• Arakawa, A., 1972: Design of the UCLA general circulation model: Numerical simulation of weather and climate. Tech. Rep. 7, Dept. of Meteorology, University of California, Los Angeles, 116 pp.

  • Arakawa, A., , and V. Lamb, 1977: Computational design of the basic dynamical processes of the UCLA general circulation model. Methods in Computational Physics, Vol. 17, J. Chang, Ed., Academic Press, 173–265.

    • Search Google Scholar
    • Export Citation
  • Arakawa, A., , and M. J. Suarez, 1983: Vertical differencing of the primitive equations in sigma coordinates. Mon. Wea. Rev, 111 , 3445.

    • Search Google Scholar
    • Export Citation
  • Arakawa, A., , and S. Moorthi, 1988: Baroclinic instability in vertically discrete systems. J. Atmos. Sci, 45 , 16881707.

  • Arakawa, A., , and C. S. Konor, 1996: Vertical differencing of the primitive equations based on the Charney-Phillips grid in hybrid σp vertical coordinates. Mon. Wea. Rev, 124 , 511528.

    • Search Google Scholar
    • Export Citation
  • Badger, J., , and B. Hoskins, 2001: Simple initial value problems and mechanisms for baroclinic growth. J. Atmos. Sci, 58 , 3849.

  • Buizza, R., , J. Barkmeijer, , T. Palmer, , and D. Richardson, 1999: Current status and future developments of the ECMWF ensemble prediction system. Meteor. Appl, 6 , 114.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G., , and N. A. Phillips, 1953: Numerical integration of the quasi-geostrophic equations for barotropic and simple baroclinic flows. J. Meteor, 10 , 7199.

    • Search Google Scholar
    • Export Citation
  • Cullen, M. J. P., , T. Davies, , M. H. Mawson, , J. A. James, , S. C. Coulter, , and A. Malcolm, 1997: An overview of numerical methods for the next generation U.K. NWP and climate model. Numerical Methods in Atmospheric and Ocean Modelling: The Andre J. Robert Memorial Volume, C. A. Lin, R. Laprise, and H. Ritchie, Eds., Canadian Meteorological and Oceanographic Society, 425–444.

    • Search Google Scholar
    • Export Citation
  • Davis, C. A., , and K. A. Emanuel, 1991: Potential vorticity diagnosis of cyclogenesis. Mon. Wea. Rev, 119 , 19291952.

  • Downton, R. A., , and R. S. Bell, 1988: The impact of analysis differences on a medium-range forecast. Meteor. Mag, 117 , 279285.

  • Eady, E. T., 1949: Long waves and cyclone waves. Tellus, 1 , 3352.

  • Farrell, B. F., 1982: The initial growth of disturbances in a baroclinic flow. J. Atmos. Sci, 39 , 16631686.

  • Farrell, B. F., 1984: Modal and non-modal baroclinic waves. J. Atmos. Sci, 41 , 16631686.

  • Harrison, M. S. J., , T. Palmer, , D. S. Richardson, , and R. Buizza, 1999: Analysis and model dependencies in medium-range ensembles: Two transplant case studies. Quart. J. Roy. Meteor. Soc, 125 , 24872515.

    • Search Google Scholar
    • Export Citation
  • Hollingsworth, A., 1995: A spurious mode in the “Lorenz” arrangement of ϕ and T which does not exist in the “Charney-Phillips” arrangement. ECMWF Tech. Memo. 211, 12 pp.

  • Lorenz, E. N., 1960: Energy and numerical weather prediction. Tellus, 12 , 364373.

  • Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci, 20 , 130141.

  • Lorenz, E. N., 1989: Effects of analysis and model errors on routine weather forecasts. Proc. ECMWF Seminars on Ten Years of Medium-Range Weather Forecasting, Reading, United Kingdom, ECMWF, 115–128.

  • Lorenz, E. N., 1995: Predictability—A problem partly solved. Proc. ECMWF Seminars on Predictability, Reading, United Kingdom, ECMWF, 1–18.

