Chapter 6 Enginereing Sustainability: BioGeoChemCycle

Chapter 6 Enginereing Sustainability: BioGeoChemCycle#

  1. Introduction: BioGeoChem

  2. Simulation: BioGeoChem

  3. Self-Assessment

1. Introduction#

🌿 Nitrogen and Phosphorus Cycles – Watershed Scale Overview#

Biogeochemical cycles—such as the carbon, nitrogen, phosphorus, sulfur, and water cycles—describe how essential elements move through the biosphere, atmosphere, lithosphere, and hydrosphere. For civil engineers, understanding these cycles is crucial for several reasons:


1. 🌊 Environmental Infrastructure Design#

Civil engineers design systems like wastewater treatment plants, stormwater management systems, and landfills, which directly interact with nutrient and contaminant cycles. For example:

  • Nitrogen and phosphorus removal is essential in wastewater treatment to prevent eutrophication in receiving waters.

  • Carbon cycling affects greenhouse gas emissions from infrastructure and land use.


2. 🌱 Sustainable Site Development#

Knowledge of soil nutrient dynamics and hydrology helps engineers design sustainable landscapes, green infrastructure, and erosion control systems. Engineers must understand how nutrients move through soil and water to avoid degradation and pollution.


3. 🌍 Climate and Pollution Mitigation#

Biogeochemical cycles are tightly linked to climate change and air/water pollution. Civil engineers contribute to mitigation through:

  • Designing low-carbon infrastructure

  • Managing nutrient runoff

  • Modeling pollutant transport in air and water systems


4. 🧪 Remediation and Restoration#

In contaminated sites, engineers use biogeochemical principles to guide remediation strategies. For instance:

  • Bioremediation uses microbial processes to transform pollutants

  • Phytoremediation leverages plant uptake in nutrient cycles


5. 🔄 Modeling and Systems Thinking#

Modern engineering increasingly relies on systems models that integrate biogeochemical processes. Tools like:

  • SWMM (Storm Water Management Model)

  • HSPF (Hydrological Simulation Program – FORTRAN)

  • Coupled climate-land models

Biogeochemical cycles are not just ecological concepts—they are engineering fundamentals for managing water quality, designing sustainable infrastructure, and addressing climate and pollution challenges. Civil engineers who grasp these cycles can better predict environmental impacts, optimize resource use, and contribute to resilient, regenerative design.


🧪 What Are the Nitrogen and Phosphorus Cycles?#

  • Nitrogen Cycle: Describes the movement of nitrogen through the atmosphere, soil, water, and living organisms. Key processes include nitrogen fixation, mineralization, nitrification, denitrification, and assimilation.

  • Phosphorus Cycle: Tracks phosphorus movement through rocks, soil, water, and biota. Unlike nitrogen, phosphorus does not cycle through the atmosphere. Key processes include weathering, uptake, sedimentation, and mineralization.


🔍 Factors Influencing N and P Storage at Watershed Scale#

Factor

Nitrogen Impact

Phosphorus Impact

Land Use

Agriculture increases N runoff

Fertilizer and erosion increase P loading

Vegetation Type

Affects uptake and retention

Influences P demand and cycling

Soil Type

Controls N mineralization and leaching

Governs P adsorption and mobility

Hydrology

Runoff and infiltration affect N transport

Sediment flow influences P movement

Climate

Temperature and rainfall affect microbial activity

Alters weathering and runoff dynamics

Human Inputs

Fertilizer, wastewater, fossil fuels

Fertilizer, detergents, urban runoff


🎯 Why Study These Cycles?#

  • Water Quality: Excess N and P lead to eutrophication, algal blooms, and hypoxia

  • Agricultural Efficiency: Optimizing nutrient use improves crop yield and reduces pollution

  • Ecosystem Health: Nutrient balance supports biodiversity and aquatic life

  • Climate Feedbacks: N₂O from nitrogen cycle is a potent greenhouse gas

  • Infrastructure Planning: Informs wastewater treatment, riparian buffer design, and land management


