Numerical Weather Prediction Meteorology 311 Fall 2011Closed Set of Equations • Same number of equations as unknown variables. • Equations – Momentum equations (3) – Thermodynamic energy equation – Continuity equation – Equation of state • Variables: u, v, w, T, p, ρNomenclature • Dynamics: Atmospheric motions and their time evolution – Application of Newton’s second law. • Kinematics: Properties that can be deduced without reference to Newton’s second law.Solve Equations • Approximate mathematical equations – Not enough data to compute continuous derivatives. • Discretization needed. – Approximation needed in both time and space. – Centered difference and one-sided upstream scheme are both used. • What about edges of domain or boundaries? – Model approximates conditions at the boundary, or – Model gets data from another model. • Regional models get boundary data from global models.Method • Collect observations of weather (data). • Quality control data to remove spurious reports. • Perform Objective Analysis to model grid points. – Observations don’t match the model grid. – They need to be “gridded” before they are useful to the model. • Initialize the model insuring that balance occurs. • Integrate the model forward in time to produce model forecast. • Post-process results to produce nice looking graphs. • Interpret the results. – Adjustment based on forecaster understanding and model biases.Model Types • Finite difference models – Gridded data – Use methods that you learned in class. • Centered-difference and One-sided upwind difference. • Taylor-series expansions about a point. • Accuracy and computational error depends on how many terms you keep. – Typically regional models. • Spectral models – Fourier series to represent waves in the atmosphere. – Global models. – Resolution given by R (Rhomboidal truncation) or T numbers (Triangular truncation). – T162 ~ 105km, T382 ~ 40km.Important Features • Horizontal resolution – “Effective” resolution is 4-5 times model grid spacing. • Vertical coordinate – Sigma coordinate – terrain following coordinate. • Vertical resolution – Spacing of vertical grid. • Domain – Regional or Global.NCEP Operational Models • New NAM (NMM) – North American Mesoscale – Currently WRF-NMM – WRF-ARW • Old NAM – ETA • GFS – Global Forecast System • RUC – Rapid Update CycleNon-NCEP models • ECMWF – European Centre for Medium-Range Weather Forecast • UKMET – British atmospheric model • GEM – Global Environmental Multiscale – Canadian forecast modelMOS/FOUS • MOS – Model Output Statistics. – Statistical equations used to calculate. meteorological variables. – Accounts for persistent model biases. • FOUS – Forecast Output United States – Raw model data. – Data will contain model biasesMOS features • Equations developed over time. – Types of events that occurred over the development time are well handled. – Rare events will not be well handled by MOS equations. – New models require time to develop robust MOS equations • Different equations for different regions. • Two sets of equations based on time of year. – Summer/Winter set of equations. • Three slides: Advantages/Disadvantages/Poor MOS forecasts.MOS Advantages • Account for persistent model bias. • Take advantage of model derived variables that are not observed. – Vorticity. – Upward vertical velocity. • Emphasize reliability of forecast.MOS Disadvantages • Change in model requires the development of new MOS equations. • Long development time for MOS equations (2 seasons of data). – 2 years, thousands of equations to develop. • MOS forecasts tend to lack sharpness.When will MOS produce a poor forecast? • After a model change. • If the current weather was not experienced during the development period of the MOS equations. • If the circumstances from today’s weather differ from the norm. • If the forecast depends on mesoscale effects not accounted for in the MOS