By Vyacheslav NAYDENOV, Dr. Sc. (Phys. & Math.), and Valentina SHVEIKINA, Cand. Sc. (Geogr.), RAS Institute of Water Management

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The human race is so much anxious about global warming due to the hot house effect that it is trying to reduce industrial discharges of carbon dioxide into the atmosphere. But will this make the planet cooler? Unlikely, because the hot house effect is only the consequence rather than the cause.

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NATURAL INDICATORS OF GLOBAL WARMING

The revolutionary impact of new ideas of the thermodynamics of irreversible processes as well as non-linear dynamics and classic mechanics on various natural sciences has made scientists realize that such a complex and heterogeneous system as our planet is developing by nonlinear laws. This is fully true of its water shell as well. The authors of this article spell out a new global warming concept, in which dry land's humidity plays the main part.

The past 10-15 years have proved to be the warmest and most humid period not only in the last century but over the millennium too. All kinds of natural objects react to such dramatic warming. Dr. I. Borzen-kova (State Hydrology Institute, Rosgidromet), for one, has proved on the basis of various empirical data that the earth's humid phase is getting more water. The 1980s and 1990s were the most significant years in this respect: precipitation in the form of torrential rains statistically increased then, especially in North America, Eastern and Western Europe, and Australia. Mountain glaciers were melting away fast in Central Europe, Asia, tropical Africa, and Iceland. And arctic ice and antarctic shelf glaciers were shrinking.

By analyzing centennial series of dates of the ice breakup and freezing of the largest Russian rivers, specialists have found a statistically significant trend in the way these dates have been changing over the last few years. In the river basins of the country's European territory, the ice period has over the last 100 years shrunk by over 15 days, and in the Don basin even by 20-25 days.

On the Siberian rivers White Ob and Irtysh it has become 9-14 days shorter. In the North Hemisphere spring now comes earlier, and the vegetation period has become longer.

The year 1998 proved the warmest over one hundred years-air temperature on Earth averaged 16.6 C then. In Moscow, despite the frightful Hydro Meteorologic Center forecasts, it turned out one degree warmer, and precipitation was 37 percent above norm. All across Northwestern Europe, an Icelandic super cyclone (low pressure areas with the center between North Atlantic and South Greenland) caused heavy precipitation with a huge amount of heat entering the north of the European continent from the Atlantic. In many regions, floods have become common.

What are the causes of these phenomena?

THREE VARIABLES OF ONE MODEL

About 30 years ago, British meteorologist Edward Lorenz raised a fundamental question: whether the earth's climate was stable. But this problem has acquired special urgency now when large-scale anomalies have reached a climacteric point.

We believe that the simplest models, taking the global thermal and water balance into account, should give a tentative answer to this question. But in the earlier theories developed by the Americans William Sellers and Barry Saizman, and Academician Mikhail Budyko of Russia, the water balance dynamics was neglected, and for this reason the problem of stability defied solution.

We have pioneered a global climate model, containing three variables: the temperature of the low atmosphere, dry land's moisture capacity, and river runoff into the world ocean. The model consequently consists of three non-linear equations: two relate to the dynamics of the earth's heat and water balance, and the third-to the dynamics of global river runoff into the world ocean. The assumption that the amount of water on the planet is constant has allowed to exclude the ocean's water balance from the model.

To begin with, let us consider the earth's heat balance. It has long been proved that the planet reflects back to outer space a significant part of the energy it is getting from the sun- otherwise, our planet would have burned up long ago. The reflected energy is a highly variable factor since it depends on the state of the earth's surface. The overall mass of ice and snow on dry land and of clouds in the sky, world ocean area, the degree of dry land's humidity and the nature of vegetation-all this affects the amount of solar energy going back to space. We believe the key to the climate problem lies in the understanding of the mechanism of the earth surface's refractory capacity, which is characterized by the albedo (from Latin albus- white) factor-a correlation between the value of reflected energy and that of incident energy.

