bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Computation of Invariant Measures in Random Dynamical Systems
Authors: Imkeller Peter , Kloeden Peter
Published: July 2003

Invariant measures of dynamical systems generated e.g. by difference equations can be computed by discretizing the originally continuum state space, and replacing the action of the generator by the transition mechanism of a Markov chain. In fact they are approximated by stationary vectors of these Markov chains. Here we extend this well-known approximation result and the underlying algorithm to the setting of random dynamical systems, i.e. dynamical systems on the skew product of a probability space carrying the underlying stationary stochasticity and the state space, a particular non-autonomous framework. The systems are generated by difference equations driven by stationary random processes modelled on a metric dynamical system. The approximation algorithm involves spatial discretizations and the definition of appropriate random Markov chains with stationary vectors converging to the random invariant measure of the system.
Existence and Uniqueness of Solutions for Delay Stochastic Evolution Equations of Second Order in Time
Authors: Garrido-Atienza María J. , Real José
Published: July 2003

Some results on the existence and uniqueness of solutions for stochastic evolution equations of second order in time, containing some hereditary characteristics, are proved. Our theory is developed from a variational point of view and in a general functional setting which permit us to deal with several kinds of delay terms in a unified formulation. The theory is illustrated with two examples.
The Exponential Behaviour of Nonlinear Stochastic Functional Equations of Second Order in Time
Authors: Caraballo Tomás , Garrido-Atienza María J. , Real José
Published: July 2003

Sufficient conditions for exponential mean square stability of solutions to delayed stochastic partial differential equations of second order in time are established. As a consequence of these results, some on the pathwise exponential stability of the system are proved. The stability results derived are applied also to partial differential equations without hereditary characteristics. The results are illustrated with several examples.
Profinite and finite groups associated with loop and diffeomorphism groups of non‐Archimedean manifolds
Authors: Ludkovsky S. V. , Diarra B.
Published: July 2003

We investigate p‐adic completions of clopen (i.e., closed and open at the same time) subgroups W of loop groups and diffeomorphism groups G of compact manifolds over non‐Archimedean fields. We outline two different compactifications of loop groups and one compactification of diffeomorphism groups, describe associated finite groups in projective limits, and
discuss relations with the representation theory.
Local spectral theory for 2 × 2 operator matrices
Authors: Elbjaoui H. , Zerouali E. H.
Published: July 2003

We discuss the spectral properties of the operator MC ∈ ℒ(X ⊕ Y) defined by , where A ∈ ℒ(X), B ∈ ℒ(Y), C ∈ ℒ(Y, X), and X, Y are complex Banach spaces. We prove that for all C ∈ ℒ(Y, X). This allows us to give a partial positive answer to Question 3 of Du and Jin (1994) and generalizations of some results of Houimdi and Zguitti (2000). Some applications to the similarity problem are also given.
Stochastic antiderivational equations on non‐Archimedean Banach spaces
Authors: Ludkovsky S. V.
Published: July 2003

Stochastic antiderivational equations on Banach spaces over local
non‐Archimedean fields are investigated. Theorems about existence and uniqueness of the solutions are proved under definite conditions. In particular, Wiener processes are considered in relation to the non‐Archimedean analog of the Gaussian measure.
α‐fuzzy compactness in I‐topological spaces
Authors: Gregori Valentín , Künzi Hans-peter A.
Published: July 2003

Using a gradation of openness in a (Chang fuzzy) I‐topological space, we introduce degrees of compactness that we call
α‐fuzzy compactness (where α belongs to the unit interval), so extending the concept of compactness due to C. L. Chang. We obtain a Baire category theorem for α‐locally compact spaces and construct a one‐point α‐fuzzy compactification of an I‐topological space.
The full nonrigid group theory for trimethylamine
Authors: Hamadanian Masood , Ashrafi Ali Reza
Published: July 2003

The nonrigid molecule group theory (NRG) in which the dynamical
symmetry operations are defined as physical operations is a new field in chemistry. Smeyers in a series of papers applied this notion to determine the character table of restricted NRG of some molecules. In this note, a simple method is described by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of methyl groups attached to a rigid framework. We study the full NRG of trimethylamine and prove that it is a group of order 1296 with 28 conjugacy classes. The method can be generalized to apply to other nonrigid molecules. The full
nonrigid (f‐NRG) molecule group theory is seen to be used advantageously to study the internal dynamics of such molecules.
Properties of certain p‐valently convex functions
Authors: Yang Dinggong , Owa Shigeyoshi
Published: July 2003

A subclass 𝒞p(λ, μ)(p ∈ ℕ,  0 < λ < 1,   − λ≦μ < 1) of p‐valently convex functions in the open unit disk 𝕌 is introduced. The object of the present paper is to discuss some interesting properties of functions belonging to the class 𝒞p(λ, μ).
T‐fuzzy multiply positive implicative BCC‐ideals of BCC‐algebras
Authors: Zhan Jianming , Tan Zhisong
Published: July 2003

