Changing Temporal Patterns of Forest Carbon Stores and Net Ecosystem Carbon Balance: the Stand to Landscape Transformation

Abstract

Short- and long-term patterns of net ecosystem carbon balance (NECB) for small, relatively uniform forest stands have been examined in detail, but the same is not true for landscapes, especially those with heterogeneous disturbance histories. In this paper, we explore the effect of two contrasting types of disturbances (i.e., fire and tree harvest) on landscape level NECB by using an ecosystem process model that explicitly accounts for changes in carbon (C) stores as a function of disturbance regimes. The latter were defined by the average disturbance interval, the regularity of the disturbance interval (i.e., random, based on a Poisson frequency distribution, or regular), the amount of C removed by the disturbance (i.e., severity), and the relative abundance of stands in the landscape with unique disturbance histories. We used the model to create over 300 hypothetical landscapes, each with a different disturbance regime, by simulating up to 200 unique stand histories and averaging their total C stores. Mean NECB and its year-to-year variability was computed by calculating the difference in mean total C stores from one year to the next. Results indicated that landscape C stores were higher for random than for regular disturbance intervals, and increased as the mean disturbance interval increased and as the disturbance severity decreased. For example, C storage was reduced by 58% when the fire interval was shortened from 250 years to 100 years. Average landscape NECB was not significantly different than zero for any of the simulated landscapes. Year-to-year variability in landscape NECB, however, was related to the landscape disturbance regime; increasing with disturbance severity and frequency, and higher for random versus regular disturbance intervals. We conclude that landscape C stores of forest systems can be predicted using the concept of disturbance regimes, a result that may be a useful for adjusting estimates of C storage to broad scales that are solely based on physiological processes.

Appendices

Appendix A

Equations in the disturbance model to calculate the C pool size of live, dead, and stable pools.

In general, C pools equal input minus output fluxes at each time-step:

$$\eqalign{\hbox{C}_{\rm POOL} (t)=\ \hbox{C}_{\rm POOL} (t-1) + \Sigma \hbox{ Input}_{\rm POOL} (t)\cr - \Sigma \hbox{ Output}_{\rm POOL} (t)}$$

(1)

$$\hbox{a. }\Sigma \hbox{Output}_{\rm POOL} (t)= \Sigma \hbox{Loss}_{\rm POOL} (t) +\Sigma \hbox{ TR}_{\rm POOL} (t)$$

$$\hbox{b. }\Sigma\hbox{ Input}_{\rm POOL} (t)=\Sigma\hbox{ TR}_{\rm POOL}(t)$$

Live Pools

An exception to Eq. (1) is the calculation of foliage C (C_FOL):

$$\hbox{C}_{\rm FR} (t)=\hbox{C}_{\rm FOL} (t)^* {\bf FR:FOL}$$

(2)

All live pools transfer C to their corresponding dead pool because of tree mortality:

$$\hbox{M}_{\rm LIVE\ POOL}\hbox{(t)}=\hbox{C}_{\rm LIVE\ POOL} (t-1)^* {\bf M}_{{\bf LIVE\ POOL}}$$

(3)

Additionally, fine root and foliage pools transfer C to dead pools via turnover:

$$\Sigma\hbox{ TR}_{\rm POOL}(t)=\hbox{ TU}_{\rm POOL} (t) + \hbox{M}_{\rm POOL} (t)$$

(4)

$$ \hbox{a. TU}_{\rm POOL} (t)=\hbox{C}_{\rm POOL} (t)^* {\bf TU}_{{\bf POOL}}$$

The SW, HR, BR, and CR pools lose C via respiration:

$$ \Sigma\hbox{ Loss}_{\rm POOL} (t)=\hbox{R}_{\rm POOL} (t)$$

(5)

$$\hbox{a. R}_{\rm POOL} (t)=\hbox{C}_{\rm POOL} (t-1)^* {\bf R}_{\bf{POOL}}$$

Allocation of C to sapwood is proportional to foliage C:

$$\Sigma\hbox{ Input}_{\rm SW} (t)=\hbox{C}_{\rm FOL} (t)^* {\bf BGE},$$

(6)

