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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

  1. Using the ScaLINg Macroweather Model (SLIMM) to exploiting the atmosphere’s elephantine memory for long- term forecast Stochastic Seasonal to Interannual Prediction System Lenin Del Rio Amador and Shaun Lovejoy

  2. Beyond the deterministic limit: GCM’s Stochastic scales <≈ 10 days prediction = initial value problem (weather prediction) “Brute force” “butterfly effect” Weather systems generated by GCMs = random weather noise … but not fully realistic Averages: slow convergence to High level scaling laws Model generate realistic climate (empirically based) Our climate statistics (noise) 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

  3. Preprocessing of the data: Ref: (NCEP/NCAR) Example for the grid point (-72.5, 47.5), Montreal Raw Data Remove Trend Anomalies Remove Annual Cycle

  4. Scaling LInear Macroweather model (SLIMM) Prediction of fGn 𝑢 1 2−𝐼 𝛿 𝑢 ′ 𝑒𝑢 ′ 𝑢 − 𝑢 ′ − 𝑈 𝑢 = 𝜏 𝛿 −∞ Gaussian noise • Power law correlation. Vast memory that can be exploited. • Predictor for -0.5 < H < 0 based on past data. kernel 0 Weight 𝐻 𝐼,𝜐 𝑢, 𝑢 ′ 𝑈 𝑢 ′ 𝑒𝑢 ′ 𝑈 𝑢 = of −𝜐 present Weight of the data predictor distant past Kernel for H = -0,1.

  5. Skill 1.0 Skill as a function of forecast lead time S k Skill = 1- (Error variance)/(temperature variance) 0.8 68% (theory analytical) 64% (theory numeric) 0.6 61% (monthly, hindcasts) 58% (seasonal, hindcasts) Global H = -0.085 0.4 Dimensionless 1 Forecast 2 horizon/resolution 4 l =t/ t 0.2 Gaussian white noise: 64 H= -0.5 - 0.4 - 0.3 - 0.2 - 0.1 - 0.5 H H = 0: Pure “ 1/f ” noise Land Ocean

  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.

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