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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.

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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 Targeted Observations for Tropical Cyclone Steering: An Improved Methodology

assimilation system

forecast model

ob’s and bkgrnd

analysis

forecast

adjoint of assimilation system

adjoint of forecast

model

sensitivity

to forecast

sensitivity to ob’s and background

sensitivity to analysis

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.


An Adjoint-Based Targeting Strategy Targeted Observations for Tropical Cyclone Steering: An Improved Methodology

forecast model

analysis

forecast

The focus of this talk: “How to define best the response function, R?”

adjoint of forecast

model

sensitivity

to forecast

sensitivity to analysis


Steering response function

6 Targeted Observations for Tropical Cyclone Steering: An Improved Methodology

9

Steering Response Function

R1 = Average zonal wind in a box centered on the TC:


Steering response function1

6 Targeted Observations for Tropical Cyclone Steering: An Improved Methodology

9

Steering Response Function

R1 = Average zonal wind in a box centered on the TC:

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


Steering response function2

6 Targeted Observations for Tropical Cyclone Steering: An Improved Methodology

9

Steering Response Function

R1 = Average zonal wind in a box centered on the TC:

A northward displacement of the TC will result in a positive contribution to zonal flow in the box


What happens to the environmental flow
What Happens to the “Environmental Flow”? Targeted Observations for Tropical Cyclone Steering: An Improved Methodology

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 flow1
What Happens to the “Environmental Flow”? Targeted Observations for Tropical Cyclone Steering: An Improved Methodology

1. Vorticity and Divergence …


What happens to the environmental flow2
What Happens to the “Environmental Flow”? Targeted Observations for Tropical Cyclone Steering: An Improved Methodology

1. Vorticity and Divergence … are removed from response function box


What happens to the environmental flow3
What Happens to the “Environmental Flow”? Targeted Observations for Tropical Cyclone Steering: An Improved Methodology

  • Vorticity and Divergence … are removed from response function box

  • Streamfunction and velocity potential are calculated from “environment”


What happens to the environmental flow4
What Happens to the “Environmental Flow”? Targeted Observations for Tropical Cyclone Steering: An Improved Methodology

  • Vorticity and Divergence … are removed from response function box

  • Streamfunction and velocity potential are calculated from “environment”

  • Environmental flow is calculated


What happens to the environmental flow5
What Happens to the “Environmental Flow”? Targeted Observations for Tropical Cyclone Steering: An Improved Methodology

“Environmental flow” for control run

“Environmental flow” for run with perturbed initial conditions

Perturbation “environmental flow” (perturbed – control)


What happens to the environmental flow6

6 Targeted Observations for Tropical Cyclone Steering: An Improved Methodology

9

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


We need a new response function
We Need a New Response Function… Targeted Observations for Tropical Cyclone Steering: An Improved Methodology

  • 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


R Targeted Observations for Tropical Cyclone Steering: An Improved Methodology1 Perturbation

RE1 Perturbation

6

6

9

9

6

9

Perturbations to the “environmental flow” are significantly different


R Targeted Observations for Tropical Cyclone Steering: An Improved Methodology1 Perturbation

RE1 Perturbation

6

6

9

9

6

9

Perturbations to the “environmental flow” are significantly different

R1 perturbations create a southerly advecting flow, while RE1 perturbations create a purely zonal advecting flow


Conclusions
Conclusions Targeted Observations for Tropical Cyclone Steering: An Improved Methodology

  • 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


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