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This function plots gridded back trajectories. This function requires that data are imported using the importTraj function.


  lon = "lon",
  lat = "lat",
  pollutant = "height",
  type = "default",
  smooth = FALSE,
  statistic = "frequency",
  percentile = 90,
  map = TRUE, = 1, = 1,
  min.bin = 1,
  .combine = NA,
  sigma = 1.5,
  map.fill = TRUE,
  map.res = "default",
  map.cols = "grey40",
  map.alpha = 0.3,
  projection = "lambert",
  parameters = c(51, 51),
  orientation = c(90, 0, 0),
  grid.col = "deepskyblue",
  origin = TRUE,



Data frame, the result of importing a trajectory file using importTraj


Column containing the longitude, as a decimal.


Column containing the latitude, as a decimal.


Pollutant to be plotted. By default the trajectory height is used.


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.


Should the trajectory surface be smoothed?


For trajLevel. By default the function will plot the trajectory frequencies.

For trajLevel, the argument method = "hexbin" can be used. In this case hexagonal binning of the trajectory points (i.e. a point every three hours along each back trajectory). The plot then shows the trajectory frequencies uses hexagonal binning. This is an alternative way of viewing trajectory frequencies compared with statistic = "frequency".

There are also various ways of plotting concentrations.

It is also possible to set statistic = "difference". In this case trajectories where the associated concentration is greater than percentile are compared with the the full set of trajectories to understand the differences in freqeuncies of the origin of air masses. The comparsion is made by comparing the percentage change in gridded frequencies. For example, such a plot could show that the top 10% of concentrations of PM10 tend to orginate from air-mass origins to the east.

If statistic = "pscf" then a Potential Source Contribution Function map is produced. If statistic = "cwt" then concentration weighted trajectories are plotted.

If statistic = "cwt" then the Concentration Weighted Trajectory approach is used. See details.


For trajLevel. The percentile concentration of pollutant against which the all trajectories are compared.


Should a base map be drawn? If TRUE the world base map from the maps package is used.

The longitude-interval to be used for binning data for trajLevel.

The latitude-interval to be used for binning data when trajLevel.


For trajLevel the minimum number of unique points in a grid cell. Counts below min.bin are set as missing. For trajLevel gridded outputs.


When statistic is "SQTBA" it is possible to combine lots of receptor locations to derive a single map. .combine identifies the column that differentiates different sites (commonly a column named site). Note that indivisual site maps are normalised first by dividing by their mean value.


For the SQTBA approach sigma determines the amount of back trajectory spread based on the Gaussian plume equation. Values in the literature suggest 5.4 km after one hour. However, testing suggests lower values reveal source regions more effectively while not introducing too much noise.


Should the base map be a filled polygon? Default is to fill countries.


The resolution of the base map. By default the function uses the ‘world’ map from the maps package. If map.res = "hires" then the (much) more detailed base map ‘worldHires’ from the mapdata package is used. Use library(mapdata). Also available is a map showing the US states. In this case map.res = "state" should be used.


If map.fill = TRUE map.cols controls the fill colour. Examples include map.fill = "grey40" and map.fill = openColours("default", 10). The latter colours the countries and can help differentiate them.


The transpency level of the filled map which takes values from 0 (full transparency) to 1 (full opacity). Setting it below 1 can help view trajectories, trajectory surfaces etc. and a filled base map.


The map projection to be used. Different map projections are possible through the mapproj package. See ?mapproject for extensive details and information on setting other parameters and orientation (see below).


From the mapproj package. Optional numeric vector of parameters for use with the projection argument. This argument is optional only in the sense that certain projections do not require additional parameters. If a projection does not require additional parameters then set to null i.e. parameters = NULL.


From the mapproj package. An optional vector c(latitude, longitude, rotation) which describes where the "North Pole" should be when computing the projection. Normally this is c(90, 0), which is appropriate for cylindrical and conic projections. For a planar projection, you should set it to the desired point of tangency. The third value is a clockwise rotation (in degrees), which defaults to the midrange of the longitude coordinates in the map.


The colour of the map grid to be used. To remove the grid set grid.col = "transparent".


should the receptor origin be shown by a black dot?


other arguments are passed to cutData and scatterPlot. This provides access to arguments used in both these functions and functions that they in turn pass arguments on to. For example, plotTraj passes the argument cex on to scatterPlot which in turn passes it on to the lattice function xyplot where it is applied to set the plot symbol size.


