ORCHIDEE v4.2 Technical Documentation

1Land use¶

1.1DONE: Land cover change¶

1.1.1DONE: Land cover change in ORCHIDEE¶

ORCHIDEE accounts for land cover change by reading time series of PFT maps that document the changes in the fraction of each PFT within each grid cell ( $f^{veg,max}$ ), with a default annual time step. The annual PFT maps are generated by making use of a cross-walking table that links ORCHIDEE PFTs with discrete land cover types, whose time-dependent distributions are derived based either on remote sensing (Bontemps et al. (2015), Poulter et al. (2015)) or reconstructions (Hurtt et al. (2011)).

The carbon and hydrological impacts of land cover changes in ORCHIDEE are accounted for based on the net land cover changes between two consecutive years. This means that the local-scale, bi-directional flows between two land cover types, known as gross land cover change, are ignored. At the usual coarse resolution of global scale simulations, i.e., between 0.25 ° x 0.25 ° and 2 ° x 2 °, simulating net instead of gross land cover changes is likely to underestimate the CO₂ emissions from land cover changes Yue et al., 2018. When ORCHIDEE is run at a high spatial resolution, issues from this simplification could be somehow mitigated.

Within ORCHIDEE, land cover change is defined as the change over time in the PFT fractions covering a grid cell, with some PFTs losing land cover, other PFTs gaining land cover. The change in land cover for each PFT is obtained by calculating the difference between two consecutive PFT maps, the sign of which determines whether each PFT is losing or gaining land cover.

\begin{align} &f^{veg,delta} = f^{veg,max}_{y+1}-f^{veg,max}_{y} \end{align}

(405)

The basic approach to account for the effects on the carbon and nitrogen cycle of land cover change is to transfer the fresh litter, together with existing litter and soil organic matter, from the shrinking PFTs to expanding PFTs through an temporary, intermediate litter and soil bank.

1.1.2DONE: Land cover loss of a PFT¶

When a PFT is losing land cover, its carbon, nitrogen and water-related vegetation stress pools are temporarily stored in pool banks. When using forest circumference classes, all circumference classes will lose their areas in proportion to their current areas. Depending on the PFT losing land cover, the biomass pools being transferred will differ. If it is forest, above-ground woody biomass is first harvested and allocated to different components of wood product pool according to the diameter of harvested stem, with different life spans of 1, 17 and 50 years (section 1.7). The unharvested above-ground forest biomass components, including branches, leaves and fruits, and the unharvested below-ground roots, are then transferred to the soil and litter bank pools. For the loss of non-forest PFTs, all biomass components are transferred to the soil and litter bank pools. Each pool bank consists of the average of shrinking pools weighted by their contribution to the total loss in land cover.

M^\text{bank,o} = \frac{\sum_k M^\text{o}_k \cdot f^{veg,delta}}{\sum\limits_{f^{veg,delta}<0} f^{veg,delta}}

(406)

1.1.3DONE: Land cover gain of a PFT¶

Patches of PFTs gaining land cover, with their $f^{veg,max}$ being equal to their areal expansion ( $f^{veg,delta}$ ), will be first established, following 1.10.3, and then merged with existing identical PFTs if ther are any. The final pool density of a given PFT ( $M^{update}$ ), with a gaining area fraction of $f^{veg,delta}$ , after integrating the transferred pools from shrinking PFTs, is thus determined as:

M^{update,o}_{k}= \frac{ M^{o}_{k} \cdot f^{veg,max} + M^\text{bank,o} \cdot f^{veg,delta}} {f^{veg,max}+f^{veg,delta}}

(407)

In the case where circumference classes are used, the vegetation characteristics for the land cover gain are initialized following 1.10.3. The gained land cover will be added to the youngest age class. The patch of the youngest circumference class will be first established, as described above, and then merged with the patch of the existing youngest age class when there is one.

1.1.4DONE: Land cover change of non-biological land¶

When the land cover change involves a gain or loss of non-biological land, the handling of soil carbon and nitrogen has to be adjusted. For gain of non-biological land (i.e. urbanization), soil organic matter is considered as being buried and thus set aside from decomposition, assuming an inert carbon pool. For loss of non-biological land (i.e. glacier retreat or lake dry-off), the initial soil organic matter for the newly vegetated land cover will be taken from the soil and litter bank filled up by corresponding land cover losses.

