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Winston C. Chao

Abstract

With appropriate modifications, a recently proposed explicit-multiple-time-step scheme (EMTSS) is incorporated into the UCLA model. In this scheme, the linearized terms in the governing equations that generate the gravity waves are split into different vertical modes. Each mode is integrated with an optimal time step, and at periodic intervals these modes are recombined. The other terms are integrated with a time step dictated by the CFL condition for low-frequency waves. This large time step requires a special modification of the advective terms in the polar region to maintain stability. Test runs for 72 h show that EMTSS is a stable, efficient and accurate scheme.

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Winston C. Chao

Abstract

The excessive precipitation over steep and high mountains (EPSM) in GCMs and mesoscale models is due to a lack of parameterization of the thermal effects of subgrid-scale topographic variation. These thermal effects drive subgrid-scale heated-slope-induced vertical circulations (SHVC). SHVC provide a ventilation effect of removing heat from the boundary layer of resolvable-scale mountain slopes and depositing it higher up. The lack of SHVC parameterization is the cause of EPSM. The author has previously proposed a method of parameterizing SHVC, here termed SHVC.1. Although this has been successful in avoiding EPSM, the drawback is that it suppresses convective-type precipitation in the regions where it is applied.

In this article, the author proposes a new method of parameterizing SHVC, here termed SHVC.2. In SHVC.2, the potential temperature and mixing ratio of the boundary layer are changed when used as input to the cumulus parameterization scheme over mountainous regions. This allows the cumulus parameterization to assume the additional function of SHVC parameterization. SHVC.2 has been tested in NASA Goddard’s GEOS-5 GCM. It achieves the primary goal of avoiding EPSM while also avoiding the suppression of convective-type precipitation in the regions where it is applied.

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Winston C. Chao

Abstract

Supported by numerical experiment results, the abrupt change of the location of the intertropical convergence zone (ITCZ), from the equatorial trough flow regime to the monsoon trough flow regime, or the monsoon onset, is interpreted as a subcritical instability. There are two balancing “forces” acting on the ITCZ. One toward the equator, or an equatorial latitude depending on the convection scheme, due to the earth’s rotation, has a nonlinear latitudinal dependence; and the other toward a latitude close to the sea surface temperature peak has a relatively linear latitudinal dependence. The highly nonlinear latitudinal dependence of the first “force” is crucial for the existence of the multiple equilibria. This work pivots on the finding that the ITCZ and Hadley circulation can still exist without the pole-to-equator gradient of radiative–convective equilibrium temperature.

The numerical experiments are done with an atmospheric general circulation model over an aquaplanet with zonally uniform sea surface temperature. The existence of the two flow regimes, the two “forces,” and the abrupt transition are all demonstrated in the experiments. Experimental results show high dependence on the choice of cumulus parameterization scheme, especially during the equatorial trough circulation regime. Although the proposed interpretation is more suitable for explaining the monsoon trough onset in the western Pacific, it is hypothesized that the same basic mechanism is also at the core of monsoon onset in other parts of the Tropics.

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Winston C. Chao

Abstract

The onset of cumulus convection in a grid column is a catastrophe, also known as a subcritical instability. Accordingly, in designing a cumulus parameterization scheme the onset of cumulus convection requires that a parameter crosses a critical value and the termination of cumulus convection requires that the same or a different parameter crosses a different critical value. Once begun, cumulus convection continues to exist, regardless of whether the onset criterion is still met, until the termination criterion is met. Also, the intensity of cumulus precipitation is related to how far the state is from the termination, not the onset, criterion.

The cumulus parameterization schemes currently in use in GCMs, however, treat the onset of cumulus convection as a supercritical instability; namely, convection is turned on when a parameter exceeds a critical value and is turned off when the same parameter falls below the same critical value. Also, the intensity of cumulus precipitation is related to how far this critical value has been exceeded. Among the adverse consequences of the supercritical-instability-concept-based cumulus parameterization schemes are that over relatively flat land the precipitation peak occurs around noon—4–6 h too soon—and that the amplitude of the precipitation diurnal cycle is too weak.

Based on the above-mentioned concept, a new cumulus parameterization scheme was designed by taking advantage of the existing infrastructure of the relaxed Arakawa–Schubert scheme (RAS), but replacing RAS's guiding principle with the catastrophe concept. Test results using NASA's Goddard Earth Observing System GCM, version 5 (GEOS-5), show dramatic improvement in the phase and amplitude of the precipitation diurnal cycle over relatively flat land.

