a solution for the northern hemisphere climatic zonation during a glacial maximum

QUATERNARY RESEARCH 5, 307-320 (19%)

A Solution for the Northern Hemisphere Climatic Zonation

During a Glacial Maximum

BARRY SALTZMAN

Department of Geology and Geophysics, Yale University,

New Haven, Connecticut 06520

AND

ANANDU D. VERNEKAR

Institute for Fluid Dynamics and Applied Mathematics, University of Maryland,

College Park, Maryland 20742

Received January 29, 1975

The same model previously used to deduce an acceptable first order picture of the present zonally averaged macroclimate is now solved for the climatic response to the “glacial” surface boundary conditions that prevailed at 18,000 BP_ in the northern hemisphere. The equilibrium solution obtained gives the distributions with latitude of the mean temperature, wind, humidity, precipitation, evaporation, heat balance, transient baroclinic eddy statistics (i.e., kinetic energy of the meridional wind and meridional flux of heat, momentum, and water vapor), and the energy integrals. In general terms, the solution shows the glacial atmosphere to be colder and drier than at present, with an intensified polar front, stronger mean zonal and poloidal winds, more intense transient baroclinic eddies (storms) transporting heat, momentum and water vapor poleward at higher rates, and reduced precipitation and evaporation. Also evident is an equatorward shift of the climatic zones (as delineated by the mean surface zonal winds, the poloidal motion, and the difference between mean evaporation and precipitation), particularly in higher latitudes. Other properties of the solution, such as the effect of zonal wind changes on the length of the day, are discussed.

1. INTRODUCTION

Recently we applied a model governing the zonally averaged macroclimate to present surface boundary conditions over the globe showing that an acceptable first approximation to the observed climatic zonation could be deduced, including some of the main differences between the seasons and the hemispheres (Saltzman and Vemekar, 19’71, 1972). In view of these results we were en- couraged to examine the consequences of changes of surface state on the solutions, and, in particular, it seemed of special interest to consider the surface conditions that prevailed during an ex-

treme Quaternary glacial state (i.e., 18,000 BP). Although the results from this application must be viewed as highly speculative because of the many approximations in the model and deficiencies in the number of degrees of freedom al- lowed, we can at least be assured that the results are consistent with all the require- ments of conservation of mass, momentum, and energy as expressed in a clearly specified, albeit crude, manner.

Further, we may indulge the hope that, in spite of the approximations, the model properly includes enough of the relevant nonlinear physics of the problem to be able to yield better estimates

307 Copyright o 1975 by the University of Washington All rights of reproduction in any form reserved.

308 SALTZMAN AND VERNEKAR

of the zonal mean climate that ac- companied past surface boundary conditions than can be arrived at by argu- ments of a more qualitative nature such as given by Brooks (1949), Flohn (1953), and Willett (1953), for examples. Other theoretical attempts along these lines using more general three-dimensional numerical models have recently been made by Alyea (1972) who treated only summer conditions, and Williams, Barry, and Washington (1974). As in these latter studies, we make no attempt here to explain how the glaciation at 18,000 BP came about, but only seek to deduce the climate that would be in near- equilibrium with the prescribed glaciation.

2. THE MODEL: NEW PARAMETERS AND

PARAMETERIZATIONS

As described in our previous articles, the model used consists of the full set of thermohydrodynamical equations (including a representation of the hydrologic cycle), averaged in time, longitude, and height. These equations are combined with a set of closure formulas suggested by baroclinic and barotropic wave theory for the horizontal transient eddy fluxes of heat, momentum, and water vapor, and a set of parameterizations for the various modes of internal heating and the vertical fluxes at the Earth’s surface. The solutions for the north-south variations of the zonal mean climatic statistics (including the variances and covariances associated with the large-scale transient eddies) are a function of the intrinsic properties of the Earth’s surface (i.e., the albedo, conductive capacity, and water availability) as well as of other specified parameters including the incoming radiation and temperature at the base of the seasonal ocean thermocline.