Water content of the soil column remains unaffected by land cover change but water-related vegetation stress is accounted for in specific cases. Since soil column is shared within soil tiles, that is either trees, herbaceous or bare soil tiles, land cover change within soil tiles maintain the consistency between vegetation stress and soil water content. In the case of land cover changes between soil tiles such as a crop PFT expanding into a tree PFT, the soil water column of the PFT gaining land cover is assumed to follow the expansion of the PFT fraction.

Since non-biological land does not initially have a value for water-related vegetation stress it does not contribute to the moisture bank. When non-biological land remains unchanged, the moisture bank is not used and each PFT has the same water-related vegetation stress as before the land cover change. When non-biological land expands or shrinks, then the moisture bank contributes to the expanding PFT water-related vegetation stress.

1.2Irrigation¶

In ORCHIDEE v4.2 the crop irrigation is optional. When irrigation is simulated, the model calculates XXX

1.3DONE: Crop and grass harvest¶

In ORCHIDEE v4.2 crop harvest is simulated either as a daily turnover throughout the growing season (See 1.1.3) or as single harvest event at the end of the growing season. When harvest a simulated at the end of the growing season, a fraction ( $c_1$ ) of the above-ground carbon and nitrogen mass of cropland PFTs is moved into the harvest pool. The remaining biomass pools are moved into the litter pool:

\begin{align} &M^{har,crop}_{t} = M^{har,crop}_{t-1} + c_1 \cdot (M^{leaf}_{l,t} + M^{res}_{l,t} + M^{lab}_{l,t} + M^{fruit}_{l,t} + M^{sap}_{l,t})) \cdot d^{ind,kill}_{l,t}, \\ &M^{lit}_{l,t} = M^{lit}_{l,t-1} + (M^{root}_{l,t} + (1-c_1) \cdot (M^{leaf}_{l,t} + M^{res}_{l,t} + M^{lab}_{l,t} + M^{fruit}_{l,t} + M^{sap}_{l,t})) \cdot d^{ind,kill}_{l,t}. \end{align}

(408)

Finally, plant biomass and number of individuals are reset to zero until the PFT is replanted in the next growing season (section 1.10.3):

\begin{align} &M^{plant}_{t} = 0,\\ &d^{ind}_{t} = 0, \end{align}

(409)

In ORCHIDEE v4.2 grasslands are simulated as unmanaged ecosystems with a constant plant density. When mortality occurs, the dead biomass is moved to the litter pools. Given that grasslands are simulated as deciduous PFTs, a dormant grassland is replanted the next day. Bud-break and subsequent growth requires suitable PFT-dependent environmental conditions (section 1.1.2).

1.4DONE: Forest management¶

1.4.1DONE: Forest management strategies¶

ORCHIDEE v4.2 uses spatially and temporally resolved management reconstructions to prescribe the forest management strategy to each PFT and grid cell. Where the European management reconstruction McGrath et al., 2015 supports this level of detail, the current global reconstruction (section 1.10) prescribes a single management strategy to the entire grid cell. ORCHIDEE v4.2 relates each management strategies to a set of rules that make forest management dependent on biomass production, diameter, and stand density but not age. As a consequence, forest management in ORCHIDEE v4.2 evolves as the environmental conditions change and the wood harvest is an emerging model outcome rather than a prescribed model input.

The default management has no human intervention and stand structure is determined by disturbances (section 1), natural mortality (section 1.6), and recruitment (section 1.10.2). In addition, four management systems with human intervention have been implemented: (a) rotational even-aged management, in which human intervention is restricted to thinning operations and occasional clear cuts Davis et al., 2005; (b) continuous cover forest management, where recruitment restores stand density following a thinning Davis et al., 2005; (c) coppice management, in which stand density is maintained through shoots sprouting from the root system following a thinning Spinelli et al., 2017; and (d) short rotation forestry, in which a limited number of thinning and re-sprouting cycles occur before the stand is clear cut Liberloo et al., 2010Spinelli et al., 2017.

