Wei et al. Carbon Balance and Management
(2023) 18:1
Page 4 of 10
are accounted for separately in the estimator. The build- ing subpool stores carbon in wood products used in con- struction. The exterior-use carbon pool represents the wood products that are employed out-of-doors such as wood dock and railway tie. The home application carbon pool includes wood products used inside such as furni- ture and wood floor. Each of these subpools is assigned a service life in the estimator, and when the end-use wood product reaches the end of its service life, it will be dis- posed (Fig. 1). The disposed wood product can be recy- cled to create new products, used as biomass fuel, or directly disposed to landfills. Waste wood products in landfills will be decomposed and the carbon is eventually released to the atmosphere after a decaying period. Wood products carbon flux Because charcoal is chemically and biologically stable, it has a relatively long residence time in the environment [23]. Therefore, although the annual production of non- energy use biochar and charcoal formed by biofuel burn- ing is relatively small, the magnitude of charcoal carbon pool represents a potentially significant long-term sink of atmospheric CO 2 [24]. The carbon stored in the charcoal pool can be released to the atmosphere by recombus- tion and decomposition. To model the annual loss from the charcoal carbon pool, a pool-size based approach is employed in WPsCS Estimator (Eq. 1) [24]. where ρ cha is the annual charcoal loss rate (fraction of the pool), τ is the basic loss rate, σ is the pool-size related loss rate, and C cha is the carbon pool size of charcoal (kg). The carbon storage lifetimes vary significantly among the different end-use wood products, from short-term directly disposed wood products such as household paper to long-lasting building materials [25]. To model the annual disposal rate for different wood products, a service-life based approach is used in WPsCS Estimator. This method incorporates the time since production and average service half-life, along with a Chi-squared regres- sion model to estimate the annual disposal rate (Eq. 2) [4, 20]. Therefore, for a given type of end-use wood prod- uct made in year i , the carbon remaining in in year j is accounted for in the product pool that has not reached its service life (Eq. 3) (Integration of Eq.2). (1) ρ cha = τ + σ × ln ( C cha )
j − i
− β × ( tw − δ) 2 δ
α
C r = C w −
(3)
e
d t
√ 2 π ×
w
e
0
where ρ wp is the annual disposal rate for a type of wood products (fraction of the pool), α and β are fitted coef- ficients (unitless), γ is the service half-life (year) of the product type, and t w is the time since production (year). In year j , C r (kg) represents the remaining carbon in the wood products pool that was produced in year i , and C w (kg) is the total carbon in these wood products produced in year i . A portion of the end-of-life wood materials will be recycled to make new wood products or reused as bio- fuel, with the remainder disposed to landfills. In WPsCS Estimator, most paper products can be recycled or used as biofuel to generate energy, but wood products for exterior use and household paper are not considered for recycling. Instead, exterior use and household paper wood products are directly disposed to landfills. The recycling rates for wood products are highly dependent on the technology advancement of the wood industry [26]; therefore, to represent the technological advance- ment in the wood industry influence on recycling rates of disposed wood products, a time-dependent approach is employed in the estimator (Eq. 4) [20]. This recycling rate includes both the carbon reused to make new wood products and as biofuel.
(4)
r = + μ × ln ( k )
where r is the recycling rate for a type of recyclable wood products, is the recycling rate in the first year (initial year), μ represents the effect of industrial advancement on wood products recycling, and k is the order of year or the year since the initial year (i.e., 0, 1, 2 … k ). The decay rate for each type of waste wood product in the landfill is primarily determined by its physical and chemical characteristics [27]. For example, waste paper has a shorter turnover time than does waste building materials and so are tracked as four separate subpools in WPsCS Estimator. The annual decay rate for each type of waste wood product is modeled by the time since dispo- sition (year) and turnover time (years), along with a log- normal regression model (Eq. 5) [27, 28]. The turnover time is the entire period (number of years) required for the waste wood product in the landfill to be completely decomposed and emitted to the atmosphere.
− β × ( tw − γ) 2 γ
ln ( t
l )
α
(5)
(2)
ρ lf = ξ ×
e
√ 2 π
ρ wp =
√ 2 π ×
ω ×
e
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