Forest Age Structure — Carbon, Harvest, Volume and Habitat: 04-For-A4 Forest Management, May 2014, Q6

Question 6: Forest Age Structure — Carbon, Harvest, Volume and Habitat (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A 70,000 ha forest of one stand type, area distributed by age class per Figure 2, with per-hectare volume, carbon and shrub-cover curves (Figures 3–5) read off the source graphs at each 10-year age class:

Given data — forest age-class structure and per-hectare development curves
Stand age (yrs)	Area (x1,000 ha)	Volume (m³/ha)	Carbon (T/ha)	Shrub cover (%)
10	8	0	0	25
20	6	0	10	35
30	9	10	20	30
40	8	40	60	20
50	7	100	120	15
60	9	140	180	8
70	8	180	220	6
80	7	200	260	5
90	4	200	280	3
100	2	200	280	1
110	1	180	280	2
120	1	140	280	3
Total = 70 (x1,000 ha) = 70,000 ha

Find. 6A: total forest carbon content today (2012). 6B: area harvested by age class over 2012–2021. 6C: harvest volume generated over 2012–2022. 6D: hectares of green-warbler habitat (≥25% shrub cover) at year 2022.

Fig. 3 — Forest age-class area (Figure 2 reproduction), 2012, with the 10,000 ha harvested over 2012–2021 under oldest-first area regulation shaded (derived in 6B).

Check: Figures 2–5 in the source are small hand-drawn curves whose own caption notes the axis scales are approximate; the table above reads each curve to the nearest labelled gridline division. Two internal checks support the reading: the area-by-age-class values (Figure 2) sum exactly to the stated 70,000 ha, and the carbon curve read on the 20 T/ha minor-gridline spacing gives a total forest carbon of exactly 9.0 million tonnes in 6A. Individual curve reads are good to about one minor gridline division, so the boxed totals should be quoted as read-off-a-graph figures, not to five significant digits.

6A — Total forest carbon content today (2012) (5 marks)

Approach. Sum, over every age class, the area (ha) times the per-hectare carbon content at that age (Given table).

Multiply area by per-hectare carbon for each age class and sum:

Age	Area (ha)	Carbon (T/ha)	Subtotal (T)
10	8,000	0	0
20	6,000	10	60,000
30	9,000	20	180,000
40	8,000	60	480,000
50	7,000	120	840,000
60	9,000	180	1,620,000
70	8,000	220	1,760,000
80	7,000	260	1,820,000
90	4,000	280	1,120,000
100	2,000	280	560,000
110	1,000	280	280,000
120	1,000	280	280,000

Sum the subtotals. $$C_{total} = \sum_i A_i \times c_i = \boxed{9{,}000{,}000\ \text{tonnes C} = 9.0\ \text{million tonnes C}}$$

6B — Area harvested by age class, 2012–2021 (5 marks)

Approach. First find the rotation length required by (b): the age of peak mean annual increment (MAI = volume ÷ age). Area regulation then sets the annual allowable cut AREA to total area ÷ rotation; apply that decade target oldest-first (per (c)) against the Figure 2 area distribution.

Find the age of peak MAI from the Given volume curve: $$MAI(60)=\frac{140}{60}=2.33,\quad MAI(70)=\frac{180}{70}=2.57,\quad MAI(80)=\frac{200}{80}=2.50\ \text{m}^3/\text{ha/yr}$$ MAI peaks at stand age 70 (consistent with the volume curve's inflection — current annual increment (140→180)/10=4.0 m³/ha/yr at age 60–70 still exceeds the MAI, while (180→200)/10=2.0 at 70–80 has fallen below it, which is exactly the MAI=CAI crossing condition). So rotation R = 70 years.
Compute the decade's target harvest area. $$\text{AAC}_{area} = \frac{70{,}000\ \text{ha}}{70\ \text{yr}} = 1{,}000\ \text{ha/yr} \quad\Rightarrow\quad \text{decade target} = 1{,}000 \times 10 = 10{,}000\ \text{ha}$$
Allocate 10,000 ha oldest-first against the Figure 2 age classes, starting from age 120 and working down:

Age class Available (ha) Harvested (ha)

120 1,000 1,000 (all)

110 1,000 1,000 (all)

100 2,000 2,000 (all)

90 4,000 4,000 (all)

80 7,000 2,000 (partial — running total reaches 10,000 ha here)

Running total: 1,000+1,000+2,000+4,000+2,000 = $\boxed{10{,}000\ \text{ha}}$, spanning the age-80 through age-120 classes.

