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When we speak of the ocean, our imagination pictures boundless water expanses, fierce storms, mighty waves and currents, and what not, all that over thousands and thousands of kilometers. As to scientists, they seek to apply the Procrustean bed of mathematical, computer-simulated models. One such model has been developed by a research team under Academician Artyom Sarkisyan. Our correspondent has interviewed him, and here's the transcript of their conversation.

- Now, modeling the dynamics of seas and oceans looks like an imponderable, puzzling problem indeed. What will we get by solving it?

- Occupying three quarters of the earth's surface, the World Ocean impacts the weather and climate on our planet, not to speak of its coastal territories. The oceanic water mass with a mean temperature of +3.8 o C is 300 fold larger than that of the atmosphere, its mean temperature equal to -17 o C. Besides, the water's specific capacity for heating is three thousand times higher than of the air. The Gulf Stream alone carries far more water than all the rivers combined. Seas and oceans are also an area of major transportation routes, and a depositary of colossal biological and mineral resources. So our interest is quite legitimate.

- This vast natural object has been the target of intensive studies by many scientists for quite some time, by means of research vessels and orbital spacecraft too. But what about mathematical studies and their role ?

- Orbital craft are supplying as good as synchronous information on the World Ocean's surface. Thousands of buoys are providing data on wind velocity, currents, water temperature on the surface and at definite depths. Research parties, for one, those arranged by the P.P. Shirshov Institute of Oceanology (of Russian Academy of Sciences), are furnishing a wealth of data too. However, this huge, everchanging data array can be optimally visualized only in the form of mathematical models from which ocular computer maps are made then. Our chief goal is to solve systems of thermohydrodynamic differential equations giving an insight into the laws of conservation of mass and energy relative to particular sea and oceanic basins. Simple problems are tackled by ordinary computers; but in most difficult cases we use the supercomputer of the RAS Computing Center.

- Well, to model the dynamics of the World Ocean and make forecasts-be it only short-term forecasts-is not enough if we proceed from surface processes alone. It is important to know vertical movements of water masses and energy flows. How do you correlate all that?

- Let me say first of all: we have but rather scant data on deep-sea regions. More or less reliable data are on the subsurface layer to a depth of one kilometer only. Buoys that travel on different horizons rise to the surface at regular intervals to transmit data to an orbital satellite and then go under again. In the past fifty years or so research vessels have often been exploring oceanic depths to 2 km. Many countries have joined forces in a full-scale international program on studying the circulation of the World Ocean. In addition, a research team under Academician Guri Marchuk worked on a long-term experiment ("Sections") back in the 1980s. Research parties involved in that experiment would make measurements in ocean depths within most active and characteristic regions. We extrapolate the materials thus obtained, in the form of mathematical equations, on the entire depth, down to the floor. We fill in data gaps by means of computations.

- But we, landsmen, are more interested in processes occurring on the ocean- atmosphere interface-the processes that impact the climate and weather on the continents. Weather reports often mention cyclones or warm air masses coming from the Atlantic. To what extent are weather forecasts possible? Maybe in-depth and costly studies of the entire World Ocean are needed for that. Perhaps we can well do with space observations alone?

- Regular observations from research vessels are quite costly indeed. That's where the advantage of mathematical models lies: they allow to cut down on the workload and focus on most important, key areas. For instance, the "Sections" Program zeroed in on the Norwegian, Newfoundland and tropical zones, and on the Gulf Stream, that is the Atlantic. Here we have the most intensive heat exchange between the atmosphere and the ocean, and we observe a high velocity of currents, all that impacting the air movement. Short-term weather forecasts for a few days ahead rely largely on direct meteorological observations, though even in this case a mathematical processing of the

Pages. 14

A-mean perennial value of Gulf Stream velocity (cm/s) calculated on mathematical model; B-Gulf Stream vortexes at concrete moment of time; C- anomalies of free surface values (cm) in the North Atlantic according to satellite observations as of June 3, 1996. The relief reflects the impact of cold cyclonic (blue spots) and warm Anticyclonic vortexes.

