Seasonal barotropic sea surface height fluctuation in relation to regional ocean mass variation

Abstract

A consistency between seasonal fluctuation of actual sea surface height (SSH) and those caused by mass and density variations in gyre-scale regions is examined. The SSH obtained from satellite altimetry (altimetric SSH) is adopted as the actual SSH. SSH caused by mass variation (mass-related SSH) is simulated using a barotropic global ocean model forced by water flux, wind stress and surface pressure. SSH caused by density variation (steric SSH) is calculated from water density profile, i.e. temperature and salinity profiles. The model SSH well represents mass-related SSH for gyre-scale regional means, and seasonal fluctuation of the altimetric SSH corrected for the model SSH is similar to that of steric SSH above a pressure level larger than 300 dbar. The results indicate that the mass-related SSH does not much respond to the baroclinic adjustment to the seasonally varying wind stress curl. The mass-related SSH forced by wind stress and surface pressure should be accounted for regional evaluation, though it is not necessary for global mean evaluation. Detection of steric SSH from altimetric SSH would be useful for assimilation approaches in which the altimetric SSH is treated as the variable reflecting subsurface temperature and salinity.

Appendix

Using the hydrostatic equilibrium hypothesis, dp = −ρgdz, the sea surface height (SSH), H ^act, from the bottom is expressed as

$$ H^{\text{act}} = \int\limits_{{P_{\text{s}} }}^{{P_{\text{b}} }} {\frac{1}{\rho g}} {\text{d}}p = \int\limits_{{\bar{P}_{\text{s}} }}^{{\bar{P}_{\text{b}} }} {\frac{1}{\rho g}} {\text{d}}p + \int\limits_{{\bar{P}_{\text{b}} }}^{{\bar{P}_{\text{b}} + P^{\prime}_{\text{b}} }} {\frac{1}{\rho g}} {\text{d}}p, $$

(9)

where g is the gravity acceleration, ρ the seawater density, and P the pressure. The variables with subscripts ‘b’ and ‘s’ represent the values at ocean bottom and sea surface, respectively. The bar and the prime represent temporal mean and fluctuation from the mean. The surface pressure P _S is assumed as a constant value $\bar{P}_{\text{S}}$ for transformation to the right-hand side. Value of the first term in the right-hand side varies with the density variation, because the density, ρ, is the only variable in this term. The value of the second term varies with variations of the density at the bottom, ρ _b, and the bottom pressure, $P_{\text{b}}^{\prime }$. However, the effect of the density variation is negligible because the density at the bottom scarecely varies. The bottom pressure, $\bar{P}_{\text{b}} + P_{\text{b}}^{\prime }$, is defined by the mass of the water column. Therefore, the fluctuation of SSH consists of those by density variation and mass variation, and is expressed as

$$ \tilde{H}^{\text{act}} = \tilde{H}^{\text{den}} + \tilde{H}^{\text{mass}} , $$

(10)

where the fluctuations from the temporal mean values, $\tilde{H}^{\text{den}}$ and $\tilde{H}^{\text{mass}}$, are expressed as

$$ \tilde{H}^{\text{den}} = \int\limits_{{\bar{P}_{\text{s}} }}^{{\bar{P}_{\text{b}} }} {\frac{1}{\rho g}} {\text{d}}p - \overline{{\int\limits_{{\bar{P}_{\text{s}} }}^{{\bar{P}_{\text{b}} }} {\frac{1}{\rho g}} {\text{d}}p}} , $$

(11)

$$ \tilde{H}^{\text{mass}} = \int\limits_{{\bar{P}_{\text{b}} }}^{{\bar{P}_{\text{b}} + P_{\text{b}}^{\prime } }} {\frac{1}{{\rho_{\text{b}} g}}} {\text{d}}p = \frac{{P_{\text{b}}^{\prime } }}{{\rho_{\text{b}} g}}, $$

(12)

respectively. The transformation to the last term of the Eq. (12) is based on the assumed constant bottom pressure, ρ _b.