Potential Vorticity Structure and Inversion of the Cyclogenesis Over the Yangtze River and Huaihe River Valleys

In this paper, the potential vorticity structure and inversion of the cyclogenesis over the Yangtze River and Huaihe River valleys during 21 23 June 2003 are investigated with a potential vorticity （PV） framework. The cyclogenesis is manifested by a lower-tropospheric PV anomaly over the Yangtze River and Huaihe River valleys at early stages mainly due to latent heat release, which greatly affects the evolution of the associated lower-tropospheric geopotential height and wind fields as demonstrated by piecewise PV inversion. At later stages, an upper-tropospheric PV anomaly develops, resulting in the growth of ridges over the cyclone in both the upstream and downstream, which provide a favorable background field for the low-level cyclone development. But the effect of a surface thermal anomaly always impedes the development of the cyclone to different extents during this cyclogenesis. It is further demonstrated that the position and the strength of the PV anomaly are closely related to the low-level cyclone development, and the lower-tropospheric PV anomaly seems to constitute the most significant feature, for instance, contributing about 60% to the low-level jet （LLJ）.

A Survey of Unbalanced Flow Diagnostics and Their Application

This paper presents an extensive survey of the most commonly used tools for diagnosing unbalanced flow in the atmosphere, namely the Lagrangian Rossby number, Psi vector, divergence equation, nonlinear balance equation, generalized omega-equation, and departure from fields obtained by potential vorticity (PV) inversion. The basic thoery, assumptions as well as implementation and limitations for each of the tools are all discussed. These tools are applied to high—resolution mesoscale model data to assess the role of unbalanced dynamics in the generation of a mesoscale gravity wave event over the East Coast of the United States. Comparison of these tools in this case study shows that these various methods agree to a large extent with each other though they differ in details. Key words Unbalanced flow - Geostrophic adjustment - Gravity waves - Nonlinear balance equation - Potential vorticity inversion - Omega equations - Rossby number This research was conducted under support from NSF grant ATM-9700626 of the United States. The numerical computations described herein were performed on the Cray T90 at the North Carolina Supercomputing Center and the Cray supercomputer at the NCAR Scientific Computing Division, which also provided the initialization fields for the MM5. Thanks are extended to Mark Stoelinga at University of Washington for the RIP post-processing package.

ON THE RELATIONSHIPS BETWEEN THE UNUSUAL TRACK OF TYPHOON MORAKOT(0908)AND THE UPPER WESTERLY TROUGH

In this paper,by carrying out sensitivity tests of initial conditions and diagnostic analysis of physical fields,the impact factors and the physical mechanism of the unusual track of Morakot in the Taiwan Strait are discussed and examined based on the potential vorticity(PV)inversion.The diagnostic results of NCEP data showed that Morakot's track was mainly steered by the subtropical high.The breaking of a high-pressure zone was the main cause for the northward turn of Morakot.A sensitivity test of initial conditions showed that the existence of upper-level trough was the leading factor for the breaking of the high-pressure zone.When the intensity was strengthened of the upper-level trough at initial time,the high-pressure zone would break ahead of time,leading to the early northward turn of Morakot.Conversely,when the intensity was weakened,the breaking of the high-pressure zone would be delayed.Especially,when the intensity was weakened to a certain extent,the high-pressure zone would not break.The typhoon,steered by the easterly flow to the south of the high-pressure zone,would keep moving westward,with no turn in the test.The diagnostic analysis of the physical fields based on the sensitivity test revealed that positive vorticity advection and cold advection associated with the upper-level trough weakened the intensity of the high-pressure zone.The upper-level trough affected typhoon's track indirectly by influencing the high-pressure zone.

Field source characteristic of gravity variation in Hexi region before Menyuan Ms6.4 earthquake based on the Euler deconvolution

This study adopted the Euler deconvolution method to conduct an inversion and interpretation of the depth and spatial distribution pattern of field source that lead to gravity variation. For this purpose, mobile gravity data from four periods in the Hexi region between 2011 and 2015 were obtained from an observation network. With a newly established theoretical model, we acquired the optimum inversion parameters and conducted calculation and analysis with the actual data. The results indicate that one is the appropriate value of the structure index for the inversion of the mobile gravity data. The inversion results of the actual data showed a comparable spatial distribution of the field source and a consistent structural trend with observations from the Qilian-Haiyuan Fault zone between 2011 and 2015. The distribution was in a blocking state at the epicenter of the Menyuan earthquake in 2016. Our quantitative study of the field source provides new insights into the inversion and interpretation of signals of mobile gravity variation.

