Which of the following statements about greenhouse gases are correct?

Methane’s GWP is larger on a 20-year horizon than on a 100-year horizon

Water vapour acts mainly as a feedback that amplifies warming

HFCs do not deplete stratospheric ozone but are strong greenhouse gases

Methane’s GWP is larger on a 20-year horizon than on a 100-year horizon

Water vapour acts mainly as a feedback that amplifies warming

The forcing of CO₂ increases linearly with its concentration

HFCs do not deplete stratospheric ozone but are strong greenhouse gases

The Antarctic ozone hole appears mainly in the southern spring because:

chlorine activated on polar stratospheric clouds during the dark winter is photolysed when sunlight returns

CFC emissions are highest in the Southern Hemisphere in spring

ozone is produced only in summer

volcanic eruptions occur mainly in spring

Which of the following help to mitigate an urban heat island?

Replacing lawns with dark asphalt

Which ecological pyramid can never be inverted?

none of them; all can be inverted

Which of the following statements about ecosystems are correct?

Net primary productivity equals gross primary productivity minus plant respiration

Lotic ecosystems are those of flowing water

Decomposers return nutrients from dead matter to the abiotic environment

Net primary productivity equals gross primary productivity minus plant respiration

Lotic ecosystems are those of flowing water

Primary succession begins on land whose soil remains after the vegetation was removed

Decomposers return nutrients from dead matter to the abiotic environment

In the IPAT relation I = P × A × T, the factor T represents:

the environmental impact per unit of consumption, set by technology

the time over which impact is measured

the temperature rise caused by the impact

Global and Regional Environmental Issues: Climate, Acid Rain, the Ozone Hole, Ecology, Biodiversity and Population

Section 8 of the GATE Environmental Science and Engineering (ES) paper. Its first line is the global effects of air pollution — greenhouse gases, radiative forcing and global warming potential, climate change, urban heat islands, acid rain and the ozone hole — and its second is ecology and the various ecosystems, biodiversity, and the factors that drive the growth of population, energy consumption and environmental degradation. The chapter follows that order and keeps to what can be derived or reasoned: the energy balance of the Earth, the logarithmic forcing of CO₂, CO₂-equivalents, the chemistry of acid rain and of polar ozone loss; energy flow and the trophic pyramids, the indices that measure diversity, and the growth equations and identities — logistic growth, IPAT and Kaya — that link people, energy and emissions. Where a figure depends on an assessment report or a year, the question gives it.

1. Greenhouse gases, radiative forcing, global warming potential and climate change

The Earth absorbs sunlight and radiates infrared. With the solar constant S (about 1361 W/m²) and planetary albedo α (about 0.3), the balance S(1 − α)πR² = 4πR²σT_e⁴ gives an effective radiating temperature T_e = [S(1 − α)/(4σ)]^(1/4) ≈ 255 K. The mean surface temperature is about 288 K; the difference of some 33 K is the natural greenhouse effect, produced by gases that are transparent to sunlight but absorb and re-emit the outgoing infrared — water vapour, CO₂, CH₄, N₂O and ozone — together with clouds. Human activity adds CO₂ (fossil fuels, cement, deforestation), CH₄ (rice paddies, livestock, landfills, fossil-fuel leakage), N₂O (fertilised soils, some industry) and the wholly synthetic halocarbons and SF₆. Water vapour is not emitted in controlling amounts; it acts as a feedback, rising as the air warms and amplifying the warming.