Sapwood transfers C to heartwood via mortality and HW formation:

$$\Sigma\hbox{ TR}_{\rm SW}(t)=\hbox{F}_{\rm HW} (t) + \hbox{M}_{\rm SW} (t)$$

(7)

$$\hbox{a. F}_{\rm HW} (t)=\hbox{C}_{\rm SW} (t-1)^* {\bf F}_{{\bf HW}}$$

$$\Sigma\hbox{Input}_{\rm HW} (t)=\hbox{F}_{\rm HW} (t)$$

(8)

Heartwood transfers C to heart rot via mortality and HR formation:

$$\Sigma\hbox{ TR}_{\rm HW} (t)=\hbox{F}_{\rm HR} (t) + \hbox{M}_{\rm HW}(t)$$

(9)

$$\hbox{a. F}_{\rm HR} (t)=\hbox{C}_{\rm HW} (t-1)^* {\bf F}_{{\bf HR}}$$

$$\Sigma\hbox{ Input}_{\rm HR} (t)=\hbox{F}_{\rm HR} (t)$$

(10)

BR and CR input is proportional to SW input:

$$\Sigma\hbox{ Input}_{POOL} (t)=\Sigma\hbox{ Input}_{\rm SW} (t)^* {\bf POOL:BOLE}$$

(11)

CR and BR transfers C to dead pools via mortality and pruning:

$$\Sigma\hbox{Output}_{\rm POOL} (t)=\hbox{M}_{\rm POOL} (t) + \hbox{P}_{\rm POOL} (t)$$

(12)

$$ \hbox{a. P}_{\rm POOL} (t)=\hbox{C}_{\rm POOL} (t-1)^* {\bf P}_{\bf{POOL}}$$

Dead Pools

Dead pools (except dead HW) receive C from their corresponding live pool:

$$\Sigma\hbox{ Input}_{{\rm DEAD-POOL}} (t)=\Sigma\hbox{ TR}_{\rm POOL} (t)$$

(13)

Dead HW receives C from HW and HR:

$$\Sigma\hbox{Input}_{{\rm DEAD-HW}} (t)=\Sigma\hbox{ TR}_{\rm HW} (t) + \Sigma\hbox{TR}_{\rm HR} (t)$$

(14)

Dead boles are separated into snags and logs. Logs receive C from snags due to snag fall:

$$\eqalign{ \Sigma\hbox{Input}_{{\rm POOL-SNAGS}} (t)\cr \quad=\Sigma\hbox{Input}_{{\rm DEAD- POOL}} (t)^* \%{\bf Snags}}$$

(15)

$$\eqalign{ \Sigma\hbox{ Input}_{{\rm POOL-LOGS}} (t)\cr \quad = (\Sigma\hbox{ Input}_{{\rm DEAD- POOL}} (t)\cr \qquad- \Sigma\hbox{ Input}_{{\rm POOL-SNAGS}} (t))\cr \qquad+ \Sigma\hbox{ TR}_{{\rm POOL-SNAGS}}(t)}$$

(16)

$$\eqalign{ \hbox{a. }\Sigma\hbox{TR}_{{\rm POOL-SNAGS}} (t)\cr \qquad = \hbox{C}_{{\rm POOL-SNAGS}} (t-1)^* {\bf FA}_{POOL}}$$

C lost via decomposition (D_DEAD-POOL) _t is calculated from the pool’s decay rate, a weighted average of the pool’s existing decay rate and the decay rate associated with its input flux (D).

$$\Sigma\hbox{ Loss}_{\rm DEAD-POOL} (t)=\hbox{D}_{\rm DEAD-POOL} (t)$$

(17)

$$\eqalign{ \hbox{a. D}_{\rm DEAD-POOL} (t)\cr \qquad\quad=\hbox{C}_{\rm DEAD-POOL} (t-1)^* \hbox{DR}_{\rm DEAD-POOL} (t)}$$

$$\eqalign{ \hbox{b. DR}_{\rm DEAD-POOL} (t)\cr =\hbox{weighted-avg}(\hbox{DR} _{\rm DEAD-POOL} (t-1), \cr \qquad\hbox{C}_{\rm DEAD-POOL} (t-1), \cr \qquad {\bf D}_{\bf {DEAD-POOL}}, \Sigma\hbox{ Input}_{\rm DEAD-POOL} (t))}$$

$$\eqalign{ \hbox{c. weighted-avg}(\hbox{rate}_{1}, \hbox{mass}_{1}, \hbox{rate}_{2}, \hbox{mass}_{2})\cr \qquad=(\hbox{rate}_{1}^* \hbox{mass}_{1} + \hbox{rate}_{2}^* \hbox{mass}_{2}) / (\hbox{mass}_{1} + \hbox{mass}_{2})}$$

