no2", cols = "RdYlBu", limits = c(-20, 20))
}
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