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revision 1.1 by dimitri, Fri Jan 31 04:42:16 2003 UTC revision 1.2 by dimitri, Tue Feb 18 05:33:55 2003 UTC
# Line 0  Line 1 
1    C
2    
3    #include "SBO_OPTIONS.h"
4    
5          _RL FUNCTION SBO_RHO( DPT, LAT, S, T )
6    C     /==========================================================\
7    C     | _RL FUNCTION SBO_RHO                                     |
8    C     | o Compute density for SBO package.                       |
9    C     |==========================================================|
10    C     | CHECK VALUE:                                             |
11    C     | DPT=5000; LAT=30; S=30; T=30; SBO_RHO=1038.298           |
12    C     \==========================================================/
13          IMPLICIT NONE
14    
15    C     == Routine arguments ==
16    C     SBO_RHO - density (kg/m^3)
17    C     DPT     - depth (m)
18    C     LAT     - latitude north (deg)
19    C     S       - salinity (PSU)
20    C     T       - potential temperature (deg C)
21          
22          _RL DPT,LAT,S,T
23    
24          _RL PLAT,D,C1,P,PR,Q,X,SR,V350P,B
25    
26          Real*8 PI
27          PARAMETER ( PI    = 3.14159265358979323844D0   )
28          
29    C     First convert depth to pressure
30    C     Ref: Saunders, "Practical Conversion of Pressure to Depth",
31    C     J. Phys. Oceanog., April 1981.
32    C     CHECK VALUE: P80=7500.004 DBARS;FOR LAT=30 DEG., DEPTH=7321.45 METERS
33    
34          PLAT=abs(LAT*pi/180.)
35          D=sin(PLAT)
36          C1=5.92E-3+(D*D)*5.25E-3
37          P=((1-C1)-sqrt(((1-C1)**2)-(8.84E-6*abs(DPT))))/4.42E-6
38    
39    C     Second convert temperature from potential to in situ
40    C     REF: BRYDEN,H.,1973,DEEP-SEA RES.,20,401-408
41    C     FOFONOFF,N.,1977,DEEP-SEA RES.,24,489-491
42    C     CHECKVALUE: THETA= 36.89073 C,S=40 (IPSS-78),T0=40 DEG C,
43    C     P0=10000 DECIBARS,PR=0 DECIBARS
44          
45          PR = P
46          P  = 0.
47          Q = PR*((((-2.1687E-16*T+1.8676E-14)*T-4.6206E-13)*P+
48         &     ((2.7759E-12*T-1.1351E-10)*(S-35.0)+
49         &     ((-5.4481E-14*T+8.733E-12)*T-6.7795E-10)*T+
50         &     1.8741E-8))*P+(-4.2393E-8*T+1.8932E-6)*(S-35.0)+
51         &     ((6.6228E-10*T-6.836E-8)*T+8.5258E-6)*T+3.5803E-5)
52          
53          T = T + 0.5*Q
54          P = P + 0.5*PR
55          x = PR*((((-2.1687E-16*T+1.8676E-14)*T-4.6206E-13)*P+
56         &     ((2.7759E-12*T-1.1351E-10)*(S-35.0)+
57         &     ((-5.4481E-14*T+8.733E-12)*T-6.7795E-10)*T+
58         &     1.8741E-8))*P+(-4.2393E-8*T+1.8932E-6)*(S-35.0)+
59         &     ((6.6228E-10*T-6.836E-8)*T+8.5258E-6)*T+3.5803E-5)
60          
61          T = T + 0.29289322*(x-Q)
62          Q = 0.58578644*x + 0.121320344*Q
63          x = PR*((((-2.1687E-16*T+1.8676E-14)*T-4.6206E-13)*P+
64         &     ((2.7759E-12*T-1.1351E-10)*(S-35.0)+
65         &     ((-5.4481E-14*T+8.733E-12)*T-6.7795E-10)*T+
66         &     1.8741E-8))*P+(-4.2393E-8*T+1.8932E-6)*(S-35.0)+
67         &     ((6.6228E-10*T-6.836E-8)*T+8.5258E-6)*T+3.5803E-5)
68          
69          T = T + 1.707106781*(x-Q)
70          Q = 3.414213562*x - 4.121320344*Q
71          P = P + 0.5*PR
72          x = PR*((((-2.1687E-16*T+1.8676E-14)*T-4.6206E-13)*P+
73         &     ((2.7759E-12*T-1.1351E-10)*(S-35.0)+
74         &     ((-5.4481E-14*T+8.733E-12)*T-6.7795E-10)*T+
75         &     1.8741E-8))*P+(-4.2393E-8*T+1.8932E-6)*(S-35.0)+
76         &     ((6.6228E-10*T-6.836E-8)*T+8.5258E-6)*T+3.5803E-5)
