26
0688-SOM-00001, Rev: 02
© Tritech International Ltd.
C.2. DelGrosso Equation
Source: NPL Technical Guides – Speed of Sound in Sea-water
Validity: T = 0 to 30oC, S = 30 to 40ppt, P = 0 to 1000 kg/cm2 (Wong and Zhu, 1995)
C.3. Wood Equation
Source: The Hydrographic Society Special Publication No. 34
Validity: Unknown.
C.4. Mackenzie Equation
Source: NPL Technical Guides – Speed of Sound in Sea-water
Validity: T = 2 to 30oC, S = 25 to 40psu, D = 0 to 8000 meters (K.V. Mackenzie, 1981)
𝐶𝐶(𝐷𝐷, 𝑆𝑆, 𝑇𝑇) = 1410 + (4.21 ∗ 𝑇𝑇) − (0.037 ∗ 𝑇𝑇
2
) + (1.14 ∗ 𝑆𝑆) + (0.018 ∗ 𝐷𝐷)
𝑇𝑇 = 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑖𝑖𝑖𝑖 𝑑𝑑𝑇𝑇𝑑𝑑𝑇𝑇𝑇𝑇𝑇𝑇𝑑𝑑 𝐶𝐶𝑇𝑇𝐶𝐶𝑑𝑑𝑖𝑖𝑇𝑇𝑑𝑑
𝑆𝑆 = 𝑆𝑆𝑇𝑇𝐶𝐶𝑖𝑖𝑖𝑖𝑖𝑖𝑇𝑇𝑎𝑎 𝑖𝑖𝑖𝑖 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑑𝑑 𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇ℎ𝑜𝑜𝑇𝑇𝑑𝑑𝑇𝑇𝑖𝑖𝑑𝑑
𝐷𝐷 = 𝐷𝐷𝑇𝑇𝑇𝑇𝑇𝑇ℎ 𝑖𝑖𝑖𝑖 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑑𝑑
𝐶𝐶(𝐷𝐷, 𝑆𝑆, 𝑇𝑇) = 1448.96 + 4.591𝑇𝑇 − 5.304 ∗ 10
−2
𝑇𝑇
2
+ 2.374 ∗ 10
−4
𝑇𝑇
3
+ 1.340(𝑆𝑆 − 35)
+ 1.630 ∗ 10
−2
𝐷𝐷 + 1.675 ∗ 10
−7
𝐷𝐷
2
− 1.025 ∗ 10
−2
𝑇𝑇(𝑆𝑆 − 35) − 7.139
∗ 10
−13
𝑇𝑇𝐷𝐷
3
𝑇𝑇 = 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑖𝑖𝑖𝑖 𝑑𝑑𝑇𝑇𝑑𝑑𝑇𝑇𝑇𝑇𝑇𝑇𝑑𝑑 𝐶𝐶𝑇𝑇𝐶𝐶𝑑𝑑𝑖𝑖𝑇𝑇𝑑𝑑
𝑆𝑆 = 𝑆𝑆𝑇𝑇𝐶𝐶𝑖𝑖𝑖𝑖𝑖𝑖𝑇𝑇𝑆𝑆 𝑖𝑖𝑖𝑖 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑑𝑑 𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇ℎ𝑜𝑜𝑇𝑇𝑑𝑑𝑇𝑇𝑖𝑖𝑑𝑑
𝐷𝐷 = 𝐷𝐷𝑇𝑇𝑇𝑇𝑇𝑇ℎ 𝑖𝑖𝑖𝑖 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑑𝑑
Table of Coefficients
Coefficients
Numerical values
C
000
1402.392
C
T1
0.5012285E1
C
T2
-0.551184E-1
C
T3
0.221649E-3
C
S1
0.1329530E1
C
S2
0.1288598E-3
C
P1
0.1560592
C
P2
0.2449993E-4
C
P3
-0.8833959E-8
C
ST
-0.1275936E-1
C
TP
0.6353509E-2
C
T2P2
0.2656174E-7
C
TP2
-0.1593895E-5
C
TP3
0.5222483E-9
C
T3P
-0.4383615E-6
C
S2P2
-0.1616745E-8
C
ST2
0.9688441E-4
C
S2TP
0.4857614E-5
C
STP
-0.3406824E-3
c(S,T,P) = C
000
+ ΔC
T
+ ΔC
S
+ ΔC
P
+ ΔC
STP
ΔC
T
(T) C
T1
T + C
T2
T
2
+ C
T3
T
3
Δ
C
S
(S) = C
S1
S + C
S2
S
2
Δ
C
P
(P) = C
P1
P + C
P2
P
2
+ C
P3
P
3
Δ
C
STP
(S,T,P) = C
TP
TP + C
T3P
T
3
P + C
TP2
TP
2
+ C
T2P2
T
2
P
2
+ C
TP3
TP
3
+
C
ST
ST + C
ST2
ST
2
+ C
STP
STP + C
S2TP
S
2
TP + C
S2P2
S
2
P
2
T = temperature in degrees Celsius
S = salinity in Practical Salinity Units
P = pressure in kg/cm
2
(where 100 kPa = 1.019716 kg/cm
2
)
Table of Coefficients
Coefficients
Numerical values
C
000
1402.392
C
T1
0.5012285E1
C
T2
-0.551184E-1
C
T3
0.221649E-3
C
S1
0.1329530E1
C
S2
0.1288598E-3
C
P1
0.1560592
C
P2
0.2449993E-4
C
P3
-0.8833959E-8
C
ST
-0.1275936E-1
C
TP
0.6353509E-2
C
T2P2
0.2656174E-7
C
TP2
-0.1593895E-5
C
TP3
0.5222483E-9
C
T3P
-0.4383615E-6
C
S2P2
-0.1616745E-8
C
ST2
0.9688441E-4
C
S2TP
0.4857614E-5
C
STP
-0.3406824E-3
c(S,T,P) = C
000
+ ΔC
T
+ ΔC
S
+ ΔC
P
+ ΔC
STP
ΔC
T
(T) C
T1
T + C
T2
T
2
+ C
T3
T
3
Δ
C
S
(S) = C
S1
S + C
S2
S
2
Δ
C
P
(P) = C
P1
P + C
P2
P
2
+ C
P3
P
3
Δ
C
STP
(S,T,P) = C
TP
TP + C
T3P
T
3
P + C
TP2
TP
2
+ C
T2P2
T
2
P
2
+ C
TP3
TP
3
+
C
ST
ST + C
ST2
ST
2
+ C
STP
STP + C
S2TP
S
2
TP + C
S2P2
S
2
P
2
T = temperature in degrees Celsius
S = salinity in Practical Salinity Units
P = pressure in kg/cm
2
(where 100 kPa = 1.019716 kg/cm
2
)