Response of a global climate model to a thirty percent reduction of the solar constant

Global and Planetary Change, 8 (1993) 219-230

219

Elsevier Science Publishers B.V., Amsterdam

Response of a global climate model to a thirty percent reduction of the solar constant K e v i n J. W a l s h a n d William D. Sellers Institme of Atmospheric Physics, The University of Arizona, Tucson, AZ 85721 USA (Received October 12, 1992; revised and accepted March 18, 1993)

ABSTRACT Walsh, K.J. and Sellers, W.D., 1993. Response of a global climate model to a thirty percent reduction of the solar constant. Global Planet. Change, 8: 219-230. An investigation is made of the "white earth" scenario, wherein the positive feedback mechanism, involving temperature, snow/ice cover, and albedo, renders the earth's surface covered with permanent snow and freezes the oceans when the solar input is sufficiently low. A three-dimensional energy budget climate model is used to simulate the earth's response to a 30% decrease in the solar constant. The decrease occurs over a period of 90 years. The model simulates an additional 100 years to allow conditions to stabilize. At the end of the model run, the planetary mean surface temperature is 204.8°K, the oceans are completely frozen over, and the maximum seasonal mean temperature for any grid point of the planet is 251.6°K in the western Gobi Desert in JJA. The highest average annual temperature is 238.7°K in western Zaire. A significant portion of the planet's land surface is free of permanent snow cover. The results of this model run suggest that the hydrologic balance may provide a significant negative feedback mechanism to counter the snow/ice-albedo positive feedback mechanism and that the earth's climate may be less sensitive to variations in the solar constant than previously believed.

Introduction

The possibility that the positive feedback mechanism resulting from the relationship between temperature and albedo could become self-sustaining and result in glaciers overrunning the planet surface was first seriously studied in the late 1960s. Eriksson (1968) suggested that, if the mean limit of glaciation reached the 50th parallel, snow and ice would continue to advance to the equator. Budyko (1969) experimented with a one-dimensional energy balance model (EBM) and found that a decrease in the solar constant of 1.6% could result in a precipitous drop in mean global t e m p e r a t u r e with equilibrium being reached at a temperature "several tens of degrees [Celsius] below zero" (ibid., p. 616). Sellers (1969) performed a similar experiment, making two runs of an EBM using two different formulae for the relationship between temperature and albedo and

a third run with the assumption of a constant albedo. The run with the relationship a = b 0.009T (a is the surface albedo, T is the mean planetary temperature in °K, and b is a coefficient assigned to each latitude belt in the model and ranges from 2.798 to 2.992) produced an equilibrium temperature of 173°K for a solar constant decrease of slightly over 2%. The model used by Schneider and Gal-Chen (1973) produced similar results, with an equilibrium temperature of 282.1°K for a 1.0% decrease in the solar constant, and 175.6°K for a 1.6% decrease. Other studies (Gal-Chen and Schneider, 1975; Wetheraid and Manabe, 1975; Ramanathan, 1977; Washington and Meehl, 1986; Harvey, 1988) using more complex climate models failed to produce a runaway snow/ice-albedo feedback with a 2% decrease in the solar constant and did not indicate how much of a decrease is necessary for this to occur. Coakley (1979), using an EBM, found that

0921-8181/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved

220

a decrease in the solar constant of 9% would be sufficient to induce planetary ice and snow cover. North (1981), also using an EBM, found that a 4% decrease would suffice. Held and Suarez (1974) found that the limit of permanent snow and ice becomes unstable and surges, with their model, when it reaches a latitude of about 45 °. This "white earth" scenario resulted from a radical increase in the earth's albedo caused by the presence of glaciers and frozen ocean surfaces at all latitudes. North's (1975) analysis of Budyko's 1969 model suggests that recovery from such a situation would be impossible or very difficult. A solar constant 2% less than the current value would establish complete planetary ice and snow cover, but a solar constant 35% larger than the current value would be needed for melting to begin. Wetherald and Manabe (1975) used a general circulation climate model to simulate the response of the e a r t h - a t m o s p h e r e system to initial "white earth" conditions. The resulting mean temperature is 193°K. The ice cover sustained itself for the duration of the model run. The hydrologic cycle was analyzed, and according to the authors, " . . . [S]nowfall slightly exceeds sublimation at every latitude circle due to a general reduction of the moisture-holding capacity of the model atmosphere with time. In order to economize on computer time, we did not attempt to reach a quasi-steady-state equilibrium for this case but rather terminated the run when the mean temperature began to level off." (ibid., p. 2057). This raises the possibility that had the run been continued, and before equilibrium was reached, sublimation might have exceeded deposition and snowfall in certain regions, and deposition and snowfall might have exceeded sublimation in others, resulting in some regions being denuded of snow and ice, lowering the planetary albedo, and increasing the planetary temperature. In the models that predict total planetary snow and ice cover (Budyko, 1969; Sellers, 1969; Schneider and Gal-Chen, 1973; North, 1975; Coakley, 1979; North, 1981), the presence of snow and ice is directly related to the mean temperature; the effects of the hydrologic cycle are not

