Search Results

You are looking at 1 - 8 of 8 items for

  • Author or Editor: Samuel Y. K. Yee x
  • Refine by Access: All Content x
Clear All Modify Search
Samuel Y. K. Yee

Abstract

This paper discusses the impact of data noise on the accuracy of derivatives obtained by differentiating a Fourier series of an observed dataset. It is first brought to the fore that the kth component of the energy density of the mth derivative of a Fourier series is proportional to k 2m . It is then argued that since the energy density of atmospheric parameters resolvable by the current observing network decreases at a rate of no less than k −2, it is desirable to apply a low-pass filter to the spectrally computed derivatives to arrest the rapid growth of noise-induced errors at the smaller scales. Based on the analysis of a sample set of atmospheric data, it is also recommended that to avoid noise-induced spurious growth of short-wave energy at the onset of a time integration, in geophysical modeling where the model grid is finer than the observational resolution, model initial conditions should contain only those scales that are resolvable by the observing network.

Full access
Samuel Y. K. Yee

Abstract

In NWP models using energy-conserving finite-difference approximations in the vertical, the imposition of different constraints of the discrete energy equation leads to different forms of the hydrostatic equation. This paper shows, using the National Meteorological Center spectral model as a specific example, that the consistent application of all the constraints suggested by Phillips (1974) on the discrete energy equation leads to an algebraic hydrostatic system of (3K–1) unknowns and equations, K being the number of layers in the model. It is emphasized that in relating the vertical structure between the mass and thermal fields, these and only these equations must be satisfied. The introduction of any additional equations without introducing an equal number of unknowns may defeat the purpose of an energy-conserving finite-difference scheme.

Full access
Samuel Y. K. Yee

Abstract

A method for the solution of Poisson's equation on the surface of a sphere is given. The method makes use of truncated double Fourier series expansions on the sphere and invokes the Galerkin approximation. It has an operation count of approximately I2J 2(1 + log2 J) for a latitude-longitude grid containing 2J(J − 1) + 2 data points. Numerical results are presented to demonstrate the method's accuracy and efficiency.

Full access
Samuel Y. K. Yee
and
Ralph Shapiro

Abstract

The nondivergent barotropic vorticity equation on a sphere supplies the framework for a series Of experiments designed to study the suitability of numerical methods commonly used in the modeling and prediction of the atmosphere. Specifically, making use of idealized initial conditions and a scale-dependent spatial filter we investigate the capabilities and limitations of a typical second-order finite-difference approximation in numerical time integrations. From comparisons with analytic solutions, it is found that for dynamically stable flows numerical methods such as second-order finite-difference approximations, together with a Shapiro-type filter, are adequate in yielding approximate solutions to the modeling differential equations. For dynamically unstable flows, numerical errors are amplified as part of the dynamics of the unstable system. The use of finite-difference approximations may yield solutions which bear no resemblance whatsoever to the true solution of the differential equations in spite of the maintenance of computational stability. It is postulated that interactions among long-wave computational modes and physical modes in a numerical model may prove to be another major obstacle in numerical prediction of an unstable flow.

Full access
Samuel Y. K. Yee

Abstract

A unified derivation for three known expressions for the Fourier decomposition of a scalar function on spheres is presented. The expressions are put in a common framework for easy comparison and are contrasted in a table. One expression is shown to be superior.

Full access
Paul R. Desrochers
and
Samuel Y. K. Yee

Abstract

Severe weather often emanates from thunderstorms that have persistent, well organized, rotating updrafts. These rotating updrafts, which are generally referred to as mesocyclones, appear as couplets of incoming and outgoing radial velocities to a single Doppler radar. Observations of mesocyclones reveal useful information on the kinematics in the vicinity of the storm updraft that, if properly interpreted, can be used to assess the likelihood and intensity of severe weather. Reliable automated detection based on such assessment would serve to enhance the warning process. However, existing data processing methodology in operational mesocyclone detection algorithms is susceptible to noise and natural small-scale variations in Doppler radar data. Reported here is a new wavelet-based approach that offers improved capability for the discrimination of mesocyclones from other shear features. This approach uses discrete wavelets to preprocess the data in order to focus on the known scales where mesocyclones are most likely to reside and extract only the relevant signals for their shape and location identification. Common data quality problems associated with radar observations such as noise and data gaps are also handled effectively as part of the processing. The approach is demonstrated first with a one-dimensional test pattern, then with a two-dimensional synthetic mesocyclone vortex, and finally with a case study.

Full access
John W. Ruge
,
Stephen F. McCormick
, and
Samuel Y. K. Yee

Abstract

A multigrid algorithm for local refinement in time and space for an Eulerian formulation of the shallow-water equations on a sphere is presented. It is shown that the accuracy obtainable on a full global grid can be reached using local patches in time and space. Results are presented using a model problem with a large-scale disturbance and a problem with topography and realistic initial conditions.

Full access
George D. Modica
,
Samuel Y-K. Yee
, and
Joseph Venuti

Abstract

Results are presented from an analysis of variance as a function of horizontal scale. The normalized difference-field spectra of kinetic energy, temperature, vapor mixing ratio, and cloud-water mixing ratio were computed as a function of wavenumber at several model levels within and just above the planetary boundary layer (PBL). The analysis was performed on simulations from a three-dimensional (3D) hydrodynamic mesoscale model that contained a soil-vegetation canopy model. The analysis was intended to highlight (in terms of wave spectra) the impact of changes in lower-boundary forcing through horizontal variations in soil and plant type. Experiments showed that the use in the model of 1° resolution databases of soil and vegetation type produced higher amounts of variance in the simulated fields at most wavelengths–often by more than 10%–when compared to a simulation that utilized a uniform distribution. Furthermore, the use of databases generated by random specification of soil and vegetation types resulted in yet higher amounts of variance at most wavelengths. The normalized difference-field spectra of energy, temperature, and water vapor mixing ratio generally displayed positive slope (largest values at highest wavenumber) at the lowest model level and tended toward negative slope at higher levels. The magnitudes of the spectra also diminished rapidly with height. The effect of the lateral boundary conditions was generally much greater in terms of the spectral magnitudes than that due to the soil-vegetation databases.

Full access