User`s manual

Appendix IV: Derived Parameter Formulas
99
density = ρ = ρ (s, t, p) [kg/m
3
]
(density of seawater with salinity s, temperature t, and pressure p, based on the
equation of state for seawater (EOS80))
(Note: To calculate gravity for the density algorithm, SEASAVE uses the
latitude from a NMEA navigation device, if NMEA is enabled in the .con file.
If your system does not have NMEA, enter the desired latitude on the
Miscellaneous tab in Configure Inputs.)
Sigma-theta = σ
θ
= ρ (s, θ(s, t, p, 0), 0) - 1000 [kg/m
3
]
Sigma-1 = σ
1
= ρ (s, θ(s, t, p, 1000), 1000) - 1000 [kg/m
3
]
Sigma-2 = σ
2
= ρ (s, θ(s, t, p, 2000), 2000) - 1000 [kg/m
3
]
Sigma-4 = σ
4
= ρ (s, θ(s, t, p, 4000), 4000) - 1000 [kg/m
3
]
Sigma-t = σ
t
= ρ (s, t, 0) - 1000 [kg/m
3
]
thermosteric anomaly = 10
5
((1000/(1000 + σ
t
)) - 0.97266) [10
-8
m
3
/kg]
specific volume = V(s, t, p) = 1/ρ [m
3
/kg]
specific volume anomaly = δ = 10
8
(V(s, t, p) - V(35, 0, p)) [10
-8
m
3
/kg]
p=p
geopotential anomaly = 10
-4
Σ
(δ x Δp) [J/kg] = [m
2
/s
2
]
Δp, p=0
dynamic meters = geopotential anomaly / 10.0
(1 dynamic meter = 10 J/kg;
(Sverdup, Johnson, Flemming (1946), UNESCO (1991)))
Density calculation:
Using the following constants -
B0 = 8.24493e-1, B1 = -4.0899e-3, B2 = 7.6438e-5, B3 = -8.2467e-7, B4 = 5.3875e-9,
C0 = -5.72466e-3, C1 = 1.0227e-4, C2 = -1.6546e-6, D0 = 4.8314e-4, A0 = 999.842594,
A1 = 6.793952e-2, A2 = -9.095290e-3, A3 = 1.001685e-4, A4 = -1.120083e-6, A5 = 6.536332e-9,
FQ0 = 54.6746, FQ1 = -0.603459, FQ2 = 1.09987e-2, FQ3 = -6.1670e-5, G0 = 7.944e-2, G1 = 1.6483e-2,
G2 = -5.3009e-4, i0 = 2.2838e-3, i1 = -1.0981e-5, i2 = -1.6078e-6, J0 =1.91075e-4, M0 = -9.9348e-7,
M1 = 2.0816e-8, M2 = 9.1697e-10, E0 = 19652.21, E1 = 148.4206, E2 = -2.327105, E3 = 1.360477e-2,
E4 = -5.155288e-5, H0 = 3.239908, H1 = 1.43713e-3, H2 = 1.16092e-4, H3 = -5.77905e-7,
K0 = 8.50935e-5, K1 =-6.12293e-6, K2 = 5.2787e-8
C Computer Code -
double Density(double s, double t, double p)
// s = salinity PSU, t = temperature deg C ITPS-68, p = pressure in decibars
{
double t2, t3, t4, t5, s32;
double sigma, k, kw, aw, bw;
double val;
t2 = t*t;
t3 = t*t2;
t4 = t*t3;
t5 = t*t4;
if (s <= 0.0) s = 0.000001;
s32 = pow(s, 1.5);
p /= 10.0; /* convert decibars to bars */
sigma = A0 + A1*t + A2*t2 + A3*t3 + A4*t4 + A5*t5 + (B0 + B1*t + B2*t2 + B3*t3 + B4*t4)*s +
(C0 + C1*t + C2*t2)*s32 + D0*s*s;
kw = E0 + E1*t + E2*t2 + E3*t3 + E4*t4;
aw = H0 + H1*t + H2*t2 + H3*t3;
bw = K0 + K1*t + K2*t2;
k = kw + (FQ0 + FQ1*t + FQ2*t2 + FQ3*t3)*s + (G0 + G1*t + G2*t2)*s32 + (aw + (i0 + i1*t +
i2*t2)*s + (J0*s32))*p + (bw + (M0 + M1*t + M2*t2)*s)*p*p;
val = 1 - p / k;
if (val) sigma = sigma / val - 1000.0;
return sigma;
}