The concept of fuzzy multiply positive BCC‐ideals of BCC‐algebras
is introduced, and then some related results are obtained. Moreover, we introduce the concept of T‐fuzzy multiply positive implicative BCC‐ideals of BCC‐algebras and investigate T‐product of T‐fuzzy multiply positive implicative BCC‐ideals
of BCC‐algebras, examining its properties. Using a t‐norm T, the direct product and T‐product of T‐fuzzy multiply positive implicative BCC‐ideals of BCC‐algebras are discussed and their properties are investigated.
The equivalence of Mann iteration and Ishikawa iteration for non‐Lipschitzian operators
Authors: Rhoades B. E. , Şoltuz Ştefan M.
Published: July 2003

We show that the convergence of Mann iteration is equivalent to the convergence of Ishikawa iteration for various classes of
non‐Lipschitzian operators.
On the Fresnel integrals and the convolution
Authors: Kiliçman Adem , Fisher Brian
Published: July 2003

The Fresnel cosine integral C(x), the Fresnel sine integral S(x), and the associated functions C+(x), C−(x), S+(x), and S−(x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel cosine integral and its associated functions with and xr are evaluated.
Fuzzy super irresolute functions
Authors: Abbas S. E.
Published: July 2003

The concept of fuzzy super irresolute function was considered and studied by Šostak's (1985). A comparison between this type and other existing ones is established. Several characterizations, properties, and their effect on some fuzzy topological spaces are studied. Also, a new class of fuzzy topological spaces under the terminology fuzzy S*‐closed spaces is introduced and investigated.
On the p‐adic spectral analysis and multiwavelet on L2(ℚpn)
Authors: Chong Wonyong , Kim Min-Soo , Kim Taekyun , Son Jin-Woo
Published: July 2003

We try to generalize an explicit construction for an orthonormal system of eigenfunctions of the Vladimirov operator on which was originally given by Vladimirov (1988). Also the multiwavelet analysis can be considered as the p‐adic spectral analysis in , using in part the recent work of Kozyrev (2002).
On some center‐like subsets of groups
Authors: Klein Abraham A. , Bell Howard E.
Published: July 2003

We study the properties of certain center‐like subsets of groups,
which are obtained by localizing setwise commutativity conditions.
On boundary value problems for degenerate differential inclusions in Banach spaces
Authors: Obukhovskii Valeri , Zecca Pietro
Published: July 2003

We consider the applications of the theory of condensing set‐valued maps, the theory of set‐valued linear operators, and the topological degree theory of the existence of mild solutions for a class of degenerate differential inclusions in a reflexive Banach space. Further, these techniques are used to obtain the solvability of general boundary value problems for a given class of inclusions. Some particular cases including periodic problems are considered.
Ill‐posed equations with transformed argument
Authors: Gramsch Simone , Schock Eberhard
Published: July 2003

We discuss the operator transforming the argument of a function in the L2‐setting. Here this operator is unbounded and closed. For the approximate solution of ill‐posed equations with closed operators, we present a new view on the Tikhonov regularization.
On the A‐Laplacian
Authors: Aïssaoui Noureddine
Published: July 2003

We prove, for Orlicz spaces LA(ℝN) such
that A satisfies the Δ2 condition, the nonresolvability of the A‐Laplacian equation ΔAu + h = 0 on ℝN, where ∫h ≠ 0, if ℝN is A‐parabolic. For a large class of Orlicz spaces including Lebesgue spaces Lp (p > 1), we also prove that the same equation, with any bounded measurable function h with compact support, has a solution with gradient in
LA(ℝN) if ℝN is A‐hyperbolic.
Minimax theorems on C1 manifolds via Ekeland variational principle
Authors: Cuesta Mabel
Published: July 2003

We prove two minimax principles to find almost critical points of
C1 functionals restricted to globally defined C1 manifolds of codimension 1. The proof of the theorems relies on Ekeland variational principle.
Regulation of Nitric Oxide-Sensitive Guanylyl Cyclase
Authors: Friebe Andreas , Koesling Doris
Published: July 2003

In this review, we outline the current knowledge on the regulation of nitric oxide (NO)-sensitive guanylyl cyclase (GC). Besides NO, the physiological activator that binds to the prosthetic heme group of the enzyme, two novel classes of GC activators have been identified that may have broad pharmacological implications. YC-1 and YC-1-like substances act as NO sensitizers, whereas the substance BAY 58-2667 stimulates NO-sensitive GC NO-independently and preferentially activates the heme-free form of the enzyme. Sensitization and desensitization of NO/cGMP signaling have been reported to occur on the level of NO-sensitive GC; in the present study, an alternative mechanism is introduced explaining the adaptation of the NO-induced cGMP response by a long-term activation of the cGMP-degrading phosphodiesterase 5 (PDE5). Finally, regulation of GC expression and a possible modulation of GC activity by other factors are discussed.
Numerical Aspects of the Application of Recursive Filters to Variational Statistical Analysis. Part II: Spatially Inhomogeneous and Anisotropic General Covariances
Authors: Purser R. James , Wu Wan-Shu , Parrish David F. , Roberts Nigel M.
Published: July 2003

In this second part of a two-part study of recursive filter techniques applied to the synthesis of covariances in a variational analysis, methods by which non-Gaussian shapes and spatial inhomogeneities and anisotropies for the covariances may be introduced in a well-controlled way are examined. These methods permit an analysis scheme to possess covariance structures with adaptive variations of amplitude, scale, profile shape, and degrees of local anisotropy, all as functions of geographical location and altitude.

