From photosynthesis to biomass — how ecosystems build and burn carbon
2026-02-26
A mature Douglas fir in the Pacific Northwest might fix 30 kg of carbon per year through photosynthesis. But it retains perhaps 15 kg as new biomass — the rest is burned in respiration, the metabolic cost of maintaining millions of living cells. Of that 15 kg, roughly half goes into new wood (the rings visible in the cross-section), a quarter into fine roots that turn over within a year, and the remainder into needles that will be shed over the next three years. The proportions are not fixed — they shift with drought, nutrient availability, and light, as the tree adjusts its investment strategy to maximise survival.
This allocation problem sits at the heart of ecosystem carbon modelling. Gross Primary Productivity (GPP) — the total carbon fixed by photosynthesis — is not the same as the carbon available for growth, because autotrophic respiration consumes roughly half of GPP in most ecosystems. Net Primary Productivity (NPP = GPP − Ra) is what remains for building biomass. Where that biomass goes — leaves, wood, roots, reproductive structures — determines the forest’s structure, its turnover rates, and how much carbon eventually enters the soil. This model builds a multi-pool carbon allocation framework that tracks the flow from GPP through to individual biomass compartments, including the controls that shift allocation under environmental stress.
Where does the carbon go after photosynthesis fixes it?
A forest canopy captures sunlight and converts CO₂ to sugars (Gross Primary Productivity, GPP). But the forest uses carbon for: - Maintaining existing tissues — respiring sugars for energy - Building new leaves — to capture more light - Growing roots — to access water and nutrients - Adding wood — structural support and long-term storage
The difference between carbon fixed (GPP) and carbon burned (respiration) is Net Primary Productivity (NPP) — the actual carbon available for growth.
The mathematical question: How do we model carbon flow from GPP to biomass pools, accounting for respiration and turnover?
Gross Primary Productivity (GPP):
Total carbon fixed by photosynthesis (Model 20).
Autotrophic Respiration (R_a):
Carbon burned by plants for energy (maintenance + growth respiration).
Net Primary Productivity (NPP):
\text{NPP} = \text{GPP} - R_a
Carbon Allocation:
NPP is allocated among plant parts: - Leaves (foliage): a_L \times \text{NPP} - Stems (wood): a_S \times \text{NPP} - Roots: a_R \times \text{NPP}
Where a_L + a_S + a_R = 1 (allocation fractions sum to 1).
Biomass Pools:
Each pool accumulates carbon but also loses it through turnover (death, litterfall).
\frac{dC_L}{dt} = a_L \cdot \text{NPP} - k_L C_L
Where: - C_L = leaf carbon (kg C/m²) - k_L = turnover rate (year⁻¹)
Maintenance respiration (R_m):
Energy to maintain existing tissues (proportional to biomass).
R_m = r_m (C_L + C_S + C_R)
Where r_m is specific maintenance rate (kg C respired per kg C biomass per year).
Growth respiration (R_g):
Energy cost of synthesizing new tissue (proportional to NPP).
R_g = r_g \cdot (GPP - R_m)
Where r_g is growth respiration fraction (typically 0.2–0.3).
Total autotrophic respiration:
R_a = R_m + R_g = R_m + r_g(\text{GPP} - R_m)
Solve for R_a:
R_a = \frac{R_m + r_g \cdot \text{GPP}}{1 + r_g}
State variables: - C_L = leaf carbon (kg C/m²) - C_S = stem (wood) carbon (kg C/m²) - C_R = root carbon (kg C/m²)
Dynamics:
\frac{dC_L}{dt} = a_L \cdot \text{NPP} - k_L C_L
\frac{dC_S}{dt} = a_S \cdot \text{NPP} - k_S C_S
\frac{dC_R}{dt} = a_R \cdot \text{NPP} - k_R C_R
Turnover rates (typical values): - Leaves: k_L = 1 year⁻¹ (leaves live 1 year average) - Fine roots: k_R = 1 year⁻¹ (similar to leaves) - Wood: k_S = 0.02 year⁻¹ (50-year lifespan)
Allocation fractions (vary by ecosystem): - Young forest: a_L = 0.3, a_S = 0.4, a_R = 0.3 (building structure) - Mature forest: a_L = 0.25, a_S = 0.50, a_R = 0.25 (less leaf, more wood) - Grassland: a_L = 0.4, a_S = 0.0, a_R = 0.6 (no wood, deep roots)
At equilibrium (mature ecosystem):
\frac{dC_L}{dt} = 0 \implies C_L^* = \frac{a_L \cdot \text{NPP}}{k_L}
Example: NPP = 1 kg C/m²/year, a_L = 0.3, k_L = 1 year⁻¹:
C_L^* = \frac{0.3 \times 1}{1} = 0.3 \text{ kg C/m}^2
Total steady-state carbon:
C_{\text{total}}^* = \frac{a_L}{k_L} \text{NPP} + \frac{a_S}{k_S} \text{NPP} + \frac{a_R}{k_R} \text{NPP}
= \text{NPP} \left(\frac{a_L}{k_L} + \frac{a_S}{k_S} + \frac{a_R}{k_R}\right)
Wood dominates because k_S is small (low turnover).
