R/sv_Fofonoff.R

In rsachse/limnotools: Help Tools of TU Dresden's Limnology Workgroup

`sv_Fofonoff` <-
function(T, p=0, S=0) {
  # see also http://www.satlab.hawaii.edu/ocn620/hydro/sv.m
  # function y = sv(p,t,s)
  #   specific volume (m^3/kg) from
  #   pressure (dbar), temperature (C), salinity (PSS-78)
  #
  # Fofonoff N.P. and R.C. Millard (1983)
  # Algorithms for Computation of Fundamental Properties of Seawater.
  # UNESCO technical papers in marine science, 44, 53 pp.
  #
  # check vals:   p(dbar) t(C)  S(PSS)    y (m^3/kg)
  #               --------------------------------------
  #                   0    5       0      1.000033251e-3
  #               10000    5       0      0.957736964e-3
  #                   0   25       0      1.002960780e-3
  #               10000   25       0      0.963482064e-3
  #                   0    5      35      0.973069835e-3
  #               10000    5      35      0.935025857e-3
  #                   0   25      35      0.977189409e-3
  #               10000   25      35      0.941142660e-3
  #
  # SCKennan(20apr95)


  p <- p / 10

  a0 <- 999.842594
  a1 <- 0.06793952
  a2 <- -0.00909529
  a3 <- 0.0001001685
  a4 <- -0.000001120083
  a5 <- 0.000000006536332

  b0 <- 0.824493
  b1 <- -0.0040899
  b2 <- 0.000076438
  b3 <- -0.00000082467
  b4 <- 0.0000000053875

  c0 <- -0.00572466
  c1 <- 0.00010227
  c2 <- -0.0000016546

  d0 <- 0.00048314

  e0 <- 19652.21
  e1 <- 148.4206
  e2 <- -2.327105
  e3 <- 0.01360477
  e4 <- -0.00005155288

  f0 <- 54.6746
  f1 <- -0.603459
  f2 <- 0.0109987
  f3 <- -0.00006167

  g0 <- 0.07944
  g1 <- 0.016483
  g2 <- -0.00053009

  h0 <- 3.239908
  h1 <- 0.00143713
  h2 <- 0.000116092
  h3 <- -0.000000577905

  i0 <- 0.0022838
  i1 <- -0.000010981
  i2 <- -0.0000016078

  j0 <- 0.000191075

  k0 <- 0.0000850935
  k1 <- -0.00000612293
  k2 <- 0.000000052787

  m0 <- -0.00000099348
  m1 <- 0.000000020816
  m2 <- 0.00000000091697

  Rw <- a0 + a1 * T + a2 * T ^ 2 + a3 * T ^ 3 + a4 * T ^ 4 + a5 * T ^ 5
  Kw <- e0 + e1 * T + e2 * T ^ 2 + e3 * T ^ 3 + e4 * T ^ 4
  Aw <- h0 + h1 * T + h2 * T ^ 2 + h3 * T ^ 3
  Bw <- k0 + k1 * T + k2 * T ^ 2

  R <- Rw + (b0 + b1 * T + b2 * T ^ 2 + b3 * T ^ 3 + b4 * T ^ 4) * S +
            (c0 + c1 * T + c2 * T ^ 2) * S ^ (3 / 2) + d0 * (S ^ 2)
  K <- Kw + (f0 + f1 * T + f2 * T ^ 2 + f3 * T ^ 3) * S +
            (g0 + g1 * T + g2 * T ^ 2) * S ^ (3 / 2)
  a <- Aw + (i0 + i1 * T + i2 * T ^ 2) * S + j0 * S ^ (3 / 2)
  B <- Bw + (m0 + m1 * T + m2 * T ^ 2) * S

  K <- K + a * p + B * (p ^ 2)

  (1 - p / K) / R
}