The input decay rate of SW or HW is used for snag and log pools:

$${\bf D}_{{\bf POOL-SNAGS}}={\bf D}_{{\bf POOL-LOGS}}={\bf D}_{{\bf DEAD-POOL}}$$

(18)

The non-bole dead pools and the log pools transfer C to the stable pools:

$$\eqalign{ \Sigma\hbox{TR}_{\rm DEAD-POOL}(t)\cr \quad=\hbox{C}_{\rm DEAD-POOL}(t-1)^* {\bf TR}_{\rm DEAD-POOL}}.$$

(19)

Stable Pools

Stable pools receive C from corresponding dead pools:

$$\Sigma\hbox{Input}_{{\rm ST-FOL}} (t)=\Sigma\hbox{ TR} _{ {\rm DEAD-FOL}} (t)$$

(20)

$$\eqalign{\Sigma\hbox{ Input}_{{\rm ST-WOOD}} (t)= \Sigma\hbox{ TR}_{{\rm SW-LOGS}} (t)\cr + \Sigma\hbox{ TR}_{{\rm HW-LOGS}} (t)\cr + \Sigma\hbox{ TR}_{{\rm DEAD-BR}} (t)}$$

(21)

$$\eqalign{\Sigma\hbox{ Input}_{{\rm ST-SOIL}} (t)= \Sigma\hbox{ TR} _{ {\rm DEAD-CR}} (t) \cr + \Sigma\hbox{ TR}_{{\rm DEAD-FR}} (t)}$$

(22)

and they lose C via decomposition:

$$\Sigma\hbox{ Loss}_{\rm ST-POOL} (t)=\hbox{C}_{\rm ST-POOL}(t-1)^* {\bf D}_{{\bf ST-POOL}}$$

(23)

Appendix B

Pools are adjusted for disturbance after the annual calculations (Appendix A).

Harvest

Harvest events are catastrophic:

$$\hbox{C}_{\rm LIVE-POOL} (t_{{\rm POST-HARVEST}})=0$$

(1)

Live non-bole pools transfer C to dead pools:

$$\eqalign{ \hbox{C}_{\rm DEAD-POOL} (t_{{\rm POST-HARVEST}})\cr \quad=\hbox{C}_{\rm DEAD-POOL} (t) + \hbox{CUT}\_\hbox{TR}_{\rm POOL} (t)}$$

(2)

$$\hbox{a. CUT}\_\hbox{TR}\_{\rm POOL} (t)=\hbox{C}_{\rm POOL} (t).$$

A user-specified portion of bole C is taken off site:

$$\eqalign{ \hbox{CUT}\_\!\_\hbox{TR}_{\rm BOLE-POOL} (t)\cr \quad=\hbox{C} _{\rm BOLE-POOL} (t) - \hbox{HARVEST}\_\hbox{TR}_{\rm BOLE-POOL} (t)}$$

(3)

$$\eqalign{ \hbox{a. HARVEST}\_\hbox{TR}_{\rm BOLE-POOL} (t)\cr \quad = \hbox{C}_{\rm BOLE-POOL} (t)^*\%{\bf taken}.}$$

The portion remaining is transferred into the log pools:

$$\eqalign{ \hbox{C}_{{\rm SW-LOGS}} (t_{{\rm POST-HARVEST}})\cr \quad = \hbox{C}_{{\rm SW-LOGS}} (t) + \hbox{CUT}\_\hbox{TR}_{\rm SW} (t)}$$

(4)

$$\eqalign{ \hbox{C}_{{\rm HW-LOGS}} (t_{{\rm POST-HARVEST}})\cr \quad = \hbox{C}_{{\rm HW-LOGS}} (t) + \hbox{CUT}\_\hbox{TR}_{\rm HW} (t)\cr \qquad+ \hbox{CUT}\_\hbox{TR}_{\rm HR} (t)}$$

(5)

Fire

If there is no harvest before the fire, then:

$$\hbox{C}_{\rm POOL} (t_{{\rm PRE-FIRE}})=\hbox{C}_{\rm POOL} (t)$$

(6)