materials is carried out too. But such data do not suffice for medium-range forecasts. Atmospheric whirlwinds may be 100 times as large as oceanic whirlpools. Yet the former continue for 5 - 10 days as a rule, why the latter-the oceanic vortexes-persist for months and even years, and have a significant effect on the temperature, humidity, velocity and direction of air streams. In energy-active zones there occur quasistationary (changing but little) anticyclonic whirlpools penetrating into the water to a depth of 500 m and more. Such vortexes operate like accumulators collecting heat in summer and giving it off in winter... In short, a mathematical model of the World Ocean's dynamics should take account of all too many various data so as to furnish a picture describing in ever greater detail the interaction of the ocean with the atmosphere for subsequent forecasting. Observable parameters are but the start-out material, while weather forecasts can be made only with the aid of equations we are out to solve.

- Over these past hundred years the science literature-popular science literature in particular-has been giving much attention to regular fluctuations of the climate and weather, which are often associated with solar rhythms. Mathematical models should identify such periodic processes quite definitely. For example, the notorious El Nino current off South America's western coast is thought to be much responsible for weather changes. * Don't you see some

* See: V. Syvorotkin, "Where from, Enfant Terrible?", Science in Russia, No. 3, 2001. - Ed.

Pages. 15

A model of the World Ocean's currents to a depth of 50 т developed at the PAS Institute of Computing Mathematics. Scale to the right, velocity in cm/s.

kind of regularity here, say, fluctuations of a cold current?

- Oh no, not at all. The full name of this natural phenomenon is El Nino de Novidad, of "nativity infant", it relates to the time when this very phenomenon was first observed most conspicuously. That happens rarely indeed.

- There have been press reports on a mathematical model of the Pacific dynamics that helped predict El Nino's comeback...

- Foreign experts made this forecast in January 2002 with a good deal of uncertainty, for 3 to 6 months ahead. The RAS Institute of Computing Mathematics has carried out with much success a numerical experiment on modeling the El Nino phenomenon. This model shows no more than the interaction of processes taking place in the ocean but has nothing to say about their cyclic nature. The authors of pop science literature tell us: "There came the warm current El Nino, the weather became hot, and the fish started dying out..." Yet the primary cause of this phenomenon resides above all in the dynamics of the atmosphere. If there are no stable winds driving the warm surface waters off the Chilean shores, these waters stagnate and heat up. The amount of oxygen and nutrient substances in the upper layers of the ocean decreases, the fish perishes en masse, and next go sea birds feeding on fish. The "nativity infant" is not the culprit, the blame is on the absence of winds to drive warm waters out. Researchers, who study and model the dynamics of the World Ocean, have no doubt: El Nino and related phenomena do not follow a rhythmic, periodic pattern.

- So a give-and-take: the atmosphere acts on the ocean and conversely...

- Yes, within a short-term framework. But sea currents, as Alexander Voyeykov, an eminent Russian climatologist and geographer, has put it, are global heaters. Say, without the warm "breath" of the Gulf Stream the mean air temperature in St. Petersburg would have been 20 to 30C lower. It is thanks to the Gulf Stream that the Murmansk port is ice-free all the year round, unlike the Mariupol port on the Black Sea, which is 3 thousand kilometers to the south.

- So, in spite of the enormous volume of information on the ocean and atmosphere dynamics, and in spite of the most sophisticated mathematical models, we still cannot hope for any major accomplishments in exact weather and climate forecasting. You see, no distinct rhythms of weather and climate changes have been discovered, while air circulation is rather fickle.

-I wouldn't say that. The point is whether our models are adequate to real processes or not. We can make a weather forecast for one, two, three days ahead without taking into account the ocean's impact. But we cannot do it for a longer period because a good deal depends on heat anomalies in the ocean. We should find out why and how they occur, how they interact with the atmosphere; this is a rather complex mechanism. For example, heat transfer accompanies evaporation: the water vapor is carried into the atmosphere and releases its heat. Precipitation may occur in quite faraway regions of enhanced humidity. Modeling such events mathematical-

Pages. 16

A model of the World Ocean's currents to a depth of 2,500 т developed at the RAS Institute of Computing Mathematics. Scale to the right, velocity in cm/s.

ly, we can come up with better weather forecasts for weeks and even months ahead.

