| Introduction. During the first quarter of the Holocene, the Black Sea (BS) experienced large
changes: amid the gradually rising water surface, Black Sea level (BSL) fluctuations
occurred. We calculated based on records (e.g., Balabanov, 2007) that the standard deviation
is ∼3.5 ÷ 5 m. Their typical duration was ∼1000 years. Time of occurrence of positive and
negative anomalies of the BS is different in different reconstructions. The source of these
discrepancies could be tectonically induced vertical motions. Before ∼7 ka BP the BSL was
higher than the level of the World Ocean. The rising BS spilled over a rocky sill at the
Bosphorus (Chepalyga, 2007).
It is clear that if the water discharge were quite large, the long-term BSL anomalies could
not be. This study focuses on the quantification of this concept.
Methodology. I use the equation of the water balance of the BS in term of the annual
averaged level anomalies. Time scales of the BSL fluctuations were determined based on the
BS basin morphology and averaged volumes of rivers runoff and water discharge via the
Bosphorus Sill. The short-term (1-2 year) contribution (like random white noise) to level
changes are due to variations of river runoff and precipitation mines evaporation. From this
perspective, the water balance equation is represented as a stochastic Langevin equation
(Kislov, 2015).
In another case, the BSL anomaly could be destructed due to relation “BSL
anomaly – value of water discharge via the Bosphorus Sill” which acts as a negative
feedback.
Results. To quantify the parameters, I use the present day information about hydrological
regime of the BS. It should not lead to serious errors, because the first and last quarters of the
Holocene exhibit similarity in their hydroclimatic regimes (Panin, Matlakhova, 2014). As
well, the paleohydrological data about dynamics of the Dnieper River runoff was used
(Swetc, 1978).
It was found that the time scale of the BSL fluctuations due to water discharge via the
Bosphorus Sill were estimated as ∼10÷30 years or less, using values of reconstructed and
calculated water flow crossing the Bosporus Sill (Chepalyga, 2007; Esin, 2014). It means,
that millennium-scale BSL anomalies could not occurred.
However, in the case of absence of water flow via the Bosphorus, the variance of
the BSL fluctuations can be calculated as solution of the Langevin equation. It
was found that sea level fluctuations during the first quarter of the Holocene are
characterized by the standard deviation ∼4 m, close to the abovementioned empirical
values.
Conclusions. The theoretical analysis showed that the empirical data are controversial:
mentioned long-term BSL fluctuations and large water discharge value via the Bosphorus Sill
could not occurred simultaneously. This fact creates problems in interpreting the BSL
fluctuations. The possibility of a "self-development" effect as a source of growth in sea-level
anomalies is not prohibited in the case if the discharge of water via the Bosporus Sill was
small. |