First, it is shown how a wider and more useful variety of covariance shapes than just the Gaussian may be obtained by the positive superposition of Gaussian components of different scales, or by further combinations of these operators with the application of Laplacian operators in order for the products to possess negative sidelobes in their radial profiles.

Then it is shown how the techniques of recursive filters may be generalized to admit the construction of covariances whose characteristic scales relative to the grid become adaptive to geographical location, while preserving the necessary properties of self-adjointness and positivity. Special attention is paid to the problems of amplitude control for these spatially inhomogeneous filters and an estimate for the kernel amplitude is proposed based upon an asymptotic analysis of the problem.

Finally, a further generalization of the filters that enables fully anisotropic and geographically adaptive covariances to be constructed in a computationally efficient way is discussed.
A Numerical Study of the Impact of Vertical Shear on the Distribution of Rainfall in Hurricane Bonnie (1998)
Authors: Rogers Robert , Chen Shuyi , Tenerelli Joseph , Willoughby Hugh
Published: July 2003

Despite the significant impacts of torrential rainfall from tropical cyclones at landfall, quantitative precipitation forecasting (QPF) remains an unsolved problem. A key task in improving tropical cyclone QPF is understanding the factors that affect the intensity and distribution of rainfall around the storm. These include the storm motion, topography, and orientation of the coast, and interactions with the environmental flow. The combination of these effects can produce rainfall distributions that may be nearly axisymmetric or highly asymmetric and rainfall amounts that range from 1 or 2 cm to >30 cm.

This study investigates the interactions between a storm and its environmental flow through a numerical simulation of Hurricane Bonnie (1998) that focuses on the role of vertical wind shear in governing azimuthal variations of rainfall. The simulation uses the high-resolution nonhydrostatic fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) to simulate the storm between 0000 UTC 22 August and 0000 UTC 27 August 1998. During this period significant changes in the vertical shear occurred in the simulation. It changed from strong west-southwesterly, and across track, to much weaker south-southwesterly, and along track. Nearly concurrently, the azimuthal distribution of convection changed from a distinct wavenumber-1 pattern to almost azimuthally symmetric by the end of the time period. The strongest convection in the core was generally located on the downshear left side of the shear vector when the shear was strong. The azimuthal distributions and magnitudes of low-level radial inflow, reflectivity, boundary layer divergence, and low-level vertical motion all varied consistently with the evolution of the vertical shear. Additionally, the vortex showed a generally downshear tilt from the vertical. The magnitude of the tilt correlated well with changes in magnitude of the environmental shear. The accumulated rainfall was distributed symmetrically across the track of the storm when the shear was strong and across track, and it was distributed asymmetrically across the track of the storm when the shear was weak and along track.
Inflow Layer Energetics of Hurricane Bonnie (1998) near Landfall
Authors: Wroe Derek R. , Barnes Gary M.
Published: July 2003

On 26 August 1998, a NOAA WP-3D aircraft executed a curved track that mimics an inflow trajectory to the eyewall of Hurricane Bonnie. Global positioning system (GPS) sondes and airborne expendable bathythermographs jettisoned along the trajectory provide the observations to conduct an energy budget for the 1600-m-deep inflow to the eyewall. Surface fluxes are estimated via the bulk aerodynamic equations and the flux at the top of the inflow is solved as a residual.

From 170- to 125-km radial distance from the circulation center the mean θe of the inflow remains constant despite combined sensible and latent surface fluxes in excess of 500 W m−2. Convective cells remove energy from the inflow boundary layer at a rate similar to the inputs from the sea. From 125 to 100 km, in the annulus adjacent to the eyewall, mean θe increases 4.5 K in response to higher surface fluxes and little loss through the inflow top. Energy balance may be achieved by either entrainment of higher θe through the top of the inflow layer, or by inclusion of just half the estimated heat from viscous dissipation. The authors infer that the secondary circulation of the eyewall inhibits convective cells from forming in this region and thus facilitates the rapid increase of energy in the inflow. The results support hypotheses that hurricane intensity appears to be strongly modulated by energy exchange in a meso-β region adjacent to and under the eyewall.
Circulation Regimes and Low-Frequency Oscillations in the South Pacific Sector
Authors: Robertson Andrew W. , Mechoso Carlos R.
Published: July 2003

The characteristics of subseasonal circulation variability over the South Pacific are examined using 10-day lowpass-filtered 700-hPa geopotential height NCEP–NCAR reanalysis data. The extent to which the variability in each season is characterized by recurrent geographically fixed circulation regimes and/or oscillatory behavior is determined. Two methods of analysis (a K-means cluster analysis and a cross-validated Gaussian mixture model) both indicate three to four geographically fixed circulation regimes in austral fall, winter, and (to some extent) spring. The spatial regime structures are found to be quite similar in each season; they resemble the so-called Pacific–South American (PSA) patterns discussed in previous studies and often referred to as PSA 1 and PSA 2. Oscillatory behavior is investigated using singular spectrum analysis. This identifies a predominantly stationary wave with a period of about 40 days and a spatial structure similar to PSA 1; it is most pronounced in winter and spring and exhibits a noticeable eastward drift as it decays. The power spectrum of variability is otherwise well approximated by a red spectrum, together with enhanced broader-band 15–30-day variability.

