A global annually-averaged climate model with cloud,water vapor and CO2 feedbacks

In consideration of the radiation transfer, latent and sensible heat exchange between oceans and at-mosphere, a three-dimensional autonomous nonlinear ordinary differential equation is established by statis-tical parameterization method. The variables of the model are the mean ocean surface temperature Ts, mean atmospheric temperature Ta and atmospheric relative humidity f, and the feedbacks of clouds, water vapor and CO2 are involved. The steady state corresponding to the present-day climate can be obtained from this model. The analysis of parameter sensibility in the steady state indicates that clouds have consid-erable negative feedback effects and water vapor may affect the sign of CO2 feedback. The stability analysis of the steady state to small disturbance indicates that with increase of the positive feedback effect of clouds, the steady state goes through such a structural variance series as a stable node→a stable focal point→an unstable focal point→an unstable node, and when the steady state becomes unstable it undergoes a subcritical Hopf bifurcation. When the steady state is at a focal point, the periodic oscillation solutions of damping or amplifying can be obtained with the period being about two years.     

Nonlinear three- wave interaction among barotropic rossby waves in a large- scale forced barotropic flow

In this paper, the coupling equations describing nonlinear three-wave interaction among Rossby waves including the forcing of an external vorticity source are obtained. Under certain conditions, the coupling equations with a constant amplitude forcing, the stability analysis indi-cates that when the amplitude of the external forcing increases to a certain extent, a pitchfork bifurcation occurs. Also, it is shown from numerical results that the bifurcation can lead to chaotic behavior of “strange” attractor. For the obtained three-variable equation, when the amplitude of modulated external forcing gradually increases, a period-doubling bifurcation is found to lead to chaotic behavior. Thus, in a nonlinear three-wave coupling model in the large-scale forced barotropic atmospheric flow, chaotic behavior can be observed. This chaotic behavior can explain in part 30-60-day low-frequency oscillations observed in mid-high latitudes.     

Three－dimensional Global Scale Permanent－wave Solutions of the Nonlinear Quasigeostrophic Potential Vorticity Equation and Energy Dispersion

The three-dimensional nonlinear quasi-geostrophic potential vorticity equation is reduced to a linear form in the stream function in spherical coordinates for the permanent wave solutions consisting of zonal wavenumbers from 0 to n and rn vertical components with a given degree n. This equation is solved by treating the coefficient of the Coriolis parameter square in the equation as the eigenvalue both for sinusoidal and hyperbolic variations in vertical direction. It is found that these solutions can represent the observed long term flow patterns at the surface and aloft over the globe closely. In addition, the sinusoidal vertical solutions with large eigenvalue G are trapped in low latitude, and the scales of these trapped modes are longer than 10 deg. lat. even for the top layer of the ocean and hence they are much larger than that given by the equatorial β-plane solutions. Therefore such baroclinic disturb-ances in the ocean can easily interact with those in the atmosphere.Solutions of the shallow water potential vorticity equation are treated in a similar manner but with the effective depth H = RT / g taken as limited within a small range for the atmosphere.The propagation of the flow energy of the wave packet consisting of more than one degree is found to be along the great circle around the globe both for barotropic and for baroclinic flows in the atmosphere.     

Effect of Nonlinear Dynamic Process on Formation and Breakdown of Blocking

With the L-P approximate method(variation of parameter method), a barotropic channel model in β-plane is used to study the effect of nonlinear interaction between two waves with different scales on the formation of blocking. The approximate analytical solution, which can describe the process of the blocking formation, maintenance and breakdown, has been obtained by using the method of aproximate expansion. The importance of nonlinear interaction between two waves with different scales is stressed in the solution. The result suggests that the nonlinear interaction is the main dynamic process of the blocking formation. Some required conditions of blocking formation are also discussed.     

