Uncertainty Quantification Using Ensemble Methods: Predictability of Extremes and Coherent Vortices. Joe Tribbia NCAR IPAM lecture 15 February 2007. Outline. General problem of uncertainty prediction Reliability prediction as practiced operationally Specific problem of extreme events
15 February 2007
Prior to 1990 all numerical weather forecasts deterministic (n.b. Pitcher and Epstein,1974)
Forecast timeThe probabilistic approach to NWP: ensemble prediction
A complete description of the weather prediction problem can be stated in terms of the time evolution of an appropriate probability density function (pdf).
Ensemble prediction based on a finite number of deterministic integration appears to be the only feasible method to predict the PDF beyond the range of linear growth.
Singular vector (upper)
Bred vector (lower)
Basic state jet
Singular vectors are the fastest growing structures into the future
Bred vectors are the fastest growing structures in the past.
Operational centers battled over which was superior.
NB: Inconsistencies in initial error will disappear with Ens KF
The degree of mixing of Z500 isolines is an index of low/high perturbation growth.
A dynamical system shows a chaotic behavior if most orbits that pass close to each other at some point do not remain close to it as time progresses.
This is illustrated by the forecasts of the storm that hit northern Europe on 4 December 1999.
4 Dec 1999, 00UTC : verifying analysis (top-left) and t+132h ensemble forecasts of mean-sea-level pressure started from slightly different initial conditions (i.e. from initially very close points).
Ensemble prediction demonstrated that IC error was important but the imperfection of models needed to be accounted for in any UQ for weather prediction
Rank histogram shows the verification of
72hr temperature predictions with ECMWF
ensemble. A perfect system would have a
flat histogram. U shape indicates the
system is underpredicting uncertainty.
T&B examined the growth of errors due to the impact of unresolved
scales by comparing integrations with identical ICs and differing
horizontal resolutions from T170 to T42.
Each ensemble member evolution is given by the time integration
of the perturbed model equations starting from the perturbed initial conditions
The model tendency perturbation is defined at each grid point by
where rj(x) is a set of random numbers.
Not enough spread
Buizza et al. (2004)
Figure 6. May-June-July 2002 average RMS error of the ensemble-mean (solid lines) and ensemble standard deviation (dotted lines) of the EC-EPS (green lines), the MSC-EPS (red lines) and the NCEP-EPS (black lines). Values refer to the 500 hPa geopotential height over the northern hemisphere latitudinal band 20º-80ºN.
Old CY28R2 EPS
New CY28R3 EPSTR-SVs’ target areas: impact of the Sep ’04 change
Results based on 44 cases (from 3 Aug to 15 Sep 2004) indicate that the implemented changes in the computation of the tropical areas has a positive impact on the reliability diagram of strike probability.
Zabusky and McWilliams1982
vortex advected in
be sensitive to
variation in x(0).
the track less
Water Vapor Channel
Note the smaller scale structure in tropics
J is strongly dependent on x(0); weakly dependent on y(0) and s(0)
Low resolution forecastEDA: towards a probabilistic analysis & forecast system?