Water and Carbon Cycles

The Hydrological (Water) Cycle

Overview

The hydrological cycle describes the continuous movement of water between the atmosphere, land surface, and oceans, driven by solar energy and gravity. It is a closed system on a global scale (the total quantity of water on Earth is approximately constant), but open at the local scale (water enters and leaves catchments).

Key Processes

Evaporation: liquid water is converted to water vapour from open water surfaces (oceans, lakes, rivers) and soil moisture. The rate of evaporation depends on temperature, humidity, wind speed, and the availability of water.

Transpiration: water absorbed by plant roots moves through the plant and is released as vapour through stomata in the leaves. Transpiration rates are influenced by temperature, humidity, wind speed, light intensity, and plant type.

Evapotranspiration: the combined process of evaporation and transpiration. Potential evapotranspiration (PET) is the maximum rate at which evapotranspiration would occur with unlimited water supply. Actual evapotranspiration (AET) is the rate that actually occurs, limited by water availability.

Condensation: water vapour cools and changes state to liquid water droplets or ice crystals, forming clouds and fog. Cooling occurs through adiabatic uplift (air rising and expanding), contact with cold surfaces, or radiative cooling.

Precipitation: any form of water (rain, snow, sleet, hail) falling from the atmosphere to the Earth's surface. Precipitation occurs when water droplets or ice crystals in clouds grow large enough to fall. Mechanisms include frontal (warm and cold fronts), convectional (warm air rising from heated surfaces), and orographic (air forced to rise over mountains).

Interception: precipitation that is caught by vegetation (leaves, stems) or artificial surfaces before reaching the ground. Intercepted water may evaporate directly back to the atmosphere (interception loss), drip to the ground (throughfall), or run down stems (stemflow).

Infiltration: water soaking into the soil surface. The infiltration rate depends on soil texture (sandy soils infiltrate faster than clay), soil moisture content (saturated soils infiltrate more slowly), vegetation cover, and surface compaction.

Percolation: the downward movement of water through the soil and underlying rock, eventually reaching the water table and contributing to groundwater storage.

Surface runoff (overland flow): water that flows over the ground surface towards rivers and streams. Occurs when the infiltration capacity of the soil is exceeded (Hortonian overland flow) or when the soil is saturated and water cannot infiltrate further (saturation overland flow).

Throughflow: the lateral movement of water through the soil towards river channels.

Baseflow: the sustained flow of a river fed by groundwater discharge from the water table. Baseflow maintains river flow during dry periods.

The Water Balance

The water balance for a given area over a given period is:

$P = Q + E \pm \Delta S$

Where $P$ is precipitation, $Q$ is runoff (including surface runoff, throughflow, and baseflow), $E$ is evapotranspiration, and $\Delta S$ is the change in storage (soil moisture, groundwater, surface water).

When $P > E + Q$, water surplus accumulates in storage. When $P < E + Q$, there is a water deficit and storage decreases.

Drainage Basins

Definition and Characteristics

A drainage basin (catchment) is the area of land drained by a river and its tributaries, bounded by a watershed (drainage divide) — a ridge of high ground separating one drainage basin from another.

Drainage Basin System

The drainage basin functions as an open system with inputs, outputs, stores, and transfers.

Inputs: precipitation (rain, snow, hail)

Outputs: evapotranspiration, river discharge to the sea/ocean

Stores: interception (vegetation canopy), surface storage (puddles, lakes), soil moisture, groundwater (aquifers), channel storage (water in the river)

Transfers (flows): interception, throughfall, stemflow, surface runoff, throughflow, percolation, groundwater flow, channel flow

Storm Hydrograph

A storm hydrograph shows how river discharge changes over time in response to a rainfall event.

Key features:

• Lag time: the time between the peak of the rainfall and the peak of the river discharge. Shorter lag time indicates a faster response and higher flood risk.
• Peak discharge: the maximum river discharge during the storm.
• Rising limb: the period of increasing discharge as water reaches the channel.
• Falling limb (recession curve): the period of decreasing discharge as inputs decline and the basin drains.