Radiative forcing ΔF is the change in the net energy flux at the tropopause caused by a change in a driver, in W/m². For CO₂ it is logarithmic in concentration, ΔF = 5.35 ln(C/C₀), because the centre of its absorption band is already saturated and additional CO₂ acts on the band’s wings; each doubling therefore adds the same 5.35 ln 2 = 3.7 W/m². The eventual equilibrium warming is ΔT = λΔF, with λ the climate sensitivity parameter. The global warming potential (GWP) compares gases: the time-integrated forcing of a pulse of 1 kg of a gas over a horizon (usually 100 years) relative to that of 1 kg of CO₂. It depends on the gas’s radiative efficiency and lifetime — methane is potent but short-lived, so its GWP is much higher on a 20-year horizon than on a 100-year one — and emissions of different gases are added as CO₂-equivalents, Σ mass × GWP. Climate change — warming of land and ocean, sea-level rise from thermal expansion and melting ice, shifting rainfall and more intense extremes, ocean acidification as the sea takes up CO₂ — is addressed internationally through mitigation (cutting emissions and enhancing sinks) and adaptation.

⚠️ Forcing is logarithmic, so doublings matter

From 280 to 420 ppm the CO₂ forcing is 5.35 ln 1.5 = 2.17 W/m², not half of the doubling value — going from 280 to 560 ppm adds 3.71 W/m², and 560 to 1120 ppm adds the same 3.71 again. A linear model would over-predict the forcing of each further increment.

2. Urban heat islands, acid rain and the ozone hole

An urban heat island is a city warmer than its surroundings, most strongly at night. Its causes are dark, impervious surfaces of low albedo that store heat by day; the loss of vegetation and so of evaporative cooling; street canyons that trap long-wave radiation and cut wind; and waste heat from vehicles, buildings and air conditioning. It raises energy demand for cooling, heat stress and the rate of ozone formation, and it alters local winds. Mitigation uses cool (high-albedo) roofs and pavements, trees, parks and water bodies, and green roofs. Acid rain is precipitation more acidic than that of clean air in equilibrium with atmospheric CO₂, whose pH is about 5.6. SO₂ and NOₓ are oxidised in the air and in cloud water to sulphuric and nitric acids, deposited wet in rain, snow and fog or dry as gases and particles, often hundreds of kilometres from the source. It acidifies poorly buffered lakes and streams, mobilises aluminium that is toxic to fish, leaches base cations from forest soils, and corrodes limestone, marble and metals; its control is the control of SO₂ and NOₓ emissions.

Stratospheric ozone is made and destroyed naturally in the Chapman cycle: O₂ + hν → 2O, O + O₂ + M → O₃ + M, O₃ + hν → O₂ + O, O + O₃ → 2O₂. Its total column is measured in Dobson units (1 DU is a 0.01 mm layer of pure ozone at standard temperature and pressure; a typical column is about 300 DU). Chlorine and bromine from CFCs, halons, carbon tetrachloride and methyl chloroform destroy it catalytically: Cl + O₃ → ClO + O₂, then ClO + O → Cl + O₂, regenerating the chlorine. The Antarctic ozone hole — a springtime (September–November) fall of the column below about 220 DU — needs the peculiar conditions of the polar winter: the air is isolated in the polar vortex, it becomes cold enough for polar stratospheric clouds, and on their surfaces the reservoir compounds HCl and ClONO₂ react to release Cl₂, which the returning spring sunlight photolyses to atomic chlorine. The Montreal Protocol (1987) and its amendments phased out the ozone-depleting substances; its Kigali Amendment (2016) extended it to the HFCs that replaced them, which do not deplete ozone but are strong greenhouse gases.

🎯 Why the hole is over Antarctica in spring

Chlorine emissions are global, but the destruction needs cold surfaces and then sunlight. The polar stratospheric clouds form only in the extreme cold of the isolated Antarctic winter vortex, and they convert inert reservoirs into Cl₂; nothing happens until the Sun returns in September to split it. The Arctic vortex is warmer and less stable, so its losses are smaller and more variable.

