The author would like to thank Ron Errico, Ron Gelaro, and Tim Palmer for helpful discussions. Tim Palmer suggested the analysis perturbation experiments discussed in the last part of section 5b. The three-level quasigeostrophic model was developed by Franco Molteni. Support of the sponsor, Office of Naval Research, and the program manager, Naval Research Laboratory, Project Element 0601153N, is gratefully acknowledged. Computing support was provided by the DoD High Performance Computing program.
Andersson, E., P. Courtier, W. Heckley, F. Rabier, J. N. Thépau, P. Undén, and D. Vasiljevic, 1995: Pre-operational tests with a three-dimensional variational analysis scheme. Proc. WMO Second Int. Symp. on Assimilation of Observations in Meteorology and Oceanography, Tokyo, Japan, WMO, 43–48.
Barkmeijer, J., 1992: Local error growth in a barotropic model. Tellus,44A, 314–323.
——, P. Houtekamer, and X. Wang, 1993: Validation of a skill prediction method. Tellus,45A, 424–434.
——, M. van Gijzen, and F. Bouttier, 1998: Singular vectors and the analysis error covariance metric. Quart. J. Roy. Meteor. Soc.,124, 1695–1714.
Buizza, R., 1994: Localization of optimal perturbations using a projection operator. Quart. J. Roy. Meteor. Soc.,120, 1647–1681.
——, 1998: Impact of horizontal diffusion on T21, T42, and T63 singular vectors. J. Atmos. Sci.,55, 1069–1083.
——, 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.
Cohn, S. E., N. S. Sivakumaran, and R. Toding, 1994: A fixed-lag Kalman smoother for retrospective data assimilation. Mon. Wea. Rev.,122, 2838–2867.
Daley, R., and T. Mayer, 1986: Estimates of global analysis error from the Global Weather Experiment Observational Network. Mon. Wea. Rev.,114, 1642–1653.
Ehrendorfer, M., and R. M. Errico, 1995: Mesoscale predictability and the spectrum of optimal perturbations. J. Atmos. Sci.,52, 3475–3500.
——, and J. J. Tribbia, 1997: Optimal prediction of forecast difference covariances through singular vectors. J. Atmos. Sci.,54, 286–313.
Farrell, B., 1990: Small error dynamics and the predictability of atmospheric flows. J. Atmos. Sci.,47, 2409–2416.
Gelaro, R., E. Klinker, and F. Rabier, 1996: Real and near-real time corrections to forecast initial conditions using adjoint methods:A feasibility study. Preprints, 11th Conf. on Numerical Weather Prediction, Norfolk, VA, Amer. Meteor. Soc., J58–J60.
——, R. Buizza, T. N. Palmer, and E. Klinker, 1998: Sensitivity analysis of forecast errors and the construction of optimal perturbations using singular vectors. J. Atmos. Sci.,55, 1012–1037.
Lorenz, E. N., 1965: A study of the predictability of a 28-variable atmospheric model. Tellus,17, 321–333.
Marshall, J., and F. Molteni, 1993: Toward a dynamical understanding of planetary-scale flow regimes. J. Atmos. Sci.,50, 1792–1818.
Ménard, R., and R. Daley, 1996: The application of Kalman smoother theory to the estimation of 4DVAR error statistics. Tellus,48A, 221–237.
Molteni, F., and T. N. Palmer, 1993: Predictability and finite-time instability of the northern winter circulation. Quart. J. Roy. Meteor. Soc.,119, 269–298.
Mureau, R., F. Molteni, and T. N. Palmer, 1993: Ensemble prediction using dynamically conditioned perturbations. Quart. J. Roy. Meteor. Soc.,119, 299–323.
Palmer, T. N., R. Gelaro, J. Barkmeijer, and R. Buizza, 1998: Singular vectors, metrics and adaptive observations. J. Atmos. Sci.,55, 633–653.
Pires, C., R. Vautard, and O. Talagrand, 1996: On extending the limits of variational assimilation in nonlinear chaotic systems. Tellus,48A, 96–121.
Pu, Z.-X., E. Kalnay, J. Sela, and I. Szunyogh, 1997: Sensitivity of forecast errors to initial conditions with a quasi-inverse linear method. Mon. Wea. Rev.,125, 2479–2503.
——, E. Kalnay, and Z. Toth, 1998a: Application of the quasi-inverse linear and adjoint NCEP global models to targeted observations during FASTEX. Proc. 12th Conf. Numerical Weather Prediction, Phoenix, AZ, Amer. Meteor. Soc., 8–9.
——, S. Lord, and E. Kalnay, 1998b: Forecast sensitivity with dropwindsonde data and targeted observations. Tellus,50A, 391–410.
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.
Reynolds, C. A., and T. N. Palmer, 1998: The impact of decaying singular vectors on analysis and forecast correction. J. Atmos. Sci.,55, 3005–3023.
Wang, Z, K. K. Droegemeier, L. White, and I. M. Navon, 1997: Application of a new adjoint newton algorithm to the 3D ARPS storm-scale model using simulated data. Mon. Wea. Rev.,125, 2460–2478.