## Shallow Convection

TURBULENCE LARGE INERTIAL VISCOUS 104 km 103km 102km 10km 1km 102m 10m lm 1dm 1cm 1mm t Figure 2 Chart showing the spectrum of atmospheric phenomena. The arrow shows a scale representing typical distances between weather stations and a typical resolution of the early and present GCMs. B. The Epoch-Making First Phase (1950 -I960) The epoch-making first phase of numerical modeling of the atmosphere (see Fig. 1) began with the successful 24-hr numerical weather prediction of 500-mb geopotential...

## Randall Z Grid And Cgridlike Be Grid Gravity Wave Schemes

Excellent geostrophic adjustment properties of the unstaggered grid for the vorticity and divergence as prognostic variables (Z Grid) were pointed out by Randall (1994). Progress in using the vorticity divergence formulation on a hexagonal grid, subsequent to Heikes and Randall (1995a,b), are reported elsewhere in this volume. Still another option is to try to benefit from both the simplicity and straightforwardness of the u, v formulation and from the excellent properties of the streamfunction...

## Chapter

Solving Problems with GCMs General Circulation Models and Their Role in the Climate Modeling Hierarchy Michael Ghil and Andrew W. Robertson Department of Atmospheric Sciences & Institute of Geophysics and Planetary Physics University of California at Los Angeles, Los Angeles, California Hierarchy II. Intraseasonal Oscillations Their Theory and Simulation III. El Ni o -Southern Oscillation, from the Devil's Staircase to Prediction IV. Interdecadal Oscillations in the Oceans' Thermohaline...

## Acknowledgments

Suarez for helpful advice. I also thank Dr. S. Lord for encouragement, Mr. K. Campana for helpful review, and all those members of the global and climate modeling branches of EMC who contributed to the development and parallel testing of the new climate model, especially Drs. S. Saha, J. Schemm, and A. Kumar. Arakawa, A., and W. H. Schubert (1974). Interaction cumulus cloud ensemble with the large-scale environment. Part I. J. Atmos. Sci. 31, 671-701. Bony, S., Y. Sud, K. M. Lau,...

## E E W W

Figure 6 Same as in Fig. 4, but for January mean outgoing long-wave radiation in W m2. The contour interval is 20 W m2. Figure 7 Same as in Fig. 4, but for January mean surface evaporation rate in mm day. The contour interval is 2 mm day. Figure 7 Same as in Fig. 4, but for January mean surface evaporation rate in mm day. The contour interval is 2 mm day. respectively, again for four values of Rk. Compared to observed estimates (not shown), in general, all fields look better for nonzero values...

## Sensitivity Experiments With The Climate Model

One general problem that is common to many atmospheric models is their inability to hold enough moisture in the model atmosphere. For example, some time ago in the operational model at NCEP, the assimilation of special sensor microwave imager (SSM I) derived precipitable water was discontinued because the MRF model could not retain the initial moisture, resulting in large spindown of precipitation in the tropics. Dry bias in the tropical atmosphere over warm oceans is very common in current...

## Sensitivity In Semiprognostic Test

Before examining the sensitivity of the climate model to parameters in RAS, we will first examine their impact in a semi-prognostic context. The original version of RAS underwent both semi-prognostic tests as well as single-column prognostic tests in MS. Their results did show that although the obtained cumulus heating profile was reasonable, the cumulus drying was excessive compared to the observed estimate. This result was consistent with the result of Lord (1978) for the standard...

## Modification Of Relaxed Arakawaschubert

Reevaporation of the Falling Convective Precipitation In the implementation of the Sud and Molod (1988) scheme into RAS, the reevaporation of rain from each cloud type occurs just after that cloud type has relaxed the environmental sounding toward quasi-equilibrium, but before invoking the next cloud type. In this way, the subsequent cloud type feels the effect of rain reevaporation from the previous cloud type. This differs from the approach of Sud and Molod (1988), in which reevaporation...

## Introduction

Cumulus convection is a major component of the atmospheric hydro-logic cycle. Accurate prediction of both heating as well as moisture change in the atmosphere due to cumulus convection is crucial to the success of numerical weather prediction, as well as climate and global change studies. The most elegant and complete theory of interaction between cumulus ensembles and the large-scale environment is presented in the pioneering General Circulation Model Development Copyright 2000 by Academic...

## Summary

Until quite recently, quasi-equilibrium has been thought of primarily as a closure for convective parameterizations its effect on the way we think about convection has been relatively slow to come about. In this paper I have reviewed and in some small ways extended Emanuel et al.'s (1994) exploration of the full implications of quasi-equilibrium. The main structure of quasi-equilibrium thinking emphasizes the following points Latent heating is a concept that applies to the dynamics of...

## Info

Buoyancy (K) of air lifted reversibly from 1000 mb Figure 7 Departure of the ambient temperature from a reference moist adiabat for each of the experiments illustrated in Fig. 6. A positive value means that the reference adiabat is warmer than the atmosphere. Buoyancy (K) of air lifted reversibly from 1000 mb Figure 7 Departure of the ambient temperature from a reference moist adiabat for each of the experiments illustrated in Fig. 6. A positive value means that the reference adiabat is warmer...

## Nonequilibrium Thinking

Most students of meteorology are conditioned to think of convection in nonequilibrium terms, being first introduced to the concept of conditional instability through the illustration of highly metastable soundings from places like Oklahoma. Instability accumulates under some lid and is released suddenly when convective temperature is attained or when some mesoscale process locally removes the potential barrier to convection. This may very well be an appropriate mode of thinking about the type...

## The Physics Of Convective Quasiequilibrium

Part of the difficulty some have in accepting the quasi-equilibrium postulate may have to do with problems visualizing how it may work in nature. In the case of dry boundary layer convection, it is relatively easy to understand the process. Suppose, for example, that the rate of radiative cooling is increased in some individual atmospheric layer above the surface. At first, this layer may be expected to cool. But as soon as it does so, it is more unstable with respect to the air just below it,...