3. Ecology and the various ecosystems

An ecosystem is a community of organisms together with its physical environment, linked by the flow of energy and the cycling of matter. Its biotic part consists of producers (autotrophs, mainly green plants and algae), consumers (herbivores, carnivores, omnivores) and decomposers (bacteria and fungi that return nutrients); its abiotic part is light, water, soil, nutrients and climate. Energy enters by photosynthesis — the gross primary productivity, of which the net primary productivity NPP = GPP − R is what remains after the plants’ own respiration — and flows one way through food chains and interlinked food webs, being lost as heat at every step. Only about 10% of the energy at one trophic level is typically passed to the next (Lindeman’s ten per cent law), which is why food chains rarely exceed four or five links and why the pyramid of energy is always upright. Pyramids of numbers and biomass can be inverted — a single tree supporting thousands of insects, or phytoplankton outnumbered in standing mass by the zooplankton that graze them quickly. Matter, by contrast, cycles: carbon, nitrogen, phosphorus, sulphur and water move between the living and non-living compartments.

The main ecosystems are terrestrial — forests (tropical, temperate, boreal), grasslands, deserts and tundra — and aquatic: fresh water, divided into lentic (standing: lakes, ponds) and lotic (flowing: rivers, streams); marine (open ocean, coral reefs); and the transitional estuaries and wetlands, among the most productive of all, which filter water, store floods and shelter fisheries. Communities change over time by ecological succession: primary succession on bare rock or new land, beginning with pioneer species such as lichens, and secondary succession on land whose vegetation was removed but whose soil remains, both tending towards a relatively stable climax community. A population grows until limited by its environment’s carrying capacity, and its niche is its role and requirements in the community.

🧠 The ten per cent law compounds

10 000 kJ fixed by producers leaves about 1000 kJ for herbivores, 100 kJ for primary carnivores and 10 kJ for secondary carnivores — three transfers, a factor of 1000. That is also why eating lower on the food chain supports more people from the same land.

4. Biodiversity

Biodiversity is variety at three levels: genetic diversity within species, species diversity, and ecosystem diversity. Species diversity has two parts — richness (the number of species) and evenness (how equally individuals are spread among them) — and indices combine them. The Shannon index is H = −Σpᵢ ln pᵢ, where pᵢ is the proportion of individuals in species i; it rises with both richness and evenness, and for S equally common species equals ln S. Simpson’s diversity index is D = 1 − Σpᵢ², the probability that two individuals drawn at random belong to different species. Diversity within a habitat is alpha diversity, the turnover between habitats beta, and the total over a region gamma. A biodiversity hotspot is a region with at least 1500 endemic vascular plant species that has lost at least 70% of its original habitat; four of them lie wholly or partly in India — the Himalaya, Indo-Burma, the Western Ghats and Sri Lanka, and Sundaland (which takes in the Nicobar Islands). The main threats are habitat loss and fragmentation, invasive species, pollution, over-exploitation and climate change. Conservation is in situ, in protected areas such as national parks, wildlife sanctuaries and biosphere reserves, and ex situ, in zoos, botanical gardens and seed and gene banks; the Convention on Biological Diversity was opened for signature at the Rio Earth Summit in 1992.

⚠️ Natural log, and proportions that sum to one

A community with proportions 0.5, 0.25 and 0.25 has H = −(0.5 ln 0.5 + 2 × 0.25 ln 0.25) = 0.347 + 0.693 = 1.04 and Simpson D = 1 − (0.25 + 0.0625 + 0.0625) = 0.625. Using log₁₀ gives H = 0.45, a different scale; mixing up D = Σp² (dominance) with 1 − Σp² (diversity) reverses the meaning.

5. Population, energy consumption and environmental degradation

A population growing without limit grows exponentially, N = N₀e^(rt), with a doubling time t_d = ln 2/r ≈ 70/(r in per cent). Real populations meet limits, and the logistic model dN/dt = rN(1 − N/K) makes growth slow as N approaches the carrying capacity K; the growth rate is greatest at N = K/2, where it equals rK/4. Human population growth is shaped by the demographic transition: death rates fall first with better food, water, sanitation and medicine, birth rates fall later with education (especially of women), urbanisation and income, and the population grows fast in the interval. The factors that increase population, energy use and degradation are linked, and two identities make the link explicit. IPAT writes impact as I = P × A × T — population, affluence (consumption per person) and technology (impact per unit of consumption). The Kaya identity applies the same idea to CO₂: emissions = population × (GDP/person) × (energy/GDP) × (CO₂/energy), so that emissions can fall only through a slower-growing economy, a less energy-intensive one, or a less carbon-intensive energy supply. Energy consumption rises with population and income, and its supply — still dominated by fossil fuels — drives air pollution, climate change, mining and water use; environmental degradation follows as deforestation, soil erosion and desertification, loss of wetlands and biodiversity, groundwater depletion, and pollution of air, water and land.

