Future Development of General Circulation Models

Akio Arakawa

Department of Atmospheric Sciences University of California, Los Angeles, California

Akio Arakawa

Department of Atmospheric Sciences University of California, Los Angeles, California


Introduction: The Beginning


Parameterizations of PBL and

of the "Great Challenge"

Stratiform Cloud Processes and

Third Phase

Representation of the Effects of


Choice of Dynamics Equations

Surface Irregularity


Discretization Problems: Choice


Cumulus Parameterization

of Vertical Grid, Vertical Coor



dinate, and Horizontal Grid



Discretization Problems:

Advection Schemes


This chapter, which is a continuation of the first chapter of this book, is based on the lecture with the same title I presented at the end of the AA Fest: Symposium on General Circulation Model Development: Past, Present, and Future, held at UCLA, January 20-22, 1998. As in the first chapter, I present a personal perspective, this time on the future development of general circulation models (GCMs), and point out some modeling issues that should be considered more seriously than they have been in the past.

Numerical modeling of the atmosphere has gone through the second phase of its history (see Fig. 1 of Chapter 1), during which its scope was

General Circulation Model Development

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"magnificently" expanded. Numerical models including GCMs are now indispensable tools for studying and predicting a variety of atmospheric phenomena.

In spite of the expansion, however, the geographical distribution of sea surface temperature (SST) was prescribed as an external condition in most GCM applications during the second phase. From the point of view of climate simulations, this assumes the most important part of the answer and, therefore, it might have hidden crucial deficiencies that may exist in the model. For example, calculation of the surface heat flux does not have to be very accurate when SST is prescribed, as long as the heat flux adjusts the low-level air temperature toward the prescribed SST with a relatively short time scale. Calculation of the vertical distribution of radiative heating/cooling also does not have to be very accurate, at least for the tropical troposphere, as long as the cumulus parameterization adjusts the temperature lapse rate toward a realistic value. Thus, parameterizations of planetary boundary layer (PBL) and radiation/cloud processes did not appear to be very demanding problems in the second phase.

Even a successful simulation of tropical precipitation does not necessarily verify the cumulus parameterization used in the model. In the subtrop-ics, the radiative cooling approximately determines the amount of the adiabatic warming in the descending branch of the Hadley circulation (see Fig. 1). Then the amount of adiabatic cooling and, therefore, the amount of condensation heating in the ascending branch are more or less determined, while its position is strongly controlled by the prescribed SST distribution. Indeed, two GCMs with cumulus parameterizations constructed using completely different reasoning can produce equally realistic gross features of tropical precipitation.

Con den sat ion Heating i I t I


Con den sat ion Heating i I t I


Radiative Cooling t t Adiabatic Warming

Middle-Latitude Eddies

Radiative Cooling t t Adiabatic Warming

Middle-Latitude Eddies



Figure 1 A schematic figure showing the balance of warming/cooling in the Hadley circulation.



Figure 1 A schematic figure showing the balance of warming/cooling in the Hadley circulation.

When I was working with earlier generations of the UCLA GCM, I was amazed that the total precipitation in the equatorial region always came up within a reasonable range almost regardless of the way in which moist convection was treated. This was even true for the "precipitation" estimated from the convective heating simulated by the Generation I UCLA GCM (Mintz-Arakawa "dry" model), in which moisture was not predicted. (In the model, the radiative cooling in the subtropics was guaranteed to be realistic because it was based on an empirical formulation. See Section V of Chapter 1 in this volume.) A good simulation of the gross features of tropical precipitation, therefore, can tell us relatively little about the validity of the cumulus parameterization used for the simulation. (Simulation of the partition of precipitation between the continents and oceans is a different story.)

When the atmospheric GCM is coupled with an oceanic GCM, however, the situation can be entirely different. Any deficiencies in the model may now appear as errors in the simulated SST and can cause a serious climate drift of the coupled system.

In my opinion, the "great challenge" third phase of numerical modeling of the atmosphere has already begun (see Fig. 1 of Chapter 1). The opening of this phase is partly stimulated by the recent development of coupled atmosphere-ocean GCMs, as well as a clearer identification of important issues in climate change, such as the global warming and ENSO prediction problems. The opening is also characterized by the increased use of large-eddy simulation models (LESs) and cloud-resolving models (CRMs) to evaluate parameterizations in larger scale models.

In the past several years, improvements in the performance of coupled atmosphere-ocean GCMs have been remarkable. As of 1995, most coupled GCMs could successfully simulate the zonal gradient of the equatorial SST over the central Pacific (see Mechoso et al., 1995). Many models even simulate the annual cycle of the equatorial SST realistically. This is in a sharp contrast to the situation only 3 years earlier (see Neelin et al., 1992). We may then wonder if something revolutionary in our modeling capability might have happened during those 3 years simultaneously at different institutions. Of course, this is not likely to be the case. More likely, the improvement was a consequence of relatively minor changes, or "tuning," of the models, which might have been done even on different aspects of the models at different institutions.

