• Baines, P. G., 1983: A survey of blocking mechanisms, with application to the Australian region. Aust. Meteor. Mag.,31, 27–36.

  • Berggren, R., B. Bolin, and C. G. Rossby, 1949: An aerological study of zonal motion, its perturbations and breakdown. Tellus,1/2, 14–37.

  • Borges, M. D., and D. L. Hartmann, 1992: Barotropic instability and optimal perturbations of observed nonzonal flows. J. Atmos. Sci.,49, 335–354.

  • Buizza, R., 1995a: Optimal perturbation time evolution and sensitivity of ensemble prediction to perturbation amplitude. Quart. J. Roy. Meteor. Soc.,121, 1705–1738.

  • ——, 1995b: The impact of orographic forcing on barotropic unstable singular vectors. J. Atmos. Sci.,52, 1457–1472.

  • ——, and T. N. Palmer, 1995: The singular-vector structure of the atmospheric global circulation. J. Atmos. Sci.,52, 1434–1456.

  • ——, and F. Molteni, 1996: The role of finite-time barotropic instability during the transaction to blocking. J. Atmos. Sci.,53, 1675–1679.

  • ——, J. Tribbia, F. Molteni, and T. N. Palmer, 1993: Computation of optimal unstable structures for a numerical weather prediction model. Tellus,45A, 388–407.

  • ——, R. Gelaro, F. Molteni, and T. N. Palmer, 1997: The impact of increased resolution on predictability studies with singular vectors. Quart. J. Roy. Meteor. Soc.,123, 1007–1033.

  • Charney, J. G., and J. G. DeVore, 1979: Multiple flow equilibria in the atmosphere and blocking. J. Atmos. Sci.,36, 1205–1216.

  • ——, and D. M. Strauss, 1980: Form-drag instability, multiple equilibria and propagating planetary waves in baroclinic, orographically forced, planetary wave systems. J. Atmos. Sci.,37, 1157–1176.

  • ——, J. Shukla, and K. D. Mo, 1981: Comparison of barotropic blocking theory with observation. J. Atmos. Sci.,38, 762–779.

  • Colucci, S. J., and W. C. Bresky, 1997: Dynamics of atmospheric preconditioning for the onset of blocking. Proc. 11th Conf. on Atmospheric and Oceanic Dynamics, Tacoma, WA, Amer. Meteor. Soc., 279–281.

  • de Pondeca, M. S. F. V., 1996: Model studies of blocking predictability using the adjoint sensitivity formalism. Ph.D. dissertation, The Florida State University, 176 pp. [Available from The Florida State University, Dept. of Meteorology, P.O. Box 3034, Tallahassee, FL 32306].

  • Dole, R. M., and R. X. Black, 1990: Life cycles of persistent anomalies. Part II: The development of persistent negative height anomalies over the North Pacific Ocean. Mon. Wea. Rev.,118, 824–846.

  • Ehrendorfer, M., and R. M. Errico, 1995: Mesoscale predictability and the spectrum of optimal perturbations. J. Atmos. Sci.,52, 3475–3500.

  • Elliot, R. D., and T. B. Smith, 1949: A study of the effects of large blocking highs on the general circulation in the northern hemisphere westerlies. J. Meteor.,6, 67–85.

  • Errico, R. M., T. Vukićević, and K. Reader, 1993: Examination of the accuracy of a tangent linear model. Tellus,45A, 462–477.

  • Farrell, B., 1984: Modal and non-modal baroclinic waves. J. Atmos. Sci.,41, 668–673.

  • ——, 1988: Optimal excitation of neutral Rossby waves. J. Atmos. Sci.,45, 163–172.

  • ——, 1989: Optimal excitation of baroclinic waves. J. Atmos. Sci.,46, 1193–1206.

  • Frederiksen, J. S., 1982: A unified three-dimensional instability theory of the onset of blocking and cyclogenesis. J. Atmos. Sci.,39, 970–982.

  • ——, 1983: The onset of blocking and cyclogenesis: Linear theory. Aust. Meteor. Mag.,31, 15–26.

