Targeting Observations Using Singular Vectors

R. Buizza European Centre for Medium-Range Weather Forecasts, Reading, Berkshire, United Kingdom

Search for other papers by R. Buizza in
Current site
Google Scholar
PubMed
Close
and
A. Montani Department of Meteorology, University of Reading, Reading, Berkshire, United Kingdom

Search for other papers by A. Montani in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Singular vectors with maximum energy at final time inside a verification area are used to identify the target area where extra observations should be taken, at an initial time, to reduce the forecast error inside the verification area itself. This technique is applied to five cases of cyclone development in the Atlantic Ocean, with cyclones reaching the British Isles at the final time. Three verification areas centered around this region are considered.

First, the sensitivity of the target area to the choice of the forecast trajectory along which the singular vectors are evolved, to the choice of the verification area where singular vector energy is maximized, and to the number of singular vectors used to define the target area is investigated. Results show little sensitivity to the choice of the verification area, but high sensitivity to the choice of the trajectory. Regarding the number of singular vectors used, results based on the first 4 or the first 10 singular vectors are shown to be very similar.

Second, the potential forecast error reduction that could be achieved by taking extra observations inside the target area is estimated by contrasting the error of a forecast started from the unperturbed analysis with the error of a forecast started by subtracting so-called pseudo-inverse perturbations (estimated using the leading singular vectors) to the unperturbed analysis. Results indicate that root-mean-square errors in the verification region could be reduced by up to 13% by adding targeted observations.

Overall, results suggest that linear models can be used to define the target area where adaptive observations should be taken.

Corresponding author address: Dr. Roberto Buizza, ECMWF, Shinfield Park, Reading, Berkshire RG2 9AX, United Kingdom.

Email: r.buizza@ecmwf.int

Abstract

Singular vectors with maximum energy at final time inside a verification area are used to identify the target area where extra observations should be taken, at an initial time, to reduce the forecast error inside the verification area itself. This technique is applied to five cases of cyclone development in the Atlantic Ocean, with cyclones reaching the British Isles at the final time. Three verification areas centered around this region are considered.

First, the sensitivity of the target area to the choice of the forecast trajectory along which the singular vectors are evolved, to the choice of the verification area where singular vector energy is maximized, and to the number of singular vectors used to define the target area is investigated. Results show little sensitivity to the choice of the verification area, but high sensitivity to the choice of the trajectory. Regarding the number of singular vectors used, results based on the first 4 or the first 10 singular vectors are shown to be very similar.

Second, the potential forecast error reduction that could be achieved by taking extra observations inside the target area is estimated by contrasting the error of a forecast started from the unperturbed analysis with the error of a forecast started by subtracting so-called pseudo-inverse perturbations (estimated using the leading singular vectors) to the unperturbed analysis. Results indicate that root-mean-square errors in the verification region could be reduced by up to 13% by adding targeted observations.

Overall, results suggest that linear models can be used to define the target area where adaptive observations should be taken.

Corresponding author address: Dr. Roberto Buizza, ECMWF, Shinfield Park, Reading, Berkshire RG2 9AX, United Kingdom.

Email: r.buizza@ecmwf.int

Save
  • Appenzeller, Ch., H. C. Davies, J. M. Popovic, S. Nickovic, and M. B. Gavrilov, 1996: PV morphology of a frontal-wave development. Meteor. Atmos. Phys.,58, 21–40.

  • Barkmeijer, J., M. van Gijzen, and F. Bouttier, 1998: Singular vectors and estimates of the analysis error covariance metric. Quart. J. Roy. Meteor. Soc.,124, 1695–1713.

  • Bishop, C. H., and Z. Toth, 1998: Ensemble transformation and adaptive observations. J. Atmos. Sci.,56, 1748–1765.

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

  • Buizza, R., 1994a: Sensitivity of optimal unstable structures. Quart. J. Roy. Meteor. Soc.,120, 429–451.

  • ——, 1994b: Localization of optimal perturbations using a projection operator. Quart. J. Roy. Meteor. Soc.,120, 1647–1682.

