Quantifying Uncertainty

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Quantifying Uncertainty Associated with
Hurricane Path
Julie LETSCHERT, INSA LYON (Mentor Svetlana
POROSEVA, Florida State University)
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A hurricane is an intensive tropical weather
system with a well defined circulation that
develops in the tropics.
Several global numerical models provide analyses
and forecasts of hurricanes. In forecasting
hurricane paths the prediction accuracy is of
vital importance. Yet, most current forecasts
lack such information.

• The objectives of the present study are
• to investigate the potential of using evidence
  theory to evaluate the accuracy of hurricane
  predictions
• - to develop an approach that uses this
  information to improve forecasts.

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Mathematical tools
Uncertainty can be aleatory (due to stochastic
influences and cannot be reduced) or epistemic
(which originates from incomplete knowledge at
any stage of modeling and simulation).
Probability theory describes the aleatory
uncertainty and possibility theory, for instance,
describes the epistemic uncertainty.
Evidence theory is the most developed of the
theories that can handle both types of
uncertainty.
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Test case
Hurricanes of year 2000.
Models
Global models from two operational centers the
European Center for Medium-Range Weather
Forecasts model (ECMRWF) and the NOGAPS (Navy
Operational Global Atmospheric Prediction System)
forecast model.
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Procedure
1rst step
The forecast accuracy (deviation) is evaluated at
each time by comparing model and observational
data Dev Lo Lm .
Here, Lo is the value of observational latitude
(longitude) and Lm is the model value.
The deviation space (from -? to ?) is divided
into intervals ?Dev. Then, we construct the
support function, which provides the degree of
support for each ?Dev S(?Dev)n(?Dev)/N, where n
is the frequency with which Dev-values fall in
?Dev and N is the total number of data given for
the time.
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Support functions are NOT probability functions.
For each time, 4 support functions are built (2
per model).
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2nd step Prediction.
Intervals of possible true latitude/longitude
values are assigned around the model value using
the support functions built in the 1rst step. The
support functions for the latitude and the
longitude are multiplied to obtain the support of
the area restricted by intervals in both
directions.
Model position (Lat, Lon)
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3rd step
Dempsters rule is applied to combine areas of
possible true latitude/longitude values predicted
by the models. We apply the rule twice for each
time with results from the 2 models (the 2
solutions are called R1 and R2).
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4th step
The 2 equally likely solutions R1 and R2 are
combined so as to average the information they
carry. The solution obtained, called R12, is
compared to the observational path.
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Conclusion
Observational data for three hurricanes from the
South Pacific region, three hurricanes from the
East pacific region, and six hurricanes from the
West Pacific region are used for the evaluation
of the quality of predictions obtained with the
new technique. The results are encouraging. This
approach can be applied to various problems.