BrineTaiwan
歡迎來教我 我想變電神
Weather ForeCast
Using computer science to solve atmospheric science problems.
Index
DifficultY
What makes weather forecasting such a hard task?
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Deterministic Systems
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Sensitive to initial conditions
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Topologically transitive
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Dense periodic orbits
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Chaos
Chaos
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Deterministic Systems
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Sensitive to initial conditions
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Topologically transitive
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Dense periodic orbits
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Weather is a chaotic dynamic system
〞
When the present determines the future, but the approximate present does not approximately determine the future.
– Edward Lorenz
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We may predict the weather if we have 100% accuracy
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We simply can't
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The world is too big
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People move
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Uncertainty principle
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data measuring
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Lyapunov time
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Difference grows exponentially
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Make forecasts that have acceptable, tiny errors
What can we do?
our method
How do we predict the weather?
History of weather prediction
How did we get here?
1904
Vilhelm Bjerknes formulated the primitive equations
1922
Lewis Fry Richardson tried to produce a forecast by hand
1950
The ENIAC was used to approximate the weather with simplified equations
1960s
Operational forecasts based on primitive equation models were made
1956
Norman Phillips developed the first successful climate model
1970s
Tracks of tropical cyclones and air quality
can be better predicted
1980s
Soil and vegetation were accounted for
1990s
Model ensemble forecasts have been used
present
The accuracy of forecasts can be acceptable for up to 14 days
Primitive equations
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A set of non linear partial differential equations
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A continuity equation
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Conservation of momentum
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A thermal energy equation
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Fundamentals of many atmospheric models
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First general-purpose computer
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Turing complete
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Programmable
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$487,000 USD($5,900,000 USD now)
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60 cubic metres
eniac
Ensemble forecasting
- The more, the merrier
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Monte Carlo method
- Randomness
- Used in many physical simulations
- High hardware requirements
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Uncertainties
- Observational error
- Imperfect model
- Any dynamical system forecast
supercomputers
They compute, perhaps faster than you can imagine
performance measuring
- FLOPS(floating point operations per second)
- IPS(instructions per second)
10^{17} \footnotesize FLOPS
10^{12} \footnotesize FLOPS
What else?
Limitations
speed
Data can't be transmissed faster than the speed of light.
heat
The generated heat could damage the machine.
power
It's very energy intensive.
solutions
speed
Circular design to minimise route.
heat
Water cooling and other liquids.
power
Lower the temperature to increase performance.
Weather forecasts in taiwan
Central Weather Bureau
supercomputer(Gen 5)
- Made by Fujitsu
- around 1.46 PFLOPS
- Replaced with a new one with 10 PFLOPS
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Resolution: 3 km -> 1 km
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Time: 7 days -> 10-14 days
accuracy
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Run many simulation
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Different initial values
ensemble system
End of presentation
Thank you for listening
questions
Are you ready for the suffering in the finals?
p1: Which one isn't turing complete?
- Lambda calculus
- ENIAC
- C++
- Primitive equations
p2-1
Give an example of Monte Carlo method.
p2-2
What is the spirit of Monte Carlo method? (1 word)
p3: Which one isn't in the primitive equations?
(1): \oint_{\partial \Sigma} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell} = - \frac{\mathrm{d}}{\mathrm{d}t} \iint_{\Sigma} \mathbf{B} \cdot \mathrm{d}\mathbf{S}
(2): 0 = -\frac{\partial \Phi}{\partial p} - \frac{RT}{p}
(3):\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial p} = 0
(4):\frac{\partial T}{\partial t} = \frac{\partial T}{\partial t} + u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} + w \frac{\partial T}{\partial z}
DW
Q4: spell the name of the father of computer science
DH
BC
CSxAS
By BrineTaiwan
CSxAS
It'd be great to turn in two homeworks with one presentation
