Harmonisation of stem volume estimates in European National Forest Inventories

Gschwantner, Thomas; Alberdi, Iciar; Balázs, András; Bauwens, Sébastien; Bender, Susann; Borota, Dragan; Bosela, Michal; Bouriaud, Olivier; Cañellas, Isabel; Donis, Jānis; Freudenschuß, Alexandra; Hervé, Jean-Christophe; Hladnik, David; Jansons, Jurģis; Kolozs, László; Korhonen, Kari T.; Kucera, Milos; Kulbokas, Gintaras; Kuliešis, Andrius; Lanz, Adrian; Lejeune, Philippe; Lind, Torgny; Marin, Gheorghe; Morneau, François; Nagy, Dóra; Nord-Larsen, Thomas; Nunes, Leónia; Pantić, Damjan; Paulo, Joana A.; Pikula, Tomas; Redmond, John; Rego, Francisco C.; Riedel, Thomas; Saint-André, Laurent; Šebeň, Vladimír; Sims, Allan; Skudnik, Mitja; Solti, György; Tomter, Stein M.; Twomey, Mark; Westerlund, Bertil; Zell, Jürgen

doi:10.1007/s13595-019-0800-8

Annals of Forest Science

Table 10 Bridging functions for harmonising the stem volume estimates. Vr_K sample tree volume according to the reference definitions including the tree parts K, Vr_k volume of tree part k according to the reference definitions, age tree age, altitude height above sea level, bd_vc bark density of virgin cork, cbh circumference at breast height, cr crown ratio, dbh diameter at breast height, dbh_dom dominant dbh, d_g quadratic mean diameter, d_h = x diameter at a specified height x, d_{stem top} base diameter of the stem top, d_stump diameter at stump height, d_{stump base} diameter at the stump base, d_tl top diameter limit, d_u debarking diameter, d_03h upper diameter in 3/10 of the height, d₆ upper diameter in 6 m height, d₇ upper diameter in 7 m height, forest type even-aged or uneven-aged or intermediate, h tree height, h_k height to the crown basis, h_dom dominant height, h_d = 7cm height where the diameter is 7 cm, h_stump stump height, l_{stem top} length of the stem top, np_desc number of main debarking branches, region regions within country, slope slope of the terrain, species tree species

From: Harmonisation of stem volume estimates in European National Forest Inventories