  • Molteni, F., , R. Buizza, , T. N. Palmer, , and T. Petroliagis, 1996: The new ECMWF ensemble prediction system: Methodology and validation. Quart. J. Roy. Meteor. Soc, 122 , 73119.

    • Search Google Scholar
    • Export Citation
  • Nicolis, C., 2003: Dynamics of model error: Some generic features. J. Atmos. Sci, 60 , 22082218.

  • Orrell, D., , L. Smith, , J. Barkmeijer, , and T. Palmer, 2001: Model error in weather forecasting. Nonlinear Processes Geophys, 9 , 357371.

    • Search Google Scholar
    • Export Citation
  • Palmer, T., 1999: A nonlinear dynamical perspective on climate prediction. J. Climate, 12 , 575591.

  • Palmer, T., 2000: Predicting uncertainty in forecasts of weather and climate. Reports on Progress in Physics, Vol. 63, Institute of Physics Publishing, 71–116.

    • Search Google Scholar
    • Export Citation
  • Rotunno, R., , and J. Bao, 1996: A case study of cyclogenesis using a model hierarchy. Mon. Wea. Rev, 124 , 10511066.

  • Rotunno, R., , W. C. Skamarock, , and C. Snyder, 1994: An analysis of frontogenesis in numerical simulations of baroclinic waves. J. Atmos. Sci, 51 , 33733398.

    • Search Google Scholar
    • Export Citation
  • Richardson, D. S., 1997: The relative effect of model and analysis differences on ECMWF and UKMO operational forecasts. Proc. ECMWF Workshop on Predictability, Reading, United Kingdom, ECMWF, 363–372.

  • Simmons, A. J., , and D. M. Burridge, 1981: An energy- and angular-momentum-conserving vertical finite-difference scheme and hybrid vertical coordinates. Mon. Wea. Rev, 109 , 758766.

    • Search Google Scholar
    • Export Citation
  • Smith, R., , W. Ulrich, , and G. Dietachmaye, 1990: A numerical study of tropical cyclone motion using a barotropic model. Part I. The role of vortex asymmetries. Quart. J. Roy. Meteor. Soc, 116 , 337362.

    • Search Google Scholar
    • Export Citation
  • Snyder, C., , T. Hamill, , and S. Trier, 2003: Linear evolution of error covariances in a quasigeostrophic model. Mon. Wea. Rev, 131 , 189205.

    • Search Google Scholar
    • Export Citation
  • Takayabu, I., 1991: “Coupling development”: An efficient mechanism for the development of extra-tropical cyclones. J. Meteor. Soc. Japan, 69 , 609628.

    • Search Google Scholar
    • Export Citation
  • Tan, Z., , F. Zhang, , R. Rotunno, , and C. Snyder, 2004: Mesoscale predictability of moist baroclinic waves: Experiments with parameterized convection. J. Atmos. Sci, 61 , 17941804.

    • Search Google Scholar
    • Export Citation
  • Thompson, P., 1957: Uncertainty of initial state as a factor in the predictability of large scale atmospheric flow patterns. Tellus, 9 , 275295.

    • Search Google Scholar
    • Export Citation
  • Tokioka, T., 1978: Some consideration on vertical differencing. J. Meteor. Soc. Japan, 56 , 89111.

  • Toth, Z., , and E. Kalnay, 1993: Ensemble forecasting at NMC: The generation of perturbations. Bull. Amer. Meteor. Soc, 74 , 23172330.

  • Vannitsem, S., , and Z. Toth, 2002: Short-term dynamics of model errors. J. Atmos. Sci, 59 , 25942604.

  • Wernli, H., , R. Fehlmann, , and D. Luethi, 1998: The effect of barotropic shear on upper-level induced cyclogenesis: Semigeostrophic and primitive equation numerical simulations. J. Atmos. Sci, 55 , 20802094.

    • Search Google Scholar
    • Export Citation
  • Zhu, H., , and R. K. Smith, 2003: Effects of vertical differencing in a minimal hurricane model. Quart. J. Roy. Meteor. Soc, 129 , 10511069.