The results presented herein indicate that low-frequency variability over the South Pacific is not dominated by a propagating wave whose quadrature phases are PSA 1 and PSA 2, as hitherto described. Rather, it is found that the variability is well described by the occurrence of three to four geographically fixed circulation regimes, with a (near) 40-day oscillation that is predominantly stationary in space. The potential subseasonal predictability implied by this duality is discussed. Only during austral spring is a strong correlation found between El Niño and the frequency of occurrence of the circulation regimes.
The Tristate Hailstorm: The Most Costly on Record
Authors: Changnon Stanley A. , Burroughs Jonathan
Published: July 2003

The most damaging hailstorm ever recorded moved from eastern Kansas to southern Illinois during an 8-h period on 10 April 2001, depositing 2.5- to 7.5-cm-diameter hailstones along a 585-km path. A classic long-lived supercell storm was the cause of the record hailfalls. The record-large hailswath size, large and often windblown hailstones, and movement over portions of the St. Louis and Kansas City urban areas led to $1.5 billion in insured losses. This tristate hailstorm and other adjacent hailstorms collectively created $1.9 billion in insured losses in a 2-day period, becoming the ninth most costly weather catastrophe in the United States since property insurance records began in 1949.
Targeted Observations to Improve Operational Tropical Cyclone Track Forecast Guidance
Authors: Aberson Sim D.
Published: July 2003

Since 1997, the Tropical Prediction Center and the Hurricane Research Division have conducted operational synoptic surveillance missions with a Gulfstream IV-SP jet aircraft to improve numerical forecast guidance. Due to limited aircraft resources, optimal observing strategies for these missions must be developed. In the current study, the most rapidly growing modes are represented by areas of large forecast spread in the NCEP bred-vector ensemble forecasting system. The sampling strategy requires sampling of the entire target region with regularly spaced dropwindsonde observations.

Three dynamical models were employed in testing the targeting and sampling strategies. With the assimilation into the numerical guidance of all the observations gathered during the surveillance missions, only the 12-h Geophysical Fluid Dynamics Laboratory Hurricane Model forecast showed statistically significant improvement. Assimilation of only the subset of data from the subjectively found fully sampled target regions produced a statistically significant reduction of the track forecast errors of up to 25% within the critical first 2 days of the forecast. This is comparable with the cumulative business-as-usual improvement expected over 18 yr.
Evaluation of a Multigrid Barotropic Tropical Cyclone Track Model
Authors: Vigh Jonathan , Fulton Scott R. , DeMaria Mark , Schubert Wayne H.
Published: July 2003

The performance of a multigrid barotropic tropical cyclone track model (MUDBAR) is compared to that of a current operational barotropic model (LBAR). Analysis of track forecast errors for the 2001 Atlantic hurricane season shows that MUDBAR gives accuracy similar to LBAR with substantially lower computational cost. Despite the use of a barotropic model, the MUDBAR forecasts show skill relative to climatology and persistence (CLIPER) out to 5 days.
Influence of Atmospheric Asymmetries on the Intensification of Hurricane Opal: Piecewise PV Inversion Diagnosis of a GFDL Model Forecast
Authors: Shapiro Lloyd J. , Möller J. Dominique
Published: July 2003

Although Hurricane Opal of 1995 is one of the most intensely studied hurricanes ever, the cause of the hurricane's rapid intensification over the Gulf of Mexico is still a matter of controversy. While some authors have concluded that an approaching upper-level atmospheric trough had a significant impact on intensification, others have inferred only a small impact of the trough on the hurricane's strengthening. A recent study by the present authors diagnosed a Geophysical Fluid Dynamics Laboratory (GFDL) model forecast and found that eddy fluxes made only a small contribution to the lower-tropospheric evolution of the model hurricane vortex near the core. Thus, at face value, this previous study supported the conclusion that the upper-level trough was not important to the intensification of Opal. As noted in that study, however, in order to isolate the contribution of the trough by itself, the technique of piecewise potential vorticity (PV) inversion is required. The present study is the first to use this method in a diagnostic framework to determine the asymmetric features that contribute to tropical cyclone intensification.