  • ——, 1984: The onset of blocking and cyclogenesis in Southern Hemisphere synoptic flows: Linear theory. J. Atmos. Sci.,41, 1116–1131.

  • ——, 1989: The role of instability during the onset of blocking and cyclogenesis in Northern Hemisphere synoptic flows. J. Atmos. Sci.,46, 1076–1092.

  • ——, 1997: Adjoint sensitivity and finite-time normal mode disturbances during blocking. J. Atmos. Sci.,54, 1144–1165.

  • ——, and R. C. Bell, 1990: North Atlantic blocking during January 1979. Linear theory. Quart. J. Roy. Meteor. Soc.,116, 1289–1313.

  • Haines, K., and J. Marshall, 1987: Eddy-forced coherent structures as a prototype for atmospheric blocking. Quart. J. Roy. Meteor. Soc.,113, 681–704.

  • Hall, M. C. G., and D. G. Cacuci, 1983: Physical interpretation of the adjoint functions for sensitivity analysis of atmospheric models. J. Atmos. Sci.,40, 2537–2546.

  • Hartmann, D. L., R. Buizza, and T. N. Palmer, 1995: Singular vectors:The effect of spatial scale on linear growth of disturbances. J. Atmos. Sci.,52, 3885–3894.

  • Jeffreys, H., and B. Jeffreys, 1956: Methods of Mathematical Physics. Cambridge University Press, 718 pp.

  • Legras, B., and M. Ghil, 1985: Persistent anomalies, blocking and variations in atmospheric predictability. J. Atmos. Sci.,42, 433–471.

  • Liu, Q., 1994: On the definition and persistence of blocking. Tellus,46A, 286–298.

  • ——, and T. Opsteegh, 1995: Interannual and decadal variations of blocking activity in a quasi-geostrophic model. Tellus,47A, 941–954.

  • McWilliams, J. C., 1980: An application of equivalent modons to atmospheric blocking. Dyn. Atmos. Oceans,5, 43–66.

  • Mitchel, H., and J. Derome, 1983: Blocking-like solutions of the potential vorticity equation: Their stability at equilibrium and growth at resonance. J. Atmos. Sci.,40, 2522–2536.

  • Molteni, F., R. Buizza, T. N. Palmer, and T. Petroliagis, 1996: The ECMWF ensemble prediction system: Methodology and validation. Quart. J. Roy. Meteor. Soc.,112, 73–119.

  • Namias, J., 1947: Characteristics of the general circulation over the northern hemisphere during the abnormal winter 1946–1947. Mon. Wea. Rev.,75, 145–152.

  • Noble, B., and J. W. Daniel, 1977: Applied Linear Algebra. Prentice-Hall, 477 pp.

  • Oortwijn, J., and J. Barkmeijer, 1995: Perturbations that optimally trigger weather regimes. J. Atmos. Sci.,52, 3932–3944.

  • Rabier, F., E. Klinker, P. Courtier, and A. Hollingsworth, 1996: Sensitivity of forecast errors to initial conditions. Quart. J. Roy. Meteor. Soc.,122, 121–150.

  • Thorncroft, C. D., B. J. Hoskins, and M. E. McIntyre, 1993: Two paradigms of baroclinic life-cycle behavior. Quart. J. Roy. Meteor. Soc.,119, 17–55.

  • Tibaldi, S., and F. Molteni, 1990: On the operational predictability of blocking. Tellus,42A, 343–365.

  • Tung, K. K., and R. S. Lindzen, 1979a: A theory of stationary long waves. Part I: A simple theory of blocking. Mon. Wea. Rev.,107, 714–734.

  • ——, and ——, 1979b: A theory of stationary long waves. Part II: Resonant Rossby waves in the presence of realistic vertical shears. Mon. Wea. Rev.,107, 735–750.

  • Zhang, Z., 1988: The linear study of zonally asymmetric barotropic flows. Ph.D. thesis, University of Reading, 177 pp. [Available from University of Reading, Dept. of Meteorology, P.O. Box 243, Earley Gate, Reading RG6 6BB, United Kingdom.].

