Probabilistic Prediction

Uncertainty in Forecasting All of the model forecasts I have talked about reflect a deterministic approach. This means that we do the best job we can for a single forecast and do not consider uncertainties in the model, initial conditions, or the very nature of the atmosphere. These uncertainties are often very significant. Traditionally, this has been the way forecasting has been done, but that is changing now.

The work of Lorenz (1963, 1965, 1968) demonstrated that the atmosphere is a chaotic system, in which small differences in the initialization, well within observational error, can have large impacts on the forecasts, particularly for longer forecasts. In a series of experiments found that small errors in initial conditions can grow so that all deterministic forecast skill is lost at about two weeks. A Fundamental Issue

Butterfly Effect: a small change at one place in a complex system can have large effects elsewhere

Not unlike a pinball game

Uncertainty Extends Beyond Initial Conditions Also uncertainty in our model physics. And further uncertainty produced by our numerical methods.

Probabilistic NWP To deal with forecast uncertainty, Epstein (1969) suggested stochastic-dynamic forecasting, in which forecast errors are explicitly considered during model integration. Essentially, uncertainty estimates were added to each term in the primitive equation. This stochastic method was not computationally practical, since it added many additional terms.

Probabilistic-Ensemble NWP Another approach, ensemble prediction, was proposed by Leith (1974), who suggested that prediction centers run a collection (ensemble) of forecasts, each starting from a different initial state. The variations in the resulting forecasts could be used to estimate the uncertainty of the prediction. But even the ensemble approach was not possible at this time due to limited computer resources. Became practical in the late 1980s as computer power increased.

Ensemble Prediction Can use ensembles to estimate the probabilities that some weather feature will occur. The ensemble mean is more accurate on average than any individual ensemble member. Forecast skill of the ensemble mean is related to the spread of the ensembles When ensemble forecasts are similar, ensemble mean skill is higher. When forecasts differ greatly, ensemble mean forecast skill is less.

T The true state of the atmosphere exists as a single point in phase space that we never know exactly. A point in phase space completely describes an instantaneous state of the atmosphere. For a model, a point is the vector of values for all parameters (pres, temp, etc.) at all grid points at one time. An analysis produced to run a model like the eta is in the neighborhood of truth. The complete error vector is unknown, but we have some idea of its structure and magnitude. e Chaos drives apart the forecast and true trajectories…predictability error growth. EF can predicted the error magnitude and give a “probabilistic cloud” of forecasts. 12h forecast 36h forecast 24h forecast 48h forecast T 48h verification phase space

e a u c j t g n M T T Analysis Region 48h forecast Region 12h forecast 36h forecast 24h forecast phase space

A critical issue is the development of ensemble systems that provide probabilistic guidance that is both reliable and sharp.

Elements of a Good Probability Forecast Reliability (also known as calibration) –A probability forecast p, ought to verify with relative frequency p. –Forecasts from climatology are reliable (by definition), so calibration alone is not enough.

Elements of a Good Probability Forecast Sharpness (a.k.a. resolution) –The variance or confidence interval of the predicted distribution should be as small as possible. Probability Density Function (PDF) for some forecast quantity Sharp Less Sharp

Early Forecasting Started Probabilistically Early forecasters, faced with large gaps in their nascent science, understood the uncertain nature of the weather prediction process and were comfortable with a probabilistic approach to forecasting. Cleveland Abbe, who organized the first forecast group in the United States as part of the U.S. Signal Corp, did not use the term “forecast” for his first prediction in 1871, but rather used the term “probabilities,” resulting in him being known as “Old Probabilities” or “Old Probs” to the public. A few years later, the term ‘‘indications’’ was substituted for probabilities and by 1889 the term ‘‘forecasts’’ received official sanction (Murphy 1997).

“Ol Probs” Professor Cleveland Abbe, who issued the first public “Weather Synopsis and Probabilities” on February 19, 1871 Cleveland Abbe (“Ol’ Probabilities”), who led the establishment of a weather forecasting division within the U.S. Army Signal Corps, Produced the first known communication of a weather probability to users and the public.

History of Probabilistic Prediction The first operational probabilistic forecasts in the United States were produced in These forecasts, for the probability of precipitation, were produced by human weather forecasters and thus were subjective predictions. The first objective probabilistic forecasts were produced as part of the Model Output Statistics (MOS) system that began in 1969.

Ensemble Prediction Ensemble prediction began an NCEP in the early 1990s. ECMWF rapidly joined the club. During the past decades the size and sophistication of the NCEP and ECMWF ensemble systems have grown considerably, with the medium-range, global ensemble system becoming an integral tool for many forecasters. Also during this period, NCEP has constructed a higher resolution, short-range ensemble system (SREF) that uses breeding to create initial condition variations.