## Is Latent Heating A Useful Concept

We are all taught that the condensation of water vapor releases a comparatively large quantity of heat to the air in which the condensate is suspended, and we are used to thinking of this just like any other heat source, like radiation, for example. The problem with this way of thinking is that it fails to recognize and take advantage of the fact that virtually all condensation in the atmosphere is very nearly reversible, and so may be usefully incorporated into the definition of the entropy of...

## Epilogue

It is not the objective of this chapter to discuss many developments in cumulus parameterization since the advent of the Arakawa and Schubert formulation. The interested reader on this topic is referred to the monograph of Emanuel and Raymond (1993), which provides excellent discussions on many aspects of cumulus parameterization schemes available today. Another useful source of information on the topic of cumulus parameterization is a recent book edited by Smith (1997b), which is a collection...

## References

Nongeostrophic effects in the baroclinic prognostic equations. Proceedings of the International Symposium on Numerical Weather Prediction, Tokyo, 1960, Meteorological Society of Japan, 161-175. Arakawa, A. (1966). Computational design for long-term numerical integration of the equations of fluid motion Two-dimensional incompressible flow. Part I. J. Comput. Phys. 1, 119-143. Arakawa, A. (1968). Parameterization of cumulus convection Proceedings of the WMD IUGG Symposium on...

## Conclusions

In the 1950s quasi-geostrophic models were used for both numerical weather prediction and general circulation modeling. Nowadays, NWP centers and GCM groups use global models based on the quasi-static primitive equations with the traditional approximation (i.e., the models use the hydrostatic equation and take advantage of the shallowness of the atmosphere to approximate the metric factors appearing in the gradient, divergence, and curl operators in spherical coordinates, a procedure that...

## Generalization To The Spectral Form Of Cumulus Parameterization Theory

Just after Arakawa wrote his 1968 paper, an effort was begun to generalize the UCLA GCM to many more layers. About this time there occurred another event with very important long-term consequences Michio Yanai left Tokyo University and accepted a faculty position at UCLA. Michio arrived with a knowledge that systematic differences in the vertical profiles of apparent heat source Qx and apparent moisture sink Q2 held important information about cumulus activity. Using certain parts of...

## Dt dt dt

A statement that the predictability of CAPE has been lost. Equation (26) is analogous to Eq. (15) in the sense that the rapid cloud ensemble adjustment process constrains the tendencies describing the time evolution of the temperature and moisture fields on the slower time scales, just as the rapid geostrophic adjustment process constrains the tendencies describing the time evolution of the balanced wind and mass fields on slower time scales. Of course, there are important conceptual...

## S Sl i rito r TPScEMS V

Which shows how the ensemble mass flux C is controlled by large-scale horizontal and vertical advective processes, surface fluxes, and radiation which would also appear in the numerator of Eq. (25) if we had included it in Eqs. (16) (18) . To summarize, with hc determined by Eq. (22), 17 by Eq. (23), and C by Eq. (25), all the terms on the right-hand sides of Eqs. (16)-(21) are known, so that the cumulus parameterization theory for type II convection is closed. As we have just seen, if the C...

## A p

Where q is the saturation mixing ratio at the pressure and temperature of the underlying surface. In Eqs. (16) (21) the large-scale horizontal and vertical advection terms are on the left-hand side, while the surface flux and cumulus terms are on the right-hand side. The first term on the right-hand side of Eq. (16) and the first term on the right-hand side of Eq. (19) are due to the detrainment of cloud air,3 while the remaining terms proportional to tjC and C are due to cumulus-induced...

## Pi

Where radiative processes have been neglected and where vt, v3, vB are the large-scale horizontal velocities at the three model levels, u> 2 and oj4 are the large-scale vertical p velocities at the layer interfaces, ps the surface air density, CE the bulk aerodynamic coefficient for surface heat and moisture exchange, vs the surface wind speed, hc is the moist static energy of the air inside the clouds in the upper layer, ss the dry static energy of the surface, and yl is defined as y (L...

## Arakawas Cumulus Parameterization Laying The Conceptual Foundation For Future Work

In his 1968 paper (Proceedings of the WMO IUGG Symposium on Numerical Weather Prediction, Tokyo) Arakawa considered a cumulus cloud ensemble that is in a statistically steady state.2 He assumed that the thermodynamical features of the individual clouds within the ensemble are alike. In other words, he did not consider subensembles with different entrainment rates and different depths. At a particular longitude and latitude in the UCLA three-level GCM, one of three types of convection could...

## Av

Note that both u and du dt vanish at t 0, as required by our initial condition. The first two terms on the right-hand side of Eq. (7) constitute a particular solution for Eq. (6), while the last two terms are the homogeneous solutions. The homogeneous solutions e 'vt and elvt represent freely propagating inertia-gravity waves. If one wishes to plot the solution in physical space, Eq. (7) can be substituted into Eq. (5b) and the integral over k evaluated numerically. The...

## Results Of Geos Simulation Experiments

As mentioned in the previous section, a history file was generated by carrying out the numerical integration of the GEOS GCM for 90 days. This file is treated throughout the remainder of the study as an exact measurement notwithstanding all of the limitations of the model. At day 30, a random perturbation or error of 1 K is introduced in the temperature fields at all grid points and all levels, and the flow is then recalculated from this initial state for 60 days. The resulting atmospheric...

