P-vector inverse method evaluated using the modular ocean model (MOM)

Several major inverse methods (Stommel-Schott method, Wunsch method, and Bernoulli method) have been successfully developed to quantitatively estimate the geostrophic velocity at the reference level from hydrographic data. No matter the different appearance, they are based on the same dynamical sophistication: geostrophy, hydrostatic, and potential density (ρ) conservation (Davis, 1978). The current inverse methods are all based on two conservation principles: potential density and potential vorticity (q =f∂p/∂z) and require β-turning. Thus, two necessary conditions can be incorporated into any inverse methods: (1) non-coincidence of potential density and potential vorticity surfaces and (2) existence of vertical turning of the velocity (β-turning.) This can be done using the P-Vector, a unit vector in the direction of ∇ρ×Vq (Chu, 1994,1995). The first necessary condition becomes the existence of the P-vector, and the second necessary condition leads to the existence of the P-vector turning in the water column. Along this line, we developed the P-vector inverse method with a pre-requirement check-up. The method was verified in this study using the Modular Ocean Model (MOM) from Pacanowski et al. (1991) version of Bryan-Cox-Semtner ocean general circulation model (OGCM), which is based on the work of Bryan (1969). The statistically steady solutions of temperature and salinity from MOM are used as a "no-error data" set for computing absolute geostrophic velocities by the P-vector inverse method. Circulations are similar between the MOM statistically steady solutions and the P-vector solutions. Furthermore, the quantitative analysis shows that this inverse method has capability of picking up the major signal of the velocity field.