Abstract
Structures of adjoint sensitivities to potential vorticity for specific initial and final norm are investigated for a short-range cyclone forecast in a three-dimensional quasigeostrophic (QG) model. Moreover, adjoint sensitivities to potential vorticity are compared with nonlinear sensitivities calculated for the same cyclogenesis case in the QG model. The adjoint sensitivities using different initial and final norms (e.g., total QG disturbance energy and potential enstrophy) show approximately similar characteristics for the horizontal and vertical structures and evolutions. Consistent with previous studies, the horizontal structure of the adjoint sensitivity is smaller for the energy norm than for the potential enstrophy norm. The dynamical mechanism of cyclone development by adjoint sensitivity coincides with that of nonlinear sensitivity, with slight differences in the region of sensitivity maxima over the upstream (nascent) low for the adjoint (nonlinear) sensitivity. The adjoint sensitivities show different vertical distributions from the nonlinear sensitivities. Consistent with the sensitive regions denoted by singular vectors and error evolution in the QG model, maxima of the adjoint sensitivities are located at both the upper and lower boundaries, with prominent secondary peaks in the lower to mid-troposphere of the domain. The level of the secondary maxima changes depending on the initial and final norm used. The secondary peak is located in the lower to mid- (mid-) troposphere for the total QG disturbance energy (potential enstrophy) as the initial and final norm. Based on the correspondence in the level of the sensitivity maxima in the interior of the domain between the adjoint and nonlinear sensitivities, adjoint sensitivities may serve as an alternative to nonlinear sensitivities given the enormous computing expenses in nonlinear sensitivity calculation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ancell BC, Mass CF (2008) The variability of adjoint sensitivity with respect to model physics and basic-state trajectory. Mon Wea Rev 136:4612–4628
Arbogast P (1998) Sensitivity to potential vorticity. Quart J Roy Meteorol Soc 124:1605–1615
Baker NL, Daley R (2000) Observation and background sensitivity in the adaptive observation-targeting problem. Quart J Roy Meteorol Soc 126:1431–1454
Beare RJ, Thorpe AJ, White AA (2003) The predictability of extratropical cyclones: nonlinear sensitivity to localized potential-vorticity perturbations. Quart J Roy Meteorol Soc 129:219–237
Bergot T (1999) Adaptive observations during FASTEX: a systematic survey of upstream flights. Quart J Roy Meteorol Soc 125:3271–3298
Bergot T, Hello G, Joly A, Malardel S (1999) Adaptive observations: a feasibility study. Mon Wea Rev 127:743–765
Bretherton FP (1966) Critical layer instability in baroclinic flows. Quart J Roy Meteorol Soc 92:325–334
Errico RM (1997) What is an adjoint model? Bull Am Meteorol Soc 78:2577–2591
Gill AE (1982) Atmosphere–ocean dynamics. Academic Press, New York, p 662
Hakim GJ (2000) Role of nonmodal growth and nonlinearity in cyclogenesis initial-value problems. J Atmos Sci 57:2951–2967
Hamill TM, Snyder C, Morss RE (2002) Analysis-error statistics of a quasigeostrophic model using three-dimensional variational assimilation. Mon Wea Rev 130:2777–2791
Hoskins BJ, McIntyre ME, Robertson AW (1985) On the use and significance of isentropic potential vorticity maps. Quart J Roy Meteorol Soc 111:877–946
Jung B-J, Kim HM (2009) Moist-adjoint based forecast sensitivities for a heavy snowfall event over the Korean peninsula on 4–5 March 2004. J Geophys Res 114:D15104. doi:10.1029/2008JD011370
Kim HM (2002) Diagnosis of error growth and propagation: Implications for adaptive observations. Ph.D. thesis, University of Wisconsin-Madison, 197 pp. (Available from Memorial Library, 728 State St., Madison, WI 53706)
Kim HM (2003) A computation of adjoint-based sensitivities in a quasigeostrophic model. Kor J Atmos Sci 6(2):71–83
Kim HM, Jung B-J (2006) Adjoint-based forecast sensitivities of Typhoon Rusa. Geophys Res Lett 33:L21813. doi:10.1029/2006GL027289
Kim HM, Morgan M (2002) Dependence of singular vector structure and evolution on the choice of norm. J Atmos Sci 59:3099–3116
Kim HM, Morgan M, Morss RE (2004) Evolution of analysis error and adjoint-based sensitivities: implications for adaptive observations. J Atmos Sci 61:795–812
Kleist DT, Morgan M (2005) Interpretation of the structure and evolution of adjoint-derived forecast sensitivity gradients. Mon Wea Rev 133:466–484
Langland RH, Shapiro MA, Gelaro R (2002) Initial condition sensitivity and error growth in forecasts of the 25 January 2000 east coast snowstorm. Mon Wea Rev 130:957–974
Majumdar SJ, Aberson SD, Bishop CH, Buizza R, Peng MS, Reynolds CA (2006) A comparison of adaptive observing guidance for Atlantic tropical cyclones. Mon Wea Rev 134:2354–2372
Palmer TN, Gelaro R, Barkmeijer J, Buizza R (1998) Singular vectors, metrics, and adaptive observations. J Atmos Sci 55:633–653
Pedlosky J (1987) Geophysical fluid dynamics, 2nd edn. Springer, Berlin, p 710
Pu Z-X, Kalnay E (1999) Targeting observations with the quasi-inverse linear and adjoint NCEP global models: performance during FASTEX. Quart J Roy Meteorol Soc 125:3329–3337
Rabier F, Klinker E, Courtier P, Hollingsworth A (1996) Sensitivity of forecast errors to initial conditions. Quart J Roy Meteorol Soc 122:121–150
Rotunno R, Bao JW (1996) A case study of cyclogenesis using a model hierarchy. Mon Wea Rev 124:1051–1066
Snyder C, Hamill TM, Trier SB (2003) Linear evolution of error covariances in a quasigeostrophic model. Mon Wea Rev 131:189–205
Acknowledgments
The authors wish to thank two anonymous reviewers for their valuable comments. This study was supported by the Korea Meteorological Administration Research and Development Program under Grant CATER 2006–2102. The first author is grateful to Prof. Michael Morgan for discussions at an earlier stage of the work.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, H.M., Beare, R.J. Characteristics of adjoint sensitivity to potential vorticity. Meteorol Atmos Phys 111, 91–102 (2011). https://doi.org/10.1007/s00703-010-0119-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00703-010-0119-3