The present study uses the same GFDL hurricane model forecast as in the previous study to diagnose the balanced contribution of various pieces of the asymmetric PV anomaly to the intensification of the model Opal vortex. Though the upper-level trough is an outer-environmental feature, its influence is found to extend into Opal's inner-core region. The eddies associated with the trough induce an upper-level inner-core acceleration. An estimate of the impact of convective feedback on the influence of the upper-level trough on Opal's evolution is made. The results elucidate and modify the conclusions of other authors. There is no indication from the present diagnosis that the upper-level trough was a significant contributor to Opal's lower-tropospheric intensification.
Climatological Characteristics and Seasonal Forecasting of Tropical Cyclones Making Landfall along the South China Coast
Authors: Liu K. S. , Chan Johnny C. L.
Published: July 2003

This paper presents the important climatological features of the tropical cyclones making landfall along the South China coast and proposes a statistical scheme for the prediction of the annual number of such tropical cyclones. This number is found to have a large variation, which is mainly due to the occurrence or nonoccurrence of the El Niño–Southern Oscillation (ENSO) phenomenon. A strong El Niño event is found to reduce the number of landfalling tropical cyclones whereas more tropical cyclones tend to make landfall in years associated with La Niña events. Such variations are more prominent in some seasons. The late season (October–November) activity is generally suppressed (enhanced) in El Niño (La Niña) years whereas the chance of a tropical cyclone striking the South China coast increases (decreases) significantly in the early season (May and June) after the mature phase of a La Niña (El Niño) event. These anomalous activities are apparently linked to the ENSO-induced anomalies in the low- and midlevel large-scale circulation.

Based on the ENSO-related indices such as the Niño-3.4 sea surface temperature anomaly and the equatorial Southern Oscillation index, a statistical prediction scheme for the annual number of such landfalling tropical cyclones by 1 April is developed using the projection–pursuit regression technique. This scheme provides a 40% skill improvement in root-mean-square error with respect to climatology. A real-time prediction made in 2001 gave reasonable results.
Assimilation of Simulated Doppler Radar Observations with an Ensemble Kalman Filter*
Authors: Snyder Chris , Zhang Fuqing
Published: July 2003

Assimilation of Doppler radar data into cloud models is an important obstacle to routine numerical weather prediction for convective-scale motions; the difficulty lies in initializing fields of wind, temperature, moisture, and condensate given only observations of radial velocity and reflectivity from the radar. This paper investigates the potential of the ensemble Kalman filter (EnKF), which estimates the covariances between observed variables and the state through an ensemble of forecasts, to assimilate radar observations at convective scales. In the basic experiment, simulated observations are extracted from a reference simulation of a splitting supercell and assimilated using the EnKF and the same numerical model that produced the reference simulation. The EnKF produces accurate analyses, including the unobserved variables, after roughly 30 min (or six scans) of radial velocity observations. Additional experiments, in which forecasts are made from the ensemble-mean analysis, reveal that forecast errors grow significantly in this simple system, so that the ability of the EnKF to track the reference solution is not simply because of stable system dynamics. It is also found that the covariances between radial velocity and temperature, moisture, and condensate are important to the quality of the analyses, as is the initialization chosen for the ensemble members prior to assimilating the first observations. These results are promising, especially given the ease of implementing the EnKF. A number of important issues remain, however, including the initialization of the ensemble prior to the first observation, the treatment of uncertainty in the environmental sounding, the role of error in the forecast model (particularly the microphysical parameterizations), and the treatment of lateral boundary conditions.
Cell Merger Potential in Multicell Thunderstorms of Weakly Sheared Environments: Cell Separation Distance versus Planetary Boundary Layer Depth
Authors: Stalker James R. , Knupp Kevin R.
Published: July 2003

Using high-resolution three-dimensional numerical experiments, this paper shows that the cell separation distance scales as 0.75 times the planetary boundary layer (PBL) depth for successful cell mergers between constructively interacting cells within multicell thunderstorms. This boundary layer scaling is determined from several simulations of convective cell pairs with a fixed PBL depth and is shown to be valid for other sensitivity simulations with larger PBL depths. This research establishes a robust and quantitative relation between prestorm ambient conditions and cell merger potential useful for research efforts on the multifaceted cell merger process of multicell thunderstorms. The weakly sheared ambient prestorm conditions of the 9 August 1991 Convection and Precipitation/Electrification Experiment (CaPE) multicell thunderstorm are used to initialize the cell pair simulations.

Since ambient wind and wind shear are assumed to be zero, only simple cell mergers, defined in this study as those between cell updraft cores joined but not overlapping in the convective stage, are shown to be possible. The coarse-resolution simulations of Stalker suggest that ambient wind shear may be necessary for forced cell mergers, defined in this study as those in which the initial updraft cores are found apart. The scenarios of overlapping initial updraft cores for cell merger are considered physically invalid in this study.
Applying a Neural Network Collocation Method to an Incompletely Known Dynamical System via Weak Constraint Data Assimilation
Authors: Liaqat Ali , Fukuhara Makoto , Takeda Tatsuoki
Published: July 2003

A method based on a neural network collocation method is proposed for approximating incompletely known dynamical systems via weak constraint data assimilation formulation. The aim of the new method is to solve several difficult issues encountered in previous research. For this purpose, the weak constraint property of the neural network collocation method is used. The problem regarding the wider assimilation window is tackled by interconnecting narrower windows with finite overlapping interfaces. The method is examined by considering the Lorenz system as an example where one of the three equations of the system is unknown. The object function of the neural network training is composed of squared residuals of differential equations at collocation points and squared deviations of the observations from their corresponding calculated values.