Our planet is so structured that of all the natural substances water has maximum heat capacity and the greatest solar energy absorption capability. For instance, the heat capacity of deserts is equal to 0.8-1, and that of the ocean-4.18 J/g; the albedo of deserts-0.28, that of the ocean-0.06. The best albedo reflectors are glaciers, and the worst-oceans; with clouds this index varies in a wide range from 0.29 to 0.86.

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Thus, dry land's albedo is one of the major parameters of the earth's climatic system, showing how much of the solar energy is absorbed by the terrestrial surface. This factor heavily depends on the type of soil, its color and structure, humidity and vegetation. For instance, the albedo of peat weakly podzolic supersandy soil is equal to 0.18-0.24; of humid soil-0.16-0.18, wet land-0.11-0.16, land soaked through-0.08-0.11. The effect of vegetation is best illustrated by the following figures: the albedo of tundra-. 15), that of plains- (0.20), that of coniferous forests (0.14); the albedo of cotton fields (0.20-0.25) exceeds that of rye and wheat fields (0.10-0.20).

It is possible to estimate how a change in the albedo of dry land affects the planet's thermal balance and its global temperature. On dry lands under contemporary climatic conditions soil humidity in a two-meter layer is low, averaging 10 percent, and this means that the water layer is 0.2 meters thick. Let us assume that the humidity of the soil cover of the earth (82 million square kilometers), and of the arid and semi-arid territories (31.3 million square kilometers) has increased by 0.1 m. Then the albedo of the "earth-atmosphere" system decreases by 0.01-0.02, which makes global temperature rise by 2.3-4.6C. In real terms, this calculation is even underrated: for higher temperature causes more steam and carbon dioxide which well contain the thermal radiation of the earth's atmosphere and contribute to its greater heating.

Now, if humidity is small, the albedo of dry land changes so abruptly that even the slightest fluctuations of land humidity must cause significant albedo and, consequently, temperature fluctuations. A global air temperature rise entails higher air humidity (a warm atmosphere has more steam) and more intensive world ocean evaporation, which, in turn, is conducive to precipitation on land. If temperature further mounts and mainlands

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become more humid, vegetation will grow profusely (for comparison: the productivity of Thailand humid-tropical forests-32 tons of dry mass per hectare, whereas in Mongolian desert lands it amounts to only 2.4 tons). Such tendency leads to a still greater decrease of the land albedo; the amount of absorbed solar energy increases as a result, sending temperature and humidity further up.

However, the moisture capacity of land can be inferred from the equation of the global water balance of the earth in the context of our model. Thus, the strong dependence of the albedo of land on its moisture capacity renders the earth's thermal balance unclosed and makes it necessary to monitor the water balance (the second equation of the model). And the water balance value, in turn, depends on the dynamics of the river runoff into the World Ocean. To describe this process the third equation of the proposed model is essential. This equation rests on the law of energy change: with the land waters movement toward the ocean the gravity-activated power is expended on overcoming the forces of friction and on increasing the kinetic energy of the river runoff.

Composed of the three equations, this simplest climate model belongs to a category of non- linear dynamic systems. We have analyzed the stability of its solutions, which proved very complex and unstable. The reason for this is that thanks to precipitation, the rate of accumulation of land water reserves exceeds that of their depletion on account of river runoff, and a rise in land humidity, as has been said already, decreases the earth's albedo. Furthermore, positive feedback takes effect, leading to an unstable climate. What this actually means is that our planet is constantly overcooled (the glacial epochs, the cooling of the climate) or is overheated (with warming and humidifying effects, and the profuse growth of vegetation-the regime of a "humid and green" earth).

Climate instability arises when planetary albedo and evaporation decrease with a humidity and precipitation increase, and with a temperature increase. Other thermal feedbacks can only lower the critical threshold of instability but cannot cancel it. The situation can be stabilized by water feedbacks: for instance, the growth of evaporation and river flow depletes the moisture reserve in soil and prevents albedo from further decreasing.