An alternative way of showing the trajectories compared with plotting trajectory lines is to bin the points into latitude/longitude intervals. For these purposes trajLevel should be used. There are several trajectory statistics that can be plotted as gridded surfaces. First, statistic can be set to “frequency” to show the number of back trajectory points in a grid square. Grid squares are by default at 1 degree intervals, controlled by and Such plots are useful for showing the frequency of air mass locations. Note that it is also possible to set method = "hexbin" for plotting frequencies (not concentrations), which will produce a plot by hexagonal binning.

If statistic = "difference" the trajectories associated with a concentration greater than percentile are compared with the the full set of trajectories to understand the differences in freqeuncies of the origin of air masses of the highest concentration trajectories compared with the trajectories on average. The comparsion is made by comparing the percentage change in gridded frequencies. For example, such a plot could show that the top 10% of concentrations of PM10 tend to orginate from air-mass origins to the east.

If statistic = "pscf" then the Potential Source Contribution Function is plotted. The PSCF calculates the probability that a source is located at latitude \(i\) and longitude \(j\) (Pekney et al., 2006).The basis of PSCF is that if a source is located at (i,j), an air parcel back trajectory passing through that location indicates that material from the source can be collected and transported along the trajectory to the receptor site. PSCF solves $$PSCF = m_{ij}/n_{ij}$$ where \(n_{ij}\) is the number of times that the trajectories passed through the cell (i,j) and \(m_{ij}\) is the number of times that a source concentration was high when the trajectories passed through the cell (i,j). The criterion for de-termining \(m_{ij}\) is controlled by percentile, which by default is 90. Note also that cells with few data have a weighting factor applied to reduce their effect.

A limitation of the PSCF method is that grid cells can have the same PSCF value when sample concentrations are either only slightly higher or much higher than the criterion. As a result, it can be difficult to distinguish moderate sources from strong ones. Seibert et al. (1994) computed concentration fields to identify source areas of pollutants. The Concentration Weighted Trajectory (CWT) approach considers the concentration of a species together with its residence time in a grid cell. The CWT approach has been shown to yield similar results to the PSCF approach. The openair manual has more details and examples of these approaches.

A further useful refinement is to smooth the resulting surface, which is possible by setting smooth = TRUE.


This function is under active development and is likely to change


Pekney, N. J., Davidson, C. I., Zhou, L., & Hopke, P. K. (2006). Application of PSCF and CPF to PMF-Modeled Sources of PM 2.5 in Pittsburgh. Aerosol Science and Technology, 40(10), 952-961.

Seibert, P., Kromp-Kolb, H., Baltensperger, U., Jost, D., 1994. Trajectory analysis of high-alpine air pollution data. NATO Challenges of Modern Society 18, 595-595.

Xie, Y., & Berkowitz, C. M. (2007). The use of conditional probability functions and potential source contribution functions to identify source regions and advection pathways of hydrocarbon emissions in Houston, Texas. Atmospheric Environment, 41(28), 5831-5847.

See also

importTraj to import trajectory data from the King's College server and trajPlot for plotting back trajectory lines.


David Carslaw


# show a simple case with no pollutant i.e. just the trajectories
# let's check to see where the trajectories were coming from when
# Heathrow Airport was closed due to the Icelandic volcanic eruption
# 15--21 April 2010.
# import trajectories for London and plot
if (FALSE) {
lond <- importTraj("london", 2010)
# more examples to follow linking with concentration measurements...

# import some measurements from KC1 - London
if (FALSE) {
kc1 <- importAURN("kc1", year = 2010)
# now merge with trajectory data by 'date'
lond <- merge(lond, kc1, by = "date")

# trajectory plot, no smoothing - and limit lat/lon area of interest
# use PSCF
trajLevel(subset(lond, lat > 40 & lat < 70 & lon >-20 & lon <20),
pollutant = "pm10", statistic = "pscf")

# can smooth surface, suing CWT approach:
trajLevel(subset(lond, lat > 40 & lat < 70 & lon >-20 & lon <20),
pollutant = "pm2.5", statistic = "cwt",  smooth = TRUE)

# plot by season:
trajLevel(subset(lond, lat > 40 & lat < 70 & lon >-20 & lon <20), pollutant = "pm2.5",
statistic = "pscf", type = "season")