The weakly and highly nonlinear cases of the Lorenz system are considered. The numerical experiments have been carried out with simulated noiseless and noisy observation data under various conditions. The performance of the method for approximating an unknown equation during the assimilation and testing periods is examined for the two cases. Also, the parameters of incomplete dynamical systems are estimated for the two cases. Satisfactory results have been obtained in both cases.
A Study of Subseasonal Predictability
Authors: Newman Matthew , Sardeshmukh Prashant D. , Winkler Christopher R. , Whitaker Jeffrey S.
Published: July 2003

The predictability of weekly averaged circulation anomalies in the Northern Hemisphere, and diabatic heating anomalies in the Tropics, is investigated in a linear inverse model (LIM) derived from their observed simultaneous and time-lag correlation statistics. In both winter and summer, the model's forecast skill at week 2 (days 8–14) and week 3 (days 15–21) is comparable to that of a comprehensive global medium-range forecast (MRF) model developed at the National Centers for Environmental Prediction (NCEP). Its skill at week 3 is actually higher on average, partly due to its better ability to forecast tropical heating variations and their influence on the extratropical circulation. The geographical and temporal variations of forecast skill are also similar in the two models. This makes the much simpler LIM an attractive tool for assessing and diagnosing atmospheric predictability at these forecast ranges.

The LIM assumes that the dynamics of weekly averages are linear, asymptotically stable, and stochastically forced. In a forecasting context, the predictable signal is associated with the deterministic linear dynamics, and the forecast error with the unpredictable stochastic noise. In a low-order linear model of a high-order chaotic system, this stochastic noise represents the effects of both chaotic nonlinear interactions and unresolved initial components on the evolution of the resolved components. Its statistics are assumed here to be state independent.

An average signal-to-noise ratio is estimated at each grid point on the hemisphere and is then used to estimate the potential predictability of weekly variations at the point. In general, this predictability is about 50% higher in winter than summer over the Pacific and North America sectors; the situation is reversed over Eurasia and North Africa. Skill in predicting tropical heating variations is important for realizing this potential skill. The actual LIM forecast skill has a similar geographical structure but weaker magnitude than the potential skill.

In this framework, the predictable variations of forecast skill from case to case are associated with predictable variations of signal rather than of noise. This contrasts with the traditional emphasis in studies of shorter-term predictability on flow-dependent instabilities, that is, on the predictable variations of noise. In the LIM, the predictable variations of signal are associated with variations of the initial state projection on the growing singular vectors of the LIM's propagator, which have relatively large amplitude in the Tropics. At times of strong projection on such structures, the signal-to-noise ratio is relatively high, and the Northern Hemispheric circulation is not only potentially but also actually more predictable than at other times.
Ensemble Forecasts and the Properties of Flow-Dependent Analysis-Error Covariance Singular Vectors
Authors: Hamill Thomas M. , Snyder Chris , Whitaker Jeffrey S.
Published: July 2003

Approximations to flow-dependent analysis-error covariance singular vectors (AEC SVs) were calculated in a dry, T31 L15 primitive-equation global model. Sets of 400-member ensembles of analyses were generated by an ensemble-based data assimilation system. A sparse network of simulated rawinsonde observations were assimilated, and a perfect model was assumed. Ensembles of 48-h forecasts were also generated from these analyses. The structure of evolved singular vectors was determined by finding the linear combination of the forecast ensemble members that resulted in the largest forecast-error variance, here measured in a total-energy norm north of 20°N latitude. The same linear combination of analyses specifies the initial-time structure that should evolve to the forecast singular vector under assumptions of linearity of error growth.

The structures of these AEC SVs are important because they represent the analysis-error structures associated with the largest forecast errors. If singular vectors using other initial norms have very different structures, this indicates that these structures may be statistically unlikely to occur. The European Centre for Medium-Range Weather Forecasts currently uses singular vectors using an initial total-energy norm [“total-energy singular vectors” or (TE SVs)] to generate perturbations to initialize their ensemble forecasts. Approximate TE SVs were also calculated by drawing an initial random ensemble with perturbations that were white in total energy and applying the same approach as for AEC SVs. Comparing AEC SVs and approximate TE SVs, the AEC SVs had maximum amplitude in midlatitudes near the tropopause, both at the initial and evolved times. The AEC SVs were synoptic in scale, deep, and did not appear to be geographically localized nor tilted dramatically upshear. This contrasts with TE SVs, which started off relatively smaller in scale, were tilted upshear, and had amplitudes typically largest in the lower to midtroposphere.

