Depth to pressure conversion. Leroy '97 equation

Mathematical definition

$$\boxed{P\left( {Z,\phi } \right) = P\left( {Z,45} \right) \times k\left( {Z,\phi } \right)}$$

This is an equation for the "standard" ocean. Use corrective terms from the table above for particular applications.

Notation Description Units Limits Conversion
$P$ pressure $\text{kPa}$ $P\left[ {{\rm{kPa}}} \right] = P\left[ {{\rm{MPa}}} \right] \times {10^3}$
$Z$ depth $\text{m}$
$\phi$ latitude $\text{deg.}$ $-90\ < \phi < 90$

$$\begin{array}{r} {P\left( {Z,45} \right) = 1.00818 \times {{10}^{ - 2}}Z + 2.465 \times {{10}^{ - 8}}{Z^2}}\\ { - 1.25 \times {{10}^{ - 13}}{Z^3} + 2.8 \times {{10}^{ - 19}}{Z^4}} \end{array}$$

$$k\left( {Z,\phi } \right) = \frac{{g\left( \phi \right) - 2 \times {{10}^{ - 5}}Z}}{{9.80612 - 2 \times {{10}^{ - 5}}Z}}$$

$$g\left( \phi \right) = 0.7803\left( {1 + 5.3 \times {{10}^{ - 3}}{{\sin }^2}\left( \phi \right)} \right)$$

Notation Description Units
$g\left( \phi \right)$ gravity $\text{ms}^{-2}$

Corrective terms for various areas

$${P_{corrected}} = P\left( {Z,\phi } \right) - \Delta P\left( Z \right)$$

Area of applicability Latitude Expression for $\Delta P\left( Z \right)$, $\text{MPa}$ Accuracy $\pm 10^{3}$, $\text{Pa}$
Common oceans $60^\circ N - 40^\circ S$ $1.0 \times {10^{ - 2}}Z/\left( {Z + 100} \right) + 6.2 \times {10^{ - 6}}Z$ $8$
North Eastern Atlantic $30^\circ N - 35^\circ S$ $8.0 \times {10^{ - 3}}Z/\left( {Z + 200} \right) + 4.0 \times {10^{ - 6}}Z$ $3$
Circumpolar Antarctic $8.0 \times {10^{ - 3}}Z/\left( {Z + 1000} \right) + 1.6 \times {10^{ - 6}}Z$ $1$
Mediterranean Sea $- 8.5 \times {10^{ - 6}}Z + 1.4 \times {10^{ - 9}}{Z^2}$ $2$
Red Sea $0$ $2$
Arctic Ocean $0$ $1$
Sea of Japan $7.8 \times {10^{ - 6}}Z$ $1$
Sulu Sea $8^\circ$ $1.0 \times {10^{ - 2}}Z/\left( {Z + 100} \right) + 1.6 \times {10^{ - 5}}Z + 1.0 \times {10^{ - 9}}{Z^2}$ $<1$
Halmahera basin $0^\circ$ $8 \times {10^{ - 3}}Z/\left( {Z + 50} \right) + 1.3 \times {10^{ - 5}}Z$ $<1$
Celebes basin $4^\circ$ $1.2 \times {10^{ - 2}}Z/\left( {Z + 100} \right) + 7.0 \times {10^{ - 6}}Z + 2.5 \times {10^{ - 10}}{Z^2}$ $2$
Weber Deep $6^\circ$ $1.2 \times {10^{ - 2}}Z/\left( {Z + 100} \right) + 7.0 \times {10^{ - 6}}Z + 2.5 \times {10^{ - 10}}{Z^2}$ $2$
Black Sea $43^\circ$ $1.13 \times {10^{ - 4}}Z$ $1$
Baltic Sea $60^\circ$ $1.8 \times {10^{ - 4}}Z$ $1$

Octave/Matlab implementation

function P = depth_to_pressure_sea_leroy_97(D,L)
% Inputs
%   D: depth \ m \ 0 < D < 4000
%   L: latitude \ degree \ -90 < L < 90
% Outputs
%   P: pressure \ kPa

    G = 9.7803*(1 + (5.3e-3)*sind(L).^2);
    P45 = (1.00818e-2)*D + (2.465e-8)*(D.^2) ...
        - (1.25e-13)*(D.^3) + (2.8e-19) *(D.^4);
    k = (G - (2e-5)*D)./(9.80612 - (2e-5)*D);

    P =  P45.*k.*1e3;
end

Computational examples

References

  1. Leroy, Claude C; Parthiot, François, "Depth-pressure relationships in the oceans and seas", 1998