Brett Hoover Michael Morgan University of Wisconsin - Madison 5 May 2009

1. 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

2. An Adjoint-Based Targeting Strategy 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.

3. An Adjoint-Based Targeting Strategy 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

4. 6 9 Steering Response Function R1 = Average zonal wind in a box centered on the TC:

5. 6 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

6. 6 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

7. What Happens to the “Environmental Flow”? 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

8. What Happens to the “Environmental Flow”? 1. Vorticity and Divergence …

9. What Happens to the “Environmental Flow”? 1. Vorticity and Divergence … are removed from response function box

10. What Happens to the “Environmental Flow”? • Vorticity and Divergence … are removed from response function box • Streamfunction and velocity potential are calculated from “environment”

11. What Happens to the “Environmental Flow”? • Vorticity and Divergence … are removed from response function box • Streamfunction and velocity potential are calculated from “environment” • Environmental flow is calculated

12. What Happens to the “Environmental Flow”? “Environmental flow” for control run “Environmental flow” for run with perturbed initial conditions Perturbation “environmental flow” (perturbed – control)

13. 6 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

14. 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

15. R1 Perturbation RE1 Perturbation 6 6 9 9 6 9 Perturbations to the “environmental flow” are significantly different

16. R1 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

17. 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