Comparison among the Consumption Structures of Different Income Groups of Urban Residents in Guangxi Based on ELES Model

According to the household consumption data of urban residents in Guangxi Statistical Yearbook in the year 2009, the ELES (Extended Linear Expenditure System) is used to analyze the consumption structure, the propensity to consume, and the consumer flexibility of urban residents in Guangxi Zhuang Autonomous Region of China in the year 2008. Result shows that urban residents in Guangxi has relatively low propensity to consume. And their consumption, especially the middle and low-income families, is mostly concentrated in food, cloth, lodging and other basic necessities of life, which account for more than a half of their income. Based on this, corresponding suggestions are put forward to enlarge the consumption demand of urban residents in Guangxi, such as increasing the regulation of income redistribution, minimizing the gap between the rich and the poor, enhancing the overall consumption level, cultivating the consumption hot spots for the urban residents, and actively guiding the enjoyable consumption.

Asymptotic solution for a class of sea-air oscillator model for El Nio-southern oscillation

The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model.

Asymptotic solution for the El Nio time delay sea-air oscillator model

A sea-air oscillator model is studied using the time delay theory. The aim is to find an asymptotic solving method for the El Nino-southern oscillation （ENSO） model. Employing the perturbed method, an asymptotic solution of the corresponding problem is obtained. Thus we can obtain the prognoses of the sea surface temperature （SST） anomaly and the related physical quantities.

VARIATIONAL ITERATION SOLVING METHOD FOR SEA-AIR OSCILLATOR MODEL OF INTERDECADAL CLIMATE FLUCTUATIONS

Atmospheric physics is a very complicated natural phenomenon and needs to simplify its basic models for the sea-air oscillator. And it is solved by using the approximate method. The variational iteration method is a simple and valid method. In this paper the coupled system for a sea-air oscillator model of interdecadal climate fluctuations is considered. Firstly, through introducing a set of functions, and computing the variations, the Lagrange multipliers are obtained. And then, the generalized expressions of variational iteration are constructed. Finally, through selecting appropriate initial iteration from the iteration expressions, the approximations of solution for the sea-air oscillator model are solved successively.

Asymptotic solving method for a sea air oscillator model of atmospheric physics

In this paper, a class of coupled system for the E1 Nifio/La Nifia southern oscillation （ENSO） atmospheric physics oscillation model is considered. We propose an ENSO atmospheric physics model using a method from the asymptotic theory. It is indicated from the results that the asymptotic method can be used for analyzing the sea surface temperature anomaly and the thermocline depth anomaly of the atmosphere-ocean oscillation for the ENSO model in the equatorial Pacific.

Threshold autoregression models for forecasting El Nino events

-In this paper, monthly mean SST data in a large area are used. After the spacial average of the data is carried out and the secular monthly means are substracted, a time series (Jan. 1951-Dec. 1985) of SST anomalies of the cold tongue water area in the eastern tropical Pacific Ocean is obtained. On the basis of the time series, an autoregression model, a self-exciting threshold autoregression model and an open loop autoregression model are developed respectively. The interannual variations are simulated by means of those models. The simulation results show that all the three models have made very good hindcasting for the nine El Nino events since 1951. In order to test the reliability of the open loop threshold model, extrapolated forecast was made for the period of Jan. 1986-Feb. 1987. It can be seen from the forecasting that the model could forecast well the beginning and strengthening stages of the recent El Nino event (1986-1987). Correlation coefficients of the estimations to observations are respectively 0. 84, 0. 88 and 0. 89. It is obvious that all the models work well and the open loop threshold one is the best. So the open loop threshold autoregression model is a useful tool for monitoring the SSTinterannual variation of the cold tongue water area in the Eastern Equatorial Pacific Ocean and for estimating the El Nino strength.

Climate variability and predictability associated with the Indo-Pacific Oceanic Channel Dynamics in the CCSM4 Coupled System Model

An experiment using the Community Climate System Model(CCSM4), a participant of the Coupled Model Intercomparison Project phase-5(CMIP5), is analyzed to assess the skills of this model in simulating and predicting the climate variabilities associated with the oceanic channel dynamics across the Indo-Pacific Oceans. The results of these analyses suggest that the model is able to reproduce the observed lag correlation between the oceanic anomalies in the southeastern tropical Indian Ocean and those in the cold tongue in the eastern equatorial Pacific Ocean at a time lag of 1 year. This success may be largely attributed to the successful simulation of the interannual variations of the Indonesian Throughflow, which carries the anomalies of the Indian Ocean Dipole(IOD) into the western equatorial Pacific Ocean to produce subsurface temperature anomalies, which in turn propagate to the eastern equatorial Pacific to generate ENSO. This connection is termed the "oceanic channel dynamics" and is shown to be consistent with the observational analyses. However, the model simulates a weaker connection between the IOD and the interannual variability of the Indonesian Throughflow transport than found in the observations. In addition, the model overestimates the westerly wind anomalies in the western-central equatorial Pacific in the year following the IOD, which forces unrealistic upwelling Rossby waves in the western equatorial Pacific and downwelling Kelvin waves in the east. This assessment suggests that the CCSM4 coupled climate system has underestimated the oceanic channel dynamics and overestimated the atmospheric bridge processes.

Variational iteration method for solving the mechanism of the Equatorial Eastern Pacific El Nino-Southern Oscillation

A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.

