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