Model errors in tree biomass estimates computed with an approximation to a missing covariance matrix

Table 1 Species group above-ground forest tree biomass (AGB kg tree⁻¹) equations

Species	#	Equation \(\widehat{{\text{AGB}}} =\)	\(\hat{R}^{2}\)	\(\hat{\sigma }_{e}^{2}\) 10³ kg	Wts
BEECH^a	1	\(0.901{\text{DBH}}^{2} - 6.382\sqrt {\text{DBH} \times {\text{HT}}}\)	0.96	75.3	n.a.
BEECH^a	2	\(\left( {9.645{\text{DBH}} - 0.648\sqrt {\text{HT}} } \right)^{2}\)	0.95	79.2	n.a.
SPRUCE^a	5	\(0.447{\text{DBH}}^{2} - 1.189\sqrt {\text{DBH} \times {\text{HT}}}\)	0.98	18.7	n.a.
SPRUCE^a	6	\(\left( {0.634{\text{DBH}} - 0.426\sqrt {\text{HT}} } \right)^{2}\)	0.98	18.2	n.a.
PINE^a	9	\(0.450{\text{DBH}}^{2} - 0.014\sqrt {\text{DBH} \times {\text{HT}}}\)	0.98	14.5	n.a.
PINE^a	10	\(0.658{\text{DBH}}^{2} - 0.124\sqrt {\text{DBH} \times {\text{HT}}}\)	0.98	14.5	n.a.
BEECH	3	\(0.887{\text{DBH}}^{2} - 6.487\sqrt {\text{DBH} \times {\text{HT}}}\)	0.96	74.4	DBH⁻²
BEECH	4	\(\left( {10.127{\text{DBH}} - 1.167\sqrt {\text{HT}} } \right)^{2}\)	0.95	75.3	DBH⁻²
SPRUCE	7	\(0.492{\text{DBH}}^{2} - 1.409\sqrt {\text{DBH} \times {\text{HT}}}\)	0.97	19.0	DBH⁻²
SPRUCE	8	\(\left( {0.689{\text{DBH}} - 0.064\sqrt {\text{HT}} } \right)^{2}\)	0.97	18.7	DBH⁻²
PINE	11	\(0.479{\text{DBH}}^{2} - 1.927\sqrt {\text{DBH} \times {\text{HT}}}\)	0.97	14.7	DBH⁻²
PINE	12	\(0.690{\text{DBH}}^{2} - 0.205\sqrt {\text{DBH} \times {\text{HT}}}\)	0.97	14.5	DBH⁻²
BEECH^b	13	\(Exp\left[ {0.006 + 10.933\,\frac{\text{DBH}}{\text {DBH} + 21.216}} \right]\)	0.99^c	n.a.	n.a.
SPRUCE^b	14	\(Exp\left[ { - 1.694 + 10.825\frac{\text{DBH}}{\text{DBH} + 11.816}} \right]\)	0.99^c	n.a.	n.a.
PINE^b	15	\(Exp\left[ { - 2.688 + 10.745\,\frac{\text{DBH}}{\text{DBH} + 8.062}} \right]\)	0.99^c	n.a.	n.a.

Sample size is 50 trees per species group.
^aBWI-1987 Predictions of AGB times a uniformly distributed random error [0.9,1.1] fitted to DBH (mm) and HT (dm).
^bGeneralized AGB equations from Table 8 (Temperate zone) in Muukkonen P and Heiskanen J [76]. DBH is in centimeters (cm).
^cAmount of variation in predicted AGB values captured by the generalized equation.
Data were selected from 335 plots from the 1987 (West) German national forest inventory (BWI-1987). Plots were dominated by one of the three species groups. Selected trees have a DBH ≥ 7 cm, and were selected with a probability proportional to their basal area at breast height (basal area factor of 4), [77, ch. 8].

ISSN: 1750-0680