simulating the weather: numerical weather prediction as computational simulation

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Simulating The Weather Simulating The Weather 13 June 2006 Ting-Shuo Yo

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A 40 mins talk about numerical weather prediction (NWP) from the aspect of computational simulation. The audience is a group of 20 computer science majors in graduate level, taking a course about simulation. Date: 2006-06-13

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Page 1: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Simulating The WeatherSimulating The Weather

13 June 2006

Ting-Shuo Yo

Page 2: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

OutlineOutline● Properties of Atmospheric Models● A Brief History● Numerical Weather Prediction (NWP)

– Parameterization– Data Assimilation– Stochastic Weather Models

Page 3: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Properties of Atmospheric Models

Properties of a model:

● Dynamic vs Static ● Continuous vs Discrete● Deterministic vs Stochastic

Page 4: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Properties of Atmospheric Models

● Dynamic

Weather changes over time

Page 5: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Properties of Atmospheric Models

● Dynamic ● Continuous

Time-Advance: fixed-increment(In contrast to discrete-event)

Solve differential equations - Physical systems can be described by a set of differential equations.

Page 6: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Properties of Atmospheric Models

● Dynamic ● Continuous● Deterministic

∂ V∂ t

V⋅∇ V=−∇ P

∂h∂ t

∇⋅H V =F

Page 7: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Properties of Atmospheric Models

● Dynamic ● Continuous● Deterministic → Stochastic (after late '90s)

Page 8: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Properties of Atmospheric Models

● Dynamic ● Continuous● Deterministic → Stochastic

Nonliearity in differential equations

Chaos

Limited predictability

Page 9: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Initial condition uncertainty 5-day forecast uncertainty

Page 10: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Properties of Atmospheric Models● The System:

Page 11: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Properties of Atmospheric Models

● Dynamic ● Continuous● Deterministic → Stochastic● Complex System

Page 12: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

A Brief History

Early 20th Centary● Bjerknes, Vilhelm (Norwegian scientist)

– 7 primitive equations– Weather can be predicted through

computation. (1904)– Graphic calculus: solve equations

through weather maps.

Page 13: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

A Brief History (2)

Early 20th Centary (1922)● Richardson, Lewis Fry

– First numerical weather prediction (NWP) system

– Calculating techniques: division of space into grid cells, finite difference solutions of DEs

– Forecast Factory: 64,000 computers (people who do computations), each one will perform part of the calculation.

Page 14: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

A Brief History (3)

Computer Age (1946~)

● von Neumann and Charney– Applied ENIAC to weather prediction

● Carl-Gustaf Rossby– The Swedish Institute of Meteorology– First routine real-time numerical

weather forecasting. (1954) ( US in 1958, Japan in 1959 )

Page 15: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Primitive Equations

Page 16: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Primitive Equations (2)

Horizontal Equations of Motion Newton's 2nd law of motion

The Hydrostatic Equation Vertical stratification

Thermodynamic Equation The 1st law of thermodynamics

Continuity Equation Conservation of Mass

Equation of State Property of the ideal gas

Water Vapor Equation

Page 17: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

                                                                                                                                                                                                                                                                                         

PE for ECMWF modelEast-west wind

North-south wind

Temperature

Humidity

Continuity of mass

Surface pressure

Page 18: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

● Simplify systems– Add extra assumptions, e.g.,

● barotropic model, ● quasi-geostraphic model.

● Increase computing power– Improved numerical methods– Parallel computing

Page 19: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

A Brief History (4)

● Norman Phillips – First general circulation model (GCM, 1955)

● Primitive equation (PE) models (late '50s ~ '70)

● 1980s : Interaction with other systems (e.g. ocean, land surface...etc.)

Page 20: Simulating the Weather: Numerical Weather Prediction as Computational Simulation
Page 21: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Properties of Atmospheric Models● The System:

Page 22: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

System of Atmospheric Models

Atmospheric Model(dynamic, cloud, precipitation )

solar heating, long-wave cooling.....

Ocean model, plant surface model...

Forcing

Coupling

Exchanging heat, momentum and energy

Adding extra energy

Page 23: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Various Atmospheric Models

Complexity

ResolutionComputing Power Required

Theoretical Models

Earth System

Operational Models

Coupled Models

Page 24: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

OutlineOutline● Properties of Atmospheric Models● A Brief History● Numerical Weather Prediction (NWP)

– Parameterization– Data Assimilation– Stochastic Weather Models

Page 25: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Parameterization● What is parameterization?

– Use parameters to represent sub-grid scale properties.

● Why use parameterization?– Make computation doable, both on computing

power and numerical stability.

