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Application of Adjoint-Derived Sensitivity Gradients to Targeted Observations for Tropical Cyclone Steering: An Improved Methodology. Brett Hoover Michael Morgan University of Wisconsin - Madison 5 May 2009. An Adjoint-Based Targeting Strategy. assimilation system. forecast model. - PowerPoint PPT Presentation
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Application of Adjoint-Derived Sensitivity Gradients to Targeted
Observations for Tropical Cyclone Steering: An Improved Methodology
Brett HooverMichael Morgan
University of Wisconsin - Madison5 May 2009
R
y,R
xb
R
xa
R
x f
y,xb
xa
x f
R
adjoint of forecastmodel
adjoint of assimilation system
forecast modelassimilation system
ob’s and bkgrndanalysis forecast
sensitivity to ob’s and background
sensitivity to analysis sensitivity to forecast
An Adjoint-Based Targeting Strategy
Sensitivities of steering to the (potential) observations are informed by the sensitivities to the analysis, the characteristics of the analysis errors, and the nature of the assimilation system.
R
xa
R
x f
xa
x f
R
adjoint of forecastmodel
forecast model
analysis forecast
sensitivity to analysis sensitivity to forecast
An Adjoint-Based Targeting Strategy
The focus of this talk: “How to define best the response function, R?”
Steering Response Function
R1 850
300A
u dx dy
850
300A
dx dy
R1 = Average zonal wind in a box centered on the TC:
69
Steering Response Function
R1 850
300A
u dx dy
850
300A
dx dy
R1 represents the zonal steering of the TC only when the TC is centered in the response function box, with the symmetric circulation around the TC being canceled out
R1 = Average zonal wind in a box centered on the TC:
69
Steering Response Function
R1 850
300A
u dx dy
850
300A
dx dy
A northward displacement of the TC will result in a positive contribution to zonal flow in the box
R1 = Average zonal wind in a box centered on the TC: 69
What Happens to the “Environmental Flow”?
R1
'
r V 'env
Use NOGAPS adjoint model to calculate sensitivity of R1 with respect to vorticity
Scale sensitivities at 500 hPa to define perturbations to vorticity at initialization
Calculate perturbation to “environmental wind” between perturbed and control run
What Happens to the “Environmental Flow”?
1. Vorticity and Divergence … are removed from response function box
r V 'env
What Happens to the “Environmental Flow”?
1. Vorticity and Divergence … are removed from response function box
2. Streamfunction and velocity potential are calculated from “environment”
r V 'env
What Happens to the “Environmental Flow”?
1. Vorticity and Divergence … are removed from response function box
2. Streamfunction and velocity potential are calculated from “environment”
3. Environmental flow is calculated
r V 'env
What Happens to the “Environmental Flow”?
“Environmental flow” for control run
“Environmental flow” for run with perturbed initial conditions
Perturbation “environmental flow” (perturbed – control)
r V 'env
What Happens to the “Environmental Flow”?
Perturbing the model using sensitivities for R1 results in a perturbation environmental flow with a strong southerly component
This southerly advection pushes the TC slightly north of the center of the response function box, allowing the TC’s own circulation to contribute positively to the response function
69
We Need a New Response Function…
• Sensitivities of R1 are largely influenced by small perturbations to the final-time location of the TC in the response function box
• This is evidenced by a strong southerly component to the environmental flow advecting the TC
• Why not just use the environmental flow as our response function? RE1
RE1 PerturbationR1 Perturbation
69
Perturbations to the “environmental flow” are significantly different
69 69
69
RE1 PerturbationR1 Perturbation
Perturbations to the “environmental flow” are significantly differentR1 perturbations create a southerly advecting flow, while RE1 perturbations create a purely zonal advecting flow
69 69
Conclusions
• Adjoint models, coupled with measures of statistical uncertainty in initial conditions, can be used to objectively define targeting regions for adaptive observations to improve specific aspects of a model forecast (e.g. TC steering)
• Response functions currently employed to define TC steering suffer from a complication: perturbations to the final-time location of the TC greatly influence these response functions
• New response functions defining the “environmental flow” in the vicinity of the TC can alleviate this problem