NCEP Global Ensemble System Begun in 1993 with the MRF (now GFS) First tried “lagged” ensembles as basis…using runs of various initializations verifying at the same time. Subsequently, they used the “breeding” method to find perturbations to the initial conditions of each ensemble members. Breeding adds random perturbations to an initial state, lets them grow, then reduce amplitude down to a small level, lets them grow again, etc. Give an idea of what type of perturbations are growing rapidly in the period BEFORE the forecast. Does not include physics uncertainty. Coarse spatial resolution..only for synoptic features.

NCEP Global Ensemble Today At 00Z: T254L64 high resolution control) out to 7 days, after which this run gets truncated and is run out to 16 days at a T170L42 resolution T62 control that is started with a truncated T170 analysis 10 perturbed forecasts each run at T62 horizontal resolution. The perturbations are from five independent breeding cycle. At 12Z: T254L64 control out to 3 days that gets truncated and run at T170L42 resolution out to 16 days Two pairs of perturbed forecasts based on two independent breeding cycles (four perturbed integrations out to 16 days.

Variety of Ways to View Ensembles and Their Output

The Thanksgiving Forecast h forecast (valid Thu 10AM) 13: avn* 11: ngps* 12: cmcg* 10: tcwb* 9: ukmo* 8: eta* Verification 1: cent 7: avn 5: ngps 6: cmcg 4: tcwb 3: ukmo 2: eta - Reveals high uncertainty in storm track and intensity - Indicates low probability of Puget Sound wind event SLP and winds

Box and whiskers

Major Global Ensembles NCEP GEFS (Global Ensemble Forecasting System): GFS, 21 members every 6 hr, T254 (roughly 70 km resolution), 64 levels Canadian CEFS: GEM Model, 21 members, 100 km grid spacing, 0 and 12Z ECMWF: 51 members, 62 levels, 0 and 12Z, T639 (roughly 27 km) eps/ eps/

Major International Global/Continental Ensembles Systems North American Ensemble Forecasting Systems (NAEFS): Combines Canadian and U.S. Global Ensembles: Sgrams_e.html

NCEP Short-Range Ensembles (SREF) Resolution of 32 km Out to 87 h twice a day (09 and 21 UTC initialization) Uses both initial condition uncertainty (breeding) and physics uncertainty. Uses the NMM and Regional Spectral Models and recently the WRF model (21 total members) US/web_js/html/mean_surface_prs.htmlhttp:// US/web_js/html/mean_surface_prs.html

SREF Current System ModelRes (km) LevelsMembers Cloud PhysicsConvection RSM-SAS 3228Ctl,n,p GFS physics Simple Arak-Schubert RSM-RAS 3228n,pGFS physics Relaxed Arak-Schubert Eta-BMJ 3260Ctl,n,pOp FerrierBetts-Miller-Janjic Eta-SAT 3260n,pOp FerrierBMJ-moist prof Eta-KF 3260Ctl,n,p Op FerrierKain-Fritsch Eta-KFD 3260n,pOp FerrierKain-Fritsch with enhanced detrainment PLUS * NMM-WRF control and 1 pert. Pair * ARW-WRF control and 1 pert. pair

British Met Office MOGREPS 24 members, 18 km

Ensemble Post-Processing Ensemble output can be post-processed to get better probabilistic predictions Can weight better ensemble members more. Correct biases Improve the width of probabilistic distributions (pdfs)

BMA (Bayesian Model Averaging) is One Example

There is a whole theory on using probabilistic information for economic savings C= cost of protection L= loss if bad event event occurs Decision theory says you should protect if the probability of occurrence is greater than C/L

Critical Event: sfc winds > 50kt Cost (of protecting): $150K Loss (if damage ): $1M Hit False Alarm Miss Correct Rejection YES NO YES NO Forecast? Observed? Decision Theory Example $150K$1000K $150K$0K Optimal Threshold = 15%

The Most Difficult Part: Communication of Uncertainty

Deterministic Nature? People seem to prefer deterministic products: “tell me exactly what is going to happen” People complain they find probabilistic information confusing. Many don’t understand POP. Media and internet not moving forward very quickly on this.

Icons are not effective in providing probabilities

Even worse…they use the same icons for likely rain and rain as they do for chance rain. Also, they used “likely rain” for 70% on this page and “chance rain” for 70% in the example on the previous page

And a “slight” chance of freezing drizzle reminds one of a trip to Antarctica

Commercial sector is no better

A great deal of research and development is required to develop effective approaches for communicating probabilistic forecasts which will not overwhelm people and allow them to get value out of them.