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CASMOFOR

version 5.0

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ACCOUNTING FUNCTION, VARIABLES AND PARAMETERS APPLIED IN CASMOFOR


I. THE CARBON CYCLE OF FORESTS AND FORESTRY
 

PRELIMINARY NOTES

Equations of CASMOFOR describing the carbon cycle are listed below by pool, and classified in various categories. Balance equations (BE) are ones that are used to calculate new values of the carbon pools at time t. FLUX IN refers to a process, i.e. a sink, by the yield of which the carbon content of the whole forestry system increases. Similarly, FLUX OUT refers to emissions by the amount of which the carbon content of the whole forestry system decreases. The emissions can come from carbon that was fixed by the FLUX IN processes, or from carbon that was already stored in the soil before the start of the simulation. Some carbon that flows through various pools eventually goes to the long-term SINK (in the soil), and remains part of the forestry system for the entire period of the simulation. Equations that are not classified into any of the above categories are used to calculate variables in the above equations, and are noted by “other.” By the forestry system all the pools and processes within the system boundary of the systems diagram are meant. Variables related to carbon pools and rates of fluxes are expressed as amount of carbon (tonnes of carbon – tC), and is calculated once for each calendar year of the simulation for each species and yield class.

Each equation is shown twice in each cell: once with the long names of the variables (in the first row(s) of each cell), and once using their symbols, respectively. Index t refers to any year in the simulation, index (t-1) refers to the previous year. Index (t-x) refers to year x year before the current year. Index (i) means that the variable is a vector of values from year 1 to year x (the factor used in the formula varies with age), where x depends on the process. The respective values of some variables are found in the database of the model, or should be specified by the user. The values of other variables are calculated by the model itself.
 

CHECKING FOR THE SECOND LAW OF THERMODYNAMICS

To check that all carbon is accounted for, i.e. all incoming fluxes equal to all outgoing fluxes + the changes of the carbon content of the system (including permanent sinks), the below equation is tested after each simulation step to ensure that mass is conserved:
 

Total Flux INt = Total (POOLSt – POOLSt-1) + Total Flux to SINKt – Total Flux OUTt

where Total Flux INt is the amount of carbon that enters the system in year t; Total Flux to SINKt is the amount of carbon that moves to long-term carbon sink pools of soil in year t; POOLSt POOLSt-1 are the amount of carbon in all pools in time t and t-1, respectively; and Total Flux OUTt is the amount of carbon that leaves the system in year t.

(Flux IN: amount entering the system; Flux OUT: amount leaving the system to air; Flus to SINK: amount leaving the system to soil and other long-term sink.)

EQUATIONS APPLIED TO MODEL CARBON DYNAMICS IN CASMOFOR:

Pool

Balance equation (BE), fluxes (IN and OUT), or other equations

Equations, variables and parameters

(pools and processes (in one-year steps) are in terms of tC)

Above-

ground

woody biomass

BE

Above-ground woody biomass = above-ground woody

biomasst-1 + woody increment – mortality – thinnings - final cuttings

AGWBt = AGWBt-1 + CAIC – M – TH – FC

Flux IN

 

current annual increment of above-ground woody biomass = current annual increment (of tree volume) * wood density * carbon content of wood

CAIC = CAI * d * cf

d = weight of oven-dry biomass / volume of fresh wood (at the stand level), tdm m-3

cf = carbon fraction of (oven dry) wood

 

mortality = above-ground woody biomasst-1 * (density dependent mortality ratio + density independent mortality ratio)

M = AGWB t-1 * (ddm + dim)

ddm: sepcies dependent

dim: randomly generated

ddm + dim <= 0,4

 

thinnings = above-ground woody biomasst-1 * thinning ratio

TH = AGWBt-1 * thr

Thr = species specific, depends on age and yield class

 

final cuttings = above-ground woody biomasst-1 of stands of rotation age

FC = AGWBt-1 of stands of rotation age

(final cutting is supposed to take place at the beginning of the year, and is immediately followed by regeneration)

Rotation age: species specific, depends on yield class

Dead

wood

BE

dead wood = dead woodt-1 + deadwood increment - decomposition of (i.e., emission from) decomposable dead wood

DWt = DWt-1 + DWI – EW

 

increase of deadwood = (mortality + thinnings * (1 – wood product part of thinning – fuelwood part of thinning) + final cuttings* (1 - wood product part of final cutting – fuelwood part of final cutting) )* (1 - non-decomposable fraction)

DWI = [M + TH * (1 – wpTH – fpTH) + FC * (1 – wpFC – fpFC)] * (1-ndf)