  • ——, 1998: Impact of horizontal diffusion on T21, T42, and T63 singular vectors. J. Atmos. Sci.,55, 1069–1083.

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

  • ——, J. Barkmeijer, R. Gelaro, and J.- F. Mahfouf, 1996: Singular vectors, norms and large-scale condensation. Preprints, 11th Conf. on Numerical Weather Prediction, Norfolk, VA, Amer. Meteor. Soc., 50–51.

  • ——, 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.

  • Courtier, P., and Coauthors, 1993: Variational Assimilation at ECMWF. ECMWF Research Department Tech. Memo. 194, 84 pp. [Available from ECMWF, Shinfield Park, Reading, Berkshire RG2 9AX, United Kingdom.].

  • Errico, E. R., and M. Ehrendorfer, 1995: Moist singular vectors in a primitive-equation regional model. Preprints, 10th Conf. on Atmospheric and Oceanic Waves and Stability, Big Sky, MT, Amer. Meteor. Soc., 235–238.

  • Farrell, B. F., 1990: Small error dynamics and the predictability of atmospheric flows. J. Atmos. Sci.,47, 2409–2416.

  • Gelaro, R., 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.

  • Hoskins, B. J., M. E. McIntyre, and A. W. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc.,111, 877–946.

  • Houtekamer, P. L., L. Lefaivre, J. Derome, H. Ritchie, and H. Mitchell, 1996: A system simulation approach to ensemble prediction. Mon. Wea. Rev.,124, 1225–1242.

  • Joly, A., and Coauthors, 1996: The Fronts and Atlantic Storm-Track Experiment (FASTEX): Scientific objectives and experimental design. Bull. Amer. Meteor. Soc.,78, 1917–1940.

  • Lacarra, J.-F., and O. Talagrand, 1988: Short range evolution of small perturbations in a barotropic model. Tellus,40A, 81–95.

  • Langland, R. H., and G. D. Rohaly, 1996: Adjoint-based targeting of observations for FASTEX cyclones. Preprints, Seventh Conf. on Mesoscale Processes, Reading, United Kingdom, Amer. Meteor. Soc., 369–371.

  • Lorenz, E., and K. A. Emanuel, 1998: Optimal sites for supplementary observations: Simulation with a small model. J. Atmos. Sci.,55, 399–414.

  • 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, 73–119.

  • Montani, A., R. Buizza, and A. J. Thorpe, 1996: Singular vector calculation for cases of cyclogenesis in the north Atlantic storm-track. Preprints, Seventh Conf. on Mesoscale Processes, Reading, United Kingdom, Amer. Meteor. Soc., 391–392.

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

  • Palmer, T. N., R. Gelaro, J. Barkmeijer, and R. Buizza, 1998: Singular vectors, metrics, and adaptive observations. J. Atmos. Sci.,55., 633–653.

  • Pu, Z.-X., E. Kalnay, J. Sela, and I. Szunyogh, 1997: Sensitivity of forecast error to initial conditions with a quasi-inverse linear method. Mon. Wea. Rev.,125, 2479–2503.

  • ——, ——, and Z. Toth, 1998: Application of the quasi-inverse linear and adjoint NCEP Global models to targeted observations during FASTEX. Preprints, 12th Conf. on Numerical Weather Prediction, Phoenix, AZ, Amer. Meteor. Soc., 8–9.

  • 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.

  • Snyder, C., 1996: Summary of an informal workshop on adaptive observations and FASTEX. Bull. Amer. Meteor. Soc.,77, 953–961.

  • Toth, Z., and E. Kalnay, 1993: Ensemble forecasting at NMC: The generation of perturbations. Bull. Amer. Meteor. Soc.,74, 2317–2330.

  • ——, and ——, 1996: Ensemble forecasting at NCEP. Proc. European Centre for Medium-Range Weather Forecasts Sem. on Predictability, Vol. II, Reading, United Kingdom, ECMWF, 39–61.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 578 137 9
PDF Downloads 206 50 9