Problem: A temperate forest has: - GPP = 2.5 kg C/m²/year - Maintenance respiration: R_m = 0.8 kg C/m²/year - Growth respiration fraction: r_g = 0.25 - Allocation: a_L = 0.25, a_S = 0.50, a_R = 0.25 - Turnover: k_L = 1, k_S = 0.02, k_R = 1 year⁻¹
(a) NPP
R_a = \frac{R_m + r_g \cdot \text{GPP}}{1 + r_g} = \frac{0.8 + 0.25 \times 2.5}{1 + 0.25}
= \frac{0.8 + 0.625}{1.25} = \frac{1.425}{1.25} = 1.14 \text{ kg C/m}^2\text{/year}
\text{NPP} = \text{GPP} - R_a = 2.5 - 1.14 = 1.36 \text{ kg C/m}^2\text{/year}
(b) Steady-state carbon
Leaves:
C_L^* = \frac{a_L \cdot \text{NPP}}{k_L} = \frac{0.25 \times 1.36}{1} = 0.34 \text{ kg C/m}^2
Stems:
C_S^* = \frac{a_S \cdot \text{NPP}}{k_S} = \frac{0.50 \times 1.36}{0.02} = \frac{0.68}{0.02} = 34 \text{ kg C/m}^2
Roots:
C_R^* = \frac{a_R \cdot \text{NPP}}{k_R} = \frac{0.25 \times 1.36}{1} = 0.34 \text{ kg C/m}^2
(c) Total carbon
C_{\text{total}}^* = 0.34 + 34 + 0.34 = 34.68 \text{ kg C/m}^2
Interpretation: Wood (stems) stores 98% of total carbon, even though only 50% of NPP goes to wood. This is because wood lives ~50 years while leaves/roots live ~1 year.
Convert to biomass: Assuming carbon is ~50% of dry biomass:
\text{Biomass} = \frac{34.68}{0.5} = 69.4 \text{ kg dry mass/m}^2 = 694 \text{ tonnes/ha}
Typical for a mature temperate forest.
Below is an interactive carbon allocation simulator.
<label>
Ecosystem type:
<select id="ecosystem-type">
<option value="young-forest">Young Forest</option>
<option value="mature-forest" selected>Mature Forest</option>
<option value="grassland">Grassland</option>
<option value="cropland">Annual Cropland</option>
</select>
</label>
<label>
GPP (kg C/m²/year):
<input type="range" id="gpp-slider" min="0.5" max="4" step="0.1" value="2.5">
<span id="gpp-value">2.5</span>
</label>
<label>
Leaf allocation (aL):
<input type="range" id="al-slider" min="0.1" max="0.6" step="0.05" value="0.25">
<span id="al-value">0.25</span>
</label>
<label>
Wood allocation (aS):
<input type="range" id="as-slider" min="0" max="0.7" step="0.05" value="0.50">
<span id="as-value">0.50</span>
</label>
<label>
Simulation years:
<input type="range" id="years-slider" min="10" max="200" step="10" value="100">
<span id="years-value">100</span> years
</label>
<div class="button-group">
<button id="run-carbon-sim">Run Simulation</button>
</div><p><strong>NPP:</strong> <span id="npp-result"></span> kg C/m²/year</p>
<p><strong>R<sub>a</sub>/GPP:</strong> <span id="ra-gpp-ratio"></span></p>
<p><strong>Final total carbon:</strong> <span id="total-carbon"></span> kg C/m²</p>
<p><strong>Equilibrium reached:</strong> <span id="equilibrium-status"></span></p>Try this: - Young forest: Higher wood allocation → rapid stem growth - Mature forest: Stem carbon accumulates to ~30-40 kg C/m² over 100 years - Grassland: No wood allocation → only leaves and roots, reaches equilibrium quickly - Cropland: Annual harvest (high turnover) → low steady-state carbon - Increase GPP: More NPP → faster accumulation - Notice: Stems take decades to reach equilibrium (slow turnover), leaves equilibrate in ~2-3 years
Key insight: Long-lived pools (wood) dominate ecosystem carbon storage, even if allocation is similar to short-lived pools.