Flux OUT

emission due to decomposition of deadwood = dead woodt-i * (1-exp(-kDW)) + deadwood increment * (kDW - 1 + exp(-kDW)) / kDW where kDW = ln(2) / half life time of deadwood

EW = DWt-i * (1-exp(-kDW)) + DWI * (kDW - 1 + exp(-kDW) / kDW

Flux to SINK

Non decomposable dead wood fraction = (M + TH – non-productTH * FC – non-productFC) * ndf

UWI = (M + TH – non-productTH * FC – non-productFC) * ndf

Leaves

BE

amount of (living) leaves at the end of year = amount of leaves at the end of previous year + increment due to tree growth – decomposable leaf loss due to harvest and mortality – undecomposable leaf loss due to harvest and mortality

LLt = LLt-1 + LI – DLI – DLI * ndf / (1 - ndf)

Flux IN

increment of leaves = aboveground woody biomass increment * (leaf increment/AG woody biomass increment)

LI = CAIC * increment ratio

 

amount of decomposable leaves that die in year (due to harvest and within year and end-of-year leaf mortality)

= [(leavest-1 + increment of leaves) * non-living/living + (leavest-1 + increment of leaves) * non-living/living * (1-non-living/living) * fraction of leaves dying and falling at the end of year)] * (1 - non-decomposable fraction)

DLI = [(LLt-1 + LI) * nll + (LL t-1 +LI) * (1 - nll) * fdlleaves] * (1-ndf)

fdlleaves: species specific (broadleaves: 1; conifers: <1)

 

non-living/living biomass ratio = increase of deadwood / aboveground woody biomass of the previous year

nll = DWI/AGWBt-1

Flux to SINK

Non decomposable fraction = amount of leaves that become decomposable dead * ndf/(1-ndf)

ULI = DLI * ndf / (1-ndf)

Dead

leaves

BE

dead decomposable leaves = dead decomposable leavest-1 + amount of decomposable leaves that die in year – decomposition of dead leaves

DLt = DLt-1 + DLI – EL

Flux OUT

emission due to decomposition of dead leaves = dead leavest-i * (1-exp(-kDL)) + amount of decomposable leaves that die in year * (kDL - 1 + exp(-kDL)) / kDL where kDL = ln(2) / half life time of dead leaves

EL = DLt-i * (1-exp(-kDL)) + DLI * (kDL - 1 + exp(-kDL) / kDL

Roots

(below ground biomass)

BE

Roots at the end of year = Rootst-1 + increase of root biomass – amount of decomposable roots that die in year – amount of undecomposable dead root that die in year

Rt = Rt-1 + RI – DRI – DRI * ndf / (1-ndf)

Flux IN

increase of root biomass = current annual woody increment * (root-to-shoot ratio)

RI = CAIC * rts

 

Decomposable dead roots increment =

= [(Root biomasst-1 + increase of root biomass ) * (non-living/living) + (increase of root biomasss ) * (1 - non-living/living) * Fraction of roots of trees (relative to root increment) that dies at the end of year ] * (1 – non decomposable fraction)

DRI = [(Rt-1 + RI) * nll + (LI t-1 + LRI) * (1-nll) * fdlroots] * (1-ndf)

Flux to SINK

Non decomposable dead root biomass increment = decomposable dead roots increment * ndf/(1-ndf)

URI = DRI * ndf/(1-ndf)

Dead

Roots

BE

Dead decomposable roots at the end of year = carbon in dead decomposable rootst-1 + total decomposable dead roots increment – decomposition of (i.e., emission from) decomposable dead roots

DRt = DRt-1 + DRI – ER

Flux OUT

emission due to decomposition of dead roots = carbon in dead decomposable rootst-i * (1-exp(-kDR)) + total decomposable dead roots increment * (kDR - 1 + exp(-kDR)) / kDR where kDR = ln(2) / half life time of dead roots

ER = DRt-i * (1-exp(-kDR)) + DRI * (kDR - 1 + exp(-kDR) / kDR

Wood products

BE

Wood products = Wood productst-1 + wood product increment – wood products becoming unused

WP = WPt-1 + WPI – EUUWP – UWPF

 

wood products increment = (timber from clearcut + timber from thinnings) * (1 – lost part)

(the increment, as well as pools, flux out and other calculations are split into three factions, using appropriate parameters: paper, wood based panels and sawnwood-based wood products, as in the IPCC KP Supplement)

WPI = [FC * used part * (1-fuelwood part) + TH * used part(t) * (1-fuelwood part(t)] * (1 - lost part)

