European Journal of Forest Research (2018) 137:153–167
Eects of competition and climate variables on modelling height
to live crown for three boreal tree species in Alberta, Canada
· Shongming Huang
Received: 10 May 2017 / Revised: 14 November 2017 / Accepted: 23 December 2017 / Published online: 30 January 2018
© Springer-Verlag GmbH Germany, part of Springer Nature 2018
Using tree data from permanent sample plots and climate data from the ClimateWNA model, mixed-eﬀects height to live
crown (HTC) models were developed for three boreal tree species in Alberta, Canada: trembling aspen (Populus tremuloides
Michx.), lodgepole pine (Pinus contorta var. latifolia Engelm.) and white spruce (Picea glauca (Moench) Voss). Three model
forms, the Wykoﬀ model, a logistic model and an exponential model, were evaluated for each species. Tree height was the
most signiﬁcant predictor of HTC and was used in all models. In addition, we investigated the eﬀects of competition and
climatic variables on HTC modelling. Height–diameter ratio and either total stand basal area or basal area of coniferous trees
were used as competition measures in the models. Diﬀerent climate variables were evaluated, and spring degree-days below
0 °C, mean annual precipitation and summer heat–moisture index were incorporated into the aspen, lodgepole pine and white
spruce models, respectively. Site index was only signiﬁcant in lodgepole pine models. Residual variances were modelled
as functions of tree height to account for heteroscedasticity still present in the mixed-eﬀects models after the inclusion of
random parameters. Based on model ﬁtting and validation results as well as biological realism, the mixed-eﬀects Wykoﬀ
models were the best for aspen and white spruce, and the mixed-eﬀects logistic model was the best for lodgepole pine.
Keywords Height to live crown · Mixed-eﬀects model · Climate variables · Competition · Boreal tree species
Crown size has long been recognized as an important com-
ponent of growth and yield models (Sattler and LeMay
2011; Temesgen et al. 2005). Tree growth and survival are
strongly related to the amount of foliage (MacFarlane et al.
2002), and longer crowns usually carry more foliage than
shorter ones (Antos et al. 2010). Therefore, crown length
has been used as a surrogate for leaf area and photosyn-
thesis when modelling tree growth (Weiskittel et al. 2011).
Crown length and other related variables have been used
for modelling individual tree diameter increment (Wykoﬀ
et al. 1982), height increment (Short and Burkhart 1992),
basal area increment (Monserud and Sterba 1996), mortality
(Burkhart et al. 1987) and volume and taper equations (Wal-
ters and Hann 1986; Hann et al. 1987).
Crown length measurements in the ﬁeld can be challeng-
ing in dense and/or multilayered stands and for tall trees
where the base of the live crown is not visible (Temesgen
et al. 2005). Crown length measurements are also prone to
errors due to conﬂicting deﬁnitions (McRoberts et al. 1994).
As a result, crown length is not typically measured in forest
inventories; when it is measured, it is often for a subsam-
ple of trees in a plot. Crown length models can be used to
compute the missing measures since they are often strongly
related to commonly measured stand and tree attributes.
Crown length can be modelled directly or indirectly
through height to live crown (HTC) or crown ratio. Crown
length, HTC and crown ratio are inter-related by simple
algebraic relationships, and all three have been modelled in
the past (Hasenauer and Monserud 1996; Antos et al. 2010;
Sattler and LeMay 2011; Rijal et al. 2012). Compared to
crown ratio, crown length and HTC were shown to have
stronger relationships with tree dimension variables such
as tree height (Rijal et al. 2012). HTC was modelled in this
study since it was directly measured in the ﬁeld.
Communicated by Arne Nothdurft.
* Yuqing Yang
Biometrics Unit, Forest Management Branch, Alberta
Agriculture and Forestry, 8th Floor, 9920-108 Street,
Edmonton, AB T5K 2M4, Canada