The 30–60-day Intraseasonal Oscillations over the Subtropical Western North Pacific during the Summer of 1998简

The features of 30-60-day convection oscillations over the subtropical western North Pacific （WNP） were investigated, along with the degree of tropical-subtropical linkage between the oscillations over the WNP during summer 1998. It was found that 30-60-day oscillations were extremely strong in that summer over both the subtropical and tro]~ical WNP, providing a unique opportunity to study the behavior of subtropical oscillations and their relationship to tropical oscillations. Further analyses indicated that 30-60-day oscillations propagate westwards over the subtropical WNP and reach eastern China. In addition, 30-60-day oscillations in the subtropics are affected by those over the South China Sea （SCS） and tropical WNP through two mechanisms： （1） direct propagation from the tropics into the subtropics; and （2） a seesaw pattern between the tropics and subtropics, with the latter being predominant.     

Topographically Forced Three-Wave Quasi-Resonant and Non-Resonant Interactions among Barotropic Rossby Waves on an Infinite Beta-Plane

In this paper, we first apply the assumption h=εh` of topographic variation (h is the nondimensional topographic height and is a small parameter) to obtain nonlinear equations describing three-wave quasi-resonant and non-resonant interactions among Rossby waves for zonal wavenumbers 1-3 over a wavenumber-two bottom topography (WTBT). Some numerical calculations are made with the fourth-order Rung-Kutta Scheme. It is found that for the case without topographic forcing, the period of three-wave quasi-resonance (TWQR) is found to be in-dependent of the zonal basic westerly wind, but dependent on the meridional wavenumber and the initial amplitudes. For the fixed initial data, when the frequency mismatch is smaller and the meridional wavelength is moderate, its pe-riod will belong to the 30-60-day period band. However, when the wavenumber-two topography is included, the pe-riods of the forced quasi-resonant Rossby waves are also found to be strongly dependent on the setting of the zonal basic westerly wind. Under the same conditions, only when the zonal basic westerly wind reaches a moderate extent, intraseasonal oscillations in the 30-60-day period band can be found for zonal wavenumbers 1-3. On the other hand, if three Rossby waves considered have the same meridional wavenumber, three-wave non-resonant interaction over a WTBT can occur in this case. When the WTBT vanishes, the amplitudes of these Rossby waves are conserved. But in the presence of a WTBT, the three Rossby waves oscillate with the identical period. The period, over a moder-ate range of the zonal basic westerly wind, is in the intraseasonal, 30-60-day range.     

Low-frequency oscillations of the East Asia–Pacific teleconnection pattern and their impacts on persistent heavy precipitation in the Yangtze–Huai River valley

Based on the daily reanalysis data from NCEP NCAR and daily precipitation data from the China National Meteorological Information Center,an ensemble empirical mode decomposition method is employed to extract the predominant oscillation modes of the East Asia Pacific(EAP) teleconnection pattern.The influences of these low-frequency modes on persistent heavy precipitation in the Yangtze Huai River(YHR)valley are investigated.The results indicate that the EAP pattern and rainfall in YHR valley both exhibit remarkable 10 30- and 30 60-day oscillations.The impacts of the EAP pattern on the YHR persistent heavy precipitation can be found on both the 10 30- and 30 60-day timescales the 10 30-day scale for most cases.Composite analysis indicates that,on the 10 30-day timescale,formation of the EAP pattern in the lower and middle troposphere is determined by convective systems near the tropical western Pacific;whereas in the middle troposphere,the phase transition is jointly contributed by both the dispersion of zonal wave energies at higher latitudes and convective systems over the South China Sea.In the context of the10 30-day EAP pattern,the anomalously abundant moisture is transported by an anomalous subtropical anticyclone system,and strong moisture convergence results from that anomalous anticyclone system and a cyclonic system in the midlatitude East Asia.Such a combination of systems persists for at least three days,contributing to the formation of persistent heavy precipitation in the YHR valley.     