Indeed, the mean SSTs simulated by coupled atmosphere-ocean models have been found to be extremely sensitive to those aspects that are relatively poorly formulated in the models, such as

• The vertical redistribution of moisture from the planetary boundary layer (PBL) to the free atmosphere due to entrainment/diffusion processes

• The amount of each cloud type (e.g., high, low, deep, shallow, liquid-water, ice, stratiform, cumuliform)

• The emissivity, reflectivity, and absorptivity of each cloud type

These sensitivities arise because surface fluxes are not determined by the processes near the surface alone. Instead, they are the consequences of complicated interactions between various processes in the atmosphere (and oceans). Let us consider surface evaporation as an example. To calculate surface evaporation E = (Fq)s over a wet surface, it is conventional to use a formula such as

where F denotes the turbulent flux, q is the specific humidify, the subscript S denotes the surface, p is the density, CE is the surface transfer coefficient for water vapor, v is the horizontal velocity, the subscript B denotes a representative value near the surface or for the entire PBL, and ql is the saturation value of q at the surface. [In Eq. (20) of Chapter 1, subscript g is used instead of S.] If the evaporated water vapor is locally stored within the PBL, qB increases through evaporation. Equation (1) then indicates that the surface evaporation is subject to a negative feedback, or an adjustment toward zero, due to the change of qB. We may then ask an important question: In nature (and in GCMs), what controls the amount of E against this eminent adjustment?

To answer this question, we first note that the value of is almost in a quasi-equilibrium beyond the time scale of adjustment, which should be on the order of a day. Then, for a longer time scale, the amount of E is approximately determined by the counteracting drying effects in the PBL, such as the dilution of moisture due to entrainment/diffusion processes through the PBL top and the horizontal advection of drier air within the PBL. Figure 2 illustrates this situation. These drying effects then "force"

Figure 2 A schematic figure showing the balance of moistening and drying effects on PBL humidity.

Advect ion surface layer

Figure 2 A schematic figure showing the balance of moistening and drying effects on PBL humidity.

the surface evaporation against the adjustment. From this point of view, Is ~ 4b in Eq. (1) is a consequence of E, rather than its cause.

Note that the quasi-equilibrium referred to here is for the PBL specific humidity, qB, which is an intensive quantity, not for the total amount of moisture in the PBL, which is an extensive quantity. This difference is important because, for example, the entrainment of mass adds moisture to the PBL (unless the entraining air is completely dry), increasing the total amount of moisture in the PBL, while the PBL specific humidity is decreased as the drier entrained air is mixed with the PBL air.

The argument given above for the surface evaporation is analogous to the quasi-equilibrium argument of Arakawa and Schubert (1974) for cumulus parameterization, in which a measure of conditional instability is assumed to be in a quasi-equilibrium beyond the moist-convective adjustment time scale. Then the intensity of cumulus activity is approximately determined by the destabilizing effects due to large-scale processes, which "force" the cumulus activity against the adjustment, not by the degree of existing instability. See Fig. 15 of Chapter 1 for an illustration of this situation.

Ma et aVs (1994) experiment with a coupled atmosphere-ocean GCM is a good demonstration of the sensitivity of the surface evaporation to various atmospheric processes. In this experiment, the emissivity of highlevel clouds was reduced by changing the radiation scheme. Then the mean SST simulated by the coupled GCM became colder. This may seem obvious since the reduced emissivity should give less greenhouse effect below. We have found, however, that the decrease in SSTs is not directly through a change in the radiation flux at the surface. Instead, as shown in Fig. 3, cumulus convection and surface evaporation play central roles in lower emissivity of high clouds weaker middle-tropospheric greenhouse warming stronger convective activity more drying more evaporation

Figure 3 Processes involved in the influence of a lower emissivity of high clouds on SST.

this decrease. See Chapter 18 in this book for more details of this experiment.

These results are of course model dependent. For example, if the cumulus parameterization used in the GCM does not directly recognize the upper level radiative cooling, or if it does not produce the low-level drying, the result can be totally different. Resolving these model dependencies is exactly among the objectives of the "great challenge" third phase.

Although simpler models will continue to be useful for many purposes, I anticipate two general trends in the development of advanced GCMs during the third phase: the expansion of internal processes and the increase of resolution. During the expansion of internal processes, more and more processes and their interactions are included in the model. The typical example is the inclusion of oceanic processes through coupling the atmospheric GCM with an oceanic GCM. Other examples are the inclusions of more detailed ground, cryosphere, biosphere, microphysical, and chemical processes. The expected benefit of this trend is, of course, a broader applicability of the GCMs. However, besides the obvious practical drawbacks from the increased complexity, this trend may tend to degrade the quality of simulated climatology as the newly added processes eliminate negative feedbacks in current models with prescribed external conditions. This has usually been the case when the atmospheric GCM is coupled with an oceanic GCM.

Due to the use of higher resolution, which is the other anticipated trend in the third phase, mesoscale processes, or even individual deep clouds, will be at least partly resolved by the model. Besides a decrease of truncation errors, the expected benefit of this trend is a reduced need for "sub-grid-scale" parameterizations. Again there can be the following concerns with this trend: Not all computational errors decrease as the resolution increases, and the nature of "sub-grid-scale" processes changes as the resolution changes while they still need to be parameterized. Correspondingly, we may have to "retune" or even reformulate the physics package as the resolution changes substantially.

In the following sections, I discuss selected aspects of future general circulation modeling with these general trends in mind. Section II discusses the problem of choosing dynamics equations, including the possibility of abandoning the primitive equations. Sections III and IV discuss discretization problems, with an emphasis on choosing the vertical grid, vertical coordinate, and horizontal grid in Section III, and on advection schemes in Section IV. Section V discusses the formulations of PBL and stratiform cloud processes and representation of the effects of surface irregularity. Section VI discusses future problems in formulating moist convection and cloud processes. Finally, Section VII gives closing remarks.

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