The difference between AEC SVs and TE SVs suggests that operational ensemble forecasts based on TE SVs could be improved by changing the type of singular vector used to generate initial perturbations. This is particularly true for short-range ensemble forecasts, where the structure of the forecast ensemble is more closely tied to the analysis ensemble.
Comparative Analysis of Conformal Mappings Used in Limited-Area Models of Numerical Weather Prediction
Authors: Bourchtein Andrei , Bourchtein Ludmila
Published: July 2003

Conformal separable projections from a sphere onto a plane are introduced to generalize the concept of conformal stereographic, conic, and cylindrical projections. The concept of equivalence of projections is used for partition of all considered projections into equivalence classes. The variation coefficient is defined as the ratio between maximum and minimum mesh sizes of numerical grids. The problem of minimization of this coefficient inside each equivalence class is studied. The obtained variation coefficients from all classes are compared and the principal relation among stereographic, cylindrical, and conic projections is established. The stereographic conformal projection is indicated as that which generates the “best” numerical grids for numerical weather prediction limited-area models.
Large-Scale Circulation Patterns Associated with Heavy Spring Rain Events over Taiwan in Strong ENSO and Non-ENSO Years
Authors: Jiang Zhihong , Tai-Jen Chen George , Wu Ming-Chin
Published: July 2003

Daily rainfall data at 15 stations in Taiwan and the grid dataset of the National Centers for Environmental Prediction–National Center for Atmospheric Research during the period of February–March 1951–2000 were used to reveal the characteristics of large-scale circulations associated with spring heavy rain events over Taiwan in strong ENSO and non-ENSO years. The effect of interdecadal variation on the relationship of spring rainfall and ENSO was also examined.

Results showed that the different regimes of interdecadal variation that occurred in the late 1970s exert significant effect on the relationship between ENSO and spring rainfall in Taiwan. A pronounced positive correlation with statistical significance between cold season Niño-3 SST and the following spring rainfall over western Taiwan was only found since the late 1970s. Large-scale environmental conditions associated with the heavy spring rain events in strong ENSO and non-ENSO years were found to be quite different. Intrusion of a weak midlatitude frontal system into the eastern China coastal area coupled with an anomalous anticyclone over the Philippine Sea (PSAC) in the lower troposphere were primarily responsible for the spring heavy rain events in strong ENSO years. On the other hand, the intrusion of a much more intense midlatitude frontal system into China and the coastal area was necessary to generate spring heavy rain events in non-ENSO years. This difference is also instrumental for more frequent occurrence of heavy rainfall events and more rainfall amount observed in ENSO years.
Sea Surface Temperature Variability in Hurricanes: Implications with Respect to Intensity Change
Authors: Cione Joseph J. , Uhlhorn Eric W.
Published: July 2003

Scientists at NOAA's Hurricane Research Division recently analyzed the inner-core upper-ocean environment for 23 Atlantic, Gulf of Mexico, and Caribbean hurricanes between 1975 and 2002. The interstorm variability of sea surface temperature (SST) change between the hurricane inner-core environment and the ambient ocean environment ahead of the storm is documented using airborne expendable bathythermograph (AXBT) observations and buoy-derived archived SST data. The authors demonstrate that differences between inner-core and ambient SST are much less than poststorm, “cold wake” SST reductions typically observed (i.e., ∼0°–2°C versus 4°–5°C). These findings help define a realistic parameter space for storm-induced SST change within the important high-wind inner-core hurricane environment. Results from a recent observational study yielded estimates of upper-ocean heat content, upper-ocean energy extracted by the storm, and upper-ocean energy utilization for a wide range of tropical systems. Results from this analysis show that, under most circumstances, the energy available to the tropical cyclone is at least an order of magnitude greater than the energy extracted by the storm. This study also highlights the significant impact that changes in inner-core SST have on the magnitude of air–sea fluxes under high-wind conditions. Results from this study illustrate that relatively modest changes in inner-core SST (order 1°C) can effectively alter maximum total enthalpy (sensible plus latent heat) flux by 40% or more.

The magnitude of SST change (ambient minus inner core) was statistically linked to subsequent changes in storm intensity for the 23 hurricanes included in this research. These findings suggest a relationship between reduced inner-core SST cooling (i.e., increased inner-core surface enthalpy flux) and tropical cyclone intensification. Similar results were not found when changes in storm intensity were compared with ambient SST or upper-ocean heat content conditions ahead of the storm. Under certain circumstances, the variability associated with inner-core SST change appears to be an important factor directly linked to the intensity change process.
The Deep-Atmosphere Euler Equations in a Generalized Vertical Coordinate
Authors: Staniforth Andrew , Wood Nigel
Published: July 2003

Previous analysis of the hydrostatic primitive equations using a generalized vertical coordinate is extended to the deep-atmosphere nonhydrostatic Euler equations, and some special vertical coordinates of interest are noted. Energy and axial angular momentum budgets are also derived. This would facilitate the development of conserving finite-difference schemes for deep-atmosphere models. It is found that the implied principles of energy and axial angular momentum conservation depend on the form of the upper boundary. In particular, for a modeled atmosphere of finite extent, global energy conservation is only obtained for a rigid lid, fixed in space and time. To additionally conserve global axial angular momentum, the height of the lid cannot vary with longitude.
Short-Term Performance of MM5 with Cloud-Cover Assimilation from Satellite Observations
Authors: Yucel Ismail , James Shuttleworth W. , Gao X. , Sorooshian S.
Published: July 2003