## Description Of Experiments

In this retrospective study, we conduct a simulation experiment that is as nearly as possible identical to the original experiment of Charney et al. (1969), except that we employ the Goddard Earth Observing System (GEOS) GCM (Takacs et al., 1994) in place of the Mintz-Arakawa GCM (Langlois and Kwok, 1969). The satellite system configuration that the original Charney et al. (1969) experiments were designed to simulate consisted of one polar orbiting NIMBUS 3 satellite carrying infrared and...

## Cautionary Conclusion

Nostalgia can cloud perceptions, yet it is clear that the scientific approach of Arakawa and Charney, toward building of models and their application to climate problems, is a paragon for researchers. The essence of that approach is a focus on the relevant climate physics and design of models to represent that physics. A close corollary is use of the models to define needed observations, with continual iterations between data and models. Technological advances in computing capabilities are...

## Global Warming Debate

It has been 20 years since the global warming discussions of Charney and Arakawa in 1979. Is our understanding of this topic improving The picture drawn by the media is one of opposing camps in perpetual fundamental disagreement. Opposing interpretations of the science seem likely to persist, because of the perceived economic stakes associated with energy policies. The public debate is not as scientific as we would prefer. It can be difficult to find references for public statements or...

## Missing Atmospheric Absorption

A prominent issue concerning climate models in the 1990s has been missing atmospheric absorption. Surface, satellite, and in situ observations have been used to surmise that most climate models underestimate solar radiation absorbed in the atmosphere by 20-40 W m2 and overesti mate solar radiation absorbed at the planetary surface by a similar amount. Such errors could affect the simulated atmospheric circulation and the drive for oceanic temperatures and motions. Comprehensive review of this...

## Transient Climate Climate Predictions

Climate Response Time Simple Ocean Models The Charney report discussed only briefly the issue of how long it takes the climate system to more or less fully respond to a climate forcing. Charney realized that it was necessary to account for the ocean heat capacity beneath the mixed layer, and I recall him suggesting that the response time to increased COz could be a few decades, on the basis of overturning times for near surface ocean layers in the tropics and subtrop-ics. What was not...

## Reaction To The Experiment

Fortunately, some of the discussion that followed Phillips's oral presentation of his work has been preserved. Excerpts from these discussions are presented, and they are followed by vignettes that feature retrospective viewpoints from several prominent scientists who worked on the general circulation problem in the 1950s. As the recipient of the first Napier Shaw Prize in 1956, Phillips was invited to deliver a seminar on his paper to the Royal Meteorological Society. The state of affairs in...

## Momentum Budget

---_ , 5T -57(u,v )+'ov,+Av - Figure 7 Latitudinal distribution of the various terms in the momentum budget equations at the upper and lower levels. The equations were averaged over the 11-day period, days 10-20 inclusive. Parameterized coefficients of lateral diffusion and friction are denoted by Av and k, respectively. The diffusion terms at both levels were negligibly small and have not been plotted. (From Phillips, 1956. With permission.) Figure 7 Latitudinal distribution of the various...

## Iiiiiil

24 20 32 i-16 Schematic of Wind Regimes i1 Figure 6 Latitudinal distribution of the mean meridional and zonal winds over the 31-day period of simulation. (From Phillips, 1956. With permission.) Because the zonal-mean meridional flow at 750 mb is equal and opposite to that at 250 mb, a three-cell pattern can be inferred. Because of the similarity between this three-cell structure and that postulated from earlier studies, the labels Ferrel and Hadley have been added. Phillips, however, did not...

## The Experiment

Norman Phillips had been exposed to much of the controversy on general circulation theory while a graduate student at the University of Chicago in the late 1940s and early 1950s. During this same period, Phillips's interest in dynamic meteorology was awakened through a careful reading of Charney's paper on the scale of atmospheric motions (Charney, 1948). He became convinced that simple baroclinic models (in particular, models that stratified the troposphere into two or three layers) could...

## Why Contribute to the Archive

The purpose of the project is to see if the interactive capability of the World Wide Web can be used not only to present information, but also to collect it. We are especially interested in information that might not otherwise be preserved or that researchers would not easily be able to find. We would like to gather information that would not be part of any official record while it is still relatively fresh in participants' memories. We seek physical material related to the development of GCMs,...

## Appendix

A family tree that describes important relations among the major modeling groups is shown in Fig. 1. While the GCM Family Tree captures only the most direct relationships among GCM groups, it can serve a useful heuristic purpose in tracing the main lines of institutional affiliation. The GCM Family Tree is part of an evolving WWW-based project in participatory history. We hope to collect archival materials including documents, informal memoirs, and any other information related to the history...

## Conclusion

By the 1980s, computer models of atmosphere and ocean general circulation had become the primary tool in studies of climate. This marked a major historical transformation from a previous era, in which virtually the only tool for climate studies was the statistical record. Perhaps the most important aspect of this shift was the ability to perform model-based experiments to project possible causes of climatic change. This led to the remarkable visibility of GCMs in political debates over...

## Spectral Transform Techniques

Spectral methods are an alternative to finite-difference schemes, the method used by all of the first-generation primitive equation GCMs. They express the horizontal variation of dynamic model fields in terms of orthogonal spherical harmonics. The technique simplifies the solution of many of the nonlinear partial differential equations used in general circulation modeling. Its utility had been explored as early as 1954 (Platz-man, 1960 Silberman, 1954). Heavy calculational demands made spectral...

## Coupled Atmosphere Ocean Models

GFDL was among the first groups to attempt coupling of an atmospheric GCM to an ocean model. Initially, highly simplified ocean models (one-layer swamp oceans) were used. These were succeeded by two-level mixed-layer ocean models. In 1969, Manabe and Bryan published the first results from a coupled ocean-atmosphere general circulation model (OAGCM). However, this model used a highly idealized continent-ocean configuration. Results from the first coupled OAGCM with more realistic configurations...

