Rapid progress of computer technology over the past few decades has opened up broad horizons for using mathematical methods in theoretical studies of the World Ocean, atmosphere and climate.
Progress and achievements in this field have been described in an interview given to our correspondent Rudolf Balandin by Acad. Valentin Dymnikov, Director of the RAS Institute of Computing Mathematics (IVM).
- Valentin Pavlovich, quite recently it seemed to be impossible to build, for example, a mathematical model of the climate of the Earth. Because what we are dealing with are the dynamics and characteristics of air currents propagating over the seas and oceans, tundras and forests, mountains and lowlands, in the tropics and icefields of Arctic and Antarctica. What intellectual potential has to be brought into action in order to try and represent all of these factors in the form of a common theoretical system, in computer diagrams which can make it possible to prognosticate various global phenomena ?
- Speaking about our own Institute, we do not have a large staff-only 62 people, including the management and not counting the post-graduates. This is how it was planned 23 years ago by Academician Guriy Marchuk. He set his sights not on the number of researchers, but on their high rating and what are called "basic" chairs of the Moscow University and the Moscow Physico-Technical Institute (FIZTEKh). Studies were conducted with their support and the organizational idea was successfully realized. At the Chair of Mathematical Modeling in FIZTEKh there were in some years up to 90 students and 30 postgraduates. Today about half of our staff have degrees of Doctor of Sciences and 6 are Members of the Academy of Sciences.
- Formal statistics are really impressive. But what about the actual state of affairs now?
- A fair measure of that, for example, are prestigeous awards. In 1999 the Academy Presidium established a gold medal and a prize awarded to budding talents on an annual basis. Out of nine areas of research-oceanology, physics of the atmosphere and geography-over a period of 4 years 2 awards were won by FVM researchers. They also get grants and, naturally enough, constantly defend theses for degrees of candidates and doctors of sciences.
- Does the credit for that belong to their tutors?
- The way I see it, this is above all thanks to our intellectual atmosphere which encourages creativity. And one important feature of our organization of labor: we have no traditional laboratories and sections. There are research projects and members of the staff can choose and change their objects of research. At the end of each year we conduct what we call review sessions at which everyone-from a second- year postgraduate to an academician have 30 minutes to report on what has been done over the period under review. This helps tighten the discipline.
- And what about the brain drain in your center which is so painful for our science?
- Over the past 15 years some 50 of our staff went to the West. Today it is practically impossible to make stay in Moscow a "non-Muscovite", even a very gifted one. As a result our staff has changed appreciably. But, as the saying goes-every cloud has a silver lining. At first I was hurt by such losses, but now I even try and help young people getting jobs abroad. This helps maintain contacts, exchange ideas and work on joint projects. Apart from that there is always a chance of their coming back-and we already have such examples.
- So, on the organizational side of the matter everything is fine. And what specific studies are being conducted at IVM now?
- Originally we had before us a non-trivial task of "rallying" mathematicians with physicists-something without which it is impossible to solve many applied problems with the use of computers. Something of this kind was done in the past at the Institute of Applied Mathematics then headed by Academician Mstislav Keldysh (whose name it bears now). Its staff had to deal on full scale with problems of cosmonautics. But the specialization of our Institute is different: computing mathematics, theory of parallel calculations, mathematical modelling of various physical processes, in particular, studies and modelling of various physical processes, in particular, studies and modelling of terrestrial processes taking place in the atmosphere, ocean*, in soil cover, permafrost and also the impact of human activities upon them. And there is yet one more area which is associated with medicine, to be more exact with immunology, with decoding human body responses to pathogenic agents-viruses and bacteria.
- You mean the identification of pathogenic microbes at the molecular and cellular levels?
- No, I have in mind another aspect: mathematic description of the human immune system response to virus propagation.
- And which of these areas are you personally directly in charge of?
- Interaction of the atmosphere with the ocean and also modelling of climate
* See: A. Sarkisyan, "Mathematical Analog of the World Ocean", Science in Russia, No. 5, 2003. - Ed.
Maps of zone averaged temperature of the atmosphere.
A - by observations (contour lines; temperature in degree on the absolute scale) as compared with model data. Shown in color are deviations from calculated data observations. On the vertical - atmospheric pressure in millibars (scale is greatly exaggerated), on the horizontal - conventional earth surface to the north and south of the equator.
B - contour lines-data for ICM model.
and its measurements. Take, for example, the air shell of the planet. As we know, this is a very fine shell which is practically impossible to model in the laboratory. While the thickness of the troposphere is of the order of 10 km, it extends horizontally over thousands of kilometers. And the responsibility for transformations of solar energy rests above all with vertical flows of air. That means that at this ratio of scales laboratory studies drop out. And experiments cannot be carried out even in the natural conditions. The only way out is building models of the global climate system.
- But climates of the Earth form a most intricate mosaic which is also variable. Its description requires taking into account millions of parameters. How do you cope with that?