🌍 Major River Basins – Nitrogen & Phosphorus Cycle Summary#

River Basin

Nitrogen Cycle Highlights

Phosphorus Cycle Highlights

Mississippi (USA)

High nitrate loads from agriculture; hypoxia in Gulf of Mexico

P from fertilizer and wastewater; contributes to eutrophication

Danube (Europe)

Diffuse N sources from agriculture; improved treatment in upper basin

P legacy in soils; sediment-bound P in floodplains

Columbia (USA)

Salmon carcasses contribute N; dams alter transport

Weathering and runoff dominate P input; estuarine export high

Yangtze (China)

Industrial and urban N inputs; seasonal monsoon effects

P from erosion and sewage; sedimentation in reservoirs

Amazon (South America)

Mostly natural N cycling; low anthropogenic input

P from weathering; low fertilizer use, high retention

Ganges (India)

N from agriculture and sewage; monsoon-driven fluxes

P from detergents and erosion; urban runoff significant

📌 These basins illustrate how land use, climate, and hydrology shape nutrient dynamics and management priorities.

🌿 Photosynthesis and the Farquhar Model – Role in Carbon Cycle & Typical Parameters#


📘 What Is Photosynthesis?#

Photosynthesis is the biological process by which green plants, algae, and some bacteria convert carbon dioxide (CO₂) and water into glucose and oxygen, using sunlight as the energy source. The simplified equation is:

\[ 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂ \]

This process is the primary pathway by which atmospheric CO₂ is captured and stored in biomass, making it a cornerstone of the global carbon cycle.


🌍 Role in the Carbon Cycle#

Function

Impact on Carbon Cycle

CO₂ Uptake

Removes CO₂ from atmosphere into plant biomass

Carbon Storage

Transfers carbon to soils via litter and roots

Respiration & Decay

Returns CO₂ to atmosphere from biomass

Climate Regulation

Influences atmospheric CO₂ and temperature

Photosynthesis is the largest natural carbon sink, balancing emissions from respiration, decomposition, and human activities.


🧪 Why Use the Farquhar Model?#

The Farquhar–von Caemmerer–Berry (FvCB) model is widely used to simulate C₃ photosynthesis because it:

  • Represents biochemical limitations (Rubisco activity, electron transport)

  • Accounts for temperature, CO₂, light, and leaf nitrogen

  • Predicts net assimilation rate (Aₙ) under varying conditions

  • Is mechanistic and scalable from leaf to canopy to ecosystem

It’s the gold standard for modeling plant carbon uptake in climate models, crop simulations, and ecological forecasting.


📊 Typical Parameter Values (at 25°C)#

Parameter

Symbol

Typical Range (µmol/m²/s)

Description

Max carboxylation

Vcmax

40–80

Rubisco-limited rate

Max electron transport

Jmax

80–160

Light-limited rate

CO₂ compensation point

Γ*

~40

CO₂ level where net assimilation = 0

Michaelis constant (CO₂)

Kc

~404

Affinity of Rubisco for CO₂

Michaelis constant (O₂)

Ko

~278

Affinity of Rubisco for O₂

Leaf respiration

Rd

~1–2

CO₂ loss in light

These values vary by species, leaf nitrogen, temperature, and growth conditions.


Reference#

[Dolman, 2019] is particularly useful for civil engineers interested in watershed modeling, climate adaptation, nutrient management, and environmental system design. [Freney and Galbally, 1982] focuses on the interactions among the C, N, S, and P cycles, especially under anthropogenic pressures such as fossil fuel combustion, land-use change, and acid rain. This book offers a Historical grounding in nutrient cycle theory prior to the rise of Earth system models, conceptual clarity on nutrient interactions and limiting factors, and useful diagrams and tables for illustrating coupled cycles in teaching modules. [Farquhar et al., 1980] presents a mechanistic model that integrates biochemical processes of photosynthesis with leaf-level gas exchange measurements. It remains the foundation for modeling C₃ photosynthesis in plant physiology, crop modeling, and Earth system science.

