Models and Their Adaptation

Abstract

This chapter describes computer simulation models developed for ­estimating greenhouse gas fluxes of different ecosystems. In general, each model is used for the simulation of specific parts of the complex systems; therefore, merging the results of various kind of models can give a better insight. In this chapter, we describe four models used for estimating biospheric fluxes of greenhouse gases in Hungary. The Biome-BGC and the DNDC models are process-based ecological models. The adapted version of Biome-BGC is capable of describing the carbon, nitrogen, and water fluxes of the Hungarian arable lands and grasslands. This model is used to estimate the net primary production (NPP) and the net biome production. DNDC is used to predict the soil fluxes of nitrous oxide and methane, and simulates the biogeochemical cycles of carbon and nitrogen occurring in agricultural soil. MOD17 is a simple lightweight model that is based on remote sensing and ancillary meteorological information, and provides gross primary production (GPP) and NPP data. The CASMOFOR model was developed to estimate how much carbon can be accumulated in afforestation projects.

Appendix

1.1 Equations and Variables Applied in the Accounting System of CASMOFOR to Model the Carbon Cycle of Forests and Forestry

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 forest and forestry system, all the pools and processes of the systems diagram in Fig. 9.1 are meant.

Variables related to carbon pools (in italics) 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.

In the equations below, index t refers to any year of the simulation, (t-1) to the previous year, whereas index (t − x) refers to year x year(s) 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.

To check that all carbon is accounted for, i.e. all incoming fluxes equal to all outgoing fluxes + changes of the carbon content of the system (including ­permanent sinks), an additional equation is tested to conserve mass:

$$\begin{array}{ll}\hbox{Total Flux IN}_{\rm t}&=\text{Total}({\text{POOLS}}_{t}-{\text{POOLS}}_{\text{t}-1})\\ &-\hbox{Total Flux OUT}_{t}-\hbox{Total Flux to SINK}_{\rm t}\end{array}$$

1.1.1 Aboveground Biomass

Type of equation	Equations, variables and parameters (all pools and processes in terms of tC, and calculated once for year t)
BE	AGWB t = AGWB t−1 + CAIC − M − TH − FC
	AGWB: Aboveground woody biomass
	CAIC: current annual increment of aboveground woody biomass
	M: mortality
	TH: thinning
	FC: final cuttings
Flux IN	CAIC = CAI * d * cf
	CAI: current annual increment of tree volume; m−3
	d: weight of oven-dry biomass/volume of fresh wood (at the stand level); tdm m−3
	cf: carbon fraction of oven dry wood; tC tdm−1
Other	M = AGWB t−1 * (ddm + dim)
	ddm: density dependent mortality rate; species dependent; dimensionless
	dim: density independent mortality rate; randomly generated; dimensionless
	ddm + dim <= 0.4
Other	TH = AGWB t−1 * thr
	thr: species specific, depends on age and yield class; dimensionless
	FC = AGWB t−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

1.1.2 Dead Wood

Type of equation	Equations, variables and parameter (all pools and processes in terms of tC ha−1)
BE	DW = DW t−1 + DWI − EW
	DW: dead wood
	DWI: deadwood increment
	EW: decomposition of (i.e., emission from) decomposable dead wood
Other	DWI = [M + TH * (1 − wpTH − fpTH ) + FC * (1 − wpFC − fpFC )] * (1 − ndf)
	wpTH : wood product part of TH, dimensionless
	fpTH : fuelwood part of TH, dimensionless
	wpFC :wood product part of FC, dimentionless
	fpFC: fuelwood part of FC; dimensionless
	ndf: nondecomposable fraction; dimensionless
Flux OUT	EW = Sum i (DW t−i /DTw i ) for i = 1 to x
	DTw: time needed for deadwood to decompose, years
Flux to SINK	UWI = [M + TH * (1 − wpTH − fpTH ) + FC * (1 − wpFC − fpFC )] * ndf
	UWI: Nondecomposable dead wood fraction

1.1.3 Living Leaves

Type of equation	Equations, variables, and parameters (all pools and processes in terms of tC ha−1)
BE	LL = LL t−1 + LI − DLI − DLI * ndf /(1 − ndf)
	LL: amount of (living) leaves
	LI: increment due to tree growth
	DLI: decomposable leaf loss due to harvest and mortality at the end of year
Flux IN	LI = CAIC * increment ratio
	increment ratio: leaf increment/aboveground woody biomass increment; dimensionless
other	DLI = [(LL t−1 + LI) * nll + (LL t−1 + LI) * (1 − nll ) * fdlleaves ] * (1 − ndf)
	nll : ratio of nonliving/living biomass = DWI/AGWB t−1 ; dimensionless
	fdlleaves : fraction of leaves dying and falling at the end of year; species specific (broadleaves: 1; conifers: <1); dimensionless
Flux to SINK	ULI = DLI * ndf /(1 − ndf)
	ULI: Nondecomposable fraction; dimensionless

1.1.4 Dead Leaves

Type of equation	Equations, variables, and parameters (all pools and processes in terms of tC ha−1)
BE	DL = DL t−1 + DLI − EL
	DL: dead decomposable leaves
	DLI: amount of decomposable leaves that die in year
	EL: decomposition of dead leaves
Flux OUT	EL = Sum i (DL t−i /DTL t ) for i = 1 to x
	EL: Total emission due to decomposition of leaves
	DTL: time needed to decompose; year