 

wood products becoming unused = wood products increment X years before

WPU = WPIt-i

X: mean life time of wood product (species specific)

Flux OUT

emission due to decomposition of wood products = unburnt * (carbon in wood productst-i * (1-exp(-kWP)) + total decomposable dead roots increment * (kWP - 1 + exp(-kWP)) / kWP) where kWP = ln(2) / half life time of wood products (different for paper, wood based panels and sawnwood-based wood products, as in the IPCC KP Supplement)

EUUWP = WPUt-i * (1-exp(-kWP)) + WPI * (kWP - 1 + exp(-kWP) / kWP

Fuelwood

BE

Fuelwood = fuelwoodt-1 + fuelwood increment from harvest + loss in wood processing + unused wood products becoming fuelwood – emission from firewood

FW = FWt-1 + FWI + LWP + UWPF – EFW

 

Fuelwood increment from harvests = fuelwood from clearcut + fuelwood from thinning

FWI = FC * used part * fuelwood part + TH * used partt * fuelwood partt

 

Loss in wood processing = wood product increment * lost part / (1 – lost part)

LWP = WPI * lost part / (1 – lost part)

 

Wood product becoming fuelwood = wood products becoming unusedt-1 * unburnt fraction

UWPF = WPUt-1 * unburnt

Flux OUT

emission from burning firewood = avoiding fossil fuel burning = fuelwood carbont-1 * (1-unburnable fraction)

EFW = FWt-1 * (1-unburn)

Flux to Sink

Unburnable fuelwood = fuelwoodt-1 * unburnable fraction

UFWI = FWt-1 * unburn

Soil

BE

soil = soil t-1 + net flux to sink – loss due to afforestation and regeneration operations – loss due to afforesting grasslands

S = St-1 + FS – CLO – GAL

(Net flux to sink, which includes soil respiration, and loss due to afforesting grasslands are only calculated for 75 years after afforestations. After that time, net flux to sink is supposed to be zero, i.e. transfer of carbon from other compartments to soil is equal to soil respiration, and no more losses are supposed to take place due to converting grassland to forest.)

 

carbon loss due to afforestation operations = afforestation area * area specific loss

CLO = A * asl

asl: to be specified by the user

 

carbon loss due to afforesting grasslands = afforestation area * percent of area of grassland * time-dependent difference of carbon stock between cropland and grassland

GAL = A * glp * diff_CL_GL

glp: to be specified by the user

 

diff_CL_GL: values are taken from a country-specific equation

Flux to SINK

Flux to permanent sink = total amount of dead organic matter becoming undecomposable and unburnt = undecomposable dead leaves pool + undecomposable dead roots + undecomposable dead wood + unburnable fraction of firewood

FS = ULI + URI + UWI + UFWI

 

 

II. CARBON ECONOMICS

1. NET ANNUAL FORESTRY COSTSt (EUR or HUF) = TOTAL of ALL ANNUAL COSTSt - TOTAL OF ALL ANNUAL REVENUESt

where TOTAL of ALL ANNUAL COSTSt (EUR or HUF) is the sum of all costs, at current prices, of all forestry operation on all area of the afforestation project that are due in year t; and TOTAL of ALL ANNUAL REVENUESt (EUR or HUF) is the sum of all revenues, at current prices, of all forestry operation on all area of the afforestation project that are due in year t.

2. TOTAL NET FORESTRY COSTSt (EUR or HUF) = SUMi(NET ANNUAL FORESTRY COSTSi)

where TOTAL NET FORESTRY COSTSt is the total costs from the beginning of the afforestation project, i.e. year 1, summed up to year t; and i = 1 to t.

3. TOTAL CARBON IN FORESTRY SYSTEMt = AGWBt + Rt + LLt + DWt + DLt + DRt + WPt + FWt + St

where TOTAL CARBON IN FORESTRY SYSTEMt is to total amount of carbon accumulated in all pools of the afforestation project area up to year t in all carbon pools since year 1; all other symbols as in the table above.

4. TOTAL NET SPECIFIC COSTSt (in EUR/tCO2 or HUF/CO2) = TOTAL NET FORESTRY COSTSt / TOTAL CARBON IN FORESTRY SYSTEMt

where TOTAL NET SPECIFIC COSTSt is the total net forestry costs per a tonne of CO2 sequestered by the afforestation system by year t.

TOTAL NET SPECIFIC COSTSt are also calculated with only the sum of AGWBt + Rt in the denominator to estimate total net specific costs of sequestering carbon in the tree biomass.



This webpage was last modified by Zoltan Somogyi 29 June 2014.

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