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CLIMATE/EARTH 401�Geophysical Fluid Dynamics�Dynamical Meteorology

Richard B. Rood

rbrood@umich.edu

https://clasp.engin.umich.edu/people/richard-b-rood/

https://openclimate.org/

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Tangential Coordinate System

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Tangential coordinates

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Tangential coordinate system on a rotating sphere

Ω

R

Earth

Place a cartesian coordinate system on the surface of Earth

​

x = west – east (longitude)

y = south – north (latitude)

z = local vertical

Φ

a

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2-D view of tangential coordinate system

Coordinate system is defined as tangent to the Earth’s surface

x

🡪i

y

🡪j

z

🡪k

east

north

Local vertical

Velocity (u) = (ui + vj + wk)

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Other important directions

Ω

R

Earth

  • Gravity towards center of Earth along a radius and this will sometime be represented as r/r. This is also the local vertical, z, with unit vector k.

​

  • Centrifugal acceleration/force is outwards along R the radius around the axis of rotation.

Φ = latitude

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Definitions

Ω

R

Earth

R=acos(φ)

Φ = latitude

a

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End: Tangential Coordinate System

Richard B. Rood

rbrood@umich.edu

https://clasp.engin.umich.edu/people/richard-b-rood/

https://openclimate.org/