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Winston C. Chao

Abstract

Excessive precipitation over steep and high mountains (EPSM) is a well-known problem in GCMs and mesoscale models. This problem impairs simulation and data assimilation products. Among the possible causes investigated in this study, it was found that the most important one, by far, is a missing upward transport of heat out of the boundary layer due to the vertical circulations forced by the daytime upslope winds, which are forced by heated boundary layer on the subgrid-scale slopes. These upslope winds are associated with large subgrid-scale topographic variation, which is found over steep and high mountains. Without such subgrid-scale heat ventilation, the resolvable-scale upslope flow in the boundary layer generated by surface sensible heat flux along the mountain slopes is excessive. Such an excessive resolvable-scale upslope flow combined with the high moisture content in the boundary layer results in excessive moisture transport toward mountaintops, which in turn gives rise to EPSM. Other possible causes investigated include 1) a poorly designed horizontal moisture flux in the terrain-following coordinates, 2) the conditions for cumulus convection being too easily satisfied at mountaintops, 3) conditional instability of the computational kind, and 4) the absence of blocked flow drag. They are all minor or inconsequential.

The ventilation effects of the subgrid-scale heated-slope-induced vertical circulation (SHVC) have been parameterized by removing heat from the boundary layer and depositing it in the layers higher up when topographic variance exceeds a critical value. Test results using the NASA Goddard Earth Observing System GCM version 5 (GEOS-5) have shown that the EPSM problem is largely solved.

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Winston C. Chao

Abstract

This study provides an explanation for the origin of the tropical intraseasonal (40–50 day) oscillation (TIO) based on a simple generalization of Gill's linear analytic model for tropical large-scale heat-induced circulation. The solution, which compares favorably with observations, contains a convective region that excites an eastward-moving Kelvin wave and a westward-moving Rossby wave. The significance of the Rossby wave, not previously emphasized, is clearly revealed. The entire system moves eastward as a response to the circulation it excites at a speed at which the latent heat energy in the tropics is best extracted. Thus, the TIO is viewed as an intrinsic instability. Its speed is related to the vertical heating profile and is a decreasing function of both dissipation and the zonal size of the convective region. This speed is a weighted mean of the speed of the Kelvin wave and that of the Rossby wave. Previous studies have erroneously equated the speed of the TIO with that of the Kelvin wave. This study also demonstrates that classification of the TIO as a wavenumber 1 phenomenon is not advisable.

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Winston C. Chao

Abstract

In this conceptual and numerical study, sudden stratospheric warnings (SSW) are identified as catastrophes. A catastrophe is the transition toward a separate new equilibrium after the original stable equilibrium state of a dynamical system terminates as an external parameter changes smoothly and slowly across a critical value. Many qualitative results of some previous modeling studies of SSW are interpreted in light of catastrophe theory. For example, the cutoff amplitudes in wave forcing as functions of initial conditions determined by Holton and Dunkerton are shown to be in the loci of unstable equilibria in a bifurcation diagram. Also the stage of warmest polar temperature represents the peak of the overshooting in a catastrophe. Moreover, the rapid restoration of westerlies corresponds to the return from the overshooting, Basic concepts in catastrophe theory related to SSW-for example, hysteresis, cusp and triggering-are demonstrated in a numerical study using the Holton-Mass model.

The transition from the steady regime to the vacillation regime in the Holton-Mass model, i.e., SSW, is explained conceptually in terms of the topographically induced Rossby wave instability. The multiple equilibria involved owe their existence to the resonant response of the system to bottom forcing. The suddenness of SSW is due to the resonant increase of wave amplitude and its positive feedback on the mean flow. The model, as well as the conceptual explanation, gives a resonant buildup of the planetary wave, followed quickly by its decay and then by the warming peak, a scenario corresponding well with observations. A surge of wave amplitude at upper tropospheric levels prior to the warming peak is a result of the instability and, as such, should not be used as a trigger td instigate SSW as in many previous mechanistic models.

Implications of the catastrophic nature of SSW for simulation and forecasting efforts are discussed. An additional and perhaps more difficult challenge in the SSW forecasting effort comes when the initial planetary wave amplitude is not yet in the rapid building-up phase; i.e., before the instability occurs.

