Buoyancy frequency between two depths

How strongly the water column is stratified: the frequency at which a parcel displaced vertically would oscillate, squared. Written \(N^2\), and equal to \(-(g/\rho_0)\,\partial\rho/\partial z\).

Usage

buoyancy_frequency(
  env_dat,
  shallow,
  deep,
  depths,
  frequency = FALSE,
  name = NULL
)

Arguments

env_dat: an sf POINT object with one row per location and time step, as datamatch's access functions return
shallow: name of the density column for the shallower level, in kg/m^3 or as sigma-theta; both give the same answer since only the difference enters
deep: name of the density column for the deeper level
depths: the two depths in metres, shallower first, positive downwards
frequency: return \(N\) in s^-1 instead of \(N^2\) in s^-2. N is NA wherever the column is unstable, since the root of a negative number is not a frequency
name: name for the new column

Value

env_dat with a stratification column

Details

This is the quantity that decides how much work mixing has to do, and it governs a great deal of what plankton do. A strongly stratified column keeps a surface bloom in the light and cuts it off from nutrients below; a weakly stratified one lets both mix. vertical_gradient() approximates the same idea with a temperature difference, which is a reasonable proxy only where salinity is uniform — and in the Gulf of Maine it is not, because Scotian Shelf inflow is fresh enough to stratify water that is barely warmer at the surface.

Getting the two levels

Two routes, depending on the source.

datamatch::accessCopernicus() takes a depth argument and returns one level per call, so a second call at a different depth gives the deeper level and the two are joined as columns on the same points:

surface <- datamatch::accessCopernicus(vars = c("SST", "SSS"), depth = c(0, 1), ...)
deep    <- datamatch::accessCopernicus(vars = c("SST", "SSS"), depth = c(90, 100), ...)

accessHYCOM() and accessFVCOM() instead serve the bottom as named variables, BOTT and BOTS beside SST and SSS, so one fetch carries both levels and the second depth is the water depth rather than a chosen one. That makes a surface-to-bottom density difference available, where a surface-and-bottom fetch from Copernicus gives a temperature difference only: Copernicus serves bottomT but no bottom salinity.

Either way, compute a density for each level with potential_density() and pass both here.

What a two-level estimate is and is not

It is a bulk stratification over the layer between the two depths, not a profile. Where a sharp pycnocline sits between the levels, the true peak \(N^2\) at that interface is far larger than the layer average reported here, and the depth of the peak is invisible.

The choice of levels therefore does much of the work, and the trap is the mixed layer. If the two straddle its base, \(N^2\) is dominated by how much of the well-mixed layer was included rather than by the stratification itself, and it will vary through the season for that reason alone. Compare the levels against MLD before reading a seasonal cycle into the result.

Negative values are returned rather than suppressed. They mean denser water sits above lighter, which is genuine convective instability in winter and otherwise usually a sign that the two levels are not what you think.

Examples

if (FALSE) { # \dontrun{
env <- potential_density(env, "SST", "SSS", name = "rho_surface")
env <- potential_density(env, "SST_deep", "SSS_deep", name = "rho_deep")
env <- buoyancy_frequency(env, "rho_surface", "rho_deep",
                          depths = c(0.494, 92.326))
} # }