steve keighton national weather service blacksburg, va
TRANSCRIPT
Steve KeightonNational Weather Service
Blacksburg, VA
OutlineChaos theory and predictability in the atmosphereNumerical Weather Prediction (NWP) and use of
“ensemble” forecast methods
Use of statistical guidance in the forecast process (Model Output Statistics) – if time
Acknowledgments• Josh Korotky – NWS Pittsburgh• Mark Antolik – NWS Meteorological Development Lab
Prelude – What is Chaos and why is it important?Chaos leads us from the laws of
nature to their consequences …shows us that simple systems
can exhibit complex behavior…and vice versa
…demonstrates that unpredictable behavior can develop in a system governed by deterministic laws
As forecasters…chaos shows us the limits of predictability …highlights the importance of
probabilistic thinking …shows us the value of
expressing uncertainty in forecasts
…helps us understand why the future of forecasting will lean heavily on ensemble rather than deterministic approaches
“… one flap of a sea-gull’s wing may forever change the future course of the weather” (Lorenz, 1963)
Small errors in the initial state estimate of a nonlinear system can limit the prediction of later states of the system
Chaos occurs when error propagation, seen as a signal in time, grows to the same size or scale as the original signal...
dxx y
dtdy
xz rx ydtdz
xy bzdt
Elements of ChaosDynamical system – future states caused by past states
(determinism)Nonlinearity – system output (response) isn't proportional to
input (forcing)…a small forcing can lead to a disproportionately large response
and vise versaa system's values at one time aren‘t proportional to the values
at an earlier timeNon-periodic behavior – future states never repeat past
statesExtreme sensitivity to initial conditions – small initial state
uncertainties amplify…a "prediction horizon” is inevitableEven though the governing laws of a system are known, long-
term predictions can be meaninglessChaos occurs only in deterministic, nonlinear, dynamical
systems
Attractors – General StatementsAn attractor is a dynamical system's set of
conditionsIn a phase space diagram, an attractor shows a
system's long-term behavior. It's a compact, global picture of all of a system's possible steady states.
All attractors are either nonchaotic or chaoticNonchaotic attractors generally are points, cycles, or
smooth surfaces (tori), and have regular, predictable trajectories…small initial errors or minor perturbations generally don't have significant long-term effects
Chaotic or strange attractors occur only after the onset of chaos. Long term prediction on a chaotic attractor is limited…small initial errors or minor perturbations can have profound long-term effects
A Strange Attractor is dynamically unstable and non periodic • - A chaotic system is unstable…its behavior
changes with time rather than settling to a fixed point
• - Chaotic systems are non periodic…trajectories do not settle into repeatable patterns …and never cross
• - A chaotic attractor shows extreme sensitivity to initial conditions… trajectories initially close, diverge, and eventually follow very different paths
Strange Attractors
Non-periodic Dynamical System A dynamical system that never settles into a steady state attractor
Non periodic systems never settle into a repeatable (predictable) sequence of behavior.
Prediction of a future state of a non periodic system is eventually impossible, due to nonlinear dynamics (feedback)
The atmosphere illustrates non periodic behavior Broad patterns in the development, evolution, and movement of
weather systems may be noticeable, but no patterns ever repeat in an exact and predictable sequence
The atmosphere is: …damped by friction of moving air and water …driven by the Sun’s energy …the ultimate feedback system
Weather patterns never settle into a steady state attractor
Small uncertainties (minute errors of measurement which enter into calculations) are amplified
Result: system behavior is predictable in the short term…unpredictable in the long term
Sensitivity to Initial Conditions
The Lorenz DiscoveryFrom nearly the same starting point (tiny rounding error), the
new forecast diverged from the original forecast…eventually reaching a completely different solution!
Why? …Slight differences in the initial conditions had profound effects on the outcome of the whole system
Lorenz found the mechanism of deterministic chaos: simply-formulated systems with only a few variables can display highly complex and unpredictable behavior
(.506) vs. (.506127)
Initial condition
Chaos and Numerical Weather Prediction (NWP)
Weather forecasts lose skill because of: Chaos …small errors in the initial state of a forecast grow exponentially
Model uncertainty Numerical models only approximate the laws of physics (important small
scale processes are parameterized) Very small errors in the initial state of a forecast model grow rapidly at
small scales, then spread upscale
Forecast skill varies both spatially and temporally as a result of both initial state and model errors, which change as the atmospheric flow evolves
If a process is chaotic… knowing when reliable predictability dies out is useful, because predictions for all later times are useless.
