Search Results

You are looking at 1 - 10 of 41 items for

  • Author or Editor: Hung-chi Kuo x
  • Refine by Access: All Content x
Clear All Modify Search
Hung-chi Kuo
and
Wendell A. Nuss

Abstract

The quasigeostrophic geopotential tendency equation is derived using P vectors in both pressure and entropy coordinates. This vector form of the geostrophic forcing in the geopotential tendency equation is similar to the Q-vector form of the ω equation. It is shown that the horizontal components of P are the advection of geostrophic momentum and the vertical component of P is the horizontal temperature advection. The P vectors are shown to be related to Q and C vectors, as well as the ageostrophic circulation. The three-dimensional pseudocurl of the P vector gives the C vector that equals the ageostrophic pseudovorticity in the quasigeostrophic model. The horizontal components of the pseudocurl of P are perpendicular and proportional to the Q. The horizontal divergence of the P vector is the geostrophic absolute vorticity advection while the three-dimensional divergence of the P vector is the geostrophic quasigeostrophic potential vorticity advection. The ageostrophic wind can be partitioned into the P vector (geostrophic advective) and isallobaric wind contributions.

A numerical simulation of an idealized cyclone is used to characterize the distribution of the P vectors and P-vector diagnostics in order to demonstrate their potential application to the diagnosis of synoptic-scale circulations. The distribution of the P vectors clearly indicates the advections of geostrophic momentum and temperature that characterize cyclogenesis. An examination of the P vectors and the isallobaric wind demonstrates that the P vectors provide insight into the ageostrophic circulation of the cyclone. Diagnoses of the three-dimensional P-vector divergence and curl are shown to produce useful depictions of cyclonic vortex spinup and the propagation of both the large- and smaller-scale features of the system. These diagnostics can be interpreted from a variety of perspectives, including the height tendency and the advection of quasigeostrophic potential vorticity. The use of P vectors to diagnose synoptic-scale circulations appears to provide potentially useful insights into the dynamics of synoptic-scale disturbances not readily obtained from other diagnoses.

Full access
Hung-Chi Kuo
and
R. T. Williams

Abstract

The choice of an appropriate spectral spatial discretization is governed by considerations of accuracy and efficiency. The purpose of this article is to discuss the boundary effects on regional spectral methods. In particular, we consider the Chebyshev τ and sinusoidal- or polynomial-subtracted sine–cosine expansion methods. The Fourier and Chebyshev series are used because of the orthogonality and completeness properties and the existence of fast transforms. The rate of convergence of expansions based on Chebyshev series depends only on the smoothness of the function being expanded, and not on its behavior at the boundaries. The sinusoidal- or polynomial-subtracted sine–cosine expansion Tatsumi-type methods do not, in general, possess the exponential- convergence property. This is due to the fact that the higher derivatives of the polynomial- or sinusoidal- subtracted function are not periodic in a model with time-dependent boundary conditions. The discontinuity in derivatives causes the slow convergence of the expanded series (Gibbs phenomenon). When a large disturbance is near the boundary so that derivative discontinuities in the expanded function are large, the Tatsumi-type method causes not only erroneous numerical values in the outgoing boundary, but also spurious oscillations in the incoming boundary region. When the wave is away from the boundary, low resolution in the Tatsumi-type method converges exponentially, just as with the Chebyshev τ method. High-resolution solutions of the Tatsumi-type method do not, however, yield high accuracy due to the discontinuity in higher derivatives of the expanded function.

Full access
Hung-chi Kuo
and
R. T. Williams

Abstract

We explore the use of semi-Lagrangian methods in a situation where the spatial scale of the flow collapses to zero during the time integration. The inviscid Burgers equation is used as the test model because it is the simplest equation that allows scale collapse (shock formation), and because it has analytic solutions. It is shown that despite the variable manner in which the gradient of the wind field approaches infinity in the neighborhood of the shock, the semi-Lagrangian method allows the error to be localized near the steep slope region. Comparisons with second-order finite difference and tau methods are provided. Moreover, the semi-Lagrangian method gives accurate results even with larger time steps (Courant number greater than 2 or 4) than are possible with the Eulerian methods. The semi-Lagrangian method, along with other recently developed numerical methods, is useful in simulating the development Of steep gradients or near discontinuities in a numerical model. Some applications of the semi-Lagrangian method are discussed.