In this connection we may wonder: how the hypothesis about the ostensibly irrelevant notion of

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"a thermal threat" for the earth, suggested by Dr. Oleg Sorokhtin (the P. Shirshov Institute of Oceanology, RAS)(*), will work, if we consider water feedback as well? Indeed, the growing evaporation produces more clouds and, consequently, sends the planetary albedo factor up, and temperature down...

But the dependence of evaporation on moisture reserves can also be a cause of contemporary climatic instability. A positive feedback is at work here: the less continental the climate is, the cooler is the summer, the weaker the evaporation, and the greater accumulation of moisture on drylands; all that diminishes temperature fluctuations still more. Apparently, such a feedback mechanism is typical of Europe and the Americas where precipitation exceeds evaporation, and land is well moistened.

A MECHANISM OF CYCLICITY

The model suggested by us demonstrates not only climatic instability: it can have complex periodical (with a period of hundreds of years) solutions with a slight change of temperature (1-2 C), land moisture reserve, and river runoff. In other words, according to our model, not only global warming but also global freezing is possible due to absolutely natural processes. Perhaps it is these cycles that have manifested themselves in the world climate changes over the last 420,000 years as proved in the 1980s and 1990s by Russian-French- American explorations of the ice core, mined from a super-deep (3,623 m) well at the antarctic station Vostok.(*)

The physical mechanism ofcyclic-ity can be described as follows. As we have said, the humidification of land leads to a decrease of the earth's albedo and to a growth of mean annual air temperatures through greater absorption of solar radiation. Thorough calculations (carried out by taking general atmospheric circulation into account) showed that a 1 degree global warming builds up atmospheric precipitation by 1.6-2.6 percent or by 2-3 cm annually, with a dependence between mean temperature indications and the amount of precipitation being essentially nonlinear.

Thus, a powerful mechanism of positive dependence emerges: while land moisture grows, the global albedo decreases, raising the mean

*See: "Global Warming: a Hoax?", Science in Russia, No. 3, 1999.-Ed.

*See: V. Kotlyakov, "Antarctica Reveals Its Secrets", Science in Russia, No. 1, 1997. -Ed.

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air temperature and evaporation from the World Ocean surface. Since the World Ocean is the main source of land moisture, the above mechanism contributes to precipitation and land moisture. However, the land moisture capacity cannot grow infinitely: its surplus quickly transforms into river runoff, and thus land moistening discontinues. The process is reversed then-the climate starts cooling off globally. Mainlands reflect more solar energy, the temperature of atmospheric air and precipitation decrease-a cold and dry epoch with a more pronounced contrast between temperatures in the equatorial and polar regions sets in. But then land retains the diminished amount of precipitation, the moisture capacity grows, the albedo factor falls, and thus the climate becomes mild with a relatively small margin of temperatures at the equator and at the poles. Then the whole cycle is repeated. In our view it is this nonlinear mechanism that prevents the climatic system from making the earth "white", that is, when its surface is wholly covered with ice and snow. Of course, in theory a "white earth" is possible; yet in practice our planet has never experienced such kind of situation over billions of years of existence.

There are nonlinear mechanisms that restrict the growth of moisture capacity on land surface and of global temperature, thereby stabilizing the climatic system. For instance, a higher temperature causes more thermal energy to escape into outer space, which can arrest the temperature growth. Or take this observation: the growth of moisture capacity saturates the albedo dependence (indeed, in any event, the albedo factor of land cannot be lower than that of the ocean), and its decrease becomes ineffective.

But there also are nonlinear mechanisms that are conducive to global warming. For instance, as has been said, the growing concentration of steam and carbon dioxide in the atmosphere contributes to more intensive absorption of heat radiated by the earth, and, consequently, to its heating. There is yet one more significant mechanism that should be mentioned: when the climate on the planet gets warmer, its snow and ice cover inevitably shrinks (a temperature rise by one degree decreases this area by 3 million square kilometers), the planetary albedo goes sharply down and temperatures up.