Non-Relativistic Treatment of a Generalized Inverse Quadratic Yukawa Potential

A bound state solution is a quantum state solution of a particle subjected to a potential such that the particle＇s energy is less than the potential at both negative and positive infinity. The particle＇s energy may also be negative as the potential approaches zero at infinity. It is characterized by the discretized eigenvalues and eigenfunctions, which contain all the necessary information regarding the quantum systems under consideration. The bound state problems need to be extended using a more precise method and approximation scheme. This study focuses on the non-relativistic bound state solutions to the generalized inverse quadratic Yukawa potential. The expression for the non-relativistic energy eigenvalues and radial eigenfunctions are derived using proper quantization rule and formula method, respectively. The results reveal that both the ground and first excited energy eigenvalues depend largely on the angular momentum numbers, screening parameters, reduced mass, and the potential depth. The energy eigenvalues, angular momentum numbers, screening parameters, reduced mass, and the potential depth or potential coupling strength determine the nature of bound state of quantum particles. The explored model is also suitable for explaining both the bound and continuum states of quantum systems.

An Explicit Formula of the Dirichlet-to-Neumann Map for a Radial Potential in Dimension 3

In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for the Schrödinger equation in 3-dimensional. We numerically implement the coefficients of the explicit formulas. In this work, Lipschitz type stability is established near the edge of the domain with giving estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neuman map.

Dirichlet-to-Neumann Map for a Hyperbolic Equation

In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann operators corresponding to a potential radial have the same properties for hyperbolic differential equations as for elliptic differential equations. We numerically implement the coefficients of the explicit formulas. Moreover, a Lipschitz type stability is established near the edge of the domain by an estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neumann map in the inverse problem for a hyperbolic differential equation.

Transport properties of dilute ammonia-noble gas mixtures from new intermolecular potential energy functions

Previously we have determined the dilute mixture transport properties of slightly polar fluorocarbons using the inverted intermolecular potential energies(Ind. Eng. Chem. Res. 45(2006) 9211–9223). In the present paper, the corresponding states correlations for reduced viscosity collision integrals were employed to obtain effective unlike interaction potential models for dilute binary mixtures of highly polar molecule ammonia with noble gases.The inverted potentials were fitted to the Morse–Spline–van der Waals(MSV), model potential. The method of least-squares fitting was then applied to identify best consistence force parameters for each ammonia-noble gas mixture, taking advantage of experimental viscosities, diffusion coefficients and thermal conductivities.The proposed potential models were compared with those obtained from other sources, in order to assess the extent of their validity.The potentials were later employed to calculate transport properties of the studied mixtures. Then, results were compared with those reported in the literature, which led to the acceptable agreement.

Estimating Field Source Parameters of Gravity Change in North China Based on the Euler Deconvolution Method

Based on the absolute and relative gravity observations in North China from 2009 to 2014,spatial dynamic variations of the regional gravity field are obtained. We employed the Euler deconvolution method and the theoretical model to get the best estimates of parameters. Gravity field change caused by the depth and distribution in North China is calculated by back analysis. The results show the structural index that equals 1 is suitable for inversion of the gravity variation data. The inversion results indicate that the depths of anomaly field sources are spread over the Hetao fault. The research method of this paper can be used in the quantitative study on the field source and may shed new light on the interpretations of gravity change, and also provide quantitative basis for earthquake prediction index criterions based on the gravity change.

High-precision inverse potentials for neutron-proton scattering using piece-wise smooth Morse functions

The aim of this study is to construct inverse potentials for various ℓ-channels of neutron-proton scattering using a piece-wise smooth Morse function as a reference.The phase equations for single-channel states and the coupled equations of multi-channel scattering are solved numerically using the 5^(th) order Runge-kutta method.We employ a piece-wise smooth reference potential comprising three Morse functions as the initial input.Leveraging a machine learning-based genetic algorithm,we optimize the model parameters to minimize the mean-squared error between simulated and anticipated phase shifts.Our approach yields inverse potentials for both single and multichannel scattering,achieving convergence to a mean-squared error≤10^(-3).The resulting scattering lengths"a_(0)"and effective ranges"r"for ^(3)S_(1) and ^(1)S_(0) states,expressed as[a_(0),r],are found to be[5.445(5.424),1.770(1.760)]and[–23.741(–23.749),2.63(2.81)],respectively;these values are in excellent agreement with experimental ones.Furthermore,the calculated total scattering cross-sections are highly consistent with their experimental counterparts,having a percentage error of less than 1%.This computational approach can be easily extended to obtain interaction potentials for charged particle scattering.

