1. Track Forecasting of 2001 Atlantic Tropical Cyclones Using a Kilo-Member Ensemble 8:30 AM April 30, 2002 Jonathan Vigh Master’s Student Colorado State University Department of Atmospheric Science

2. Acknowledgments Wayne Schubert, graduate advisor Wayne Schubert, graduate advisor Mark DeMaria Mark DeMaria Scott Fulton Scott Fulton Rick Taft Rick Taft Funding Funding –Significant Opportunities in Atmospheric Research and Science (SOARS) Program, fellowship –American Meteorological Society, fellowship

3. What causes track error? What causes track error? Inaccurate spatial and temporal sampling -> analysis uncertainty Inaccurate spatial and temporal sampling -> analysis uncertainty Incomplete representation of physical processes Incomplete representation of physical processes Discretization and truncation error Discretization and truncation error Atmosphere’s inherent chaotic nature Atmosphere’s inherent chaotic nature –Instability –Nonlinear interactions between various spatial scales (Leslie et al., 1998)

4. What is an ensemble? A collection deterministic realizations obtained by varying: A collection deterministic realizations obtained by varying: –Model (numerics, resolution, or physics) –Perturbing model parameters –Initial analysis fields  Time of analysis  Generation method (adjoint or 4DVAR methods)  Stochastic or bred perturbations

5. Benefits of an ensemble With many realizations over properly perturbed initial conditions, the subspace of dynamical pathways can be sampled With many realizations over properly perturbed initial conditions, the subspace of dynamical pathways can be sampled Ensemble mean is generally more accurate than a single deterministic forecast (Leith, 1974) Ensemble mean is generally more accurate than a single deterministic forecast (Leith, 1974) Ensemble allows estimation of higher moment statistics of the forecast Ensemble allows estimation of higher moment statistics of the forecast –Forecast uncertainty –Bifurcation of dynamical pathways –Probability density functions

6. MBAR: Multigrid Barotropic Model Modified barotropic vorticity equation Modified barotropic vorticity equation Finite difference, multigrid methods (Fulton, 2001) Finite difference, multigrid methods (Fulton, 2001) 3 Nested grids on a square 6000 km domain 3 Nested grids on a square 6000 km domain h 1 = 125 km, h 2 = 63 km, h 3 = 31 km h 1 = 125 km, h 2 = 63 km, h 3 = 31 km Efficient and accurate multigrid methods makes a kilo-scale operational model feasible Efficient and accurate multigrid methods makes a kilo-scale operational model feasible –Accuracy comparable to LBAR in only 1/38 of the computing time –Each 120-hr track forecast takes ~2.5 seconds –A 1980 member ensemble takes approximately 1.3 hours on a 1 GHz Intel PC

7. Perturbations in initial and background fields Operational MRF ensembles Operational MRF ensembles 5 independent breeding cycles are used in the analysis cycle to estimate subspace of fastest growing analysis errors (Toth and Kalnay, 1997) 5 independent breeding cycles are used in the analysis cycle to estimate subspace of fastest growing analysis errors (Toth and Kalnay, 1997) Adding and subtracting these vectors from the analysis yields 10 + control initial and background fields for MBAR Adding and subtracting these vectors from the analysis yields 10 + control initial and background fields for MBAR 00Z at 2 degree resolution 00Z at 2 degree resolution

8. Perturbations to vertical averaging Four deep layer vertical averages of wind field simulate uncertainties in steering layer depth Four deep layer vertical averages of wind field simulate uncertainties in steering layer depth Pressure weighted averages of following layers (mb): Pressure weighted averages of following layers (mb): –Shallow (850 - 700) –Medium (850 – 350) –Deep (850 – 200) –Entire (1000 – 100)

9. Perturbations to vertical decomposition of vertical modes In 2D barotropic vorticity models, ultra-long Rossby waves experience excessive retrogression (Wiin-Nielsen, 1959) In 2D barotropic vorticity models, ultra-long Rossby waves experience excessive retrogression (Wiin-Nielsen, 1959) Inclusion of inverse Rossby radius in the prognostic equation can fix this Inclusion of inverse Rossby radius in the prognostic equation can fix this Uncertainties in the vertical decomposition of the tropical atmosphere are handled by perturbing equivalent phase speed Uncertainties in the vertical decomposition of the tropical atmosphere are handled by perturbing equivalent phase speed –50 ms -1 –150 ms -1 –300 ms -1

10. Perturbations to vortex size/strength Simulates uncertainties in the size and strength of the vortex Simulates uncertainties in the size and strength of the vortex –Weak or small TS (vmax = 15 ms -1 ) –Weak or medium sized hurricane (wmax = 35 ms -1 ) –Strong or large hurricane (vmax = 50 ms -1 ) For a barotropic model, the size of the outer circulation is important factor in the track forecast For a barotropic model, the size of the outer circulation is important factor in the track forecast

11. Perturbations to storm motion vector Simulates uncertainties in the initial storm location and direction Simulates uncertainties in the initial storm location and direction Motion vector added to wind field of bogus vortex with exponentially decaying blending radius Motion vector added to wind field of bogus vortex with exponentially decaying blending radius –No motion perturbation –Fast and to right –Slow and to right –Fast and to left –Slow and to left

12. Cross-multiplication across the five perturbation classes 11 initial and background fields (180) 11 initial and background fields (180) 4 deep layer averages (495) 4 deep layer averages (495) 3 vertical decompositions (660) 3 vertical decompositions (660) 3 vortex sizes/strengths (660) 3 vortex sizes/strengths (660) 5 motion vectors (396) 5 motion vectors (396)--------------------------------------------- 1980 ensemble members 26 sub-ensembles