Factors Affecting the Storm Hydrograph

Physical factors:

• Basin size and shape: larger basins have longer lag times and more attenuated peaks. Elongated basins have longer lag times than circular basins.
• Slope: steeper slopes produce faster runoff and shorter lag times.
• Soil type: permeable soils (sand, chalk) promote infiltration and reduce surface runoff, lengthening lag time. Impermeable soils (clay) increase surface runoff.
• Rock type: permeable rocks allow percolation, reducing surface runoff. Impermeable rocks increase runoff.
• Land use: urban areas (impermeable surfaces, drainage systems) reduce lag time and increase peak discharge. Forested areas increase interception and infiltration, lengthening lag time.
• Vegetation: dense vegetation intercepts rainfall, slows overland flow, and promotes infiltration.
• Antecedent moisture conditions: wet soils (high water table, recent rainfall) reduce infiltration capacity, increasing surface runoff and shortening lag time.

Human factors:

• Urbanisation: increases impermeable surfaces, reduces infiltration, and speeds water delivery to channels through storm drains
• Agriculture: compaction of soil by heavy machinery reduces infiltration; drainage systems (tile drains, ditches) speed water movement
• River management: flood relief channels, dams, and reservoirs can attenuate flood peaks but may transfer flood risk downstream

The Carbon Cycle

Overview

The carbon cycle describes the movement of carbon between the atmosphere, biosphere, oceans, and lithosphere. Carbon is the fundamental building block of organic matter and plays a critical role in regulating climate through the greenhouse effect.

Carbon Stores

• Atmosphere: approximately $870\;\mathrm{GtC}$ (gigatonnes of carbon), primarily as $\mathrm{CO_2}$ ($415\;\mathrm{ppm}$ in 2024)
• Oceans: approximately $38000\;\mathrm{GtC}$ as dissolved $\mathrm{CO_2}$, bicarbonate ($\mathrm{HCO_3^-}$), carbonate ($\mathrm{CO_3^{2-}}$), and marine organisms
• Terrestrial biosphere: approximately $2000\;\mathrm{GtC}$ in vegetation, soils, and litter
• Fossil fuels: approximately $1000\;\mathrm{GtC}$ in coal, oil, and natural gas deposits
• Sedimentary rocks: approximately $100000000\;\mathrm{GtC}$ in limestone, chalk, and other carbonate rocks (the largest store, but very slow cycling)

Carbon Fluxes (Flows)

Natural fluxes:

• Photosynthesis: $\approx 120\;\mathrm{GtC/year}$ from atmosphere to biosphere
• Respiration: $\approx 119\;\mathrm{GtC/year}$ from biosphere to atmosphere
• Ocean-atmosphere exchange: $\approx 90\;\mathrm{GtC/year}$ in each direction (uptake and release)
• Volcanic outgassing: $\approx 0.1\;\mathrm{GtC/year}$ from lithosphere to atmosphere
• Weathering: $\approx 0.3\;\mathrm{GtC/year}$ from atmosphere to lithosphere (through formation of bicarbonate in weathering reactions)

Anthropogenic fluxes:

• Fossil fuel combustion: $\approx 9.5\;\mathrm{GtC/year}$
• Land use change (deforestation): $\approx 1.1\;\mathrm{GtC/year}$
• Total anthropogenic emissions: $\approx 10.6\;\mathrm{GtC/year}$

Approximately half of anthropogenic emissions are absorbed by natural sinks (oceans and the terrestrial biosphere); the remainder accumulates in the atmosphere, increasing $\mathrm{CO_2}$ concentration.

The Carbon Cycle and Climate Regulation

Carbon dioxide, methane, and nitrous oxide are greenhouse gases that absorb and re-emit infrared radiation, warming the Earth's surface. Without the natural greenhouse effect, the Earth's average surface temperature would be approximately $-18^{\circ}\mathrm{C}$ rather than the current $+15^{\circ}\mathrm{C}$.

Anthropogenic emissions have increased atmospheric $\mathrm{CO_2}$ from pre-industrial levels of approximately $280\;\mathrm{ppm}$ to over $415\;\mathrm{ppm}$, enhancing the greenhouse effect and driving global warming.

Carbon Feedbacks

Positive feedbacks (amplifying warming):

• Permafrost thaw: frozen soils contain approximately $1500\;\mathrm{GtC}$. Thawing releases $\mathrm{CO_2}$ and methane, accelerating warming.
• Ocean warming: warmer water holds less dissolved $\mathrm{CO_2}$, reducing oceanic carbon uptake.
• Forest dieback: warming and drought stress reduce photosynthesis and increase tree mortality, converting forests from carbon sinks to sources.
• Ice-albedo feedback: melting ice reduces surface reflectivity (albedo), increasing solar absorption and further warming.