- Nevertheless, long-term forecasts are still problematic, and it looks they will remain so in the future as well.

- The situation is going to change, I think. Computer technology has been developing by leaps and bounds in these last few decades. We cannot tell what is going to happen to it in five or ten years, to supercomputers in particular. Half a century ago, when I first started using digital methods on electric computers, the rate was from 1,000 to 1,500 operations a day. But a modern computer does a billion operations a second.

- Now what is the essential difference of your mathematical model of the ocean dynamics from other models?

- I've managed to prove: the velocity and heat exchange of sea currents depend on the cumulative action of the floor relief and density gradient. It was an uphill fight to me. It was no simple matter to have my conclusions published.

- Such regularity is obvious for shallow waters. But what about deep waters-two, four and more kilometers deep ? Do relatively small changes in the floor relief have any effect in that case too?

- Depth has nothing to do with that. A floor relief slope always affects the dynamics of all water layers, no matter how deep. The gradients of water temperature and salinity, and of the bottom surface are interdependent. Should just one parameter increase or decrease, their joint action will change correspondingly.

- But oceanic depths are thought to be inert and not implicated in the dynamics of surface layers.

- This is wrong. Here we are not dealing with a multiplayer "pie", as geologists will call sedimentary rock. Even if it moves slowly, water should come either up or down a mountain slope. If it comes up, a vertical velocity maximum will be in the lower part of the stream, but it is horizontal velocity in surface layers. Strong currents may occur above the ocean floor too, washing away sediments here and there without a trace. Say, if the velocity of the Gulf Stream on the ocean surface is something like 1 m/s, and only a twentieth part of it above the bottom, this value is still rather high.

- That's one point of your model. What else?

- My calculations of the velocity of currents depend essentially on observable temperature and salinity values, with these data collected not only from the surface and subsurface layers (most models are based on that), but all through water depths.

- Atmospheric pressure changes also affect the ocean dynamics?

- Abrupt pressure differentials do-if caused by hurricanes, deep cyclones and like that. But sluggish differentials at mean monthly and yearly values do not. The effect of wind is more pronounced. Experts will tell you: the weight of the atmosphere is equal to that of a ten-meter-thick layer of water. Even a few centimeters count here where changes are concerned. Now, the wind can raise the sea level by a meter. I do not mean waves that may be higher than that, I mean the magnitude of a stable pileup. Yet such phenomena are rather brief on a local scale, they do

Pages. 17

Movement of buoys on the surface of the World Ocean from 1978 to 1998. Blue dots-initial position; red lines-movement trajectory.

not exert any tangible effect on the dynamics of the World Ocean. But it's a different matter if we take water temperature and salinity-a large amount of data is now available here. There is also a good data array on the velocity of the Gulf Stream. But even in this case a mathematical model should take into account, as a minimum, the temperature and salinity values of the entire Atlantic and of the World Ocean at large. More than that, we have to know the horizontal and vertical velocities of currents. You cannot draw up maps from factual data alone, you can make them by modeling only.

- You have made maps like that?

- Yes, we have. Jointly with my pupils we have drawn maps of the ocean surface and 30 horizontal planes of the deep.

- But the ocean dynamics is change-prone.

- That is why we have made maps of seasonal and mean monthly currents for the World Ocean and, in particular, for the Black, Caspian and White Seas. These maps incorporate water temperature and salinity data collected over many years.

- Does all that help in bettering short-term weather forecasts?