NFI—country	Bridging function					Reference/origin
NFI—country	Approach				Volume model	Reference/origin
Austria	Tree part	Stump	Alternative	Empirical	Vr_{K = stump + bole + stem top} = fr_K (species, dbh, h), Vr_{K = stump + bole + stem top} = fr_K (species, dbh, d_03h, h, h_k)	Braun (1969); Pollanschütz (1974), re-parameterisation
		Stem top	Complementary	Empirical	Vr_{k = stem top}/Vr_{K = stump + bole + stem top} = fr_k (species, dbh, h)	Newly developed
		Branches	Complementary	Empirical	Vr_{k = large branches} = fr_k (species, dbh), Vr_{k = large branches} = fr_k (species, dbh, cr)	Gschwantner and Schadauer (2006), re-parameterisation
	dbh-threshold		Complementary	Empirical	Vr_K = stem = fr_K (species, dbh), Vr_K = stem/ha = fr_K (species, coverage)	Newly developed
Belgium	Tree part	Stump	Taper curve	Empirical, geometric	d_stump = f (species, cbh, h), Vr_{k = stump} = fr (d_stump, h_stump)	Dagnelie et al. (2013)
		Stem top	Taper curve	Empirical, geometric	h_d = 7cm = f (species, cbh, h), Vr_{k = stem top} = fr_k (d_{stem top}, l_{stem top})	Dagnelie et al. (2013)
		Branches	Complementary	Empirical	Vr_{k = large branches} = fr_k (species, dbh)	Dagnelie et al. (2013)
	dbh-threshold		Complementary	Geometric	Vr_K = stem = fr_K (dbh, h), Vr_{k = stem top} = fr_k (dbh, h)	Belgium
Czech Republic	Tree part	Stump	Complementary	Empirical	Vr_{k = stump}/Vr_{K = bole + large branches} = fr_k (species, dbh)	Parez et al. (1990)
		Stem top	Complementary	Empirical	Vr_{k = stem top}/Vr_{K = bole + large branches} = fr_k (species, dbh)	Parez et al. (1990)
		Branches	Complementary	Empirical	Vr_{k = large branches}/Vr_{K = bole + large branches} = fr_k (species, dbh)	Parez et al. (1990)
		Bark	Alternative	Empirical	Vr_{K = bole + large branches} = fr_K (species, dbh, h, age)	Lesprojekt (1952)
	dbh-threshold		Complementary	Empirical	Vr_K = stem = fr_K (species, h)	Konôpka et al. (2010), re-parameterisation, Slovakia
Denmark	Tree part	Stump	Complementary	Empirical	Vr_{K = bole + large branches} = fr_K (species, dbh, h, d_g, d_tl), Vr_{k = stump}/Vr_{K = bole + large branches} = fr_k (species, dbh)	Madsen (1985); Madsen (1987); Madsen and Heusèrr (1993); Tarp-Johansen et al. (1997); Parez et al. (1990), Czech Republic
		Stem top	Taper curve	Empirical	Vr_{K = bole + large branches} = fr_K (species, dbh, h, d_g, d_tl), Vr_{k = stem top}/Vr_{K = bole + large branches} = fr_k (species, dbh)	Madsen (1985); Madsen (1987); Madsen and Heusèrr (1993); Tarp-Johansen et al. (1997); Parez et al. (1990), Czech Republic
		Branches	Complementary	Empirical	Vr_{k = large branches}/Vr_{K = bole + large branches} = fr_k (species, dbh)	Parez et al. (1990), Czech Republic
Estonia	Tree part	Stump	Taper curve	Empirical	Vr_{k = stump} = fr_k (species, dbh, h, h_stump)	Ozolins (2002)
		Stem top	Taper curve	Empirical	Vr_{k = stem top} = fr_k (species, dbh, h, h_d = 7cm)	Ozolins (2002)
		Branches	not calculated
Finland	Tree part	Stump	Taper curve	Empirical	Vr_{K = stump + bole + stem top} = fr_K (species, dbh, h, d₆), Vr_{K = bole + stem top} = fr_K (species, dbh, h, d₆), Vr_{K = stump + bole + stem top}/ Vr_{K = bole + stem top} = fr_K (species)	Laasasenaho (1982)
		Stem top	Taper curve	Empirical	Vr_{K = bole + stem top} = fr_K (species, dbh, h, d₆), Vr_K = bole = fr_K (species, dbh, h, d₆), Vr_{K = bole + stem top}/Vr_k = bole = fr_K (species, dbh, h)	Laasasenaho (1982)
		Branches	not calculated
France	Tree part	Stump	Complementary	Geometric	Vr_{k = stump} = fr_k (dbh, h, h_stump)	Newly developed
		Stem top	Complementary	Geometric	Vr_{k = stem top} = fr_k (d_{stem top}, l_{stem top})	Newly developed