Effect of nonlinear dynamic process on formation and breakdown of blocking

With the L-P approximate method (variation of parameter method), a barotropic channel model in β-plane is used to study the effect of nonlinear interaction between two waves with different scales on the formation of blocking. The approximate analytical solution, which can describe the process of the blocking formation, maintenance and breakdown, has been obtained by using the method of approximate expansion. The importance of nonlinear interaction between two waves with different scales is stressed in the solution. The result suggests that the nonlinear interaction is the main dynamic process of the blocking formation. Some required conditions of blocking formation are also discussed.     

NONLINEAR WAVES IN BAROTROPIC MODEL

In this paper, from the system of equation describing a barotropic atmosphere using the method of Taylor expansion for the nonlinear terms, the periodic solutions of the nonlinear inertio-surface gravity waves and Rossby waves have been obtained.The finite-amplitude nonlinear inertio-surface gravity waves and Rossby waves with horizontal divergence satisfy all the KdV equation. The solutions are all the cnoidal function, i, e., the cnoidal waves which include the linear waves and form the solitary waves under certain conditions. For the finite-amplitude Rossby waves with horizontal divergence, we find the new dispersive relation including both the wave number and the amplitude parameter. In case of small amplitude it is reduced to the Yeh formula. It is shown that the larger the amplitude and width, the faster the finite-amplitude inertio-surface gravity waves and the slower the finite-amplitude Rossby waves with horizontal divergence propagate. The blocking or cut-off system in which the amplitude and width are large may be considered as Rossby solitary waves.     

A BAROTROPIC QUASI-GEOSTROPHIC MODEL WITH LARGE-SCALE TOPOGRAPHY, FRICTION AND HEATING

Based on the barotropic equations including large-scale topography, friction and heat factor, a barotropic quasi-geostrophic model with large-scale topography, friction and heating is obtained by means of scale analysis and small parameter method. It is shown that this equation is a basic one, which is used to study the influence of the Tibetan Plateau on the large-scale flow in the atmosphere. If the friction and heating effect of large-scale topography are neglected, this model will degenerate to the general barotropic quasi-geostrophic one.     

The 30–60-day Intraseasonal Variability of Sea Surface Temperature in the South China Sea during May–September

This study investigates the structure and propagation of intraseasonal sea surface temperature(SST) variability in the South China Sea(SCS) on the 30–60-day timescale during boreal summer(May–September). TRMM-based SST, GODAS oceanic reanalysis and ERA-Interim atmospheric reanalysis datasets from 1998 to 2013 are used to examine quantitatively the atmospheric thermodynamic and oceanic dynamic mechanisms responsible for its formation. Power spectra show that the 30–60-day SST variability is predominant, accounting for 60% of the variance of the 10–90-day variability over most of the SCS. Composite analyses demonstrate that the 30–60-day SST variability is characterized by the alternate occurrence of basin-wide positive and negative SST anomalies in the SCS, with positive(negative) SST anomalies accompanied by anomalous northeasterlies(southwesterlies). The transition and expansion of SST anomalies are driven by the monsoonal trough–ridge seesaw pattern that migrates northward from the equator to the northern SCS. Quantitative diagnosis of the composite mixed-layer heat budgets shows that, within a strong 30–60-day cycle, the atmospheric thermal forcing is indeed a dominant factor, with the mixed-layer net heat flux(MNHF) contributing around 60% of the total SST tendency, while vertical entrainment contributes more than 30%. However, the entrainment-induced SST tendency is sometimes as large as the MNHF-induced component, implying that ocean processes are sometimes as important as surface fluxes in generating the30–60-day SST variability in the SCS.     