2. Simulation#

🌿 Summary – Interactive Watershed Nutrient Simulator (Nitrogen + Phosphorus)#

A Python-based, interactive nutrient simulator that models nitrogen and phosphorus cycling at the watershed scale. It incorporates key factors like watershed area, precipitation, vegetation type, and fertilizer inputs to simulate fluxes such as atmospheric deposition, runoff, plant uptake, denitrification, sedimentation, and soil nutrient storage.


⚙️ How It Works#

  • Uses ipywidgets for dynamic user input (area, vegetation, precipitation, fertilizer rates)

  • Computes nitrogen inputs (atmospheric + fertilizer) and losses (uptake, leaching, denitrification)

  • Computes phosphorus inputs (weathering + fertilizer) and losses (uptake, runoff, sediment binding)

  • Adjusts nutrient dynamics based on land use and precipitation sensitivity

  • Displays summary tables and nutrient balance plots for N and P cycles


📥 Inputs#

Input

Units

Role

Watershed Area

km²

Total landscape modeled

Annual Precipitation

mm/year

Governs hydrological export and leaching intensity

Vegetation Type

Category

Determines nutrient uptake and sensitivity

N Fertilizer Rate

kg/ha

Adds nitrogen input to agricultural systems

P Fertilizer Rate

kg/ha

Adds phosphorus input to agricultural systems


📤 Outputs#

Output

Interpretation

N & P Inputs

External nitrogen/phosphorus entering the system

Plant Uptake

Nutrients absorbed by vegetation

Leaching / Runoff (N/P)

Nutrients exported via water movement

Denitrification (N)

Gaseous N loss via microbial activity

Sediment Binding (P)

P captured in soil or aquatic sediments

Soil Storage Δ (N/P)

Net nutrient accumulation or depletion


🔍 How to Interpret Results#

  • High runoff or low uptake may suggest nutrient inefficiency or environmental risk

  • Positive storage Δ → accumulation in soils; negative Δ → nutrient loss

  • Compare N and P cycles to assess eutrophication potential, crop efficiency, or watershed resilience

Let me know if you’d like to add land use fractions, seasonal inputs, or watershed export coefficients to further refine nutrient transport modeling.

# 🌱 Revised Watershed Nutrient Simulator – Includes Nitrogen + Phosphorus Cycles

import numpy as np
import matplotlib.pyplot as plt
import ipywidgets as widgets
from IPython.display import display, Markdown

# 📋 Input Widgets
area = widgets.FloatText(value=100.0, description='Watershed Area (km²)', style={'description_width': '180px'})
precip_mm = widgets.FloatSlider(value=1200, min=500, max=3000, step=100, description='Annual Precip (mm)', style={'description_width': '180px'})
veg_type = widgets.Dropdown(options=['Forest', 'Agriculture', 'Urban'], description='Vegetation:', style={'description_width': '180px'})
fert_rate_N = widgets.FloatSlider(value=40, min=0, max=300, step=10, description='N Fertilizer (kg/ha)', style={'description_width': '180px'})
fert_rate_P = widgets.FloatSlider(value=20, min=0, max=100, step=5, description='P Fertilizer (kg/ha)', style={'description_width': '180px'})

# 🌿 Nutrient Simulation Function
def simulate_nutrient_cycles(area_km2, precip_mm, veg_type, fert_N, fert_P):
    area_ha = area_km2 * 100