## Modeling Groups Proliferate

Among the important GCM groups established in 1965-1975 were these RAND Corporation (Santa Monica, California) Goddard Institute for Space Studies (New York, New York) Australian Numerical Meteorological Research Centre (Melbourne, Australia later this became the Bureau of Meteorology Research Centre) Each group initially borrowed an existing model, but subsequently made significant modifications of its own. Two important innovations of the 1965-1975 decade were coupled atmosphere-ocean models...

## Spread Of Gcms

By 1965, then, three groups in the United States had established ongoing efforts in general circulation modeling Geophysical Fluid Dynamics Laboratory UCLA Department of Meteorology National Center for Atmospheric Research In addition, a small group at the UK Meteorological Office had begun work on a GCM, under Andrew Gilchrist, but published very little until the 1970s. At this point, GCMs and modeling techniques began to spread by a variety of means. Commonly, new modeling groups began with...

## The National Center For Atmospheric Research

The National Center for Atmospheric Research, established in 1960, began a GCM effort in 1964 under Akira Kasahara and Warren Washington. Two different model series were eventually constructed, designated here as NCAR 1-3 and CCM 0-1. A. The Kasahara-Washington Models (NCAR 1-3) The first-generation NCAR GCM was developed starting in 1964, with first publication in 1967. It was a simple two-layer global model with a 5 horizontal resolution. The second-generation model, completed around 1970,...

## The Livermore Atmospheric Model

Chuck Leith began work on a GCM at Lawrence Livermore National Laboratories (LLNL). Trained as a physicist, Leith became interested in atmospheric dynamics and received the blessing of LLNL director Edward Teller for a project on the general circulation. Teller's approval stemmed from his long-term interest in weather modification. After receiving encouragement from Jule Charney, Leith spent a summer in Stockholm at the Swedish Institute of Meteorology. There he coded a...

## Ucla Iv

Work on the fourth-generation UCLA model began in the late 1970s. The chief innovation of this model generation was a new vertical coordinate system, which used the top of the planetary boundary layer as a coordinate surface. A version of this model remains in use at UCLA into the present, although a fifth-generation model was built in 1990. UCLA IV was also adopted by the Navy research centers mentioned earlier. In addition, it was taken to the Goddard Laboratory for Atmospheres in the early...

## Ucla Ii level

The second-generation UCLA model essentially extended the vertical resolution of the second-generation model to three levels. This model was carried to three NASA laboratories. In 1972, a nine-level version was begun at the Goddard Institute for Space Studies (GISS) in New York, whose current model is a direct descendant. Later in the 1970s it traveled to the Goddard Laboratory for Atmospheric Sciences and the Goddard Laboratory for Atmospheres (A. Del Genio, 1998, personal communication).

## The Ucla Department Of Meteorology

Jacob Bjerknes, who founded the UCLA Department of Meteorology in 1940, had a strong interest in the problem of the atmospheric general circulation. This tradition continued with Yale Mintz, a graduate student of Bjerknes's who received his Ph.D. in 1949. He continued to work at UCLA, becoming associate project director with Bjerknes. In the late 1950s, Mintz began to design numerical general circulation experiments (Mintz, 1958). Like Smagorinsky, Mintz recruited a Japanese meteorologist, Akio...

## The Geophysical Fluid Dynamics Laboratory

The first laboratory to develop a continuing program in general circulation modeling opened in 1955. In that year, at von Neumann's instigation, the U.S. Weather Bureau created a General Circulation Research Section under the direction of Joseph Smagorinsky. Smagorinsky felt that his charge was to continue with the final step of the von Neumann Charney computer modeling program a three-dimensional, global, primitive equation GCM of the atmospheric (Smagorinsky, 1983). The General Circulation...

## Establishment Of General Circulation Modeling

In the mid-1950s, the weather models used by forecasters were still regional or continental (versus hemispherical or global) in scale. Calculations for numerical weather prediction were limited to what could be accomplished in a couple of hours on then-primitive digital computers. In addition, the time constraints of analog-to-digital data conversion and long-distance communication imposed limitations on the scale of operational weather forecasting. Yet for theoretical meteorologists...

## Before Numerical Weather Prediction And The Prehistory Of Gcms

In the early 20th century, the Norwegian Vilhelm Bjerknes argued that atmospheric physics had advanced sufficiently to allow weather to be forecast using calculations. He developed a set of seven equations whose solution would, in principle, predict large-scale atmospheric motions. Bjerknes proposed a graphical calculus, based on weather maps, for solving the equations. Although his methods continued to be used and developed until the 1950s, both the lack of faster calculating methods and the...

## Paul N Edwards

Program in Science, Technology & Society, Stanford University, Stanford, California II. Before 1955 Numerical Weather Prediction and the Prehistory of GCMs III. 1955-1965 Establishment of General Circulation Modeling IV. The Geophysical Fluid Dynamics Laboratory V. The UCLA Department of Meteorology VII. The National Center for Atmospheric Research VIII. 1965-1975 Spread of GCMs IX. 1975-1985 GCMs Mature X. Conclusion Appendix References

## Appendix B

A Fourth-Order Horizontal Difference Scheme for the Thermodynamic Equation Consider a square grid in orthogonal coordinates, f and 17. In Fig. B.l, the circles show the scalar points such as the 6 points. We define the difference and average operators as in Eqs. (A.l) and (A.2). In addition, as in Eq. (A.8) and (A.9), we define the mass fluxes U* 77'-A , U* TTi AV, (B.l) where 7t is the pseudo-density of the vertical coordinate, m and n are the map factors for the and 17 directions,...

