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Use non-parametric methods to calculate time series trends


  pollutant = "nox",
  deseason = FALSE,
  type = "default",
  statistic = "mean",
  avg.time = "month",
  percentile = NA,
  data.thresh = 0,
  simulate = FALSE,
  n = 200,
  autocor = FALSE,
  cols = "brewer1",
  shade = "grey95",
  xlab = "year",
  y.relation = "same",
  ref.x = NULL,
  ref.y = NULL,
  key.columns = length(percentile),
  name.pol = pollutant,
  ci = TRUE,
  alpha = 0.2,
  date.breaks = 7,
  auto.text = TRUE,
  k = NULL,



A data frame containing the field date and at least one other parameter for which a trend test is required; typically (but not necessarily) a pollutant.


The parameter for which a trend test is required. Mandatory.


Should the data be de-deasonalized first? If TRUE the function stl is used (seasonal trend decomposition using loess). Note that if TRUE missing data are first imputed using a Kalman filter and Kalman smooth.


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 used for calculating monthly values. Default is “mean”, but can also be “percentile”. See timeAverage for more details.


Can be “month” (the default), “season” or “year”. Determines the time over which data should be averaged. Note that for “year”, six or more years are required. For “season” the data are plit up into spring: March, April, May etc. Note that December is considered as belonging to winter of the following year.


Percentile value(s) to use if statistic = "percentile" is chosen. Can be a vector of numbers e.g. percentile = c(5, 50, 95) will plot the 5th, 50th and 95th percentile values together on the same plot.


The data capture threshold to use ( the data using avg.time. A value of zero means that all available data will be used in a particular period regardless if of the number of values available. Conversely, a value of 100 will mean that all data will need to be present for the average to be calculated, else it is recorded as NA. Not used if avg.time = "default".


Should simulations be carried out to determine the Mann-Kendall tau and p-value. The default is FALSE. If TRUE, bootstrap simulations are undertaken, which also account for autocorrelation.


Number of bootstrap simulations if simulate = TRUE.


Should autocorrelation be considered in the trend uncertainty estimates? The default is FALSE. Generally, accounting for autocorrelation increases the uncertainty of the trend estimate sometimes by a large amount.


Colours to use. Can be a vector of colours e.g. cols = c("black", "green") or pre-defined openair colours --- see openColours for more details.


The colour used for marking alternate years. Use “white” or “transparent” to remove shading.


x-axis label, by default “year”.


This determines how the y-axis scale is plotted. "same" ensures all panels use the same scale and "free" will use panel-specfic scales. The latter is a useful setting when plotting data with very different values. ref.x See ref.y for details. In this case the correct date format should be used for a vertical line e.g. ref.x = list(v = as.POSIXct("2000-06-15"), lty = 5).


See ref.y.


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.


Number of columns used if a key is drawn when using the option statistic = "percentile".


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.


Should confidence intervals be plotted? The default is FALSE.


The alpha transparency of shaded confidence intervals - if plotted. A value of 0 is fully transparent and 1 is fully opaque.


Number of major x-axis intervals to use. The function will try and choose a sensible number of dates/times as well as formatting the date/time appropriately to the range being considered. This does not always work as desired automatically. The user can therefore increase or decrease the number of intervals by adjusting the value of date.breaks up or down.


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.


This is the smoothing parameter used by the gam function in package mgcv. By default it is not used and the amount of smoothing is optimised automatically. However, sometimes it is useful to set the smoothing amount manually using k.


Other graphical parameters are passed onto cutData and lattice:xyplot. For example, smoothTrend passes the option hemisphere = "southern" on to cutData to provide southern (rather than default northern) hemisphere handling of type = "season". Similarly, common graphical arguments, such as xlim and ylim for plotting ranges and pch and cex for plot symbol type and size, are passed on xyplot, although some local modifications may be applied by openair. For example, axis and title labelling options (such as xlab, ylab and main) are passed to xyplot via quickText to handle routine formatting. One special case here is that many graphical parameters can be vectors when used with statistic = "percentile" and a vector of percentile values, see examples below.


As well as generating the plot itself, smoothTrend 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. Note that data is a list of two data frames: data (the original data) and fit (the smooth fit that has details of the fit and teh uncertainties). If retained, e.g. using output <- smoothTrend(mydata, "nox"), this output can be output <- smoothTrend(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 summarise.


The smoothTrend function provides a flexible way of estimating the trend in the concentration of a pollutant or other variable. Monthly mean values are calculated from an hourly (or higher resolution) or daily time series. There is the option to deseasonalise the data if there is evidence of a seasonal cycle.

smoothTrend uses a Generalized Additive Model (GAM) from the gam package to find the most appropriate level of smoothing. The function is particularly suited to situations where trends are not monotonic (see discussion with TheilSen for more details on this). The smoothTrend function is particularly useful as an exploratory technique e.g. to check how linear or non-linear trends are.

95 confidence intervals are also available through the simulate option. Residual resampling is used.

Trends can be considered in a very wide range of ways, controlled by setting type - see examples below.

See also

TheilSen for an alternative method of calculating trends.


David Carslaw


# load example data from package

# trend plot for nox
smoothTrend(mydata, pollutant = "nox")

# trend plot by each of 8 wind sectors
if (FALSE) smoothTrend(mydata, pollutant = "o3", type = "wd", ylab = "o3 (ppb)")

# several pollutants, no plotting symbol
if (FALSE) smoothTrend(mydata, pollutant = c("no2", "o3", "pm10", "pm25"), pch = NA)

# percentiles
if (FALSE) smoothTrend(mydata, pollutant = "o3", statistic = "percentile",
percentile = 95)

# several percentiles with control over lines used
if (FALSE) smoothTrend(mydata, pollutant = "o3", statistic = "percentile",
percentile = c(5, 50, 95), lwd = c(1, 2, 1), lty = c(5, 1, 5))