A Case Study on a Quasi-Stationary Meiyu Front Bringing About Continuous Rainstorms with Piecewise Potential Vorticity Inversion

A 4-day persistent rainstorm resulting in serious flooding disasters occurred in the north of Fujian Province under the influences of a quasi-stationary Meiyu front during 5-8 June 2006. With 1°× 1° latitude and longitude NCEP reanalysis data and the ground surface rainfall, using the potential vorticity （PV） analysis and PV inversion method, the evolution of main synoptic systems, and the corresponding PV and PV perturbation （or PV anomalies） and their relationship with heavy rainfall along the Meiyu front are analyzed in order to investigate the physical mechanism of the formation, development, and maintenance of the Meiyu front. Furthermore, the PV perturbations related to different physics are separated to investigate their different roles in the formation and development of the Meiyu front. The results show： the formation and persistence of the Meiyu front in a quasi-WE orientation are mainly due to the maintenance of the high-pressure systems in its south/north sides （the West Pacific subtropical high/ the high pressure band extending from the Korean Peninsula to east of North China）. The Meiyu front is closely associated with the PV in the lower troposphere. The location of the positive PV perturbation on the Meiyu front matches well with the main heavy rainfall area along the Meiyu front. The PV inversion reveals that the balanced winds satisfying the nonlinear balanced assumption represent to a large extent the real atmospheric flow and its evolution basically reflects the variation of stream flow associated with the Meiyu front. The unbalanced flow forms the convergence band of the Meiyu front and it mainly comes from the high-pressure system in the north side of the Meiyu front. The positive PV perturbation related to latent heat release in the middle-lower troposphere is one of the main factors influencing the formation and development of the Meiyu front. The positive vorticity band from the total balanced winds is in accordance with the Meiyu front band and the magnitude of the positive vorticity from the balanced wind is very close to that from real winds. The PV perturbation in the boundary layer is to a certain degree favorable for the formation and development of Meiyu front. In general, the lower boundary potential temperature perturbation is not beneficial to the formation and development, which is attributed to the relatively low surface temperature due to surface evaporation and solar short-wave radiation reduction shaded by clouds on the Meiyu front band, however, it has some diurnal variation. The effect of PV perturbation in the upper troposphere on the formation and development of the Meiuyu front is relatively weaker than others＇ and not beneficial to the formation and development of the Meiyu front, but it is enhanced in the period of Meiyu front＇s fast southward movement when the deep North China trough develops and moves southeastward. Rest PV perturbation unrelated to latent heat release in the middle-lower troposphere plays a certain role in the Meiyu front＇s fast southward movement. Lastly, it should be pointed out that the different PV perturbations maybe play a different role in different stages of the Meiyu front development.

POTENTIAL INVERSION PROBLEMS FOR COUPLED SYSTEM OF DOWNGOING AND UPCOMING ONE-WAY WAVE EQUATIONS

By using wave splitting method the formulation of the two-dimensional potential inversion problem is set up in terms of the coupled system for downgoing and upcoming wavefields. The boundary counditions on the characteristic surface needed for solving the problem are derived by singularity analysis. Two stability theorems are given for the direct problems of the system treated as Cauchy problems in the direction of depth.

Wave Kernels with Bi-Inverse Square Potentials on Euclidean Plane

The Cauchy problem for the wave equation with bi-inverse square potential on Euclidean plane is solved in terms of the two variables Appell F2 hypergeometric functions. Our principal tools are the Hankel transforms and the special functions of mathematical physics.

LAYER STRIPPING METHOD FOR POTENTIAL INVERSION

To solve the potential inversion problem of the coupled system for one-way wave equations, the absorbing boundary conditions in the lateral direction are derived. The difference schemes are constructed and a layer stripping method is proposed. Some numerical experiments are presented.

Optical third-harmonic generation of spherical quantum dots under inversely quadratic Hellmann plus inversely quadratic potential

The third-harmonic generation(THG)coefficient for a spherical quantum dot system with inversely quadratic Hellmann plus inversely quadratic potential is investigated theoretically,considering the regulation of quantum size,confinement potential depth and the external environment.The numerical simulation results indicate that the THG coefficient can reach the order of 10~(-12)m~2V~(-2),which strongly relies on the tunable factor,with its resonant peak experiencing a redshift or blueshift.Interestingly,the effect of temperature on the THG coefficient in terms of peak location and size is consistent with the quantum dot radius but contrasts with the hydrostatic pressure.Thus,it is crucial to focus on the influence of internal and external parameters on nonlinear optical effects,and to implement the theory in practical experiments and the manufacture of optoelectronic devices.

