# Equations For Biomass

Equation 2.7 Annual change in carbon stocks in biomass in land remaining in a particular land use -category (Gain-Loss Method)

Where:

AC = annual change in carbon stocks in biomass (the sum of above-ground and below-ground biomass

terms in Equation 2.3) for each land sub-category, considering the total area, tonnes C yr-1 ACq= annual increase in carbon stocks due to biomass growth for each land sub-category, considering the total area, tonnes C yr-1

ACl = annual decrease in carbon stocks due to biomass loss for each land sub-category, considering the total area, tonnes C yr-1 Where:

ACb= annual change in carbon stocks in biomass (the sum of above-ground and below-ground biomass terms in Equation 2.3 ) in land remaining in the same category (e.g., Forest Land Remaining Forest Land), tonnes C yr-1

C t2 = total carbon in biomass for each land sub-category at time t2, tonnes C C ti = total carbon in biomass for each land sub-category at time tl, tonnes C C = total carbon in biomass for time t1 to t2

A = area of land remaining in the same land-use category, ha (see note below) V = merchantable growing stock volume, m3 ha-1 i = ecological zone i (i = 1 to n) j = climate domain j (j = 1 to m)

R = ratio of below-ground biomass to above-ground biomass, in tonnes d.m. below-ground biomass (tonne d.m. above-ground biomass)-1

CF = carbon fraction of dry matter, tonnes C (tonne d.m.)-1

BCEFS = biomass conversion and expansion factor for expansion of merchantable growing stock volume to above-ground biomass, tonnes above-ground biomass growth (m3 growing stock volume)-1, (see Table 4.5 for Forest Land). BCEFS transforms merchantable volume of growing stock directly into its above-ground biomass. BCEFS values are more convenient because they can be applied directly to volume-based forest inventory data and operational records, without the need of having to resort to basic wood densities (D). They provide best results, when they have been derived locally and based directly on merchantable volume. However, if BCEFS values are not available and if the biomass expansion factor (BEFS) and D values are separately estimated, the following conversion can be used:

Equation 2.9

Annual increase in biomass carbon stocks due to biomass increment in land remaining in the same land-use category

Where:

AC = annual increase in biomass carbon stocks due to biomass growth in land remaining in the same land-use category by vegetation type and climatic zone, tonnes C yr-1 A = area of land remaining in the same land-use category, ha Gtotal = mean annual biomass growth, tonnes d. m. ha-1 yr-1 i = ecological zone (i = 1 to n) j = climate domain (j = 1 to m)

CF = carbon fraction of dry matter, tonne C (tonne d.m.)-1

Equation 2.10 Average annual increment in biomass Tier 1

Gtotal = Z • (1 + R)} Biomass increment data (dry matter) are used directly

Tiers 2 and 3

Gtotal = • BCEFj • (1 + R)} Net annual increment data are used to estimate GW by applying a biomass conversion and expansion factor

Where:

GTotal = average annual biomass growth above and below-ground, tonnes d. m. ha-1 yr-1

GW = average annual above-ground biomass growth for a specific woody vegetation type, tonnes d. m. ha-1 yr-1

R = ratio of below-ground biomass to above-ground biomass for a specific vegetation type, in tonne d.m. below-ground biomass (tonne d.m. above-ground biomass)-1. R must be set to zero if assuming no changes of below-ground biomass allocation patterns (Tier 1).

IV = average net annual increment for specific vegetation type, m3 ha- yr-

BCEFI = biomass conversion and expansion factor for conversion of net annual increment in volume (including bark) to above-ground biomass growth for specific vegetation type, tonnes above-ground biomass growth (m3 net annual increment)-1, (see Table 4.5 for Forest land). If BCEFI values are not available and if the biomass expansion factor (BEF) and basic wood density (D) values are separately estimated, then the following conversion can be used:

Equation 2.11

Annual decrease in carbon stocks due to biomass losses in land remaining in the same land-use category

= Lwood - removals + L fuelwood + Ldisturbance

Where:

ACl = annual decrease in carbon stocks due to biomass loss in land remaining in the same land-use category, tonnes C yr-1

Lwood-removais = annual carbon loss due to wood removals, tonnes C yr-1 (See Equation 2.12) Lfueiwood = annual biomass carbon loss due to fuelwood removals, tonnes C yr-1 (See Equation 2.13) Ldisturbance = annual biomass carbon losses due to disturbances, tonnes C yr-1 (See Equation 2.14)

Equation 2.12 Annual carbon loss in biomass of wood removals

Lwood - removals = {H • BCEFR • (1 + R) • CF}

Where:

Lwood-removals = annual carbon loss due to biomass removals, tonnes C yr-1

H = annual wood removals, roundwood, m3 yr-1

R = ratio of below-ground biomass to above-ground biomass, in tonne d.m. below-ground biomass (tonne d.m. above-ground biomass)-1. R must be set to zero if assuming no changes of below-ground biomass allocation patterns (Tier 1).