The notation to be used here is identi- cal to that employed in our previous articles, which we hereafter refer to as S-V (Saltzman-Vernekar). In particular,

we consider only northern hemisphere conditions as in S-V (1971a, b), and use the same model equations and parameters given in S-V (1971a) with the following exceptions:

(1) From S-V (1972) we adopt: (i) the resolution of the surface state into five categories representing fractional cover- age by ocean jr, sea ice jz, land js, snow j,, and glacier j,; (ii) the constant values of the large-scale thermal exchange coef- ficient (K = 1.66 X lOlo cm2 set-‘) and long-wave absorptivity (I = 0.95); and (iii) the formulations for the oceanic conductive capacity factor, h,,,,n, atmospheric albedo r,,, and surface albedo r s0. The formula for r,, is applied to the improved values of the zonal and time averaged fractional cloud cover, n,, derived from data summarized recently by Schutz and Gates (1973, 1974) and listed in Table 1.

(2) On the assumption that partial melting of ice occurs in summer, a uni- form value of water availability (w) of 0.5, rather than zero, is adopted for glacier, snow, and sea ice in this season.

(3) The values of the subsurface land temperatures TDL are now deduced from the formulas

TDL (@)

0 $j:) - jiw) TDH + (1 - jiw)) 0 g,’

2 (l- jiw)) = (@ > 20”)

($5 < 20”)

where 062’ and 0 & are the winter and summer values, respectively, of the zonal and time average surface temperature. This formula is based on the assumptions that in winter the mean ocean surface temperature in extratropical latitudes, $ > 20”) is the same as the temperature at the base of the seasonal thermocline, T DHY ice.,

Tf“’ (Q;ocean)= TDH(@) (4 > 20”);

NORTHERNHEMISPHERE GLACIAL CLIMATE-PAST 309

TABLE1 Parameters Prescribed for Ice Age Conditions at 18,000 BP

jl i2 j3 j5 Ocean Sea ice Land s&v

(10-y (10-y Glacier

(10-2) (10-2) (10-y TDH degK -

Winter (Ott-Mar)

90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10

5 0

Summer (Apr-Sept)

0 5

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

0 0 0 0 0 0 3

22 37 47 54 53 57 61 68 71 72 78 74

74 78 72 71 68 61 57 53 54 47 38 32 15 4 0 0 0 0 0

100 100

68 50 17 14 21 11

1 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 9

10 17 50 68

100 100

0 0 0 55 273 0 0 0 48 273 0 0 32 46 273 0 3 47 49 273 0 25 58 54 273 0 25 61 59 273 0 28 48 64 273 0 25 42 66 273 0 33 29 67 274 0 40 13 65 275 4 35 7 62 278

19 24 4 58 281 26 14 3 53 285 39 0 0 47 289 32 0 0 44 292 29 0 0 41 294 28 0 0 39 295 22 0 0 43 296 26 0 0 48 297

25 1 0 48 297 21 1 0 50 296 28 0 0 55 295 29 0 0 55 294 32 0 0 53 292 39 0 0 50 289 40 0 3 49 285 42 1 4 52 281 39 0 7 57 278 40 0 13 64 275 30 3 29 70 274 13 12 42 73 273 0 28 48 71 273 0 25 61 70 273 0 25 58 73 273 0 3 47 78 273 0 0 32 82 273 0 0 0 84 273 0 0 0 87 273

and in tropical winter latitudes (6 < 20” ), and in summer at all latitudes, the mean ocean surface temperature can be ap- proximated by the zonal average mean surface temperature around the entire latitude circle, i.e.,

T$“) (4; ocean) = 06:’ (@) (@ < 20”)

Tp) ((I; ocean) = 0 &$ (c#J).

3. THE GLACIAL BOUNDARY CONDITIONS

In Table 1 we list the percentage of the Earth covered by ocean (jl), sea ice (j2), land (j3), snow (j4), and glacier (j,), as a function of north latitude, that is be- lieved to have prevailed during the height of the last major glacial advance at 18,000 BP, as derived from information

given by Flint (1971). The present day edge about the cloud variations, and our values were given in S-V (1972). lack of a parameterization scheme for