Full access
Hung-Chi Kuo
and
R. T. Williams

Abstract

The accuracy of a numerical model is often scale dependent. Large spatial-scale phenomena are expected to be numerically solved with better accuracy, regardless of whether the discretization is spectral, finite difference, or finite element. The purpose of this article is to discuss the scale-dependent accuracy associated with the regional spectral model variables expanded by sine–cosine series. In particular, the scale-dependent accuracy in the Chebyshev-tau, finite difference, and sinusoidal- or polynomial-subtracted sine–cosine expansion methods is considered. With the simplest examples, it is demonstrated that regional spectral models may possess an unusual scale-dependent accuracy. Namely, the numerical accuracy associated with large-spatial-scale phenomena may be worse than the numerical accuracy associated with small-spatial-scale phenomena. This unusual scale-dependent accuracy stems from the higher derivatives of basic-state subtraction functions, which are not periodic. The discontinuity is felt mostly by phenomena with large spatial scale. The derivative discontinuity not only causes the slow convergence of the expanded Fourier series (Gibbs phenomenon) but also results in the unusual scale-dependent numerical accuracy. The unusual scale-dependent accuracy allows large-spatial-scale phenomena in the model perturbation fields to be solved less accurately.

Full access
Full access
Satoki Tsujino
and
Hung-Chi Kuo

Abstract

The inner-core dynamics of Supertyphoon Haiyan (2013) undergoing rapid intensification (RI) are studied with a 2-km-resolution cloud-resolving model simulation. The potential vorticity (PV) field in the simulated storm reveals an elliptical and polygonal-shaped eyewall at the low and middle levels during RI onset. The PV budget analysis confirms the importance of PV mixing at this stage, that is, the asymmetric transport of diabatically generated PV to the storm center from the eyewall and the ejection of PV filaments outside the eyewall. We employ a piecewise PV inversion (PPVI) and an omega equation to interpret the model results in balanced dynamics. The omega equation diagnosis suggests eye dynamical warming is associated with the PV mixing. The PPVI indicates that PV mixing accounts for about 50% of the central pressure fall during RI onset. The decrease of central pressure enhances the boundary layer (BL) inflow. The BL inflow leads to contraction of the radius of the maximum tangential wind (RMW) and the formation of a symmetric convective PV tower inside the RMW. The eye in the later stage of the RI is warmed by the subsidence associated with the convective PV towers. The results suggest that the pressure change associated with PV mixing, the increase of the symmetric BL radial inflow, and the development of a symmetric convective PV tower are the essential collaborating dynamics for RI. An experiment with 500-m resolution shows that the convergence of BL inflow can lead to an updraft magnitude of 20 m s−1 and to a convective PV tower with a peak value of 200 PVU (1 PVU = 10−6 K kg−1 m2 s−1).

Free access
Satoki Tsujino
,
Kazuhisa Tsuboki
, and
Hung-Chi Kuo

Abstract

Typhoons with long-lived concentric eyewalls (CEs) are more intense than those with short-lived CEs. It is important for more accurate prediction of typhoon intensity to understand the maintenance mechanism of the long-lived CEs. To study the mechanism of the long-term maintenance of CEs, a numerical experiment of Typhoon Bolaven (2012) is performed using a nonhydrostatic model with full physics. Two aspects of the maintenance of simulated CEs are investigated: the maintenance of the inner eyewall and the contraction of the outer eyewall. To examine the maintenance of the inner eyewall, the equivalent potential temperature budget and air parcel trajectories of the simulated inner eyewall are calculated. The results show that the entropy supply to the inner eyewall is sufficient to maintain the inner eyewall after secondary eyewall formation (SEF). During the early period after SEF, entropy is supplied by an axisymmetric inflow, and later it is supplied by nonaxisymmetric flows of the outer eyewall. To examine the contraction of the outer eyewall, the potential vorticity (PV) budget of the outer eyewall is diagnosed. The result reveals that the negative contribution to the contraction of the outer PV peak (i.e., the outer eyewall) in the early period is the negative PV generation due to axisymmetric advection and diabatic heating just inside of the outer PV peak. In the later period, the negative PV generation due to nonaxisymmetric structure is important for the prevention of contraction. The present study reveals that the structure of the outer eyewall plays important roles in the maintenance of long-lived CEs.