Negative feedbacks (dampening warming):

• $\mathrm{CO_2}$ fertilisation: elevated $\mathrm{CO_2}$ concentrations can enhance plant growth and photosynthesis, increasing carbon uptake by the terrestrial biosphere (though this effect is limited by nutrient availability and may be offset by heat stress).
• Increased weathering: warmer, wetter conditions accelerate the chemical weathering of silicate rocks, which consumes atmospheric $\mathrm{CO_2}$ over geological timescales.

Climate Change Impacts on Water and Carbon Cycles

Impacts on the Water Cycle

• Increased evapotranspiration: higher temperatures increase the rate of evaporation and transpiration, intensifying the hydrological cycle
• Changed precipitation patterns: some regions experience increased rainfall intensity and frequency; others experience prolonged droughts. Overall, wet areas tend to get wetter and dry areas tend to get drier
• Accelerated glacier and ice sheet melt: contributing to sea level rise and altering downstream water availability
• Reduced snow cover and earlier snowmelt: shifting the timing of peak river flow, with implications for water supply and flood risk
• Changes in soil moisture: increased evapotranspiration can dry soils even where precipitation increases, as higher temperatures increase moisture loss faster than rainfall replenishes it
• More intense extreme events: higher atmospheric water vapour content (Clausius-Clapeyron relation: the atmosphere can hold approximately $7\%$ more water vapour per $1^{\circ}\mathrm{C}$ of warming) intensifies storms and flooding

Impacts on the Carbon Cycle

• Ocean acidification: the oceans absorb approximately $25\%$ of anthropogenic $\mathrm{CO_2}$, decreasing ocean pH (from approximately $8.2$ to $8.1$ since pre-industrial times). This impairs shell-forming organisms (corals, molluscs, plankton) and threatens marine food webs.
• Reduced carbon sink efficiency: warming reduces the capacity of both the oceans and the terrestrial biosphere to absorb $\mathrm{CO_2}$.
• Permafrost carbon release: thawing permafrost in the Arctic is a potentially massive source of carbon that could significantly accelerate warming.
• Wildfire increases: more frequent and severe wildfires release stored carbon from forests and peatlands, creating a positive feedback loop.
• Vegetation shifts: changes in species composition and biome boundaries alter carbon storage patterns (e.g., boreal forest retreat reduces the northern hemisphere carbon sink).

Common Pitfalls

• Confusing the water cycle (a closed system globally) with the carbon cycle. While the total water on Earth is essentially constant, carbon moves between stores with varying residence times, and anthropogenic emissions are adding to the atmospheric store.
• Stating that the oceans "absorb all" anthropogenic $\mathrm{CO_2}$. The oceans absorb approximately $25\%$, the terrestrial biosphere absorbs approximately $25\%$, and the remaining $50\%$ accumulates in the atmosphere.
• Confusing infiltration with percolation. Infiltration is the entry of water into the soil surface; percolation is the downward movement of water through the soil profile to the water table.
• Describing the greenhouse effect as inherently harmful. The natural greenhouse effect is essential for maintaining habitable temperatures; it is the enhanced greenhouse effect from anthropogenic emissions that drives climate change.
• Confusing positive feedback with "good" feedback. In systems theory, a positive feedback amplifies the initial change, regardless of whether the change is beneficial or harmful.

Practice Problems

Problem 1: Water Balance Calculation

A drainage basin receives $1200\;\mathrm{mm}$ of precipitation in a year. Evapotranspiration is $500\;\mathrm{mm}$ and river discharge is $600\;\mathrm{mm}$. Calculate the change in water storage.

$P = Q + E \pm \Delta S$

$1200 = 600 + 500 + \Delta S$

$\Delta S = 1200 - 600 - 500 = +100\;\mathrm{mm}$

Storage increased by $100\;\mathrm{mm}$, indicating a wet year with surplus water accumulating in soil moisture, groundwater, or surface water bodies.

Problem 2: Storm Hydrograph Analysis

Two drainage basins of similar size experience identical rainfall events. Basin A has a lag time of $4$ hours and peak discharge of $150\;\mathrm{m^3/s}$. Basin B has a lag time of $8$ hours and peak discharge of $80\;\mathrm{m^3/s}$. Explain the likely differences in the physical characteristics of the two basins.