## MW Ui Aj

1 2 flA< > , j 1, , + 1, (S*)i 2 0, (Sx)j+i 2 (< 5x ) .+ 1 2, j 1, , - 1, (5> 0i (5> 0I 2, (8j0y 2, , - 1, (A2)i (5j)i 2(Sx)i, (A2) (S> 0, ( )., 2, ,7-l, (A2) (8y)J+l 2(8x)j. The discrete continuity equation used is where the mass fluxes are defined by f+i 2 j (h')i+1 2jui+1 2j(sy)j, j 1, , (A.8) v*j+i 2 (h1)itj+1 2vij+1 2(Sx)i+i 2, j 0, ,J. (A.9) The zonal and meridional components of the first term on the right-hand side of Eq. (19) are discretized as (Sx)j 1 2,7 *+ 1, j+ 1 2 + 1...

## Closing Remarks

So far, I haven't said much about the currently developing Generation V UCLA GCM. This is because the focus of this article is on the early years of general circulation modeling at UCLA. Here I simply list some of the recent or ongoing revisions for the Generation V change of the radiation scheme following Harshvardan et al. (1987, 1989), inclusion of an orographic gravity wave drag parameterization following Kim and Arakawa (1995), inclusion of convective downdraft effects in the cumulus...

## Formulation Of Moist Processes In The Ucla

Formulation of Moist Processes in the Generation I GCM As mentioned earlier, the formulation of convective processes in the Generation I UCLA GCM (Mintz, 1965) was based on moist-convective adjustment assuming that a sufficient amount of water vapor is available for condensation whenever conditional instability exists. Besides boundary layer convection described in Section IX.A, the two-level GCM includes internal convection, through which temperatures at the upper and lower levels of the...

## Formulation Of Pbl Processes In The Ucla

Formulation of PBL Processes in the Generation I GCM The formulation of convective processes in the Generation I UCLA GCM (Mintz, 1965) was based on moist-convective adjustment assuming that a sufficient amount of water vapor was available for condensation whenever conditional instability existed. In this sense, the model is fully moist rather than dry, although no grid-scale condensation was included. The idea of moist-convective adjustment was partially used even in determining the surface...

## Horizontal Differencing In The Ucla

Horizontal Differencing in the Generation I GCM As mentioned earlier, the first task in horizontal discretization for constructing the Generation I GCM was to derive a finite-difference scheme for momentum advection that is equivalent to the use of the Arakawa Jacobian for vorticity advection when the motion is nondivergent. This approach was followed almost throughout the entire history of the UCLA GCM, with the exception of Generation II. The first step in this task was to decide the way...

## The March Of The Seasons And Reversible Isentropic Processes

In Johnson's (1989) concept of an energy phase space for reversible isentropic processes, the increase of the reversible component of total energy was expressed by A a G(E) - G(EJ - D(AEa), (116) where the generation of the reversible component of total energy G(AEa) is the difference of the generation of the total energy in the actual atmosphere G(E) minus the generation in the equilibrium atmosphere G(Ea). In this energy phase space, net heating G(E) > 0 expands the admissible region of...

## The Expected Magnitudes Of

There is every reason to expect local errors in heat addition A Qm both directly from the difficulties encountered in physical parameterization, and indirectly from numerical diffusion in simulating the long-range transport of energy and water substances. Indirect errors also stem from strong dependence of latent heat of phase changes and radiative flux on temperature and thus AT at the same time. However, Johnson (1997) noted that if the boundary conditions of energy flux are satisfied, then...

## Energy Balance And Aphysical Sources Of Entropy

Now the added component of model generation due to aphysical sources of entropy will be determined for both (g(E)) and (g(AEa)) in order to contrast differences that emerge. The substitution of Eq. (69) into Eq. (45) yields (g(E)) (Qm) + < sj> . (88) With use of Eq. (73), followed by expansion into products of means and deviations, Eq. (88) becomes (g(E)) (Qm) + < AQm> + < ia> < r> + < i*r*> . (89) With the added component of the generation Ag(E) as the difference between...

## The Entropy Balance

0 ((sAT - AQJ T) < i - (AQm AT) (AT T)). With AT finite, Eq. (80) requires the ratio of the error of heat addition A m to the error in temperature AT to equal the true entropy source s everywhere. Since s is the true Lagrangian source, there is no means for AQm to induce an immediate response in temperature AT for a Lagrangian parcel. Furthermore, partitioning Eq. (80) into the products of mean and eddy components expressed by ((AQm AT))((AT T)) < s - (A m Ar) *(A7yT)*> (81) reveals an...

## Sources Of Entropy In The Modeled Climate State

The development heretofore has provided a perspective of the role of entropy and its sources in maintaining the atmosphere's circulation against dissipative processes, and related classical perspectives to the Lorenz energy cycle. In his previous study of the modeled climate state, Johnson (1997) determined from entropy balance that aphysical sources of entropy in the presence of the constrained equilibrium state with ( s) equal to zero requires the climate state to be cold. This requirement...

## The Classical Concept Of Efficiency In Relation To And giAEj

Within the set of equations utilized to illustrate the relation between the classical concept of the Carnot cycle and driftless climate state, the requirement for systematic differences in mean value temperatures in conjunction with the entropy sources led to the concept of a global efficiency as expressed by Eq. (23). Under the conditions just derived for (g(E)) and (g(AE)), a definition of an efficiency corresponding with the Carnot cycle is now derived which, however, is a function of...

## The Climate State And The Reversible Component Of Total Energy

In developing the concepts of global monsoonal circulations, Johnson (1989) derived the following expression for the reversible component of total energy where the total energy (E), the total energy of a constrained equilibrium state (Ea) with equilibrium temperature Ta(6, t), the kinetic energy (K) of the atmosphere, and the available potential energy (A) of the atmosphere are respectively expressed as integrals in isentropic coordinates by The definition of the total energy of the constrained...

