A Diagnostic of the Vertical Velocity for the Equatorial Atlantic A Diagnostic of the Vertical...

A Diagnostic of the Vertical Velocity for the Equatorial A Diagnostic of the Vertical Velocity for the Equatorial Atlantic Atlantic Hervé Giordani and Guy Caniaux (CNRM/GAME (Météo-France/CNRS) 42, Av. G. Coriolis 31057 Toulouse Cedex) Corresponding author: [email protected] Tel: 33(5)-61-07-93-81. Fax: 33(5)-61-07-96-10 Estimating the vertical velocity (w) in the upper-layers of the ocean is a key issue for understanding the cold tongue development in the eastern equatorial Atlantic. For that, we developed a general formulation of the vertical velocity based on the primitive equation (PE) system, in order to gain new insight into the physical processes responsible for the development of the equatorial and Angola upwellings. This approach is more accurate for describing the real ocean than simple considerations based on just the wind-driven patterns of surface layer divergence (i.e., the Ekman theory). The w-sources are diagnosed from a realistic ocean simulation of the equatorial Atlantic. Conclusions Sources of w are numerous in the eastern equatorial Atlantic and express the complexity of processes related to the turbulent momentum flux, to the circulation and to the mass fields. The equatorial upwelling is found to be mainly induced by: (1) the zonal wind-stress, (2) the stress-curl and (3) the imbalance between the circulation and the pressure fields. The Angola upwelling in the eastern part of the basin is mainly controlled by the stress-curl. A strong cross-regulation is evidenced between the forcing terms dependent on w and those independent of w. This cross-regulation suggests the existence of References Giordani, H., G. Caniaux, and L. Prieur, 2005: A simplified oceanic model assimilating geostrophic currents: application to the POMME experiment. J. Phys. Oceanogr., 35, 628-644. Giordani, H., and G. Caniaux, 2011: diagnosing vertical motion in the equatorial Atlantic. Submitted to Ocean Dynamics. Holton, J., 1992: An introduction to dynamic meteorology. Third Edition, Academic Press, Sao Diego, 511pp. W May-August 2006 averaged w at 20 m depth provided by a realistic open boundary PE model (Giordani et al., 2005) All the fields are at 20 m depth and averaged during the period May- August 2006. Units are in m/day² Derivation of the Vertical Velocity Equation We start from the divergence equation (Holton, 1992): The first term on the r.h.s. is expanded as: for which the vorticity and zonal momentum equations are used. Then, by using the continuity equation, we obtain the following vertical velocity equation: The r.h.s. of this equation is composed of 18 terms, which were grouped in external (independent of w or D) and internal (dependent on w or D) forcing terms. External forcings (first three lines) are due to the stress (terms 7, 8, 10), the pressure (terms 2, 3, 9, 12) or the horizontal current (terms 1, 4, 5, 6, 11); internal terms (last two lines) represent the negative feedback of the ocean to the external forcings. z v y w z u x w D x v y u y v x u P z D w D U z P u f t D h h h 2 2 . 1 . 1 2 2 t t t dt t u t f u f u f 0 0 ) ( ) ( dz z v y w z u x w D z D w D U dzdt x w z u y w f z v y w x w f z u w z fw dzdt z w f f dz P x v y u y v x u z dzdt P k f z fk z U U fU fv x P dz P u f z t w z h t z t z z h h t z x h h z t 0 2 0 0 0 0 0 0 0 2 0 2 0 2 . ) ( ) ( . 1 2 . . 2 1 ) ( 3 1 4 5 6 10 13 (vortex stretching) 12 11 (deformation of D) 9 (baroclinic term of the vorticity) 8 7 14 15 16 (tilting) 17 18 (deformation of D) 2 Term 7 Zonal wind-stress Term 8 Stress-curl Term 10 Stress divergence Term 1 – Term 2 Imbalance between the circulation and pressure Term 4 Planetary vorticity advection by the meridional current Terms 1 to 12 External forcings Terms 13 to 18 Internal forcings Term 13 Vortex stretching Terms 14 to 18 Non linear terms

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Transcript of A Diagnostic of the Vertical Velocity for the Equatorial Atlantic A Diagnostic of the Vertical...

Page 1: A Diagnostic of the Vertical Velocity for the Equatorial Atlantic A Diagnostic of the Vertical Velocity for the Equatorial Atlantic Herv Giordani and.

A Diagnostic of the Vertical Velocity for the Equatorial AtlanticA Diagnostic of the Vertical Velocity for the Equatorial Atlantic Hervé Giordani and Guy Caniaux (CNRM/GAME (Météo-France/CNRS) 42, Av. G. Coriolis 31057 Toulouse Cedex)

Corresponding author: [email protected] Tel: 33(5)-61-07-93-81. Fax: 33(5)-61-07-96-10

Estimating the vertical velocity (w) in the upper-layers of the ocean is a key issue for understanding the cold tongue development in the eastern equatorial Atlantic. For that, we developed a general formulation of the

vertical velocity based on the primitive equation (PE) system, in order to gain new insight into the physical processes responsible for the

development of the equatorial and Angola upwellings. This approach is more accurate for describing the real ocean than simple considerations based on just the wind-driven patterns of surface layer divergence (i.e., the Ekman theory). The w-sources are diagnosed from a realistic ocean

simulation of the equatorial Atlantic.

Conclusions Sources of w are numerous in the eastern equatorial Atlantic and express the complexity of processes related to the turbulent momentum flux, to the circulation and to the mass fields. The equatorial upwelling is found to be mainly induced by: (1) the zonal wind-stress, (2) the stress-curl and (3) the imbalance between the circulation and the pressure fields. The Angola upwelling in the eastern part of the basin is mainly controlled by the stress-curl. A strong cross-regulation is evidenced between the forcing terms dependent on w and those independent of w. This cross-regulation suggests the existence of an equatorial balanced-dynamics (Giordani and Caniaux, 2011).

ReferencesGiordani, H., G. Caniaux, and L. Prieur, 2005: A simplified oceanic model assimilating geostrophic currents: application to the POMME experiment. J. Phys. Oceanogr., 35, 628-644. Giordani, H., and G. Caniaux, 2011: diagnosing vertical motion in the equatorial Atlantic. Submitted to Ocean Dynamics.Holton, J., 1992: An introduction to dynamic meteorology. Third Edition, Academic Press, Sao Diego, 511pp.

WMay-August 2006 averaged w at 20

m depth provided by a realistic open boundary PE

model(Giordani et al.,

2005)

All the fields are at 20 m depth and

averaged during

the period May-

August 2006.

Units are in m/day²

Derivation of the Vertical Velocity EquationWe start from the divergence equation (Holton, 1992):

The first term on the r.h.s. is expanded as:

for which the vorticity and zonal momentum equations are used. Then, by using the continuity equation, we obtain the following vertical velocity equation:

The r.h.s. of this equation is composed of 18 terms, which were grouped in external (independent of w or D) and internal (dependent on w or D) forcing terms. External forcings (first three lines) are due to the stress (terms 7, 8, 10), the pressure (terms 2, 3, 9, 12) or the horizontal current (terms 1, 4, 5, 6, 11); internal terms (last two lines) represent the negative feedback of the ocean to the external forcings.

xwD

xuP

zDwDU

zPuf

hhh 22.1.1 22

tt dttu

tfufuf

00)()(

dzzv

xwD

zDwDU

dzdtxw