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Initial Conditions Of the UW S hort R ange E nsemble F orecast System

Initial Conditions Of the UW S hort R ange E nsemble F orecast System Tony Eckel, UW Atmos. Grad. Student Advisor: Prof. Cliff Mass. From our point of view, truth is random sample from the pdf. - Let all ICs evolve to build PDF at future time (i.e., a forecast pdf)

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Initial Conditions Of the UW S hort R ange E nsemble F orecast System

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  1. Initial Conditions Of the UW Short Range Ensemble Forecast System Tony Eckel, UW Atmos. Grad. Student Advisor: Prof. Cliff Mass

  2. From our point of view, truth is random sample from the pdf - Let all ICs evolve to build PDF at future time (i.e., a forecast pdf) - Error growth spreads out PDF as forecast lead time increases 24hr Forecast State 48hr Forecast State Ensemble Forecasting Theory - Construct the initial state of the atmosphere with multiple, equally likely analyses, or initial conditions (ICs) Frequency Initial State

  3. truth’s pdf Limitations of EF Difficult to consistently construct the “correct” analysis/forecast pdf. Errors in mean and spread result from: 1) Model error 2) Choice of ICs 3) Under sampling due to limits of computer processing Result: EF products don’t always perform the way they should. (especially a problem for SREF) ensemble pdf Frequency Initial State 24hr Forecast State 48hr Forecast State

  4. UW SREF Methodology Overview 5 “independent” atmospheric analyses Analysis pdf cmc eta T ngp mrf avn Forecast pdf 48hr true state 48hr forecast state (core) Analysis pdf : Forecast pdf : 5 divergent, “equally likely” solutions using the same primitive equation model, mm5 phase space

  5. UW SREF Methodology Overview Analysis pdf cmc cwb gsp eta C T ngp mrf avn Forecast pdf uk 5-1+3=7 “independent” atmospheric analyses, plus the Centroid (C) Analysis pdf : Forecast pdf : 8 divergent, “equally likely” solutions using the same primitive equation model, mm5 phase space 48hr true state 48hr forecast state (core)

  6. UW SREF Methodology Overview cwb avn cmc cwb cwb gsp gsp eta ngp C gsp T ngp cmc avn uk eta Forecast pdf uk uk Analysis pdf 7 “independent” atmospheric analyses, Centroid, plus 7 “mirrored” ICs Analysis pdf : Forecast pdf : 15 divergent, “equally likely” solutions using the same primitive equation model, mm5 phase space 48hr true state 48hr forecast state (core) 48hr forecast state (perturbation)

  7. UW SREF Methodology Overview Analysis pdf cwb avn cwb cmc gsp eta ngp C gsp T ngp cmc avn eta uk Forecast pdf uk 7 “independent” atmospheric analyses, Centroid, plus 7 “mirrored” ICs Analysis pdf : Forecast pdf : 15 divergent, “equally likely” solutions using the same primitive equation model, mm5 phase space 48hr true state 48hr forecast state (core) 48hr forecast state (perturbation)

  8. C C cmc cmc Sea Level Pressure (mb) ~1000 km cmc cent new Generating New Initial Conditions STEP 1: Find vector in model phase space between an analysis and centroid by differencing all state variables over all grid points. STEP 2: Make a perturbation by vector multiplying analysis error by a perturbation factor (pf) (I.e., actual error could be smaller or larger, but in the same “direction”.) P = pf *(C – cmc) STEP 3: Make a new IC by adding/subtracting the perturbation to the centroid. new = C + P

  9. C C cmc cmc Sea Level Pressure (mb) ~1000 km cmc cent new Generating New Initial Conditions STEP 1: Find vector in model phase space between an analysis and centroid by differencing all state variables over all grid points. STEP 2: Make a perturbation by vector multiplying analysis error by a perturbation factor (pf) (I.e., actual error could be smaller or larger, but in the same “direction”.) P = pf *(C – cmc) STEP 3: Make a new IC by adding/subtracting the perturbation to the centroid. new = C + P –0.5 • -1.0 < pf < 1.0 • Over samples center of analysis pdf • Perturbations don’t diverge • Non-unique solutions

  10. C C cmc cmc –1.5 Sea Level Pressure (mb) ~1000 km cmc cent new Generating New Initial Conditions STEP 1: Find vector in model phase space between an analysis and centroid by differencing all state variables over all grid points. STEP 2: Make a perturbation by vector multiplying analysis error by a perturbation factor (pf) (I.e., actual error could be smaller or larger, but in the same “direction”.) P = pf *(C – cmc) STEP 3: Make a new IC by adding/subtracting the perturbation to the centroid. new = C + P • pf > 1.0 or pf < –1.0 • Samples “out of bounds” of analysis error • Less likely solutions (greater error) • Overspread forecast pdf

