MME

Michael K. Tippett

International Research Institute for Climate and Society

The Earth Institute, Columbia University

ERFS Climate Predictability Tool Training Workshop May 4-9, 2009

Outline

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Uncalibrated methods

▶ Forecast pdf is constructed without use of observations. ▶ Past performance is not taken into account. ▶ Variety of methods of extracting information from the

ensemble

“Counting” methods

Pool ensemble members

P(event) = Ensemble frequency of event

Examples.

P(T > 26.3^{∘}C) = \frac{# ensemble members with T > 26.3^{∘}C}{# ensemble members} Does not account for ensemble bias. Mean. Spread.

Define event with respect to model history.

P(T > 85 th percentile) = \frac{# ensemble members with T > 85%}{# ensemble members}

percential = model percential (history) Accounts for bias of multimodel ensemble. Does not account for bias of individual models.

“Counting” methods (2)

Pool anomalies of each model ensemble. Define events in terms of anomalies

P(event) = Ensemble frequency of event

Accounts for mean biases of individual models.

“Counting” methods (3)

Pool standardized anomalies of each model ensemble. Define events in terms of standardized anomalies

P(event) = Ensemble frequency of event

Accounts for mean biases and spread biases of individual models.

Honest cross-validation

Any method that uses parameters from forecast histories must do so in a manner that replicates real-time forecasting. Compute parameters leaving out the year to be forecast.

▶ Median ▶ Percentiles ▶ Climatology ▶ Variances

Sampling error

▶ Even if the models are perfect, ensemble size limits

accuracy of probabilities. ▶ P(event) = 0 may occur simply because the event is rare

compared to the ensemble size, not because it is impossible.

▶ The only time a probablistic forecast can be “wrong” is when it is deterministic. Must avoid P = 0 or P = 1.

Continuous pdf

Replace ensemble with a continuous pdf f

▶ Parametric – e.g., Gaussian with mean μ and variance σ^{2}

from ensemble ▶ Nonparametric – kernel density estimator

Example. f (T ) Guassian.

f = \frac{1}{\sqrt{2π}} e^{\frac{(T −μ)^{2}}{2σ^{2}}}

P(T > T_{0}) = \frac{1}{\sqrt{2π}} ∫_{−∞}^{T_{0}} e^{\frac{(T −μ)^{2}}{2σ^{2}}} dT

Probabilities vary continuously with threshoods. Probability of rare events is not zero.

▶ In some problems, there is evidence that the forecast mean

varies from year to year but the forecast spread is constant. ▶ If so, a much larger ensemble can be formed by centering

the ensembles of past forecasts on the ensemble mean of the current forecast.

▶ Form a GLM regression between ensemble based probabilities and the ensemble mean. Predict the probabilities from the ensemble mean.

Summary

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