### 4.1. Geostrophic balance and Geostrophic Currents

**Geostrophic balance** is the basic balance in the open ocean. It is the balance between Coriolis forces and the horizontal pressure gradient that determines the first order circulation patterns (large scale patterns) in the ocean's surface. Using satellite altimetry, it is possible todetermine the level of the sea surface relative to a geoid which is used asreference system. The large-scale flows of the ocean can be determined bybalancing the Coriolis force with the observed pressure gradients.

**Geostrophic currents,** are the surface currents caused bythe variablity of sea surface elevation. Due to the difference in surfaceelevation the is a horizontal pressure gradient and subsequiently a current(water flow) from areas with higher elevation to areas with lower elvation. Due to the large scale of geostrophic current coriolis is important and the current direction is such that a balance between pressure gradient and coriolis force is possible.

**Example: Calculate the geostrophic current...**

### 4.2. Satelite Altimetry

The satellite Topex/Poseidon was the first satellite deticated to provice constant ocean surface topography. It made precise measurements of the ocean surface from 1992 to 2006. Nowadays, sattelites Jason-1 and Jason-2 continiue the ocean sureface topography mission. More info at NASA Ocean Surface Topography site and Wikipedia.

### 4.3. Derivation of Geostrophic balance equations

To derive the equations of geostrophic balance we assume:

1. The flow has no accelerations

2. Horizontal velocities are much larger than the vertical

3. Friction is small and can be neglected.

With those assumtions the Momentum Equations (Navier-Stokes) are simplified to:

1.

2.

3.

Geostrophic wind