CF = carbon fraction of dry matter, tonne C (tonne d.m.)-1

BCEFr = biomass conversion and expansion factor for conversion of removals in merchantable volume to total biomass removals (including bark), tonnes biomass removal (m3 of removals)-1, (see Table 4.5 for Forest Land). However, if BCEFR values are not available and if the biomass expansion factor for wood removals (BEFR) and basic wood density (D) values are separately estimated, then the following conversion can be used:

Equation 2.13 Annual carbon loss in biomass of fuelwood removal

Lfuelwood = [{FGrees • BCEFr • (1 + R)} + FGpat • D] • CF

Where:

Lfuelwood = annual carbon loss due to fuelwood removals, tonnes C yr-1 FGtrees = annual volume of fuelwood removal of whole trees, m3 yr-1 FGpart = annual volume of fuelwood removal as tree parts, m3 yr-1

R = ratio of below-ground biomass to above-ground biomass, in tonne d.m. below-ground biomass (tonne d.m. above-ground biomass)-1; R must be set to zero if assuming no changes of below-ground biomass allocation patterns. (Tier 1)

CF = carbon fraction of dry matter, tonne C (tonne d.m.)-1

BCEFr = biomass conversion and expansion factor for conversion of removals in merchantable volume to biomass removals (including bark), tonnes biomass removal (m3 of removals)-1, (see Table 4.5 for Forest Land). If BCEFR values are not available and if the biomass expansion factor for wood removals (BEFR) and basic wood density (D) values are separately estimated, then the following conversion can be used:

Equation 2.14 Annual carbon losses in biomass due to disturbances

Ldisturbance = {Adisturbance • BW • (1 + R) • CF • fd}

Where:

Ldisturbances = annual other losses of carbon, tonnes C yr-1 (Note that this is the amount of biomass that is lost from the total biomass. The partitioning of biomass that is transferred to dead organic matter and biomass that is oxidized and released to the atmosphere is explained in Equations 2.15 and 2.16).

Adisturbance = area affected by disturbances, ha yr-1

BW = average above-ground biomass of land areas affected by disturbances, tonnes d.m. ha-1

R = ratio of below-ground biomass to above-ground biomass, in tonne d.m. below-ground biomass (tonne d.m. above-ground biomass)-1. R must be set to zero if no changes of below-ground biomass are assumed (Tier 1)

CF = carbon fraction of dry matter, tonne C (tonnes d.m.)-1

fd = fraction of biomass lost in disturbance (see note below)

Note: The parameter fd defines the proportion of biomass that is lost from the biomass pool: a stand-replacing disturbance will kill all (fd = 1) biomass while an insect disturbance may only remove a portion (e.g. fd = 0.3) of the average biomass C density. Equation 2.14 does not specify the fate of the carbon removed from the biomass carbon stock. The Tier 1 assumption is that all of Ldisturbances is emitted in the year of disturbance. Higher Tier methods assume that some of this carbon is emitted immediately and some is added to the dead organic matter pools (dead wood, litter) or HWP.

Equation 2.15

Annual change in biomass carbon stocks on land converted to other land-use category (Tier 2)

ACb = ACG + ACCONVERSION - ACl

Where:

AC = annual change in carbon stocks in biomass on land converted to other land-use category, in tonnes C yr-1

ACq= annual increase in carbon stocks in biomass due to growth on land converted to another land-use category, in tonnes C yr-1

AC = initial change in carbon stocks in biomass on land converted to other land-use category,

in tonnes C yr-1

ACl = annual decrease in biomass carbon stocks due to losses from harvesting, fuel wood gathering and disturbances on land converted to other land-use category, in tonnes C yr-1

Equation 2.16

Initial change in biomass carbon stocks on land converted to another land category

ACCONVERSION = 2 {(BAFTERt - BBEFOREi ) • AATO _ OTHERSt } • CF

Where:

AC = initial change in biomass carbon stocks on land converted to another land category,

### CONVERSION tonnes C yr-1

Bafter. = biomass stocks on land type i immediately after the conversion, tonnes d.m. ha-1 BBEFOREi = biomass stocks on land type i before the conversion, tonnes d.m. ha-1 AATO_OTHERSi = area of land use i converted to another land-use category in a certain year, ha yr-1 CF = carbon fraction of dry matter, tonne C (tonnes d.m.)-1 i = type of land use converted to another land-use category 