This section focusses on estimating timber harvest, logging mortality, wood products, sawnwood, sawnwood wastes, wood wastes, belowground dead root, branches and top logs of harvested trees (Figure 1) in production forest in Southeast Asia under two logging practices, namely CVL and RIL. The former is assumed to be the business-as-usual practice while the latter is assumed to be a practice adopted when financial support under the UN’s REDD+ scheme is available. The difference between CVL and RIL is the amount of logging damages, wood wastes caused by logging and wood processing inefficiency (See [14] ).

According to Khun and Sasaki [15] , harvest wood and logging mortality (the latter due to damages by logging) can be obtained by

where

: Harvested wood at time t (MgC ha⁻¹∙year⁻¹)

: Logging mortality caused by logging (MgC ha⁻¹∙year⁻¹)

is aboveground carbon stocks (MgC) defined in Equation (5) of Khun and Sasaki [15] .

Description of other values and parameters are given in Table 1.

Wood products (WP), sawnwood (SW), wood wastes in the forests (WPW), branches and top logs of harvested and damaged trees (BRA) and belowground dead root (BLD) can be derived by

where

: Proportion of wood wastes to harvested logs. These wastes include broken trunks and high stumps. Based on various sources, Sasaki et al. [13] adopted s = 0.3% or 30% for CVL and s = 0.1% or 10% for RIL. We used same value for this study.

: Wood processing efficiency at sawmills (i.e. proportion of wood waste at sawmill). We used same values adopted by Sasaki et al. [13] for wood processing inefficiency (a = 0.5 for CVL, and a = 0.4 for RIL).

BEF: Biomass expansion factor. We used 1.74 as reported by Brown [18] .

0.16% or 16% is the proportion of root to aboveground biomass [19] .

Carbon fluxes in each wood component above at every time step are estimated by first order decay function followed Grier [20] . This method was also recently used by Stockmann et al. [3] to estimate carbon storage in harvested woodproducts from the United States forest service northern region. Carbon remaining in any wood component created by selective logging at any time carbon is obtained by:

where

: Initial amount of carbon at year zero (i.e. starting year of the model)

: Elapsed time (years)

: constant decay rate for wood component i, which can be derived by

where

: Half-life time (years) of wood component i. HL is the time after which half the carbon is no longer in use. Table 2 provides information on HL for various wood component.

Based on 32 native tree species in Malaysian Borneo, Mori et al. [21] estimated HL time ranging about just about 1 year to as high as 28 years for dead trees, with average of about 4.3 years. Tobin et al. [22] estimated the decay rates of 31 stumps and 51 logs at 0.0592 and 0.0466 or 11.7 and 14.9 years of HL time, respectively. Based on data from 199 dead trees in Amazonian forest, Chambers et al. [23] estimated average decay rate of medium-size trees of 0.17 - 0.19 per year or about 4 years of HL time. There are large variations of decay rates ranging from 0.015 (HL = 46.2 years) to 0.67 (HL = 1.0 year) year^?1. Annual temperature in tropical forests is warmer than that in temperate forests, and therefore the decay rate of dead trees in tropical forests is much faster. Given these large variations and for simplicity, we assumed that HL times for SWW, WPW, BRA, and BLD at 3, 5, 4, and 5 years, respectively (Table 2).

Cumulative carbon fluxes in each wood component per hectare are obtained by

where

: carbon fluxes in wood component occurred at harvest time t = n (MgC ha⁻¹)

Cumulative carbon fluxes in each wood component due to logging in production forest in Southeast Asia are therefore

where

: Cumulative carbon fluxes in each wood component (TgC).

: Area of production forest (million ha) taken from our previous study [15] .

Since existing publications on carbon stock changes affected by logging in Southeast Asia are rare, we need to convert carbon stocks in harvested timber, wood products, and sawn wood to cubic volume so that results of this study can be validated against that in previous studies. We converted harvested timber, wood products, and sawn wood from carbon to cubic meter of wood using the following equation:

where

: Amount of wood in wood component i (harvested wood, wood products or sawnwood) at time t (m³∙ha⁻¹).

: Amount of carbon in wood component i (MgC ha⁻¹).

: Wood density (Mg m⁻³). WD is 0.56 [18] .

