Soil respiration source density profiles using steady-state inverse methods

Worldwide there is a rapidly increasing network of ecological sites at which carbon budgets are being monitored. A large component of these budgets is respiration from the soil which is due to both soil microbes and plant roots. Determining the depth profile of the source density of respiration in the soil would contribute to better understanding of the biology of respiration and help partition between the two carbon sources. Typically the flux of carbon dioxide released from the soil is measured continuously either by eddy correlation or chamber methods. Continous time series of carbon dioxide concentration profiles can also be measured now fairly routinely. The UBC Biometeorology/Soil Physics group has been making such measurements under various forest canopies in Western Canada for the last 5-10 years. We have found that to a very good approximation half-hour average profiles of carbon dioxide concentration are in quasi steady-state equilibrium with the surface flux and that diffusion is the dominant mode of transport of carbon dioxide in soil. In this paper we apply steady state solutions of the diffusion equation to the soil and show how they can be used in inverse mode to infer the soil respiration source density distribution. We use numerical methods applied to time varying problems to investigate the accuracy of the distributions calculated by inversion.