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 1 st 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 2 nd 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 1 st Law of Thermodynamics, principle of work, conservation of energy, (Clausius, 1850) 2 nd 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