    # Nitrogen Inputs
    N_atm = 8.0 * area_ha
    N_fert = fert_N * area_ha if veg_type == 'Agriculture' else 0
    N_input = N_atm + N_fert
    N_uptake_base = {'Forest': 20.0, 'Agriculture': 30.0, 'Urban': 5.0}[veg_type]
    N_uptake = min(N_input, N_uptake_base * area_ha + N_atm * 0.3)
    N_leach = 0.12 * precip_mm / 1000 * area_ha * (1 + 0.1 * fert_N / 100)
    N_deni = 0.02 * N_input + 0.005 * max(0, N_input - N_uptake)
    N_storage = N_input - N_uptake - N_leach - N_deni

    # Phosphorus Inputs
    P_fert = fert_P * area_ha if veg_type == 'Agriculture' else 0
    P_weather = 1.5 * area_ha
    P_input = P_fert + P_weather
    P_uptake_base = {'Forest': 5.0, 'Agriculture': 10.0, 'Urban': 2.0}[veg_type]
    P_uptake = min(P_input, P_uptake_base * area_ha + P_weather * 0.3)
    P_runoff = 0.08 * precip_mm / 1000 * area_ha * (1 + 0.05 * fert_P / 50)
    P_sediment = 0.015 * P_input
    P_storage = P_input - P_uptake - P_runoff - P_sediment

    return {
        'Nitrogen': {
            'Atmospheric Deposition': N_atm,
            'Fertilizer Input': N_fert,
            'Plant Uptake': N_uptake,
            'Leaching / Runoff': N_leach,
            'Denitrification': N_deni,
            'Soil Storage Δ': N_storage
        },
        'Phosphorus': {
            'Weathering Input': P_weather,
            'Fertilizer Input': P_fert,
            'Plant Uptake': P_uptake,
            'Runoff Loss': P_runoff,
            'Sediment Binding': P_sediment,
            'Soil Storage Δ': P_storage
        }
    }

# 🔘 Run Button
run_btn = widgets.Button(description='Simulate Nutrient Cycles', layout=widgets.Layout(width='260px'))
output_box = widgets.Output()

def on_run_click(b):
    with output_box:
        output_box.clear_output()
        result = simulate_nutrient_cycles(area.value, precip_mm.value, veg_type.value, fert_rate_N.value, fert_rate_P.value)

        # Summary Tables
        display(Markdown(f"""
### 🌿 Watershed Nutrient Summary – Vegetation: **{veg_type.value}**

**Area**: {area.value:.0f} km²  
**Annual Precipitation**: {precip_mm.value:.0f} mm  
**Fertilizer N**: {fert_rate_N.value:.0f} kg/ha  
**Fertilizer P**: {fert_rate_P.value:.0f} kg/ha  

#### 🧪 Nitrogen Fluxes (kg/year)

| Component              | Value |
|------------------------|--------|
| Atmospheric Deposition | {result['Nitrogen']['Atmospheric Deposition']:.0f} |
| Fertilizer Input       | {result['Nitrogen']['Fertilizer Input']:.0f} |
| Plant Uptake           | {result['Nitrogen']['Plant Uptake']:.0f} |
| Leaching / Runoff      | {result['Nitrogen']['Leaching / Runoff']:.0f} |
| Denitrification        | {result['Nitrogen']['Denitrification']:.0f} |
| Soil Storage Change    | {result['Nitrogen']['Soil Storage Δ']:.0f} |

#### 🧬 Phosphorus Fluxes (kg/year)

| Component              | Value |
|------------------------|--------|
| Weathering Input       | {result['Phosphorus']['Weathering Input']:.0f} |
| Fertilizer Input       | {result['Phosphorus']['Fertilizer Input']:.0f} |
| Plant Uptake           | {result['Phosphorus']['Plant Uptake']:.0f} |
| Runoff Loss            | {result['Phosphorus']['Runoff Loss']:.0f} |
| Sediment Binding       | {result['Phosphorus']['Sediment Binding']:.0f} |
| Soil Storage Change    | {result['Phosphorus']['Soil Storage Δ']:.0f} |
"""))