		Branches	Alternative	Empirical	Vr_{K = stump + bole + large branches} = fr_K (species, cbh, h)	C. Deleuze, personal communication, dataset (EMERGE)
	dbh-threshold		Complementary	Geometric, empirical	Vr_K = stem = fr_K (dbh, h), Vr_K = stem/ha = fr_K (Vc_K/ha_plot, species, coverage, humus, topography)	Newly developed
Germany	Tree part	Stump	Complementary	Empirical	Vr_{k = stump}/Vr_{K = bole + large branches} = fr_k (species, dbh)	Parez et al. (1990), Czech Republic
		Stem top	Complementary	Empirical	Vr_{k = stem top}/Vr_{K = stump + bole + stem top} = fr_k (species, dbh, h)	Newly developed, Austria
		Branches	Complementary	Empirical	V_{k = large branches} = fr_k (species, dbh, altitude)	Kaufmann (2001), Switzerland
	dbh-threshold		Complementary	Empirical	Vr_K = stem = fr_K (species, dbh)	Newly developed, Austria
Hungary	Tree part	Stump	Complementary	Empirical, geometric	d_stump = f (species, dbh), Vr_{k = stump} = fr_k (d_stump, h_stump)	Hungary
		Stem top	Complementary	Empirical	Vr_{k = stem top}/Vr_{K stump + bole + stem top} = fr_k (species, dbh)	Newly developed, Austria
		Branches	Complementary	Empirical	Vr_{k = large branches} = fr_k (species, dbh)	Gschwantner and Schadauer (2006), re-parameterisation, Austria
	dbh-threshold		Complementary	Geometric	Vr_K = stem = fr_K (d_h/2, h_mean)	Hungary
Ireland	Tree part	Stump	Taper curve	Empirical	Vr_{k = stump} = fr_k (species, dbh, h, d_h = x)	Riemer et al. (1995)
		Stem top	Taper curve	Empirical	Vr_{k = stem top} = fr_k (species, dbh, h, d_h = x)	Riemer et al. (1995)
		Branches	Complementary	Empirical	Vr_{k = large branches} = fr_k (species, dbh, cr)	Gschwantner and Schadauer (2006), re-parameterisation, Austria
	dbh-threshold		Complementary	Empirical	Vr_K = stem = fr_K (species, dbh, h, d_h = x), Vr_{K = stem top} = fr_K (species, dbh, h, d_h = x)	Riemer et al. (1995), re-parameterisation
Latvia	Tree part	Stump	Complementary	Empirical, geometric	d_stump = f (species, dbh, h), d_stumpbase = f (species, dbh), Vr_{k = stump} = fr_k (d_stump, d_stumpbase, h_stump)	Ozolins (2002), Newly developed
		Stem top	Complementary	Empirical, geometric	l_{stem top} = f (dbh, h), Vr_{k = stem top} = fr_k (d_{stem top}, l_{stem top})	Newly developed
		Branches	Complementary	Empirical	Vr_{k = large branches} = fr_k (species, dbh)	Dagnelie et al. (2013), Belgium
	dbh-threshold		Complementary	Geometric	Vr_K = stem = fr_K (d_h/2, h_mean)	Latvia
Lithuania	Tree part	Stump	Complementary	Empirical	Vr_{k = stump} = fr_k (species, dbh)	Kuliešis and Kulbokas (2009)
		Stem top	Complementary	Empirical	Vr_{k = stem top} = fr_k (species, dbh)	Kuliešis and Kulbokas (2009)
		Branches	Complementary	Empirical	Vr_{k = large branches} = fr_k (species, dbh)	Newly developed
	dbh-threshold		Complementary	Empirical	Vr_K = stem = fr_K (dbh)	Lithuania
Norway	Tree part	Stump	Complementary	Empirical, geometric	d_stump = f (dbh), Vr_{k = stump} = fr_k (d_stump, h_stump)	Norway
		Stem top	Complementary	Empirical	Vr_{k = stemtop} = fr_k (species, dbh, h)	Spruce and pine: Vestjordet (1967), Birch: newly developed, Finland
		Branches	Complementary	Empirical	Vr_{k = large branches} = fr_k (species, dbh)	Dagnelie et al. (2013), Belgium
	dbh-threshold		Complementary	Empirical	Vr_K = stem = fr_K (dbh)	Jonson (1928)
Portugal	Tree part	Stump	Complementary	Empirical, geometric	d_stump = f (species, dbh), Vr_{k = stump} = fr_k (d_stump, h_stump)	Riemer et al. (1995), Ireland
		Stem top	Complementary	Geometric	Vr_{k = stem top} = fr_k (d_stemtop, l_stemtop)	Portugal
		Branches	Complementary	Empirical	Vr_{k = large branches} = fr_k (species, dbh)	IFN2 (1986–1995), Spain
		Bark	Complementary	Empirical	Vr_{k = virgin cork} = fr_k (species, d_u, np_desc, bd_vc)	Only cork oak: newly developed
