Analog forecasting errors from a dynamical systems point of view
Paul Platzer (feb. 10, 1993)IMT-A & RIKEN workshop :
Statistical Modeling and Machine Learningin Meteorology and Oceanography, feb. 10, 2020
IMT-A & RIKENFeb. 10, 2020
Paul Platzer2/20
Analog forecasting errors from a dynamical systems point of view
Paul Platzer (feb. 10, 1993)IMT-A & RIKEN workshop :
Statistical Modeling and Machine Learningin Meteorology and Oceanography, feb. 10, 2020
Marc Schoenauer,Naonori Ueda,Said Ouala,Maha Mdini…→ bridge the gap betweendata-driven andprocess-driven→ « 5th science »
Pierre Tandeo,Yicun ZhenAnDA
IMT-A & RIKENFeb. 10, 2020
Paul Platzer3/20
Two analog maps correspond to close points in phase space(Courtesy of D. Farandaand P. Yiou)
What is an analog ?
→ Introduced by Lorenzin 1969 for atmospheric predictability
IMT-A & RIKENFeb. 10, 2020
Paul Platzer4/20
● ak0 = analogs of x0 : « close » to x0
● akt successors ( time t ) → estimate xt
Analog forecasting : the idea
(Lguensat et al. 2017)
0 t
a10
aK-10aK0
a1t
aK-1taKt
IMT-A & RIKENFeb. 10, 2020
Paul Platzer5/20
Analog forecasting : cheap ML
IMT-A & RIKENFeb. 10, 2020
Paul Platzer6/20
Analog forecasting : in practice● Large database called « catalog » (reanalysis, model output) ● Select K nearest neighbors of x0 (fast thanks to ML libraries)● Assign weights to the analogs (discard bad analogs)● Apply a given analog forecasting operator
• • •
IMT-A & RIKENFeb. 10, 2020
Paul Platzer7/20
Analog forecasting operators
0
0
0
0 0
0 t
t
t
t
t
t
x0a10
a20
x0a10
a20
x0 a10
a20
x0
a20
a10
x0
a20
a10
x0
a20
a10
µLCa1t
a2t
µLIa1t
a2tµLLa1t
a2t
µLCa2t
a1t
µLI
a2t
a1t
µLL
a2t
a1t
(figure from Lguensat et al. 2017)
IMT-A & RIKENFeb. 10, 2020
Paul Platzer8/20
Dynamical systems● Hypotheses :
● Distance between successor and future state :
IMT-A & RIKENFeb. 10, 2020
Paul Platzer9/20
Dynamical systems● Here → looking at local error
→ similar to Nicolis et al. (2009)● Zhao and Giannakis (2016)
→ looking at global dynamical properties
IMT-A & RIKENFeb. 10, 2020
Paul Platzer10/20
Dynamical systems : mean error● Hypotheses :
● Mean error of analog forecasting operators :
IMT-A & RIKENFeb. 10, 2020
Paul Platzer11/20
Dynamical systems : mean error● Hypotheses :
● Mean error of analog forecasting :
→ experiments on L96 with δ=0
(figure from Lguensat et al. 2017)
IMT-A & RIKENFeb. 10, 2020
Paul Platzer12/20
Dynamical systems : mean error● Hypotheses :
● Mean error of analog forecasting :→experiments on L63 with δ=0
– LC empirical error-- LC error estimation– LI empirical error-- LI error estimation
(figure from Platzer et al. 2019)
IMT-A & RIKENFeb. 10, 2020
Paul Platzer13/20
Dynamical systems : mean error● Hypotheses :
● Mean error of analog forecasting :→experiments on L63 with δ=0
– LC -- LI-- LI+mean correction
-·-· LI+local correction(figure from Platzer et al. 2019)
IMT-A & RIKENFeb. 10, 2020
Paul Platzer14/20
Relation between operators● Locally-linear :
residuals
→
● Locally-constant, locally-incremental :
IMT-A & RIKENFeb. 10, 2020
Paul Platzer15/20
The locally-linear and the Jacobian
IMT-A & RIKENFeb. 10, 2020
Paul Platzer16/20
The locally-linear and the Jacobian
Mean error of LL forecast
Quality of Jacobian estimation using LL
IMT-A & RIKENFeb. 10, 2020
Paul Platzer17/20
What about the covariance ?
IMT-A & RIKENFeb. 10, 2020
Paul Platzer18/20
What about the variance ?
LC (Lguensat estimation)LC (empirical from several catalogs)LI (Lguensait estimation)LI (empirical from several catalogs)
→ Experiments on L63
IMT-A & RIKENFeb. 10, 2020
Paul Platzer19/20
What about the variance ?(logscale)
occu
ren c
es
IMT-A & RIKENFeb. 10, 2020
Paul Platzer20/20
Conclusion● Analog forecasting = empirical, simple ML● Using dynamical systems helps
→ interpretation→ error estimation→ data-based + model-based hybrid method ?→ finer tuning ?
● Combine analogs and NN ? (analogs=first guess)
IMT-A & RIKENFeb. 10, 2020
Paul Platzer21/20
Thank you !Bibliography :• Lguensat, R., Tandeo, P., Ailliot, P., Pulido, M., & Fablet, R. (2017). The analog data assimilation. Monthly Weather Review, 145(10), 4093-4107.• Lorenz, E. N. (1969). Atmospheric predictability as revealed by naturally occurring analogues. Journal of the Atmospheric sciences, 26(4), 636-646.• Nicolis, C., Perdigao, R. A., & Vannitsem, S. (2009). Dynamics of prediction errors under the combined effect of initial condition and model errors. Journal of the atmospheric sciences, 66(3), 766-778.• Platzer, P., Yiou, P., Tandeo, P., Naveau, P., & Filipot, J. F. (2019, October). Predicting Analog Forecasting Errors using Dynamical Systems.• Tippett, M. K., & DelSole, T. (2013). Constructed analogs and linear regression. Monthly Weather Review, 141(7), 2519-2525.• Zhao, Z., & Giannakis, D. (2016). Analog forecasting with dynamics-adapted kernels. Nonlinearity, 29(9), 2888.
Diapo 1Diapo 2Diapo 3Diapo 4Diapo 5Diapo 6Diapo 7Diapo 8Diapo 9Diapo 10Diapo 11Diapo 12Diapo 13Diapo 14Diapo 15Diapo 16Diapo 17Diapo 18Diapo 19Diapo 20Diapo 21
Top Related