    • Search Google Scholar
    • Export Citation
  • Zhu, H., , R. K. Smith, , and W. Ulrich, 2001: A minimal three-dimensional tropical cyclone model. J. Atmos. Sci, 58 , 19241944.

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Predictability of Extratropical Cyclones: The Influence of Initial Condition and Model Uncertainties

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  • 1 Department of Meteorology, University of Reading, Reading, United Kingdom
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Abstract

Errors in numerical weather forecasts can be attributed to two causes: deficiencies in the modeling system and inaccurate initial conditions. Understanding of the characteristics of the growth of forecast spread related to model uncertainty is less developed than that for initial condition uncertainty. In this research, the authors aim to construct a theoretical basis for describing such forecast error growth resulting from model uncertainty using mostly an empirical modeling approach. Primitive equation models with different vertical discretization and different horizontal resolutions are used to investigate the impacts of model uncertainties on the predictability of extratropical cyclones. Three sets of initial perturbations related to an upper-level trigger, with slightly different amplitudes, are designed for representing the situation when the initial condition uncertainty leads to significant forecast error growth.

Forecast error growth is here estimated by following the properties of a developing cyclone in the simulations. Generally, there are three phases for forecast error growth in the experiments with initial condition and model uncertainties. For the experiments with the structured initial condition uncertainties, the errors grow rapidly at the earlier transient stage, with the growth rate well above the fastest growing normal mode. Afterward the error grows exponentially at approximately the same growth rate as the cyclone, followed by a saturation period, when the growth rate starts to decline. For the experiments with the model uncertainties, the forecast errors are initially zero and increase as time to a power of μ, which is between 0.5 and 3 depending on the strength of the cyclone at the time the simulation is initiated. After a certain time interval, the exponential growth phase and saturation period start as in the initial error experiments. Starting an integration with a stronger initial cyclone, the forecast error associated with the model uncertainty takes a shorter time to reach the exponential growth period and the forecast error grows more rapidly initially with a smaller value of μ. Also, when the initial cyclone is strong enough, then the exponential growth phase may only last for a very short time.

Corresponding author address: Dr. Hongyan Zhu, Dept. of Meteorology, University of Reading, Earley Gate, P.O. Box 243, Reading, United Kingdom. Email: hongyan.zhu@reading.ac.uk

Abstract

Errors in numerical weather forecasts can be attributed to two causes: deficiencies in the modeling system and inaccurate initial conditions. Understanding of the characteristics of the growth of forecast spread related to model uncertainty is less developed than that for initial condition uncertainty. In this research, the authors aim to construct a theoretical basis for describing such forecast error growth resulting from model uncertainty using mostly an empirical modeling approach. Primitive equation models with different vertical discretization and different horizontal resolutions are used to investigate the impacts of model uncertainties on the predictability of extratropical cyclones. Three sets of initial perturbations related to an upper-level trigger, with slightly different amplitudes, are designed for representing the situation when the initial condition uncertainty leads to significant forecast error growth.

Forecast error growth is here estimated by following the properties of a developing cyclone in the simulations. Generally, there are three phases for forecast error growth in the experiments with initial condition and model uncertainties. For the experiments with the structured initial condition uncertainties, the errors grow rapidly at the earlier transient stage, with the growth rate well above the fastest growing normal mode. Afterward the error grows exponentially at approximately the same growth rate as the cyclone, followed by a saturation period, when the growth rate starts to decline. For the experiments with the model uncertainties, the forecast errors are initially zero and increase as time to a power of μ, which is between 0.5 and 3 depending on the strength of the cyclone at the time the simulation is initiated. After a certain time interval, the exponential growth phase and saturation period start as in the initial error experiments. Starting an integration with a stronger initial cyclone, the forecast error associated with the model uncertainty takes a shorter time to reach the exponential growth period and the forecast error grows more rapidly initially with a smaller value of μ. Also, when the initial cyclone is strong enough, then the exponential growth phase may only last for a very short time.

Corresponding author address: Dr. Hongyan Zhu, Dept. of Meteorology, University of Reading, Earley Gate, P.O. Box 243, Reading, United Kingdom. Email: hongyan.zhu@reading.ac.uk

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