1. Collect All Weather Data

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1 Numerical Weather Prediction (NWP) Operational numerical weather prediction (i.e., routine predictions for practical use) began in 1955 under a joint project by the U.S. Air Force, Navy, and Weather Bureau. Summary of Weather Modeling: 4 Steps 1. Input all available observations. 2. Interpolate data to points on an evenly spaced grid. 3. Apply laws of physics, including parameterization of surface and cloud processes too small for the model to directly include - integrate equations forward in time. 4. Output resulting forecast as contoured maps for easy interpretation. Recent NCEP IBM machine: 1.3 trillion calculations per second 1 2 Numerical Weather Prediction 1. Collect All Weather Data OBSERVATIONS Radar Data Mobile Mesonets Surface Observations Analysis/Assimilation Quality Control Retrieval of Unobserved Quantities Creation of Gridded Fields Prediction PCs to Teraflop Systems Product Generation, Display, Dissemination Upper-Air Balloons Commercial Aircraft Geostationary and Polar Orbiting Satellite Wind Profilers GPS Satellites End Users Nat l Weather Service Private Companies Students Input all available observations: surface, ship, buoy, radiosonde, aircraft, radar, satellite, etc

2 2. Evenly Spaced Grid of Values 3. Apply the Laws of Motion All data, including satellite data over the ocean are interpolated to an evenly spaced grid. Apply the laws of motion. Integrate the equations forward in time to predict the future state of the atmosphere. 5 6 Eulerian framework in x-y-p coordinates, the primitive equations can be written as: These equations are called primitive, because they are fundamental or basic. (1) (2) (3) (4) (5) (6) What is parameterized? Any physical process that is subgrid scale must be estimated or parameterized in the model based on the variables the model calculates, examples include Convection* Cloud Microphysics precip particles Turbulence - (surface roughness) Soil Moisture* Radiation (only global models*) 7 8

3 4. Output to Forecast Maps Computer Models of the Atmosphere To resolve the impact of mountains on weather in Hawaii, high resolution models use a series of nested grids. Kona Low Simulation animation allows forecaster to make prediction about wind and rainfall Designing a nested grid over Hawaii Impact of Model Grid Spacing A nested grid puts the computer power where you need it. Input all observations Interpolate to a grid and apply laws of motion. Plot output

4 Operational NWP models Models 1-7 are run daily at the National Centers for Environmental Prediction (NCEP) 1. RUC (Rapid Update Cycle) 2. WRF (Weather Research and Forecast Model) 3. NAM (North American Model) AKA Eta (named after vertical coordinate) 4. GFS, AVN, MRF (Global Forecast System, Aviation, Medium Range Forecast) 5. NOGAPS and COAMPS are run at NRL in Monterey (Navy Operational Global Atmospheric Prediction System, Coupled Ocean-Atmosphere Prediction System) 6. ECMWF model run at ECMWF in England (European Center for Medium Range Weather Forecasting) Regional models (1-3), Global Spectral Models (4-6) Gaussian Grids Global-spectral models NCEP T62 gaussian grid Global-spectral models Spectral models spectral methods take advantage of the fact that the atmosphere can be decomposed into a series of waves by writing the solution as its Fourier series, substituting this series into the partial differential equations to get a system of ordinary differential equations in the time-dependent coefficients of the trigonometric terms in the series (written in complex exponential form), and using a time-stepping method to solve those ODEs. AVN, MRF, GSF, NOGAPS, ECMWF Global-spectral models Convert data into a large number of mathematical waves which the model uses for its calculations and then returns the waves in a manner that will produce a forecast map. These models go out farther in time than the regional models. AVN-384 hours 15 16

