Browsing by Author "Taylor, Gerald D., committee member"

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Open Access
Forecasting of Atlantic tropical cyclones using a kilo-member ensemble
(Colorado State University. Libraries, 2004) Vigh, Jonathan L., author; Schubert, Wayne H., advisor; DeMaria, Mark, committee member; Gray, William M., committee member; Taylor, Gerald D., committee member
The past 30 years have witnessed steady improvements in the skill of tropical cyclone track forecasts. These increases have been largely driven by improved numerical weather prediction models and increased surveillance of the storm environment through aircraft reconnaissance and satellite remote sensing. The skill of deterministic track forecasts from full-physics models is gradually approaching the theoretical limit of predictability that arises due to the atmosphere's chaotic nature and limitations in determining the initial state. To make further progress, it is necessary to treat the uncertainty of the initial condition. One practical approach is to sample this uncertainty by perturbing the initial state. The resulting suite of forecasts that result from integrating such perturbations is known as an ensemble. This thesis describes the design, implementation, and evaluation of a semi-operational ensemble forecasting system using an efficient multigrid barotropic vorticity equation model (MBAR). Five perturbation classes are used to simulate uncertainties in the storm environment and vortex structure. Uncertainties in the storm environment are simulated by using the background environmental flow evolutions provided by the NCEP Global Forecasting System (GFS) ensemble forecasts. Several deep layer-mean wind averages account for uncertainty in the depth of the storm steering layer. Uncertainties in the decomposition of the tropical atmosphere's vertical modes are simulated by varying the model equivalent phase speed. Finally, uncertainties in the vortex structure are simulated by varying the vortex size and storm motion vector. Each perturbation in a given class is cross-multiplied with all other perturbations of other classes to obtain an ensemble with 1980 members. One of the fundamental questions addressed by this research is whether such cross-multiplication increases the degrees of freedom in the ensemble. The ensemble is run for 294 cases from the 2001-2003 Atlantic hurricane seasons. Theory dictates that a properly-perturbed ensemble should, on average, be more accurate than any single ensemble member, but it was found that the kilo-ensemble mean forecast did not demonstrate substantial improvement over the control forecast. However, the ensemble mean did show substantial skill relative to the five-day climatology and persistence model (CLP5) throughout the 120-h forecast period. The ensemble mean spread (the mean distance of the individual members from the ensemble mean), x-bias, and y-bias statistics are also evaluated. Probabilistic interpretations are valid with an ensemble of this size, so cumulative strike probabilities are calculated explicitly from the kilo-ensemble output. In a related possibilistic interpretation, the ensemble can be looked upon as mapping out the subspace of all possible storm tracks, so the reliability of this ensemble envelope is examined. Finally, if the ensemble can accurately simulate the uncertainties in the dynamical system, then there should be a positive relationship between ensemble mean spread and the error of the ensemble mean forecast. A strong relationship allows useful forecasts of forecast skill to be made at the time of the forecast. The kilo-member ensemble was found to have a weak spread-error relationship that peaks at 60 h.
Open Access
Spectral methods for limited area models
(Colorado State University. Libraries, 1984) Fulton, Scott R., author; Schubert, Wayne H., advisor; Taylor, Gerald D., committee member; Krueger, David A., committee member; Stevens, Duane E., committee member; Johnson, Richard H. (Richard Harlan), committee member
This study investigates the usefulness of Chebyshev spectral methods in limited area atmospheric modeling. Basic concepts of spectral methods and properties of Chebyshev polynomials are reviewed. Chebyshev spectral methods are illustrated by applying them to the linear advection equation in one dimension. Numerical results demonstrate the high accuracy obtained compared to finite difference methods. The nonlinear shallow water equations on a bounded domain in two dimensions are then considered as a more realistic prototype model. Characteristic boundary conditions based on Reimann invariants are developed, and contrasted with wall conditions and boundary conditions based on the assumption of balanced flow. Chebyshev tau and collocation methods are developed for this model. Results from one-dimensional tests show the superiority of the characteristic conditions in most situations. Results from two-dimensional tests are also presented. Comparison of the tau and collocation methods shows that each has its own advantages and both are practical. Time differencing schemes for Chebyshev spectral methods are studied. The stability condition obtained with explicit time differencing, often thought to be "severe", is shown to be less severe than the corresponding condition for finite difference methods. Numerical results and asymptotic estimates show that time steps may in fact be limited by accuracy rather than stability, in which case simple explicit time differencing is practical and efficient. Two modified explicit schemes are reviewed, and implicit time differencing is also discussed. A Chebyshev spectral method is also used to solve the vertical structure problem associated with vertical normal mode transforms in a hydrostatic atmosphere. Numerical results demonstrate the accuracy of the method, and illustrate the aliasing which can occur unless the vertical levels at which data is supplied are carefully chosen. Vertical transforms of observed forcings of tropical wind and mass fields are presented. The results of this study indicate that Chebyshev spectral methods are a practical alternative to finite difference methods for limited area modeling, especially when high accuracy is desired. Spectral methods require less storage than finite difference methods, are more efficient when high enough accuracy is desired, and are at least as easy to program.