  11. C C cmc cmc 1.0 Sea Level Pressure (mb) ~1000 km cmc cent new Generating New Initial Conditions STEP 1: Find vector in model phase space between an analysis and centroid by differencing all state variables over all grid points. STEP 2: Make a perturbation by vector multiplying analysis error by a perturbation factor (pf) (I.e., actual error could be smaller or larger, but in the same “direction”.) P = pf *(C – cmc) STEP 3: Make a new IC by adding/subtracting the perturbation to the centroid. new = C + P • pf = 1.0 • Within analysis error with unique, realistic structure • “Equally likely” solution, with similar or reduced error • Divergent forecast

  12. ICs: Analyses, Centroid, and Mirrors • Strengths • Good representation of analysis error • Perturbations to synoptic scale disturbances • Reasonable sample of PDF? • Magnitude of perturbation(s) set by spread among analyses • Bigger spread  Bigger perturbations • Dynamically conditioned ICs • Weaknesses • Limited by number and quality of available analyses • May miss key features of analysis error • Analyses must be independent (i.e., dissimilar biases) • Calibration difficult; no stability since analyses may change techniques

  13. C cmc CASE STUDY: Annual UW Atmos Department Hike Scheduled Hike: 28 Sep 17z  29 Sep 00z Forecast Initialization: 27 Sep 00z Blanca Lake 48h eta 29 Sep 00z Case study: thirteen 36km mm5 runs. Begin by examining just three… 1.0 Blanca Lake

  14. 00h cmc 27 Sep 00z 00h 1.0cmc 27 Sep 00z 00h cent 27 Sep 00z

  15. 24h cmc 28 Sep 00z 24h 1.0cmc 28 Sep 00z 24h cent 28 Sep 00z 00h eta 28 Sep 00z

  16. 48h cmc 29 Sep 00z 48h 1.0cmc 29 Sep 00z 48h cent 29 Sep 00z 00h eta 29 Sep 00z

  17. Blanca Lake All 13, 48h Forecasts for slp and 6hr precip Valid 29 Sep 00z Probability of Precip > 0mm: 6/13 = 46.2% > 2mm: 4/13 = 30.8% > 4mm: 1/13 = 7.7% cent 1.0ngps ngps eta 1.0eta 1.0cmc ukmo cmc 1.0ukmo tcwb 1.0tcwb 1.0avn avn

  18. EXTRA SLIDES

  19. C cmc new Linear vs. Nonlinear Dispersion What is gained by running all those perturbations? pf = 1.0 00h cent – cmc 00h 1.0cmc – cent

  20. 12h cent – cmc 12h 1.0cmc – cent 24h 1.0cmc – cent 24h cent – cmc

  21. 36h cent – cmc 36h 1.0cmc – cent 48h cent – cmc 48h 1.0cmc – cent

  22. Bulk Error Stats • Used eta analysis as the verification • Variable: geopotential height • Sample Size: • 150 x 126 x 11 • = 207900 Case Study Init Date: 18 Sep 00z

  23. Ensemble Forecasting Process M O D E L M O D E L M O D E L Model Confidence Consensus Data Range Probability N Analyses (equally likely) N 48hr Forecasts (equally likely) Products 500mb Hght/Vort O B S M O D E L

  24. Model Confidence Products Variance (Spread) Chart Spaghetti Diagram A visualization of predictability Increase Spread in Decreased Less confidence the different forecasts Predictability in forecast

  25. Consensus Products • Assuming a big enough sample and a near normal distribution, the average yields the expected value or the “best guess” forecast • Averaging washes out the important small scale features

  26. Data Range Products • Shows the range of possibilities (spread of the PDF) for any weather element at a given location • Value is in defining the possible extremes for a forecast situation

  27. Probability Products • Shows the probability of occurrence of critical event (i.e., surface winds > 35 kts) • Calculation: P(event) = (# exceeding threshold) / (total #) , or 1–p value of PDF • Can be tailored for ANY weather element and threshold of interest

  28. Probability of Quantitative Precipitation Forecast (PQPF) 0.25” 0.50” 1.00” 0 10 20 30 40 50 60 70 80 90 100 Probability Scale Initial Time: 00Z, 27 Mar 00 FCST Lead Time: 48 hrs Probability of 24hr Precip > 0.10”

  29. Future Products ? For DoD operations, products tailored to a specific location or mission could be produced from a fine scale model ensemble. These products could be similar to the previous examples, or something like this

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