K . J W A I , S H A N D W.I). S E L t . E R S

considered. The assumption that there is a great excess of precipitation over sublimation at subfreezing temperatures and thal therefore melting is the only important process by which snow cover is removed is generally valid with current conditions, but with the equatorward progress of snow and ice, water vapor from the tropical oceans needed to maintain this excess will probably cease to be available as the ocean surface cools and freezes. Several studies (Loewc, 1962; Lettau, 1969; Mercer, 1970; Beaty, 1975; Hastenrath, 1978; Fujii and Kusunoki, 1982; Hastenrath, 1984; Mclntyre, 1985) have shown (a) that sublimation is the most important ablation mechanism for cold glaciers (those which never or extremely rarely experience air temperatures above the freezing point) and other glaciers and snowpacks during periods of subfreezing temperatures, (b) that the annual total sublimation from a cold glacier or snowpack is almost always much greater than the annual total deposition onto a cold glacier or snowpack, although there are some periods during the winter when deposition is greater than sublimation, and (c) that the bulk of accumulation on both polar ice sheets and high altitude temperate and tropical glaciers consists of precipitation resulting from the advection of water vapor from other regions of the Earth. This suggests that it is highly unlikely that a global ice sheet could be maintained by a perfect balance of sublimation and accumulation on every part of the planet. Riordan (1976) showed that a permanent snow cover in the Lake Vanda region of Antarctica would not melt and that therefore the current absence of snow ctwer is due to the excess of sublimation and wind transport over accumulation. It is believed that, at the time of the early stages of life on Earth, the solar constant was about 30% smaller than it is today. All life requires liquid water at some time. If a solar constant which is only 70% of its current value would result in the absence of liquid water and an ice-covered Earth, life could not evolve. Many attempts have been made to resolve this paradox. Most of these have been summarized by Kasting (1989) and Kasting and Toon (1989).

R E S P O N S E O F G L O B A L C L I M A T E M O D E L T O T H I R T Y P E R C E N T R E D U C T I O N OF SO L A R C O N S T A N T

These authors favor the popular theory that during the early stages of the Earth's history, when the Earth may have been completely watercovered, it had a thick (1-10 bars) CO 2 atmosphere, which greatly enhanced the greenhouse effect and produced surface temperatures as high as 373°K (Kasting and Toon, 1989). We will use a relatively simple three-dimensional global climate model with a complete hydrologic cycle to see whether it would be possible to have regions on Earth free of snow and ice with a greatly reduced solar constant, maintaining the present atmospheric composition (except for water vapor) and distribution of land and oceans. If so, would local temperatures in snow-free regions be high enough to permit the existence of liquid water and, thus, to sustain life? The entire model run simulates 200 years of real time at five-day time steps. During the first 10 years, the solar constant is kept at its present value, 1368 W / m 2. In the eleventh through the 100th years, it is gradually decreased, by about 0.0054% per time step, to 70% of its initial value at the beginning of the 101st year and kept constant thereafter. The run required almost 4 hours of C O N V E X C240 computer time, so it is something we are not likely to repeat very often, except possibly on a faster computer. The model

A slightly modified version of the three-dimensional global climate model described by Sellers (1983, 1985) is used in this analysis. Several major modifications have been made. First, the meridional eddy mass flux introduced into the model to simulate the strong southern hemisphere westerlies has been dropped. Instead we now include in the equations of motion for the boundary layer a term representing the downward flux of horizontal momentum, associated with the vertical shear of the horizontal wind, through the top of the layer. Using the thermal wind equation, this shear is parameterized as a function of the horizontal temperature gradient. Second, the tropospheric lapse rate parameterization has been modified slightly to constrain the lapse rate, which is a function of the surface temperature, Ts, or the

221

temperature, Ta, at the top of the boundary layer, to approach the dry adiabatic lapse rate when the global annual mean surface temperature, Ts, is very low. For the boundary layer lapse rate, FA, and the lapse rate for the rest of the troposphere, F B, both in K / k m , we now use:

