Determining vertical root and microbial biomass distributions from soil samples

When vertical density distributions of root or microbial biomass are calculated using each sampling interval's midpoint as the depth coordinate, the calculated distribution is biased if it is a nonlinear function with depth. In the root biomass literature, distributions are often described by a power function R proportional to B-z, where beta is a decay coefficient and z is depth. A common alternative formulation is an exponential function, R proportional to e(-z/Zr) where Z(r) is a characteristic length scale. These functions are equivalent when Z(r) = -1/In beta, so the data according to either function may be unified. The bias can be eliminated by representing the vertical distribution with a continuous function, integrating it over the sampling interval, and using a least squares method to determine the function's parameters. The bias increased by nearly threefold when the sampling interval increased from 0.01 to 1 m. As the sampling interval increases, the bias shifts the function down the z axis. This results in the intercept increasing with increasing sampling interval. When a single profile was sampled at different intervals, the function's intercept and Z(r) changed. The parameter Z(r) changed fivefold when the sampling interval increased from 0.1 to 0.5 m, while the calculated fraction of roots above a depth of 0.1 in decreased threefold for the same change in sampling interval. Beneath a tropical forest where root biomass and microbial respiration were sampled throughout the same soil profile, the corresponding microbial and root biomass length scales averaged 0.17 m and differed by only 11%.