Growth models and identities
Relation	Form	Key result
Exponential growth	N = N₀e^(rt)	t_d = ln 2/r ≈ 70/r%
Logistic growth	dN/dt = rN(1 − N/K)	Maximum rate rK/4 at N = K/2
IPAT	I = P × A × T	Impact grows with each factor
Kaya identity	CO₂ = P × (GDP/P) × (E/GDP) × (CO₂/E)	Decarbonisation acts on the last two

Key takeaways

T_e = [S(1 − α)/(4σ)]^(1/4) ≈ 255 K against a 288 K surface: the 33 K greenhouse effect. ΔF = 5.35 ln(C/C₀), so each doubling adds 3.7 W/m²; ΔT = λΔF; CO₂-eq = Σ mass × GWP.
Heat islands come from low albedo, lost vegetation, canyons and waste heat. Clean rain is pH 5.6; acid rain is SO₂ and NOₓ converted to strong acids and controlled at the source.
Chlorine destroys ozone catalytically; the Antarctic hole needs the vortex, polar stratospheric clouds and returning sunlight; Montreal (1987) phased out ODS and Kigali (2016) added HFCs.
Energy flows one way and about 10% passes each trophic level, so the energy pyramid is always upright; matter cycles. Shannon H = −Σp ln p, Simpson D = 1 − Σp²; India shares four biodiversity hotspots.
t_d = ln 2/r; logistic growth peaks at rK/4 when N = K/2; IPAT I = PAT and Kaya CO₂ = P × GDP/P × E/GDP × CO₂/E tie population and affluence to energy and emissions.

