The Carbon Cycle

Month by month variations in atmospheric carbon dioxide concentrations from natural causes mask any variation from the recent COVID-19 lock-down. Such rapid variations are due to the absorption and out-gassing of carbon dioxide by the mixed layer of the ocean as it is warmed and cooled by fluctuating weather systems such as El Nino.

At longer time scales, the response of the carbon dioxide concentration in the atmosphere to a perturbation in production rate is governed by a first order differential equation. Hence variations over time are smoothed by the convolution of the perturbation with the impulse response curve characterised by that equation. The impulse response curve is exponential with a half-time of 43~years and zero remnant fraction. A perturbation in production rate such as the Covid-19 Lock-down would need to last for a comparable time in order to be detectable as a change in concentration.

The mixed layer is a turbulent layer in which winds and waves have homogenized temperature and chemistry down to some depth which varies between about 10m and 200m. Wind stress increases the depth while solar radiation in calm conditions renews stratification. The mixed layer is in intimate contact with the atmosphere, so that heat and soluble gases exchange rapidly between the two reservoirs. The highly stratified thermocline lies below the mixed layer. Apart from regions of upwelling and downwelling, heat and dissolved substances are transferred through the thermocline to and from the deep ocean by diffusion.

In effect, there are three reservoirs: the atmosphere, the mixed layer and the deep ocean. At time scales of months, exchange of carbon dioxide between the mixed layer and the atmosphere predominate whereas at time scales of years to decades, the exchange of carbon dioxide between the deep ocean and the mixed layer predominates. At these longer time scales the mixed layer and atmosphere can be regarded as a single reservoir. The rapid variations in temperature seen during El Nino events only involve the atmosphere and the mixed layer. On the other hand the variation in carbon 14 from nuclear testing is the result of the much slower rate of diffusion of from the atmosphere and mixed layer reservoirs into the deep ocean.

The impulse response and sensitivity of carbon dioxide concentration estimated statistically are quite different from conventionally accepted values. The impulse response has an exponential decay with no significant airborne fraction. A possible explanation is the following: the deep ocean is bounded by a turbulent mixed layer and by the highly turbulent Antarctic Circumpolar Current and will therefore be internally mixed by a Kolmogorov cascade of turbulent eddies, some with spatial scales as large as ocean basins and with time scales of, perhaps, decades. Turbulence is a stochastic phenomenon which is difficult to observe at large spatial and temporal scales and which cannot be readily emulated by deterministic models. The complexity of the eddy transports calls for reconsideration of how they are estimated in practice, particularly in general circulation models. Eddy diffusion generated by such eddy transports would greatly increase the capacity of the deep ocean to absorb carbon dioxide and so would account for the shorter half time of the observed impulse response of atmospheric carbon dioxide concentration. Whatever the explanation, there is no observational evidence for the long half times and airborne fraction of atmospheric carbon dioxide concentration presently assumed by most modellers.

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