A Global Spectral Element Model for Poisson Equations and Advective Flow over a Sphere

A global spherical Fourier-Legendre spectral element method is proposed to solve Poisson equations and advective flow over a sphere. In the meridional direction, Legendre polynomials are used and the region is divided into several elements. In order to avoid coordinate singularities at the north and south poles in the meridional direction, Legendre-Gauss-Radau points are chosen at the elements involving the two poles. Fourier polynomials are applied in the zonal direction for its periodicity, with only one element. Then, the partial differential equations are solved on the longitude-latitude meshes without coordinate transformation between spherical and Cartesian coordinates. For verification of the proposed method, a few Poisson equations and advective flows are tested. Firstly, the method is found to be valid for test cases with smooth solution. The results of the Poisson equations demonstrate that the present method exhibits high accuracy and exponential convergence. High- precision solutions are also obtained with near negligible numerical diffusion during the time evolution for advective flow with smooth shape. Secondly, the results of advective flow with non-smooth shape and deformational flow are also shown to be reasonable and effective. As a result, the present method is proved to be capable of solving flow through different types of elements, and thereby a desirable method with reliability and high accuracy for solving partial differential equations over a sphere.

Impact of Wind on Tide-Induced Advective Salt Transport in A Well- Mixed Estuary

The tide-induced net advective salt flux in well-mixed estuaries consists of five terms according to the method from Kjerfve.The term resulted from the vertical variation in salinity can be negligible in well-mixed estuaries with four tide-induced salt flux terms,known as F1−F4.To explore the effects of wind on these salt fluxes,the current-salinity analytical model combined with the perturbation analysis is extended by including wind.Analytical expressions for the four salt fluxes are derived separately in the present model.Under the assumption that only the M_(2) tidal component is accounted for and the salt flux generated by diffusion is not studied,the tide-induced net advective salt flux Q_(sx) is in the seaward direction without the wind effect.By applying the Western Scheldt estuary case,the wind influence on the tidal advection salt flux(TASF)distribution in the F4 term was investigated.The phase difference between zero-order velocity and first-order salinity(Δφ)at the surface layer of the estuary is larger than 90°and smaller than 90°at the bottom layer,which leads to landward TASF in the surface layer and seaward TASF in the bottom layer.The distribution ofΔφis not uniform in the horizontal direction with wind included,which differs from the result without wind.In the case of seaward wind with the speed of 18 m/s,the decrease in the zeroth-order velocity phase(φu)at the surface layer is larger than that of the first-order salinity phase(φs)downstream,which leads to an abnormal seaward TASF in this region.Owing to the surface stress caused by wind,the Stokes compensation flow in the middle and lower reaches increases/decreases with the increase of the landward/seaward wind,while the upstream situation is opposite.Thus,the first-order velocity in the middle and lower reaches increases/decreases with the increase of the landward/seaward wind,while the upstream situation is also opposite.The first-order salinity also increases/decreases with the increase of landward/seaward wind,while the upstream salinity tends to zero.Therefore,the tide-induced net advective salt flux Q_(sx) increases/decreases with the increase of the landward/seaward wind,which is contrary to the usual recognition.

APPLICATION OF ADVECTIVE VORTICITY EQUATION TO TYPHOON FUNG-WONG

The momentum advection vorticity equation in the form of cross multiplication is introduced, in which the divergence term in the classic vorticity equation does not appear explicitly. This equation includes the rotation effect of the horizontal wind advection, which are not explicitly included in the classic vortieity equation. The vorticity and its tendency of Typhoon Fung-Wong （0808） that occurred in July 2008 are analyzed. The computed results show that the rotation effect of the advection of the horizontal wind is a leading factor in determining the change of vertical vorticity for Fung-Wong during its life cycle, especially in the period leading up to landfall. The advection term represents the tendency variation of the vertical vortieity, and the positive-value region of the vertical vorticity tendency is almost in accord with the track of Fung-Wong, which may be taken as a factor to locate the key observational region of Fung-Wong. The equation provides a supplementary diagnostic tool for the systems related with strong advection of horizontal wind.