1.4.2DONE: Forest management rules¶

The state of the forest is described through: (1) two production related indicators, i.e., mean annual wood increment over the life time of the forest ( $F^{npp,wood,lt}$ ) and mean periodic wood increment ( $F^{npp,wood,10year}$ ) both in g C m $^{-2}$ s $^{-1}$ ; (2) two density related indicators, i.e., relative density index ( $f^{RDI,act}$ ) and the target relative density index ( $f^{RDI,upp}$ ) both unitless; and (3) four structural indicators, i.e., the quadratic mean diameter ( $d^{qmdia}$ ), the quadratic mean diameter of the 50 % largest trees of the stand ( $d^{qmdia,50\%}$ ), the height of the tallest 100 individuals ( $d^{h,100trees}$ ), and the stand density that exceed the PFT-specific clear cut diameter ( $d^{ind,ccdia}$ ). Diameters and height are expressed in m, the stand density in m $^{-2}$ . $d^{qmdia}$ , $f^{RDI,act}$ and $f^{RDI,upp}$ are calculated following equations 342, %s and %s, respectively. Note that $f^{RDI,upp}$ is a function of the management strategy. The remaining indicators are calculated as:

\begin{align} &F^{npp,wood,lt}_{t} = F^{npp,wood,lt}_{t-1} \cdot (lt-1) + F^{npp,wood,lt}_{t},\\ &F^{npp,wood,10year}_{t} = F^{npp,wood,10year}_{t-1} \cdot 9 + F^{npp,wood,10year}_{t},\\ &d^{qmdia,50\%} = \sqrt{\frac{4 \cdot \sum_{n=0.5 \cdot d^{ind}}^{d^{ind}}{{d^{dia}_{n}}^{2}}}{\pi \cdot 0.5 \cdot d^{ind}}},\\ &d^{h,100trees}= \frac{\sum_{n=d^{ind}-100}^{d^{ind}}{d^{h}_{n}}}{100}, \end{align}

(410)

where $t-1$ , $t$ , and $lt$ denote respectively the previous year, the current year, and the life time or age of the forest (years). $d^{ind}$ is the stand density (m $^{-2}$ ), $d^{dia}_{n}$ the diameter of individual $n$ , and $d^{h}_{n}$ the height of individual $n$ . In addition to these indicators, the PFT-specific tree diameter above which a stand is cut ( $c_1$ ; m), the PFT-specific tree diameter above which a stand is coppiced ( $c_2$ ; m), the PFT-specific stand density below which a stand is cut ( $c_3$ ; m $^{-2}$ ), the PFT-specific minimum age at which a stand is cut ( $c_4$ ; years) are used to decide if management measures are to be taken at a given PFT and grid cell.

For an unmanaged forest the following rules decide whether the forest has to be self-thinned, converted, or left growing:

\text{unmanaged} \begin{cases} % thinning of unmanaged stands is described in stomate_mark_to_kill.f90 \text{self-thin, if}\ &f^{RDI,act} > f^{RDI,upp}\ \text{and}\ d^{qmdia,50\%} > 0.66 \cdot c_1\\ % density driven mortality is described in stomate_kill.f90 \text{replant or convert, if}\ &d^{ind} < c_3\\ \end{cases}

(411)

Contrary to other management strategy, an unmanaged forest is killed and then replanted. Where in the case of unmanaged forests, "killing" and "replanting" are ORCHIDEE terminology for, an unspecified stand-replacing disturbance and natural regeneration, respectively. Because the stand is unmanaged, the same PFT as before the stand-replacing disturbances is replanted.

For a forest under rotational even-aged management the following rules decide whether the forest has to be thinned, cut, converted, or left growing:

\text{manage} \begin{cases} \text{thin from above, if}\ &f^{RDI,act} > f^{RDI,upp}\ \text{and}\ d^{qmdia,50\%} > 0.66 \cdot c_1\\ \text{thin from below, if}\ &f^{RDI,act} > f^{RDI,upp}\ \text{and}\ d^{qmdia,50\%} < 0.66 \cdot c_1\\ \text{cut or convert, if}\ &F^{npp,wood,lt}_{t} > F^{npp,wood,10year}\ \text{and}\ lt > c_4\\ \text{cut or convert, if}\ &d^{ind,ccdia} > c_3\ \text{and}\ d^{qmdia,50\%} > c_1\\ \text{cut or convert, if}\ &d^{ind} < c_3 \end{cases}

(412)

If changes in forest management are accounted for in the simulation (section

) abandoning rotational even-aged management in favor of unmanaged forest occurs when one of the criteria for a cut are met and, at that time, replaces the final cut.