FA=(O.2159Ts-57.39x)y 2 0 < F A < 10

(la)

FA = 0.9223T~ - 245.2x FA < 0

(lb)

and F B = (0.0649Ta - 12.37x)y, F B ~< 10

(2)

where: x = ( T J 2 8 8 ) and y = 0.5y_ l ( 5 m -- 3), where: m is the annual average ratio of the outgoing infrared radiation to the net incoming solar radiation at the top of the atmosphere, and where y is recomputed annually from its previous value, y_ 1, and m. Note that when m = 1, signifying a radiation balance at the top of the atmosphere, y = y_ 1 and the system is in quasi-equilibrium. This formulation points out one of the risks of applying an ad-hoc model, parameterized to fit present conditions, to conditions far outside the range of those currently experienced. The parameterization simply may not be valid. For example, in Eqns. 1 and 2, with x = 1.0, as used originally, the lapse rates obtained at very low global mean temperatures would be either very small or negative, whereas, in fact, they should approach the dry adiabatic lapse rate, except where modified by convection and advection of sensible heat. The total atmospheric carbon dioxide content, T C O 2, is also assumed to vary directly with x, TCO2(ppm) = 315x z

(3)

This relationship is arbitrary, but seems better than assuming constant CO 2 and is in line with observations suggesting that atmospheric CO 2 increases as the temperature increases and vice versa. In the original version of this model, the albedos of low, middle, and high clouds were assumed to equal 0.69, 0.48, and 0.21, respectively. These values would not be appropriate for the much colder atmosphere visualized in this experiment. Therefore, we have elected to modify each by

222

K.J. WAI.SH AND W.D. SELLERS

multiplying by x 2. This is also done for the inflared emissivity of clouds, Ec, originally set equal to 1.0 for low and middle clouds and 0.5 for high clouds. Admittedly these parameterizations are arbitrary, but we believe they are more nearly correct than the fixed values used originally. Their net effect on the model results is hard to estimate, since a decreasing cloud albedo with decreasing solar constant would tend to retard the cooling while the decreasing cloud emissivity and CO 2 would tend to accelerate it, by allowing more of the infrared radiation from the lower, warmer portions of the atmosphere to escape to space. Results

The results are summarized in Table I. S is the solar constant ( W / m 2 ) ; T S is the global mean surface temperature (°K); m is the ratio of the infrared radiation lost to space to the solar radiation absorbed by the e a r t h - a t m o s p h e r e system, i.e., a measure of the radiation balance of the planet; at, is the planetary albedo; r is the global

mean precipitation ( m m / m o ) ; n is the global mean fractional cloud cover; A~ is the fractional area of the earth's oceans covered by ice; and A s is the fractional area of the earth's land covered by snow or ice. T, and m are annual average values for the year prior to the year indicated. The other variables are for January of the given year. As the solar constant decreases between year 10 and year 100, the global mean surface temperature drops from about 290°K to 208°K, the world's oceans become completely iced over, the planetary albedo more than doubles from 0.28 to 0.64, precipitation decreases to less than 0.1 m m / m o , and cloud cover increases by about 27%. However, at such low temperatures, clouds are very tenuous and not a major factor in the energy balance. The largest temperature decrease, 23.4°K, occurs between years 70 and 80. At the same time, the world's oceans become completely iced over. During the last 100 years of the run, the mean surface temperature drops an additional 3.4°K to 204.8°K. Global precipitation, cloud cover, and

TABLE t Summary of the results of a 200-year model run with a varying solar constan! Year

S ( W / m 2)

T~ (°K)

m

ap

r (ram/mo)

n

A~

As

l 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191 201

1 368 1 368 1 315 1 264 1 215 1 167 1 122 1 078 1 037 996 958 958 958 958 958 958 958 958 958 958 958

288.5 289.6 288.4 285.0 282.2 274.4 264.7 254.4 221.0 212.4 208.2 207.0 206.5 206.1 205.6 205.4 205.3 205. l 205.0 204.9 204.8

1.000 1.003 0.999 1.005 1.009 1.045 1.110 1.107 1.052 1.036 1.025 1.019 1.015 1.008 1.005 1.003 1.001 0.998 1.000 1.000

0.277 0.289 0.284 0.295 0.297 0.354 (}.392 0.459 0.614 0.628 0.633 0.635 0.636 0.636 0.635 0.636 0.636 0.635 0.633 (].632 0.632