Global dynamics of a Leslie-Gower predator-prey model in open advective environments

This paper investigates the global dynamics of a reaction-diffusion-advection Leslie-Gower predator-prey model in open advective environments.We find that there exist critical advection rates,intrinsic growth rates,diffusion rates and length of the domain,which classify the global dynamics of the Leslie-Gower predator-prey system into three scenarios:coexistence,persistence of prey only and extinction of both species.The results reveal some significant differences with the classical specialist and generalist predator-prey systems.In particular,it is found that the critical advection rates of prey and predator are independent of each other and the parameters about predation rate have no influence on the dynamics of system.The theoretical results provide some interesting highlights in ecological protection in streams or rivers.

Threshold dynamics of a cooperation-diffusion-advection model in open advective environments

This paper is concerned with a Lotka-Volterra cooperation-reaction-diffusion-advection model in open advective environments.It is found that there are two critical advection rates,which classify the dynamic behavior of this system into three different scenarios,namely,(i)both species go extinct;(ii)one species survives in the long run,the other goes extinct and(ii)both species can persistently survive.The theoretical results provide some interesting highlights in ecological protection in streams and rivers.

Seasonal Variation of the Sea Surface Temperature Growth Rate of ENSO

El Ni?o–Southern Oscillation(ENSO) exhibits a distinctive phase-locking characteristic, first expressed during its onset in boreal spring, developing during summer and autumn, reaching its peak towards winter, and decaying over the next spring. Several studies have demonstrated that this feature arises as a result of seasonal variation in the growth rate of ENSO as expressed by the sea surface temperature(SST). The bias towards simulating the phase locking of ENSO by many state-of-the-art climate models is also attributed to the unrealistic depiction of the growth rate. In this study, the seasonal variation of SST growth rate in the Ni?o-3.4 region(5°S–5°N, 120°–170°W) is estimated in detail based on the mixed layer heat budget equation and recharge oscillator model during 1981–2020. It is suggested that the consideration of a variable mixed layer depth is essential to its diagnostic process. The estimated growth rate has a remarkable seasonal cycle with minimum rates occurring in spring and maximum rates evident in autumn. More specifically, the growth rate derived from the meridional advection(surface heat flux) is positive(negative) throughout the year. Vertical diffusion generally makes a negative contribution to the evolution of growth rate and the magnitude of vertical entrainment represents the smallest contributor. Analysis indicates that the zonal advective feedback is regulated by the meridional immigration of the intertropical convergence zone, which approaches its southernmost extent in February and progresses to its northernmost location in September, and dominates the seasonal variation of the SST growth rate.

Diagnostic Study of an Extreme Explosive Cyclone over the Kuroshio/Kuroshio Extension Region

Explosive cyclones(ECs)occur frequently over the Kuroshio/Kuroshio Extension region.The most rapidly intensified EC over the Kuroshio/Kuroshio Extension region during the 42 years(1979-2020)of cold seasons(October-April)was studied to reveal the variations of the key factors at different explosive-developing stages.This EC had weak low-level baroclinicity,mid-level cyclonic-vorticity advection,and strong low-level water vapor convergence at the initial explosive-developing stage.The low-level baroclinicity and mid-level cyclonic-vorticity advection increased substantially during the maximum-deepening-rate stage.The diagnostic analyses using the Zwack-Okossi equation showed that diabatic heating was the main contributor to the initial rapid intensification of this EC.The cyclonic-vorticity advection and warm-air advection enhanced rapidly in the middle and upper troposphere and contributed to the maximum rapid intensification,whereas the diabatic heating weakened slightly in the mid-low troposphere.The relative contribution of the diabatic heating decreased from the initial explosive-developing stage to the maximum-deepening-rate stage due to the enhancement of other factors(the cyclonic-vorticity advection and warm-air advection).Furthermore,the physical factors contributing to this EC varied with the explosive-developing stage.The non-key factors at the initial explosive-developing stage need attention to forecast the rapid intensification.