This study investigates the extent to which assimilating high-resolution remotely sensed cloud cover into the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) provides an improved regional diagnosis of downward shortwave surface radiation fluxes and precipitation and enhances the model's ability to make short-range prediction. The high-resolution (4 km × 4 km) clear- and cloudy-sky radiances derived using a cloud-screening algorithm from visible band Geostationary Operational Environmental Satellite (GOES) data were used in the University of Maryland Global Energy and Water Cycle Experiment's Surface Radiation Budget (UMD GEWEX/SRB) model to infer the vertically integrated cloud mass via cloud optical thickness. Three-dimensional cloud fields were created that took their horizontal distribution from the satellite image but derived their vertical distribution, in part, from the fields simulated by MM5 during the time step immediately prior to assimilation and, in part, from the observed cloud-top height derived from the infrared band of GOES. Linear interpolation was used to derive 1-min cloud images between 15-min GOES samples, and the resulting images were ingested every minute. Comparisons were made between modeled and observed data taken from the Arizona Meteorological Network (AZMET) in southern Arizona for model runs with and without cloud ingestion. Cloud ingestion substantially improved the ability of the MM5 model to capture temporal and spatial variations in surface fields associated with cloud cover. Experiments in which the model was operated in forecast mode suggest that cloud ingestion gave some limited enhancement in MM5 short-term prediction ability for up to 3 h. However, an analysis suggests that, in order to get additional forecasting capability, it will be necessary to modify the atmospheric dynamics and thermodynamics in the model to be consistent with the ingested cloud fields.
Evolution of Cloud-to-Ground Lightning and Storm Structure in the Spencer, South Dakota, Tornadic Supercell of 30 May 1998
Authors: Carey Lawrence D. , Petersen Walter A. , Rutledge Steven A.
Published: July 2003

On 30 May 1998, a tornado devastated the town of Spencer, South Dakota. The Spencer tornado (rated F4 on the Fujita tornado intensity scale) was the third and most intense of five tornadoes produced by a single supercell storm during an approximate 1-h period. The supercell produced over 76% positive cloud-to-ground (CG) lightning and a peak positive CG flash rate of 18 flashes min−1 (5-min average) during a 2-h period surrounding the tornado damage. Earlier studies have reported anomalous positive CG lightning activity in some supercell storms producing violent tornadoes. However, what makes the CG lightning activity in this tornadic storm unique is the magnitude and timing of the positive ground flashes relative to the F4 tornado. In previous studies, supercells dominated by positive CG lightning produced their most violent tornado after they attained their maximum positive ground flash rate, whenever the rate exceeded 1.5 flashes min−1. Further, tornadogenesis often occurred during a lull in CG lightning activity and sometimes during a reversal from positive to negative polarity. Contrary to these findings, the positive CG lightning flash rate and percentage of positive CG lightning in the Spencer supercell increased dramatically while the storm was producing F4 damage on Spencer.

These results have important implications for the use of CG lightning in the nowcasting of tornadoes and for the understanding of cloud electrification in these unique storms. In order to further explore these issues, the authors present detailed analyses of storm evolution and structure using Sioux Falls, South Dakota, (KFSD) Weather Surveillance Radar-1988 Doppler (WSR-88D) radar reflectivity and Doppler velocity and National Lightning Detection Network (NLDN) CG lightning data. The analyses suggest that a merger between the Spencer supercell and a squall line on its rear flank may have provided the impetus for both the F4 tornadic damage and the dramatic increase in positive CG lightning during the tornado, possibly explaining the difference in timing compared to past studies.
The Taiwan Central Weather Bureau Regional Spectral Model for Seasonal Prediction: Multiparallel Implementation and Preliminary Results
Authors: Henry Juang Hann-Ming , Shiao Chih-Hui , Cheng Ming-Dean
Published: July 2003

A regional spectral model (RSM) is developed at the Taiwan Central Weather Bureau (CWB). It is based on the same model structure, dynamics, and physics of the CWB global spectral model (GSM) and the perturbation concept of the National Centers for Environmental Prediction (NCEP) RSM for lateral boundary treatment. The advantages of this new regional model include minimization of possible inconsistency between GSM and RSM through lateral boundary influence and reduction of resources used to manage and maintain the model.

One-dimensional decomposition is utilized to slice the model into subdomains to run on a massive parallel-processor machine. The Message-Passing Interface (MPI) is adopted to communicate among each subdomain. The computational dependency, such as the summation in spectral transformation, is a restriction for the decomposition, so that the reproducibility using different numbers of processors is achieved. The performance in terms of wall-clock time follows the theoretical curve of parallelization. It can reach 95% parallelization by “homemade” PC Linux cluster, and 90% by CWB Fujitsu VPP5000.

One case is selected to perform 2-month integration in a simulation mode and a forecast mode. The results indicate a reasonable monsoon frontal evolution as compared with analysis, and it has similar or less root-mean-square error (rmse) as compared to that of CWB GSM. The same run with NCEP RSM nested into CWB GSM shows a larger rmse than CWB RSM; it demonstrates the advantage of having the same model structure, dynamics, and physics between CWB GSM and CWB RSM.