: Carbon content in dry wood (MgC Mg⁻¹). CT is 0.5 [24] .

Total production for each wood component is therefore

where

: Total production of wood component i (million∙m³).

Wood products are important sources for housing and economic development in Southeast Asia. Between 2015 and 2050 of the modeling timeframe, logging produced about (±for standard error) 0.83 (±0.01) m³∙ha⁻¹, declining about −0.57% year⁻¹. This decline was due to overexploitation and logging damages (harvested wood and logging damages are greater than mean annual increment). Other studies have found that selective logging in the tropics resulted in significant decrease of stand volume or carbon stocks [25] -[28] .

Wood products (roundwood) from logging in production forest in Southeast Asia were 146.6 (±5.4) million∙ m³∙year⁻¹ between 2015 and 2050. Overexploitation coupled with decline in area of production forests [15] caused a decrease of roundwood production of about 2.2 million∙m³ annually over the same period (Figure 2). Of the 146.6 million∙m³, about 73.3 (±2.7) million∙m³ were processed further to sawnwood. The remainder (50%) were wood wastes at the processing sawmills. Other wood components created by selective logging include 217.0 (±8.0), 46.5 (±1.7), and 62.8 (±2.3) million∙m³∙year⁻¹ of branches and top logs, belowground dead root, and wood wastes due to felling, trimming and transporting to sawmills, respectively (Table 3). Wood components (except sawnwood) are usually excluded in any reports by any government and so are carbon fluxes in

these wood components.

Waggener and Lane [29] reported industrial roundwood production in Southeast Asia about 68.1 million∙m³ in 1980 and increased to 87.1 million∙m³ in 1992. Using these data (Figure 3) and based on linear projection, average roundwood production between 2015 and 2050 was 134.4 (±2.3) million∙m³, only about 8% lower than our estimate. This lower prediction may be due to the fact that data of Waggener and Lane [29] did not include wood production from illegal logging. If 50% of illegal logging was included, wood production using data from Waggener and Lane [29] went up to 268.8 million∙m³. This higher value would be possible given that their data were collected when Southeast Asia still had higher forest cover and countries such as Philippines and Thailand were the among major producers of roundwood [30] . Since 1990s, forest resources in the Philippines and Thailand became exhausted. In addition, forest cover in Cambodia, Myanmar, Indonesia, and Laos has declined sharply over the last 15 years [16] . As forest resources in many countries in Southeast Asia continue to decline, it is expected that roundwood product from natural forests (i.e. production forest in our study) will continue to decline. Based on data published by [30] , roundwood production in Southeast Asia peaked at about 105 million∙m³ in 1993 but decline to about 80 million∙m³ in 2007. Whiteman et al. [12] projected the production of industrial roundwood in Malaysia and Indonesia alone to 95.2 million∙m³ in 2010. Our findings of roundwood production are well within the range of previous studies.

Annual fluxes in sawnwood product declined from 0.26 MgC in 2015 to 0.21 MgC ha⁻¹ in 2015 with annual decline rate of about 0.57%. Average fluxes were 0.23 (±0) MgC ha⁻¹ over the same period. Cumulative carbon fluxes in sawnwood were just 0.26 MgC ha⁻¹ in 2015 but cumulatively increased to 5.68 MgC ha⁻¹ in 2050 with increase rate of about 59.2% annually between 2015 and 2050 (Figure 4).

Cumulative carbon fluxes in wood wastes at sawmill (SWW) were 0.26 MgC in 2015 and 1.04 MgC in 2050 after reaching the highest point at 1.14 MgC in 2030. Similar patterns of cumulative fluxes were also seen in wood wastes in the forests (WPW), branches and top logs (BRA), and belowground dead root (BLD). Cumulative carbon fluxes were 0.22, 0.77, and 0.17 MgC ha⁻¹ in 2015 and 1.43, 4.01, and 1.06 MgC ha⁻¹ in 2050 for WPW, BRA, and BLD, respectively (Figure 4). Cumulative carbon fluxes began to decline quickly and emit carbon in about 10 years after harvesting.

