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ROBERT SADOURNY
,
AKIO ARAKAWA
, and
YALE MINTZ

Abstract

A finite difference scheme is developed for numerical integration of the nondivergent barotropic vorticity equation with an icosahedral-hexagonal grid covering the sphere. The grid is made by dividing the 20 triangular faces of an icosahedron into smaller triangles, the vertices of which are the grid points. Each grid point is surrounded by six neighboring points, except the 12 vertices of the icosahedron which are surrounded by five points. The difference scheme for the advection of vorticity exactly conserves total vorticity, total square vorticity, and total kinetic energy. A numerical test is made, with a stationary Neamtan wave as the initial condition, by integrating over 8 days with 1-hr. time steps and a grid of 1002 points for the sphere. There is practically no distortion of the waves over the 8 days, but there is a phase displacement error of about 1° of long. per day toward the west.

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Akio Arakawa
and
Vivian R. Lamb

Abstract

To improve the simulation of nonlinear aspects of the flow over steep topography, a potential enstrophy and energy conserving scheme for the shallow water equations is derived. It is pointed out that a family of schemes can conserve total energy for general flow and potential enstrophy for flow with no mass flux divergence. The newly derived scheme is a unique member of this family, that conserves both potential enstrophy and energy for general flow. Comparison by means of numerical experiment with a scheme that conserves (potential) enstrophy for purely horizontal nondivergent flow demonstrated the considerable superiority of the newly derived potential enstrophy and energy conserving scheme, not only in suppressing a spurious energy cascade but also in determining the overall flow regime. The potential enstrophy and energy conserving scheme for a spherical grid is also presented.

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Carlos R. Mechoso
,
Akio Kitoh
,
Shrinivas Moorthi
, and
Akio Arakawa

Abstract

The atmospheric response to a sea surface temperature anomaly over the equatorial eastern Pacific Ocean (SSTA) is investigated using the UCLA General Circulation Model. The SSTA used is an idealization of that compiled by Rasmusson and Carpenter for the mature phase of El Niño. Two simulations over seasons, one without and the other with the SSTA, are performed and their results are compared for the Northern Hemisphere winter season.

In the tropics the SSTA enhances precipitation over the central and eastern equatorial Pacific, while it decreases precipitation over the adjacent regions. The anomalous precipitation is predominantly balanced by the anomalous moisture flux convergence, which has comparable magnitude in the planetary boundary layer (PBL), and in the free atmosphere with quite different geographical distribution. This suggests that the anomalous precipitation, and hence the anomalous tropical cumulus heating, cannot be related exclusively to either flow anomalies in the PBL or in the free atmosphere.

In the midlatitudes, it is found that the SSTA results in a more zonal flow over the Pacific with an intensification of the upper-tropospheric westerlies. Associated with this intensification, synoptic-scale transient baroclinic waves become more active. This is consistent with interannual differences in observed spectral distributions of transients for five winters, two of which were El Niño winters. Geographically, the increase in baroclinic wave activity occurs in a zonal bell extending from the northeastern Pacific to the northern Atlantic.

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Carlos R. Mechoso
,
Koji Yamazaki
,
Akio Kitoh
, and
Akio Arakawa

Abstract

The predictability of the stratospheric warming events during the winter of 1979 is investigated by performing a series of 10-day forecasts using the UCLA general circulation model. In general, those events are predictable from several days in advance. The accuracy of the prediction, however, can be sensitive to the starting date and such model characteristics as the horizontal resolution. This sensitivity seems to arise because relatively small errors in the predicted tropospheric zonal mean wind can produce large differences in the characteristics of upward wave propagation and thereby large errors in the stratospheric forecast.

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Chien-Ming Wu
,
Bjorn Stevens
, and
Akio Arakawa

Abstract

In this study, a 2D cloud-system-resolving model (CSRM) is used to assess the control mechanism for the transition from shallow to deep convection in the diurnal cycle over land. By comparing with a 3D CSRM under conditions taken from the Large-Scale Biosphere–Atmosphere field study (in the Amazon), the authors show that the 2D CSRM reproduces the main features evident in previous 3D simulations reasonably well. To extract the essence of the transition from shallow to deep convection, the observed case is idealized to isolate two control parameters, the free troposphere stability and the relative humidity. The emergence of a distinct transition between shallow and deep convection shows that the convective transition is an intrinsic property of the system. A transition time is defined to evaluate the key mechanism of the transition. The authors show that the transition coincides with the time when the lapse rate of the virtual potential temperature of the clouds becomes larger than that of the environment, suggesting that the transition happens when shallow clouds become, on average, buoyant. This suggests that, given the opportunity, convection prefers to be shallow.

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Rafael Terra
,
Carlos R. Mechoso
, and
Akio Arakawa

Abstract

This paper examines the impact of orographically induced mesoscale heterogeneities on the macroscopic behavior of planetary boundary layer (PBL) stratiform clouds, and implements and tests a physically based parameterization of this effect in the University of California, Los Angeles (UCLA), atmospheric general circulation model (AGCM). The orographic variance and associated thermal circulations induce inhomogeneities in the cloud field that can significantly alter the PBL evolution; an effect that has been largely ignored in existing climate models. The impact of this effect on AGCM simulations is examined and the mechanisms at work are studied by analyzing a series of Cloud System Resolving Model (CSRM) simulations.