71.5 74.5 64.9 55.0 48.0 36.2 25.4 18.1 0.69 0.23 0.13 0.12 0.12 0.10 0.093 0.090 0.087 (}.087 0.083 0.083 0.083

0.511 0.530 0.509 0.495 0.495 0.594 0.588 0.561 0.583 0.591 0.590 0.580 0.583 0.567 0.530 0.527 0.523 0.515 0.488 0.459 0.457

0.060 0.065 0.073 0.100 0. t 25 0.186 0.335 0.526 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

0.342 0.346 0.379 0.393 0.401 0.441 0.522 0.660 0.744 0.747 0.745 0.741 0.737 0.729 0.724 0.719 0.715 0.708 I).696 0.694 0.694

RESPONSE OF GLOBAL CLIMATE MODEL TO THIRTY PERCENT REDUCTION OF SOLAR CONSTANT

land s n o w / i c e also decrease, by 27, 10, and 4%, respectively. For the 200th year x = 0.711 and y = 1.428 in Eqns. 1 and 2, giving lapse rate variations from - 3 6 . 0 ° K / k m (Ts=150°K) to 10°K/km (T~> 211.7°K) in the boundary layer and from 1.3°K/ km (Td = 150°K) to 9 . 7 ° K / k m ( Ta = 240°K) in the rest of the troposphere. The average annual pole to equator surface temperature difference in year 200 is 44°K in the northern hemisphere and 64°K in the southern hemisphere, 4°K larger and 5°K larger, respectively, than their present values. The e a r t h - a t m o s p h e r e system remains within 5% of a radiation balance throughout the run, except from years 61-89 when sea ice is rapidly expanding. The largest departure from a balance occurs in year 76. At that time the infrared emission exceeds the solar absorption by 19.5%. The ability of the model to maintain a radiation balance through most of the run under climatic conditions drastically different than the present is encouraging. Of principal interest in Table 1 is the change in s n o w / i c e cover over land that occurs as the solar constant decreases. A s increases from 0.342 in January of the first year to 0.747 in January of

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223

the 91st year. Thereafter, it decreases slightly so that at the end of the run only 69.4% of the earth's land area is snow-covered. The time variation of s n o w / i c e cover in January for the two hemispheres is shown in Fig. 1. There are several points of interest in the figure: (a) Permanent snow cover on the southern hemisphere continents, excluding Antarctica, is absent until year 62, at which time s n o w / i c e already covers 63% of the northern hemisphere land masses. This result suggests that the distribution of land and water is critical to the timing of glaciation. Had all the continents been on or near the equator, one might have anticipated an even greater delay in the onset of permanent snow cover, especially if the oceans were initially much warmer than they are today. (b) In both hemispheres s n o w / i c e cover over land reaches a maximum in year 85 and decreases slowly thereafter. The percentage decrease by year 201 is largest in the southern hemisphere (14.3%), equivalent to an area of 4.5 x 106 k m 2, compared to 4.9% and 3.8 x 106 km 2 in the northern hemisphere. The decrease in s n o w / i c e cover over land after year 85 is accompanied by a very small decrease in snow cover over the frozen

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224

K.J WALSH AND

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oceans and by an 80% decrease in global precipitation. The distribution of areas with less than complete snow cover in mid-January of year 201 is shown in Fig. 2. Since there is very little precipitation or sublimation, this pattern is representative of the entire year. The largest change in fractional snow cover from mid-July of year 200 to mid-January of year 201 is an increase of 0.009. The major snow-free areas in Fig. 1 are in

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Asia, Africa, South America and over the tropical oceans between 20°N and 20°S. The snow-free areas are dictated to some extent by the distribution of climatic types predicted by the model for present climatic conditions. This distribution, based on a 100-year control run, is shown in Fig. 3. As the criterion for determining the climatic type of a particular region, we used the ratio of the mean annual evaporation (E) to the mean annual precipitation (~)

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225

RESPONSE OF GLOBAL CLIMATE MODEL TO THIRTY PERCENT REDUCTION OF SOLAR CONSTANT

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for the region. Over land, one minus this ratio is Budyko's runoff coefficient, the ratio of the mean annual runoff to the mean annual precipitation (Sellers, 1965). Values of this coefficient greater than 0.7 are characteristic of tundra (1) regions; values between 0.3 and 0.7 of forested (2) regions; values between 0.3 and 0.1 of steppe (3)

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regions; values between 0.03 and 0.1 of semidesert (4) regions; and values less than 0.03 of desert (5) regions. This classification is much less detailed than the modified K6ppen classification used by Guetter and Kutzbach (1990), but it serves our purpose. Over the oceans, in Fig. 3 we distinguish be-

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226

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tween regions (1), with F>E; regions (2), with < E; and regions (3), with ~ < 0.5 E. Considering the nature of the model, it gives a realistic distribution of climates. Most of the dry regions of the world are where they belong, as are the major forested and wet regions. The bulk of the regions with less than complete snow cover over land lie in Africa, South America, and central Asia. Both southern and central Africa and South America are essentially snow-free by the end of the run.