With harvest:

$$\hbox{C}_{\rm POOL} (t_{{\rm PRE-FIRE}})=\hbox{C}_{\rm POOL} (t_{{\rm POST-HARVEST}}).$$

(7)

Fire events are catastrophic:

$$\hbox{C}_{\rm LIVE-POOL} (t_{\rm POST-FIRE})=0$$

(8)

Live pools transfer C to dead pools depending on fire intensity (low, moderate, or high).

$$\eqalign{ \hbox{BURN}\_\hbox{TR}_{\rm LIVE-POOL} (t)\cr =\hbox{C}_{\rm LIVE-POOL} (t_{{\rm PRE-FIRE}})^* {\bf \%transfer}_{{\bf fire intensity}}}$$

(9)

The remaining amount is combusted:

$$\eqalign{ \hbox{BURN}\_\hbox{LOSS}_{\rm LIVE-POOL} (t)\cr \quad=\hbox{C}_{\rm LIVE-POOL} (t_{{\rm PRE-FIRE}})\cr \qquad- \hbox{BURN}\_\hbox{TR}_{\rm LIVE-POOL} (t)}$$

(10)

The amount of dead and stable pool C that remains is:

$$\eqalign{ \hbox{BURN}\_\hbox{LOSS}_{\rm POOL} (t)\cr \quad=\hbox{C}_{\rm POOL} (t_{{\rm PRE-FIRE}})^*\cr \qquad\quad (100\% - {\bf \%remaining}_{{\bf fire\ intensity}}).}$$

(11)

Non-bole dead C is adjusted for the burn loss and transfer from the live pool:

$$\eqalign{ \hbox{C}_{\rm DEAD-POOL} (t_{{\rm POST-FIRE}})\cr \quad=\hbox{C}_{\rm DEAD-POOL} (t_{{\rm PRE-FIRE}})\cr \qquad- \hbox{BURN}\_\hbox{LOSS}_{\rm DEAD-POOL} (t)\cr \qquad+ \hbox{BURN}\_\hbox{TR}_{\rm LIVE-POOL} (t).}$$

(12)

Transfers from live pools are added to dead bole pools:

$$\eqalign{ \hbox{C}_{{\rm SW-SNAGS}} (t_{{\rm POST-FIRE}})\cr \quad=\hbox{C}_{{\rm SW-SNAGS}} (t_{{\rm PRE-FIRE}})\cr \qquad- \hbox{BURN}\_\hbox{LOSS}_{{\rm SW-SNAGS}} (t)\cr \qquad + \hbox{BURN}\_\hbox{TR}_{{\rm SW-SNAGS}} (t)}$$

(13)

$$ \eqalign{ \hbox{C}_{{\rm HW-SNAGS}} (t_{{\rm POST-FIRE}})\cr \quad = \hbox{C}_{{\rm HW-SNAGS}} (t_{{\rm PRE-FIRE}})\cr \qquad - \hbox{BURN}\_\hbox{LOSS}_{{\rm HW-SNAGS}} (t)\cr \qquad+ \hbox{BURN}\_\hbox{TR}_{{\rm HW-SNAGS}} (t) + \hbox{BURN}\_\hbox{TR}_{{\rm HR}} (t)}$$

(14)

$$\eqalign{ \hbox{C}_{{\rm SW-LOGS}} (t_{{\rm POST-FIRE}})\cr \quad =\hbox{C}_{{\rm SW-LOGS}} (t_{{\rm PRE-FIRE}})\cr \qquad - \hbox{BURN}\_\hbox{LOSS}_{{\rm SW-LOGS}} (t)\cr \qquad+ \hbox{BURN}\_\hbox{TR}_{{\rm SW-LOGS}} (t)}$$

(15)

$$\eqalign{ \hbox{C}_{{\rm HW-LOGS}} (t_{{\rm POST-FIRE}})\cr \quad =\hbox{C}_{{\rm HW-LOGS}} (t_{{\rm PRE-FIRE}})\cr \qquad- \hbox{BURN}\_\hbox{LOSS}_{{\rm HW-LOGS}} (t)\cr \qquad+ \hbox{BURN}\_\hbox{TR}_{{\rm HW-LOGS}} (t) + \hbox{BURN}\_\hbox{TR}_{{\rm HR}}(t).}$$

(16)