The Processes-Based Attributes of Four Major Surface Melting Events over the Antarctic Ross Ice Shelf

The Ross-Amundsen sector is experiencing an accelerating warming trend and a more intensive advective influx of marine air streams.As a result,massive surface melting events of the ice shelf are occurring more frequently,which puts the West Antarctica Ice Sheet at greater risk of degradation.This study shows the connection between surface melting and the prominent intrusion of warm and humid air flows from lower latitudes.By applying the Climate Feedback-Response Analysis Method(CFRAM),the temporal surge of the downward longwave(LW)fluxes over the surface of the Ross Ice Shelf(RIS)and adjacent regions are identified for four historically massive RIS surface melting events.The melting events are decomposed to identify which physical mechanisms are the main contributors.We found that intrusions of warm and humid airflow from lower latitudes are conducive to warm air temperature and water vapor anomalies,as well as cloud development.These changes exert a combined impact on the abnormal enhancement of the downward LW surface radiative fluxes,significantly contributing to surface warming and the resultant massive melting of ice.

A Numerical Simulation of Air Flow in the Human Respiratory System Based on Lung Model

The lung is an important organ that takes part in the gas exchange process. In the study of gas transport and exchange in the human respiratory system, the complicated process of advection and diffusion (AD) in airways of human lungs is considered. The basis of a lumped parameter model or a transport equation is modeled during the inspiration process, when oxygen enters into the human lung channel. The quantitative measurements of oxygen are detached and the model equation is solved numerically by explicit finite difference schemes. Numerical simulations were made for natural breathing conditions or normal breathing conditions. The respiratory flow results for the resting conditions are found strongly dependent on the AD effect with some contribution of the unsteadiness effect. The contour of the flow rate region is labeled and AD effects are compared with the variation of small intervals of time for a constant velocity when breathing is interrupted for a negligible moment.

Analysis of A Heavy Snow Process in Liaoning Province in 2009

Based on the conventional meteorological data and 4 times daily NCEP reanalysis data,the causes of rain changing snowstorm in Liaoning during February 12-13 of 2009 were discussed.The low-level jet conditions,temperature conditions and coupling mechanism of water vapor and dynamics of heavy snow were diagnosed and analyzed.The low-level jet provided abundant water vapor for this process.The convergence at low level,divergence in the upper troposphere and strong ascend movement provided dynamic conditions for the snowstorm.The wedging of cold air was the chief cause of rain changing snow.The strongprecipitation area corresponded to the moist potential vorticity well.

UPWIND SCHEME FOR IDEAL 2-D MHD FLOWS BASED ON UNSTRUCTURED MESH

An upwind scheme based on the unstructured mesh is developed to solve ideal 2-D magnetohydrodynamics （MHD） equations. The inviscid fluxes are approximated by using the modified advection upstream splitting method （AUSM） scheme, and a 5-stage explicit Runge-Kutta scheme is adopted in the time integration. To avoid the influence of the magnetic field divergence created during the simulation, the hyperbolic divergence cleaning method is introduced. The shock-capturing properties of the method are verified by solving the MHD shock-tube problem. Then the 2-D nozzle flow with the magnetic field is numerically simulated on the unstructured mesh. Computational results demonstrate the effects of the magnetic field and agree well with those from references.

Optimal nonlinear excitation of decadal variability of the North Atlantic thermohaline circulation

Nonlinear development of salinity perturbations in the Atlantic thermohaline circulation(THC) is investigated with a three-dimensional ocean circulation model,using the conditional nonlinear optimal perturbation method.The results show two types of optimal initial perturbations of sea surface salinity,one associated with freshwater and the other with salinity.Both types of perturbations excite decadal variability of the THC.Under the same amplitude of initial perturbation,the decadal variation induced by the freshwater perturbation is much stronger than that by the salinity perturbation,suggesting that the THC is more sensitive to freshwater than salinity perturbation.As the amplitude of initial perturbation increases,the decadal variations become stronger for both perturbations.For salinity perturbations,recovery time of the THC to return to steady state gradually saturates with increasing amplitude,whereas this recovery time increases remarkably for freshwater perturbations.A nonlinear(advective) feedback between density and velocity anomalies is proposed to explain these characteristics of decadal variability excitation.The results are consistent with previous ones from simple box models,and highlight the importance of nonlinear feedback in decadal THC variability.

