A Bayesian Stochastic method for the short period prediction of heavy rainfall

1. A Bayesian Stochastic method for the short period prediction of heavy rainfall Neil Fox, Department of Soil and Atmospheric Sciences Chris Wikle and Bill Xu Department of Statistics, University of Missouri – Columbia

2. Content • What is nowcasting? • Why is it important? • Weather radar • Current methods and their shortcomings • Why use Bayesian methods? • Other statistical approaches • What we’ve done • Our methodology • Data and preliminary results • Future work

3. What is nowcasting? • Short period forecasting of weather • ‘Short period’ can be stretched to 6 hours, but more often implies less than 2 hours • Usually concerned with severe weather • Precipitation and flash floods are becoming increasingly of interest

4. Severe weather and precipitation nowcasting • Rely on radar • Gives a real-time areal indication of location, motion and intensity of storms • Backscattered power can be related to precipitation rate • Other spatial considerations and wind patterns derived from Doppler observations can indicate storm type and the presence of severe weather features

6. Observation of storm motion

7. Nowcasting techniques - current • Extrapolation techniques • Mostly linear extrapolation • Do not account for development • Modeling approaches • Forecasts motion and development • Lack of knowledge of: • Storm scale dynamics (model accuracy) • Atmospheric environment (observation limitation)

8. TITAN product

9. Nowcasting techniques - experimental • NCAR: Autonowcaster • Information on likely areas of development • Not explicit forecast • Requires interpretation and skill

10. ANC product example

11. Limitations of Current Nowcasting • Only good for short periods • Poor at simulating development • Predict position but not characteristics of storms • No information of forecast rainfall, damaging winds or hail • Tend to smooth high intensity features • Little or no indication of forecast uncertainty • Computationally intensive

12. Nowcasting techniques - statistical • In their infancy • Basic stochastic approaches • Other than one other group we are aware of all statistical precipitation forecasting techniques are basically randomized-stochastic.

13. Our approach • Bayesian • Produces knowledge of uncertainty • Spatio-temporal • Provides realizations of future fields for display • Hierarchical • Can incorporate more observational data to constrain method • Provides physical basis for statistical approach

14. Nowcast formulation Stochastic integro-difference equation Continuous in space Discrete in time The nowcast field (yt+1) is related to the current field (yt) by where s and r are spatial locations in the domain of interest, ks(r; θs) is a redistribution kernel that describes how the process at time t is redistributed in space at time t+1. η represents the noise and γ is a growth / stationarity parameter

15. Kernel The kernel is centered at θ1 + s and thus is shifted by θ1 spatial units relative to location s, and θ2 is the scale parameter. We refer to θ1 as the translation parameter and θ2 as the dilation parameter. The equations above are the simplified 1-dimensional version analogous to the 2-dimensional version used.

16. Advantages of Statistical Approach • Provide full distribution of forecasts allowing realistic assessment of uncertainty • Avoid detailed physical modeling of atmosphere • Can ‘train’ system • Can incorporate further observations to constrain equation parameters

17. Example • Nowcast of supercell motion from 11/03/00 • Sydney, Australia (to prove we can cope with any hemisphere) • Storm produced localized flooding, F1 tornadoes, damaging large hail • Very complex situation • Other nowcast systems did okay

18. Estimated propagation orientation Spatially-varying kernels

19. Actual obs. vs nowcast vs realizations with variance field

20. Comparing nowcast and actual

21. Sample realizations

22. For comparison

23. Nowcast – Actual T+20

24. Nowcast – Actual T+60

25. What we saw

26. · 3 Nov. 2000 Norah Head 0630 · Gosford 0530 0430 TITAN 0330 Katoomba · Dissipates at 0620 · Actual Path Nowcaster 0300 0230 SPROG · · Nimrod Bowral · Kiama 40 60 km 20 0 Fig 10

27. Results • Retains high intensity rainfall features • Forecast location similar to accuracy from other nowcast systems

28. To do list • Analyze entire event(s) • Statistical evaluation of performance • Overall • Point forecasts • Areal (watershed) forecasts • Distinguishing quantitative error from motion • Assessment of variance • Use of nowcasts for hydrology

29. More to do • Refinements • Use of wind field information • Other Bayesian formulations (ask Chris) • More studies • Using local radar data • Different types of event