ONE-DIMENSIONAL OXYGEN DIFFUSION INTO SOIL WITH EXPONENTIAL RESPIRATION - ANALYTICAL AND NUMERICAL-SOLUTIONS

A numerical model for one-dimensional diffusion of oxygen into soil wh ich incorporates a soil respiration function that decreases exponentia lly with depth, is compared with an analytical solution. The results s how that the assumption of zero flux at the bottom boundary for the nu merical solution means that the assumed depth to the bottom boundary, z(n), is a critical parameter. The analytical solution shows that this boundary condition leads to two distinct oxygen concentration profile s. The first occurs when the oxygen concentration approaches a constan t value, C, as z --> infinity. The second occurs when the oxygen conc entration goes to zero at some depth, L. With the analytical solution, the nature of the profile can be determined a priori and either C or L calculated. With the numerical solution it is not possible to deter mine which of these profiles will occur a priori. This can only be obt ained by increasing z(n) and noting what happens to the oxygen concent ration profile. The results illustrate the care needed in using numeri cal solutions and the extra physical insight that may be gained from u sing analytical solutions where they are available.