(588e) Modeling of Ozone Layer Depletion

Widespread use of chlorofluorocarbons has led to about 3% ozone depletion by the end of the 80's. This fact has resulted in sharp decline in subsequent chloroflurocarbon use and manufacture in conformation to Montreal Protocol (1987). Turco and Whitten(1975) have reported dynamic solution to establish quantitative effect of chloroflorocrbons. A one dimensional time dependant model was used and results were arrived at considering the prevalent increase of chloroflorocarbon production and emmision at that time. Taking cognizance of this fact, the ozone layer stability and the projected ultimate equilibrium condition has been studied in this paper. The steady state solution of the system outlines the fact that the ozone layer can reach a steady state for any pollutant concentration values. The natural limit of the ozone concentration, as well as the upper limits for the pollutant concentration is calculated. The procedure suggests a way of assessing the effect of anthropogenetic activities on ozone layer. The transmission coefficients of the UV radiation are calculated establishing the lower limits of the “permitted” pollution. Ozone layer stability is studied in the framework of irreversible thermodynamics. The model of ozone layer leads to a system of non-linear differential equations. The following 16 chemical reactions describe the ozone creation and destruction processes in the stratosphere

O₂ + hv→ 2O,

O+O₂ + M→ O₃ + M,

O₃ + hv→ O₂ + O^*,

O₃ + O^*→ 2O₂,

HO + O₃→ HO₂ + O₂,

HO₂ + O→ OH + O₂,

NO₂ + hv→ NO + O,

NO + O₃→ NO₂ + O₂,

NO₂ + O→ NO + O₂,

Cl + O₃→ ClO + O₂,

ClO + O→ Cl + O₂,

ClO + NO→ NO₂ + Cl,

HO₂ + Cl→ HCl + O₂,

HCl + OH→ H₂O + Cl,

CF₂Cl₂ + hv→ CF₂Cl +Cl,

CFCl₃ + hv→ CFCl₂ + Cl

In the above, M stands for a catalyst Species continuity equation is applied for 11 relevant species taking into account vertical motion through eddy diffusion term. This gives a set of 11 partial and coupled differential equations dependent on time and altitude. To solve these equations, numerical discretization method is employed using semi-implicit finite difference schemes. Steady state solution of the system indicates that ozone layer stability is independent of pollutant concentration viz Freon-11 and Freon-12 and is instead strongly dependent on the relation between HO₂ and NO₂ concentration in the stratosphere. Hypothetical fluctuations appearing in the system are also studied to get a better measure of the stability of the system. Real and negative eigen values are obtained indicating good damping characteristics. Natural limits of pollutants have been calculated knowing ozone lifetime. Thereafter, putting a condition on change in UV transmission coefficient, which is consonant with the risk of skin cancer, the upper limits of pollutants are also obtained which indicates that current concentrations of Freons are well within the permitted range. Dynamic simulation has been carried out which gives predicted future concentrations of all species with altitude. Despite halt in production of CFC's, the concentration does not show much decline. Consequently, because of the photochemical dissociation of the molecules already in the stratosphere, free chlorine concentration keeps on increasing. However, the increasing free chlorine seems to take the HCl route rather than the depletion causing ClO route. Solution indicates that ozone will reach normal levels by 2050. Freon concentrations owing to their large lifetimes may take much longer to reach accepatable levels.

References:

Turco R.P., Whiten R.C., Chlorofluoromethanes in the atmosphere andd some possible consequences for ozone, Atmospheric Environment (1975),9,1045-1061