        # Bar Charts
        fig, axs = plt.subplots(1, 2, figsize=(12, 4))
        axs[0].barh(list(result['Nitrogen'].keys()), list(result['Nitrogen'].values()), color='#1f77b4')
        axs[0].set_title('Nitrogen Cycle')
        axs[0].set_xlabel('kg/year')

        axs[1].barh(list(result['Phosphorus'].keys()), list(result['Phosphorus'].values()), color='#ff7f0e')
        axs[1].set_title('Phosphorus Cycle')
        axs[1].set_xlabel('kg/year')

        plt.tight_layout()
        plt.show()

run_btn.on_click(on_run_click)

# 🧩 Display Interface
display(widgets.VBox([
    widgets.HBox([area, veg_type]),
    widgets.HBox([precip_mm, fert_rate_N]),
    widgets.HBox([fert_rate_P]),
    run_btn,
    output_box
]))

3. Simulation#

🌿 Summary – Farquhar Model of C₃ Photosynthesis (Interactive Python Simulator)#


A Python-based interactive simulator that models leaf-level C₃ photosynthesis using the Farquhar–von Caemmerer–Berry (FvCB) model. It computes net CO₂ assimilation (Aₙ) based on environmental and biochemical inputs, highlighting limitations from Rubisco activity and light-driven electron transport.


⚙️ How It Works#

  • Uses the FvCB equations to calculate photosynthesis limited by:

    • Rubisco carboxylation (A𝚌)

    • Electron transport rate (A𝚓)

  • Adjusts Vcmax and Jmax with leaf temperature and nitrogen using Arrhenius functions

  • Simulates the limiting factor and subtracts leaf respiration (R𝚍)

  • Graphs Aₙ vs. Ci to visualize response curve


📥 Inputs#

Input

Meaning

Ci

Intercellular CO₂ concentration (µmol/mol)

PPFD

Incident light (photosynthetic photon flux)

Leaf Temp (°C)

Temperature affecting enzyme kinetics

Leaf Nitrogen (g/m²)

Proxy for biochemical capacity (Vcmax, Jmax)


📤 Outputs#

Output

Interpretation

Vcmax

Maximum Rubisco capacity at given temperature

Jmax

Maximum electron transport rate (light-driven)

Net Assimilation (Aₙ)

Final photosynthetic rate after accounting for R𝚍

Aₙ vs. Ci Plot

Shows saturation and CO₂ response behavior


🔍 How to Interpret Results#

  • If Aₙ is limited by A𝚌, CO₂ concentration is the main constraint

  • If Aₙ is limited by A𝚓, light or electron transport is limiting

  • A decline in Vcmax or Jmax may indicate heat stress or low nitrogen

  • The curve helps identify saturation thresholds and optimal conditions


# 🌿 Farquhar Model of C₃ Photosynthesis – Interactive Simulator

import numpy as np
import matplotlib.pyplot as plt
import ipywidgets as widgets
from IPython.display import display, Markdown

# 📥 Physiological Inputs
Ci_slider = widgets.FloatSlider(value=250, min=50, max=800, step=10, description='Ci (µmol/mol)', style={'description_width': '150px'})
PPFD_slider = widgets.FloatSlider(value=1200, min=0, max=2000, step=50, description='PPFD (µmol/m²/s)', style={'description_width': '150px'})
T_leaf_slider = widgets.FloatSlider(value=25, min=10, max=40, step=1, description='Leaf Temp (°C)', style={'description_width': '150px'})
N_leaf_slider = widgets.FloatSlider(value=1.8, min=0.5, max=3.0, step=0.1, description='Leaf N (g/m²)', style={'description_width': '150px'})

# 📘 Constants and Temperature Dependency
def arrhenius(base, Ea, T):
    R = 8.314  # J/mol/K
    T0 = 298.15
    TK = T + 273.15
    return base * np.exp((Ea/R) * ((1/T0) - (1/TK)))

def photosynthesis_FvCB(Ci, PPFD, Tleaf, Nleaf):
    # Temp-dependent Vcmax & Jmax (proxy from N content)
    Vcmax25 = 50 + 25 * (Nleaf - 1.5)
    Jmax25 = 100 + 50 * (Nleaf - 1.5)
    Ea_v = 65000
    Ea_j = 30000

