C $Header: /u/gcmpack/MITgcm/pkg/sbo/sbo_rho.F,v 1.4 2011/05/13 14:57:22 jahn Exp $
C $Name: $
#include "SBO_OPTIONS.h"
_RL FUNCTION SBO_RHO( DPT, LAT, S, T )
C /==========================================================\
C | _RL FUNCTION SBO_RHO |
C | o Compute density for SBO package. |
C |==========================================================|
C | CHECK VALUE: |
C | DPT=5000; LAT=30; S=30; T=30; SBO_RHO=1038.298 |
C \==========================================================/
IMPLICIT NONE
C == Routine arguments ==
C SBO_RHO - density (kg/m^3)
C DPT - depth (m)
C LAT - latitude north (deg)
C S - salinity (PSU)
C T - potential temperature (deg C)
_RL DPT,LAT,S,T
_RL PLAT,D,C1,P,PR,Q,X,SR,V350P,B
Real*8 PI
PARAMETER ( PI = 3.14159265358979323844D0 )
C First convert depth to pressure
C Ref: Saunders, "Practical Conversion of Pressure to Depth",
C J. Phys. Oceanog., April 1981.
C CHECK VALUE: P80=7500.004 DBARS;FOR LAT=30 DEG., DEPTH=7321.45 METERS
PLAT=abs(LAT*pi/180.)
D=sin(PLAT)
C1=5.92E-3+(D*D)*5.25E-3
P=((1-C1)-sqrt(((1-C1)**2)-(8.84E-6*abs(DPT))))/4.42E-6
C Second convert temperature from potential to in situ
C REF: BRYDEN,H.,1973,DEEP-SEA RES.,20,401-408
C FOFONOFF,N.,1977,DEEP-SEA RES.,24,489-491
C CHECKVALUE: THETA= 36.89073 C,S=40 (IPSS-78),T0=40 DEG C,
C P0=10000 DECIBARS,PR=0 DECIBARS
PR = P
P = 0.
Q = PR*((((-2.1687E-16*T+1.8676E-14)*T-4.6206E-13)*P+
& ((2.7759E-12*T-1.1351E-10)*(S-35.0)+
& ((-5.4481E-14*T+8.733E-12)*T-6.7795E-10)*T+
& 1.8741E-8))*P+(-4.2393E-8*T+1.8932E-6)*(S-35.0)+
& ((6.6228E-10*T-6.836E-8)*T+8.5258E-6)*T+3.5803E-5)
T = T + 0.5*Q
P = P + 0.5*PR
x = PR*((((-2.1687E-16*T+1.8676E-14)*T-4.6206E-13)*P+
& ((2.7759E-12*T-1.1351E-10)*(S-35.0)+
& ((-5.4481E-14*T+8.733E-12)*T-6.7795E-10)*T+
& 1.8741E-8))*P+(-4.2393E-8*T+1.8932E-6)*(S-35.0)+
& ((6.6228E-10*T-6.836E-8)*T+8.5258E-6)*T+3.5803E-5)
T = T + 0.29289322*(x-Q)
Q = 0.58578644*x + 0.121320344*Q
x = PR*((((-2.1687E-16*T+1.8676E-14)*T-4.6206E-13)*P+
& ((2.7759E-12*T-1.1351E-10)*(S-35.0)+
& ((-5.4481E-14*T+8.733E-12)*T-6.7795E-10)*T+
& 1.8741E-8))*P+(-4.2393E-8*T+1.8932E-6)*(S-35.0)+
& ((6.6228E-10*T-6.836E-8)*T+8.5258E-6)*T+3.5803E-5)
T = T + 1.707106781*(x-Q)
Q = 3.414213562*x - 4.121320344*Q
P = P + 0.5*PR
x = PR*((((-2.1687E-16*T+1.8676E-14)*T-4.6206E-13)*P+
& ((2.7759E-12*T-1.1351E-10)*(S-35.0)+
& ((-5.4481E-14*T+8.733E-12)*T-6.7795E-10)*T+
& 1.8741E-8))*P+(-4.2393E-8*T+1.8932E-6)*(S-35.0)+
& ((6.6228E-10*T-6.836E-8)*T+8.5258E-6)*T+3.5803E-5)
T = T + (x-2.0*Q)/6.0
C Third compute density
C BASED ON 1980 EQUATION
C OF STATE FOR SEAWATER AND 1978 PRACTICAL SALINITY SCALE.
C REFERENCES
C MILLERO, ET AL (1980) DEEP-SEA RES.,27A,255-264
C MILLERO AND POISSON 1981,DEEP-SEA RES.,28A PP 625-629.
C BOTH ABOVE REFERENCES ARE ALSO FOUND IN UNESCO REPORT 38 (1981)
C CHECK VALUE: SIGMA = 59.82037 KG/M**3 FOR S = 40 (IPSS-78) ,
C T = 40 DEG C, P0= 10000 DECIBARS.
C CONVERT PRESSURE TO BARS AND TAKE SQUARE ROOT SALINITY.
P=P/10.
SR = sqrt(abs(S))
C INTERNATIONAL ONE-ATMOSPHERE EQUATION OF STATE OF SEAWATER
x = (4.8314E-4 * S +
& ((-1.6546E-6*T+1.0227E-4)*T-5.72466E-3) * SR +
& (((5.3875E-9*T-8.2467E-7)*T+7.6438E-5)*T-4.0899E-3)*T
& +8.24493E-1)*S + ((((6.536332E-9*T-1.120083E-6)
& *T+1.001685E-4)*T-9.095290E-3)*T+6.793952E-2)*T-28.263737
C SPECIFIC VOLUME AT ATMOSPHERIC PRESSURE
V350P = 1.0/1028.1063
x = -x*V350P/(1028.1063+x)
C COMPUTE COMPRESSION TERMS
SR = ((((9.1697E-10*T+2.0816E-8)*T-9.9348E-7) * S +
& (5.2787E-8*T-6.12293E-6)*T+3.47718E-5) *P +
& (1.91075E-4 * SR + (-1.6078E-6*T-1.0981E-5)*T+2.2838E-3) *
& S + ((-5.77905E-7*T+1.16092E-4)*T+1.43713E-3)*T-0.1194975)
& *P + (((-5.3009E-4*T+1.6483E-2)*T+7.944E-2) * SR +
& ((-6.1670E-5*T+1.09987E-2)*T-0.603459)*T+54.6746) * S +
& (((-5.155288E-5*T+1.360477E-2)*T-2.327105)*T+148.4206)*T -
& 1930.06
C EVALUATE PRESSURE POLYNOMIAL
B = (5.03217E-5*P+3.359406)*P+21582.27
x = x*(1.0 - P/B) + (V350P+x)*P*SR/(B*(B+SR))
SR = V350P*(1.0 - P/B)
SBO_RHO = 1028.106331 + P/B/SR - x / (SR*(SR+x))
RETURN
END