Lecture 5

Weather Maps and Models

Chapters 5 and Chapter 6

Homework Due Friday, October 3, 2014

TYU Ch 6: 1,2,5,7,11,14,17,18,20; TYPSS Ch 6: 2

TYU Ch 7: 1,5,10,11,13,14,15,18,20; TYPSS Ch 7: 1

TYU Ch 8: 1,2,6,7,12,14,15,18,20; TYPSS Ch 8: 2

Weather Models• Deterministic Prediction: Bjerknes (1906), Richardson (1924): weather can be

predicted from Newtonian equations as an initial value problem.• Mathematical equations describe how:

– Conservation of momentum (Newton, ~ 1700 AD)• Newton’s 1st Law: Objects (or air parcel) in a state of uniform motion tends to

remain in motion unless acted upon by an external force…concept of inertia• Newton’s 2nd Law: The acceleration of an object (or air parcel) due to the

application of a force is proportional to and in the direction of the force applied and inversely proportional to the mass

– Conservation of mass (Lavoiser, 18th Century)• Air mass is conserved• Moisture is conserved

– Conservation of energy • 1st Law of Thermodynamics, principle of work , conservation of energy,

(Clausius, 1850)• 2nd Law of Thermodynamics, entropy (disorder), (Carnot, 1824)

– For any thermodynamic process, total entropy must increase or remain constant

– Chaos, predictability and probabilistic forecasting Lorenz (1963)

Two Basic types of Models

• Finite Difference Model– Solved on a grid– Taylor series approximations to continuous equations

• Spectral Model– Analysis of variables on a grid in real space is

transformed to a grid in wave space grid using a Fourier transform

– Equations moved forward in wave space analytically– Variables transformed back to real space

Examples of Horizontal Grids

Vertical Grid

Vertical grid may be :

•Height coordinate

•Pressure coordinate

•Sigma or terrain following coordinate

Map Projection

Various map projections are used to take into account the curved Earth surface. For instance:

1. Mercator projection

2. Polar Stereographic Grid

3. Lambert Conformal

4. Spherical Grid

Topography Representation

Ensemble Prediction

Key Prediction Models for this Class

• Global Forecasting System (GFS):– NOAA model run 4 times per day out to 20 days – Global model– ~ 30 km resolution, but spectral– comprehensive global data assimilation– No lateral boundaries

• North American Model (NAM)– NOAA model run 4 times per day out to 3.5 days– Limited area over North America– < 10 km resolution– 1 way nest in GFS for lateral boundaries

• Nonhydrostatic Modeling System NMS model– Run 4 times per day out to 48 hours– Tripoli (UW) locally run limited area model over North America– 60 km resolution– Separate runs nested in GFS or NAM