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The cited mechanisms, in our view, can act jointly (in synergy). Consequently, simultaneous processes: a decreasing planetary albedo (because of the increasing soil humidity, growing vegetation and the shrinking snow and ice cover), and a higher concentration of basic hot house gases (water steam and carbon dioxide) may touch off a rapid melting of continental glacial shields. This explains the phenomenon of extremely abrupt warming periods, which, according to paleo-climatologists, repeatedly occurred in the distant past. For instance, the thorough calculations of the land albedo carried out for the early Pliocene (about six million years ago) showed that it was then 0.06 lower in the Northern Hemisphere than now. Paleodata indicate that the climate of that epoch was warmer and damper; in the medium and high latitudes of Eurasia and North America, the vegetation cover was distinguished for greater species variety with forests spreading to the northern coasts of the continents and south of the border of the modern forest zone.

TOO MUCH WATER

Research carried out at the State Hydrological Institute of the State Hydro-Meteorology Committee shows that at present the amount of water on a vast territory embracing the European part of the former USSR and West Siberia is increasing. Data obtained by seven water-balance stations has provided an insight into the causes of contemporary changes of the water regime of rivers and enabled us to analyze hydrologic cycle processes. Situated in the forest and steppe zones of the East European plain, these stations have been monitoring all hydrologic cycle elements for about 50 years now. Their data on moisture circulation processes suggest the following conclusions:

First, total annual precipitation has considerably increased (up to 50-120 mm) in the last 10- 15 years, especially in the summer-autumn period.

Second, increasing precipitation takes place under the conditions of higher temperatures in the cold period of the year and somewhat lower temperatures in the summer season.

Third, due to the moisture increase, the concentration of water in a meter-thick soil layer has risen by 10-30 mm.

Fourth, as a result of this situation, favorable conditions are obtained for the seepage of underground waters, and thus the levels of the main water-carrying horizons are up by 50- 100 cm.

Fifth, the underground water reserves have increased, and so has the underground seepage of rivers.

Still earlier, it was found out that in the basins of the Volga, Dnieper, Ural, and Ob rivers the underwater flow increase in 1978-1990 reached 20-40 percent of the norm. The Caspian Sea level was rapidly rising then too.

The key indicators of the water mechanism of global warming are these: higher evaporation from the World Ocean surface; abundant precipitation on land; bigger volumes of underground water and greater concentration of water in soil. Indeed, in the last few years, evaporation from the ocean surface has grown by 4 percent, and so has the amount of atmospheric precipitation on land; the volume of underground water in 1985-1990 was increasing at a rate of 593 cubic meters a year. As for the soil moisture, its concentration in a meter-thick layer of the soil in Russia's European part grows at a rate of 1 -3 cm every ten years (according to the data of the State Hydrological Institute).

SOME HYPOTHESES

The detected thermo-physical mechanism of the global heat and water imbalance invites the following quite plausible hypotheses for explaining some climatic phenomena:

- the observable global warming is a consequence of the increase in solar energy absorbed, i.e. progressive weakening of the land albedo;

- annual close-to-surface air temperatures, especially at medium and sub-polar latitudes, decrease during warming at the expense of mounting moisture reserves and the heat capacity of land, which, for this reason, warms up less in summer and cools off less in winter with the earth's continental climate becoming less pronounced;

- the non-glacial, warm and humid state of the biosphere, for which the Cretaceous Period was noted, was determined by the lower albedo of the planet thanks to the spread of the vegetation cover and increased soil humidity;

- the prevalence of the non-glacial period in the history of the earth is explained by its greater stability as compared with the glacial period, in which sharp planetary albedo changes were common;

- and last but not least, the concentration of carbon dioxide in the atmosphere increases owing to the earth surface heating (a warm ocean absorbs gas worse than a cold one).

So the threat of global warming is a real thing. However, according to our model, it is a consequence of natural processes rather than the result of hydrocarbon fuel combustion as it is assumed now. A reduction of carbon dioxide discharges into the atmosphere, as scientists are urging, will hardly bring global air temperatures down.

This work has been financed by RFFI (grant No. 99-05-64905) and by the program of support for Russia's leading scientific schools (head-Academician Martin Khublaryan, grant No. 96-15-98355).