In the absence of a dynamical model them, this choice seems less objection- of the oceans we must prescribe the able than any other. In any event, our zonal mean oceanic temperature at the solutions are subject to these limitations base of the seasonal thermocline T,,. and we recognize that they should be re- If, as before, we assume TDH is equal to moved in the future with more general the winter sea surface temperature, we models that treat all of the parameters as can use the estimates of the January sea dependent rather than prescribed quanti- surface temperature during the last ice ties. This would apply also to TDH. The age, given by Williams et al. (1974), to solutions we present here may therefore construct a plausible distribution of T,, be viewed simply as a test of the “sen- for 18,000 BP (see Table 1). sitivity” of our model to some prescribed

In this study we shall calculate the ef- changes in parameters keeping all other fects only of variations in the surface parameters fixed (cf., Warshaw and state parameters, h (conductive capac- Rapp, 1973; Sellers 1973). ity), r, (albedo), and w (water availabil- We note also that our model deals only ity), and of the prescribed ocean tem- with the axially symmetric component perature TDH, which are associated with of the total climatic field, to which the altered glacial state of the Earth. All should be added an asymmetric compo- other external and internal parameters of nent representing the departures due to the problem are held fixed at the previ- continent and ocean. In essence, we are ously used values which were appropriate treating here a somewhat artificial, lati- for present conditions. This includes for tudinally varying but longitudinally example, the incoming radiation Ro, the homogeneous surface having h, r,, and w- atmospheric radiation parameters ul, v2, properties that are weighted in propor- p, x, and!,, and the humidity parameters tion to the fractional amounts of land, C; and hOS (for definitions see S-V, water, and ice along latitude circles. 1971a, p. 1505). Thus, the solutions can only be taken as

From the tables given by Vernekar suggestive of the zonal average climatic (1972) it can be seen that the distribu- state for varying proportions of the above tion of incoming solar radiation, R,, at surface state components and cannot be 18,000 BP differed only slightly from identified with the local climate at spe- the present distribution, due to the cific geographic positions where pure known Earth-orbital changes. Moreover, ocean, land, or ice exist. To determine we have already shown (S-V, 1971b) this local climate we must couple the that even when the values of R, ap- solutions obtained here with the “stand- propriate for 10,000 and 25,000 BP are ing wave” solutions (cf., Saltzman, 1968). used, representing periods of maximum departures from present conditions, only 4. THE SOLUTIONS minor changes in the climatic equilibrium solutions are obtained that are certainly

The solutions, obtained by the pro- cedure described in S-V 1971a, are

insignificant compared to those we shall shown in Figs. 1-15. The full curves report on here due to varied surface represent the “control” solution for the glaciation conditions.

The application of the atmospheric present surface state and associated TDH- field; this solution may vary slightly

radiation parameters appropriate for from those presented in either S-V present cloud conditions to the “ice age” (1971a) or S-V (1972) because of the conditions is much more questionable. changes described in Section 2. The However. in view of our lack of knowl- _ dashed curves represent the new solution


NORTHERN HEMISPHERE GLACIAL CLIMATE-PAST 311

I I I I I I I I I I . 1 L I I I I I

90807oMMU)Y)aJ I O 0 K) W)Y)4o~Y)M7oIDEc

WlWTER LATITUDE (ON) SlAWR

FIG. 1. Mean surface temperature 80~ and vertically averaged atmospheric potential temperature 6&, for present (full curve) and 18,000 BP (dashed curve).

corresponding to the “glacial” surface state. The left and right halves of each figure represent the solutions for the northern hemisphere winter and summer, respectively.

The quantities shown are the surface (subscript s) and atmosphere (subscript a) values of the potential temperature Be (Fig. 1); meridional gradient of surface temperature ae,,/a&# (Fig. 2); zonal wind us (Fig. 3); individual pressure change, i.e., poloidal vertical motion, we (Fig. 4); precipitable water We (Fig. 5); standard deviation of transient meridional motion (v’~)~” (Fig. 6); meridional transport of heat by transient motion (m)e and by poloidal motion (uOBO) (Fig. 7), of momentum (u’v’), and (uOvo) (Fig. 8), and of water vapor (zp, and (Fo) (Fig. 9); the surface

and atmospheric heat balance components due to short-wave solar radiation H,(l) and pa’), effective long-wave radiation e2) and fia2), small-scale vertical convection fiS3) and Hi’), water vapor phase transformations, i.e., evaporation and precipitation e4) and pa*, subsurface heat flux Hj5), and horizontal convergence of heat due to large-scale atmospheric motions Hi’) (Figs. 10-14); and the difference between evaporation and precipitation (Ee-PO) (Fig. 15). Fi- nally, in Fig. 16 we show the annual mean atmospheric energy cycle corresponding to present conditions and to glacial conditions (magnitudes in parentheses).