The role of oceanic feedbacks in the 2014–2016 El Niño events as derived from ocean reanalysis data

Why did the predicted“super El Niño”fade out in the summer 2014 and the following year develop into one of the three strongest El Niño on record?Although some hypotheses have been proposed in previous studies,the quantitative contribution of oceanic processes to these events remains unclear.We investigated the role of various oceanic feedbacks,especially in response to intra-seasonal westerly wind busts,in the evolution of the 2014–2016 El Niño events,through a detailed heat budget analysis using high temporal resolution Estimating the Circulation and Climate of the Ocean—Phase II(ECCO2)simulation outputs and satellite-based observations.Results show that the Ekman feedback and zonal advective feedback were the two dominant oceanic processes in the developing phase of the warm event in the spring of 2014 and its decay in June.In the 2015–2016 super El Niño event,the zonal advective feedback and thermocline feedback played a signifi cant role in the eastern Pacifi c warming.Moreover,the thermocline feedback tended to weaken in the central Pacifi c where the zonal advection feedback became the dominant positive feedback.

Application of a Shape-Preserving Advection Scheme to the Moisture Equation in an E-grid Regional Forecast Model

This paper presents a methodology which is very useful to design shape-preserving advection finite difference scheme on general E-grid horizontal arrangement of variables through introducing a two-step shape-preserving positive definite advection scheme in the moisture equation of the LASG-REM (LASG regional E-grid eta-coordinate forecast model). By trial-forecasting six local heavy raincases, the efficiency of the shape-preserving advection scheme in practical application has been examined. The LASG-REM with the shape-preserving advection scheme has a good forecasting ability for local precipitation.

Characteristics of the Boundary Layer Structure of Sea Fog on the Coast of Southern China

Using boundary layer data with regard to sea fog observed at the Science Experiment Base for Marine Meteorology at Bohe,Guangdong Province,the structure of the atmospheric boundary layer and the characteristics of the tops of the fog and the clouds were analyzed.In addition,the effects of advection,radiation,and turbulence during sea fog were also investigated.According to the stability definition of saturated,wet air,the gradient of the potential pseudo-equivalent temperature equal to zero was defined as the thermal turbulence interface.There is evidence to suggest that two layers of turbulence exist in sea fog.Thermal turbulence produced by long-wave radiation is prevalent above the thermal turbulence interface,whereas mechanical turbulence aroused by wind shear is predominant below the interface.The height of the thermal turbulence interface was observed between 180 m and 380 m.Three important factors are closely related to the development of the top of the sea fog：（1） the horizontal advection of the water vapor,（2） the long-wave radiation of the fog top,and（3） the movement of the vertical turbulence.Formation,development,and dissipation are the three possible phases of the evolution of the boundary-layer structure during the sea fog season.In addition,the thermal turbulence interface is the most significant turbulence interface during the formation and development periods;it is maintained after sea fog rises into the stratus layer.

Diagnosis of a Moist Thermodynamic Advection Parameter in Heavy-Rainfall Events

A moist thermodynamic advection parameter, defined as an absolute value of the dot product of hori- zontal gradients of three-dimensional potential temperature advection and general potential temperature, is introduced to diagnose frontal heavy rainfall events in the north of China. It is shown that the parameter is closely related to observed 6-h accumulative surface rainfall and simulated cloud hydrometeors. Since the parameter is capable of describing the typical vertical structural characteristics of dynamic, thermodynamic and water vapor fields above a strong precipitation region near the front surface, it may serve as a physical tracker to detect precipitable weather systems near to a front. A tendency equation of the parameter was derived in Cartesian coordinates and calculated with the simulation output data of a heavy rainfall event. Results revealed that the advection of the parameter by the three-dimensional velocity vector, the covariance of potential temperature advection by local change of the velocity vector and general potential temperature, and the interaction between potential temperature advection and the source or sink of general potential temperature, accounted for local change in the parameter. This indicated that the parameter was determined by a combination of dynamic processes and cloud microphysical processes.

A Two-Step Shape-Preserving Advection Scheme

This paper proposes a new two-step non-oscillatory shape-preserving positive definite finite difference advection transport scheme, which merges the advantages of small dispersion error in the simple first-order upstream scheme and small dissipation error in the simple second-order Lax-Wendroff scheme and is completely different from most of present positive definite advection schemes which are based on revising the upstream scheme results. The proposed scheme is much less time consuming than present shape-preserving or non-oscillatory advection transport schemes and produces results which are comparable to the results obtained from the present more complicated schemes. Elementary tests are also presented to examine the behavior of the scheme.