The homotopic method of travelling wave solution for El Nio tropic sea-air coupled oscillator

The EI Nimo and Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific sea-air interactions. In this paper, an asymptotic method of solving nonlinear equations for the ENSO model is proposed. And based on a class of oscillator of the ENSO model and by employing the method of homotopic mapping, the approximate solution of equations for the corresponding ENSO model is studied. It is proved from the results that homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial Pacific of the sea-air oscillator for the ENSO model.

Dissipative Travelling Wave Solution for El Nio Tropic Sea-air Coupled Oscillator

El Nifio and Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific sea-air interactions. An asymptotic method of solving equations for the ENSO model is proposed. Based on a class of oscillator of ENSO model and by employing a simple and valid method of the variational iteration, the coupled system for a sea-air oscillator model of interdecadal climate fluctuations is studied. Firstly, by introducing a set of functionals and computing the variationals, the Lagrange multipliers are obtained. And then, the generalized variational iteration expressions are constructed. Finally, by selecting appropriate initial iteration, and from the iterations expressions, the approximations of solution for the sea-air oscillator ENSO model are solved successively. The approximate dissipative travelling wave solution of equations for corresponding ENSO model is studied. It is proved from the results that the method of the variational iteration can be used for analyzing the sea surface temperature anomaly in the equatorial Pacific of the sea-air oscillator for ENSO model.

Processes involved in the second-year warming of the 2015 El Nio event as derived from an intermediate ocean model

The tropical Pacific experienced a sustained warm sea surface condition that started in 2014 and a very strong El Nio event in 2015. One striking feature of this event was the horseshoe-like pattern of positive subsurface thermal anomalies that was sustained in the western-central equatorial Pacific throughout 2014–2015. Observational data and an intermediate ocean model are used to describe the sea surface temperature(SST) evolution during 2014–2015. Emphasis is placed on the processes involved in the 2015 El Nio event and their relationships with SST anomalies, including remote effects associated with the propagation and reflection of oceanic equatorial waves(as indicated in sea level(SL) signals) at the boundaries and local effects of the positive subsurface thermal anomalies. It is demonstrated that the positive subsurface thermal anomaly pattern that was sustained throughout 2014–2015 played an important role in maintaining warm SST anomalies in the equatorial Pacific. Further analyses of the SST budget revealed the dominant processes contributing to SST anomalies during 2014–2015. These analyses provide an improved understanding of the extent to which processes associated with the 2015 El Nio event are consistent with current El Nio and Southern Oscillation theories.

On the “spring predictability barrier” for strong El Nio events as derived from an intermediate coupled model ensemble prediction system

Using predictions for the sea surface temperature anomaly(SSTA) generated by an intermediate coupled model(ICM)ensemble prediction system(EPS), we first explore the "spring predictability barrier"(SPB) problem for the 2015/16 strong El Nio event from the perspective of error growth. By analyzing the growth tendency of the prediction errors for ensemble forecast members, we conclude that the prediction errors for the 2015/16 El Nio event tended to show a distinct season-dependent evolution, with prominent growth in spring and/or the beginning of the summer. This finding indicates that the predictions for the 2015/16 El Nio occurred a significant SPB phenomenon. We show that the SPB occurred in the 2015/16 El Nio predictions did not arise because of the uncertainties in the initial conditions but because of model errors. As such, the mean of ensemble forecast members filtered the effect of model errors and weakened the effect of the SPB, ultimately reducing the prediction errors for the 2015/16 El Nio event. By investigating the model errors represented by the tendency errors for the SSTA component,we demonstrate the prominent features of the tendency errors that often cause an SPB for the 2015/16 El Nio event and explain why the 2015/16 El Nio was under-predicted by the ICM EPS. Moreover, we reveal the typical feature of the tendency errors that cause not only a significant SPB but also an aggressively large prediction error. The feature is that the tendency errors present a zonal dipolar pattern with the west poles of positive anomalies in the equatorial western Pacific and the east poles of negative anomalies in the equatorial eastern Pacific. This tendency error bears great similarities with that of the most sensitive nonlinear forcing singular vector(NFSV)-tendency errors reported by Duan et al. and demonstrates the existence of an NFSV tendency error in realistic predictions. For other strong El Nio events, such as those that occurred in 1982/83 and 1997/98, we obtain the tendency errors of the NFSV structure, which cause a significant SPB and yield a much larger prediction error. These results suggest that the forecast skill of the ICM EPS for strong El Nio events could be greatly enhanced by using the NFSV-like tendency error to correct the model.

Computational method for singularly perturbed delay differential equations of the reaction-diffusion type with negative shift

A numerical method for solving singularly perturbed delay differential equations with a layer or oscillatory behavior for which a small shift is introduced in the reaction term is presented.The stability and convergence of the method have been investigated.To demonstrate the efficiency of the method,two model examples have been presented.Numerical results obtained by the present scheme described that the finding of the present method is accurate than the findings of the previous studies.

A PERTURBED SOLUTION OF SEA-AIR OSCILLATOR FOR THE ENSO MECHANISM

A class of coupled system of the El Nino/La Nino-Southern Oscillation (ENSO)mechanism is studied. Using the perturbed theory, the asymptotic expansions of the solution for ENSOmodel are obtained and the asymptotic behavior of the solution for corresponding problem isconsidered. And it is pointed out that the solution tends to the corresponding attractor as t → ∞.