Smooth a section, in any of several ways, working either in the vertical direction or in both the vertical and lateral directions.

  method = "spline",
  gamma = 0.5,
  iterations = 2,
  trim = 0,
  pregrid = FALSE,
  debug = getOption("oceDebug"),



A section object containing the section to be smoothed. For method="spline", the pressure levels must match for each station in the section.


A string or a function that specifies the method to use; see “Details”.


Optional numerical vector, of the same length as the number of stations in section, which will be used in gridding in the lateral direction. If not provided, this defaults to geodDist(section).

xg, xgl

ignored in the method="spline" case, but passed to interpBarnes() if method="barnes", to kriging functions if method="kriging", or to method itself, if it is a function. If xg is supplied, it defines the x component of the grid, which by default is the terms of station distances, x, along the track of the section. (Note that the grid xg is trimmed to the range of the data x, because otherwise it would be impossible to interpolate between stations to infer water depth, longitude, and latitude, which are all stored within the stations in the returned section object.) Alternatively, if xgl is supplied, the x grid is established using seq(), to span the data with xgl elements. If neither of these is supplied, the output x grid will equal the input x grid.

yg, ygl

similar to xg and xgl, but for pressure. (Note that trimming to the input y is not done, as it is for xg and x.) If yg is not given, it is determined from the deepest station in the section. If ygl was not given, then a grid is constructed to span the pressures of that deepest station with ygl elements. On the other hand, if ygl was not given, then the y grid will constructed from the pressure levels in the deepest station.

xr, yr

influence ranges in x (along-section distance) and y (pressure), passed to interpBarnes() if method="barnes" or to method, if the latter is a function. If missing, xr defaults to 1.5X the median inter-station distance and yr defaults to 0.2X the pressure range. Since these defaults have changed over the evolution of sectionSmooth, analysts ought to supply xr and yr in the function call, tailoring them to particular applications, and making the code more resistant to changes in sectionSmooth.


Degree-of-freedom parameter, passed to smooth.spline() if method="spline", and ignored otherwise. If df is not provided, it defaults to 1/5-th of the number of stations containing non-NA data at the particular pressure level being processed, as sectionSmooth works its way through the water column.

gamma, iterations, trim, pregrid

Values passed to interpBarnes(), if method="barnes", and ignored otherwise. gamma is the factor by which xr and yr are reduced on each of succeeding iterations. iterations is the number of iterations to do. trim controls whether the gridded data are set to NA in regions with sparse data coverage. pregrid controls whether data are to be pre-gridded with binMean2D() before being passed to interpBarnes().


A flag that turns on debugging. Set to 1 to get a moderate amount of debugging information, or to 2 to get more.


Optional extra arguments, passed to either smooth.spline(), if method="spline", and ignored otherwise.


A section object of that has been smoothed in some way. Every data field that is in even a single station of the input object is inserted into every station in the returned value, and therefore the units represent all the units in any of the stations, as do the flag names. However, the flags are all set to NA values.


This function produces smoothed fields that might be useful in simplifying graphical elements created with plot,section-method(). As with any smoothing method, a careful analyst will compare the results against the raw data, e.g. using plot,section-method(). In addition the problem of falsely widening narrow features such as fronts, there is also the potential to get unphysical results with spars sampling near topographic features such as bottom slopes and ridges.

The method argument selects between three possible methods.

  • For method="spline", i.e. the default, the section is smoothed laterally, using smooth.spline() on individual pressure levels. (If the pressure levels do not match up, sectionGrid() should be used first to create a section object that can be used here.) The df argument sets the degree of freedom of the spline, with larger values indicating less smoothing.

  • For method="barnes", smoothing is done across both horizontal and vertical coordinates, using interpBarnes(). The output station locations are computed by linear interpolation of input locations, using approx() on the original longitudes and longitudes of stations, with the independent variable being the distance along the track, computed with geodDist(). The values of xg, yg, xgl and ygl control the smoothing.

  • For method="kriging", smoothing is done across both horizontal and vertical coordinates, using autoKrige() from the automap package (along with support from the sp package to format the data). Note that the format of the value returned by autoKrige() has changed over the years, and method="kriging" can only handle two particular formats, one of which is the result from version 1.1.9 of automap.

  • If method is a function, then that function is applied to the (distance, pressure) data for each variable at a grid defined by xg, xgl, yg and ygl. The function must be of the form function(x,y,z,xg,xr,yg,yr), and must return a matrix of the gridded result, with first index indicating the "grid" station number and second index indicating "grid" pressure. The x value that is supplied to this function is set as the distance along the section, as computed with geodDist(), and repeated for each of the points at each station. The corresponding pressures are provided in y, and the value to be gridded is in z, which may be temperature on one call to the function, salinity on another call, etc. The other quantities have the meanings as described below.

Sample of Usage

# I have seen problems with kriging as the automap package has
# evolved, so please be aware that the following may fail.
if (requireNamespace("automap", quietly=TRUE)
       && requireNamespace("sf", quietly=TRUE)) {
    gsKriging <- sectionSmooth(gs, "kriging", xr=50, yr=200)
    plot(gsKriging, which="temperature")
    mtext("sectionSmooth(..., method=\"kriging\")", line=0.5)


Dan Kelley


# Unsmoothed (Gulf Stream)
gs <- subset(section, 115 <= stationId & stationId <= 125)
par(mfrow = c(2, 2))

plot(gs, which = "temperature")
mtext("Original data, without smoothing", line = 0.5)

# Spline
gsg <- sectionGrid(gs, p = seq(0, 5000, 100))
gsSpline <- sectionSmooth(gsg, "spline")
plot(gsSpline, which = "temperature")
mtext("sectionSmooth(..., method=\"spline\")", line = 0.5)

# Barnes
gsBarnes <- sectionSmooth(gs, "barnes", xr = 50, yr = 200)
plot(gsBarnes, which = "temperature")
mtext("sectionSmooth(..., method=\"barnes\")", line = 0.5)