Practice questions (18)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

Taking the solar constant as 1361 W/m², the planetary albedo as 0.3 and σ = 5.67 × 10⁻⁸ W/(m²·K⁴), what is the Earth’s effective radiating temperature, in K? Give the answer to the nearest whole number.
Numerical answer — type the value.
Show answer
Answer: 255
T_e = [S(1 − α)/(4σ)]^(1/4) = [1361 × 0.7/(4 × 5.67 × 10⁻⁸)]^(1/4) = (4.201 × 10⁹)^(1/4) = 254.6 ≈ 255 K. Omitting the factor 4 — the ratio of the Earth’s surface area to its cross-section — gives 360 K.
Using ΔF = 5.35 ln(C/C₀), what is the radiative forcing of an increase in CO₂ from 280 ppm to 420 ppm, in W/m²? Give the answer to two decimal places.
Numerical answer — type the value.
Show answer
Answer: 2.17
ΔF = 5.35 ln(420/280) = 5.35 ln 1.5 = 5.35 × 0.4055 = 2.17 W/m². Using log₁₀ gives 0.94 W/m²; the coefficient 5.35 belongs with the natural logarithm.
With a climate sensitivity parameter of 0.8 K per W/m² and ΔF = 5.35 ln(C/C₀), what equilibrium warming results from a doubling of CO₂, in K? Give the answer to two decimal places.
Numerical answer — type the value.
Show answer
Answer: 2.97
ΔF = 5.35 ln 2 = 3.708 W/m²; ΔT = λΔF = 0.8 × 3.708 = 2.97 K. The result is the same for 280 → 560 ppm as for 400 → 800 ppm, because the forcing depends only on the ratio.
A facility emits 100 t of CO₂, 10 t of CH₄ and 1 t of N₂O in a year. Taking 100-year GWPs of 28 for CH₄ and 265 for N₂O, what are its emissions in tonnes of CO₂-equivalent?
Numerical answer — type the value.
Show answer
Answer: 645
CO₂-eq = 100 × 1 + 10 × 28 + 1 × 265 = 100 + 280 + 265 = 645 t. Methane and nitrous oxide are only 11 t of the 111 t emitted by mass but 545 t of the 645 t by warming effect.
Which of the following statements about greenhouse gases are correct?
1. Methane’s GWP is larger on a 20-year horizon than on a 100-year horizon
2. Water vapour acts mainly as a feedback that amplifies warming
3. The forcing of CO₂ increases linearly with its concentration
4. HFCs do not deplete stratospheric ozone but are strong greenhouse gases
Show answer
Answer: A — Methane’s GWP is larger on a 20-year horizon than on a 100-year horizon; B — Water vapour acts mainly as a feedback that amplifies warming; D — HFCs do not deplete stratospheric ozone but are strong greenhouse gases
(a) methane is removed in about a decade, so its effect is concentrated early in the horizon. (b) its concentration is set by temperature. (d) is why the Kigali Amendment brought HFCs under the Montreal Protocol. (c) is false: the forcing is logarithmic, ΔF = 5.35 ln(C/C₀).
Rain at an industrial site has a pH of 4.3, while clean rain in equilibrium with atmospheric CO₂ has a pH of 5.6. How many times greater is the hydrogen-ion concentration of the acid rain? Give the answer to the nearest whole number.
Numerical answer — type the value.
Show answer
Answer: 20
[H⁺] ratio = 10^(5.6 − 4.3) = 10^1.3 = 19.95 ≈ 20. The pH difference of 1.3 is not a ratio of 1.3: each pH unit is a factor of ten.
The Antarctic ozone hole appears mainly in the southern spring because:
1. chlorine activated on polar stratospheric clouds during the dark winter is photolysed when sunlight returns
2. CFC emissions are highest in the Southern Hemisphere in spring
3. ozone is produced only in summer
4. volcanic eruptions occur mainly in spring
Show answer
Answer: A — chlorine activated on polar stratospheric clouds during the dark winter is photolysed when sunlight returns
During the polar night the isolated vortex grows cold enough for polar stratospheric clouds, on which HCl and ClONO₂ react to form Cl₂. When sunlight returns in September it splits Cl₂ into atoms that destroy ozone catalytically. The emissions themselves are global and well mixed, and not seasonal.
Which of the following help to mitigate an urban heat island?
1. High-albedo (cool) roofs
2. More trees and parks
3. Replacing lawns with dark asphalt
4. Green roofs
Show answer
Answer: A — High-albedo (cool) roofs; B — More trees and parks; D — Green roofs
Cool roofs reflect sunlight; trees, parks and green roofs shade surfaces and cool by evapotranspiration. Dark asphalt has a low albedo and no evaporation, so it stores heat by day and releases it at night — a cause of the heat island, not a remedy.
Producers in an ecosystem fix 10 000 kJ of energy. Applying the ten per cent law, how much energy reaches the secondary carnivores (the fourth trophic level), in kJ?
Numerical answer — type the value.
Show answer
Answer: 10
Three transfers separate producers from secondary carnivores: 10 000 → 1000 (herbivores) → 100 (primary carnivores) → 10 kJ. Counting four transfers because it is the fourth level gives 1 kJ, one step too many.
