## 1st International Congress on Environmental Modelling and Software - Lugano, Switzerland - June 2002

#### Paper/Presentation Title

Simple Spatially Distributed Model of the Global Carbon Cycle and its Dynamic Properties

#### Keywords

global carbon cycle, modelling

#### Start Date

1-7-2002 12:00 AM

#### Abstract

A specially simplified spatially distributed model of the Global Carbon Cycle (GCC) is presentedthat is allowed to get a general solution and to study its basic dynamic properties (like spectral portrait,composition and decomposition of solutions, etc.). Assuming that the productivity depends linearly onconcentration of carbon in the atmosphere, the problem is reduced to a standard linear one. For calibrationthe Bazilevich data containing information on plant productivity, living biomass and soil organic matter ofdifferent biomes is used. Calculating the matrix eigenvalues of the basic linear problem we get its spectralportrait. The characteristic times change sufficiently smoothly from several years to several hundreds.Among all the exponentially damped solutions there are three oscillating ones with very long periods: from100 to 4,000 years. This portrait is very stable in relation to variations in the areas, covered by differentbiomes. Therefore, the terrestrial part of the GCC is a well-structured dynamic system with very wideopportunities to compensate disturbances with different time characteristics.Note that any distribution is described by its statistical moments and namely these moments are very robustin respect to numerical meanings of the distributed value. A special operation of convolution to the generalsolution of a spatially distributed model is suggested. This allows getting a dependence of convolutedsolution on first moments such as means and covariance. One can see that non-homogeneity of thesedistributions on the whole increases the amount of carbon in the atmosphere.

Simple Spatially Distributed Model of the Global Carbon Cycle and its Dynamic Properties

A specially simplified spatially distributed model of the Global Carbon Cycle (GCC) is presentedthat is allowed to get a general solution and to study its basic dynamic properties (like spectral portrait,composition and decomposition of solutions, etc.). Assuming that the productivity depends linearly onconcentration of carbon in the atmosphere, the problem is reduced to a standard linear one. For calibrationthe Bazilevich data containing information on plant productivity, living biomass and soil organic matter ofdifferent biomes is used. Calculating the matrix eigenvalues of the basic linear problem we get its spectralportrait. The characteristic times change sufficiently smoothly from several years to several hundreds.Among all the exponentially damped solutions there are three oscillating ones with very long periods: from100 to 4,000 years. This portrait is very stable in relation to variations in the areas, covered by differentbiomes. Therefore, the terrestrial part of the GCC is a well-structured dynamic system with very wideopportunities to compensate disturbances with different time characteristics.Note that any distribution is described by its statistical moments and namely these moments are very robustin respect to numerical meanings of the distributed value. A special operation of convolution to the generalsolution of a spatially distributed model is suggested. This allows getting a dependence of convolutedsolution on first moments such as means and covariance. One can see that non-homogeneity of thesedistributions on the whole increases the amount of carbon in the atmosphere.