In general, we find the “glacial” atmosphere to be colder, drier, and more energetic (both in terms of existing kinetic energy and rate of energy trans-

FIG. 2. Mean surface temperature gradient ae&aa$ for present (full) and 18,000 BP (dashed).


J

LAllTliE I’NI 405080700 so

-

FIG. 3. Mean surface zonal wind speed UG (lower curves) and vertically averaged zonal wind speed pOa (upper curves) for present (full) and 18,000 BP (dashed).

FIG. 4. Mean individual pressure change, oo, at 500 mb for present (full) and 18,000 BP (dashed).

‘I-

3-

! !*-

I-

o-

FIG. 5. Mean precipitable water Wo for present (full) and 18,000 BP (dashed).


FIG. 6. Mean standard deviation of the meridional wind (7):” for present (full) and 18,000 BP (dashed).

-,.I I) 00 70 60 so 40 30 w 00 0 IO a3 YI 40 50 60 m m sa

WWlER LATITUDE 1-N) PMER

FIG. 7. Mean vertically averaged meridional flux of potential temperature by transient eddies

(v’B’)o and poloidal motions (x), for present (full) and 18,000 BP (dashed).

FIG. 8. Mean vertically averaged meridional flux of zonal momentum by transient eddies

(T)o and poloidal motions (z), for present (full) and 18,000 BP (dashed).


FIG. 9. Mean vertically averaged flux of water vapor by transient eddies (Vlfl)o and poloidal motions (s), for present (full) and 18,000 BP (dashed).

¶0110loMY)4oYliD100 10 PO 32 40 u) M 10 m 50 ll”TER UTITUCEI’N ) -

FIG. 10. Mean energy flux toward the surface due to short-wave (solar) radiationH$l), and effective long-wave radiation i3j2’, for present (full) and 18,000 BP (dashed).

FIG. 11. Mean energy flux toward the surface due to small scale atmospheric convection Hi3), and water vapor phase transformations Hi4), for present (full) and 18,000 BP (dashed).


90 80 m 60 50 40 50 20 10 0 10 20 m 40 m 60 lo 80 90 WmlER LATITUOE I’N) WYKR

FIG. 12. Mean energy flux toward the surface from below Hi5), and mean vertically averaged horizontal convergence of heat in the atmosphere due to eddy and poloidal motions H,“‘, for present (full) and 18,000 BP (dashed).

-MO- I I I I ,,,,,I I,, 1 , , , ,

90 (LD m 8D Y) 40 30 to to 0 omou)Jowloll)eo RmER LATITIEE (*N) -

FIG. 13. Mean rate of heat addition to the atmosphere due to short-wave (solar) energy H,$l’, and long-wave radiation Hi2’, for present (full) and 18,000 BP (dashed).

FIG. 14. Mean rate of heat addition to the atmosphere due to small-scale convection HA3’, and latent heat release HL4) (= LPo), for present (full) and 18,000 BP (dashed).


t

FIG. 15. Mean difference between evaporation and precipitation (Eo - PO), for present (full) and 18,000 BP (dashed).

I I

0 I

‘I?i.;::

% - 4 / L--- ---,

22 1101 I

M.ssI~IoN

FIG. 16. Annual mean energy cycle for the northern hemisphere for the present, and for 16,000 Bl (values in parentheses), in units of watts m . K, is the zonal kinetic energy, KM the mean poloidal kinetic energy, KT the transient eddy kinetic energy, KS the standing eddy kinetic energy, A, the zonal available potential energy, AT the transient eddy available potential energy, and A, the standing eddy available potential energy, all averaged over the northern hemisphere. The arrows indicate the direction of the generation, conversion, and dissipation of these forms of energy (see S-V, 1971a, p. 1502).

formation) than the present atmosphere, with relatively smaller departures from present conditions in tropical latitudes and in summer.