Age class	Available (ha)	Harvested (ha)
120	1,000	1,000 (all)
110	1,000	1,000 (all)
100	2,000	2,000 (all)
90	4,000	4,000 (all)
80	7,000	2,000 (partial — running total reaches 10,000 ha here)

6C — Harvest volume, 2012–2022 (5 marks)

Approach. Multiply the harvested area in each age class from 6B by that age class's per-hectare volume (Given table) and sum.

Multiply and sum by age class:

Age Harvested (ha) Volume (m³/ha) Subtotal (m³)

120 1,000 140 140,000

110 1,000 180 180,000

100 2,000 200 400,000

90 4,000 200 800,000

80 2,000 200 400,000
Sum. $$V_{harvest} = 140{,}000+180{,}000+400{,}000+800{,}000+400{,}000 = \boxed{1{,}920{,}000\ \text{m}^3}$$

Age	Harvested (ha)	Volume (m³/ha)	Subtotal (m³)
120	1,000	140	140,000
110	1,000	180	180,000
100	2,000	200	400,000
90	4,000	200	800,000
80	2,000	200	400,000

6D — Green warbler habitat at year 2022 (5 marks)

Approach. Age every stand by 10 years to 2022; the 10,000 ha harvested during the decade regenerates and is treated as the new youngest (age-10) class by 2022. Apply the ≥25% shrub-cover habitat threshold (Given table) to the resulting 2022 age structure.

Build the 2022 age structure. Unharvested area in each class ages by +10 yr; the harvested 10,000 ha becomes the new age-10 class:

2022 age	Area (ha)	Origin
10	10,000	regenerated (harvested 2012–2021)
20	8,000	was age 10
30	6,000	was age 20
40	9,000	was age 30
50	8,000	was age 40
60	7,000	was age 50
70	9,000	was age 60
80	8,000	was age 70
90	5,000	was age 80 (7,000 − 2,000 harvested)

(Ages 100–120 are fully harvested by 2012–2021, so no area remains there; total = 10+8+6+9+8+7+9+8+5 = 70 ×1,000 ha = 70,000 ha, confirming area is conserved.)

Apply the ≥25% shrub-cover threshold (Given table): age 10→25% (qualifies), age 20→35% (qualifies), age 30→30% (qualifies), age 40→20% (fails). Only the three youngest 2022 age classes qualify: $$\text{Habitat} = 10{,}000+8{,}000+6{,}000 = \boxed{24{,}000\ \text{ha}}$$

Question 6 — final results
Part	Quantity	Result
6A	Total forest carbon content, 2012	9,000,000 t C (9.0 million t)
6B	Area harvested, 2012–2021	10,000 ha (all of ages 90–120, plus 2,000 of 7,000 ha at age 80)
6C	Harvest volume, 2012–2022	1,920,000 m³
6D	Green warbler habitat, 2022	24,000 ha

Topic. Area-regulated (Hanzlik-type) sustained-yield harvest scheduling, and reading multiple stand-development curves against an age-class inventory.

Key relations. Rotation $R = \arg\max_a MAI(a)$, $MAI(a)=V(a)/a$; annual allowable cut area $= \text{Total area}/R$; any stock (volume, carbon, habitat) $= \sum_i \text{Area}_i \times \text{stock-per-ha}(age_i)$.

Why this works. Area regulation targets a constant harvested AREA each year (not a constant volume), which is exactly what is needed to converge an irregular existing age-class structure toward a fully regulated forest over one rotation; because the areas being harvested first (the oldest classes) carry different volumes per hectare than the areas harvested later, harvested VOLUME is not constant during that transition even though harvested area is — visible directly in 6C, where 2,000 ha at 200 m³/ha and 1,000 ha at 140 m³/ha do not scale the same way.

Common pitfall. Forgetting that the newly regenerated (harvested) area re-enters the forest as a NEW age-10 class in 6D, rather than vanishing from the total — a forest's total area is conserved through harvest and regeneration, only its age-class distribution shifts.

Source. Davis, Johnson, Bettinger & Howard, Forest Management, area/volume regulation and MAI-based rotation-age chapters.

Question 6 of 7: Forest Age Structure — Carbon, Harvest, Volume and Habitat

Question 6: Forest Age Structure — Carbon, Harvest, Volume and Habitat (20 marks)

6A — Total forest carbon content today (2012) (5 marks)

6B — Area harvested by age class, 2012–2021 (5 marks)

6C — Harvest volume, 2012–2022 (5 marks)

6D — Green warbler habitat at year 2022 (5 marks)