Page 26: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Parameterization

Much of the weather occurs at scales smallerthan those resolved bythe weather forecast model. Model musttreat, or “parameterize” the effects of the sub-grid scale on the resolved scale.

Source: MODIS

Page 27: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

A lot happens inside a grid box

Approximatesize of one grid box in NCEP ensemble system

Source: accessmaps.com

Denver

Rocky Mountains

Page 28: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Systems to be Parameterized

● Land surface● Cloud micro-physics● Turbulent diffusion and interactions with surface

● Orographic drag● Radiative transfer

Page 29: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Parameterization Example

1.Build a detailed cloud model from observation.2.Build a classifier for its output as a function with limited complexity.

3.Use this function in a mature regional/global model.

4.Repeat step 1 ~ 3 till satisfied.

Cloud Micro-physics

Page 30: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

NWP Flowchart

Page 31: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Data Assimilation

Data assimilation is the process through which real world observations:

● Enter the model's forecast cycles● Provide a safeguard against model error growth● Contribute to the initial conditions for the next

model run

Page 32: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Data Assimilation (2)

A model analysis is not made from observations alone. Rather, observations are used to make SMALL corrections to a short-range forecast, which is assumed to be good.

Example:● Obs. at 09:00 -> initial condition for a 3-hr

forecast.● At 12:00, new obs. is corrected by the forecast

done at 09:00, and then used for correcting the forecast for next 3-hr.

Page 33: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Data Assimilation (3)

Page 34: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Data Assimilation Procedure● Ingesting the data● Decoding coded observations● Weeding out bad data● Comparing the data to the model's short-range

"first-guess" fields● Interpolating the data (in the form of model

corrections) onto the model grid for making the forecast

Page 35: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Data Assimilation Procedure

Page 36: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Two Fundamental Difficulties in Data Assimilation

● Transferring information from the scattered locations and times of the observations to the model grid, while at the same time.

● Preserving the interrelated physical, dynamical, and numerical consistency in the short-range forecast, since these are essential to making consistently good NWP forecasts

Page 37: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Current state-of-the-art data assimilation:4-dimensional variational assimilation (4D-Var)

CourtesyECMWF

Page 38: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

4D-VAR● Introduced in November 1997● The influence of an observation in space and

time is controlled by the model dynamics which increases its realism of the spreading out of the information.

● The algorithm is designed to find a compromise between the previous forecast at the beginning of the time window, the observations, and the model evolution inside the time window.

Page 39: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Stochastic Weather Models● Stochastic-dynamic approach (climate prediction)

- Ensemble of multiple models- Stochastic differential equations

● Pure probabilistic approachFor events hardly sketch by dynamics (e.g. precipitation)

Page 40: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Initial condition uncertainty 5-day forecast uncertainty

Page 41: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Ensemble forecasts

● Generating initial conditions: Each center has adopted their own approximate way of sampling from initial condition pdf.● Breeding (NCEP)● Singular vector (ECMWF)● Perturbed observation (Canada)

● Stochastic-dynamic ensemble work just beginning (e.g., Buizza et al. 1999)

● Many attempts to post-process ensemble forecasts to provide reliable probability forecasts.

Page 42: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Pure Stochastic Weather Models● Bayesian Network

Antonio et.al. (2002)

The performance is fair for the preliminary study.

Page 43: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Conclusion● Dynamic, continuous, and deterministic models● Early development:

– Dynamic equations– Numerical methods

● Recent development:– Parameterization– Data assimilation– Probabilistic (stochastic) approach

Page 44: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Questions?

Page 45: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Reference● P. N. Edwin, A Brief History of Atmospheric General Ciculation Modeling. General Circulation

Model Development: Past, Present and Future, D. Randall, ed. (Academic Press, San Diego, 2000), pp. 67-90.

● A. Arakawa, Future Development of General Circulation Models. General Circulation Model Development: Past, Present and Future, D. Randall, ed. (Academic Press, San Diego, 2000), pp. 721-780.

● T. N. Krishnamurti and L. Bounoua, An Introduction to Numerical Weather Prediction Techniques. CRC Press, Boca Raton, 1996, pp. 121-150.

● J. R. Holton, An introduction to dynamic meteorology. (3rd Edition). International Geophysics Series, Academic Press, San Diego, 1992.

● Wilks, D. S., and R. L. Wilby 1999 The weather generation game: a review of stochastic weather models. Progr. Phys. Geogr., 23, 329—357.

● Antonio S. Cofiño, R. Cano, C. Sordo, José Manuel Gutiérrez: Bayesian Networks for Probabilistic Weather Prediction. ECAI 2002: 695-699

Page 46: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Okay. So how's NWP work? 1. First settle on the area to be looked at and define a grid with

an appropriate resolution.

