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Hai-Ru Chang and Hampton N. Shirer

Abstract

The accuracies of the usual centered differencing, compact differencing and finite element methods are compared linearly with a geostrophic adjustment problem and nonlinearly with a vorticity advection problem. The finite element method provides the best approximation in the geostrophic adjustment problem on either a staggered or an unstaggered grid. The compact scheme provides the most accurate representation of the wavenumber distribution for the vorticity advection when the Arakawa Jacobian J 7 is used.

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Hai-Ru Chang and Peter J. Webster

Abstract

A fully nonlinear model is used to reexamine the impact of a zonally varying basic state on the propagation characteristics of latitudinally equatorially trapped modes. Linear studies have shown that such modes are longitudinally trapped in regions of negative stretching deformation of the equatorial time-mean zonal flow (i.e., where Ux < 0) forming “accumulation” regions of wave action flux. Furthermore, the accumulation regions tend to act as local emanation regions to the extratropics. These physical communications between the tropics and extratropics are referred to as fast teleconnections due to their rapidity (periods of days to weeks) compared to the much slower climatological differences in the mean states such as occur between El Niño and La Niña. The latter form of communication between low and high latitudes, which is induced by very low frequency SST changes, is referred to as a slow teleconnection.

It is generally found that accumulation and emanation regions are present in the nonlinear regime with much the same character as with the linear model. The similarity exists even when realistic forcing functions are used with amplitudes and temporal and spatial characteristics that correspond to impulsive convection in the western Pacific Ocean. A description of the convection is given. A diagnosis of the linear and nonlinear results shows that, in the tropics, the linear advection by the mean flow plays a dominant role and probably is the reason for the great similarity of the linear and nonlinear tropical atmosphere. However, there are some differences between the linear and nonlinear results. Nonlinear waves appear to propagate more rapidly through the maximum westerlies along the equator and with less difficulty than linear waves. The differences that do occur arise from the nonlinear changes in the tropical mass field, especially in the accumulation zone. Differences between linear and nonlinear responses in the midlatitude response to equatorial forcing appear to reflect changes in the tropics. Nonlinear maxima occur poleward of the region of tropical westerlies but only after accumulation has occurred along the equator.

The results of the study are used to discuss the problem of why there is considerable similarity between simple linear models and more sophisticated nonlinear models. Such similarity would probably explain why the NMC and the NEPRF global models exhibit phase locked responses in the middle latitudes to imposed and impulsive tropical forcing. The role of fast teleconnenions in the longer term general circulation of the atmosphere is discussed, especially during El Niño and La Niña. Whereas an aggregate role for the fast teleconnections in producing very slowly evolving climate features remains obscure, it does appear that the accumulation-emanation theory may infer different routings for transient communications between the tropics and higher latitudes and vice vera depending upon the state of the basic flow.

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Hai-Ru Chang and Peter J. Webster

Abstract

Short equatorially trapped Rossby waves are usually thought to he trapped and dissipated nea the region of creation because of their relatively slow group speeds and because of the relatively low amplitude basic state within which they reside. Only long Rossby waves, with stronger group speeds, are assumed to move far away from the forcing area producing remote effects or teleconnections. These restrictions on the regions of influence of Rossby waves are only valid in a motionless basic state or in a basic state that is constant with longitude. If the basic state changes in the zonal direction, even short waves have considerable remote effects. Using ray-tracing techniques and nonlinear numerical models, the impact of a zonally varying basic state on the characteristics of equatorial modes is investigated.

The original low-latitude energy accumulation zone theory of Webster and Chang is extended to include the complete family of tropical waves. In equatorial regions, the majority of Rossby waves are longitudinally trapped in regions where the stretching deformation of the background flow is negative. Most of the Rossby packet will reach the energy accumulation area from the east. This kind of wave action flux accumulation (i.e., from the east) is referred to as “forward accumulation.” However, some shortwaves of the packet will propagate into the accumulation region from the west. This reverse propagation into an accumulation zone is referred to as “backward accumulation.” Mixed Rossby-gravity waves are also considered. Ray tracing technics indicate that the mixed wave is less likely to be longitudinally trapped. However, if the wave is trapped, the energy accumulation area is generally located in the same place as that of Rossby wave and that the energy is accumulated through backward processes. A nonlinear global spectral model is used to cheek the WKB approximations used in the ray tracing.