For a forest under continuous cover management the following rules decide whether the forest has to be thinned, converted, or left growing:

\text{manage} \begin{cases} \text{thin from above, if}\ &f^{RDI,act} > f^{RDI,upp}\ \text{and}\ d^{qmdia,50\%} > 0.66 \cdot c_1\\ \text{thin from below, if}\ &f^{RDI,act} > f^{RDI,upp}\ \text{and}\ d^{qmdia,50\%} < 0.66 \cdot c_1\\ \text{convert, if}\ &F^{npp,wood,lt}_{t} > F^{npp,wood,10year}\ \text{and}\ lt > c_4\\ \text{convert, if}\ &d^{ind} < c_3 \end{cases}

(413)

For a forest under coppice management, the stand density at which the first cut happens ( $d^{ind,cop}$ ; m $^{-2}$ ) is recorded and the following rules decide whether the forest has to be thinned, cut, converted, or left growing:

\text{manage} \begin{cases} \text{thin, if}\ &f^{RDI,act} > f^{RDI,upp}\\ \text{first cut or convert, if}\ &d^{qmdia,50\%} > c_2\\ \text{subsequent cut or convert, if}\ &d^{qmdia,50\%} > c_2\ \text{and}\ d^{ind} > d^{ind,cop}\\ \end{cases}

(414)

For a short rotation coppice forest, the number of rotations ( $n_{rot}$ ; unitless) is calculated from a PFT-specific parameter for rotation length ( $c_5$ ; years), the maximum number of rotations is prescribed ( $c_6$ ; unitless) and the following rules decide whether the forest has to be thinned, cut, converted, or left growing:

\text{manage} \begin{cases} \text{thin, if}\ &f^{RDI,act} > f^{RDI,upp}\\ \text{first cut or convert, if}\ &n_{rot} = 1\\ \text{subsequent cut or convert, if}\ &n_{rot} > 1\ \text{and}\ n_{rot} < c_6\\ \text{final cut or convert, if}\ &n_{rot} = c_6 \end{cases}

(415)

When a forest meets one of the criteria to be cut, converted, or replanted, all trees are marked for harvesting ( $d^{ind,kill}_{l}$ ; m $^{-2}$ ):

d^{ind,kill}_{l} = d^{ind}_{l},

(416)

The management strategy determines which biomass pools of the marked trees are harvested and which not (section 1.4.3). One exception to this general rule is when management is abandoned and the forest management is changed to unmanaged (section

). In that case the biomass for the PFT and grid cell under consideration is preserved reflecting the logic that setting aside older forests with a high biomass provide suitable initial condition to restore the exceptional provision of ecosystems services by intact forests Watson et al., 2018.

When a forest meets one of the criteria to be thinned, only part of the trees are marked for harvesting. Marking depends on the thinning approach ( $c_7$ ; unitless) which in ORCHIDEE v4.2 is PFT-specific and varies continuously from a thinning from below (indicated by a positive value for $c_7$ ) to a thinning from above (indicated by a negative value for $c_7$ ). The probability that circumference class $l$ is thinned ( $p^{thin}_{l}$ ; unitless) is calculated as:

p^{thin}_{l} \begin{cases} \text{if}\ c_7>0,\ &\frac{c_8+(c_9-c_8) \cdot (\max(d^{circ})-d^{circ}_{l})}{(\max(d^{circ})-\min(d^{circ}))^{c_7}}\\ \text{else,}\ &\frac{c_8+(c_9-c_8) \cdot (d^{circ}_{l}-\min(d^{circ})}{(\max(d^{circ})-\min(d^{circ}))^{|c_7|}}\\ \end{cases}

(417)

where $c_8$ (unitless) is the PFT-specific minimum probability that a circumference class is thinned, $c_9$ (unitless) is the PFT-specific maximum probability that a circumference class is thinned, $d^{circ}$ (m) is the circumference of each model tree, and $d^{circ}_{l}$ is the circumference of class $l$ . Thinning is calculated following an iterative approach:

\begin{align} &b_{1} = p^{thin}_{l} \cdot (d^{ind}_{l} - d^{ind,thin}_{l}),\\ &d^{ind,kill}_{l} = d^{ind,thin}_{l} + b_{1},\\ &f^{RDI,pot} = \frac{\sum_{l=1}^{ncirc}{d^{ind}_{l} - d^{ind,kill}_{l}}}{d^{ind,max}} \end{align}

(418)

The probability $p^{thin}_{l}$ enables estimating the stand density that is thinned ( $b_{1}$ ), this estimate is added to previous estimates to record the total stand density marked for killing ( $d^{ind,kill}_{l}$ ), which in turn can be used to calculate the relative density index following the thinning. Iterations continue until $f^{RDI,pot}$ equals $f^{RDI,low}$ for the management strategy under consideration. In case $f^{RDI,pot}$ is less than $f^{RDI,low}$ , the stand density marked for thinning is reduced. The management strategy determines which biomass pools are harvested and which not (section 1.4.3).