    Vcmax = arrhenius(Vcmax25, Ea_v, Tleaf)
    Jmax = arrhenius(Jmax25, Ea_j, Tleaf)
    
    Kc = arrhenius(404, 79430, Tleaf)
    Ko = arrhenius(278, 36380, Tleaf)
    O = 210  # mmol/mol
    Gamma_star = arrhenius(42.75, 37830, Tleaf)

    Rd = 0.015 * Vcmax

    # Photosynthetic limitations
    Ac = Vcmax * (Ci - Gamma_star) / (Ci + Kc * (1 + O / Ko))
    J = Jmax * PPFD / (PPFD + 300)  # Light saturation
    Aj = J * (Ci - Gamma_star) / (4 * Ci + 8 * Gamma_star)

    # Net assimilation
    An = min(Ac, Aj) - Rd
    return An, Vcmax, Jmax

# 🔘 Simulate Button
run_btn = widgets.Button(description='Simulate Photosynthesis', layout=widgets.Layout(width='200px'))
output_box = widgets.Output()

def on_run_click(b):
    with output_box:
        output_box.clear_output()
        Ci = Ci_slider.value
        PPFD = PPFD_slider.value
        Tleaf = T_leaf_slider.value
        Nleaf = N_leaf_slider.value
        An, Vc, Jm = photosynthesis_FvCB(Ci, PPFD, Tleaf, Nleaf)

        display(Markdown(f"""
### 🌿 FvCB Model Results

- **Ci**: {Ci:.0f} µmol/mol  
- **PPFD**: {PPFD:.0f} µmol/m²/s  
- **Leaf Temp**: {Tleaf:.1f} °C  
- **Leaf N**: {Nleaf:.2f} g/m²  

| Parameter           | Value |
|---------------------|--------|
| Vcmax (Temp-adj)    | {Vc:.1f} µmol/m²/s |
| Jmax (Temp-adj)     | {Jm:.1f} µmol/m²/s |
| Net Assimilation (Aₙ) | {An:.2f} µmol/m²/s |

"""))

        fig, ax = plt.subplots(figsize=(6, 4))
        Ci_vals = np.linspace(50, 800, 50)
        An_curve = [photosynthesis_FvCB(ci, PPFD, Tleaf, Nleaf)[0] for ci in Ci_vals]
        ax.plot(Ci_vals, An_curve, label='Aₙ vs. Ci', color='green')
        ax.axvline(Ci, color='gray', linestyle='--', label=f'Ci = {Ci}')
        ax.set_xlabel('Intercellular CO₂ (µmol/mol)')
        ax.set_ylabel('Net Assimilation Aₙ (µmol/m²/s)')
        ax.set_title('Farquhar Photosynthesis Response')
        ax.legend()
        plt.tight_layout()
        plt.show()

run_btn.on_click(on_run_click)

# 🔧 Display Controls
display(widgets.VBox([
    widgets.HBox([Ci_slider, PPFD_slider]),
    widgets.HBox([T_leaf_slider, N_leaf_slider]),
    run_btn,
    output_box
]))

