oce (version 0.9-20)

swN2: Squared buoyancy frequency for seawater

Description

Compute $N^2$, the square of the buoyancy frequency for a seawater profile.

Usage

swN2(pressure, sigmaTheta = NULL, derivs, df, eos = getOption("oceEOS", default = "gsw"), ...)

Arguments

pressure

either pressure [dbar] (in which case sigmaTheta must be provided) or an object of class ctd object (in which case sigmaTheta is inferred from the object.

sigmaTheta

Surface-referenced potential density minus 1000 [kg/m$^3$]

derivs

optional argument to control how the derivative $d(sigmaTheta)/d(pressure)$ is calculated. This may be a character string or a function of two arguments. See “Details”.

df

argument passed to smooth.spline if this function is used for smoothing; set to NA to prevent smoothing.

eos

equation of state, either "unesco" or "gsw".

...

additional argument, passed to smooth.spline, in the case that derivs="smoothing". See “Details”.

Value

Square of buoyancy frequency [$radian^2/s^2$].

Details

Smoothing is often useful prior to computing buoyancy frequency, and so this may optionally be done with smooth.spline, unless df=NA, in which case raw data are used. If df is not provided, a possibly reasonable value computed from an analysis of the profile, based on the number of pressure levels.

If eos="gsw", then the first argument must be a ctd object, and processing is done with gsw_Nsquared, based on extracted values of Absolute Salinity and Conservative Temperature (possibly smoothed, depending on df).

If eos="unesco", then the processing is as follows. The core of the method involves differentiating potential density (referenced to median pressure) with respect to pressure, and the derivs argument is used to control how this is done, as follows.

• if derivs is not supplied, the action is as though it were given as the string "smoothing"

if derivs equals "simple", then the derivative of density with respect to pressure is calculated as the ratio of first-order derivatives of density and pressure, each calculated using diff. (A zero is appended at the top level.)

if derivs equals "smoothing", then the processing depends on the number of data in the profile, and on whether df is given as an optional argument. When the number of points exceeds 4, and when df exceeds 1, smooth.spline is used to calculate smoothing spline representation the variation of density as a function of pressure, and derivatives are extracted from the spline using predict. Otherwise, density is smoothed using smooth, and derivatives are calculated as with the "simple" method.

if derivs is a function taking two arguments (first pressure, then density) then that function is called directly to calculate the derivative, and no smoothing is done before or after that call.

For deep-sea work, the eos="gsw" option is the best scheme, because it uses derivatives of density computed with local reference pressure.

For precise work, it makes sense to skip swN2 entirely, choosing whether, what, and how to smooth based on an understanding of fundamental principles as well as data practicalities.

See Also

Other functions that calculate seawater properties: T68fromT90, T90fromT48, T90fromT68, swAbsoluteSalinity, swAlphaOverBeta, swAlpha, swBeta, swCSTp, swConservativeTemperature, swDepth, swDynamicHeight, swLapseRate, swPressure, swRho, swRrho, swSCTp, swSTrho, swSigma0, swSigma1, swSigma2, swSigma3, swSigma4, swSigmaTheta, swSigmaT, swSigma, swSoundAbsorption, swSoundSpeed, swSpecificHeat, swSpice, swTFreeze, swTSrho, swThermalConductivity, swTheta, swViscosity, swZ

Examples

library(oce)
data(ctd)
# Illustrate difference between UNESCO and GSW
p <- ctd[["pressure"]]
ylim <- rev(range(p))
par(mfrow=c(1,3), mar=c(3, 3, 1, 1), mgp=c(2, 0.7, 0))
plot(ctd[["sigmaTheta"]], p, ylim=ylim, type='l', xlab=expression(sigma[theta]))
N2u <- swN2(ctd, eos="unesco")
N2g <- swN2(ctd, eos="gsw")
plot(N2u, p, ylim=ylim, xlab="N2 Unesco", ylab="p", type="l")
d <- 100 * (N2u - N2g) / N2g
plot(d, p, ylim=ylim, xlab="N2 UNESCO-GSW diff. [%]", ylab="p", type="l")
abline(v=0)