How much model error in a 6h Ensemble forecast? · GMAO gmao.gsfc.nasa.gov National Aeronautics and Space Administration Forecast differences {f48-f24} Stochastically perturbed Physics

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



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?



Motivation

Assim

ilatio

n w

indo

w

Uwind

0 6 12 24 48 72hours

Different perturbation / initialization scenarios! Same growth shape.



Ensemble-Variational Hybrid 4DEnVar

Modern

Sophisticated

Complex

Complicated

Unsustainable?



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



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



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)



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



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



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



Ensemble size

96 vs 32

6h 5d

Wave number Wave number

Spectral decomposition of ensemble variance (at 6h, and 5d)

Vorticity variance Vorticity variance



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?



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.

Documents

How much model error in a 6h Ensemble forecast? · GMAO gmao.gsfc.nasa.gov National Aeronautics and Space Administration Forecast differences {f48-f24} Stochastically perturbed Physics