Basin A has a shorter lag time and higher peak discharge, indicating a faster hydrological response. This is characteristic of:

• Steeper slopes accelerating overland flow
• Impermeable soils or rock (e.g., clay, granite) reducing infiltration
• Limited vegetation cover (e.g., urban or agricultural land) reducing interception
• Higher antecedent soil moisture
• More compact or circular basin shape

Basin B has a longer lag time and lower peak discharge, indicating a slower, more attenuated response. This is characteristic of:

• Gentler slopes
• Permeable soils or rock (e.g., chalk, sandstone) promoting infiltration
• Dense vegetation cover (e.g., forest) increasing interception and slowing overland flow
• Drier antecedent conditions
• More elongated basin shape

Basin B is at lower flood risk than Basin A because its hydrological response is more gradual and peak discharge is lower.

Problem 3: Carbon Budget Calculation

Global anthropogenic $\mathrm{CO_2}$ emissions are $10.6\;\mathrm{GtC/year}$. The oceans absorb $2.5\;\mathrm{GtC/year}$ and the terrestrial biosphere absorbs $3.0\;\mathrm{GtC/year}$. Calculate the atmospheric accumulation rate and the proportion of emissions remaining in the atmosphere.

Total natural sinks $= 2.5 + 3.0 = 5.5\;\mathrm{GtC/year}$

Atmospheric accumulation $= 10.6 - 5.5 = 5.1\;\mathrm{GtC/year}$

Proportion remaining in atmosphere $= \frac{5.1}{10.6} \times 100 \approx 48\%$

Approximately $48\%$ of anthropogenic emissions accumulate in the atmosphere, while $52\%$ is absorbed by natural sinks. This airborne fraction has remained relatively stable over recent decades, though there are concerns that sink efficiency may decline as the climate warms.

Problem 4: Climate Change and Flooding

Explain how climate change may increase flood risk in a temperate drainage basin, considering multiple pathways.

Climate change increases flood risk through several interconnected pathways:

1. Increased rainfall intensity: the Clausius-Clapeyron relation predicts approximately $7\%$ more atmospheric water vapour per $1^{\circ}\mathrm{C}$ of warming, leading to more intense rainfall events that exceed infiltration capacity.

2. Changed seasonality: earlier snowmelt and more winter rainfall (rather than snow) concentrate runoff in shorter periods, increasing the magnitude of winter floods.

3. Reduced soil moisture deficits: warmer, wetter winters reduce the soil's capacity to absorb spring and summer rainfall, increasing surface runoff.

4. Urbanisation feedback: climate-driven migration to urban areas increases impermeable surface coverage, compounding the hydrological response.

5. Land use changes: agricultural adaptation to changing climate (e.g., removal of hedgerows, increased compaction) may reduce infiltration.

6. Sediment transport: increased erosion delivers more sediment to river channels, reducing channel capacity and increasing flood levels.

Problem 5: Ocean Acidification

Atmospheric $\mathrm{CO_2}$ dissolves in seawater according to the reaction: $\mathrm{CO_2 + H_2O \rightleftharpoons H_2CO_3 \rightleftharpoons H^+ + HCO_3^-}$. Explain the consequences for marine organisms and ecosystems.

When $\mathrm{CO_2}$ dissolves in seawater, it forms carbonic acid ($\mathrm{H_2CO_3}$), which dissociates to release hydrogen ions ($\mathrm{H^+}$), decreasing pH (increasing acidity). The increased availability of $\mathrm{H^+}$ also shifts the carbonate equilibrium:

$\mathrm{H^+ + CO_3^{2-} \rightleftharpoons HCO_3^-}$

This reduces the concentration of carbonate ions ($\mathrm{CO_3^{2-}}$), which are essential for calcifying organisms to build their shells and skeletons from calcium carbonate ($\mathrm{CaCO_3}$).

Consequences:

• Coral reefs: reduced calcification rates weaken coral skeletons, making reefs more susceptible to erosion and breakage. At pH levels projected for $2100$, coral growth may be unable to keep pace with erosion, leading to reef collapse.
• Shellfish and plankton: organisms such as pteropods, foraminifera, and bivalves struggle to maintain their shells in more acidic water, with impacts on survival and reproduction.
• Food web effects: calcifying plankton form the base of many marine food webs; their decline would cascade through the ecosystem, affecting fish stocks and marine mammals.
• Behavioural effects: experiments suggest that elevated $\mathrm{CO_2}$ can impair the behaviour of some fish species, reducing predator avoidance and navigation ability.