Both the CSRM and AGCM results show that, in the absence of the orographic effect, the continental PBL tends to be in one of two regimes: the solid regime characterized by a cold and overcast PBL and the broken regime characterized by a low time-mean cloud incidence and a large-amplitude diurnal cycle. Without the orographic effect, the PBL may lock in the convectively stable solid regime, with deep convection displaced to the surrounding oceans and subsidence induced over land further contributing to the persistence of the cloud deck. The inclusion of the orographic effect weakens the feedback between the cloud's albedo and the ground temperature responsible for the existence of the two regimes and, therefore, conspires against the persistence of the solid regime rendering the behavior of the PBL–ground system less bimodal. The parameterization featured in this paper also increases the amplitude of the diurnal cycle in the AGCM and reduces the excessive seasonality in PBL cloud incidence, resulting in an improved simulation of convective precipitation over regions where the solid regime was spuriously dominating.

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David Randall
,
Marat Khairoutdinov
,
Akio Arakawa
, and
Wojciech Grabowski

A key factor limiting the reliability of simulations of anthropogenic climate change is the inability to accurately represent the various effects of clouds on climate. Despite the best efforts of the community, the problem has resisted solution for several decades. The reasons for this are briefly reviewed and it is argued that it will be many more decades before the problem can be solved through the approaches to cloud parameterization that have been used up to now. An alternative approach, called superparameterization, is then outlined, in which high-resolution cloud system-resolving models (CSRMs) are used in place of the conventional cloud parameterizations. Tests performed with the Community Atmosphere Model show that superparameterizations can give more realistic simulations of the current climate, including greatly improved simulations of the Madden–Julian oscillation and other tropical wave disturbances. Superparameterizations increase the cost of climate simulation by a factor of several hundred dollars, but can make efficient use of massively parallel computers. In addition, superparameterizations make it possible for a climate model to converge to a global CSRM as the horizontal grid spacing of the climate model decreases to a few kilometers. No existing global atmospheric model has this convergence property. Superparameterizations have the potential to greatly increase the reliability of climate change simulations.

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Young-Joon Kim
,
Sajal K. Kar
, and
Akio Arakawa

Abstract

A sponge layer is formulated to prevent spurious reflection of vertically propagating quasi-stationary gravity waves at the upper boundary of a two-dimensional numerical anelastic nonhydrostatic model. The sponge layer includes damping of both Newtonian-cooling type and Rayleigh-friction type, whose coefficients are determined in such a way that the reflectivity of wave energy at the bottom of the layer is zero. Unlike the formulations in earlier studies, our formulation includes the effects of vertical discretization, vertical mean density variation, and nonhydrostaticity. This sponge formulation is found effective in suppressing false downward reflection of waves for various types of quasi-stationary forcing.

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Akio Arakawa
,
Joon-Hee Jung
, and
Chien-Ming Wu

Abstract

One of the most important contributions of Michio Yanai to tropical meteorology is the introduction of the concepts of apparent heat source Q 1 and apparent moisture sink Q 2 in the large-scale heat and moisture budgets of the atmosphere. Through the inclusion of unresolved eddy effects, the vertical profiles of apparent sources (and sinks) are generally quite different from those of true sources taking place locally. In low-resolution models, such as the conventional general circulation models (GCMs), cumulus parameterization is supposed to determine the apparent sources for each grid cell from the explicitly predicted grid-scale processes. Because of the recent advancement of computer technology, however, increasingly higher horizontal resolutions are being used even for studying the global climate, and, therefore, the concept of apparent sources must be expanded rather drastically. Specifically, the simulated apparent sources should approach and eventually converge to the true sources as the horizontal resolution is refined. For this transition to take place, the conventional cumulus parameterization must be either generalized so that it is applicable to any horizontal resolutions or replaced with the mean effects of cloud-scale processes explicitly simulated by a cloud-resolving model (CRM). These two approaches are called ROUTE I and ROUTE II for unifying low- and high-resolution models, respectively. This chapter discusses the conceptual and technical problems in exploring these routes and reviews the authors’ recent work on these subjects.

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Stephen J. Lord
,
Winston C. Chao
, and
Akio Arakawa

Abstract

An application of the Arakawa-Schubert (1974) cumulus parameterization to a prognostic model of the large-scale atmospheric circulations is presented. The cloud subensemble thermodynamical properties are determined from the conservation of mass, moist static energy and total water (vapor, suspended liquid water and precipitation). Algorithms for calculating the large-scale forcing and the mass flux kernel are presented. Several methods for solving the discrete version of the integral equation for the cumulus mass flux are discussed. Equations describing the cumulus feedback on the large-scale thermodynamical fields are presented.

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