1.4.3DONE: Moving biomass to litter and harvest pools¶

For each circumference class either none, part, or all of the individuals are marked for killing ( $d^{ind,kill}_{l}$ ; m $^{-2}$ ) because of forest management (sections 1.4.2. Subsequently, the biomass of the individuals that were marked for killing, is moved into the appropriate biomass pools. Following the thinning or the cut, the stand density is updated. For forest under rotational even-aged management the above-ground wood is harvested and the remainder of the biomass is added to the litter for both a thinning and a cut:

\begin{align} &M^{har,forest}_{t} = M^{har,forest}_{t-1} + (1-c_{10}) \cdot M^{stem}_{l,t} \cdot d^{ind,kill}_{l,t}, \\ &M^{lit}_{t} = M^{lit}_{t-1} + (M^{plant}_{l,t} - (1 - c_{10}) \cdot M^{stem}_{l,t}) \cdot d^{ind,kill}_{l,t}, \\ &d^{ind}_{l,t} = d^{ind}_{l,t-1} - d^{ind,kill}_{l,t}, \end{align}

(419)

where $c_{10}$ is the PFT-specific branch fraction, $M^{har,forest}_{t}$ and $M^{har,forest}_{t-1}$ are the harvest pools at respectively time step $t$ and $t-1$ for a single PFT within a grid cell, $M^{lit}_{t}$ and $M^{lit}_{t-1}$ are the litter mass at respectively time step $t$ and $t-1$ for a single PFT within a grid cell, $M^{stem}_{l,t}$ is the above-ground stem biomass (g plant $^{-1}$ ), and $M^{plant}_{l}$ (g plant $^{-1}$ ) is the plant mass in circumference class $l$ . This calculation is repeated for the carbon and nitrogen biomass.

Continuous cover forests are only subjected to thinning for which the above-ground wood is harvested and the remainder of the biomass is added to the litter following equations 419 to %s.

Under coppice management the root system is preserved for both thinning and cutting:

\begin{align} &M^{har,forest}_{t} = M^{har,forest}_{t-1} + (1-c_{10}) \cdot M^{stem}_{l,t} \cdot d^{ind,kill}_{l,t}, \\ &M^{lit}_{t} = M^{lit}_{t-1} + (M^{plant}_{l,t} - (1 -c_{10}) \cdot M^{stem}_{l,t} - M^{stem,below}_{l,t}) \cdot d^{ind,kill}_{l,t}, \end{align}

(420)

When the stand is thinned, the number of individual stems which share the same root system is updated:

d^{ind}_{l,t} \begin{cases} \text{if thin,}\ &d^{ind}_{l,t} = d^{ind}_{l,t-1} - d^{ind,kill}_{l,t},\\ \text{if cut,}\ &d^{ind}_{l,t} = d^{ind,cop} \end{cases}

(421)

Under short rotation coppice, harvest, litter and biomass pools are treated in the same way (i.e., equations 420 to 421) as if the forest was coppiced. At the last cycle of the rotation the entire forest is cut and the harvest, litter and biomass pools are treated as a clear cut following equations 419 to %s.

1.5DONE: Forest PFT and management change¶

Most land surface models, including previous versions of ORCHIDEE are developed to work with a historical land cover and land management reconstruction, hence, the PFT and its management are prescribed and independent of the stand characteristics. When, for example, the reconstruction prescribed a land cover in the year 1950, this change will be implemented irrespective of whether the stand was thinned the year before or whether the stand was only 10 years old. A difference between ORCHIDEE v4.2 and previous versions of the model is the optional functionality to account for anthropogenic changes in forest PFTs and forest management as a function of the stand dynamics. If changes in forest PFTs and forest management are simulated, ORCHIDEE v4.2 calculates stand growth and forest management but when the stand has reached maturity and needs to be harvested the stand can be replaced by: (1) a stand of a different PFT with under the same forest management, (2) the same PFT under different forest management, (3) a different forest PFT under different forest management, or (4) replanted with the same PFT under the same management as before.

