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

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

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

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

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.

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

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.