5 Spectral models ECMWF (European Center for Medium-Range Weather Forecasts) and Canadian Spectral models used for medium range forecasts (7-10 days) Considered by many to be the most advanced model in the world. Evolution of forecast skill for the northern and southern hemispheres: Anomaly correlation coefficients of 3, 5, and 7-day ECMWF 500- mb height forecasts for the extratropical northern and southern hemispheres, plotted in the form of running means for the period of January November Shading shows differences in scores between hemispheres at the forecast ranges indicated (from Holingsworth, et al. 2002) Skill Improvements (ECMWF) NCEP Regional Models Useful skill until: 1 - day day day 8 NAM/Eta Grid point model using either a 22 or 12 km grid. Accounts for changes in terrain as a series of steps each of which corresponds to a level of the models vertical coordinate, eta. (Eta is analogous to pressure). NAM North American Mesoscale Model Improvements from 1980 to 2001 result from: Northern hemi. obs. system 23% model+da 77% Southern hemi. obs. system 45% model+da 55% 19 20

6 Regional Models COAMPS - Coupled Ocean-Atmosphere Predication System (Navy - NRL) WRF Weather Research and Forecasting Model (NCAR) WRF is designed to run at higher resolution and is heavily used in research, but there are some groups and individuals running WRF operationally. Care to start up your own forecast service? Here s the link Ensemble Predictions Method uses a collection of two or more forecasts for the same time. These forecasts either use different initial conditions or are based on different forecasting procedures or models. The various forecasts represent possibilities of how the weather might change in the future. An estimate of the probabilities of various events as well as an average ( consensus ) forecast is obtained. If several forecasts all give the same result, this result is more likely to occur, and we have more confidence in our forecast. Training page: Products page: The quality of atmospheric forecasts decreases as a function of time Lothar UK France France NCEP ensemble forecasts Dundee Satellite Station: 0754 UTC 26 December

7 Lothar (T+42 hour TL255 rerun of operational EPS) Numerical Forecast Errors Two sources of errors affecting the forecasts and the data assimilation process: initial condition errors a lack of observations or errors in the observations model errors Errors from subgrid scale physical processes such as convection, cloud microphysics, turbulence, etc. See C. Nicolis, Rui A. P. Perdigao, and S. Vannitsem Dynamics of Prediction Errors under the Combined Effect of Initial Condition and Model Errors, Journal of the Atmospheric Sciences, 66, , Numerical Forecast Errors Questions? How can we improve the forecast quality (Besides improving of the model and the observational system)? Use of techniques to post-process the forecasts in order to improve their quality or extend their scope. In general these methods are called Model Output Statistics (MOS) 27 28

8 MFE 658 Lecture 2b Objective Interpretation of NWP Model Output Model Output Statistics (MOS) Regression Analysis Binomial Data Probability Gridded MOS National Digital Forecast Database WHY STATISTICAL GUIDANCE? Add value to direct NWP model output Objectively interpret model remove systematic biases quantify uncertainty Predict what the model does not Produce site-specific forecasts (i.e. a downscaling technique) Assist forecasters First Guess for expected local conditions Built-in model/climo memory valuable for new staff Model Output Statistics (MOS) MOS Properties MOS relates observations of the weather element to be predicted (PREDICTANDS) to appropriate variables (PREDICTORS) via a statistical method. Predictors can include: NWP model output interpolated to observing site Prior observations Geoclimatic data terrain, normals, lat/lon, etc. Current statistical method: Multiple Linear Regression (forward selection) Mathematically simple, yet powerful technique Produces probability forecasts from a single run of the underlying NWP model Can use other mathematical approaches such as logistic regression or neural networks Can develop guidance for elements not directly forecast by models; e.g. thunderstorms 31 32