Young forest (0–50 years): - Rapid growth - NPP high - Carbon accumulation ~0.5–2 kg C/m²/year - Carbon sink
Mature forest (> 100 years): - Near equilibrium - Growth balanced by mortality - NPP still positive but slower accumulation - Weak carbon sink or neutral
Old-growth debate: Do old forests continue to sequester carbon?
Evidence suggests some continued net uptake (~0.1–0.2 kg C/m²/year).
Carbon use efficiency:
\text{CUE} = \frac{\text{NPP}}{\text{GPP}}
Typical values: - Young forest: 0.60 (low respiration costs) - Mature forest: 0.50 (higher maintenance from large biomass) - Stressed ecosystem: 0.30 (high respiration, drought, heat)
Global average: CUE ≈ 0.47 (forests), 0.55 (grasslands), 0.60 (croplands)
Clear-cut harvest: - Removes most aboveground biomass (C_L, C_S) - Roots partially remain (C_R) - Regrowth from sprouts/seeds - Carbon rebounds over 20–50 years
modelling:
Reset C_L = 0.1, C_S = 0.1, keep C_R reduced, simulate regrowth.
Real allocation changes with: - Tree age: Young trees allocate more to leaves/roots, mature trees to wood - Resource availability: Nutrient-limited → more roots, light-limited → more leaves - CO₂ fertilization: Elevated CO₂ may shift allocation toward roots
Dynamic allocation models: Make a_L, a_S, a_R functions of resource status.
Dead leaves/roots don’t disappear—they become soil organic matter (SOM).
Complete carbon cycle:
\text{GPP} \to \text{NPP} \to \text{Biomass} \to \text{Litter} \to \text{SOM} \to \text{Respiration (decomposition)}
Our model stops at biomass. Full model needs soil carbon pools (next-level complexity).
Turnover varies with: - Temperature: Faster decomposition in tropics - Moisture: Slow in deserts (dry) and peat bogs (waterlogged) - Disturbance: Fire, insects, disease accelerate mortality
Q₁₀ rule: Decomposition doubles per 10°C warming.
Plants allocate carbon to seeds, flowers, fruits—our model lumps this into “leaves” or ignores it.
For crops: Grain yield is a separate allocation pool.
Net Ecosystem Productivity (NEP):
\text{NEP} = \text{NPP} - R_h
Where R_h is heterotrophic respiration (decomposition of dead organic matter by microbes).
NEP > 0: Ecosystem is a carbon sink
NEP < 0: Ecosystem is a carbon source
NEP ≈ 0: Ecosystem at steady state
Global NEP:
Terrestrial ecosystems sequester ~2–3 Pg C/year (about 1/4 of fossil fuel emissions).
Next model will shift to atmospheric interactions—wind profiles and turbulent mixing that transport heat, moisture, and CO₂ between surface and atmosphere.
A multi-compartment model has: - State variables: C_1, C_2, ..., C_n (pool sizes) - Flows: F_{ij} from pool i to pool j - Inputs/outputs: External sources/sinks
\frac{dC_i}{dt} = \sum_j F_{ji} - \sum_j F_{ij}
For linear flows (F_{ij} = k_{ij} C_i):
\frac{d\mathbf{C}}{dt} = \mathbf{A} \mathbf{C} + \mathbf{u}
Where: - \mathbf{C} = vector of pool sizes - \mathbf{A} = transfer matrix - \mathbf{u} = input vector
Steady state: \mathbf{A} \mathbf{C}^* + \mathbf{u} = 0
Our model:
\mathbf{C} = \begin{pmatrix} C_L \\ C_S \\ C_R \end{pmatrix}, \quad \mathbf{A} = \begin{pmatrix} -k_L & 0 & 0 \\ 0 & -k_S & 0 \\ 0 & 0 & -k_R \end{pmatrix}, \quad \mathbf{u} = \text{NPP} \begin{pmatrix} a_L \\ a_S \\ a_R \end{pmatrix}