Modelling of anoxic conditions formation as an example of the Black Sea


P.P.Shirshov Institute of Oceanology, 36 Nakhimovskiy Pr., Moscow, 117851,

1. Introduction
2. Chemical-biological sources parameterization
3. 1D vertical distribution modelling
4. Results
5. Conclusion

ABSTRACT: An O-N-S-Mn model is considered to describe the biogeochemical sources. Rates of biochemical processes mediated by bacteria are described by first-order equations using semiempirical functions of O2 concentration. The processes of turbulent diffusion, sedimentation, and biogeochemical transformation of compounds were paramaterized in the frames of one-dimensional model. The model was calibrated using data observed for the vertical distribution of compounds in the of the Black Sea. The calculated spatial distributions of nitrogen compounds (total organic nitrogen, ammonium, nitrate, nitrite), inorganic reduced sulfur compounds (hydrogen sulfide, elemental sulfur, thiosulfate, sulfate), dissolved and particulate manganese, as well as dissolved oxygen agree reasonably well with the observations. Model estimations confirm that the existence of anoxic conditions is controlled primarily by the peculiarities of organic matter decay (a consequence of oxidant consumption) in conjunction with restricted aeration.


The study of anoxia conditions formation is important because they can be formed in both natural and anthropogenic ways. Such a study is particularly important in the case of the Black Sea, the biggest natural water body with extensive anoxia, where about 80% of waters are anoxic and localised areas of hypoxia and anoxia occur in polluted shelf regions. A representative case study of the oxic/anoxic transformation is the Black Sea redox layer. This is the zone of contact between oxic and anoxic waters, which can be named also Nepheloid Redox Layer (NRL) (Volkov et al. 1997), because of its low transparency.

In contrast with modelling devoted to other oceanographic problems, modelling of the oxic/anoxic contact zone can provide more than just quantitative results but also insights into the qualitative nature of the zone, about which relatively little is currently known

Modelling of biogeochemical processes in sea water requires parameterization of the chemical elements cycling. The first stage of the construction of each model is the choice of the relevant variables. Two basic approaches can be used: the ratio of concentrations of certain forms of chemical elements present in the sea water and/or the time scales over which the process is studied.

The current data for nutrient (N, P, Si, C, O, S) distribution confirm that even in the euphotic zone the majority of these elements are contained in the form of dissolved inorganic material, while nutrients in the cells of living organisms account for only a very small percentage. Below the euphotic zone, the share of inorganic matter increases to more than 95-99 %.

The formation and maintenance of the chemical structure occurs over time scales varying from one week to decades. The time required exceeds the time scales of biological processes.

Therefore if the goal of the study is the formation of hydrochemical structures and their variability, we should describe the inorganic forms in detail, while the biological parameters can remain generalised.

If we compare the peculiarities of the biogeochemical cycles in oxic and anoxic conditions we find that there is a principal difference: in oxic conditions the cycles of different nutrients are parallel. It is therefore possible to use the stoichiometric law (Redfield ratios) and to describe the cycle of only one element and to extend the results to other elements.

In anoxic conditions, every element cycle plays its own geochemical role because the oxidation of organic matter occurs in different stoichimetric reactions. Modelling of oxic/anoxic transformation therefore requires the simultaneous parameterization of cycles of several elements.

Figure 1. Diagrammatic representation of the coupled model of sulfur, nitrogen, manganese and oxygen cycling showing the compartments and the modeled rates of transformation processes.


The model (Figure 1) computes the content of hydrogen sulfide (H2S), total elemental sulfur (S0+Sn2-), thiosulfate (and sulfites) (S2O32-+SO32-), sulfate (SO42-), total organic nitrogen (Norg), ammonium (NH4+), nitrite (NO2-), nitrate (NO3-), dissolved manganese (Mn2+), particulate manganese (Mn4+) and dissolved oxygen (O2).

The transformation of sulfur occurs as a result of hydrogen sulfide oxidation and sulfate reduction. Nitrogen transformation occurs as a result of ammonification, nitrification, nitrate reduction (denitrification), thiodenitrification and ammonium assimilation. In addition, the processes of manganese oxidation and reduction are also considered (Figure1).