- Only thanks to the remarkable potentialities of modern computer technology. Some quarter of a century ago we could do nothing of this kind, and today digital modelling has reached incredible achievements.
How a mathematic experiment takes place? To begin with, we develop a model, say of the air envelope of the Earth. We build a system of equations in partial derivatives describing the hydrothermodynamics of the atmosphere, transfer of radiation in it (longwave and short-wave), process of condensation (cloud formation) and convection, border layers, horizontal and vertical diffusion and other "energy- significant" processes. Of course we cannot find an analytical solution for this kind of system and therefore have to use this or that method of approximation. And I will not delve into the associated mathematical problems. What is important is something else: we write a program of implementation of the finite-dimensional computer model. And here we again run into problems. Since in the latest models of atmospheric circulation the number of variables reaches - 10 8 - 10 9 long-time count (as required by climatic problems) can be done only on up-to-date parallel computation systems. That means that it is necessary to build parallel algorithm version. And if we begin counting what we want to achieve with arbitrary initial and given "external" parameters (solar constant, angle of axis of rotation, etc.) then after some time the trajectory of the system will gravitate to a certain multitude of states (attractor) where it will be functioning always. Statistical characteristics of the given multitude is climate. At this stage there appear most interesting tasks of studying the structure and stability of multitude-an area which we have called the mathematical climate theory.
- And do the results of your calculations match the reality?
- In general - well enough. I can show you maps of zone averaged temperature and zonal wind according to results of observations and also averaged by all models used in the CMIP international program and that of our Institute. By certain characteristics there is practically no difference between them. And in any respect the achievements are great and there is no comparison with what we had, say, 30 years ago. Let me stress that what we need now is not just describe the current climate, but forecast its changes. And a distinct feature of the method, its convincing proofs: one has to clearly show how and what is reproduced by a model and with what accuracy so that its sensitivity of external impacts be maximally similar to the response of the real system.
- But, naturally enough, you do not conduct global climatic experiments. How then can you verify the accuracy for your results?
- Do not forget that during the past half a century many important atmospheric parameters have been authentically measured and can be used for orientation.
- According to data supplied by the American meteorological station on the Hawaii the levels of carbon dioxide in the atmosphere keep rising. To what extent does this factor match the global processes? They say that such link does exist.
Zone wind maps: velocity (m/s). Other markings - same as on Fig. 1.
And what is shown by mathematical models?
- They bear out the above regularity. Incidentally, this matter is discussed in many publications and there are constant comparisons of global models developed by teams of experts of different countries. And we do maintain with them active cooperation and with complete mutual understanding. But that does not mean that we are conducting our studies only within the framework of international programs. We have a direction of our own and our own approach. But it is nevertheless necessary to compare our results with those of others. And, believe me, we are in an exceptionally difficult situation - we do not possess such advanced technologies as the leading research centers of the West which are ahead of us in the level of computer technology.
- But could it be so that the matter is not only in the technical, but also theoretical superiority of the Western colleagues?
- As often as not the key factor is computer backing. Here is an example: 15 years ago it was necessary to calculate, to solve a certain problem and send the results to Los Alamos. They saw nothing special about that, and we faced a task of great complexity. The Americans were saying: if you have problems, come to us and calculate. And that was exactly what we did in the beginning.
- And why don't you cooperate with other teams like yours working in Russia?
- Unfortunately, it is only our Institute which is working on international programs on joint models. Our federal Weather Service has its Central Geophysical Observatory. Its staff are doing comparative studies of the atmosphere, but without taking into consideration oceanic processes. Therefore we are working now single-handed, and insufficient technical equipment puts upon us what one can call psychological pressure. We are unable now to conduct multiple calculations and then, after comparison of the obtained results present the best of them. And when you do your calculations only once or twice, there is always the chance of making mistakes which will be discovered by your "competitors". A mass of negative emotions! But that also makes you try and do your utmost best. The aforesaid international program provides for a detailed analysis of each accepted model by comparing the results of 30 teams.
- And you in your turn analyze their results?
- Yes, we do, and they supply to us all their data. Everyone is working for the common good. The positive effect is great! Each of us gets timely information about the advantages and drawbacks of his own and also his colleagues. And this cannot be done in isolation. Because a model is complicated: it takes into account millions of characteristics which reflect in mathematical terms the global dynamic system.
- And do you not become hostages of models of such complexity? Even more so since they deny common understanding...
- Yes, this menace is really there. In a certain sense we are forced to keep up in the same direction the colossal work already done. There is nothing you can do about it. In Russia no one is developing technologies of this kind, and our Institute has limited resources. That is why international cooperation is of invaluable benefit for us.
- But you have to rival mighty concerns. Hopefully, you are not lagging behind?