Physical processes causing the formation of hypoxia off the Changjiang estuary after Typhoon Chan-hom, 2015

Severe hypoxia was observed in the submarine canyon to the east of the Changjiang estuary in July 14, 2015, two days after typhoon Chan-hom. The oxygen concentration reached as low as 2.0 mg/L and occupied a water column of about 25 m. A ROMS model was con?gured to explore the underlying physical processes causing the formation of hypoxia. Chan-hom passed through the Changjiang estuary during the neap tide. The strati?cation was completely destroyed in the shallow nearshore region when typhoon passing. However, it was maintained in the deep canyon, though the surface mixed layer was largely deepened. The residual water in the deep canyon is considered to be the possible source of the later hypoxia. After Chan-hom departure, not only the low salinity plume water spread further of fshore, but also the sea surface temperature(SST) rewarmed quickly. Both changes helped strengthen the strati?cation and facilitate the formation of hypoxia. It was found that the surface heat ?ux, especially the solar short wave radiation dominated the surface re-warming, the of fshore advection of the warmer Changjiang Diluted Water(CDW) also played a role. In addition to the residual water in the deep canyon, the Taiwan Warm Current(TWC) was found to ?ow into the deep canyon pre-and soon post-Chan-hom, which was considered to be the original source of the hypoxia water.

Planetary Wave Reflection and Its Impact on Tropospheric Cold Weather over Asia during January 2008

Reflection of stratospheric planetary waves and its impact on tropospheric cold weather over Asia during January 2008 were investigated by applying two dimensional Eliassen-Palm （EP） flux and three-dimensional Plumb wave activity fluxes.The planetary wave propagation can clearly be seen in the longitude-height and latitude-height sections of the Plumb wave activity flux and EP flux,respectively,when the stratospheric basic state is partially reflective.Primarily,a wave packet emanating from Baffin Island/coast of Labrador propagated eastward,equatorward and was reflected over Central Eurasia and parts of China,which in turn triggered the advection of cold wind from the northern part of the boreal forest regions and Siberia to the subtropics.The wide region of Central Eurasia and China experienced extreme cold weather during the second ten days of January 2008,whereas the extraordinary persistence of the event might have occurred due to an anomalous blocking high in the Urals-Siberia region.

Improvement of the Semi-Lagrangian Advection Scheme in the GRAPES Model:Theoretical Analysis and Idealized Tests

ABSTRACT The Global/Regional Assimilation and PrEdiction System （GRAPES） is the newgeneration numerical weather predic- tion （NWP） system developed by the China Meteorological Administration. It is a fully compressible non-hydrostatical global/regional unified model that uses a traditional semi-Lagrangian advection scheme with cubic Lagrangian interpola tion （referred to as the SL_CL scheme）. The SL_CL scheme has been used in many operational NWP models, but there are still some deficiencies, such as the damping effects due to the interpolation and the relatively low accuracy. Based on Reich＇s semi-Lagrangian advection scheme （referred to as the R2007 scheme）, the Re_R2007 scheme that uses the low- and high-order B-spline function for interpolation at the departure point, is developed in this paper. One- and two-dimensional idealized tests in the rectangular coordinate system with uniform grid cells were conducted to compare the Re..R2007 scheme and the SL_CL scheme. The numerical results showed that： （1） the damping effects were remarkably reduced with the Re_R2007 scheme; and （2） the normalized errors of the Re_R2007 scheme were about 7.5 and 3 times smaller than those of the SL_CL scheme in one- and two-dimensional tests, respectively, indicating the higher accuracy of the Re..R2007 scheme. Furthermore, two solid-body rotation tests were conducted in the latitude-longitude spherical coordinate system with non uniform grid cells, which also verified the Re_R2007 scheme＇s advantages. Finally, in comparison with other global advection schemes, the Re_R2007 scheme was competitive in terms of accuracy and flow independence. An encouraging possibility for the application of the Re_R2007 scheme to the GRAPES model is provided.