In reality, the species distribution of managed forest is the outcome of human preferences within a climate envelope rather than a natural climate-driven process. Therefore, the ORCHIDEE user can define the forest PFT that is planted at each grid cell if an opportunity emerges. In ORCHIDEE v4.2 opportunities for a change in forest PFT are: (1) a die-back, (2) a clear cut, or (3) a stand replacing disturbance of the current PFT. At present, PFT changes (this section) and land cover changes (section 1) cannot be combined in a single simulation. The functionality to change to prescribed PFTs has been used to quantify the climate impact of future changes in species preferences Luyssaert et al., 2018.

Similarly, the ORCHIDEE user can opt to simulate changes in forest management strategy when an opportunity arises. In ORCHIDEE v4.2 opportunities for forest management changes are: (1) a die-back, (2) a clear cut, and (3) a stand replacing disturbance. To avoid that all unmanaged forests are taken into management in the first year of the simulation, the model waits until the unmanaged forest has reached a stand diameter that would make it qualify for a clear cut if it would have been managed. Forest management strategy changes has been used to quantify the climate impact of changes in forest management policies Luyssaert et al., 2018.

ORCHIDEE v4.2 treats age classes of the forest MTC as different PFTs. Following a change in forest management, different age classes of the same species can thus be under different management strategies, i.e., the youngest age class will follow the new strategy whereas the older age classes will still follow the previous forest management. When biomass from different age classes has to merged into a single age class, the management of the youngest age class of this merge is applied to the entire merged age class to maintain the intention to change forest management. Forests are replanted as different PFTs regardless if they died from human intervention (i.e., a clearcut for high stand management or any harvest with coppice) or from natural causes. If a forest died from a natural cause it is not replanted until January 1st of the following year.

1.6DONE: Forest litter raking¶

Towards the end of the middle ages, farmers began to keep their cattle inside during winter, which led to a demand of forest litter to absorb animals’ wastes Mantel, 1990. In spring, the waste-soaked litter would then be spread on the fields as a form of fertilizer. From 1750 throughout the 1800s litter demand increased Selter, 1995Schenk, 1996. The expanding railroad network, however, made straw more easily available for areas without grain production, and forest litter collection was abandoned towards the end of the 1800s and beginning of the 1900s.

In ORCHIDEE v4.2 litter raking is optional. If litter raking is accounted for in the simulations, the maps of annual litter raking give an estimate of the amount of litter to be removed from each grid cell at the end of every year. If a grid cell does not have enough litter to cover the demand, all is removed but no litter is taken from surrounding grid cells. Subsequently the carbon and nitrogen contained in the raked litter is added to the litter pools of the agricultural PFTs on the same grid cell. The main result of litter raking is thus that forest carbon and nitrogen are diverted to croplands.

1.7DONE: Products use and decay¶

The product pool distinguished three types of biomass products: short-lived ( $M^{prod,s}$ ), medium-lived ( $M^{prod,m}$ ), and long-lived products ( $M^{prod,l}$ ) with a default longevity of 1 ( $lshort)$ , 17 ( $lmedium$ ), and 50 ( $llong$ ) years Eggers, 2002, respectively. Once per year, at the end of the calendar year, the harvest pool is allocated to the three product pools according to one out of two approaches, i.e., a prescribed or dynamic allocation. Once the biomass is allocated to the different product pools, their decomposition follows the same approach irrespective of the allocation approach.

The prescribed approach allocates all harvested biomass from grassland and cropland PFTs to the short-lived products. The biomass harvested from forest is distributed over the short, medium and long-lived pools according to the parameters $c_1$ and $c_2$ which denote the fraction of forest harvest allocated to the short and medium-lived pool respectively:

\begin{align} &M^{prod,s}_{1} = M^{har,crop} + M^{har,grass} + c_1 \cdot M^{har,forest} \\ &M^{prod,m}_{1} = c_2 \cdot M^{har,forest} \\ &M^{prod,l}_{1} = (1 - c_1 - c_2) \cdot M^{har,forest} \end{align}

(422)

The dynamic allocation moves all harvested biomass from grassland and cropland PFTs to the short-lived products as well as the biomass from the forest with a diameter of less than 0.2 m ( $M^{har,forest,<0.2m}$ ).