Some noteworthy specific features of the glacial solution are the following:

(1) The zonal mean surface and mid- tropospheric temperatures (Fig. 1) are uniformly cooler than at present, with the surface values at high winter latitude showing a steplike profile similar to that pictured by Brooks (1949, p. 44). This step profile implies an increased temperature gradient near the edge of the ice sheet at 55”N and constitutes an en- hanced low level “polar front” (Fig. 2). These results are in general agreement with those of Alyea (1972) and Williams et al. (1974).

(2) Associated with this winter polar frontal zone are southward shifted surface polar easterlies and midlatitude westerlies (Fig. 3) with maximum shear (i.e., maximum vorticity, CO =- au&&$) coinciding with the frontal zone. Newell (1974, p. 124) has cited some evidence for such a southward shift of the polar easterlies during the last glacial maximum. The boundary between the midlatitude surface westerlies and the trades in winter is essentially unchanged how-


ever, resulting in a contraction of the surface westerly zone. In summer there is a southward shift of roughly 4 degrees of latitude in both the polar easterlies and westerlies.

(3) The most striking feature of Fig. 3 is the marked increase in the strengtb of the free atmospheric zonal westerlies, u,-,~, in middle and subtropical latitudes during both seasons, with a smaller decrease of the westerlies poleward of 60-65”N. This “high zonal index” condition implies that the storm systems of middle latitudes (which according to the results shown in Fig. 6 were more energetic during the ice age) tended to progress eastward more rapidly than they do at present. Similar u,distributions were obtained by Alyea, and Williams et al, for summer. However, our results for winter seem to differ from those of Williams et al., who find a slight decrease in the strength of the westerlies in this season.

(4) As an interesting side consequence of the above, the increased zonal westerly regime during both seasons implies a slightly increased annual mean “length of the day” 7 (or, equivalently, a reduced mean rate of rotation of the Earth) during the ice age, neglecting the effects of all other factors (e.g., mass shifts of the Earth’s core, atmosphere, oceans, and ice sheets; meteor invasions).

The approximate formula for this increase, 87, of the length of the day is (cf., Mintz and Munk, 1951)

67 = 2~ a9070 6A

gcn ’

where a is the radius of the Earth (6370 km), p. the mean surface atmospheric pressure (1000 mb), 7. the mean length of the day (8.64 X lo4 set), C the moment of inertia of the Earth (8.12 X 10&g cm2), a the mean angular velocity of the earth (7.29 X 10m5 set-l), and &A is the increase of the integral

I n/2

A= uoa COS~I#I d$. -77 12

From our present northern hemisphere solutions (Fig. 3) we find by evaluating A over both seasons that

A =

I

13.89 m set-l (present)

16.34 m set-’ (18,000 BP).

Thus, 6A = 2.45 m set-l and we obtain 67 = 0.594 msec or &7/7 (= -&a/a) = 6.87 X 1O-g. This magnitude is com- parable to the present seasonal change in 7 due to the asymmetry of the zonal winds in the northern and southern hemispheres (Lambeck and Cazenave, 1973), but is an order of magnitude smaller than the “historical” changes pictured by Anderson (1974, Fig. 1) who also offers some interesting speculations regarding the possible geophysical sig- nificance of long-term variations in T.

(5) The mean poloidal motions, the vertical component of which is measured by w. (Fig. 4), shows the largest varia- tion in high winter latitudes. In particular, we find in winter an intensification and southward shift of the polar direct cell, along with smaller intensifications of the Ferrel and Hadley cells. This pattern is consistent dynamically with the shifts of uos described above and with the increases in baroclinic eddy ampli- tudes and transports in middle latitudes depicted in Figs. 6-9 (cf., Newell 1974). The summer patterns of w. show changes of the same order as those re- ported by Alyea. Figure 4 shows no shift in the position of the ITCZ (the tropical ocrminimum) as is also the case in the Williams et al. simulation. How- ever, this finding is at variance with the plausible suggestions of Newell and others that such shifts occurred-we feel that judgments concerning this feature must await better resolution and strengthened parameterizations for the tropical portion of our model.