2.1. Chemical-biological sources

To describe the transformation of matter between the model compartments carried out by micro-biological or chemical means, first order equations were used. Stoichiometric coefficients mi were calculated according to the following equations:

(CH2O)106(NH3)16H3PO4 + 53SO42- =
= 106CO2 + 106H2O + 16NH3 + H3PO4 + 53S2- (Richards 1965);

1/2CH2O + NO3­ NO2- + 1/2H2O + 1/2CO2 (Anderson et al. 1982)
3/4CH2O + H+ + NO2- 1/2N2 + 5/4H2O + 3/4CO2 (Anderson et al. 1982)
where Corg:Norg =106:16 (Richards 1965);

(CH2O)106(NH3)16H3PO4 + 84.8HNO3 =
= 106CO2 + 42.4N2 + 148.4H2O + 16NH3 + H3PO4 (Nealson et al. 1991);

3H2S + 4NO3- + 6OH- 3SO42- + 2N2 + 6H2O (Volkov 1984);

2H2S + O2 2S0 + 2H2O (Tebo 1991);

2S0 + O2 + H2O S2O32- + 2H+ (Kondrat'eva 1983);

S2O32- + 2O2 + 2OH- 2SO42- + H2O (Jorgensen 1989);

NH4+ + 3/2O2 NO2- + 2H+ + H2O (Jorgensen 1989);

NO2- + 1/2O2 NO3- (Jorgensen 1989);

(CH2O)106(NH3)16H3PO4 + 106O2 = 106CO2 + 16NH3 + H3PO4 + 106H2O (Nealson et al. 1991).

MnO2 + H2S + 2CO2 Mn2+ + S0 +2HCO3 (Volkov 1984)

Mn2+ + O2+2H2O MnO2 +4H+ (Rozanov 1995)

The majority of these reactions like other redox-zone processes are mediated by bacteria (Volkov 1984, Murray et al. 1991).

Instead of considering special compartments for describing bacteria biomass dynamics, we describe the ammonia to organic nitrogen assimilation in relation to the intensity of the microbiological processes (chemosynthesis in nitrogen units).

As = p1 Th1 + p1 Th2 + p1 Th3 + p2 Nf1 + p2 Nf2 + p3 Td + p4 Nr1 + p4 Nr2 - where pi - the quantity of consumed nitrogen of NH4+ in units of consumed substrate (S2-, S0, S2O32-, NH4+, NO2-). This assumption can be made because the main objective of this study is to describe the chemical structure of the redox layer, and not detailed modelling of its bacterial ecosystem.

Therefor the chemical sources of the model are the following:

RNorg = -Am - m2 Nr1 - m3 Nr2 - m5 Sr1 + As

RNH4+ = Am + m4 Nr1 + m5 Sr1 - Nf1 - As

RNO2- = Nf1 - Nf2 + Nr1 - Nr2

RNO3- = Nf2 - Nr1 - m6 Td

RH2S = -Th1 + Sr2 - Td - m13 Mr

RS0 = Th1 - Th2

RS2O32- = Th2 - Th3 + Sr1 - Sr2

RSO42- = Th3 - Sr1 + Td

RO2 = -m7 Th1 - m8 Th2 - m9 Th3 - m10 Nf1 - m11 Nf2 - m12 Am - m14 Mox,

RMn2+ = Mr - Mox;

RMn4+ = Mox - Mr;

where mi ( i = 2-12) - stoichiometric coefficients of the model.

The values of the coefficients used are the values presented in Table 1.

Table 1. Model coefficients
Constant of ammonification
KAm, day-1
0.01 (Sergeev 1979)
Constant of ammonium oxidation
KNf1, day-1
0.1 (Sergeev 1979)
Constant of nitrite oxidation
KNf2, day-1
0.3 (Sergeev 1979)
Constant of nitrate reduction
KNr1, day-1
Constant of denitrification
KNr2, day-1
Constant of thiodenitrification
KTd, day-1
Constant of hydrogen sulfide oxidation
KTh1, day-1
0.45 (Sorokin et al. 1991)
Constant of elemental sulfur oxidation
KTh2, day-1
0.7 (Sorokin et al. 1992)
Constant of thiosulfate oxidation
KTh3, day-1
0.4 (Sorokin et al. 1991)
Constant of the first stage of sulfate reduction
KSr1, day-1
Constant of thiosulfate reduction
KSr2, day-1
Constant of manganese oxidation
KMox, day-1
Constant of manganese reduction
KMr, day-1
Ammonium assimilation coefficients for:
p1, M(N)/M(S)
Percentage of total organic nitrogen that is particulate
a, %
10 (Skopintsev 1975)
Specific rate of organic matter sedimentation
W, m day-1
1-50 (Sergeev 1979)
Coefficient of the vertical turbulence diffusion
Kz, cm2 s-1
[5, 8]

For the dependence of processes considered on oxygen content, the following linear functions were proposed (Table 2).