Which ecological pyramid can never be inverted?
1. the pyramid of energy
2. the pyramid of numbers
3. the pyramid of biomass
4. none of them; all can be inverted
Show answer
Answer: A — the pyramid of energy
Energy is lost as heat at every transfer, so each trophic level receives less energy per unit time than the one below it and the energy pyramid is always upright. Numbers invert when one tree supports many insects; biomass inverts in open water, where a small standing stock of fast-growing phytoplankton supports a larger mass of zooplankton.
Which of the following statements about ecosystems are correct?
1. Net primary productivity equals gross primary productivity minus plant respiration
2. Lotic ecosystems are those of flowing water
3. Primary succession begins on land whose soil remains after the vegetation was removed
4. Decomposers return nutrients from dead matter to the abiotic environment
Show answer
Answer: A — Net primary productivity equals gross primary productivity minus plant respiration; B — Lotic ecosystems are those of flowing water; D — Decomposers return nutrients from dead matter to the abiotic environment
(a), (b) and (d) are correct. (c) is false: that is secondary succession. Primary succession starts where there is no soil at all — bare rock, fresh lava, a retreating glacier’s moraine — with pioneers such as lichens that begin to make it.
A community has three species making up 50%, 25% and 25% of the individuals. What is its Shannon diversity index, using natural logarithms? Give the answer to two decimal places.
Numerical answer — type the value.
Show answer
Answer: 1.04
H = −Σpᵢ ln pᵢ = −[0.5 ln 0.5 + 2 × 0.25 ln 0.25] = 0.5 × 0.693 + 0.5 × 1.386 = 0.347 + 0.693 = 1.04. Three equally common species would give ln 3 = 1.10, the maximum for three species; the unevenness costs 0.06.
For the same community (proportions 0.5, 0.25 and 0.25), what is Simpson’s diversity index 1 − Σpᵢ²? Give the answer to three decimal places.
Numerical answer — type the value.
Show answer
Answer: 0.625
Σpᵢ² = 0.25 + 0.0625 + 0.0625 = 0.375, so D = 1 − 0.375 = 0.625: the chance that two individuals picked at random are of different species. Σpᵢ² itself, 0.375, is the dominance, which falls as diversity rises.
Which of the following is NOT one of the biodiversity hotspots that lie wholly or partly in India?
1. The Thar Desert
2. The Western Ghats and Sri Lanka
3. Indo-Burma
4. The Himalaya
Show answer
Answer: A — The Thar Desert
India’s share of hotspots is the Himalaya, Indo-Burma, the Western Ghats and Sri Lanka, and Sundaland (through the Nicobar Islands). The Thar is an important arid ecosystem but does not meet the hotspot criteria of at least 1500 endemic vascular plants and at least 70% of habitat lost.
A population follows logistic growth with r = 0.2 per year and a carrying capacity of 1000. What is its maximum rate of increase, in individuals per year?
Numerical answer — type the value.
Show answer
Answer: 50
dN/dt = rN(1 − N/K) is greatest at N = K/2 = 500, where it equals rK/4 = 0.2 × 1000/4 = 50 per year. Evaluating rK = 200 assumes the population is both at K and growing freely, which contradicts the model.
A population grows exponentially at 2% per year. What is its doubling time, in years? Give the answer to one decimal place.
Numerical answer — type the value.
Show answer
Answer: 34.7
t_d = ln 2/r = 0.6931/0.02 = 34.7 years. The rule of 70 gives 70/2 = 35, a quick approximation of the same result. Dividing 100 by 2 (50 years) assumes linear, not compound, growth.
A country has 1.4 × 10⁹ people, a GDP of 2500 dollars per person, an energy intensity of 5 MJ per dollar and a carbon intensity of 0.07 kg CO₂ per MJ. Using the Kaya identity, what are its annual CO₂ emissions, in million tonnes?
Numerical answer — type the value.
Show answer
Answer: 1225
CO₂ = P × (GDP/P) × (E/GDP) × (CO₂/E) = 1.4 × 10⁹ × 2500 × 5 × 0.07 = 1.225 × 10¹² kg = 1.225 × 10⁹ t = 1225 million tonnes. A 20% cut in carbon intensity alone would lower this by 245 Mt, whatever the population does.
In the IPAT relation I = P × A × T, the factor T represents:
1. the environmental impact per unit of consumption, set by technology
2. the time over which impact is measured
3. the total population
4. the temperature rise caused by the impact
Show answer
Answer: A — the environmental impact per unit of consumption, set by technology
P is population, A affluence (consumption per person) and T technology, the impact per unit of consumption. Cleaner technology lowers T and can offset growth in P and A — which is the argument for efficiency and decarbonisation.