On the Application of a Genetic Algorithm to the Predictability Problems Involving "On-Off" Switches

The lower bound of maximum predictable time can be formulated into a constrained nonlinear opti- mization problem, and the traditional solutions to this problem are the filtering method and the conditional nonlinear optimal perturbation (CNOP) method. Usually, the CNOP method is implemented with the help of a gradient descent algorithm based on the adjoint method, which is named the ADJ-CNOP. However, with the increasing improvement of actual prediction models, more and more physical processes are taken into consideration in models in the form of parameterization, thus giving rise to the on-off switch problem, which tremendously affects the effectiveness of the conventional gradient descent algorithm based on the ad- joint method. In this study, we attempted to apply a genetic algorithm (GA) to the CNOP method, named GA-CNOP, to solve the predictability problems involving on-off switches. As the precision of the filtering method depends uniquely on the division of the constraint region, its results were taken as benchmarks, and a series of comparisons between the ADJ-CNOP and the GA-CNOP were performed for the modified Lorenz equation. Results show that the GA-CNOP can always determine the accurate lower bound of maximum predictable time, even in non-smooth cases, while the ADJ-CNOP, owing to the effect of on-off switches, often yields the incorrect lower bound of maximum predictable time. Therefore, in non-smooth cases, using GAs to solve predictability problems is more effective than using the conventional optimization algorithm based on gradients, as long as genetic operators in GAs are properly configured.     

Role of Parameter Errors in the Spring Predictability Barrier for ENSO Events in the Zebiak–Cane Model

ABSTRACT The impact of both initial and parameter errors on the spring predictability barrier （SPB） is investigated using the Zebiak Cane model （ZC model）. Previous studies have shown that initial errors contribute more to the SPB than parameter errors in the ZC model. Although parameter errors themselves are less important, there is a possibility that nonlinear interactions can occur between the two types of errors, leading to larger prediction errors compared with those induced by initial errors alone. In this case, the impact of parameter errors cannot be overlooked. In the present paper, the optimal combination of these two types of errors [i.e., conditional nonlinear optimal perturbation （CNOP） errors] is calculated to investigate whether this optimal error combination may cause a more notable SPB phenomenon than that caused by initial errors alone. Using the CNOP approach, the CNOP errors and CNOP-I errors （optimal errors when only initial errors are considered） are calculated and then three aspects of error growth are compared： （1） the tendency of the seasonal error growth; （2） the prediction error of the sea surface temperature anomaly; and （3） the pattern of error growth. All three aspects show that the CNOP errors do not cause a more significant SPB than the CNOP-I errors. Therefore, this result suggests that we could improve the prediction of the E1 Nifio during spring by simply focusing on reducing the initial errors in this model.     

AN APPLICATION OF THE THRESHOLD AUTOREGRESSION PROCEDURE TO CLIMATE ANALYSIS AND FORECASTING

In this paper a nonlinear method of time series analysis-threshold autoregressive (TAR) model in discrete time is used. The TAR procedure consists of four parts: model building, statistical identification, parameter estimation and forecasting.The object of this study is to estimate monthly total precipitation of Shanghai and Beijing by using open loop TAR model. We can see that the trend of forecasting is in agreement with observations.     

LINEAR AND NONLINEAR BAROTROPIC INSTABILITY

Based on a non-frictional and non-divergent nonlinear barotropic vorticity equation and its solutions oftravelling waves,the criteria for linear and nonlinear barotropic instability are gained respectively at an equilibriumpoint of the equation on a phase plane.The linear and nonlinear analytical solutions to instability waves arealso found.The computational results show that if their amplitudes are equal at the initial time,the amplitudeincrements of nonlinear instable barotropic wave are always less than those of linear instable barotropic wave.The nonlinear effects can slow down the exponential growth of linear instability.The time needed for makingthe amplitude double that of initial time by instabilities,is about 6h for linear instability and about 18h fornonlinear instability,the latter is in agreement with the observations in the real atmosphere.     

Study of the Optimal Precursors for Blocking Events

The precursors of dipole blocking are obtained by a numerical approach based upon a quasi-geostrophic barotropie planetary- to synoptic-scale interaction model without topography and with a localized synopticscale wave-maker. The optimization problem related to the precursors of blocking is formulated and the nonlinear optimization method is used to examine the optimal synoptic-scale initial field successfully. The results show that the prominent characteristics of the optimal synoptic-scale initial field are that the synoptic-scale wave train structures exist upstream of the incipient blocking. In addition, the large-scale low/high eddy-forcing pattern upstream of the incipient blocking is an essential precondition for the onset of dipole blocking.     