- We are running up front, and are even in the lead by certain parameters. And that however does not concern our technical equipment. Say, the Japanese have developed their Earth Simulator of a truly giant capacity which can model even some concrete cumulus clouds. From the point of view of a classical scientist of the 19th and even 20th centuries this cannot longer be regarded as scientific investigation. Assessed in this case are what we call integral characteristics of dynamics of such clouds and their coordination with different wave, or undulatory, processes.
Maps of ground temperature changes on the planet with rising levels of carbon dioxide in the atmosphere over 20 years by the rate of one percent a year. Color shows mean square deviations by all models.
Maps of changing atmospheric pressure at ground surface with rising CO 2 levels by one percent a year over 20 years.
Color shows mean square variations by all models.
- Can you cite, please, a most interesting example from your experience?
- At the 2003 International Congress on Global Climate Changes they were discussing the problem of sensitivity of the climatic system to external factors, such as rising levels of carbon dioxide taking into account the interaction of the atmosphere and the ocean. They were discussing the following scenario: this factor keeps growing by one percent a year and it is doubled over a period of 80 years. This is about what really happens. And it was necessary to try and assess changes of the global climate over 20 years. They were analyzing, as usual, the results of 30 models. And the scatter happened to be too great-from one degree to 3.5°C at near-ground temperature.
- This is clear enough: if the mean temperature on the planet grows by Г С this is yet nothing to worry about. But if it rises by 3.5° - this borders on a catastrophe. Why is the difference in forecasts so great?
- Our young researcher, Dr. Yevgeni Volodin (Phys. & Math.), observed that in high- sensitivity models which suggested maximum changes of near-ground temperature, they failed to take into account one, apparently unimportant detail: fine subinversive clouds formed in the border layer of the atmosphere mainly at the altitude of 1.5 km. And it proved to be very important.
- And did they take into account the carbonic cycle of green plants? They actively "consume" carbon dioxide and destruction of forests should have a marked effect upon the levels of "hothouse" gas in the atmosphere and, consequently, boost global warming?
- In the model under consideration carbonic biological cycle was not included. Otherwise it would be necessary to make the system much more complicated, build above all a good diagram of the cycle and the chemical processes in the atmosphere, ocean and soils.
- Today everyone is concerned with something else-the probability of a global climatic catastrophe.
- This is no simple matter. Changes of climate on the Earth accrue from two factors: irregular oscillations of its own and those caused by anthropogenic processes. When they are speaking about a catastrophe, they have in mind
Global changes of temperature near ground surface. Averaged data from ICM model. Black line - at constant level of carbon dioxide in the atmosphere. Green line - at an increase of one percent a year. Time - from a conditionally accepted zero.
artificial impacts and they have to be singled out against the background of natural ones. Unfortunately, we do not know yet enough about what "climatic regimes" can the system be present in time intervals of some one hundred years. Therefore, apart from mean values, of say mean global temperature, I also take into account dynamic parameters which also characterize regional variability. We have no long rows of such observations and have to resort to models. And that not only calls for their high quality, but requires considerable expenses.
Here is one example. In the 20th century the mean global surface temperature rose by about 0.6°K, which explains in principle changing carbon dioxide levels in the atmosphere. But regional temperature variations, say in the north of Western Siberia were much greater obviously because of specifics of atmospheric dynamics. But our models do not confirm such changes only on account of carbon dioxide. Other mechanisms should also be taken into account; and most likely what we are dealing with are natural climatic variations.
On the whole our climate system, with its great number of "degrees of freedom" is stable with respect of minor changes of external parameters. And it is important to determine what are these minor changes from the points of view of its response, especially on a regional level. Current studies show: in the next few decades there will be no global catastrophes due to rising levels of hothouse gases in the atmosphere.
- Over the past few decades there have been growing contrasts in our weather and climate*. Can they be dealt with without waiting for "favors" from Mother Nature?
- The question is grounded. Calculations give ground for hopes that we shall be able to develop an appropriate theory with time. Today some American journals already carry articles on this subject, but mostly at the level of general discussions. Thus they suggest learning to "correct" the movements of hurricanes dangerous for the United States. At our own Institute there is a team dealing with this problem but only in a mathematical aspect and not through interference with natural processes. Acad. Nikolai Basov has long suggested "discharging" excessive energy of our atmosphere into space with the help of powerful lasers. As for us, we are studying the possibility of weather control in principle and are solving systems of equations describing the dynamics of the atmosphere.
- As far as I understand mathematical modelling of global processes makes it possible to stage theoretical experiments and judge by their results what can happen to the atmosphere and the ocean. Do you believe that your objective consists in building models which are maximally close to reality?
- Yes, we have to develop a "technological product" which can help specialists to conduct deeper studies of the climate. This should be a very special instrument and a very useful one which would make it possible to "rehearse" different scenarios of natural phenomena. And we are prepared to put it at the disposal of all interested organizations.
Illustrations supplied by the author
* See: G. Golitsyn, "Methane... and Hothouse Effect", Science in Russia, No. 6, 2002. - Ed.