Федотов Валерий Павлович (matholimp) wrote,
Федотов Валерий Павлович

The Dynamics of Hydrographic Changes in the Basin of Lake Ladoga in the Past 25 Centuries

Под катом - те же тезисы (см. http://matholimp.livejournal.com/650954.html#cutid1 ), но по-английски. Буду весьма признателен англоговорящим френдам за указания на переводческие ляпы.

Lake Ladoga and its drainage-basin is one of few places on our planet where even in the historical period hydrography has changed drastically. Only a thousand years ago the lake was just the continuation of the Gulf of Finland. Until the beginning of the Great Northern War Swedish ships passed freely from Vyborg to Kexholm. Two hundred years ago the Vuoksa river on Kiviniemi threshold flew as fast in the opposite direction.
I tried to reconstruct the process by using the methods of mathematical modeling and taking into account historical artifacts. The key questions is what could the outlines of the coast of Lake Ladoga and other lakes be like depending on the level of water in them and how did they change?
As is known, the northern and southern shores of Lake Ladoga are on the different tectonic plates, that causes changing the height of their reciprocal position (among themselves as well as regarding the level of the ocean). To indicate these heights I introduced two functions h1(t) and h2(t) with the time t for the argument.
Stating the values of h1(t) and h2(t) for each specific t allows us to build the family of level lines F(x,y)=H (altitudes of the locality place above the ocean level – they are horizontal lines of the physical maps), one of them corresponding to the border of the lake. The third function H(t) is choosing the value H of the difference in altitudes between the water levels in Lake Ladoga and the Gulf of Finland at each moment of time. Clearly, depending on the configuration of the whole system of level lines, in some cases there was no alternative left but zero for the third function.
First of all, I considerated the model in which the functions h1(t) and h2(t) were linear. Since their variation during the last 25 centuries is approximately known from the works of historians and geologists, so in this case the functions h1(t) and h2(t) restored by no means. This model wasn’t confirmed as the conclusions made on its bases didn’t correspond to historical facts at all.
Moreover, for the same reasons the models in which the functions h1(t) and h2(t) kept theircontinuity were not confirmed either. Spasmodic changes in the functions h1(t) and h2(t) assume their only interpretation as the result of catastrophic earthquakes. Analyzing the works of specialists, I found out that the northern shore of Lake Ladoga was situated in the zone of high seismic activity. Alexander Dumas witnessed one of them. He left its detailed description in his memoirs [1]. What is much more important is that earthquakes registered from 7 points or more can happen here through rather seldom (twice a thousand years on the average).
Therefore, the functions h1(t) and h2(t) are piecewise linear in the simplest of the models available. They have relatively a small finite number of strong jumps. Since during the intervals between them these functions are almost constant (they have a derivative close zero), the requirement of their linearity during this intervals does not lead to a loss of the generality.
It was the continuity that proved to be the only a priori requirement for the function H(t). indeed in case of environmental disaster the drop of water levels in Lake Ladoga could not happen instantly and taking into account relatively small range of changing the function H(t) not be too fast.
Requiring the linearity of the function H(t) is absurd, since there is no reason for speaking about its monotony. However, requiring its piecewise linearity (without jumps) is quite reasonable).
The conclusious obtained were compared to historical maps and records in the Russian and western chronicles. The historical facts were assessed as to their authenticity [2].
Historians found a number of documents and evidence to be erroneous. For example, the assertion of Herodotus about the location of the Northern Ocean in the place of the present Baltic Sea is also considered to be erroneous. Another alleged error is the lack of Lake Ladoga on many carefully drawn maps of the Middle Ages.
When speaking about the time intervals of several thousand years however, historians acknowledge significant changes in the outlines of continents and hydrography. But such changes took place constantly including the most recent period. So the “errors” mentioned above are perfectly conformed to the geological facts in Karelia.
To begin with, they allow us to conclude that there was a sea strait connecting the Baltic Sea and the White Sea 25 centuries ago. Later the sea went back. The northern part of Lake Ladoga is most likely to have remained the sea bay till VI-IX centuries AD. It was connected with the Vyborg bay by the Karelian straits. The medieval Danish chronicler Saxo Grammaticus described the grand battle for Karelian straits.
About two years ago I visited the place where that battle had probably occurred. Owing to the considerable land rising, the place was much higher than the present sea level. The first root in the name Linnalichki of the rock proves the fact that there was a city there, although there is no direct evidence about this city in any annals.
Twelve and a half centuries later, a wide gap in the rock was overgrown with trees. However, at the time of the battle the rock had been bare. The natural corridor gave a chance of quick, easy and imperceptible passing from one side of the island to another.
The ancient Karelian capital also protected this straits. The great Russian artist Nicholas Roerich who lived in the estate Tervu of the philanthropist S.Gurevich in 1917-19 found the ruins of this town on the neighbouring island Linnasaari. Since Roerich discovered this place on the eve of his emigrating to India, and the very land itself “emigrated” to Finland for 22 years, the place had to be rediscovered in the posthumous publication of Roerich’s archives [2].
In summer 2009 an archeological expedition led by S.Kochkurkina worked on Linnasaari. The remains of the foundation of an ancient building were found then.
The town arose on the island not later then in the III-V centuries AD, and in the XII century it fell into decay. The fact almost half (6 out of 16) points mentioned in Novgorod-Swedish peace treaty of 1323 were in immediate proximity to Linnasaari shows how important the place for both countries.
A fundamental question is the one of the age of the Neva River. Historians and philologists are unanimous in asserting that the meaning of the name Neva is “New River”. The question is how “new” it is [3].
Geologists suppose it is from a thousand and half to 7 thousands. Most often it say it is about 3 thousand years old.
I venture to assume that the Neva is half younger than the minimal of these values. By a way, the first record about the Neva River dates back to 1228. In any case, Neva can’t arisen before the VI century AD.
The analysis of the depth of Lake Ladoga and its comparison to Mercator map of the end of XVI century draws a very interesting conclusion about the breaking of the Neva River. If there is a “channel” of more than 20 meters deep near the southern shore, then in the north it is separated from the rest deep part of the lake by the wide stripe of 5-8 meters deep extending from the mouth of the Obzha on the eastern shore to the month of the Morya on the western shore. The origin of the stripe is beyond any doubt. Since Lake Ladoga and Baltic Sea were originally the single water reservation, the water level was just 5 meters lower and the stripe was a spit like the ones of Visla or Neman.
When it became a lake, at first Ladoga was connected with the Gulf of Finland by the flow to Vyborg. It couldn’t provide the force of water necessary for breaking. As long as it remained the sea bay, there was not any height drop.
It was the spit that played the role of a dam owing to which there appeared the conditions necessary for breaking. It is important to empliasize that in some periods the spit entirely separated the southern part (ancient “Lake Nevo”) from the rest lake. So it is possible that the level of water in a little Lake Nevo had the height about 10-20 meters regarding the level of the ocean (and northern part of Lake Ladoga). If it had not occurred, the deep “channel” of over 200km long could not have arisen.
The reason for its forming is the flow of large volumes of water from the Volkhov, Svir, Syas and other rivers, separated by the spit from the main lake, into Neva. Most probably the spit had the shape of a chain of islands in the Middle Ages which served as a barrier tj navigators. These islands can be found on the ancient maps.

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Здесь не нужен обширный исторический экскурс, но небольшое введение я считаю не лишним. Прежде всего, я вспоминаю лично прослушанные на ФПК в МГУ лекции великого математика Арнольда по теории катастроф. Одним из примеров он назвал превращение маньяков в гениев (и обратно) в науке. История науки…
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