Scale-dependent localization: test with quasi-geostrophic models

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Presentation transcript:

Scale-dependent localization: test with quasi-geostrophic models Michael Ying Group meeting, Dec 2016

Motivation Localization distance: too large: suffer from sampling error too small: lose useful covariance information Higher model and observation resolution: Smaller optimal localization distance. shorter correlation length for small-scale dynamics; and more sampling error due to rank deficiency. Multi-scale localization (Zhang et al. 2009 SCL; Li et al. 2015; Miyoshi Kondo 2015; Buehner et al. 2015) In this study, I attempt to use simplified model to demonstrate the necessity of scale awareness in ensemble filtering.

Surface quasi-geostrophic model (SQG) 2D turbulence maintained by Markovian forcing from k=1~4 domain size: 256*256, maximum wavenumber k=128, cyclic boundary condition full animation (Held et al. 1995, Eq 2)

Kinetic energy spectra and predictability Reference power -5/3 Error power

Covariance structure at different scales All scales k=1~4 k=4~10 k=10~50 N=2000 N=200 N=20

Sampling error at each scale Sampling error = RMS Difference of using 20 and 2000 members

Scale dependency in analysis error Fixed localization distance l for all observation, 80 members, results from 1 cycle, observation resolution: Δobs=4 grid points; optimal l ? obs error reference power prior error analysis error with l = 5 15 30 50

Remedy of larger sampling error at small scale reference power prior error analysis error with obs thin: Δobs = 4 8 16 24 32 l = 2 Δobs Thinning observation Super observation Reduce impact for correlated obs using AOEI (Huber norm) SCL (Zhang et al. 2009) Cons: Losing information when throwing away observation / impact Better solution: treat analysis increment at each scale separately

One of the bred vectors (fast-growing error modes) local bred vector

Bred vector dimension (local effective dimension) Ψ members can span the subspace formed by the k bred vectors. Indicator of necessary ensemble size 1 of 20 bred vectors bred vector dimension

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