The dynamical range of global circulations—I
 Gareth P Williams
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The dynamical range of atmospheric circulations is examined by integrating a global circulation model (GCM) over a wide range of parameter values. We study the influence of rotation rate on moist and dry atmospheres with regular, dragfree, and interiorheated surfaces in Part I, and on axisymmetric, oblique, and diurnally heated moist atmospheres in Part II. Despite their variety, the circulations are composed of only a few elementary forms whose existence, scale, and mix alter as the parameters vary. These elements can be interpreted in terms of standard symmetricHadley (SH) and quasigeostrophic (QG) theories. The naturalHadley (NH) circulation consists of a polar jet and a hemispheric direct cell, such as occur in slowly rotating SH flows, together with Rossby waves generated by moist convection and barotropic cascades. The quasiHadley (QH) circulation consists of a tropical westerly jet and a narrow direct cell, such as occur in the lowlatitude part of rapidly rotating SH flow, together with Rossby waves generated by baroclinic instabilities in the neighboring midlatitude part of the SH flows; it occurs only in moist atmospheres. The two QG circulations represent the two extremes of eddy momentum flux produced during eddy cyclesthe special form of enstrophy acscade describing nonlinear baroclinically unstable wave growth and barotropic wave dispersion. The QG_{γ} element has a latitudinally asymmetric wave dispersion that gives a poleward, jettraversing momentum transport, while QG_{β} has a symmetric wave dispersion that gives a jetconverging momentum transport. Both elements have a westerly jet and three cells. (In Part II, we describe the solstitial symmetricHadley, the QGHadley, the diurnally modified NH, and the Halley circulations.) In moist atmospheres, NH circulations exist in the rotational low range \((\Omega ^* = 0  {\raise0.5ex\hbox{\(\scriptstyle 1\)}\kern0.1em/\kern0.15em\lower0.25ex\hbox{\(\scriptstyle 4\)}})\) ; overlapping QG_{γ} and QH elements in the midrange \((\Omega ^* = {\raise0.5ex\hbox{\(\scriptstyle 1\)}\kern0.1em/\kern0.15em\lower0.25ex\hbox{\(\scriptstyle 2\)}}  1)\) ; and QG_{γ}, QG_{β}, and QH elements in the high range (Ω^{✻}=2−8); here Ω^{✻}=Ω/Ω_{ E } is the rotation rate normalized by the terrestrial value. In dry atmospheres, circulations follow a similar progression but have a simpler blend because they lack a QH element. Kinetic energy peaks at \(\Omega ^* = {\raise0.5ex\hbox{\(\scriptstyle 1\)}\kern0.1em/\kern0.15em\lower0.25ex\hbox{\(\scriptstyle 8\)}}\) in the moist, Hadleydominated atmospheres but at \(\Omega ^* = {\raise0.5ex\hbox{\(\scriptstyle 1\)}\kern0.1em/\kern0.15em\lower0.25ex\hbox{\(\scriptstyle 2\)}}\) in the dry, QGdominated atmospheres. Instabilitygenerated Rossby waves propagate equatorward more easily in the westerlies of the diabatically driven (moist) Hadley cell than in the easterlies of the eddyinduced (dry) ditropic at Ω^{✻}=0 to almost radiativeconvective at Ω^{✻}=8, while maintaining almost constant global means. In modifiedsurface systems, freeslip conditions eliminate the QH element from a moist atmosphere and allow strong deep easterlies to arise in low latitudes to balance the strongly barotropic westerly jets that occur in midlatitudes. In a regular dry atmosphere, enhanced surface heating in low latitudes imitates latents latent heating and produces a tropical circulation resembling that of the moist QH element. Overall, circulation theory works well in explaining the GCM states but does not, as yet, describe the interactions among elements or reveal how jet scales are determined, nor explain phenomena at the extremes of the parameter range.
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 Title
 The dynamical range of global circulations—I
 Journal

Climate Dynamics
Volume 2, Issue 4 , pp 205260
 Cover Date
 19880601
 DOI
 10.1007/BF01371320
 Print ISSN
 09307575
 Online ISSN
 14320894
 Publisher
 SpringerVerlag
 Additional Links
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 Authors

 Gareth P Williams ^{(1)}
 Author Affiliations

 1. Geophysical Fluid Dynamics Laboratory/NOAA, Princeton University, 08542, Princeton, New Jersey, USA