MATHEMATICAL MODELLING OF ANOXIC CONDITIONS FORMATION IN NATURAL WATERS

The main goal of this work was to describe biogeochemical processes of nitrogen and reduced sulphur in natural aquatic ecosystems with a mathematical model. There was parameterized variability of chemical elements: oxygen, nitrogen (nitrate, nitrite, ammonia, organic nitrogen) and sulphur (sulphate, thiosulphate and sulphite, elemental sulphur, sulphide).

The model considered processes of ammonification, nitrification, nitrate reduction, denitrification, thiodenitrification, sulphate reduction and hydrogen sulphide oxidation. Transformation of the model compounds have been accepted to proceed on the base of microbiological approach. The dependencies of the transformation rates upon the oxygen concentration were parameterized by the semiempirical functions. Latter were set according to the nature conditions.

Fig.1. Model scheme of the elements transformation, where:

O₂ - dissolved oxygen, NO₃- nitrate, NO₂ - nitrite, NH₄ - ammonia, Norg - organic nitrogen, N₂ - gaseous nitrogen, SO₄ - sulphate, S₂O₃ - thiosulphate, SO₃ - sulphite, S⁰ - elementar sulphur, H₂S - sulphide.

The calculation was made with a simplified equation for the transport of a nonconservative substarate. All compound distributions are calculated on the base of one- and two-dimensional equation of diffusion with sources according to the task. The boundary conditions of 1 and 2 (Orlansly similarity) were used.

The subject of modeling estimations was first of all inter-relation zone between oxic and anoxic waters and hydrogen sulfide zone of the Black Sea.

Model clearly demonstrates the process of organic matter oxidation in progress. When organic matter quantity excessively increases, its oxidation may use up first of all oxygen, then all nitrates, and finally takes place because of sulphates. It results in hydrogen sulphide zone formation.

On the base of the one-dimensional equation there were calculated the curves of the vertical distribution of parameters in the natural waters in oxic (open Ocean) , anoxic (Black Sea) and intermediate (Arabian Sea) conditions.

The effects of anoxic conditions formation can be observed when the water flow rich with oxygen is decreased by the peculiarities of the bottom relief, as in fjords or after dam constructing:

Fig.1. The distribution of parameters in a bay before a dam construction

Fig.2. The process of formation of an anoxic zone after a dam construction

Fig.3. The distribution of parameters in a bay with anoxic conditions forced by a dam construction

On the base of model the inorganic reduced sulphur and nitrogen fluxes in the oxic-anoxic interface zone and contribution of biogeochemical transformation processes and hydrophysical factors in the compounds distribution were evaluated. Model estimations confirm that the existence of reduced conditions mainly controlled by the peculiarities of organic matter decay (consequence of oxidants consumption) accompanied by restricted aeration of deep waters. The value of hydrogen sulphide flux in the Black Sea sediments is incomparably less then in water pool. That is why all main transformation processes of sulphur are concentrated in the water column and particularly in the interface zone. The model applied to the description of sulphur cycle in this zone allowed to investigate common features and peculiarities of hydrogen sulphide column existence of the basin at all. The model was calibrated using the observed data on the components vertical distribution in the upper layers of the Black Sea.

Besides description of the contemporary situation, it was used to demonstrate the process of anoxic zone formation in the Black Sea after the Bosphorus appearance:

The obtained results could be used to the description of nitrogen and sulphur cycles in other natural aquatic ecosystems where anoxic environment presents or is possible. According to the hydrophysical processes parameterization the model could be used for the Arabian Sea, upwelling regions, fjords and etc.: it is possible to calculate the consequences of anthropogenic organic matter flux increasing as well as dam building in river estuaries, inlets and fjords.

The detailed description of this model is in:

Yakushev E.V., Neretin L.N., Volkov I.I. Mathematical modeling of the transformation of inorganic sulfur compounds in the Redox zone of the Black Sea // Oceanology, Vol.32, No 6, 718-723.(in Russian).

The new model version description is available here. Thank you for your interest.