## Q Q

The energy dissipation expressed as a function of heat removed is given by The first efficiency e+ just defined corresponds with the classical definition for a Carnot heat engine defined as the ratio for the work output Q++ Q to the heat input Q+. A negative value of the reciprocal s corresponds with the coefficient of performance for a Carnot refrigerator defined as the negative ratio of Q to Q++ Q (Sommerfeld, 1964). From the mean value theorem applied to Eq. (15), the relation of the heat...

## Global Thermodynamics And Monsoonal Circulations

In setting forth basic concepts concerning the global thermodynamics of atmosphere motion, Dutton (1973) emphasizes the predictive aspect of entropy stemming from the second law. Subject to the constraint of isolation in the sense that the flux of energy through the bounding surfaces of the atmosphere vanishes, he equated the total energy of the actual atmosphere to a corresponding total energy of a hydrostatic reference atmosphere E0 with maximum entropy. He then noted that the reference state...

## Brightness Temperature

FEB 03 FEB 04 FEB 05 FEB 06 FEB 07 Date (1993) FEB 03 FEB 04 FEB 05 FEB 06 FEB 07 Date (1993) Figure 2 Model versus observation comparisons for significant precipitation conditions. izations are overestimating the cloudiness and or cloud optical thickness. Further analysis of the model results indicates that very large errors in cloud optical thickness would be necessary solely to explain the model discrepancies in albedo and surface short-wave. Thus, overestimation of the fractional cloud...

## Model Experiments

Long-Term Experiments in the TOGA-COARE Region As an example of the use of single-column models, we first present a series of seven long-term experiments from TOGA-COARE. The model configuration in each experiment differs only in the specification of the cumulus convection parameterization, the cloud prognostication scheme, and or the parameterization of cloud-radiative properties. The parameterizations used in each experiment are shown in Table I. In each experiment, the SCM was applied at...

## Parameterization Validation And Singlecolumn Diagnostic Models

The single-column model is numerically integrated in time as an initial value problem that is forced and constrained by observational data. The input is an observed initial state, plus observationally derived estimates of the time-dependent advection terms in the conservation equations, provided at all model layers. Its output is a complete heat and water budget, including temperature and moisture profiles, clouds and their radiative properties, diabatic heating terms, surface energy balance...

## Singlecolumn Modeling

Progress in attacking these questions depends on a multifaceted research strategy. It is now well recognized in the GCM and numerical weather prediction (NWP) communities that single-column models (SCMs) are tools that have a valuable role to play in testing and improving parameterizations by evaluating them empirically against field observations (e.g., see Randall et al., 1996). This chapter explores the potential of SCMs in attacking the central questions of cloud-radiation feedbacks in...

## Plumes Generated By Arctic Leads

The interactions between sea ice, open ocean, atmospheric radiation, and clouds over the Arctic Ocean exert a strong influence on global climate. Uncertainties in the formulation of interactive air-sea-ice processes in global climate models (GCMs) result in large differences between the Arctic and global climates simulated by different models. In particular, the effects of leads on the atmosphere and the surface heat budget of the Arctic Ocean must be more accurately represented in climate...

## Enhancement Of Surface Fluxes By Tropical Convection

Large-scale models typically diagnose the surface turbulent fluxes of sensible and latent heat over the ocean using the large-scale (i.e., area-averaged) near-surface temperature and water vapor mixing ratio and the speed of the large-scale wind vector. These fluxes may be called the vector-mean surface fluxes. Esbensen and McPhaden (1996) defined mesoscale enhancement as the difference between the vector-mean surface fluxes and the actual large-scale surface fluxes. In the absence of mesoscale...

## Stratocumulustotrade Cumulus Transition In The Subtropical Marine Boundary Layer

In the eastern and equatorward quadrants of the subtropical high-pressure zones, the low level air flow (or trajectory) is generally equatorward and westward, across a progressively warmer sea surface and into regions of decreased subsidence. As air flows equatorward over the subtropical oceans, the initially stratocumulus-topped boundary layer (STBL) evolves into a trade cumulus boundary layer (TCBL). This stratocumulus-to-cumulus transition (SCT) involves both a radical decrease in cloud...

## E

Figure 7 The liquid water mixing ratio field for the altocumulus cloud layer simulation at 2 hr. Figure 8 The vertical velocity field for the altocumulus cloud layer simulation at 2 hr. Figure 8 The vertical velocity field for the altocumulus cloud layer simulation at 2 hr. that the updrafts are associated with regions of large qc, and the down-drafts with regions of small qc. The evolution of the profiles of the horizontally averaged liquid water mixing ratio for the diurnal case is shown in...

## Thin Midlevel Stratiform Altocumulus Clouds

Altocumulus (Ac) and altostratus (As) clouds together cover approximately 22 of the Earth's surface (Warren et al., 1986, 1988). Thus, they may play an important role in the Earth's energy budget through their effects on solar and infrared (IR) radiation. However, Ac clouds have been little investigated by either modelers or observational programs. Heymsfield et al. (1991) examined two thin Ac clouds at about -30 C. They concluded that Ac clouds containing a convective structure are dynamically...

## Interactions Between Radiation And Convection In Tropical Cloud Clusters

The results of this study were published in 1995 by Fu et al. (hereafter, FKL95). The goal was to better understand the interactions of infrared (IR) radiation and convection in tropical squall cloud clusters on the time scales and space scales of an individual cloud system (about 500 km and 12 hr). The life cycle of a tropical squall line was simulated over a 12-hr period using thermodynamic and kinematic initial conditions as well as large-scale advective forcing typical of a GATE Phase III...

## What Is a CRM Good

CRMs have been extensively used for simulating convective cloud systems. How good are they for this purpose Similar to GCMs, spatial resolution and sub-grid-scale physics are issues. Unlike GCMs, dimensionality and lateral boundary conditions (i.e., large-scale forcing) are additional issues. Recently, concerted efforts have been made to evaluate CRM simulations of convective cloud systems observed during GATE and TOGACOARE (e.g., Grabowski et al., 1996 Xu and Randall, 1996 Wu et al, 1998...

