Plant and Soil 229: 295–304, 2001.
© 2001 Kluwer Academic Publishers. Printed in the Netherlands.
295
Estimation of tree root lengths using fractal branching rules: a
comparison with soil coring for Grevillea robusta
D.M. Smith
Centre for Ecology & Hydrology, Crowmarsh Gifford, Wallingford, Oxfordshire OX10 8BB, UK
∗
Received 7 March 2000. Accepted in revised form 31 October 2000
Key words: branching algorithm, calibration, root branching, root length estimation, root system size
Abstract
Previous theoretical research has suggested that lengthsof 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
ˆ
L
r
= n
l
L
l
, 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
,whereL
r
is measured by a reference method such as soil coring.
Introduction
Estimation of root lengths for tree root systems using
conventional methods is invariably a difficult and la-
borious task. Commonly-used methods of determining
root lengths (see Böhm, 1979) are most suited to stud-
ies of field crops and it is frequently not feasible to
apply them to large trees, because they can require a
greater investment in time and labour than is often pos-
sible. Soil coring can provide detailed information on
quantities and distributions of roots, but large numbers
of cores are needed to adequately sample root systems
of trees (Smith et al., 1999), while sample numbers
are constrained by the availability of labour to collect
cores, wash root samples, remove debris from samples
and measure root lengths. Profile wall methods, in
∗
FAX No: +44-1491-692424. E-mail: dms@ceh.ac.uk
which roots on the exposed face of a soil trench are
counted, are ideal for assessing spatial variation in the
distribution of roots, but not root lengths (Huxley et
al., 1994). Similarly, in-growth bags and minirhizo-
trons enable determination of changes in root quantit-
ies with time rather than lengths of whole root systems
(Hendrick and Pregitzer, 1996). Entire root systems
for crop plants or grass swards can be recovered from
soil using pinboard methods, but these methods cannot
realistically be used on the scale required by trees.
An alternative method is needed, therefore, to en-
able routine estimation of the size of tree root systems.
Van Noordwijk et al. (1994) proposed that this could
be accomplished by taking advantage of the fractal
characteristics of tree roots to estimate total root
lengths from simple branching rules. Root branching
has a fractal pattern if the rules governing branching
are independent of scale; branching is then self-similar