Key Formulas & Equations
Core Concepts
Climate Change & Global Warming
The long-term increase in Earth's average surface temperature, primarily driven by greenhouse gas emissions (CO₂, CH₄, N₂O) from human activities. The greenhouse effect traps heat; enhanced by fossil fuel combustion, deforestation, and industrial agriculture. Impacts: sea level rise, extreme weather, ecosystem disruption.
Biodiversity & Ecosystem Services
Variability of life at genetic, species, and ecosystem levels. Ecosystem services: provisioning (food, water), regulating (climate, flood), supporting (nutrient cycling), and cultural (recreation). Biodiversity loss threatens these services and ecosystem resilience.
Sustainability & Triple Bottom Line
Meeting present needs without compromising future generations. Three pillars: environmental protection, social equity, and economic viability. Sustainable development balances resource use, waste generation, and ecosystem health with human prosperity.
Carbon Cycle
The movement of carbon through atmosphere, biosphere, hydrosphere, and geosphere. Photosynthesis removes CO₂; respiration and decomposition return it. Fossil fuel burning adds ~35 billion tons CO₂ annually. Oceans absorb ~25%, land plants ~30%, leaving ~45% in atmosphere.
Environmental Impact Assessment (EIA)
A systematic process to identify, predict, and evaluate environmental effects of proposed projects before decisions are made. Steps: screening, scoping, baseline studies, impact prediction, mitigation, monitoring. Required by law in most countries for major developments.
Circular Economy
An economic model that minimizes waste by keeping materials in use through reuse, repair, refurbishment, and recycling. Contrasts with the linear "take-make-dispose" model. Aims to decouple economic growth from resource consumption and environmental degradation.
Worked Examples
Example 1: Carbon Footprint Calculation
Problem: A household uses 500 kWh/month of electricity (EF = 0.5 kg CO₂/kWh) and drives 1,000 km/month (EF = 0.2 kg CO₂/km). Find annual CO₂ emissions.
Step 1: Electricity: 500 × 0.5 = 250 kg/month × 12 = 3,000 kg/year
Step 2: Transport: 1,000 × 0.2 = 200 kg/month × 12 = 2,400 kg/year
Step 3: Total = 3,000 + 2,400 = 5,400 kg CO₂/year = 5.4 tonnes CO₂/year
Answer: The household emits 5.4 tonnes of CO₂ per year.
Example 2: Population Growth
Problem: A city has 1 million people growing at 2%/year. What is the population in 10 years?
Step 1: N(t) = N₀(1 + r)^t = 1,000,000 × (1.02)¹⁰
Step 2: (1.02)¹⁰ ≈ 1.219
Step 3: N = 1,000,000 × 1.219 ≈ 1,219,000
Answer: The population will be approximately 1.22 million after 10 years.
Example 3: Greenhouse Radiative Forcing
Problem: CO₂ increased from 280 ppm (pre-industrial) to 420 ppm (current). Calculate ΔRF.
Step 1: ΔRF = 5.35 × ln(C/C₀) = 5.35 × ln(420/280)
Step 2: ln(420/280) = ln(1.5) = 0.405
Step 3: ΔRF = 5.35 × 0.405 = 2.17 W/m²
Answer: The additional radiative forcing is approximately 2.17 W/m².
Example 4: Pollutant Decay
Problem: A pollutant decays with k = 0.05/day. What remains after 30 days if initial concentration was 100 mg/L?
Step 1: C(t) = C₀ × e^(-kt) = 100 × e^(-0.05 × 30)
Step 2: C(30) = 100 × e^(-1.5) = 100 × 0.223
Step 3: C = 22.3 mg/L
Answer: The concentration drops to 22.3 mg/L after 30 days.
Practice Problems
Problem 1
Convert 450 ppm CO₂ to a percentage of the atmosphere.
Answer: 450 / 1,000,000 × 100 = 0.045%
Problem 2
A city generates 10,000 tons of waste/year and recycles 3,500 tons. What is the diversion rate?
Answer: 3,500/10,000 × 100 = 35%
Problem 3
Calculate the doubling time of a population growing at 3%/year.
Answer: t = ln(2)/r = 0.693/0.03 ≈ 23.1 years
Problem 4
Solar panels produce 1,000 kWh with an embodied energy cost of 50 kWh. What is the EROI?
Answer: EROI = 1,000/50 = 20:1
Problem 5
If atmospheric CH₄ is 1.9 ppm with GWP of 28, what is its CO₂-equivalent concentration?
Answer: 1.9 × 28 = 53.2 ppm CO₂-eq
Problem 6
A wetland has NPP = 800 g C/m²/yr and R_a = 300 g C/m²/yr. What is GPP?
Answer: NPP = GPP - R_a → GPP = 800 + 300 = 1,100 g C/m²/yr