## A LES Results

Figure 9 shows the temperature contours at the inversion and the flow velocity vectors from the LES. In the upper right corner, we also plot the grid mesh in the entrainment zone. Compared to the grid mesh, the Figure 9 A vertical cross section showing the temperature field (temperatures below 287.8 K are shown as white in the shaded table shown at the top) and flow velocity vectors from a smoke-cloud LES. Indicated at the upper right corner is the numerical grid size used in the entrainment...

## Current Effort In Further Understanding And Developing Parameterizations Of The Stbl

Our understanding of the STBL described in Section II is mostly qualitative to put our knowledge into parameterizations requires quantita- Figure 7 (a) The low-level cloud amount in plane view and (b) a vertical cross section of the cloud amount (shaded) and the eddy viscosity (contoured, in m2 s) from an NCAR CCM run where some fractional amount of low-level clouds is allowed to form for all levels under the inversion if the relative humidity is larger than 80 . Figure 8 Interactions between...

## Ab

Low Cloud Amount Run 01 Cloud Amount Run 02 Figure 6 The low-level cloud amount from (a) a 1-year standard NCAR CCM run compared to (b) a run where no frontal clouds are allowed to form under an inversion. Figure 6 The low-level cloud amount from (a) a 1-year standard NCAR CCM run compared to (b) a run where no frontal clouds are allowed to form under an inversion. To eliminate this unrealistic feature, we made the following simple improvement to the current cloud scheme. We allow for a...

## Existing Stbl Turbulence And Cloud Schemes In Gcms And Their Problems

Existing Marine Stratocumulus PBL Schemes Here we survey PBL and stratocumulus parameterizations used by 24 of the GCMs participating in the Atmospheric Model Intercomparison Project (AMIP). In all, more than 30 models participated in the project we survey only those that are well documented and those that either have a PBL model or have 3 or more points below 800 mb. Because the physical packages within most GCMs are continually evolving (although not as rapidly as one might imagine), our...

## Summary And Conclusions

RAS is a simple and more economical way of implementing the Arakawa-Schubert parameterization. In this paper we include a scheme for reevaporation of falling convective precipitation following the method of Sud and Molod (1988). Results from a semi-prognostic test using GATE phase III data show that RAS produces excessive drying and warming when the values of dry and moist static energies at the top of the boundary layer are assumed to be the same as those within the boundary layer. Figure 14...

## Opportunities For Development Of Mediumrange And Extendedrange Weather Forecasts

ECMWF's long-term goal is to deliver useful weather forecasts to 8 days and beyond. In addition the Centre will contribute to the realization of a useful seasonal forecast capability. The ensemble prediction approach will play a major role in attaining these goals, and its success will depend crucially on the quality of the assimilation system and the forecast model. Accurate and reliable medium-range weather forecasts for precipitation, wind, and temperature continue to be the Centre's most...

## Conclusions And Additional Considerations

Among the scientists engaged in modeling of atmospheric circulation, Professor Arakawa is foremost in emphasizing the appropriate conservation of atmospheric properties. He is also foremost in ensuring that the numerics employed satisfy appropriate constraints concerning mass, momentum, energy, entropy, enstrophy, and circulation. He has also emphasized comparisons of the dynamics of discrete systems with that of the continuous system and the need to maintain integral constraints of physical...

## Giss Global Climate Models

When I came to GISS as a postdoctoral candidate in the late 1960s my primary interest was in planetary atmospheres, especially the clouds of Venus, and I focused on radiative transfer theory as a tool to study the Venus clouds. But at about that time the director of GISS, Robert Jastrow, concluded that the days of generous NASA support for planetary studies were numbered, and he thus began to direct institutional resources toward Earth applications. The principal upshot was a concerted effort...

## Equilibrium Thinking

The underlying proposition in quasi-equilibrium thinking is that convection rapidly adjusts the temperature profile back toward a moist adiabat in a way that preserves the vertically integrated enthalpy. To a first order of approximation, convection keeps the atmospheric temperature profile on a moist adiabat tied to the subcloud layer entropy. This strongly constrains the vertical structure of the horizontal and vertical velocities as well as the temperature perturbations associated with...

## Climate System Dynamics

We need a strategy to investigate the dynamics of the climate system, because we lack sufficient data to describe the behavior of the climate Figure 6 Height-time cross section of the zonally averaged -component of simulated wind field over the equator. Units are m s ', and intervals are 6 units. Full lines are for positive values broken lines are for negative values. system. One way to overcome our lack of data is to recover hidden data and use paleo-data. However, note that the accuracy of...

## The Progress Achieved

As background for a look to follow into the gain in the time validity of the precipitation forecasts, Fig. 12a shows equitable threat scores for Eq. Threat t 24h fcst Valid 1 Jan 97-31 Dec 97 0.50 0.75 1.00 20672 11205 6554 THRESHOLD IN TOTAL OBS PTS ETA 80 KM GRID 0.50 0.75 1.00 20672 11205 6554 THRESHOLD IN TOTAL OBS PTS ETA 80 KM GRID Eq. Threat Valid 1 Jan 97 - 31 Dec 97 0.01 0.10 0.25 0.50 0.75 130902 76253 43216 20970 11370 THRESHOLD IN

## Entropy the Lorenz Energy Cycle and Climate

Space Science and Engineering Center and Department of Atmospheric and Oceanic Sciences University of Wisconsin and Division of Earth Sciences Universities Space Research Association Columbia, Maryland II. Global Thermodynamics and Monsoonal Circulations III. A Historical Perspective Concerning Entropy and Caratheodory's Statement of the Second Law IV. The Classical Concept of the Carnot Cycle and the Driftless Climate State V. The Climate State and the Reversible Component of Total Energy...

