swDynamicHeight: Dynamic Height of a Seawater Profile

Description

Compute the dynamic height of a column of seawater.

Usage

swDynamicHeight(
  x,
  referencePressure = 2000,
  subdivisions = 500,
  rel.tol = .Machine$double.eps^0.25,
  eos = getOption("oceEOS", default = "gsw")
)

Value

In the first form, a list containing distance, the distance (km( from the first station in the section and height, the dynamic height (m). In the second form, a single value, containing the dynamic height (m).

Arguments

x: a section object.
referencePressure: reference pressure (dbar). If this exceeds the highest pressure supplied to swDynamicHeight(), then that highest pressure is used, instead of the supplied value of referencePressure.
subdivisions: number of subdivisions for call to integrate(). (The default value is considerably larger than the default for integrate(), because otherwise some test profiles failed to integrate.
rel.tol: absolute tolerance for call to integrate(). Note that this call is made in scaled coordinates, i.e. pressure is divided by its maximum value, and dz/dp is also divided by its maximum.
eos: equation of state, either "unesco" or "gsw".

Sample of Usage


library(oce)
data(section)

# Dynamic height and geostrophy par(mfcol=c(2, 2)) par(mar=c(4.5, 4.5, 2, 1))

# Left-hand column: whole section # (The smoothing lowers Gulf Stream speed greatly) westToEast <- subset(section, 1<=stationId&stationId<=123) dh <- swDynamicHeight(westToEast) plot(dh$distance, dh$height, type="p", xlab="", ylab="dyn. height [m]") ok <- !is.na(dh$height) smu <- supsmu(dh$distance, dh$height) lines(smu, col="blue") f <- coriolis(section[["station", 1]][["latitude"]]) g <- gravity(section[["station", 1]][["latitude"]]) v <- diff(smu$y)/diff(smu$x) * g / f / 1e3 # 1e3 converts to m plot(smu$x[-1], v, type="l", col="blue", xlab="distance [km]", ylab="velocity (m/s)")

# right-hand column: gulf stream region, unsmoothed gs <- subset(section, 102<=stationId&stationId<=124) dh.gs <- swDynamicHeight(gs) plot(dh.gs$distance, dh.gs$height, type="b", xlab="", ylab="dyn. height [m]") v <- diff(dh.gs$height)/diff(dh.gs$distance) * g / f / 1e3 plot(dh.gs$distance[-1], v, type="l", col="blue", xlab="distance [km]", ylab="velocity (m/s)")

Author

Dan Kelley

Details

If the first argument is a section, then dynamic height is calculated for each station within a section, and returns a list containing distance along the section along with dynamic height.

If the first argument is a ctd, then this returns just a single value, the dynamic height.

If eos="unesco", processing is as follows. First, a piecewise-linear model of the density variation with pressure is developed using stats::approxfun(). (The option rule=2 is used to extrapolate the uppermost density up to the surface, preventing a possible a bias for bottle data, in which the first depth may be a few metres below the surface.) A second function is constructed as the density of water with salinity 35PSU, temperature of 0$^\circ$C, and pressure as in the ctd. The difference of the reciprocals of these densities, is then integrated with stats::integrate() with pressure limits 0 to referencePressure. (For improved numerical results, the variables are scaled before the integration, making both independent and dependent variables be of order one.)

If eos="gsw", gsw::gsw_geo_strf_dyn_height() is used to calculate a result in m^2/s^2, and this is divided by 9.7963$m/s^2$. If pressures are out of order, the data are sorted. If any pressure is repeated, only the first level is used. If there are under 4 remaining distinct pressures, NA is returned, with a warning.

References

Gill, A.E., 1982. Atmosphere-ocean Dynamics, Academic Press, New York, 662 pp.