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Moscow Biosphere Model

A System of Models of the Global Biosphere Cycles

Global Spatial Model of Carbon Dioxide and Nitrogen Cycles in Ocean - Atmosphere System

1. Description of the carbon cycle model
2. Biotic components
3. Complete model
4. Results of modeling

Zero dimensional, zonal, and spatial models of carbon and nitrogen cycle for the atmosphere - ocean system were consequently developed by A.M Tarko together with E.P Novichikhin, E.I. Nefedova and V.S. Pervanyuk. Here are the results of a spatial model investigation.
1. Description of the carbon cycle model

     Three vertical layers are allocated in the ocean: well-mixed layer (WML), thermocline with variable depth, and deep layer. The border between thermocline and deep ocean is fixed.
     All the ocean area is subdivided to cells 4x5o in size. Based on this, the cells of WML having identical directions of meridional or zonal horizontal speeds of ocean water are aggregated in blocks. The sizes of blocks are 8o in latitude and about 20o in longitude. The deep layer is supposed to be as one block.
     The model variables are the values of carbon concentration in each block of ocean and values of mass of carbon dioxide in each zone of the atmosphere. In each WML block the following factors are taken into consideration: water and air temperatures at the sea level, salinity of water, speed of water flows between boundaries of the blocks, speed of the wind. The time unit is one month.
     In the model, one-level vertical atmosphere is divided into 20 zones on latitude from South Pole up to the North. It is taken into account that the flow of carbon dioxide between zones in the atmosphere is proportional to difference of its concentrations.
     Carbon exchange between blocks within one level of ocean depends on water circulation. The field of speeds of water is given on boundaries of blocks for each month.
     Exchange between WML and thermocline we describe according to B.A. Kagan and V.A. Ryabchenko. Carbon exchange between WML and thermocline is carried out during seasonal raising and lowering of its boundaries.
     The flow of carbon dioxide at the atmosphere - ocean border is considered to be proportional to the difference between the partial pressures of carbon dioxide in the air at the sea level and in the upper layer of ocean. It also depends wind speed. The partial pressure of carbon dioxide in each zone of atmosphere is proportional to mass and temperature of carbon.
     The dependence of partial pressure of dissolved carbon dioxide on the concentration of inorganic carbon in WML, temperature and salinity of sea water in WML is determined on the basis of solving the system of equations for constants of chemical balance of ocean buffer carbonate system.
     In order to calculate the greenhouse effect of air carbon dioxide we use values of air temperature from general circulation models (GCM). The value of atmospheric temperature at a sea level depends on the seasonal component and the annual change of temperature. Annual change of the sea level temperature we set to be equal to change of air temperature.

2. Biotic components

     The nitrogen cycle is considered in order to describe biotic processes in the ocean. In a WML, having a sufficient value of light intensity, the inorganic carbon and nitrogen transfer to their organic form as a result of photosynthesis. The net primary production of phytoplankton depends on the concentration of inorganic nitrogen and the temperature and does not depend on carbon concentration. We use the phyto-zooplankton equations to describe the seasonal variability of organic carbon in the sea. The main part of organic matter is decomposed in WML. The rest of organic matter falls to deeper layers and then is decomposed in it.

3. Complete model

     The seasonal dynamics of the spatially distributed carbon and nitrogen cycle in the atmosphere - ocean system is described by a system of the ordinary nonlinear differential equations with periodic coefficients.
     We assume that in absence of anthropogenic emissions of carbon dioxide to the atmosphere the quantity of carbon in the atmosphere - ocean system remains constant. We also consider that during the pre-industrial period the system was at a steady state.

4. Results of modeling

     The computer program, which realizes the model works under the control of Windows 95/98. Dynamics of carbon cycle was investigated in the absence and presence of anthropogenic influences. Initial values of the variables were set, and a system of differential equations was numerically integrated to receive a periodic solution. The period is equal to one year.
     The values of variables describing carbon cycle in the ocean are different in latitudes and inside any latitudinal zone. Increase of carbon concentration in the ocean with depth is observed. It can be explained by the presence of biota in WML and a permanent lowering of the dead organic matter to the deep layers.
     In WML, the seasonal fluctuations of concentration of carbon are taking place. The largest amplitude of such fluctuations is observed in the latitudinal zone between 30o N and 60o N. Increase in carbon concentration from the equator to the poles is markedly expressed. Differences of concentration between equator and poles are significantly greater than seasonal fluctuations in any block of ocean. These results correspond to the data of measurements.
     At the figure the distribution of the partial pressure of carbon dioxide which is dissolved in WML in January is shown. In contrast to concentration of carbon, the highest values are observed at the equator and low latitudes. Towards the poles, the partial pressure of dissolved carbon dioxide is decreased. The maximal values are displaced from the equator to the South Pole in the summer months and from equators to the North Pole in winter months. The annual difference of partial pressures values is 30 ppm.

Map of January CO2 pressure in ocean, 6 kb

Map of partial pressure of CO2 in WML in January (ppm)

     Distribution of seasonal carbon dioxide flows through boundary atmosphere - ocean is presented at the next figure. Zones where absorption of carbon dioxide takes place are in high and moderate latitudes, and in different oceans the absorption occurs differently. In all the oceans carbon dioxide emissions are located near equator.

Animated map of seasonal CO2 flows in ocean, 55 kb

Scale, 2 kb

Computer animated map of seasonal carbon dioxide flows through the boundary
atmosphere - ocean ( g C/m2 month). Positive values correspond to carbon dioxide absorption by ocean

     Simulating of the consequences of instant releases of carbon dioxide into the atmosphere was done. Such experiments give an opportunity to investigate potential ability of the ocean to absorb the anthropogenic emissions of carbon dioxide. As result of emission, the ocean absorbs CO2. Computing experiment in which the amount of atmospheric CO2 was instantly increased by 10 % was made. The results are shown in the figure. Absorption of carbon dioxide by different oceans is  presented. All the oceans during the first years after the release are carbon dioxide sinks. The most powerful absorbers are the Northern part of the Pacific and Atlantic oceans. The oceans of a Southern Hemisphere absorb carbon dioxide during the first years after release and then, after several decades, become to emit CO2. The Southern Hemisphere part of the Pacific ocean in 40 years after the release becomes the first CO2 releaser. Then in 55 years the Indian ocean, and in 70 years the Southern part of the Atlantic ocean begin to emit carbon dioxide.

Instant release absorption by oceans, 6 kb

Absorption of 10 % instant release of carbon dioxide to atmosphere
by different oceans. The flows of CO2 are shown (g C/m2 year)

Copyright c A.M. Tarko, 1999, 2000, 2009

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