Lysbilde 1

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Probabilistic forecasts of rare visibility events
using neural nets
John Bjørnar Bremnes Norwegian Meteorological
Institute P.O. Box 43 Blindern, NO-0313 Oslo,
Norway j.b.bremnes_at_met.no
Silas Chr. Michaelides Meteorological
Service P.O. Box 43059, Larnaka Airport, CY-6650
Cyprus silas_at_ucy.ac.cy
Introduction
Visibility Forecasting at Larnaca Airport 3 hours
ahead

• Data
• Predictand
• Runway Visual Range (five categories)
• Predictors
• Hourly change in Runway Visual Range (not
  categorised)
• Height of cloud base
• Dew point temperature
• The predictors were selected by a stepwise
  forward search among 16 subjectively chosen
  variables and were kept fixed during the
  experiments.

• Motivation
• Rare visibility events are of considerable
  importance
• Should one proceed as normal?
• Can simple statistical approaches improve
  forecasting?

• Aim
• Compare various statistical approaches for
  probabilistic forecasting of rare visibility
  events

Experiments

• Neural Networks
• Neural networks are very flexible functions that
  in our context map predictors into probabilities.
  The details are
• One hidden layer
• Logistic input and output functions
• Cross-entropy loss function with quadratic weight
  decay
• Number of hidden units and weight decay are
  selected on basis of cross-validated predictions
  on the training set
• 5 neural nets (with random initial values) are
  fitted to deal with local minima. The average of
  the estimated probabilities are applied.

Statistical Approaches

• Modelling
• Standard
• Neural net for probabilities of all visibility
  classes
• Conditional
• Neural net for probabilities of good and reduced
  visibility classes (2 classes) ? P(G) and
  P(R)
• Neural net for probabilities of the reduced
  visibility classes given that visibility will be
  in one of these.
  ? P(RkR), k1, ,
  K.
• Use laws of probability to obtain the remaining
  probabilities ? P(Rk) P(Rk
  and R) P(RkR) P(R), k1, , K.

The experiments were repeated 15 times and only
the average scores are shown.

• Sampling and Use of Weights
• Sampling based on predictor (x)
• Randomly reduce unimportant cases by predictor
  value
• Use of weights based on predictor (x)
• Increase influence of important cases
• Use of weights based on predictand (y)
• Increase influence of cases with observed reduced
  visibility
• Note will result in biased probabilities
• Sampling and use of weights based on predictand
  (y)
• Randomly reduce cases with observed good
  visibility
• Introduce weights to account for the sampling

• Sampling
• X sampling based on predictor (RVR good)
• Y sampling based on predictand (observed RVR
  good)
• 110 ratio of number of cases with reduced and
  good visibility is 110
• 11 ratio of number of cases with reduced and
  good visibility is 11

• Use of Weights
• X weights based on predictor (RVR). The weight
  for each case is one minus its prior class
  probability.
• Y weights based on predictand (observed RVR).
  - If no sampling, the weight for each case
  is one minus its prior class probability. - If
  sampling, the weights are equal to the ratio
  between prior class probability and new class
  probability after sampling.

• CV score
• WRPS weighted RPS where the weight for each
  case is one minus its prior class probability.

• Summary and Recommendations
• Sampling and use of weights based on predictand
  give best results, but mostly due to better
  predictions for the good visibility cases
• Naïve approach second best
• Standard and conditional modelling give similar
  results, but the latter is computationally faster
  (not shown)
• Introducing weights in the model selection score
  (RPS) do not improve results and is not
  recommended
• Either sampling or use of weights based on
  predictand only is not recommended implies
  biased probabilities and poor scores
• The best proposed approaches are clearly better
  than persistence

• Model Selection Score
• Ranked Probability Score (RPS)
• Weighted Ranked Probability Score (WRPS)
• Similar to RPS, but cases are given weights based
  on the observed visibility class.

Note that the proposed statistical approaches can
be combined and applied to other statistical
methods than neural nets.