Our models suggested that selective logging created huge amount of wood residues remained in the forests and at sawmills. Feldpausch et al. [31] found that logging produced more wood residues in the selectively logged forests. Onsite residues that include branches and top logs, wood waste due to logging (broken logs, stumps), and belowground dead root account for high cumulative carbon fluxes but these fluxes began to decline when inflow fluxes are smaller than outflow fluxes due to wood decay. Offsite fluxes in wood waste at the sawmills has same pattern to that of onsite fluxes. Fluxes in sawnwood continue to increase depending on how sawnwood is further utilized to further make furniture or houses or other building infrastructures.

Cumulative carbon fluxes in sawnwood, onsite and offsite wood components created by selective logging under CVL in production forest in Southeast Asia were estimated at 378.7, 433.0, and 69.1 TgC in 2050 increasing from 29.1, 129.4, and 29.1 TgC in 2015, respectively. Cumulative fluxes in onsite and offsite wood components declined sharply after reaching the highest level at 2028 (13 years after logging) and 2025, respectively (Figure 5). In contrast and despite decline in area of production forests [15] , cumulative fluxes in sawnwoon still increased and reached the highest level at 378.8 TgC in 2049. These fluxes began to decline gradually thereafter due to the decline in area of production forest in Southeast Asia [15] . Totally, selective logging under CVL in Southeast Asia resulted in cumulative carbon fluxes of 187.5 TgC in 2015 and 880.8 TgC in 2050. Depending on carbon accounting methods, the increase in cumulative carbon fluxes could be used to offset carbon emissions from tropical deforestation.

Reduced impact logging (RIL) is assumed as a logging practice that will be adopted for “sustainable management of forests” element of the REDD+ scheme. As RIL was able to significantly reduce wood wastes in the forests (WPW), wood wastes at sawmills (SWS), and logging damages, carbon fluxes in short-lived wood components can be reduced and therefore reduce emissions when inflow fluxes are smaller than outflow fluxes. By being able to reduce damages, more sawnwood production can be achieved from the same amount of harvested timber. Because sawnwood has longer half-life time carbon, more carbon storage can be achieved as shown in Figure 6. Cumulative fluxes in sawnwood under RIL and CVL increased to 608.4 and 378.7 TgC in 2050 from 44.8 and 29.1 TgC in 2015, respectively. After 35 years, cumulative fluxes under RIL were 229.7 TgC higher than that in CVL. In addition, RIL was able to reduce fluxes in short-lived wood components at 100.6 TgC (Figure 6, Table 4). Not only RIL could retain more carbon in standing forests [13] , but it can also increase sawnwood product and carbon fluxes in sawnwood.

Our study findings suggest that adopting RIL not only lead to more carbon being retained in forests but also increase wood production and carbon storage in long-lived wood product. In addition, long-lived wood products could be achieved by technology transfer. If half-life time in sawnwood can be lengthened, more carbon storage in harvested wood products can be further achieved.

There are several potential sources of uncertainty in this study. Initial carbon stocks in tropical forests vary

greatly depending on many factors such as forest types, locations, and levels of disturbance. These variations could result in up to 60% biases of carbon estimates in tropical forests [32] -[34] . For instance, FAO [16] estimated average carbon stocks in tropical Asia at 93 MgC ha⁻¹, while Friedlingstein et al. [35] (2010) and Baccini et al. [2] estimated at 160 and 115 MgC ha⁻¹, respectively. Another potential source of uncertainty is the use of illegal logging (50% of all harvested wood). Illegal logging usually is not reported in any official data of wood production in tropical countries. This is due probably to the lack of proper investigation or the difficulty in controlling illegal logging over large area of tropical forests. Using 166, 115, and 93 MgC ha⁻¹ as initial value for our study, wood products in Southeast Asia were 154.6, 114.3, and 94.7 million∙m³∙year⁻¹, respectively between 2015 and 2050 for 50% (r = 0.5) rate of illegal logging was used. Using same initial carbon stocks but different rates of illegal logging, wood products changed significantly over the same period (Table 5).

There are other factors that could affect results of our study. Not all tropical production forests are suitable for logging due to the presence of water surface, villagers, and environmentally and socially sensitive areas (such as steep slopes, bufferzones around villagers, heritage sites, and so on). These areas are commonly referred to inoperable area, an area where logging can not be carried out. By logging regulation, logging on environmentally and socially sensitive areas is strictly prohibited.