Open access
Hung-Chi Kuo
,
George T-J. Chen
, and
Chung-Hsien Lin

Abstract

The merger of tropical cyclones Zeb and Alex is described. The process includes mutual cyclonic rotation, followed by merger of Zeb and Alex. The cyclonic rotation of Alex around Zeb accelerated as the separation distance decreased to 850 km. During the merger process, Alex was quickly elongated and wrapped cyclonically around Zeb to become a spiral band of Zeb. The final merger occurred at a distance of 450 km. The observed merger processes appear to be in good agreement with the potential vorticity theories of vortex interaction and the formation of spiral bands. Despite the presence of moist convections, the straining-out regime of Dritschel and Waugh appears to be applicable to the interaction between Alex and Zeb.

Full access
Li-Huan Hsu
,
Hung-Chi Kuo
, and
Robert G. Fovell

Abstract

This paper examines the effect of topographically phase-locked convection on the motion of typhoons across the island of Taiwan. Data for 84 typhoons that reached Taiwan’s eastern coast from 1960 to 2010 are analyzed, with motions compared to the long-term average overland translation speed. For 61 continuous-track typhoons among all cases, 77% of the slow-moving tropical cyclones (TCs) made landfall on the northern end of Taiwan’s eastern coast, while 60% of the fast storms had southeastern coastal landfalls.

This geographic asymmetry with respect to typhoon translation speeds widened after landfall, as the slow movers typically decelerated during the overland period, whereas the faster TCs sped up. In particular, the average overland duration was 16 h for the slow class, compared to only 3 h for the fast-moving typhoons. The combination of slower translation with longer duration for the northern class of TCs led to large rainfall on the southwestern slope of the island’s Central Mountain Range.

Weather Research and Forecasting model experiments are used to study the effect of convection on storm motion over a mountainous island resembling Taiwan. The authors find that the topographically phase-locked convection acts to slow down (speed up) the northern (southern) landfalling typhoons. The model results also suggest that a positive feedback mechanism exists for the slow storms, in which the convective heating pattern forced by topography acts to reduce the TC motion, leading to even more prolonged precipitation and heating, yielding further speed reductions.

Full access
Hung-Chi Kuo
,
R. T. Williams
, and
Jen-Her Chen

Abstract

An elliptical eye that rotated cyclonically with a period of approximately 144 minutes in Typhoon Herb 1996 was documented. The elliptical region had a semimajor axis of 30 km and a semiminor axis of 20 km. Two complete periods of approximately 144 min were observed in the Doppler radar data. The rotation of the elliptical eye in the context of barotropic dynamics at three levels were explored: linear waves on a Rankin vortex, a nonlinear Kirchhoff vortex, and with a nonlinear spectral model. The linear wave theory involves the existence of both the high (potential) vorticity gradient near the eye edge and the cyclonic mean tangential flow in the typhoon. The propagation of (potential) vorticity waves in the cyclonic mean flow makes the elliptical eye rotate cyclonically. The rotation period is longer than the period of a parcel trajectory moving in the cyclonic mean flow around the circumference, because the vorticity wave propagates upwind. The nonlinear theory stems from the rotation of Kirchhoff’s vortex. Estimates of the eye rotation period from both linear and nonlinear theories agree with observations of the eye rotation period when the observed maximum wind from Herb is used. Nonlinear numerical computations suggest the importance of the interaction of neutral vorticity waves, which determine the shape and the rotation period of the eye. The calculations also support the rotation of the eye in approximately 144 min in the presence of axisymmetrization, vorticity redistribution, wave breaking, and vortex merging processes.

Full access