	dbh-threshold		Complementary	Empirical	Vr_K = stem = fr_K (dbh, h), Vr_K = stem = fr_K (species, d_u, wd)	AFN (2010), cork oak: newly developed
Romania	Tree part	Stump	Complementary	Empirical	Vr_{k = stump} = fr_k (species, dbh, h, h_stump)	Newly developed, Austria
		Stem top	Complementary	Empirical	Vr_{k = stem top} = fr_k (species, dbh, h)	Newly developed, Austria
		Branches	Complementary	Empirical	Vr_{k = large branches} = fr_k (species, dbh)	Parez et al. (1990); Gschwantner and Schadauer (2006), re-parameterisation, Austria
	dbh-threshold		Complementary	Empirical	Vr_K = stem/ha = fr_K (Vc_K/ha_plot, species)	Romania
Serbia	Tree part	Stump	Complementary	Empirical	Vr_{k = stump} = fr_k (species, dbh, h_stump)	Newly developed, Austria
		Stem top	Complementary	Empirical	Vr_{k = stem top} = fr_k (species, dbh)	Newly developed, Austria
		Branches	Complementary	Empirical	Vr_{k = large branches} = fr_k (species, dbh)	Gschwantner and Schadauer (2006), re-parameterisation, Austria
	dbh-threshold		Complementary	Geometric	Vr_K = stem = fr_K (dbh, h)	Serbia
Slovakia	Tree part	Stump	Complementary	Empirical	Vr_{K = stump + bole + stem top}/ Vr_{K = bole + stem top} = fr_k (dbh, slope)	Newly developed, Austria
		Stem top	Alternative	Empirical	Vr_{K = bole + stem top} = fr_K (species, dbh, h)	Petráš and Pajtík (1991)
		Branches	Alternative	Empirical	Vr_{K = bole + large branches} = fr_K (species, dbh, h)	Petráš and Pajtík (1991)
		Bark	Alternative	Empirical	Vr_{K = bole + large branches} = fr_K (species, dbh, h)	Petráš and Pajtík (1991)
	dbh-threshold		Complementary	Empirical	Vr_K = stem = fr_K (species, h)	Konôpka et al. (2010), re-paramerisation
Slovenia	Tree part	Stump	Complementary	Empirical	Vr_{k = stump} = fr_k (species, dbh, h_stump)	Newly developed, Austria
		Stem top	Complementary	Empirical	Vr_{k = stemtop} = fr_k (species, dbh)	Newly developed, Austria
		Branches	Complementary	Empirical	Vr_{k = large branches} = fr_k (species, dbh)	Gschwantner and Schadauer (2006), re-parameterisation, Austria
	dbh-threshold		Complementary	Geometric	Vr_K = stem = fr_K (dbh, h), Vr_{k = stemtop} = fr_k (species, dbh, h)	Slovenia; newly developed, Austria
Spain	Tree part	Stump	Complementary	Empirical, geometric	d_stump = f (dbh, h), Vr_{k = stump} = fr_k (d_stump, h_stump)	Spain
		Stem top	Complementary	Empirical, geometric	l_{stem top} = f (dbh, h), Vr_{k = stem top} = fr_k (d_{stem top}, l_{stem top})	Spain
		Branches	Complementary	Empirical	Vr_{k = large branches} = fr_k (species, dbh)	IFN2 (1986–1995)
	dbh-threshold		Complementary	Empirical	Vr_K = stem = fr_K (species, dbh)	Newly developed, Austria
Sweden	Tree part	Stump	Complementary	Empirical	Vr_{k = stump} = fr_k (species, dbh, h_stump)	Marklund (1988); Petersson and Ståhl (2006)
		Stem top	Complementary	Empirical	Vr_{k = stem top} = fr_k (species, dbh)	Marklund (1988); Petersson and Ståhl (2006)
		Branches	Complementary	Empirical	Vr_{k = large branches} = fr_k (species, dbh)	Marklund (1988); Petersson and Ståhl (2006)
Switzerland	Tree part	Stump	Taper curve	Empirical, geometric	Vr_{k = stump} = fr_k (species, dbh, h, d₇), Vr_{k = stump} = fr_k (d_stump, h_stump)	Kaufmann (2001)
		Stem top	Taper curve	Empirical, geometric	Vr_{k = stem top} = fr_k (species, dbh, h, d₇), Vr_{k = stem top} = fr_k (d_{stem top}, l_{stem top})	Kaufmann (2001)
		Branches	Complementary	Empirical	Vr_{k = large branches} = fr_k (species, dbh, altitude, region)	Kaufmann (2001)
	dbh-threshold		Complementary	Empirical	Vr_K = stem = fr_K (species, dbh), Vr_{k = stemtop} = fr_k (species, dbh)	Newly developed, Austria

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