A Diagnostic and Numerical Study on a Rainstorm in South China Induced by a Northward-Propagating Tropical System

A strong cyclonic wind perturbation generated in the northern South China Sea （SCS） moved northward quickly and developed into a mesoscale vortex in southwest Guangdong Province, and then merged with a southward-moving shear line from mid latitudes in the period of 21-22 May 2006, during which three strong mesoscale convective systems （MCSs） formed and brought about torrential rain or even cloudburst in South China. With the 1° ×1° NCEP （National Centers for Environment Prediction） reanalysis data and the Weather and Research Forecast （WRF） mesoscale model, a numerical simulation, a potential vorticity inversion analysis, and some sensitivity experiments are carried out to reveal the formation mechanism of this rainfall event. In the meantime, conventional observations, satellite images, and the WRF model outputs are also utilized to perform a preliminary dynamic and thermodynamic diagnostic analysis of the rainstorm systems. It is found that the torrential rain occurred in favorable synoptic conditions such as warm and moist environment, low lifting condensation level, and high convective instability. The moisture transport by strong southerly winds associated with the rapid northward advance of the cyclonic wind perturbation over the northern SCS provided the warm and moist condition for the formation of the excessive rain. Under the dynamic steering of a southwesterly flow ahead of a north trough and that on the southwest side of the West Pacific subtropical high, the mesoscale vortex （or the cyclonic wind perturbation）, after its genesis, moved northward and brought about enormous rain in most parts of Guangdong Province through providing certain lifting forcing for the triggering of mesoscale convection. During the development of the mesoscale vortex, heavy rainfall was to a certain extent enhanced by the mesoscale topography of the Yunwu Mountain in Guangdong. The effect of the Yunwu Mountain is found to vary under different prevailing wind directions and intensities. The location of the heavy rainfall was in a degree determined by the trumpet-shaped topography of the Zhujiang Delta. It is identified that the topographic effect on precipitation depends on the relative position between the terrain and the mesoscale storm systems. The short distance from the SCS to South China facilitates the moisture transport, which offers ease for the heavy rain to form in South China. Finally, the role played by land-sea contrast in the fast intensification of the MCSs in South China is not yet clear, and the interaction between the MCSs and the mesoscale vortex needs to be clarified as well.

Adjoint Sensitivity Study on Idealized Explosive Cyclogenesis

The adjoint sensitivity related to explosive cyclogenesis in a conditionally unstable atmosphere is investigated in this study.The PSU/NCAR limited-area,nonhydrostatic primitive equation numerical model MM5 and its adjoint system are employed for numerical simulation and adjoint computation,respectively.To ensure the explosive development of a baroclinic wave,the forecast model is initialized with an idealized condition including an idealized two-dimensional baroclinic jet with a balanced three-dimensional moderateamplitude disturbance,derived from a potential vorticity inversion technique.Firstly,the validity period of the tangent linear model for this idealized baroclinic wave case is discussed,considering different initial moisture distributions and a dry condition.Secondly,the 48-h forecast surface pressure center and the vertical component of the relative vorticity of the cyclone are selected as the response functions for adjoint computation in a dry and moist environment,respectively.The preliminary results show that the validity of the tangent linear assumption for this idealized baroclinic wave case can extend to 48 h with intense moist convection,and the validity period can last even longer in the dry adjoint integration.Adjoint sensitivity analysis indicates that the rapid development of the idealized baroclinic wave is sensitive to the initial wind and temperature perturbations around the steering level in the upstream.Moreover,the moist adjoint sensitivity can capture a secondary high sensitivity center in the upper troposphere,which cannot be depicted in the dry adjoint run.

Balanced and Unbalanced Components of Moist Atmospheric Flows with Phase Changes

Atmospheric variables(temperature, velocity, etc.) are often decomposed into balanced and unbalanced components that represent low-frequency and high-frequency waves, respectively. Such decompositions can be defined, for instance, in terms of eigenmodes of a linear operator. Traditionally these decompositions ignore phase changes of water since phase changes create a piecewise-linear operator that differs in different phases(cloudy versus non-cloudy). Here we investigate the following question: How can a balanced–unbalanced decomposition be performed in the presence of phase changes? A method is described here motivated by the case of small Froude and Rossby numbers,in which case the asymptotic limit yields precipitating quasi-geostrophic equations with phase changes. Facilitated by its zero-frequency eigenvalue, the balanced component can be found by potential vorticity(PV) inversion, by solving an elliptic partial differential equation(PDE), which includes Heaviside discontinuities due to phase changes. The method is also compared with two simpler methods: one which neglects phase changes, and one which simply treats the raw pressure data as a streamfunction. Tests are shown for both synthetic, idealized data and data from Weather Research and Forecasting(WRF) model simulations. In comparisons, the phase-change method and no-phase-change method produce substantial differences within cloudy regions, of approximately 5K in potential temperature, due to the presence of clouds and phase changes in the data. A theoretical justification is also derived in the form of a elliptic PDE for the differences in the two streamfunctions.