2. Then gather weather readings for each grid point (temperature, humidity, barometric pressure, wind speed and direction, precipitation, etc.) at a number of different altitudes;

3. run your assimilation scheme to initialize the data so it fits your model;

4. now run your model by stepping it forward in time -- but not too far;

5. and go back to Step 2 again.

6. When you've finally stepped forward as far as the forecast outlook, publish your prediction to the world.

7. And finally, analyze and verify how accurately your model predicted the actual weather and revise it accordingly.

Page 47: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Is the weather even predictable or is the atmosphere chaotic?

That's a loaded question. We all know that weather forecasters are right only part of the time, and that they often give their predictions as percentages of possibilities. So can forecasters actually predict the weather or are they not doing much more than just playing the odds?

Part of the answer appears trivially easy -- if the sun is shining and the only clouds in the sky are nice little puffy ones, then even we can predict that the weather for the afternoon will stay nice -- probably. So of course the weathermen are actually doing their jobs (tho' they do play the odds).

But in spite of the predictability of the weather -- at least in the short-term -- the atmosphere is in fact chaotic, not in the usual sense of "random, disordered, and unpredictable," but rather, with the technical meaning of a deterministic chaotic system, that is, a system that is ordered and predictable, but in such a complex way that its patterns of order are revealed only with new mathematical tools.

Page 48: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Who first studied deterministic chaos?Well, not so new. The French mathematical genius Poincaré studied the

problem of determined but apparently unsolvable dynamic systems a hundred years ago working with the three-body problem. And the American Birkhoff and many others also studied chaotic systems in various contexts.

But its principles were serendipitously rediscovered in the early 1960s by the meteorologist Edward Lorenz of MIT. While working with a simplified model in fluid dynamics, he solved the same equations twice with seemingly identical data, but the second run through, trying to save a little computer time, he truncated his data from six to three decimal places, thinking it would make no difference to the outcome. He was surprised to get totally different solutions. He had rediscovered "sensitive dependence on initial conditions."

A 2-D image of a Lorenz attractor. Lorenz went on to elaborate the principles of chaotic systems, and is now considered to be the father of this area of study. He is usually credited with having coined the term "butterfly effect" -- can the flap of a butterfly's wings in Brazil spawn a tornado in Texas?

Page 49: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Characteristics of a chaotic system

Deterministic chaotic behavior is found throughout the natural world -- from the way faucets drip to how bodies in space orbit each other; from how chemicals react to the way the heart beats; from the spread of epidemics of disease to the ecology of predator-prey relationships; and, of course, in the dynamics of the earth's atmosphere.

Page 50: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

Characteristics of a chaotic system (2)

Sensitive dependence on initial conditions -- starting from extremely similar but slightly different initial conditions they will rapidly move to different states. From this principle follow these two:

* exponential amplification of errors -- any mistakes in describing the initial state of a system will therefore guarantee completely erroneous results; and

* unpredictability of long-term behavior -- even extremely accurate starting data will not allow you to get long-term results: instead, you have to stop after a bit, measure your resulting data, plug them back into your model, and continue on.

Local instability, but global stability -- in the smallest scale the behavior is completely unpredictable, while in the large scale the behavior of the system "falls back into itself," that is, restabilizes.

Aperiodic -- the phenomenon never repeats itself exactly (tho' it may come close).

Non-random -- although the phenomenon may at some level contain random elements, it is not essentially random, just chaotic.

Page 51: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

How many models are there?

Today, worldwide, there are at least a couple of dozen computer forecast models in use. They can be categorized by their:

● resolution;● outlook or time-frame -- short-range, meaning

one to two days out, and medium-range going out from three to seven days; and

● forecast area or scale -- global (which usually means the Northern hemisphere), national, and relocatable.

Page 52: Simulating the Weather: Numerical Weather Prediction as Computational Simulation

How good are these models and the predictions based on them?

The short answer is, Not too bad, and a lot better than forecasting without them. The longer answer is in three parts:

* Some of the models are much better at particular things than others; for example, as the USA Today article points out, the AVN "tends to perform better than the others in certain situations, such as strong low pressure near the East Coast," and "the ETA has outperformed all the others in forecasting amounts of precipitation." For more on this subject, here's a slide show from NCEP.

* The models are getting better and better as they are validated, updated, and replaced -- the "new" MRF has replaced the old (1995), and the ETA is replacing the NGM.

* That's why they'll always need the weather man -- to interpret and collate the various computer predictions, add local knowledge, look out the window, and come up with a real forecast.