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RESPONSE OF GLOBAL CLIMATE MODEL TO THIRTY PERCENT REDUCTION OF SOLAR CONSTANT

ture has dropped to 261°K and precipitation to only about 38% of its initial value. A similar explanation should hold for the snow-free land areas in the tropics and subtropics. With the rest of the earth snow- and icecovered, these regions should serve as global hot spots and dominate the patterns of sea-level temperature and pressure, shown for DJF and JJA in Figs. 5-8. These patterns are averages for years 191-200. In DJF, temperatures in excess of 230°K occur in central South America and southern Africa, reaching 247.9°K, the highest value, in Bolivia (Fig. 5). The lowest pressure, 991.9 hPa, occurs in eastern Zaire (Fig. 6). The dominant features of the pressure field are oceanic subtropical highs and intense thermal lows over Africa and South America. In JJA the major features of both the temperature and pressure fields shift northward, as might be expected. The highest temperature, 251.6°K, and the lowest pressure, 985.5 hPa, occur in the Gobi desert (Figs. 7 and 8). A broad and intense high pressure area extends eastward from the central Pacific to Asia at 45°N. Other than in central Asia, temperatures exceed 230°K in JJA only in equatorial Africa and South America.

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Discussion Although not all conditions had perfectly stabilized by the 200th year of simulation, a reasonable approximation to equilibrium had been reached. During the last fifty years of the model simulation, the average global surface temperature decreased by only 0.6°K. The extent and location of snow cover varied little in the last century, during which time the ocean was completely frozen (Table 1). The results suggest that the theory that snow and ice cover will surge when the mean limit of permanent snow and ice reaches a certain parallel of latitude is valid, but only to a point, since the advance ended over land well short of the equator. During the aforesaid surge, ocean temperatures decreased, and the oceans were no longer able to supply the water vapor needed to sustain the snowfall rates needed for the further advance of the snow cover zone over land. The advance of sea ice was self-sustaining all the way to the equator, since there was no problem with water supply. The advance of snow cover was much more rapid in the northern hemisphere than in the southern hemisphere (Fig. 1). Initially, the mean

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limits of January land snow cover were 40°N and 70°S (Antarctica). By the 50th year, snow cover had advanced to 20°N but was still limited to Antarctica in the southern hemisphere. January snow cover did not reach any southern hemisphere land outside of Antarctica until year 62. The seasonal cycle can account for a small part of this result, since January is in the boreal winter. More important, however, is probably the higher heat capacity of the southern hemisphere, which would tend to retard its cooling, and the isolation of most of the southern hemisphere land masses from Antarctica by the Antarctic Ocean. It was not until sea ice was extensive north to 40°S that the southern hemisphere land masses started to accumulate permanent snow cover. The planetary temperature by the end of the run was higher than previous predictions for the "white earth" scenario indicate. Extrapolating 175.6°K (the mean planetary temperature found by Schneider and Gal-Chen, 1973, for a 1.6% decrease in the solar constant) to a 30% decrease in the solar constant (assuming the albedo and emissivity remain constant and applying the Stefan-Boltzmann law) yields a temperature of 161.3°K. Extrapolating the 193.2°K for a forced "white earth" with the present solar constant (Wetherald and Manabe, 1975) to a 30% decrease yields a temperature of 176.7°K. These values are low compared to the mean temperature of 204.8°K found using our model. Reversing the process and extrapolating 204.8°K to the current solar constant yields a mean temperature of 223.9°K. Doing the same for the maximum monthly mean temperature of 251.6°K yields a temperature of 275.1°K, which is above the melting point of pure water and, thus, high enough to allow some snow melt and the consequent albedo decrease. This raises the possibility that the "white earth" scenario is far more difficult to establish or approximate than previously believed and that it may be possible for the planetary climate to recover from such a situation without increasing the solar constant above its present value. Whether or not life could exist on Earth with such low temperatures is debatable. The same question has been considered by McKay and

t~.l. W A I .SH A N D W . D . S E L L E R S

Stoker (1989) for Mars, which has a mean surface temperature of 215°K. Since liquid water is a prerequisite for life as we know it, they conclude that microbial life could survive only if there existed either (1) transient sources of near-surface liquid water, (2) meltwater within a dusty snowpack, or (3) subsurface reservoirs of meltwater deep within the regolith or at the base of the polar caps. For present-day Earth, to these might be added springs and groundwater in snow-free regions once blessed with abundant rainfall; for example, in Nigeria (see Figs. 2 and 3).

