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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.

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.

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.

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 c...

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 attrac...

The Madden-Julian oscillation (MJO), or the tropical intraseasonal oscillation, has attracted much attention, ever since its discovery in the early seventies for reasons of both scientific understanding and practical forecasts. Among the theoretical interpretations of the MJO, the wave-CISK (conditional instability of the second kind) mechanism is the most popular. The basic idea of the wave-CISK interpretation is that the cooperation between the low-level convergence associated with the eastward moving Kelvin wave and the cumulus convection generates an eastward moving Kelvin-wave-like mode. Later it was recognized that the MJO has an important Rossby-wave-like component. However linear analysis and numerical simulations based on it (even when conditional heating is used) have revealed two problems with the wave-CISK interpretation; i.e., excessive speed and the most preferred scale being zero or grid scale. Chao (1995) presented a discussion of these problems and attributed these problems to the particular type of expression for the cumulus heating used in the linear analyses and numerical studies (i.e., the convective heating is proportional to low-level convergence and a fixed vertical heating profile). It should be pointed out that in the relatively successful simulation of MJO with general circulation models the problem of grid scale being the most preferred scale does not appear and die problem of excessive speed is not as severe as in the linear analysis.

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 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 remain, but still this can mean different latitudinal locations for the single ITCZ. A single idea based on two off-equator attractors for the ITCZ, due to earth's rotation and symmetric with respect to the equator, 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. The "force" acting on the ITCZ due to earth's rotation is the sum of the "forces" of the two attractors. 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 general circulation model, 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 Nino forecast and to tropical forecast in general is discussed.

Chao and Lin’s work on tropical intraseasonal oscillations, super cloud clusters, and cumulus convection schemes is extended from a 2D model setup to a 3D aquaplanet setup. It is found that super cloud clusters can be simulated in a 3D model and that the 3D setup has more stringent requirements on the cumulus convection scheme than the 2D setup does for a successful simulation of super cloud clusters. Three cumulus convection schemes are compared in experiments simulating super cloud clusters. In the more successful experiments, individual cloud cluster pairs in the meridional direction, once generated near the equator by the cloud cluster tele-induction mechanism, assume a poleward movement while exhibiting weak zonal movement. The combination of two or three successive cloud cluster pairs (i.e., vortex pairs) straddling the equator gives rise to westerly wind burst events of sizable longitudinal range and duration. Thus, the westerly wind burst, as appeared in the model, is really a part of the...

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.

A generalized form of the second-order van Leer transport scheme is derived. Several constraints to the implied subgrid linear distribution are discussed. A very simple positive-definite scheme can be derived directly from the generalized form. A monotonic version of the scheme is applied to the Goddard Laboratory for Atmospheres (GLA) general circulation model (GCM) for the moisture transport calculations, replacing the original fourth-order center-differencing scheme. Comparisons with the original scheme are made in idealized tests as well as in a summer climate simulation using the full GLA GCM. A distinct advantage of the monotonic transport scheme is its ability to transport sharp gradients without producing spurious oscillations and unphysical negative mixing ratio. Within the context of low-resolution climate simulations, the aforementioned characteristics are demonstrated to be very beneficial in regions where cumulus convection is active. The model-produced precipitation pattern using the new transport scheme is more coherently organized both in time and in space, and correlates better with observations. The side effect of the filling algorithm used in conjunction with the original scheme is also discussed, in the context of idealized tests. The major weakness of the proposed transport scheme with a local monotonic constraint is its substantial implicit diffusion at low resolution. Alternative constraints are discussed to counter this problem.

A new framework for interpreting the origin of the tropical intraseasonal oscillation (TISO), which avoids the speed and scale selection problems in the previous theories, is proposed in this study. In this interpretation TISO is viewed as an oscillation driven by an eastward moving convective region. This convective region consists of one or more super cloud clusters originating in the Indian Ocean and terminating in mid-Pacific, and is then followed by another convective region arising in the Indian Ocean in a period of 40-50 days. Additionally, a formal analogy is pointed out between super cloud clusters and the middle-latitude baroclinic wave packets. This study includes a simulation of TISO in a 2D model to support our interpretation. Experiments were conducted with four different convection schemes. The authors advocate that the successful simulation of TISO depends on the successful simulation of super clouds cluster, which in turn depends on the successful simulation of the life cycle of cloud clusters, which further in turn depends on the choice of cumulus convection scheme. What makes a cumulus convection scheme successful in simulating TISO is discussed.

