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

Ry, Rxb

Rxa

Rx 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.

Rxa

Rx 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:

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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:

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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:

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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

TC Steering• Simulation of Typhoon Meari (2004) at

T159L30 resolution:

Sensitivity of R1 with respect to vorticity at 500 hPa

Perturbation vorticity added to model initial conditions at 500 hPa

From Hoover (2009) Comments on “Interaction of Typhoon Shanshan (2006) with the Midlatitude Trough from both Adjoint-Derived Sensitivity Steering Vector and Potential Vorticity Perspectives”8

TC Steering• At the final time, perturbation zonal flow in the response

function box is largely due to a northward translation of the TC.

Perturbation heights at 500 hPa Perturbation zonal flow at 500 hPaFrom Hoover (2009) Comments on “Interaction of Typhoon Shanshan (2006) with the Midlatitude Trough from both Adjoint-Derived Sensitivity Steering Vector and Potential Vorticity Perspectives”

9

What Happens to the “Environmental Flow”?

1. Vorticity and Divergence …

r V 'env

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

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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

New Steering Response Function

R1

at 300 hPa for NOGAPS simulation of Typhoon Meari (2004) (36 hour integration)

RE1

at 300 hPa for NOGAPS simulation of Typhoon Meari (2004) (36 hour integration)

RE1 PerturbationR1 Perturbation

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Perturbations to the “environmental flow” are significantly different

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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

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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

Interpretation

*From Wu et al. 2007. Targeted observations of tropical cyclone movement based on the adjoint-derived sensitivity steering vector. J. Atmos. Sci. 64, 2611-2626.

MM5 simulation of Typhoon Minduelle (2004)* (12 hour integration)

2-D barotropic, non-divergent simulation of idealized vortex (24 hour integration)