The results of this study suggest that the ubiquity of the longwave approximation for equatorial modes should be questioned. As the basic state modifies the scale of the mode such that initially very long modes may evolve to shorter scales during propagation through the longitudinally varying flow (and vice versa for initially short modes), the approximation appears questionable in any region where the magnitude of the basic state is similar to the group speeds of the mode, the basic state changes sign, and the basic state possesses a significant stretching deformation. With the longwave approximation, not only does the mixed Rossby-gravity wave disappear but the dispersive Rossby modes are rendered effectively nondispersive. Furthermore, the accumulation property of equatorial waves is also eliminated.

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Peter J. Webster and Hai-Ru Chang

Abstract

Previous studies have suggested that the regions of mean anomalous perturbation kinetic energy which exist in the vicinity of the equatorial upper-tropospheric westerlies are the result of the propagation of extratropical synoptic and low frequency waves through the equatorial “westerly duet” where a subsequent wave energy convergence occurs. The proposition that these perturbed equatorial regions may arise from remote equatorial energy sources is investigated. It is shown that three criteria must be met. The first two, the existence of wave energy sources along the equator and a mechanism to transport that energy longitudinally, are accounted for relatively easily with existing theory of divergent, trapped equatorial modes. The third criterion, the requirement of a mechanism for an accumulation of transient energy in the equatorial stretch flow (i.e., nonzero ūx), is not immediately obvious and requires exploration to develop new concepts.

Using simple WKBJ arguments it is shown that within a realistic parameter range, a combination of longitudinal stretch in the basic state along the equator and the characteristics of the equatorial trapped waves satisfy the third criterion. The equatorial waves must possess a divergent structure which insists on equatorial trapping. It is shown that purely barotropic modes, which cannot be equatorially trapped, do not represent the real atmospheric structure at low latitudes. Regions of negative longitudinal stretch along the equator (i.e., westerlies decreasing, or easterlies increasing, towards the cast) are shown to be wave energy accumulation regions. Regions with positive stretch, on the other hand, are wave energy depletion regions. A free-surface barotropic model with fully nonlinear basic states, containing both stretch and shear, confirm the results of the simpler model, i.e., regardless of the position of the energy source within the tropical atmosphere the wave energy accumulates in the same region; namely, on the eastern side of the westerly maximum. Thus, the third criterion is accounted for by the longitudinal trapping of the equatorial Rossby waves in specific regions as they move through the longitudinal stretch flow. It is argued that the existence of energy depletion and accumulation regions provides for the existence of an equatorial teleconnection system allowing for remote regions of the tropics to be connected by the equatorial transient modes. A number of alternate hypotheses such as the instability of the longitudinal varying basic flow are tested, although, in this case, the basic state is found to be very stable, indicating a robustness of the wave energy accumulation hypothesis.

The numerical results indicate that the equatorial wave accumulation regions are also emanation regions of equatorial transient influence to higher latitudes. That is, wherever the equatorial regions are excited, a wave train to higher latitudes will originate from the same longitude belt along the equator, producing a phase locked response at higher latitudes given the same mean basic equatorial flow. It is argued that the concept of tropical emanation regions provides a significant modification to the tropical-extratropical wave train teleconnection theory.

It is shown that thew new theories of atmospheric teleconnections (i.e., the equatorial and the modified tropical-extratropical theories) may allow interpretation of some rather difficult questions that have been posed in both modeling and observational studies.

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Hai-Ru Chang and Hampton N. Shirer

Abstract

A generalized seven-coefficient model of two-dimensional Rayleigh-Bénard convection is presented. The model simulates successfully one means by which lateral cell expansion can occur as the value of the imposed vertical temperature difference is changed. Such changes in the horizontal wavelengths of the convective rolls are accomplished by the nonlinear transfer of energy from cells to other cells with smaller wavenumbers. The crucial effect is one represented by the advective term v˙∇v in the equation of motion, and as a consequence an interacting triad of harmonics must be included in the spectral model. Thus, the generalized model has basically the same form as that used by Saltzman or Shirer and Dutton, but in the generalized model the triad of interacting wavenumbers is varied as the vertical heating rate is varied. Actual values of the horizontal wavenumbers are determined by assuming that the first unstable wave will have the largest growth rate, or equivalently that the bifurcation point will have the smallest value. Thus, only the energetically active components are retained; in this way, transitional behavior within two-dimensional convective flow can be simulated properly, and can be interpreted physically as representing the cell expansion process, via successive secondary branching.