13. So what does the kilo-ensemble look like? Chantal Chantal Dean Dean Erin Erin Iris Iris Michelle Michelle Olga Olga

14. Chantal August 17 and 18 Well handled by the ensemble Well handled by the ensemble A fairly weak storm embedded in trade flow A fairly weak storm embedded in trade flow For first several days of forecast, a tight envelope, indicating high confidence For first several days of forecast, a tight envelope, indicating high confidence

31. Dean August 23 Example of the challenges of recurvature off the East Coast Example of the challenges of recurvature off the East Coast Total ensemble mean lagged behind actual path Total ensemble mean lagged behind actual path Ensemble ‘swarm’ stretched out in the direction of recurvature Ensemble ‘swarm’ stretched out in the direction of recurvature

43. Erin September 3 A storm which weakened to a tropical depression, then later strengthened to a strong hurricane A storm which weakened to a tropical depression, then later strengthened to a strong hurricane Ensemble mean successfully predicted path, although significant cross-track spread developed Ensemble mean successfully predicted path, although significant cross-track spread developed

55. Iris October 5 Another example of a tight envelope early on, suggesting high forecast confidence Another example of a tight envelope early on, suggesting high forecast confidence Ensemble spreads out at end, but actual track still contained in envelope Ensemble spreads out at end, but actual track still contained in envelope A minority of members experience recurvature A minority of members experience recurvature

67. Michelle Storm tracked along edge and then outside of envelope – an example of the ensemble’s failure to accurately span all dynamical pathways Storm tracked along edge and then outside of envelope – an example of the ensemble’s failure to accurately span all dynamical pathways An example of rapid growth in ensemble spread with time, suggesting low confidence in ensemble mean forecast An example of rapid growth in ensemble spread with time, suggesting low confidence in ensemble mean forecast Ensemble mean caught in middle of bifurcation -> large errors Ensemble mean caught in middle of bifurcation -> large errors

79. Olga Forecasts for 11/24/02 inaccurately predict recurvature – large spread develops Forecasts for 11/24/02 inaccurately predict recurvature – large spread develops Forecasts for 11/25/02 catch onto the correct path. Large spread but ensemble means are accurate Forecasts for 11/25/02 catch onto the correct path. Large spread but ensemble means are accurate Forecasts for 11/26/02 show an example of one sub-ensemble correctly picking the storm path Forecasts for 11/26/02 show an example of one sub-ensemble correctly picking the storm path

123. Conclusions Swarm diagrams can lead to useful estimates of forecast confidence Swarm diagrams can lead to useful estimates of forecast confidence Ensembles are useful for spotting bifurcations in possible future tracks Ensembles are useful for spotting bifurcations in possible future tracks The ensemble mean isn’t more accurate than control The ensemble mean isn’t more accurate than control But great utility of ensembles is the estimation of higher moments, such as forecast spread -> estimates of forecast reliability But great utility of ensembles is the estimation of higher moments, such as forecast spread -> estimates of forecast reliability

124. Future Work Tune ensemble perturbation classes to reduce bias of ensemble mean Tune ensemble perturbation classes to reduce bias of ensemble mean Tune ensemble spread to be the ‘right’ size Tune ensemble spread to be the ‘right’ size Calculate probability density functions of storm location from ensemble output Calculate probability density functions of storm location from ensemble output Use fuzzy logic/adaptive weighting/neural network to select more accurate custom sub-ensembles Use fuzzy logic/adaptive weighting/neural network to select more accurate custom sub-ensembles Automate for operational use, web output Automate for operational use, web output Create ensemble toolbox for forecasters allowing effect of perturbations in parameters on the forecast track to be easily seen and quantified Create ensemble toolbox for forecasters allowing effect of perturbations in parameters on the forecast track to be easily seen and quantified

125. References Fulton, S. R., 2001: An adaptive multigrid barotropic cyclone track model. Mon. Wea. Rev., 129, 138-151. Fulton, S. R., 2001: An adaptive multigrid barotropic cyclone track model. Mon. Wea. Rev., 129, 138-151. Leith, C. E., 1974: Theoretical skill of Monte Carlo forecasts. Mon. Wea. Rev., 102, 409-418. Leith, C. E., 1974: Theoretical skill of Monte Carlo forecasts. Mon. Wea. Rev., 102, 409-418. Leslie, L. M., Abbey, R. F., and Holland, G. J., 1995: Tropical Cyclone Track Predictability. Meteorol. Atmos. Phys., 65, 223-231. Leslie, L. M., Abbey, R. F., and Holland, G. J., 1995: Tropical Cyclone Track Predictability. Meteorol. Atmos. Phys., 65, 223-231. Toth, Z., and E. Kalnay, 1997: Ensemble forecasting at NCEP and the breeding method. Mon. Wea. Rev., 125, 3207-3310. Toth, Z., and E. Kalnay, 1997: Ensemble forecasting at NCEP and the breeding method. Mon. Wea. Rev., 125, 3207-3310. Wiin-Nielsen, A., 1959: On barotropic and baroclinic models, with special emphasis on ultra long waves. Mon. Wea. Rev., 87, No. 5, 171-183. Wiin-Nielsen, A., 1959: On barotropic and baroclinic models, with special emphasis on ultra long waves. Mon. Wea. Rev., 87, No. 5, 171-183.