Recent developments in the field of data assimilation have pointed to variational analysis (essentially least-squares fitting of a model solution to observed data) using the adjoint method as a new direction that holds the potential of major improvements over the current optimal interpolation method. This paper describes the initial effort in the development of a 4D variational analysis system. Although the development is based on the Goddard Laboratory for Atmospheres General Circulation Model (GCM), the methods and procedures described in this paper can be applied to any model. The adjoint code that computes the gradients needed in the analysis can be written directly from the GCM code. An easy error-detection technique was devised in the construction of the adjoint model. Also, a method of determining the weights and the preconditioning scales for the cases where model-generated data, which are error free, are used as observation is proposed. Two test experiments show that the dynamics part of the system has been successfully completed.

The influence of a cumulus convection scheme on the simulated atmospheric circulation and hydrologic cycle is investigated by means of a coarse version of the GCM. Two sets of integrations, each containing an ensemble of three summer simulations, were produced. The ensemble sets of control and experiment simulations are compared and differentially analyzed to determine the influence of a cumulus convection scheme on the simulated circulation and hydrologic cycle. The results show that cumulus parameterization has a very significant influence on the simulation circulation and precipitation. The upper-level condensation heating over the ITCZ is much smaller for the experiment simulations as compared to the control simulations; correspondingly, the Hadley and Walker cells for the control simulations are also weaker and are accompanied by a weaker Ferrel cell in the Southern Hemisphere. Overall, the difference fields show that experiment simulations (without cumulus convection) produce a cooler and less energetic atmosphere.

The roles of the Critical Cloud Work Function (CCWF) data set and the upper and lower bounds on entrainment by cumulus plumes in the Arakawa-Schubert cumulus parameterization (ASCP) in the GLA GCM (Geller et al., 1988) were investigated in two sets of experiments. It was found that the horizontal and vertical distribution of cumulus heating can be altered in ASCP by adjusting these parameters. These changes can have a strong influence on the vertical structure of condensation heating, water vapor distribution, temperature, and rainfall. The CCWF is an important limiting parameter that controls the onset of different cloud types; increasing the threshold values of CCWF for all clouds tends to concentrate the rainfall into a narrower ITCZ and affects the rainfall during the initial adjustment period.

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 contains a convective region that excites an eastward-moving Kelvin wave and a westward-moving Rossby wave. 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. The TIO speed is a weighted mean of the speed of the Kelvin wave and that of the Rossby wave.

The Arakawa-Schubert (1974) parameterization is applied to a prognostic model of large-scale atmospheric circulations and used to analyze data in a general circulation model (GCM). The vertical structure of the large-scale model and the solution for the cloud subensemble thermodynamical properties are examined to choose cloud levels and representative regions. A mass flux distribution equation is adapted to formulate algorithms for calculating the large-scale forcing and the mass flux kernel, using either direct solution or linear programming. Finally, the feedback of the cumulus ensemble on the large-scale environment for a given subensemble mass flux is calculated. All cloud subensemble properties were determined from the conservation of mass, moist static energy, and total water.

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.

The sudden stratospheric warming (SSW) process is qualitatively studied using a conceptual and numerical approach guided by catastrophe theory. A simple example of a catastrophe taken from nonlinear dynamics is given, and results from previous modelling studies of SSW are interpreted in light of catastrophe theory. Properties of this theory such as hysteresis, cusp, and triggering essential to SSW are numerically demonstrated using the truncated quasi-geostrophic beta-plane model of Holton and Mass (1976). A qualitative explanation of the transition from the steady regime to the vacillation regime is given for the Holton and Mass model in terms of the topographically induced barotropic Rossby wave instability. Some implications for the simulation and prediction of SSW are discussed.

When a global atmospheric basic state has constant angular velocity and its temperature varies with altitude only, there exist normal mode solutions to the linearized global primitive equations. The use of these normal modes, which have known behavior in time, is superior to the use of the Rossby-Haurwitz wave as initial conditions for detecting errors in the dynamics part of primitive equation global models. With these initial conditions, integration through only one time step is sufficient to detect many formulation and coding errors. Other tests are still required for detecting problems of nonlinear instability and conservation of integral properties, however.