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Plots the diurnal, day of the week and monthly variation for different variables, typically pollutant concentrations. Four separate plots are produced.


  pollutant = "nox", = NULL,
  normalise = FALSE,
  xlab = c("hour", "hour", "month", "weekday"),
  name.pol = pollutant,
  type = "default",
  group = NULL,
  difference = FALSE,
  statistic = "mean", = 0.95,
  B = 100,
  ci = TRUE,
  cols = "hue",
  ref.y = NULL,
  key = NULL,
  key.columns = 1, = 1,
  auto.text = TRUE,
  alpha = 0.4,
  month.last = FALSE,



A data frame of hourly (or higher temporal resolution data). Must include a date field and at least one variable to plot.


Name of variable to plot. Two or more pollutants can be plotted, in which case a form like pollutant = c("nox", "co") should be used.

Should the results be calculated in local time that includes a treatment of daylight savings time (DST)? The default is not to consider DST issues, provided the data were imported without a DST offset. Emissions activity tends to occur at local time e.g. rush hour is at 8 am every day. When the clocks go forward in spring, the emissions are effectively released into the atmosphere typically 1 hour earlier during the summertime i.e. when DST applies. When plotting diurnal profiles, this has the effect of “smearing-out” the concentrations. Sometimes, a useful approach is to express time as local time. This correction tends to produce better-defined diurnal profiles of concentration (or other variables) and allows a better comparison to be made with emissions/activity data. If set to FALSE then GMT is used. Examples of usage include = "Europe/London", = "America/New_York". See cutData and import for more details.


Should variables be normalised? The default is FALSE. If TRUE then the variable(s) are divided by their mean values. This helps to compare the shape of the diurnal trends for variables on very different scales.


x-axis label; one for each sub-plot.


Names to be given to the pollutant(s). This is useful if you want to give a fuller description of the variables, maybe also including subscripts etc.


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.

Only one type is allowed intimeVariation.


This sets the grouping variable to be used. For example, if a data frame had a column site setting group = "site" will plot all sites together in each panel. See examples below.


If two pollutants are chosen then setting difference = TRUE will also plot the difference in means between the two variables as pollutant[2] - pollutant[1]. Bootstrap 95% confidence intervals of the difference in means are also calculated. A horizontal dashed line is shown at y = 0. The difference can also be calculated if there is a column that identifies two groups e.g. having used splitByDate. In this case it is possible to call timeVariation with the option group = "" and difference = TRUE.


Can be “mean” (default) or “median”. If the statistic is ‘mean’ then the mean line and the 95% confidence interval in the mean are plotted by default. If the statistic is ‘median’ then the median line is plotted together with the 5/95 and 25/75th quantiles are plotted. Users can control the confidence intervals with

The confidence intervals to be plotted. If statistic = "mean" then the confidence intervals in the mean are plotted. If statistic = "median" then the and 1 - quantiles are plotted. can be of length 2, which is most useful for showing quantiles. For example = c(0.75, 0.99) will yield a plot showing the median, 25/75 and 5/95th quantiles.


Number of bootstrap replicates to use. Can be useful to reduce this value when there are a large number of observations available to increase the speed of the calculations without affecting the 95% confidence interval calculations by much.


Should confidence intervals be shown? The default is TRUE. Setting this to FALSE can be useful if multiple pollutants are chosen where over-lapping confidence intervals can over complicate plots.


Colours 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")


A list with details of the horizontal lines to be added representing reference line(s). For example, ref.y = list(h = 50, lty = 5) will add a dashed horizontal line at 50. Several lines can be plotted e.g. ref.y = list(h = c(50, 100), lty = c(1, 5), col = c("green", "blue")). See panel.abline in the lattice package for more details on adding/controlling lines.


By default timeVariation produces four plots on one page. While it is useful to see these plots together, it is sometimes necessary just to use one for a report. If key is TRUE, a key is added to all plots allowing the extraction of a single plot with key. See below for an example.


Number of columns to be used in the key. With many pollutants a single column can make to key too wide. The user can thus choose to use several columns by setting columns to be less than the number of pollutants.

What day of the week should the plots start on? The user can change the start day by supplying an integer between 0 and 6. Sunday = 0, Monday = 1, ... For example to start the weekday plots on a Saturday, choose = 6.


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.


The alpha transparency used for plotting confidence intervals. 0 is fully transparent and 1 is opaque. The default is 0.4


Should the order of the plots be changed so the plot showing monthly means be the last plot for a logical hierarchy of averaging periods?


Other graphical parameters passed onto lattice:xyplot and cutData. For example, in the case of cutData the option hemisphere = "southern".


As well as generating the plot itself, timeVariation also returns an object of class ``openair''. The object includes three main components: call, the command used to generate the plot;

data, the data used to make the four components of the plot (or subplots); and plot, the associated subplots. If retained, e.g. using output <- timeVariation(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.