(6) As noted above, accompanying the intensification of middle latitude temperature gradients in the glacial solution there is an intensification of baroclinic eddy activity (i.e., “storminess”) measured by (v’2)A12 (Fig. 6) and the associated meridional eddy flux of heat, momentum, and water vapor (Figs. 7-9). This result is in agreement with Alyea’s July results. The increased magnitude of the poloidal cells also leads to augmented transports of the atmospheric properties, except that of water vapor which suffers a decrease in its zonal mean value due to the general cooling of the atmosphere (Fig. 5).

(7) Along with the increase in the kinetic energy level revealed by uO, o.

r2 l/2 and (v )o , we also find a more intense energy cycle in the glacial solution as measured by the conversions and transformations shown in Fig. 16. Thus, for example, the rate of conversion of transient eddy available potential energy (AT) to eddy kinetic energy (KT) isabout 35% greater for the glacial boundary conditions than for the present. Note that because each of the different energy transfer integrals is measured indepen- dently by a finite-difference version of the approximate formula given in S-V (1971a) an exact steady-state balance need not be obtained in all cases. An im- balance is most evident for (Kz + K,), which, however, involves values that are an order of magnitude less than the main branches of the energy cycle.

(8) The departures of the glacial heat balance components from the values deduced for present conditions, at the surface (H,) and in the atmosphere (H,), tend to be largest in higher latitudes near the ice sheet (Figs. 10-14). We note, in particular, the large increase of the flux of sensible heat (e3)) from the atmosphere to the ice sheet during the winter (Fig. ll), and a corresponding decrease in the upward subsurface flux, Hi5’ (Fig. 12). Also evident in Fig. 10 is

the summer decrease of absorbed solar radiation at the surface over the ice sheet.

(9) The hydrologic cycle, depicted in Figs. 9, 11, 14, and 15 by the curves of

- (zyo, (Vofo), H,c$’ (= -LE,), H$j (=LP,), and (E, - PO), is characterized by a global decrease in both evaporation and precipitation along with an increase in the poleward eddy flux of water vapor. The climatologically significant net effect is a somewhat equatorward-shifted pattern of (E, - PO) with increased amplitude in the winter, resulting in a more positive surface water balance from 25 to 75”N and a less positive balance in the remain- ing tropical and polar latitudes.

It may be noted that the winter precipitation excess over evaporation is a maximum near the edge of the ice sheet where it would serve to build the leading ice edge. Conversely some reduction in (PO- E,) below present values prevails poleward of about 70”N in winter. The profile of (E, - PO) shown can be viewed as an atmospheric “forcing function” for the ice mass balance, which, along with other processes such as internal ice flow, snow drift, melting, and calving, deter- mines the ultimate depth profile of the ice sheet.

5. CONCLUDING REMARKS

Using the same model from which we previously deduced an acceptable first approximation to present zonal climatic conditions, we have now solved for the response to the “glacial” surface boundary conditions that probably prevailed at 18,000 BP. To summarize from the previous section, we find the glacial atmosphere to be colder and drier than at present, with an intensified polar front, stronger mean zonal and poloidal winds, more intense transient baroclinic eddies (storms) transporting heat, momentum, and water vapor poleward at higher rates, and reduced precipitation and evaporation. A tendency for an equatorward shift of the climatic zones [as delineated


by the mean surface zonal winds ues, the

factors are already included in the nu-

poloidal motions we, and (E, - P,)] is evident, particularly in higher latitudes.

merical models used by Alyea (1972)

These results are not really surprising though they do differ in some respects

and Williams et al. (1974), and could ac-

from previous qualitative portrayals of the ice age zonation of climate based on intuitive physical reasoning and geologic

count for some of the differences be-

evidence (cf., Fairbridge, 1961).

tween their results and ours.

While we may hope that most of the properties of the solutions presented here are valid in their broad aspects (i.e., they portray correctly the signs of the larger departures of the glacial solution from the present one), the obvious limitations of the model certainly preclude a ready acceptance of the details. In this connection, few of the improvements in the model suggested as desirable in the concluding section of S-V (1971a) have yet been incorporated. Moreover, we have not yet performed a complete analysis of the “sensitivity” of the model to small changes in internal parameters, by means of which we might be able to measure the “noise” in the model (due to inherent uncertainties and inadequa- cies of the parameterizations employed) and hence more clearly distinguish the true effects of the changes in boundary conditions.