Table 2. Formulations, names of processes, dependence on oxygen content
Process, Formula
Dependence on oxygen

Am = KAm [Norg] FAm (O2)

1 and 2 stages of nitrification:

Nf1 = KNf1 [NH4+] FNf(O2)

Nf2 = KNf2 [NO2-] FNf (O2)

nitrate reduction:

Nr1 = KNr1 [NO3-] FNr (O2)


Nr2 = KNr2 [NO2-] FNr (O2)

1, 2 and 3 stages of H2S oxidation:

Th1 = KTh1 [H2S] FTh (O2)

Th2 = KTh2 [S0] FTh (O2)

Th3 = KTh3 [S2O32-]FTh(O2)

1 and 2 stages of sulphate reduction:

Sr1 = m1 KSr1 [Norg] FSr (O2)

Sr2 = KSr2 [S2O32-] FSr (O2)


Td = KTd [H2S] FTd (O2) Fi (NO3)

manganese oxidation:

Mox = KMox [Mn2+] Fmox(O2)

manganese reduction:

Mr = KMr [Mn4+] Fmox(O2)

Where Ki are constants of the corresponding reactions, mi are the stoicheometric coefficients and Fi (O2), Fi (NO3-) are the dependencies of reaction rates on oxygen and nitrate content respectively.

Figure 2. Calculated vertical distribution of the model parameters (click on image to enlarge).


For 1D modelling we considered a column of water with a depth range from 50 m (lower boundary of the euphotic zone) to 150 m.

3.1. Equation

The following was used as the basic equation for dissolved components:


where RCi - sources and sinks of a substance (rates of transformation), Ci - concentration of nitrogen compounds (NH4+, NO2-, NO3- ), sulfur compounds (H2S, S0, S2O32-, SO42-), dissolved manganese (Mn2+), and dissolved oxygen (O2). Kz - vertical turbulent diffusion coefficient. We assume Kz to be a model constant with the value of 0.3 cm2/s.

The total organic nitrogen and particulate manganese (Mn4+) concentrations were calculated according to (1) supplemented by the introduction of a particulate matter sinking rate term:


Where a = the fraction of organic matter that is particulate and where W = sinking rate of the particulate matter (Table 1).

3.2. Boundary conditions

It was assumed that at the upper boundary of the water columns being studied here, the chemical, biological and physical processes are balanced and maintain constant concentrations of most chemical elements throughout the year. Therefore, we specify constant values of all model components at the upper boundary.

The values of all the compounds in the model were set to zero, except for the following: Norg=3.8 mM/l, NO3-=1.0 mM /l, O2=300 mM /l, SO4=15 M/l.

The pronounced halocline (pycnocline) in the Black Sea restricts vertical motion and hence the contact of deep waters with the surface. Because of this weak mixing, the existence of the deep Bosphorus current has little effect on the renewal of the intermediate horizons. Thus, the Black Sea system may be considered to be closed to the input of oxygen-rich water from the deeper levels. Therefore, at the lower boundary in the Black Sea model, a flux boundary condition (radiation condition) was implemented for all compounds (except the Mn2+ and sulfate ion) (Yakushev, Neretin, 1997):


where the "" symbol represents the boundary, Ci* is the next time step concentration at the boundary (node outside the integration area), is the gradient at the boundary. The phase velocity Cf was calculated on the basis of the Orlanski approximation:


where is the change on the adjacent-to-boundary node, is the previous step concentration at the boundary (the node outside the zone of integration).

The implication of this radiation condition is that the value at the lower boundary is determined by parameter concentration changes within the integrated area. Therefore concentrations at the lower boundary in the Black Sea model are consequently formed only by the processes that occur within the zone of integration.

For sulfate at the lower boundary, a boundary condition of the first order was given, because model processes do not essentially change the content of this compartment. The constant value was accepted also for the Mn2+( Mn2+=5.3 mM)

For all sulfur compounds, with the exception of sulfates, zero concentrations were given as initial conditions; for nitrogen compounds and oxygen, constant values at all depths corresponding to the upper boundary values were given.

Therefore, the calculations were started with initial conditions characteristic of an "oxic" sea, without any anoxia even at the lower boundary.

3.3. Application

The model was calculated for the layer 50-150 m with vertical resolution of 2 m. The model equations (1) were integrated using a first-order Eurelian method with time step of 0.1 day for at least 1 year after the stable solution was reached (Figure 2).


The results of vertical distribution 1D modelling are presented Figure 2.

They reflect the main features of the vertical structure of compounds in the aphotic layer. One can see the decrease of oxygen concentrations from about 300 mM at the upper boundary to zero at a depth about 100 m.

The vertical profiles of nitrogen compounds (Norg, NH4+, NO2-, NO3-) calculated in the model reflect the main features of the distributions of these compounds observed in nature (Skopintsev 1975).