Inducing Unstable Grassland Equilibrium States Due to Nonlinear Optimal Patterns of Initial and Parameter Perturbations: Theoretical Models

Due to uncertainties in initial conditions and parameters,the stability and uncertainty of grassland ecosystem simulations using ecosystem models are issues of concern.Our objective is to determine the types and patterns of initial and parameter perturbations that yield the greatest instability and uncertainty in simulated grassland ecosystems using theoretical models.We used a nonlinear optimization approach,i.e.,a conditional nonlinear optimal perturbation related to initial and parameter perturbations (CNOP) approach,in our work.Numerical results indicated that the CNOP showed a special and nonlinear optimal pattern when the initial state variables and multiple parameters were considered simultaneously.A visibly different complex optimal pattern characterizing the CNOPs was obtained by choosing different combinations of initial state variables and multiple parameters in different physical processes.We propose that the grassland modeled ecosystem caused by the CNOP-type perturbation is unstable and exhibits two aspects:abrupt change and the time needed for the abrupt change from a grassland equilibrium state to a desert equilibrium state when the initial state variables and multiple parameters are considered simultaneously.We compared these findings with results affected by the CNOPs obtained by considering only uncertainties in initial state variables and in a single parameter.The numerical results imply that the nonlinear optimal pattern of initial perturbations and parameter perturbations,especially for more parameters or when special parameters are involved,plays a key role in determining stabilities and uncertainties associated with a simulated or predicted grassland ecosystem.     

THE HEATING FIELD IN AN ASYMMETRIC HURRICANE -PART I:SCALE ANALYSIS

A closed system of equations describing an asymmetric disturbance in cylindrical geometry is expanded about a small parameter. The small parameter describes the ratio of the magnitude of divergence in the boundary layer to that above that layer. A low order system describes a gradient wind balance in the radial direction and is quasi-symmetric with respect to the pressure and temperature fields. This system can be solved as an inverse problem for a mature steady state hurricane. The procedure entails asking the questions what structure and heating distributions are required to maintain a given asymmetric distribution of the tangential velocity (i. e. the angular momentum) in steady state. The method of characteristics enables us to solve for the vertical motion. That in turn determines the radial motion from the mass continuity equation. Application of the hydrostatics to the cylindrical thermal wind equation determines the pressure and the thermal fields and finally the required heating fields are dedu     

Modulation of the Intensity of Nascent Tibetan Plateau Vortices by Atmospheric Quasi-Biweekly Oscillation

The modulation of the intensity of nascent Tibetan Plateau vortices(ITPV) by atmospheric quasi-biweekly oscillation(QBWO) is investigated based on final operational global analysis data from the National Centers for Environmental Prediction. The spatial and temporal distributions of the ITPV show distinct features of 10–20-day QBWO. The average ITPV is much higher in the positive phases than in the negative phases, and the number of strong TPVs is much larger in the former,with a peak that appears in phase 3. In addition, the maximum centers of the ITPV stretch eastward in the positive phases,indicating periodic variations in the locations where strong TPVs are generated. The large-scale circulations and related thermodynamic fields are discussed to investigate the mechanism by which the 10–20-day QBWO modulates the ITPV. The atmospheric circulations and heating fields of the 10–20-day QBWO have a major impact on the ITPV. In the positive QBWO phases, the anomalous convergence at 500 hPa and divergence at 200 hPa are conducive to ascending motion. In addition, the convergence centers of the water vapor and the atmospheric unstable stratification are found in the positive QBWO phases and move eastward. Correspondingly, condensational latent heat is released and shifts eastward with the heating centers located at 400 hPa, which favors a higher ITPV by depressing the isobaric surface at 500 hPa. All of the dynamic and thermodynamic conditions in the positive QBWO phases are conducive to the generation of stronger TPVs and their eastward expansion.