9 MOS Guidance GFS (MAV) 4 times daily (00,06,12,18Z) GFS Ext. (MEX) once daily (00Z) Eta/NAM (MET) 2 times daily (00,12Z) Variety of formats: text bulletins, GRIB and BUFR messages, graphics MODEL OUTPUT STATISTICS (MOS) Advantages Recognition of model predictability Removal of some systematic model biases Optimal predictor selection Reliable probabilities Specific element and site forecasts Challenges Short samples Changing NWP models Availability & quality of observations GFS MOS GUIDANCE MESSAGE FOUS21-26 (MAV) KLNS GFS MOS GUIDANCE 11/29/ UTC DT /NOV 29/NOV 30 /DEC 1 /DEC 2 HR N/X TMP DPT CLD CL BK BK BK OV OV OV OV OV OV OV OV OV OV OV OV OV BK CL CL CL WDR WSP P P Q Q T06 0/ 0 0/18 0/ 3 0/ 0 0/ 0 0/18 2/ 1 10/ 4 0/ 3 1/ 0 T12 0/26 0/17 0/27 10/25 1/38 POZ POS TYP R R R R R R R R R R R R R R R R R R R R R SNW CIG VIS OBV N N N N N N N N N N N N BR BR BR BR N N N N N How to Read MOS Honolulu MOS sta=phnl 35 36

10 Marine MOS GFS MOS GUIDANCE 11/22/ UTC DT /NOV 22/NOV 23 /NOV 24 /NOV 25 HR TMP WD WS WS DT /NOV 25 / HR TMP Now approx sites Marine MOS sites Standard MOS sites MOS Snowfall Guidance Uses Observations from Cooperative Observer Network 4 - < <8 >Trace < 4 36-hr forecast 12Z 12/05/03 12Z 12/06/03 Verification Max/Min Guidance for Co-op Sites GFS-BASED MOS COOP MAX/MIN GUIDANCE 12/01/ UTC THU 02 FRI 03 SAT 04 GYLP HAWP HBGP HRBP INDP JMSP KANP LAPP LBGP LCRP LDVP LEBP LHGP LMPP LNVP LOKP LRLP LSTP MATP MCKP MERP Lancaster 2 NE Landisville, PA 39 40

11 Western Pacific MOS Guidance MOS LINEAR REGRESSION JANUARY 1 - JANUARY 30, UTC KCMH (Columbus, Ohio) Saipan, ROM Wake, US Midway, US MAX T = (0.3 x mb THK) NSTU GFS MOS GUIDANCE 11/07/ UTC DT /NOV 7/NOV 8 /NOV 9 /NOV 10 HR TMP DPT WDR WSP P P NSTU - Tafuna/Pago Pago International Airport TODAY'S MAX ( F) RV=93.1% H NGM MB THICKNESS (M) PREDICTAND REDUCTION OF VARIANCE RV A measure of the goodness of fit and Predictor / Predictand correlation Variance - Standard Error = Variance RV { } UNEXPLAINED VARIANCE * PREDICTOR MEAN TODAY'S MAX ( F) MOS LINEAR REGRESSION JANUARY 1 - JANUARY 30, UTC KUIL (Quillayute, WA) RV=26.8% Same predictor, Different site, Different relationship! H NGM MB THICKNESS (M) 43 44

12 DEFINITION of PROBABILITY The degree of belief, or quantified judgment, about the occurrence of an uncertain event. or The long-term relative frequency of an event. (Wilks, 2006) H PRECIPITATION.01" 1 0 If the predictand is BINARY, MOS regression equations produce estimates of event PROBABILITIES... P = 30% KCMH 3 Events RF= 30% 7 Events AVG H NGM ~ MB RH EXAMPLE REGRESSION EQUATIONS Y = a + bx AREAL PROBABILITIES 3-hr Eta MOS thunderstorm probability forecasts valid 0000 UTC 8/27/2002 (21-24h fcst) KCMH MAX TEMPERATURE EQUATION MAX T = (0.3 x mb THICKNESS) KCMH PROBABILITY OF PRECIPITATION EQUATION POP = (0.007 x MEAN RH) + (0.478 x BINARY MEAN RH CUTOFF AT 70%)* *(IF MRH 70% BINARY MRH = 1; else BINARY MRH = 0) 40-km gridbox 10% contour interval 20-km gridbox 10% contour interval 47 48

