1. STEPS: An empirical treatment of forecast uncertainty Alan Seed BMRC Weather Forecasting Group

2. Outline  Where does uncertainty come from?  Can we get rid of it?  How can we quantify it?  Where to from here?

3. Sources of forecast uncertainty  Radar rainfall estimation  Field motion estimation  Development during forecast period

4. Radar Measurement Error  Major contribution to forecast error in the first hour Mean square error of rainfall forecast (1km, 15min) as a function of lead time based on a 5-day storm, 200 rain gauges for ground truth

5. Radar Measurement Error  Radar measurement errors are highly variable in time Errors increase in significant convective weather

6. Errors Due to Changes in Field Velocity Bowler et al 2005; submitted to QJR

7. Development during the forecast lead time  Climatology- topography, diurnal cycle  Rate of temporal development depends on scale- predictability limits  Situation dependent

8. Effect of topography

9. Effect of Topography

10. Predictability is a Function of Scale

11. Can We Get Rid of Uncertainty? No, but we can reduce it we can understand it we can tell our users about it

12. Quantifying Forecast Uncertainty  Physical ensembles  Statistical ensembles

13. Multi Model Ensemble 3500 campers were evacuated ahead of a flood at Tamworth after a qualitative assessment of risk based on the ensemble mean. Gordon McKay, Beth Ebert

14. Short Term Ensemble Prediction System  Generate a deterministic nowcast based on radar data  Estimate the error for the nowcast and a NWP forecast over a hierarchy of spatial scales  Merge the nowcast with the NWP forecast using weights that are a function of the forecast error and spatial scale  Generate an ensemble by perturbing the deterministic blend with a stochastic component

15. 256-128 km 64-32 km 8-4 km 32-16 km 4-2 km 128-64 km 16-8 km Spectral Decomposition

16. Temporal Development Model  The Lagrangian temporal development for each level in the cascade is forecast using an AR(2) model  AR(2) parameters are estimated at each time step for each level  The innovation term  is spatially correlated, temporally uncorrelated

17. Forecast Skill  Model skill is taken to mean the fraction of the observed variance that is explained by the model, r 2  Skill of Nowcast is given by the AR-2 model  Skill of the NWP is calculated as the correlation between the NWP cascade and radar cascades

18. Telling the users  Observation uncertainty  Forecast uncertainty

19. Observation Uncertainty 15-min average interpolated from gauge network Error as a fraction of the rain field variance

20. 15-min rainfall accumulation forecast- 20 member stochastic nowcast ensemble Ensemble mean Ensemble standard deviation Stochastic nowcast model does not yet include the observation error model

21. Way Forward: Heuristic Probabilistic Forecasting?  Held a workshop in Montreal- presentations can be found at http://www.radar.mcgill.ca/~cwrp/http://www.radar.mcgill.ca/~cwrp/ NWP has improved significantly but errors will remain Use persistence of NWP errors to develop post-processing systems to mitigate the error Need to model initiation, growth, decay Conceptual probabilistic models are likely to be useful Would like to develop a common framework and to collaborate on developing probabilistic forecast models

22. Thank you