3. Self-Assessment#

🧠 Watershed Nutrient Simulator – Conceptual, Reflective & Quiz Questions#


🔍 Conceptual Questions#

  1. What are the major input and output pathways in the nitrogen and phosphorus cycles at the watershed scale?

  2. Why does agricultural land use typically result in higher nutrient fluxes than forested land?

  3. How does precipitation intensity influence nitrogen and phosphorus export from a watershed?

  4. What distinguishes sediment-bound phosphorus from dissolved forms in runoff?

  5. Why is it important to simulate both storage and loss components when evaluating nutrient sustainability?


💭 Reflective Questions#

  1. Based on the simulation, which land cover type seems most efficient in nutrient retention?

  2. How does increasing fertilizer rate affect soil storage versus runoff in your selected scenario?

  3. What management strategies could reduce nutrient losses without compromising plant uptake?

  4. If sediment binding increases, does that always mean phosphorus pollution risk decreases? Why or why not?

  5. How would seasonal variability (e.g. monsoon vs. dry season) alter nutrient fluxes in this simulation?


🧪 Quiz Questions#

Nitrogen Dynamics#

Q1. Which process contributes to gaseous nitrogen loss from the watershed?

  • A. Plant Uptake

  • B. Leaching

  • C. Denitrification ✅

  • D. Sediment Binding

Q2. In this simulator, nitrogen fertilizer input is only active when:

  • A. Precipitation exceeds 1000 mm

  • B. Vegetation type is set to Agriculture ✅

  • C. Area is greater than 100 km²

  • D. Uptake exceeds fertilizer rate

Phosphorus Dynamics#

Q3. Why is phosphorus less mobile than nitrogen in the environment?

  • A. It is gaseous

  • B. It binds to sediments ✅

  • C. It dissolves in water easily

  • D. It cycles through the atmosphere

Q4. Which pathway increases with erosion and rainfall in the P cycle?

  • A. Plant Uptake

  • B. Runoff Loss ✅

  • C. Fertilizer Input

  • D. Mineralization

Application#

Q5. A negative soil storage Δ value implies:

  • A. Nutrient accumulation

  • B. Balanced cycling

  • C. Nutrient depletion ✅

  • D. Denitrification dominance


🌿 Photosynthesis & Farquhar Model – Conceptual, Reflective & Quiz Questions#


🔍 Conceptual Questions#

  1. What are the primary biochemical limitations that govern C₃ photosynthesis according to the Farquhar model?

  2. Why does leaf nitrogen content affect Vcmax and Jmax in the model?

  3. How does the Farquhar model distinguish between Rubisco-limited and light-limited photosynthesis?

  4. What is the significance of Γ* (CO₂ compensation point), and how is it used in calculating net assimilation?

  5. How do environmental factors like temperature and light intensity alter the photosynthetic response curve?


💭 Reflective Questions#

  1. When simulating Aₙ, which variable (Ci, PPFD, Tleaf, or leaf nitrogen) had the greatest impact in your tests?

  2. In what scenarios might the Farquhar model underestimate real-world plant carbon uptake?

  3. How does the assumption of steady-state internal CO₂ concentration (Ci) affect the realism of predictions?

  4. Why do plants sometimes operate below their theoretical Aₙ potential despite favorable conditions?

  5. How could this model be adapted or scaled for use in canopy or ecosystem-level carbon balance studies?


Biochemical Components#

Q1. In the Farquhar model, Vcmax refers to:

  • A. Maximum light absorption

  • B. Maximum Rubisco carboxylation capacity ✅

  • C. Leaf nitrogen content

  • D. Stomatal conductance

Q2. Net CO₂ assimilation (Aₙ) is calculated as:

  • A. Rubisco rate + light rate

  • B. Maximum of Ac or Aj

  • C. Minimum of Ac or Aj, minus respiration ✅

  • D. Ci × PPFD

Environmental Controls#

Q3. Increasing leaf temperature generally causes:

  • A. Higher Γ* and enzyme activity ✅

  • B. Lower light saturation

  • C. Reduced stomatal closure

  • D. Zero net assimilation

Q4. Ci represents:

  • A. Chloroplast index

  • B. Canopy influence

  • C. Intercellular CO₂ concentration ✅

  • D. Internal nitrogen ratio

Application & Interpretation#

Q5. A high PPFD but low Aₙ suggests:

  • A. Rubisco limitation ✅

  • B. Light saturation

  • C. Elevated Vcmax

  • D. Nitrogen sufficiency