Solution

1. Current annual CO₂ removal rate:
CCPs: 50 plants × 1 million metric tons/plant = 50 million metric tons
Reforested areas: 10 million hectares × 6 metric tons/hectare = 60 million metric tons
Total current removal: 110 million metric tons per year

2. Time to reach equilibrium:
Let t be the number of years.
Annual removal after t years:
CCPs: (50 + 10t) × 1 million = (50 + 10t) million
Reforestation: (10 + t) × 6 million = (60 + 6t) million
Renewable transition: 0.3 × 2t billion = 600t million

Equilibrium equation:
(50 + 10t) + (60 + 6t) + 600t = 36,000
616t + 110 = 36,000
616t = 35,890
t ≈ 58.26 years

3. Cumulative CO₂ removal function:

The cumulative CO₂ removed over $t$ years is the sum of annual removals:

C(t)=∑n=1t(0.11+0.016n)=0.11t+0.008t(t+1) billion metric tonsC(t) = \sum_{n=1}^{t} \left( 0.11 + 0.016n \right) = 0.11t + 0.008t(t + 1) \, \text{billion metric tons}C(t)=n=1∑t​(0.11+0.016n)=0.11t+0.008t(t+1)billion metric tons

b) Calculating Total CO₂ Removed After 20 Years:

$$C(20)=0.11\times 20+0.008\times 20\times 21=2.2+3.36=5.56\text{billion metric tons}$$

Answer:

The cumulative CO₂ removed over $t$ years is given by:

$$C(t)=0.11t+0.008t(t+1)\text{billion metric tons}$$

After 20 years, the total CO₂ removed will be approximately 5.56 billion metric tons.

4. Doubling efforts:
New equilibrium equation:
(50 + 20t) + (60 + 12t) + 600t = 36,000
632t + 110 = 36,000
632t = 35,890
t ≈ 56.79 years

The time to reach equilibrium is reduced by about 1.47 years.

5. 45% reduction in 10 years:
Current plan in 10 years:
Removal = (50 + 10(10)) + (60 + 6(10)) + 600(10) = 6,270 million metric tons
Emissions after 10 years: 36,000 – (0.3 × 2 × 10) × 1000 = 30,000 million metric tons
Net emissions: 30,000 – 6,270 = 23,730 million metric tons
Reduction: (36,000 – 23,730) / 36,000 × 100% ≈ 34.08%

The current plan does not meet the 45% reduction goal. Recommendations:
– Accelerate renewable energy transition (e.g., 4% per year)
– Increase CCP construction rate
– Expand reforestation efforts
– Implement additional strategies (e.g., improved energy efficiency, carbon pricing)

6. Potential Feedback Loops:

1. Positive Feedback Loops:

   • Permafrost Melting: Higher temperatures cause permafrost to melt, releasing methane and CO₂, further increasing global temperatures.
   • Ocean Acidification: Warmer oceans absorb less CO₂, reducing natural carbon sinks and increasing atmospheric CO₂.

2. Negative Feedback Loops:

   • Enhanced Vegetation Growth: Higher CO₂ levels can stimulate plant growth, increasing CO₂ absorption.

Impact on Equilibrium and Effectiveness:

• Positive Feedbacks can accelerate climate change, making it more challenging for the WCC to reach equilibrium, as emissions may increase beyond current projections.
• Negative Feedbacks may aid in CO₂ removal but are often insufficient to counteract positive feedbacks.
• Adaptive Management: The WCC must monitor these feedbacks and adjust strategies accordingly, possibly increasing removal efforts or accelerating emission reductions.

Answer:

Feedback loops, such as permafrost melting releasing additional greenhouse gases (positive feedback) and increased plant growth absorbing more CO₂ (negative feedback), can significantly affect the system. Positive feedback loops may exacerbate emissions, delaying or preventing equilibrium, while negative feedback loops may enhance CO₂ removal. The WCC’s efforts must account for these dynamics by incorporating adaptive strategies and potentially increasing mitigation efforts to counteract adverse feedback effects.

7. System dynamics model:

Key Components:

• CO₂ Emissions
• CO₂ Removal Efforts (CCPs, Reforestation)
• Global CO₂ Concentration
• Global Temperature
• Renewable Energy Usage
• Feedback Loops (Permafrost Melting, Ocean Absorption)

Interactions:

1. CO₂ Emissions → Global CO₂ Concentration → Global Temperature (Positive Loop)
2. CO₂ Removal Efforts → Decrease Global CO₂ Concentration (Negative Loop)
3. Global Temperature → Permafrost Melting → Increase CO₂ Emissions (Positive Feedback)
4. Renewable Energy Usage → Decrease CO₂ Emissions (Negative Loop)
5. Global Temperature → Affects Ocean CO₂ Absorption (Positive Feedback)

Using the Model:

• Simulation: By adjusting variables like renewable energy adoption or CCP construction rates, the model can simulate future CO₂ concentrations and temperatures.
• Prediction: It helps predict long-term climate trends, identifying potential tipping points where positive feedbacks may dominate.
• Policy Evaluation: The model aids in evaluating the effectiveness of different strategies and policies over time.

Answer:

A system dynamics model with causal loop diagrams represents the interactions between CO₂ emissions, removal efforts, and global temperature. Positive loops illustrate how increased emissions raise temperatures, leading to further emissions (e.g., permafrost melt). Negative loops show how removal efforts and renewable energy reduce emissions and concentrations. This model can predict long-term climate trends by simulating how changes in one part of the system affect the whole, helping policymakers assess the potential impact of different interventions and adapt strategies to achieve climate goals.