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

Observation Impact on Forecasts for lead-times beyond 24–hours Rahul Mahajan 12 Ronald Gelaro 1 Ricardo Todling 1 6 th 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 g f b a t 0 t � � �� ∂ J g ∂ J f δ e g ( y − Hx b ) , K T M T + M T f = t , t 0 t , t 0 ∂ x g ∂ x f Langland and Baker 2004 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 δ x 0 is given as: δ x i = M i δ x 0 SB12 proposed a combination of TL model integrations each linearized about a slightly different nonlinear model trajectory: J � � x b 0 + β j δ x a � δ x i = α j M i δ x 0 0 j =1 where ( α j , β j ) correspond to Gaussian Quadrature terms. Here, we employ j = 1, such that ( α 1 , β 1 ) = (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 TL AGCM Goddard-developed physics Simplified physics: vertical diffusion & surface drag Interactive ozone & GOCART aerosols Simplified moist parameterization, when OSTIA-prescribed SST & applicable SeaICE Resolution: 0.5 x 0.625 x 72 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 ( x b + δ x a ) − M ( x b ) , M δ x a ) GQ = 0 GQ = 1 b b a a t 0 t t 0 t M is linearized about background M is linearized about averaged trajectory trajectory RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

TLM Correlations at Forecast hour = 24 T U 0" 1" RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

TLM Correlations at Forecast hour = 48 T U 0" 1" RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

GEOS DAS & Observation Impact Configuration Atmospheric GCM Adjoint AGCM Goddard-developed full physics Simplified physics (vert. diffusion & Interactive ozone & GOCART drag) aerosols OSTIA-prescribed SST & SeaICE Simplified moist param. (when appl.) Resolution: 0.5 x 0.625 x 72 Resolution: 1 x 1.25 x 72 Atmospheric analysis: GSI Backward analysis: GSI Double-PCG minimization SQRT(B)-PCG minimization Resolution: 0.5 x 0.625 x 72 RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

Observation Impact � � ∂ J g ∂ J f �� δ e g ( y − Hx b ) , K T M T + M T f = t , t 0 t , t 0 ∂ x g ∂ x f GQ = 0 GQ = 1 g g f f b b a a t 0 t 0 t t � ∂ J g � ∂ J g ∂ J f + ∂ J f M T + M T M T t , t 0 t , t 0 t , t 0 ∂ x g ∂ x f ∂ x g ∂ x f RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

Observation impact recovered at Forecast hr = 24 0 ¡ 1 ¡ RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

Observation impact recovered at Forecast hr = 48 0 ¡ 1 ¡ RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours

Observation impact recovered Percent of Obs Impact recovered 140 120 Recovered Obs Impact (%) 100 80 60 40 20 Control+Dry Quadrature+Dry Control+Moist Quadrature+Moist 0 24 48 72 Forecast lead time (hours) 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 observation impact estimate as well as saves on one adjoint integration. RM RG RT Observation Impact on Forecasts for lead-times beyond 24–hours