77          T = T + (x-2.0*Q)/6.0
78    
79    C     Third compute density
80    C     BASED ON 1980 EQUATION
81    C     OF STATE FOR SEAWATER AND 1978 PRACTICAL SALINITY SCALE.
82    C     REFERENCES
83    C     MILLERO, ET AL (1980) DEEP-SEA RES.,27A,255-264
84    C     MILLERO AND POISSON 1981,DEEP-SEA RES.,28A PP 625-629.
85    C     BOTH ABOVE REFERENCES ARE ALSO FOUND IN UNESCO REPORT 38 (1981)
86    C     CHECK VALUE: SIGMA = 59.82037  KG/M**3 FOR S = 40 (IPSS-78) ,
87    C     T = 40 DEG C, P0= 10000 DECIBARS.
88    
89    C     CONVERT PRESSURE TO BARS AND TAKE SQUARE ROOT SALINITY.
90          P=P/10.
91          SR = sqrt(abs(S))
92    
93    C     INTERNATIONAL ONE-ATMOSPHERE EQUATION OF STATE OF SEAWATER
94          x = (4.8314E-4 * S +
95         &     ((-1.6546E-6*T+1.0227E-4)*T-5.72466E-3) * SR +
96         &     (((5.3875E-9*T-8.2467E-7)*T+7.6438E-5)*T-4.0899E-3)*T
97         &     +8.24493E-1)*S + ((((6.536332E-9*T-1.120083E-6)
98         &     *T+1.001685E-4)*T-9.095290E-3)*T+6.793952E-2)*T-28.263737
99          
100    C     SPECIFIC VOLUME AT ATMOSPHERIC PRESSURE
101          V350P = 1.0/1028.1063
102          x = -x*V350P/(1028.1063+x)
103    
104    C     COMPUTE COMPRESSION TERMS
105          SR = ((((9.1697E-10*T+2.0816E-8)*T-9.9348E-7) * S +
106         &     (5.2787E-8*T-6.12293E-6)*T+3.47718E-5) *P +
107         &     (1.91075E-4 * SR + (-1.6078E-6*T-1.0981E-5)*T+2.2838E-3) *
108         &     S + ((-5.77905E-7*T+1.16092E-4)*T+1.43713E-3)*T-0.1194975)
109         &     *P + (((-5.3009E-4*T+1.6483E-2)*T+7.944E-2) * SR +
110         &     ((-6.1670E-5*T+1.09987E-2)*T-0.603459)*T+54.6746) * S +
111         &     (((-5.155288E-5*T+1.360477E-2)*T-2.327105)*T+148.4206)*T-1930.06
112          
113    C     EVALUATE PRESSURE POLYNOMIAL
114          B  = (5.03217E-5*P+3.359406)*P+21582.27
115          x = x*(1.0 - P/B) + (V350P+x)*P*SR/(B*(B+SR))
116          SR = V350P*(1.0 - P/B)
117          SBO_RHO = 1028.106331 + P/B/SR - x / (SR*(SR+x))
118    
119          RETURN
120          END
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