When the solutions are compared with those obtained by Clever and Busse from a large three-dimensional spectral model, it is found that for small values of the Prandtl number P (∼0.1), a two-dimensional cell broadening mechanism is likely to operate, but for larger values of P (∼0.7), a three-dimensional mechanism is expected. Consequently, these results suggest that this generalized seven-component model can be used to simulate successfully some transitions in a system having more degrees of freedom, because the seven components apparently form the basic unit by which steady two-dimensional flow develops. Moreover, the modeling philosophy presented here can provide the basis for development of simple atmospheric convection models.

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Quanan Zheng, Xiao-Hai Yan, Chung-Ru Ho, and Chang-Kou Tai

Abstract

The effects of strong meridional shear of mean flow on propagation of long waves having a wavelength of about 1000 km and period of 25 days observed in the equatorial Pacific and Atlantic Oceans are analyzed in this paper. Information from the weekly multichannel sea surface temperature images derived from the Advanced Very High Resolution Radiometer on board the NOAA series satellites from January 1986 to March 1992 is used for the statistics of the visual parameters of the waves. The characteristic scales of the waves are estimated based on the results by previous investigators and the statistical results of the present study. Solving a potential vorticity equation, the authors obtain a dispersion relation with an additional term depending on the flow shear strength compared with that of the free Rossby wave. The theoretical model provides a good explanation for the variable behavior of long-wave propagation.

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Da-Lin Zhang, Hai-Ru Chang, Nelson L. Seaman, Thomas T. Warner, and J. Michael Fritsch

Abstract

A two-way interactive, nested-grid system tested with The Pennsylvania Slate University/INCAR three-dimensional mesoscale model is described. A mesh structure, designed to minimize numerical noise, together with a procedure for obtaining compatible coarse grid mesh (COM) and fine grid mesh (FOM) terrain conditions, is presented. Also, a method to initialize the nested-grid meshes is proposed. The nested-grid system has been tested with real data and raw terrain under different severe conditions. A 12-h simulation of a propagating jet streak over complex terrain is presented; the results indicate relatively noise-free solutions on both the OGM and FGM domains.

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Peter J. Webster, Jun Jian, Thomas M. Hopson, Carlos D. Hoyos, Paula A. Agudelo, Hai-Ru Chang, Judith A. Curry, Robert L. Grossman, Timothy N. Palmer, and A. R. Subbiah

The authors have developed a new extended-range flood forecasting system for large river basins that uses satellite data and statistically rendered probabilistic weather and climate predictions to initialize basin-scale hydrological models. The forecasting system overcomes the absence of upstreamflow data, a problem that is prevalent in the developing world. Forecasts of the Ganges and Brahmaputra discharge into Bangladesh were made in real time on 1–10-day time horizons for the period 2003–08. Serious flooding of the Brahmaputra occurred in 2004, 2007, and 2008. Detailed forecasts of the flood onset and withdrawal were made 10 days in advance for each of the flooding events with correlations at 10 days ≥0.8 and Brier scores <0.05. Extensions to 15 days show useable skill. Based on the 1–10-day forecasts of the 2007 and 2008 floods, emergency managers in Bangladesh were able to act preemptively, arrange the evacuation of populations in peril along the Brahmaputra, and minimize financial loss. The particular application of this forecast scheme in Bangladesh represents a “world is f lat” approach to emergency management through the collaboration of scientists in Europe (generating global ensemble meteorological and climate forecasts), the United States (developing and producing the integrated flood forecasts), and the developing world (integrating the flood forecasts into their disaster management decision-making protocol), all enabled by high-speed Internet connections. We also make suggestions of how scientific and technical collaborations between more developed and developing nations can be improved to increase their prospects for sustaining the technology adoption and transfer.

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