1. The talk: *The problem with current thunderstorm forecasting. *What would be ideal. *Thunderstorm statistics. *Our assumptions. *The algorithm and its mathematics. *Sample output. *How it performs. *The future. THESPA: A new method for thunderstorm strike probability forecasting.

2. Current thunderstorm trackers and forecasters, ie, TIFS (thunderstorm interactive forecast system), show a threat area based on detecting and linear projecting thunderstorm motion: Problem: this is ad hoc, and its output cannot be used by other systems. We need to generate a strike probability with mathematical meaning.

3. Strike probabilities would allow us to make this kind of product: a combination of thunderstorm strike probabilities from different detectors.

4. Thunderstorm statistics Histogram of detected TS positions compared with their forecasts (from a database of 1682 thunderstorm tracks).

5. Statistical analysis of storm database showed that standard deviation of velocity and direction errors (wrt forecast) was reasonably constant over forecast time (unlike most other measures).

6. To produce thunderstorm strike probabilities, we assume: the thunderstorm motion is linear, the TS lives for the full forecast period (ie, 1 hour), the TS shape is unchanged over the forecast period, the distribution of TS speed and direction errors (difference between actual speed and direction and forecast speed and direction) is a 2 dimensional bivariate normal distribution, the standard deviations of this distribution are constant over the forecast period. r = range, V = velocity, t = forecast time, = angle, = angle std dev,= velocity std dev.

7. Example of bivariate normal distribution

8. The algorithm is divided into 2 steps. Firstly, the probability density function that any given point meets the center of gravity (CoG) of the thunderstorm at any time in the forecast period is calculated. This is based on integrating the probability density of all possible trajectories of the CoG that pass through that point up to the forecast time. erf = error function

9. The second step is to compute the probability that a given point is affected by any part of the thunderstorm during the forecast period. Thus, for any given point, we combine the probabilities of all the possible thunderstorm CoG trajectories whose thunderstorms touch the point.

10. The second step is to compute the probability that a given point is affected by any part of the thunderstorm during the forecast period. Thus, for any given point, we combine the probabilities of all the possible thunderstorm CoG trajectories whose thunderstorms touch the point.

11. The second step is to compute the probability that a given point is affected by any part of the thunderstorm during the forecast period. Thus, for any given point, we combine the probabilities of all the possible thunderstorm CoG trajectories whose thunderstorms touch the point.

12. Example output (with contours added)

13. Results: Histogram of 1682 thunderstorm track errors (again): this bears some resemblance to the previous figure

14. In fact, if for each of those 1682 tracks we compute the strike probability using THESPA, and compare that with the observed frequency (pixel by pixel), we get the following reliability chart:

15. Example of THESPA used in TIFS, in which TS strike probabilities for multiple storms around Beijing are combined and presented in 3 probability bands 10- 25%, 25-50% and 50-100%. Usage:

16. Future developments include incorporating functional dependence of the standard deviations upon thunderstorm initial speed, dealing with storm lifetimes of less than the forecast period, and performing the calculations within Cartesian coordinates. This last step has been coded up and looks very promising.