Observation Impact on Forecasts for lead-times beyond 24hours Rahul - - PowerPoint PPT Presentation

Observation Impact on Forecasts for lead-times beyond 24–hours

Rahul Mahajan12 Ronald Gelaro1 Ricardo Todling1 6th WMO Symposium on Data Assimilation College Park, MD, USA October 2013

Overview

Why extend impact calculation beyond 24-hours? How would one go about doing so? Validation of technique Observation impact estimates Summary

RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

Observation Impact

Langland and Baker 2004

a b t0 t g f δeg

f =

• (y − Hxb) , KT
• MT

t,t0

∂Jg ∂xg + MT

t,t0

∂Jf ∂xf

• RM RG RT

Observation Impact on Forecasts for lead-times beyond 24–hours

Why extend impact calculation beyond 24–hours?

At present, observation impacts are operationally calculated at 24 hours. As the quality of the analysis and forecasts improve, it is getting difficult to distinguish between the two errors at short lead times. At shorter lead times, there is a strong correlation between the forecast error and the analysis error. At longer lead times, as the forecast error grows non-linearly, the two quantities de-correlate. Thus, one should be computing impacts at longer lead times, but are limited to reliability of the tools used.

RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

Extending impact calculation beyond 24–hours?

Reliability of results from observation impact calculations beyond 24 hours depends on the validity of the adjoint (AD) integration, which in turn depends on the tangent-linear (TL) approximations. TL (AD) reliability depends on complexity of the underlying linearized dynamics simplifications made to physics, resolution, etc. Stappers and Barkmeijer (2012) [SB12] proposed a way to improve the TL (AD) linearization approximation.

RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

Gaussian Quadrature

The TL model integration of an initial perturbation δx0 is given as: δxi = Miδx0 SB12 proposed a combination of TL model integrations each linearized about a slightly different nonlinear model trajectory: δxi =

J

• j=1

αjMi

• xb

0 + βjδxa

• δx0

where (αj, βj) correspond to Gaussian Quadrature terms. Here, we employ j = 1, such that (α1, β1) = (1, 1

2)

RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

GEOS-5 Atmospheric GCM and its TLM

GEOS-5 AGCM Goddard-developed physics Interactive ozone & GOCART aerosols OSTIA-prescribed SST & SeaICE Resolution: 0.5 x 0.625 x 72 TL AGCM Simplified physics: vertical diffusion & surface drag Simplified moist parameterization, when applicable Resolution: 0.5 x 0.625 x 72

RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

TLM Validation

correlation (M (xb + δxa) − M (xb) , Mδxa) GQ = 0

a b t0 t

M is linearized about background trajectory GQ = 1

a b t0 t

M is linearized about averaged trajectory

RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

TLM Correlations at Forecast hour = 24

U

1" 0"

T

RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

TLM Correlations at Forecast hour = 48

U

1" 0"

T

RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

GEOS DAS & Observation Impact Configuration

Atmospheric GCM

Goddard-developed full physics Interactive ozone & GOCART aerosols OSTIA-prescribed SST & SeaICE Resolution: 0.5 x 0.625 x 72

Atmospheric analysis: GSI

Double-PCG minimization Resolution: 0.5 x 0.625 x 72

Adjoint AGCM

Simplified physics (vert. diffusion & drag) Simplified moist param. (when appl.) Resolution: 1 x 1.25 x 72

Backward analysis: GSI

SQRT(B)-PCG minimization

RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

Observation Impact

δeg

f =

• (y − Hxb) , KT
• MT

t,t0

∂Jg ∂xg + MT

t,t0

∂Jf ∂xf

• GQ = 0

a b t0 t g f

MT

t,t0

∂Jg ∂xg + MT

t,t0

∂Jf ∂xf GQ = 1

a b t0 t g f

MT

t,t0

∂Jg ∂xg + ∂Jf ∂xf

• RM RG RT

Observation Impact on Forecasts for lead-times beyond 24–hours

Observation impact recovered at Forecast hr = 24

1 ¡ 0 ¡

RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

Observation impact recovered at Forecast hr = 48

1 ¡ 0 ¡

RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

Observation impact recovered

24 48 72 Forecast lead time (hours) 20 40 60 80 100 120 140 Recovered Obs Impact (%)

Percent of Obs Impact recovered

Control+Dry Control+Moist Quadrature+Dry Quadrature+Moist

RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

Observation impact

RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

But,

RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

Summary

The correlations suggest that the TLM seems to be valid at 48-hours, thus an adjoint-based impact at those lead times is viable. Using the averaged-trajectory GQ=1 / Quadrature yeilds improved correlations as compared to single trajectory GQ=0 / Control. Fraction of observation impact at 48 hours is similar to that at 24 hours, however there is a larger uncertainity in the estimate. The observation impact at 48-hours in most observing systems seem to be roughly twice than that at 24-hours. Radiosondes and Satellite winds show differently (not shown). Using an averaged trajectory approach yields slight improvement in

• bservation impact estimate as well as saves on one adjoint

integration.

RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours