gam smoothing
is carried out using mgcv.
polarPlot(mydata, pollutant = "nox", x = "ws", wd = "wd", type = "default", statistic = "mean", resolution = "normal", limits = NA, 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 = "", key.footer = pollutant, key.position = "right", key = TRUE, auto.text = TRUE, ...)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
= "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).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 =
"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.When 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", 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.
c(lower, upper), so limits = c(0, 100)
would force the plot limits to span 0-100.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.TRUE three plots are produced on the
same scale showing the predicted surface together with the
estimated lower and upper uncertainties at the 95
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".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.
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")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.
polarFreq function can be of use in such
circumstances.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".angle.scale to another value (between 0 and 360
degrees) to mitigate such problems. For example
angle.scale = 45 will draw the scale heading in a NE
direction.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
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.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.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 = "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.footer."top",
"right", "bottom" and "left".drawOpenKey.
See drawOpenKey for further details.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.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.polarPlot
also returns an object of class ``openair''. The object includes
three main components: call, the command used to generate
the plot; data, the data frame of summarised information
used to make the plot; and plot, the plot itself. If
retained, e.g. using output <- polarPlot(mydata, "nox"),
this output can be used to recover the data, reproduce or rework
the original plot or undertake further analysis.An openair output can be manipulated using a number of generic
operations, including print, plot and
summary.polarPlot surface data can also be extracted directly
using the results, e.g. results(object) for
output <- polarPlot(mydata, "nox"). This returns a data
frame with four set columns: cond, conditioning based on
type; u and v, the translational vectors
based on ws and wd; and the local pollutant
estimate.
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.
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
intervals, which take account of the frequency of measurements.
Variants on polarPlot include polarAnnulus and
polarFreq.
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.
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.
polarCluster for identifying features in
bivairate polar plots and for post processing and
polarAnnulus, polarFreq,
percentileRose for other ways of plotting
directional data.
# load example data from package
data(mydata)
# basic plot
polarPlot(mydata, pollutant = "nox")
# polarPlots by year on same scale
## Not run: polarPlot(mydata, pollutant = "so2", type = "year", main = "polarPlot of so2")
# set minimum number of bins to be used to see if pattern remains similar
## Not run: polarPlot(mydata, pollutant = "nox", min.bin = 3)
# plot by day of the week
## Not run: polarPlot(mydata, pollutant = "pm10", type = "weekday")
# show the 95% confidence intervals in the surface fitting
## Not run: polarPlot(mydata, pollutant = "so2", uncertainty = TRUE)
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