  • Zou, X., A. Barcilon, I. M. Navon, J. Whitaker, and D. G. Cacuci, 1993: An adjoint sensitivity study of blocking in a two-layer isentropic model. Mon. Wea. Rev.,121, 2833–2857.

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An Adjoint Sensitivity Study of the Efficacy of Modal and Nonmodal Perturbations in Causing Model Block Onset

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  • 1 Department of Meteorology and Geophysical Fluid Dynamics Institute, The Florida State University, Tallahassee, Florida
  • | 2 Mesoscale and Microscale Meteorology Division, National Center for Atmospheric Research, Boulder, Colorado
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Abstract

With a blocking index as the response function, the adjoint sensitivity formalism is used to assess the impact of normal modes, adjoint modes, and regional singular vectors on prediction of block onset in a two-layer model. The authors focus on three blocks excited by perturbing the model’s state vector at times preselected using the maximal perturbation that defines the direction in phase space associated with the largest possible change in the response function. The sets of normal modes, adjoint modes, and regional singular vectors (using the total energy or the L2 norm) are computed on instantaneous basic-state flows for the preselected times and sensitivity results are presented for a time window of 3 days.

When ordered by decreasing values of the growth rates of the normal modes, the authors find that some distant normal modes and adjoint modes can produce larger changes in the response function than some of their leading counterparts. In contrast, the sets of regional singular vectors contain easily identifiable subsets of structures associated with relatively large changes in the response function. The largest changes are produced by less than the first 20 regional singular vectors. Some of these individual regional singular vectors capture the onset of the block when used as perturbations to the initial condition in a nonlinear model integration, a result of the importance for ensemble forecasting. It is found that the first five most explosive regional singular vectors of the energy (L2) norm explain over 20% (60%) of the norm contained in the maximal perturbation at initial time.

Despite the failure of all individual normal modes to excite the block, as opposed to adjoint modes and regional singular vectors, the authors argue that, paradoxically, the normal mode concept remains a viable tool to explain the dynamics of block onset.

Corresponding author address: Dr. Albert I. Barcilon, Geophysical Fluid Dynamics Institute, The Florida State University, 18 Keen Bldg., Tallahassee, FL 32306-3017.

Email: barcilon@gfdi.fsu.edu

Abstract

With a blocking index as the response function, the adjoint sensitivity formalism is used to assess the impact of normal modes, adjoint modes, and regional singular vectors on prediction of block onset in a two-layer model. The authors focus on three blocks excited by perturbing the model’s state vector at times preselected using the maximal perturbation that defines the direction in phase space associated with the largest possible change in the response function. The sets of normal modes, adjoint modes, and regional singular vectors (using the total energy or the L2 norm) are computed on instantaneous basic-state flows for the preselected times and sensitivity results are presented for a time window of 3 days.

When ordered by decreasing values of the growth rates of the normal modes, the authors find that some distant normal modes and adjoint modes can produce larger changes in the response function than some of their leading counterparts. In contrast, the sets of regional singular vectors contain easily identifiable subsets of structures associated with relatively large changes in the response function. The largest changes are produced by less than the first 20 regional singular vectors. Some of these individual regional singular vectors capture the onset of the block when used as perturbations to the initial condition in a nonlinear model integration, a result of the importance for ensemble forecasting. It is found that the first five most explosive regional singular vectors of the energy (L2) norm explain over 20% (60%) of the norm contained in the maximal perturbation at initial time.

Despite the failure of all individual normal modes to excite the block, as opposed to adjoint modes and regional singular vectors, the authors argue that, paradoxically, the normal mode concept remains a viable tool to explain the dynamics of block onset.

Corresponding author address: Dr. Albert I. Barcilon, Geophysical Fluid Dynamics Institute, The Florida State University, 18 Keen Bldg., Tallahassee, FL 32306-3017.

Email: barcilon@gfdi.fsu.edu

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