## The Classical Concept Of The Carnot Cycle And The Driftless Climate State

As a point of departure, the purpose in this section is to relate entropy, its balance, and energy dissipation within the driftless climate state to the classic Carnot cycle. Many texts discuss the Carnot cycle when introducing thermodynamics e.g. Sears, 1953 Godske et al., 1957 Carrington, 1994 in which heat is added and removed isothermally at two different temperatures with intermediate stages of adiabatic contraction and expansion. Goody 1995 notes the need to understand the entropy balance...

## Rh

Figure 15 A schematic illustration of the equilibrium, large-scale forcing and adjustment in an idealized T - RH B space, where T is the mean lapse rate, rd is the dry-adiabatic lapse rate, rm is the moist-adiabatic lapse rate, RH B is the relative humidity of the PBL, A 0 represents the marginal moist-convective instability defined in step 2 in the text, which is the destination of the adjustment. Step 1 and step 2 define the direction and rate of the adjustment, respectively, responding to...

## The New Ncep Climate Model

At NCEP, a climate model provides guidance to seasonal and long-term climate prediction. The current operational climate model is based on a substantially older version of the operational medium-range forecast MRF model. A new initiative is under way with collaborative efforts between the Environmental Modeling Center and the Climate Prediction Center to develop a new generation climate model starting from the latest version of the operational MRF model. The new climate model dynamics is...

## The Eta Model An Arakawa Approach Story

The so-called Eta model is a limited-area model with the numerical formulation designed following the Arakawa principles. It has been used so far primarily for weather forecasting, so one could question the appropriateness of covering it within the symposium carrying the general circulation model GCM development title. My reasons for finding this appropriate are twofold. The first is that nowadays limited-area models are increasingly used as integral parts of general circulation models for...

## Climate Sensitivity

In 1979 the president's science advisor requested the National Academy of Science to study the carbon dioxide and climate issue. This resulted in the famous Charney 1979 report from a group of climate researchers, including Akio Arakawa, who met at Woods Hole in the summer of 1979. Jule Charney, the panel chairman, decided to focus on a well-defined question If the amount of atmospheric COz were doubled, how much would the global average temperature increase by the time the system came to a new...

## Contributors

Numbers in parentheses indicate the pages on which the authors' contributions begin. Akio Arakawa 1, 539, and 721 , Department of Atmospheric Sciences, University of California, Los Angeles, California 90095 Chia Chou 457 , Department of Atmospheric Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095 Paul N. Edwards 67 , School of Information, University of Michigan, Ann Arbor, Michigan 48109 Kerry Emanuel 225 , Program in...

## Personal Perspective on the Early Years of General Circulation Modeling at UCLA

Early History of Numerical Modeling of the Atmosphere 2 B. The Epoch-Making First Phase 1950-1960 6 III. AA's Personal Pre-UCLA History 8 IV. The Arakawa Jacobian 13 V. Development of the Mintz-Arakawa Model 18 VI. Second Phase of Numerical Modeling of the Atmosphere and the Evolution of Different Generations of the UCLA GCM 21 A. The Magnificent Second Phase 1960-1990 21 B. Evolution of Different Generations of the UCLA GCM 22 VII. Vertical Differencing in the UCLA GCM 25 A. Background...

## Solving Problems with GCMs General Circulation Models and Their Role in the Climate Modeling Hierarchy

Robertson I. Introduction The Modeling Hierarchy 285 B. Ocean and Coupled Modeling 289 C. Dynamical Systems Theory 290 II. Intraseasonal Oscillations Their Theory A. Extratropical Oscillations Observations and Theory 292 B. GCM Simulations and Their Validation 296 III. El Nino-Southern Oscillation, from the Devil's Staircase to Prediction 299 A. ENSO's'Regularity and Irregularity 299 B. The Devil's Staircase across the Modeling Hierarchy 301 C. Regularity and...

## Development Of The Mintz Arakawa Model

After finishing the derivation of the Arakawa Jacobian in late 1961, I began to work on designing dynamics for the primitive equation model. Influenced by the successful work of Phillips 1956 , and for economic reasons, a two-level model excluding the stratosphere was an almost obvious choice. Yet developing a primitive equation model for a global domain with surface topography was an extremely challenging task in many ways. For the vertical coordinate, we chose the a coordinate proposed by...

## Hurricane Tracks

Still another indication of the benefits from emphasizing a large model domain of uniform resolution, and an Arakawa-style design, may be the Eta performance in forecasting tracks of major 1996 Atlantic hurricanes in comparison with that of models employing two competing concepts Mesinger, 1998b . Successful Eta performance in forecasting tracks of various hurricanes, tropical storms, or Pacific tropical cyclones was already noted early in the developmental work on the model e.g., Kerr, 1990,...

## Threedimensional Version Of The Model With An Isentropic Vertical Coordinate

Hsu and Arakawa 1990 hereafter HA discussed the many advantages of the isentropic vertical coordinate for numerical modeling of the large-scale circulation of the atmosphere. These advantages include the following Drastic reduction of the numerical difficulties associated with vertical advection Figure 5 The simulated January-mean boundary-layer wind streamlines and precipitation field obtained in a simulation using a geodesic grid and the a coordinate, with an embedded variable-depth boundary...

## SCEP and SMIC

With the rise of the environmental movement in the early 1970s came early interest in world-scale environmental problems. Two important stud ies, both prepared as input to the 1972 United Nations Conference on the Human Environment, noted the possibility of inadvertent climate modification. The Study of Critical Environmental Problems SCEP focused on pollution-induced changes in climate, ocean ecology, or in large terrestrial ecosystems. It cited GCMs as indispensable in the study of possible...