In upper level oxic conditions, where ammonification is the dominant process, one can see the maximum nitrate concentration. Below this gives way to a small nitrite maximum with increased ammonia concentrations. Concentrations of ammonia in deep waters correspond to those actually observed (Skopintsev 1975).

H2S profile also reflects the observed situation of an increasing concentration of this parameter with depth (Volkov et al. 1992). Elemental sulphur values increase near the depth at which hydrogen sulphide appears. Then the distribution of this parameter is uniform. This is a consequence of the model assumption that S0 forms as an intermediate compound in sulphide oxidation processes which take place near the upper boundary of the anoxic zone. In the layers below the are no sources or sinks for this parameter. Thiosulfates are intermediate products of both the sulfate reduction and sulfide oxidation processes.

Manganese compound profiles derived in the model also reflect the main features of this parameter's vertical distribution in nature. Dissolved manganese is oxidised by oxygen and the particulate manganese forms. The particulate manganese reacts with hydrogen sulphide and is transformed into dissolved manganese. A dissolved manganese maximum appeared in the model experiments when the oxygen supply increased and both processes intensified.

A significant feature of the model is the increase of organic matter in the contact zone (Figure2) resulting from the assimilation of ammonia during bacteria mediated processes of matter transformation. This corresponds to empirical data (Sorokin et al. 1992) and confirms the view that the nature of the NRL is connected primarily with intensive bacteria activity at this depths (Volkov et al. 1992).

Compared with the previous version of this model [25], which didn't consider manganese, this version illustrates significant differences of H2S depletion and NH4+ depletion with depth. This relates to the fact that H2S can be oxidised by oxygen and by particulate manganese, while ammonia can only be oxidised by oxygen.

Nevertheless in frames of parameterization of processes used in this model Mn can not be the sole or even the dominant oxidiser of H2S.

According to model, the H2S depletion point is characterised by the following concentrations: H2S = 1.89 mM, O2= 1.84 mM, Mn4=0.035 mM, NO3=0.78 mM. Hence Mn can oxidise only a small fraction of the hydrogen sulphide. It can therefore be concluded that model supports the idea of Tebo (Tebo 1991) that Mn cycle processes "help to maintain broad suboxic zone", because this metal is being used as an electron-transfer mediator between oxygen and sulfide (Lewis & Landing 1991 ) (Nealson et al. 1991). Model concentrations of oxygen are formally in agreement with the opinion that in the suboxic zone, oxygen concentrations can vary from 2 to 10 mM (Murray et al. 1989). But nevertheless the present model can not explain H2S oxidation in the absence of oxygen.

The main difference between the model results and the empirical observations appears to be the distance between the oxycline depletion point and the H2S depletion point (10 m in the model and about 30-40 m in nature). During iterations of the quantitative experiments it was possible to reduce this divergence, but in these cases the gradient of all the parameters in the redox layer was significantly smoother than that observed in nature. Similar smoothed curves or an absence of distance between O2 and H2S depletion points can be found in the results of other models (Ayzatullin & Leonov 1975, Belyaev et al. 1997, Nealson et al. 1991, Oguz et al. 1996) describing the contact between oxic and anoxic layers.


The main goal of this model was to study the role of chemical-biological sources affecting the profiles of the compounds investigated.

Although this is a simplistic model, it is capable of reproducing the basic features of the redox zone structure. This correlation suggests that the theoretical knowledge generated by the approach taken in this model can explain the main features of the phenomena observed.

Modelling of oxic/anoxic transformation requires parameterization of the cycles of several elements simultaneously, in contrast to models dealing only with nutrient cycles under oxic conditions.

Model estimations confirm that the existence of anoxic conditions is controlled primarily by the peculiarities of organic matter decay (a consequence of oxidant consumption) in conjunction with restricted aeration.

According to the model simulations, the most sensitive hydrochemical parameters from point of view of vertical advection anomalies are particulate manganese, organic matter and elemental sulphur. All these parameters influence transparency, and the transparency layer anomalies can result from the hydrophysical process peculiarities.

The model was calibrated using data observed for the vertical distribution of compounds in the upper layers of the Black Sea. The results obtained could be used to describe the nitrogen, sulphur and manganese cycles in other natural aquatic ecosystems where anoxic environments are present or possible.

The results of work undertaken so far suggests that future development of the model should concentrate on the improvement of parameterization of peculiarities of sedimentation connected with manganese cycle, organic matter balance, and the use of hydrophysical model results for the description of advection and diffusion.


This work was conducted with the financial support of the Russian Foundation for Basic Research, grants 96-05-66169 and 96-05-65134.


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