1. Historical Overview
Vilhelm Bjerknes (1904): Future state of atmosphere determined by a set of equations, dependent on initial conditions.
Proposed program of observation, graphical analysis of data and graphical solution of governing equations, two step process: diagnostic and prognostic.

2. Historical Overview
Lewis Fry Richardson (1922): Published Weather Prediction by Numerical Processes.

3. Historical Overview
Carl-Gustaf Rossby: Propagation of longwaves –conservation of absolute vorticity, Geostrophic Adjustment Problem(1939)

4. Historical Overview
Jule Charney: Scale analysis of atmospheric motion, Quasi Geostrophic equations (1948)

5. Conceptual view of Atmospheric Flow

6. Dot (Scalar) Product
Often require product of the magnitude of the component of a first vector in the direction of second vector, to the magnitude of the second vector. The result of the product is a scalar
Example: Work is defined as product of force applied and displacement in the direction of the force. Alternatively, it is the product of distance moved to the component of force in the direction motion

7. Cross (vector) Product
Other instances product of the magnitude of the component of a first vector, in the direction of normal to the second vector, and the magnitude of the second vector is required. A direction is also associated with this product, thus vector product
Example: Torque is defined as product of force applied and the normal distance between the point of application of the force and axis of rotation.

8. Cross (vector) Product

9. Vector Addition B E D A C F

10. Dot (Scalar) Product

11. Dot (Scalar) Product
Component form
Angle between two vectors:

12. Cross (Vector) Product
The unit vector is orthogonal to the plane containing and . Direction of the unit vector is given by the right hand rule. Keep right hand parallel to in such a manner where your fingers will curl towards , then the thumb points in the direction of .
Component form

13. Cross (Vector) Product
The unit vector is orthogonal to the plane containing and . Direction of the unit vector is given by the right hand rule. Keep right hand parallel to in such a manner where your fingers will curl towards , then the thumb points in the direction of .
Component form

14. Derivative