The four components of timeVariation are: day.hour, hour,

day and month. Associated data.frames can be extracted directly using the subset option, e.g. as in plot(object, subset = "day.hour"), summary(output, subset = "hour"), etc, for

output <- timeVariation(mydata, "nox")


The variation of pollutant concentrations by hour of the day and day of the week etc. can reveal many interesting features that relate to source types and meteorology. For traffic sources, there are often important differences in the way vehicles vary by vehicles type e.g. less heavy vehicles at weekends.

The timeVariation function makes it easy to see how concentrations (and many other variable types) vary by hour of the day and day of the week.

The plots also show the 95% confidence intervals in the mean. The 95% confidence intervals in the mean are calculated through bootstrap simulations, which will provide more robust estimates of the confidence intervals (particularly when there are relatively few data).

The function can handle multiple pollutants and uses the flexible type option to provide separate panels for each 'type' --- see cutData for more details. timeVariation can also accept a group option which is useful if data are stacked. This will work in a similar way to having multiple pollutants in separate columns.

The user can supply their own ylim e.g. ylim = c(0, 200) that will be used for all plots. ylim can also be a list of length four to control the y-limits on each individual plot e.g. ylim = list(c(-100,500), c(200, 300), c(-400,400), c(50,70)). These pairs correspond to the hour, weekday, month and day-hour plots respectively.

The option difference will calculate the difference in means of two pollutants together with bootstrap estimates of the 95% confidence intervals in the difference in the mean. This works in two ways: either two pollutants are supplied in separate columns e.g. pollutant = c("no2", "o3"), or there are two unique values of group. The difference is calculated as the second pollutant minus the first and is labelled as such. Considering differences in this way can provide many useful insights and is particularly useful for model evaluation when information is needed about where a model differs from observations by many different time scales. The manual contains various examples of using difference = TRUE.

Note also that the timeVariation function works well on a subset of data and in conjunction with other plots. For example, a polarPlot may highlight an interesting feature for a particular wind speed/direction range. By filtering for those conditions timeVariation can help determine whether the temporal variation of that feature differs from other features --- and help with source identification.

In addition, timeVariation will work well with other variables if available. Examples include meteorological and traffic flow data.

Depending on the choice of statistic, a subheading is added. Users can control the text in the subheading through the use of sub e.g. sub = "" will remove any subheading.


David Carslaw


# basic use
timeVariation(mydata, pollutant = "nox")

# for a subset of conditions
if (FALSE) {
timeVariation(subset(mydata, ws > 3 & wd > 100 & wd < 270),
pollutant = "pm10", ylab = "pm10 (ug/m3)")

# multiple pollutants with concentrations normalised
if (FALSE) timeVariation(mydata, pollutant = c("nox", "co"), normalise = TRUE)

# show BST/GMT variation (see ?cutData for more details)
# the NOx plot shows the profiles are very similar when expressed in
# local time, showing that the profile is dominated by a local source
# that varies by local time and not by GMT i.e. road vehicle emissions

if (FALSE) timeVariation(mydata, pollutant = "nox", type = "dst", = "Europe/London")

## In this case it is better to group the results for clarity:
if (FALSE) timeVariation(mydata, pollutant = "nox", group = "dst", = "Europe/London")

# By contrast, a variable such as wind speed shows a clear shift when
#  expressed in local time. These two plots can help show whether the
#  variation is dominated by man-made influences or natural processes

if (FALSE) timeVariation(mydata, pollutant = "ws", group = "dst", = "Europe/London")

## It is also possible to plot several variables and set type. For
## example, consider the NOx and NO2 split by levels of O3:

if (FALSE) timeVariation(mydata, pollutant = c("nox", "no2"), type = "o3", normalise = TRUE)

## difference in concentrations
if (FALSE) timeVariation(mydata, poll= c("pm25", "pm10"), difference = TRUE)

# It is also useful to consider how concentrations vary by
# considering two different periods e.g. in intervention
# analysis. In the following plot NO2 has clearly increased but much
# less so at weekends - perhaps suggesting vehicles other than cars
# are important because flows of cars are approximately invariant by
# day of the week

if (FALSE) {
mydata <- splitByDate(mydata, dates= "1/1/2003", labels = c("before Jan. 2003", "After Jan. 2003"))
timeVariation(mydata, pollutant = "no2", group = "", difference = TRUE)

## sub plots can be extracted from the openair object
if (FALSE) {
myplot <- timeVariation(mydata, pollutant = "no2")
plot(myplot, subset = "day.hour") # top weekday and plot

## individual plots
## plot(myplot, subset="day.hour") for the weekday and hours subplot (top)
## plot(myplot, subset="hour") for the diurnal plot
## plot(myplot, subset="day") for the weekday plot
## plot(myplot, subset="month") for the monthly plot

## numerical results (mean, lower/upper uncertainties)
## results(myplot, subset = "day.hour") # the weekday and hour data set
## summary(myplot, subset = "hour") #summary of hour data set
## head(myplot, subset = "day") #head/top of day data set
## tail(myplot, subset = "month") #tail/top of month data set

## plot quantiles and median
if (FALSE) {
timeVariation(mydata, stati="median", poll="pm10", col = "firebrick")

## with different intervals
timeVariation(mydata, stati="median", poll="pm10", = c(0.75, 0.99),
col = "firebrick")