It is also clear from an examination of the pattern of Wurm/Wisconsin glaciation that the last ice age was far from axially symmetric. A first order improve- ment of our study would accordingly result from a consideration of the effects of the global quasistationary waves forced bv the continents and oceans. These

partment of Defense monitored by the U.S. Army Research Office under Grant DAHC06 74-G-0229; and at the University of Maryland by the National Science Foundation under Grant GA-22900.

We thank the reviewers for their constructive comments.

REFERENCES

Alyea, F. N. (1972). Numerical simulation of an ice age paleoclimate. Atmospheric Science Paper No. 193 (120 pp.), Colorado State University.

Anderson, D. L. (1974). Earthquakes and the rotation of the earth. Science 186,49-50.

Brooks, C. E. P. (1949). “Climate Through the Ages.” 2nd Ed., 395 pp. Ernest Benn, London (republished, Dover Press, NY, 197 0).

Fairbridge, R. W. (1961). Convergence of evidence on climatic change and ice ages. An- nals of the New York Academy of Science 95,542-579.

Flint, R. F. (1971). “Glacial and Quaternary Geology.” 892 Pp. Wiley, New York.

Flohn, H. (1953). Studien iiber die atmo- spharische Zirkulation in der letzen Eiszeit. Erdkunde 7, 266-275.

Lambeck, K. and Cazenave, A. (1973). The earth’s rotation and atmospheric circulation- I. Seasonal variations. Geophysical Journal 32,79-93.

Mintz, Y. and Munk, W. (1951). The effect of winds and tides on the length of the day.

component of the earth’s macroclimate. Jour-

Tellus 3, 117-121. Newell, R. E. (1974). Changes in the poleward

nal of Geophysical Research 76, 1498-1524.

energy flux by the atmosphere and ocean as a

Saltzman, B. and Vernekar, A. D. (1971b).

possible cause for ice ages. Quaternary Re- search 4,117-127.

Note on the effect of earth orbital radiation

Saltzman, B. (1968). Surface boundary effects on the general circulation and macroclimate:

variations on climate. Journal of Geophysical

a review of the theory of the quasi-stationary perturbations in the atmosphere. Meteorolog-

Research 76, 4195-4197. Saltzman, B. and Vernekar, A. D. (1972).

ical Monographs 30,4-19. Saltzman, B. and Vernekar, A. D. (1971a). An

equilibrium solution for the axially-symmetric

ACKNOWLEDGMENTS Global equilibrium solutions for the zonally- averaged macroclimate. Journal of Geo-

This work has been supported at Yale Uni- physical Research 77, 3936-3945. versity by the National Science Foundation Schutz, C. and Gates, W. L. (1973). Supple- under Grant DES75-00351 and by the Ad- mental global climatic data: January. Rand vanced Research Projects Agency of the De- Report R-915/2-ARPA, 38 pp.


Schutz, C. and Gates, W. L. (1974). Supple- mental global climatic data: July. Rand Re- port R-1029/l-ARPA, 38 pp.

Sellers, W. D. (1973). A new global climatic model. Journal of Applied Meteorology 12, 241-254.

Vernekar, A. D. (1972). Long-period global variations of incoming solar radiation. Mete- orological Monographs 12, No. 34, 21 pp. + tables.

Warshaw, M. and Rapp, R. R. (1973). An ex- periment on the sensitivity of the global circu-

lation model. Journal of Applied Meteorology 12,43-49.

Willett, H. C. (1953). Atmospheric and oceanic circulation as factors in glacial-interglacial changes of climate. In “Climatic Change.” (H. Shapley, Ed.), pp. 51-71. Harvard Uni- versity Press, Cambridge.

Williams, J., Barry, R. G., and Washington, W. M. (1974). Simulation of the atmospheric circulation using the NCAR global circulation model with ice age boundary condrtions. Journal of Applied Meteorology 13, 305-317.

a solution for the northern hemisphere climatic zonation during a glacial maximum

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