Estimation of tree root lengths using fractal branching rules: a comparison with soil coring for Grevillea robusta

Previous theoretical research has suggested that lengths of tree roots can be estimated on the basis of their branching characteristics, if branching has a fractal pattern that is independent of root diameter. This theory and its underlying assumptions was tested for Grevillea robusta trees at a site in Kenya by comparing estimates of root length from conventional soil coring and the output of a fractal branching algorithm. The trees were in a 4-year-old stand established on a 3 × 4 m planting grid. Root lengths (L _r) in four units of the planting grid were estimated by soil coring. Branching characteristics determined by examination of 32 excavated roots from 16 trees were: The number of branches at each branching point; the length of links between branching points (L _l); the diameter of root tips; and parameters which describe the change in diameter at each branching point. Each was found to be independent of root size. These data were used to parameterise a branching algorithm, which was then used to estimate numbers of root links in the four grid units (n _l) from root diameters at the bases of the four trees at the corners of each unit. Root lengths, from L _r = n₁ L₁, severely underestimated L _r. This discrepancy probably resulted from inaccuracy in the parameterisation of the branching algorithm, as output from the algorithm was very sensitive to small changes in parameter values. Use of fractal branching rules alone to estimate roots length does not appear possible unless the algorithm is calibrated to adjust for errors in parameter estimation. Calibration can be achieved by calculation of an 'effective link length', L ^eff ₁, from L _r/n _l, where L _r is measured by a reference method such as soil coring.