Polar plots considering changes in concentrations between two time periods
polar_diff.Rd
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.
Arguments
- data_before, data_after
Data frames that represent the "before" and "after" cases. See
polar_plot()
for details of different input requirements.- 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”.
- alpha
The transparency of the plot. This is mainly useful to overlay it on a map.
- ...
Arguments passed on to
openair::polarPlot
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 usingpolarFreq
will be better. Settingstatistic = "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. 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.cols
Colours to be used for plotting. Options include “default”, “increment”, “heat”, “jet” and
RColorBrewer
colours --- see theopenair
openColours
function for more details. For user defined the user can supply a list of colour names recognised by R (typecolours()
to see the full list). An example would becols = 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, useweights = 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.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 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.key.footer
see
key.footer
.key.position
Location where the scale key is to plotted. Allowed arguments currently include
"top"
,"right"
,"bottom"
and"left"
.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.
Details
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.
See also
Other polar directional analysis functions:
polar_annulus()
,
polar_cluster()
,
polar_freq()
,
polar_plot()
,
rose_metbias()
,
rose_percentile()
,
rose_pollution()
,
rose_wind()