# And the talk

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```					        THESPA: A new method for thunderstorm
strike probability forecasting.
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.
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.
Strike probabilities would allow us to make this kind
of product:

a combination of thunderstorm strike probabilities from different
detectors.
Thunderstorm statistics

Histogram of detected TS positions compared with their forecasts
(from a database of 1682 thunderstorm tracks).
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).
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.
Example of bivariate normal distribution
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
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.
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.
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.
Results:
Histogram of 1682 thunderstorm track errors (again):

this bears some resemblance to the previous figure
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:
Usage:

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%.
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.

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 views: 2 posted: 3/9/2012 language: pages: 16