13 DEVELOPMENTAL CONSIDERATIONS Selection and QC of Suitable Observational Datasets ASOS? Remote sensor? Which mesonet? Predictand Definition Must be precise Choice of Predictors Appropriate formulation Binary or other transform? PREDICTAND DEFINITION MUST BE PRECISE Daytime Maximum Temperature Daytime is 0700 AM PM LST Nighttime Minimum Temperature Nighttime is 0700 PM AM LST Probability of Precipitation Precipitation occurrence is accumulation of 0.01 inches of liquid-equivalent at a gauge location within a specified period GFS MOS Warm Season PoP/QPF Regions MOS Verification MOS significantly improves on the skill of model output. National Weather Service verification statistics have shown a narrowing gap between human and MOS forecasts. In 2003 MOS won the UW Atmos. Sci. Dept. forecast contest for the first time. With GFS MOS forecast sites (1720) + PRISM (Parameter-elevation. Regressions on Independent Slopes Model) 51 52

14 Temperature Verification UTC GFS MOS vs. GFS DMO (4/2004-5/2006) PoP Verification UTC 6/2005-2/ M TEMPERATURE Mean Absolute Error at 1591 STATIONS GFS DMO GFS MOS 0.15 MAE (DEGREES F) Brier Score PROJECTION (HOURS) Projection (Hours) Max Temperature Verification AEV Local; Cool Season h End of an era? Mean Absolue Error (F) h Perf. Pg. / PE MOS LFM Day/Nite NGM EDAS AVN WANTED! High-resolution, gridded guidance for NDFD 55 56

15 Gridded MOS Gridded MOS GFS-based Now CONUS and AK! Products added: June 2007 Sky Cover QPF Snowfall Wind Gusts Gridded MOS AK GMOS: Introduced June 2008 Max /Min 2m Temperature 2m Dewpoint Approx sites RH 3-, 6-, 12-h Tstm 59 60

16 Geophysical Datasets Approx. 10,550 sites! 5-km Terrain 5-km Land Cover Gridded MOS Concept - Step 1 Blending first guess and high-density station forecasts Day 1 Max Temp 00 UTC 03/03/05 Day 1 Max Temp 00 UTC 03/03/05 Gridded MOS Concept - Step 2 Add further detail to analysis with high-resolution geophysical data and smart interpolation Day 1 Max Temp 00 UTC 03/03/05 Day 1 Max Temp 00 UTC 03/03/05 First guess field from Generalized Operator Equation or other source First guess + guidance at all available sites First guess + guidance at all available sites First guess + station forecasts + terrain 63 64

17 NDGD vs. NDFD Are we there yet? AK GMOS Temps & Observing Sites Even fewer obs available Yikes! Max Temperature 00 UTC 03/11/06 Max Temperature 00 UTC 03/11/06 NDGD Max T NDFD Max T 65 3-km grid 66 Hawaii Gridded Forecast Fields The Future of MOS Enhanced-Resolution, Gridded MOS Systems MOS at any point (e.g. GMOS) Support new NWS digital forecast database 2.5 km - 5 km resolution Emphasis on high-density surface networks Equations valid away from observing sites Use high-resolution geophysical data True gridded MOS Observations and forecasts valid on fine grid Use remotely-sensed predictand data e.g. WSR-88D QPE, Satellite clouds, NLDN 67 68

18 Remotely-sensed precipitation data Satellite-based effective cloud amount REFERENCES So You Wanna Be a MOS Developer? Wilks, D.: Statistical Methods in the Atmospheric Sciences, 2nd Ed., Chap. 6, p Draper, N.R., and H. Smith: Applied Regression Analysis, Chap. 6, p Glahn, H.R., and D. Lowry, 1972: The use of model output statistics in objective weather forecasting, JAM, 11, Carter, G.M., et al., 1989: Statistical forecasts based on the NMC s NWP System, Wx. & Forecasting, p Consider the NOAA SCEP Program! MDL contact: Mr. Carl McCalla 1325 East-West Highway, Rm Silver Spring, MD (301) ext. 169 Carl.Mccalla@noaa.gov 71 72