\begin{align} &M^{prod,s}_{1} = M^{har,crop} + M^{har,grass} + M^{har,forest,<0.2m} \\ &M^{prod,m}_{1} = \frac{c_2}{c_2 + c_3} \cdot M^{har,forest,\ge0.2m} \\ &M^{prod,l}_{1} = \frac{c_3}{c_2 + c_3} \cdot M^{har,forest,\ge0.2m} \end{align}

(423)

In both approaches, $M^{prod,s}_{t}$ , $M^{prod,m}_{t}$ , and $M^{prod,l}_{t}$ are expressed in gram per grid cell. This overcomes the need to store the harvest areas at the PFT and grid cell for the longevity of the long-lived products. $t$ refers to the number of years prior to the current year. For example, $M^{prod,l}_{40}$ would represent the remainder of the biomass added 40 years ago to the long-lived pool.

Both allocation approaches calculate the decomposition of the product pools and the remaining product pools in the same way. First, the annual decomposition rates of the harvested biomass added to this year’s age class ( $t$ =1) ( $F^{prod,s}_{1}$ , $F^{prod,m}_{1}$ , and $F^{prod,l}_{1}$ ; g year $^{-1}$ ) are calculated:

\begin{align} &F^{prod,s}_{1} = \frac{M^{prod,s}_{1}}{lshort}\\ &F^{prod,m}_{1} = \frac{M^{prod,m}_{1}}{lmedium}\\ &F^{prod,l}_{1} = \frac{M^{prod,l}_{1}}{llong} \end{align}

(424)

Given the crude assumptions made in the allocation of the woody biomass to the products pools and the global parametrization of the longevity of the product pools, their decomposition is kept simple by considering a linear decomposition rate although an exponential decomposition rate might be more realistic especially for the short-lived product pool Eggers, 2002. This year’s decomposition rate, together with the decomposition rates calculated in the previous years are summed to obtain the total decomposition of each product pool ( $F^{prod,s}$ , $F^{prod,m}$ , and $F^{prod,l}$ ; g year $^{-1}$ ). The number of previous years considered in this calculation depends on the longevity of the product pool:

\begin{align} &F^{prod,s} = \sum_{t=1}^{lshort}{F^{prod,s}_{t}}\\ &F^{prod,m} = \sum_{t=1}^{lmedium}{F^{prod,m}_{t}}\\ &F^{prod,l} = \sum_{t=1}^{llong}{F^{prod,l}_{t}} \end{align}

(425)

$F^{prod,s}$ , $F^{prod,m}$ , and $F^{prod,l}$ represent the carbon and nitrogen that was once stored in a product pool but now returns back to the atmosphere due because part of the product pool reached the end of its live. Due to these emissions, the carbon and nitrogen that remains in the different age classes of each product pools is calculated as follows:

\begin{align} &M^{prod,s}_{t} = M^{prod,s}_{t} - F^{prod,s}_{t} \\ &M^{prod,m}_{t} = M^{prod,m}_{t} - F^{prod,m}_{t}\\ &M^{prod,l}_{t} = M^{prod,l}_{t} - F^{prod,l}_{t} \end{align}

(426)

Owing to the assumption that the decomposition of the product pools is linear, each year, the following applies:

\begin{align} M^{prod,s}_{lshort} = F^{prod,s}_{1},\\ M^{prod,m}_{lmedium} = F^{prod,m}_{1},\\ M^{prod,l}_{llong} = F^{prod,l}_{1}, \end{align}

(427)

Because of equalities 427, %s, and %s, $M^{prod,s}_{lshort}$ , $M^{prod,m}_{lmedium}$ , and $M^{prod,l}_{llong}$ are zero after applying equations 426 to %s. This implies that $F^{prod,s}_{lshort}$ , $F^{prod,m}_{lmedium}$ , and $M^{prod,l}_{llong}$ are no longer needed. Because the last age classes are now empty or no longer needed, the mass or fluxes contained in each age class is moved to the one year older age class which frees the first age class to receive next year’s harvest in $M^{prod,s}_{1}$ , $M^{prod,m}_{1}$ , and $M^{prod,l}_{1}$ and its annual decomposition in $F^{prod,s}_{1}$ , $F^{prod,m}_{1}$ , and $F^{prod,l}_{1}$ .

