Compute \(N^2\), the square of the buoyancy frequency for a seawater profile.

## Usage

```
swN2(
pressure,
sigmaTheta = NULL,
derivs,
df,
debug = getOption("oceDebug"),
...
)
```

## 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 \(d\sigma_\theta/dp\) 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.- debug
an integer specifying whether debugging information is to be printed during the processing. This is a general parameter that is used by many

`oce`

functions. Generally, setting`debug=0`

turns off the printing, while higher values suggest that more information be printed. If one function calls another, it usually reduces the value of`debug`

first, so that a user can often obtain deeper debugging by specifying higher`debug`

values.- ...
additional argument, passed to

`smooth.spline()`

, in the case that`derivs="smoothing"`

. See “Details”.

## 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.

The core of the method involves computing potential density referenced to median
pressure, using the UNESCO-style swSigmaTheta function, and then differentiating
this with respect to pressure. 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 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.

## Deprecation Notice

Until 2019 April 11, `swN2`

had an argument named `eos`

. However,
this did not work as stated, unless the first argument was a `ctd`

object. Besides, the argument name was inherently deceptive, because the UNESCO
scheme does not specify how N2 is to be calculated.
Nothing is really lost by making this change, because the new default is the
same as was previously available with the `eos="unesco"`

setup, and the gsw-formulated estimate of N2 is provided
by `gsw::gsw_Nsquared()`

in the gsw package.

## See also

The `gsw::gsw_Nsquared()`

function of the gsw
provides an alternative to this, as formulated in the GSW system. It
has a more sophisticated treatment of potential density, but it is based
on simple first-difference derivatives, so its results may require
smoothing, depending on the dataset and purpose of the analysis.

Other functions that calculate seawater properties:
`T68fromT90()`

,
`T90fromT48()`

,
`T90fromT68()`

,
`computableWaterProperties()`

,
`locationForGsw()`

,
`swAbsoluteSalinity()`

,
`swAlpha()`

,
`swAlphaOverBeta()`

,
`swBeta()`

,
`swCSTp()`

,
`swConservativeTemperature()`

,
`swDepth()`

,
`swDynamicHeight()`

,
`swLapseRate()`

,
`swPressure()`

,
`swRho()`

,
`swRrho()`

,
`swSCTp()`

,
`swSR()`

,
`swSTrho()`

,
`swSigma()`

,
`swSigma0()`

,
`swSigma1()`

,
`swSigma2()`

,
`swSigma3()`

,
`swSigma4()`

,
`swSigmaT()`

,
`swSigmaTheta()`

,
`swSoundAbsorption()`

,
`swSoundSpeed()`

,
`swSpecificHeat()`

,
`swSpice()`

,
`swSpiciness0()`

,
`swSpiciness1()`

,
`swSpiciness2()`

,
`swSstar()`

,
`swTFreeze()`

,
`swTSrho()`

,
`swThermalConductivity()`

,
`swTheta()`

,
`swViscosity()`

,
`swZ()`

## Examples

```
library(oce)
data(ctd)
# Left panel: density
p <- ctd[["pressure"]]
ylim <- rev(range(p))
par(mfrow = c(1, 2), mar = c(3, 3, 1, 1), mgp = c(2, 0.7, 0))
plot(ctd[["sigmaTheta"]], p, ylim = ylim, type = "l", xlab = expression(sigma[theta]))
# Right panel: N2, with default settings (black) and with df=2 (red)
N2 <- swN2(ctd)
plot(N2, p, ylim = ylim, xlab = "N2 [1/s^2]", ylab = "p", type = "l")
lines(swN2(ctd, df = 3), p, col = 2)
```