1.1.5 Living Roots (Belowground Biomass)

Type of equation	Equations, variables and parameters (all pools and processes in terms of tC ha−1)
BE	R = R t−1 + RI − DRI − DRI * ndf /(1 − ndf)
	R: amount of roots
	RI: increase of root biomass
	DRI: amount of decomposable roots that die in year
Flux IN	RI = CAIC * rts
	rts : root-to-shoot ratio
Other	DRI = [(R t−1 + RI) * nll + (LI t−1 + LRI) * (1 − nll ) * fdlroots ] * (1 − ndf)
	fdlroots : Fraction of roots of trees (relative to root increment) that dies at the end of year
Flux to SINK	URI = DRI * ndf /(1 − ndf)
	URI: Nondecomposable fraction; dimensionless

1.1.6 Dead Roots

Type of equation	Equations, variables, and parameters (all pools and processes in terms of tC ha−1)
BE	DR = DR t−1 + DRI – ER
	ER: decomposition of (i.e., emission from) decomposable dead roots
Flux OUT	ER = DR t−i / DTR i
	DTR: time needed to decompose; year

1.1.7 (Industrial) Wood Products

Type of equation	Equations, variables, and parameters (all pools and processes in terms of tC ha−1)
BE	WP = WP t−1 + WPI – WPU
	WP: wood products
	WPI: wood product increment
	WPU: wood products becoming unused
Other	WPI = [FC * used part * (1 − fuelwood part ) + TH * used part (t) * (1 − fuelwood part (t)] * (1 − lost part)
	used part : ratio of wood harvested that is used for wood products, dimensionless
	fuelwoodpart : ratio of wood harvested that is used for fuelwood, dimensionless
	lost part: ratio unused part of wood harvested, dimensionless
Other	WPU = WPI t−i
	Maximum of i: mean life time of wood product (species-specific); years
Flux OUT	EUUWP = WPU t−1 * (1 − unburnt )* WTD
	EUUWP: Emission from (decomposition of) unused and unburned wood product
	unburnt: unburned fraction; dimensionless
	WTD: (mean) time needed to decompose the wood products

1.1.8 Fuelwood

Type of equation	Equations, variables, and parameters (all pools and processes in terms of tC ha−1)
BE	FW = FW t−1 + FWI + LWP + UWPF − EFW
	FW: fuelwood
	FWI: fuelwood increment (from harvest)
	LWP: loss in wood processing
	UWPF: unused wood products becoming fuelwood
	EFW: emission from firewood
Other	FWI = FC * used part * fuelwood part + TH * used part t * fuelwood part t
Other	LWP = WPI * lost part /(1 − lost part)
Other	UWPF = WPU t−1 * unburnt
Flux OUT	EFW = FW t−1 * (1 − unburn)
	unburn: unburnable fraction; dimensionless
Flux to Sink	UFWI = FW t−1 * unburn
	UFWI: unburnable fuelwood

1.1.9 Soil

Type of equation	Equations, variables, and parameters (all pools and processes in terms of tC ha−1) Equations, variables, and parameters (all pools and processes in terms of tC ha−1)
BE	S = St−1 + FS − CLO − GAL
	S: soil
	FS: net flux to sink
	CLO: loss of C from soil due to afforestation and regeneration operations
	GAL: loss of C from soil due to afforesting grasslands
	(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.)
Other	CLO = A * asl
	A: afforestation area by tree species and yield class; ha (to be provided by the user before running of the model)
	asl: area specific carbon loss; to be specified by the user; tC ha-1
Other	GAL = A * glp * diff _CL_GL
	glp: percent of area afforested on former grassland; to be specified by the user; percent
	diff_CL_GL: time-dependent difference of carbon stock between cropland and grassland; tC ha−1
Flux to SINK	FS = ULI + URI + UWI + UFWI

1.2 Equations and Variables Applied to Model Carbon Economics in CASMOFOR

$$ \begin{array}{ll}Net\,annual\,forestry\,costs_{t}&=Total\,of\,all\,annual\,costs_{t}\\ &-total\,of\,all\,annual\,revenues_{t}\end{array} $$

where Total of all annual costs _t is the sum of all costs, at current prices, (in either EUR or Hungarian Forints, HUF) of all forestry operation on all area of the afforestation project that are due in year t; and Total of all annual revenues _t 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.

$$ Total\,net\,forestry\,costs_{t}=SUM_{i}\left(Net\,annual\,forestry\,cost{s}_{i}\right) $$

where Total net forestry costs _t 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.

$$ \begin{array}{ll}Total\,carbon\,in\,forestry\,system_{t}&=AGWB_{t}+L{L}_{t}+{R}_{t}+D{W}_{t}\\ &+D{L}_{t}+D{R}_{t}+W{P}_{t}+F{W}_{t}+{S}_{t}\end{array} $$

where Total carbon in forestry system _t is the total amount of carbon accumulated in the afforestation project area up to year t in all carbon pools since year 1; all other symbols as in the table above.

$$ \begin{array}{ll}&\quad Total\,net\,specific\,costs_{t}\left(in\,EUR/tCO_{2}or\,HUF/tCO\right)\\ &=Total\,net\,forestry\,cost{s}_{t}/Total\,carbon\,in\,forestry\,system_{t}\end{array} $$

where Total net specific costs _t is the total net forestry costs per tonne of CO₂ ­sequestered by the afforestation system by year t.

Total net specific costs _t are also calculated with only the sum of AGWB _t + R _t in the denominator to estimate total net specific costs of sequestering carbon in the tree biomass only.