References¶

Bontemps, S., Boettcher, M., Brockmann, C., Kirches, G., Lamarche, C., Radoux, J., Santoro, M., Van Bogaert, E., Wegmüller, U., Herold, M., & others. (2015). MULTI-YEAR GLOBAL LAND COVER MAPPING AT 300 M AND CHARACTERIZATION FOR CLIMATE MODELLING: ACHIEVEMENTS OF THE LAND COVER COMPONENT OF THE ESA CLIMATE CHANGE INITIATIVE. International Archives of the Photogrammetry, Remote Sensing & Spatial Information Sciences.
Poulter, B., MacBean, N., Hartley, A., Khlystova, I., Arino, O., Betts, R., Bontemps, S., Boettcher, M., Brockmann, C., Defourny, P., & others. (2015). Plant functional type classification for earth system models: results from the European Space Agency’s Land Cover Climate Change Initiative. Geoscientific Model Development, 8, 2315–2328.
Hurtt, G. C., Chini, L. P., Frolking, S., Betts, R. A., Feddema, J., Fischer, G., Fisk, J. P., Hibbard, K., Houghton, R. A., Janetos, A., Jones, C. D., Kindermann, G., Kinoshita, T., Klein Goldewijk, K., Riahi, K., Shevliakova, E., Smith, S., Stehfest, E., Thomson, A., … Wang, Y. P. (2011). Harmonization of land-use scenarios for the period 1500–2100: 600 years of global gridded annual land-use transitions, wood harvest, and resulting secondary lands. Climatic Change, 109, 117–161. 10.1007/s10584-011-0153-2
Yue, C., Ciais, P., Luyssaert, S., Li, W., McGrath, M. J., Chang, J., & Peng, S. (2018). Representing anthropogenic gross land use change, wood harvest, and forest age dynamics in a global vegetation model ORCHIDEE-MICT v8. 4.2. Geoscientific Model Development, 11(1), 409–428.
McGrath, M. J., Luyssaert, S., Meyfroidt, P., Kaplan, J. O., Bürgi, M., Chen, Y., Erb, K., Gimmi, U., McInerney, D., Naudts, K., Otto, J., Pasztor, F., Ryder, J., Schelhaas, M.-J., & Valade, A. (2015). Reconstructing European forest management from 1600 to 2010. Biogeosciences, 12(14), 4291–4316. 10.5194/bg-12-4291-2015
Davis, L. S., Johnson, K. N., & Bettinger, P. (2005). Forest Management: To Sustain Ecological, Economic, and Social Values. Waveland Press. https://books.google.be/books?id=mP5rAAAACAAJ
Spinelli, R., Magagnotti, N., & Schweier, J. (2017). Trends and perspectives in coppice harvesting. Croatian Journal of Forest Engineering: Journal for Theory and Application of Forestry Engineering, 38(2), 219–230.
Liberloo, M., Luyssaert, S., Bellassen, V., Djomo, S. N., Lukac, M., Calfapietra, C., Janssens, I. a, Hoosbeek, M. R., Viovy, N., Churkina, G., Scarascia-Mugnozza, G., Ceulemans, R., & Njakou Djomo, S. (2010). Bio-Energy Retains Its Mitigation Potential Under Elevated CO2. PLoS ONE, 5(7), e11648. https://doi.org/e11648 10.1371/journal.pone.0011648
Watson, J. E., Evans, T., Venter, O., Williams, B., Tulloch, A., Stewart, C., Thompson, I., Ray, J. C., Murray, K., Salazar, A., & others. (2018). The exceptional value of intact forest ecosystems. Nature Ecology & Evolution, 2(4), 599–610.
Luyssaert, S., Marie, G., Valade, A., Chen, Y.-Y., Njakou Djomo, S., Ryder, J., Otto, J., Naudts, K., Lansø, A. S., Ghattas, J., & others. (2018). Trade-offs in using European forests to meet climate objectives. Nature, 562(7726), 259–262.
Mantel, K. (1990). Wald und Forst in der Geschichte. Schaeper.
Selter, B. (1995). Waldnutzung und ländliche Gesellschaft - Landwirtschaftlicher Nährwald und neue Holzökonomie im Sauerland des 18. und 19. Jahrhunderts (p. 482). Paderborn.
Schenk, W. (1996). Waldnutzung, Waldzustand und regionale Entwicklung in vorindustrieller Zeit im mittleren Deutschland. Historisch-geographische Beiträge zur Er forschung von Kulturlandschaften in Mainfranken und Nordhessen (Vol. 117, p. 325). Steiner.
Eggers, T. (2002). The impacts of manufacturing and utilisation of wood products on the European carbon budget [Techreport]. European Forest Institute Joensuu.