Models must simulate numerous irresolvable processes
NWP Skill as a Function of Scale and Time
Predictability falls off as a function of scale
Large scale features (planetary waves) may be predictable up to a week in advance
Small systems (fronts) are well forecasted to day 2.. cyclonic systems to day 4
Some skill in 5-10 day QPFGoodVery GoodQPF/ mean clouds
Skill with max/minVery GoodExcellentTemp / wind
--------FairGoodMesoscale banded structuresConvective clusters
----FairGoodExcellentFronts
Low skill-FairFair-GoodVery GoodExcellentCyclone life cycle
GoodVery GoodExcellentExcellentHemispheric flow transitions
Days 6-7Days 3-5Days 1-2< Day1Feature/Variable
FairGoodVery GoodPrecip/ mean clouds
Skill with max/min TempVery GoodExcellentTemp / wind
--------FairGoodMesoscale banded
structuresConvective clusters
----FairGoodExcellentFronts
Low skill-FairFair-GoodVery GoodExcellentCyclone life cycle
GoodVery GoodExcellentExcellentHemispheric flow
transitions
Days 6-7Days 3-5Days 1-2< Day1Feature/Variable
Why can’t we count exclusively on single model NWP?
Overlooks forecast uncertainty Initial condition and model uncertainty Chaotic flows vs. stable flow regimes
Potentially misleading Oversells forecast capability
GFS 84 hr forecastValid 00Z 22 Nov
NAM 84 hr forecastValid 00Z 22Nov
Single Model NWP
Which model do you believe?
Ensembles and PDF
Recognizing the eventuality of chaos…weather forecasts can provide more useful information by describing the time evolution of an ensemble probability density function (PDF)
Initial PDF represents initial uncertainty Single forecast doesn’t account for initial and model error…often fails to
predict the real future state past a certain point Ensemble of perturbed forecasts accounts for initial and model error… PDF
of solutions more likely to contain real future state Ensemble PDF contains additional information, including forecast
uncertainties
High Res Control
RealityPDF PDF
Time
Single Forecast
Reality
Ensemble Prediction System (EPS) Goals
Represent initial condition and/or model uncertainty
Determine a range of possible forecast outcomes Estimate the probability for any individual
forecast outcomeGeneral: provide a framework for decision
assistance
23
General EPS forecasting toolsSpaghetti Plots (shows all solutions)Mean/Spread (“middleness” and variability)ProbabilitiesMost Likely Event
“Spaghetti” Plots
25
Mean and SpreadCharacteristics of mean
The ensemble mean performs better on average than operational model on which it is based. Why?
Because predictable features remain intact, less predictable features are smoothed out
Characteristics of spreadAllows assessment of
uncertainty, since more spread means more uncertainty
12
3
4
• Helps determine the probability of a specified event.• Gives probability of exceeding meaningful threshold
• Calculation represents count of what % of ensemble members exceed the threshold of interest
• Example here is for 12-hour precipitation exceeding 0.25 inches.
Probability of Exceedance
• Used to show what is most often predicted by the ensemble forecast
• A common example– Precipitation type
(snow, sleet, freezing rain, rain)
Most Likely or Dominant Event Diagram
SummaryChaos and model uncertainties impose a very real
physical limit on predictabilityPredictability falls off (sometimes rapidly) as a
function of scale and timeForecast accuracy varies both spatially and
temporally as a result of initial state and model errors, which change as the atmospheric flow evolves
Ensemble NWP optimizes predictability for all scales, and extends the utility of forecasts…especially at extended ranges (days 4-7)
Allows for quantification of uncertainty, and foundation for decision assistance
Statistical Guidance in the Forecast Process
WHY STATISTICAL GUIDANCE?
●Add value to direct NWP model output
Objectively interpret model - remove systematic biases - quantify uncertainty Predict what the model does not Produce site-specific forecasts (i.e. a “downscaling” technique)
●Assist forecasters “First Guess” for expected local conditions “Built-in” model/climatology
MODEL OUTPUT STATISTICS (MOS)
1. Numerical Weather Prediction (NWP) Model Forecasts 2. Prior Surface Weather Observations3. Geoclimatic Information
Current Statistical Method: MULTIPLE LINEAR REGRESSION (Forward Selection)
Relates observed weather elements (PREDICTANDS) to appropriate variables (PREDICTORS) via astatistical approach.
Predictors are obtained from:
MODEL OUTPUT STATISTICS (MOS)
Properties●Mathematically simple, yet powerful
●Need historical record of observations at forecast points (Hopefully a long, stable one!)
●Equations are applied to future run of similar forecast model
●Probability forecasts possible from a single run of NWP model
●Other statistical methods can be used e.g. Polynomial or logistic regression; Neural networks
MODEL OUTPUT STATISTICS (MOS)
●ADVANTAGES - Recognition of model predictability - Removal of some systematic model bias - Optimal predictor selection - Reliable probabilities - Specific element and site forecasts ●DISADVANTAGES - Short samples - Changing NWP models - Availability & quality of observations
Now approx. 1820 sites
Gridded MOS
●“MOS at any point (GMOS) - Support NWS digital forecast database 2.5 km - 5 km resolution - Equations valid away from observing sites - Emphasis on high-density surface networks - Use high-resolution geophysical data - Some problems over steep terrain or data-sparse regions
Gridded MOS
Use of MOS at a Forecast Office
• Can ingest GMOS directly into local digital forecast database• Can apply bias correction (based on performed in past 30 days)• Can ingest point-based MOS and spread it to entire grid• MOS from single models or from ensemble mean/max/min• We verify our forecast against MOS, so we may use as a starting point but we try to improve on it based on local experience or recent trends
Questions?