Conclusions In this paper, using a simplified three-dimensional global climate model, we have considered the hypothetical problem of what would happen if the solar constant were decreased slowly, over a 90 year period, to 70% of its present value. The model is not as physically and dynamically rigorous as a typical general circulation model (GCM) and it makes use of several simple parameterizations. However, it is unlikely that different, equally realistic parameterizations, for example, of the temperature lapse rate in the troposphere, would significantly change the results. Further, the noise level of the model is very low. It is a true climate model in the sense that day-to-day weather variations are filtered out, primarily by the use of a 5-day time step. Among the results of this study, one of the most important has to be the stability of the model with drastically altered initial conditions, in this case a 30% decrease in the value of the solar constant. The model behaves well and the results are certainly believable. Whether they are correct or not will probably never be known, although application of a G C M to this problem might help. Although the temperatures projected by the model suggest that most or all life on Earth would become extinct if the solar constant were to be reduced by 30% for a significant period of time, the absence of permanent snow cover on many parts of the tropical and subtropical land masses suggests that previous models may have overestimated the planetary albedo resulting from

R E S P O N S E OF G L O B A L C L I M A T E M O D E L T O T H I R T Y P E R C E N T R E D U C T I O N OF SOLAR C O N S T A N T

a radical decrease in the solar constant, and, hence, underestimated the equilibrium temperature. Since albedo increase is a key link in the r a d i a t i o n - t e m p e r a t u r e - s n o w / i c e - a l b e d o feedback mechanism, this potential error would also indicate that the feedback mechanism is weaker than previously believed and that Earth's climate is less sensitive to variations in solar radiation than previously believed. Based on our results, it seems likely that to get an ice-covered ocean might require as much as a 15-20% decrease in the solar constant. By changing the distribution of land and water and the composition of the atmosphere, it is not hard to imagine an equable climate on Earth with a greatly reduced solar input. Decreasing the solar constant by 30% did not seem to reduce the meridional temperature gradient, nor did it significantly affect the zonal and meridional pressure gradients in the tropics and subtropics. Strong thermal lows tended to form over land areas which were free of permanent snow cover, but these lows formed near areas which currently experience semi-permanent or seasonal thermal lows (Africa, South America, and central Asia). The sub-tropical anticyclones formed at or near the locations where they currently form, and the Hadley circulation cells were intact. The Ferrel and Polar cells were not intact, and polar anticyclones were non-existent. Temperature contrast between land and ocean surfaces was significant in the tropics and the middle latitudes of the summer hemisphere, but in high latitudes and during the winter in middle latitudes, isotherms were nearly zonal. Since the frozen oceans could not transport heat, and since ice has a lower specific heat and therefore heat storage capacity than liquid water, the current pattern of meridional isotherms over the oceans during the winter in middle latitudes, especially in the northern hemisphere, would not be expected to occur. The l a n d - o c e a n temperature contrast in the tropics was the result of differential heating, since much of the land in the tropics was free of permanent snow cover, and therefore had a lower albedo than the ocean surfaces. The lack of a strong l a n d - o c e a n temperature contrast in high latitudes and in middle latitudes of the

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winter hemisphere resulted in weak pressure gradients and no distinct polar anticyclones or subpolar cyclones. Possibilities for further research include duplicating the experiment described but gradually returning the solar constant to its present value and determining if the planetary climate recovers. It may also be of interest to use less extreme decreases in the solar constant (perhaps 10% or 15%) to determine what value is needed to initiate the complete freezing of the ocean surface.

Acknowledgements The authors are grateful to the Center for Computing and Information Technology at the University of Arizona for almost unlimited use of computer resources, to Janis Upson for typing the manuscript, to Margaret Sanderson Rae for editing it, and to Jim Abbott for drafting the figures. This study was partially supported by the National Science Foundation under grant No. ATM-8619467.

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