and Shaun Lovejoy Beyond the deterministic limit: GCMs Stochastic - - PowerPoint PPT Presentation

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and Shaun Lovejoy Beyond the deterministic limit: GCMs Stochastic - - PowerPoint PPT Presentation

Nov 07, 2023 1.46k likes •1.6k views

Using the ScaLINg Macroweather Model (SLIMM) to exploiting the atmospheres elephantine memory for long- term forecast Stochastic Seasonal to Interannual Prediction System Lenin Del Rio Amador and Shaun Lovejoy Beyond the deterministic

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SLIDE 1

Lenin Del Rio Amador and Shaun Lovejoy

Stochastic Seasonal to Interannual Prediction System

Using the ScaLINg Macroweather Model (SLIMM) to exploiting the atmosphere’s elephantine memory for long- term forecast

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SLIDE 2

scales <≈ 10 days prediction = initial value problem

(weather prediction)

“butterfly effect”

Weather systems generated by GCMs = random weather noise… but not fully realistic High level scaling laws generate realistic (empirically based) statistics (noise)

“Brute force”

Model climate Our climate

Averages: slow convergence to

Potential advantages of stochastic forecasting: a) More realistic weather “noise” ” (statistics: based on empirical data, not constrained by model). b) Ability to use empirical data to force convergence to the real climate

Beyond the deterministic limit: GCM’s Stochastic

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SLIDE 3

Preprocessing of the data:

Raw Data Remove Trend Remove Annual Cycle Anomalies

Ref: (NCEP/NCAR) Example for the grid point (-72.5, 47.5), Montreal

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SLIDE 4

Scaling LInear Macroweather model (SLIMM) Prediction of fGn

Gaussian noise

Kernel for H = -0,1.

Weight of the distant past Weight

  • f

present

  • Power law correlation. Vast memory that can be exploited.
  • Predictor for -0.5 < H < 0 based on past data.

predictor data kernel

𝑈 𝑢 =

−𝜐

𝐻𝐼,𝜐 𝑢, 𝑢′ 𝑈 𝑢′ 𝑒𝑢′

𝑈 𝑢 = 𝜏𝛿

−∞ 𝑢

𝑢 − 𝑢′ −

1 2−𝐼 𝛿 𝑢′ 𝑒𝑢′

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SLIDE 5
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

H 0.2 0.4 0.8 1.0 Sk

1 2 4 64

Dimensionless Forecast horizon/resolution l=t/t

Skill

Gaussian white noise: H= -0.5 H = 0: Pure “1/f” noise

Skill = 1- (Error variance)/(temperature variance)

Skill as a function of forecast lead time

Land Ocean

Global H = -0.085

0.6

58% (seasonal, hindcasts) 61% (monthly, hindcasts)

68% (theory analytical) 64% (theory numeric)

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SLIDE 6

References

  • Lovejoy, S. (2015), Using scaling for macroweather

forecasting including the pause, Geophys. Res. Lett., 42, 7148–7155 doi: DOI: 10.1002/2015GL065665.

  • Lovejoy, S., L. del Rio Amador, and R. Hébert ( 2015),

The ScaLIng Macroweather Model (SLIMM): using scaling to forecast global-scale macroweather from months to Decades, Earth Syst. Dynam., 6, 1–22 doi: http://www.earth-syst-dynam.net/6/1/2015/, doi:10.5194/esd-6-1-2015.