- It does not, unfortunately, and there is hardly going to be any change in this situation soon. You must act quickly in collecting a required volume of information. Say, if you want to know all about ocean currents in a few days from now, you must proceed from adequate data at least for the past week. But such data are not available so far, and it's hard to say whether they will ever be someday. The condition of the atmosphere, however, is a quite different thing. On land surface, many meteorological stations are conducting observations to supplement data from orbital spacecraft. Every day balloons are sent up from many points of the globe to register the vertical parameters of the changing air envelope. This body of information is computer- processed.

- Still and all, weather forecasts do not always come true.

- Mistakes and inaccuracies are possible of course, because one cannot take in all of the global and local factors that go to make the weather. But what of the ocean dynamics prognosis, with scant and disparate data obtained at different times!?

- Modeling the World Ocean dynamics is a highly laborious job. Theoretically, it enables a better understanding of the two great envelopes of our planet, the water and the air envelopes. But what is the practical use of such studies?

- This is a grandiose task indeed- providing a full mathematical description of the ocean/atmosphere interaction. Then we shall be able to predict weather and climate changes, sea currents and other processes with better fidelity. The model developed by the RAS Institute of Computing Mathematics can be of much help to navigators of the Northern Sea Route: in winter they should know when the ocean will be clear of ice, and in summer-about the onset of icing. Now let us take fishing. Fish schools prefer frontal zones in the ocean where temperature and salinity differentials are rather high horizontally. Deep-sea waters rising to the surface bring oxygen and feed for the

Pages. 18

A plot of ocean water temperature deviations from mean values off South America's eastern seaboard from 1950 to 1998, showing an increase of El Nifto and a decrease of La Nina ("little girl", or inflow of cold waters).

plankton and all the way down the ecological food chain. This is the phenomenon of upwelling. Such regions are usually the target of commercial fishing. It is highly important to know when and where upwelling takes place. It arises through the interaction of the atmosphere with the ocean. Most frequently, cold waters rise up if the warm waters are blown off by wind. In turn, major movement of air masses depends on the condition of sea water areas. Needless to say, a mathematical model cannot supply a seiner's captain with absolutely correct coordinates of a particular site promising good catches; but it is quite possible to tip him off about fish-rich areas like that.

One more practical aspect: for ships out on the high seas it is important to have optimal routes taking account of the weather, sea currents, choppiness and other related data provided by orbital craft.

- Now one private question. You, a native of the land-locked Nagorny Karabakh region in Azerbaijan, are working on a model of the World Ocean, which means you are an oceanologist in fact. Any dreams of the seas in your childhood and youth ?

- No, I had no dreams like that. I developed an interest in mathematics in my early years. I am not alone in the modeling of seas and oceans- this job is done by a group of experts of the RAS Institute of Computing Mathematics where I am working. As to me personally, on leaving high school I became enrolled in the Department of Physics and Mathematics of Baku State University. At that time the national Academy of Sciences was recruiting students to a post-graduate school and, as an A-grade student, I went to Moscow and was assigned to the Institute of Geophysics. Yu. Bulanzhe, a geologist and geophysicist (he is Corresponding Member of the Academy of Sciences) did not beat about the bush. "We need mathematicians", said he.

- Did you take part in expeditions?

- Now and then. I've been to the Pacific, the Sea of Japan and the White Sea. It was useful to me to see the main at first hand and get to know observation methods. But I've never been interested in the romance of sea voyages, my sole interest was in mathematical problem solving related to the study of the World Ocean.

- At one time you headed a research group of the Russian Academy of Sciences that conceptualized a federal goal-oriented program on the World Ocean. Just a few words about the program.

- It involved more than 40 scientists of this country. Its significance is very great indeed. The realization of this program will allow to rationalize sea hunting and fishing as well as navigation; it will fortify our country's sea defenses, and ensure better protection of the population, especially in the coastal areas, against natural calamities. Unfortunately, the present state of our economy does not make it possible to gain a good economic effect (excuse this pun!).

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WORLD OCEAN'S MATHEMATICAL ANALOG // London: Libmonster (LIBMONSTER.COM). Updated: 07.09.2018. URL: (date of access: 23.04.2021).


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