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Winston C. Chao and Litao Deng

Abstract

This study deals with the origin of the phase lag between deep cumulus convection and low-level convergence in tropical synoptic-scale systems, known since 1974. Several possible causes, including 1) propagation of the heating field, 2) β, 3) vertical shear of the basic flow, and 4) vertical tilt of the heat source, are examined. The last one is found to be the reason for the phase lag. The vertical tilt of the heat source occurs as a result of evolution and propagation of mesoscale convective systems within the synoptic system. During this evolution the change of vertical heating profile results in the tilt of heating field. Previous efforts of incorporating such phase lag in wave-CISK studies are commented on.

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Winston C. Chao and Baode Chen

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The monsoon is interpreted as an intertropical convergence zone (ITCZ) substantially away (more than 10°) from the equator and the existence of the ITCZ does not have to rely on land–sea contrast. Land–sea contrast can provide a favorable longitudinal location for the ITCZ but this role can be replaced by sea surface temperature contrast in the longitudinal direction. Thus, the interpretation of the monsoon presented herein differs from the long-held fundamental belief that its basic cause is land–sea thermal contrast on the continental scale in the sense that the existence of landmass is not considered a necessary condition for monsoons. Through general circulation model experiments, support has been found for this interpretation. The Asian and Australian summer monsoon circulations are largely intact in an experiment in which Asia, maritime continent, and Australia are replaced by ocean with sea surface temperature (SST) taken from that of the surrounding oceans. Thus, in these areas land–sea contrast is not a necessary condition for monsoon. This also happens to the Central American summer monsoon. The same thing can also be said about the African and South American summer monsoons, if these continents are replaced by ocean of sufficiently high SST. It is also shown that in the Asian monsoon the change resulting from such replacement is due more to the removal of topography than to the removal of land–sea contrast. In the Asian and Australian winter monsoons land–sea contrast also plays only a minor role.

The origin of the ITCZs and their latitudinal locations have been previously interpreted by Chao. The circulation associated with an off-equator ITCZ, previously interpreted by Chao and Chen through a modified Gill solution and briefly described in this paper, explains the monsoon circulation. The longitudinal location of the ITCZ is determined by the distribution of surface conditions. ITCZs favor locations of high SST as in the western Pacific and Indian oceans, or tropical landmass, due to land–sea contrast, as in tropical Africa and South America. Thus, the role of landmass, when it is important, in the origin of monsoons can be replaced by ocean of sufficiently high SST. Furthermore, the ITCZ circulation extends into the tropics in the other hemisphere to give rise to the winter monsoon circulation there. Also through the equivalence of land–sea contrast and high SST, it is argued that the basic monsoon onset mechanism proposed by Chao is valid for all monsoons.

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Winston C. Chao and Baode Chen

Abstract

Chao's numerical and theoretical work on multiple quasi equilibria of the intertropical convergence zone (ITCZ) and the origin of monsoon onset is extended to solve two additional puzzles. One is the highly nonlinear dependence on latitude of the “force” acting on the ITCZ due to the earth's rotation, which makes the multiple quasi equilibria of the ITCZ and monsoon onset possible. The other is the dramatic difference in such dependence when different cumulus parameterization schemes are used in a model. Such a difference can lead to a switch between a single ITCZ at the equator and a double ITCZ, when a different cumulus parameterization scheme is used. Sometimes one of the double ITCZ can diminish and only the other remains strong, but still this can mean different latitudinal locations for the single ITCZ.

A single idea based on two off-equator attractors for the ITCZ symmetric with respect to the equator, due to the earth's rotation, and the dependence of the strength and size of these attractors on the cumulus parameterization scheme solves both puzzles. The origin of these rotational attractors, explained in Part I, is further discussed. Each attractor exerts on the ITCZ a force of simple shape in latitude; but the sum gives a shape highly varying in latitude. Also the strength and the domain of influence of each attractor vary when change is made in the cumulus parameterization. This gives rise to the high sensitivity of the force shape to cumulus parameterization. Numerical results, of experiments using Goddard's GEOS GCM, supporting this idea are presented. It is also found that the model results are sensitive to changes outside of the cumulus parameterization. The significance of this study to El Niño forecast and to tropical forecast in general is discussed.

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