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Global Modeling and Assimilation Officegmao.gsfc.nasa.govGMAO
National Aeronautics and Space Administration
How much model error in a 6h Ensemble forecast?
Amal EL Akkraoui1,2, Ricardo Todling1, Ron Errico1,3
1 NASA-Global Modeling and Assimilation office (GMAO) 2 Science Systems and Applications, Inc. (SSAI)
3 Morgan State University
Global Modeling and Assimilation Officegmao.gsfc.nasa.govGMAO
National Aeronautics and Space Administration
Motivation
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Days
Ensemble spread Uwnd, 500hPa
5-day
6h
• Accepted idea: a good ensemble isable to represent the time evolutionof the uncertainty, and that itimplicitly accounts for both the initialcondition and model errors in what itencompasses as forecast error.
• Can a short 6h model integrationcapture/accurately represent themodel error component of theforecast error?
Global Modeling and Assimilation Officegmao.gsfc.nasa.govGMAO
National Aeronautics and Space Administration
Motivation
Assim
ilatio
n w
indo
w
Uwind
0 6 12 24 48 72hours
Different perturbation / initialization scenarios! Same growth shape.
Global Modeling and Assimilation Officegmao.gsfc.nasa.govGMAO
National Aeronautics and Space Administration
Ensemble-Variational Hybrid 4DEnVar
Modern
Sophisticated
Complex
Complicated
Unsustainable?
Global Modeling and Assimilation Officegmao.gsfc.nasa.govGMAO
National Aeronautics and Space Administration
Filter-Free hybrid scheme
Vertical correlations
Temperature ~830mb
Vert
ical l
evel
s
Vertical correlations
N. Hemisphere Tropics S. Hemisphere
- - - - - EnKF-based ensemble _____ Filter-Free ensemble
Global Modeling and Assimilation Officegmao.gsfc.nasa.govGMAO
National Aeronautics and Space Administration
Vert
ical l
evel
s
Vert
ical l
evel
s
Hybrid 3DVar (S-EnKF)) Hybrid 3DVar (Filter-free)
Hybrid 3DVar / Control 3DVar
Innovation statistics
(Uwind tropics) BIAS
RMS RMS
BIAS
Filter-Free hybrid scheme
Global Modeling and Assimilation Officegmao.gsfc.nasa.govGMAO
National Aeronautics and Space Administration
It’s all about representing uncertainties within the assimilation window
Uncertainties in initial conditions(Additive inflation)
Uncertainties in model representation of certain processes (SPPT, SKEB)
Global Modeling and Assimilation Officegmao.gsfc.nasa.govGMAO
National Aeronautics and Space Administration
Forecast differences {f48-f24}
Stochastically perturbed Physics Tendencies
Stochastic kinetic Energy Backscattter
Tendency DTDT Physics, 700 mb (K/day)
Zonal mean NMC-pert RMS – Uwnd
Kinetic Energy rotational wind
Global Modeling and Assimilation Officegmao.gsfc.nasa.govGMAO
National Aeronautics and Space Administration
Ensemble spread (at 6h, 1d, 5d) : Zonal mean - U Wind 6h 1 day 5 days
SKEB
SPPT
AINF
SKEB
SPPT
AINF
SKEB
SPPT
AINF
Mod
el le
vels
Latitudes Latitudes Latitudes
Global Modeling and Assimilation Officegmao.gsfc.nasa.govGMAO
National Aeronautics and Space Administration
Spectral decomposition of ensemble variance (at 6h, and 5d) 5 days6h
Temperature Humidity
Vorticity Divergence
Varia
nce
Wavenumber Wavenumber
Wavenumber Wavenumber Wavenumber Wavenumber
Wavenumber Wavenumber
Varia
nce
Varia
nce
Va
rianc
e
Temperature Humidity
Vorticity Divergence
Global Modeling and Assimilation Officegmao.gsfc.nasa.govGMAO
National Aeronautics and Space Administration
Ensemble size
96 vs 32
6h 5d
Wave number Wave number
Spectral decomposition of ensemble variance (at 6h, and 5d)
Vorticity variance Vorticity variance
Global Modeling and Assimilation Officegmao.gsfc.nasa.govGMAO
National Aeronautics and Space Administration
Are we any closer to representingmodel error?
Observations at the end of thewindow are weighed against a“converged climatology” of the errorstatistics.
6h
24h
What about a long-window Hybrid 4D-EnVar?
Global Modeling and Assimilation Officegmao.gsfc.nasa.govGMAO
National Aeronautics and Space Administration
Discussion points
§ The simplified scheme (filter-free) may help mitigate the need to maintain two full-scale DAsystems. We will be exploring more ways to create and propagate the initial perturbations.
§ Regardless of the type of perturbations (additive inflation, stochastic physics), the ensemblespread tends quickly toward a converged climatology of the forecast error; the same used tocreate the climatological NMC-based background error statistics.
§ Perturbations affect the spread at different scales within the first hours of the forecast.§ From day-1 onwards, all cases saturate to the same structure as the NMC-perturbations.
§ Similar to the need to question the validity of the tangent linear approximation and thestrong constraint in a long window assimilation, we also need to be mindful of theinterpretations we attribute to ensembles and their properties.
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