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4.8.2 Ocean

The bulk formulas used to determine the turbulent fluxes of momentum (stress), water (evaporation, or latent heat), and sensible heat into the atmosphere over ocean surfaces are

$\displaystyle ( \boldsymbol {\tau}, E, H) = \rho_A \left\vert\Delta {\boldsymb...
...right\vert(C_D \Delta {\boldsymbol {v}}, C_E \Delta q, C_p C_H \Delta\theta),$ (4.427)

where $ \rho_A$ is atmospheric surface density and $ C_p$ is the specific heat. Since CAM2 does not allow for motion of the ocean surface, the velocity difference between surface and atmosphere is $ \Delta {\boldsymbol {v}}= {\boldsymbol {v}}_A$, the velocity of the lowest model level. The potential temperature difference is $ \Delta\theta =
\theta_A - T_s$, where $ T_s$ is the surface temperature. The specific humidity difference is $ \Delta q = q_A - q_s(T_s)$, where $ q_s(T_s)$ is the saturation specific humidity at the sea-surface temperature.

In (4.427), the transfer coefficients between the ocean surface and the atmosphere are computed at a height $ Z_A$ and are functions of the stability, $ \zeta$:

$\displaystyle C_{(D,E,H)} = \kappa^2 {\left[\ln\left(\frac{Z_A}{Z_{0m}}\right) ...
...} {\left[\ln\left(\frac{Z_A}{Z_{0(m,e,h)}}\right) - \psi_{(m,s,s)}\right]}^{-1}$ (4.428)

where $ \kappa = 0.4$ is von Kármán's constant and $ Z_{0(m,e,h)}$ is the roughness length for momentum, evaporation, or heat, respectively. The integrated flux profiles, $ \psi_m$ for momentum and $ \psi_s$ for scalars, under stable conditions ($ \zeta >
0$) are

$\displaystyle \psi_m(\zeta) = \psi_s(\zeta) = -5 \zeta.$ (4.429)

For unstable conditions ($ \zeta < 0$), the flux profiles are

$\displaystyle \psi_m(\zeta) =$ $\displaystyle 2 \ln[0.5(1 + X)] + \ln[0.5(1 + X^2 )]$    
  $\displaystyle - 2 \tan^{-1} X + 0.5 \pi,$ (4.430)
$\displaystyle \psi_s(\zeta) =$ $\displaystyle 2 \ln[0.5(1 + X^2 )],$ (4.431)
$\displaystyle X =$ $\displaystyle (1 - 16 \zeta)^{1/4} .$ (4.432)

The stability parameter used in (4.429)-(4.432) is

$\displaystyle \zeta = \frac{\kappa g Z_A}{u^{*2}}\left(\frac{\theta^*}{\theta_v} + \frac{Q^*}{(\epsilon^{-1} + q_A)}\right),$ (4.433)

where the virtual potential temperature is $ \theta_v = \theta_A(1 +
\epsilon q_A)$; $ q_A$ and $ \theta_A$ are the lowest level atmospheric humidity and potential temperature, respectively; and $ \epsilon =
0.606$. The turbulent velocity scales in (4.433) are

$\displaystyle u^* =$ $\displaystyle C_D^{1/2} \vert\Delta {\boldsymbol {v}}\vert,$    
$\displaystyle (Q^*,\theta^*) =$ $\displaystyle C_{(E,H)}\frac{\vert\Delta {\boldsymbol {v}}\vert}{u^*} (\Delta q,\Delta\theta).$ (4.434)

Over oceans, $ Z_{0e} = 9.5 \times 10^{-5}$ m under all conditions and $ Z_{0h} = 2.2 \times 10^{-9}$ m for $ \zeta >
0$, $ Z_{0h} = 4.9 \times
10^{-5}$ m for $ \zeta \le 0$, which are given in Large and Pond [1982]. The momentum roughness length depends on the wind speed evaluated at 10 m as

$\displaystyle Z_{om}$ $\displaystyle = 10 \exp\left[-\kappa{\left(\frac{c_4}{U_{10}} + c_5 + c_6 U_{10}\right)}^{-1}\right] ,$    
$\displaystyle U_{10}$ $\displaystyle = U_A {\left[1 + \frac{\sqrt{C_{10}^N}}{\kappa}\ln\left(\frac{Z_A}{10} - \psi_m\right)\right]}^{-1} ,$ (4.435)

where $ c_4 = 0.0027$  m s$ {}^{-1}$, $ c_5 = 0.000142$, $ c_6 =
0.0000764$ m$ {}^{-1}$ s, and the required drag coefficient at 10-m height and neutral stability is $ C^{N}_{10} = c_4 U^{-1}_{10} + c_5 +
c_6 U_{10}$ as given by Large et al. [1994].

The transfer coefficients in (4.427) and (4.428) depend on the stability following (4.429)-(4.432), which itself depends on the surface fluxes (4.433) and (4.434). The transfer coefficients also depend on the momentum roughness, which itself varies with the surface fluxes over oceans (4.435). The above system of equations is solved by iteration.


next up previous contents
Next: 4.8.3 Sea Ice Up: 4.8 Surface Exchange Formulations Previous: 4.8.1.2 Monin-Obukhov similarity theory   Contents
Jim McCaa 2003-03-03