Notes: Global Water and Carbon Cycles — Concepts, Calculations, and Policy Context

Global Water Cycle: steady state, turnover time, and perturbations

• Overview of the session: pick up at the end of the global water cycle, include Poll Everywhere activities, define systems, discuss the global carbon cycle, estimate carbon increase in the atmosphere since the industrial revolution, and define tipping points.

• Steady-state concept for a reservoir (pool): inputs = outputs, so the size of the pool remains constant over time.

  • Turnover time (residence time) of a reservoir can be estimated as
    T \,=\, \frac{V}{F}
    where $V$ is the size of the reservoir and $F$ is the flux in or out (when steady state, $F{in}=F{out}$).

• Simple water-cycle model (steady-state): the ocean’s volume stays the same over time if inputs and outputs balance.

• Units and conversions: always check units (grams, moles, prefixes like kilo-, mega-, etc.) to convert between papers/slides.

• Note on non-steady-state reality: the real system is not in steady state; forcing changes (e.g., warming) perturb the cycle.

• Poll Everywhere (interactive): QR code or web link to a live poll; the instructor will activate questions for student responses.

• Water-cycle fluxes around atmospheric water:

  • Inputs to the atmosphere: evaporation.

  • Outputs from the atmosphere: rainfall.

  • The evaporation and rainfall fluxes determine the atmospheric moisture pool size; the system can be studied by asking which fluxes drive turnover of atmospheric water.

• What happens when the Earth warms (effect on evaporation and rainfall):

  • Increased energy → higher molecular motion → greater evaporation.

  • More evaporation increases atmospheric moisture content (humidity).

  • To maintain balance, more rainfall eventually occurs, accelerating the hydrological cycle overall.

  • Global hydrological cycle accelerates with warming, but regional outcomes (precipitation and river flow) are heterogeneous due to local climate, weather systems, and sensitivities.

• Evaporation vs rainfall in various regions:

  • In some places, warming leads to drought-like conditions (more evaporation without proportional rainfall).

  • In other places, increased rainfall occurs; the timing and amount depend on local drivers.

  • Prediction of rainfall is more complex than predicting temperature in climate models.

• Glaciers and snow as part of freshwater reservoirs:

  • The largest freshwater pool is often discussed as glaciers and snow, which thaw with warming.

  • Major point: when ice and snow melt, liquid water is redistributed into lakes/rivers/ocean; oceans gain long-term storage.

  • Key volumes (rough comparisons): glaciers hold a very large volume relative to rivers; rivers are a conduit for water from land to ocean and hold comparatively little water in total.

  • Thawing contributes to sea-level rise and exposes new terrestrial habitats; the Arctic responses are uncertain.

• Phase partitioning of water on Earth:

  • Water exists in gas, liquid, and ice phases; total amount of water remains constant while its distribution among phases shifts.

  • Phase changes and redistribution contribute to sea-level changes and regional hydrology.

• Conceptual takeaway: size (pool) vs flux (flow) are both critical; a pool may be large but change slowly (low flux) or small but highly dynamic (high flux).

• Implications for environmental change: understanding which pools are large vs highly fluxional helps predict system response to perturbations.

Global carbon cycle: closed system view, fluxes, and interpretation

• Carbon cycle framing: Earth is treated as a closed system for carbon with a small external input from extraterrestrial sources (e.g., meteoritic organic carbon).

• The carbon cycle diagram (IPCC context): pre-industrial and current/anthropogenic fluxes shown; black lines = pre-industrial estimates, red = anthropogenic impacts.

• Focus for today: size of the atmospheric carbon pool and how it changes due to human activities; perform a simple back-of-the-envelope calculation to relate atmospheric carbon to CO₂ concentration.

• Mauna Loa CO₂ observations as a basis for the interpretation:

  • Contemporary atmospheric CO₂ concentration is around ~ ext{ppm} (parts per million). Historical context: ~414 ppm previously; today ~424–425 ppm; an approximate change of about +10 to +11 ppm over the recent period discussed.

  • Seasonal cycle in the Northern Hemisphere: plant growth in spring/summer leads to CO₂ drawdown (photosynthesis exceeds respiration), causing atmospheric CO₂ to fall; respiration dominates in fall/winter, causing CO₂ to rise.

  • The Northern Hemisphere’s seasonal CO₂ cycle creates a sawtooth pattern when viewed monthly, with the amplitude modulated by the growing season.

• Dated interpretation of the cycle:

  • May–August: photosynthesis is strong; CO₂ uptake reduces atmospheric CO₂ levels.

  • September–November: respiration dominates as photosynthesis wanes; CO₂ starts to rise again through winter and into spring.

  • The long-term trend of rising CO₂ is much larger than the year-to-year seasonal variability.

• The historical record and interpretation:

  • Ice-core data provide a pre-industrial CO₂ baseline (around ~280 ppm).

  • Modern observations (Mauna Loa and other sites) show a steady rise from ~280 ppm in the pre-industrial era toward current values above ~420 ppm.

  • The 2013 IPCC carbon-cycle diagram is referenced as a schematic; later reports refine numbers but the basic balance concept remains: photosynthesis and respiration largely balance, the terrestrial and marine reservoirs exchange carbon, and anthropogenic emissions add to the atmospheric pool.

• Pre-industrial atmospheric carbon pool and the change since the industrial revolution:

  • Pre-industrial carbon in the atmosphere (as CO₂-derived carbon): about 589 \text{ PgC}.

  • Current carbon in the atmosphere (as CO₂-derived carbon): about 918 \text{ PgC}.

  • Carbon added since the industrial revolution:
    \Delta P_g!C = 918 - 589 = 329 \text{ PgC}.

  • Percentage increase since the industrial revolution:
    \%\Delta = \frac{329}{589} \approx 0.56 \approx 56\%.

• Conversion between different units and the rationale for using PgC:

  • 1 Petagram (Pg) = 10^{15} \text{ g}.

  • 1 Petamole (Pm) = 10^{15} \text{ mol}; 1 Petamole = 1000 Teramoles (Tm).

  • 1 Teramole = 10^{12} \text{ mol}.

• Stoichiometric link between carbon and oxygen cycles:

  • In respiration and combustion: CO₂ is produced while O₂ is consumed, maintaining a roughly 1:1 mole balance between CO₂ produced and O₂ consumed over time for the whole system.

• Unit consistency and caveat in the transcript:

  • The speaker states a one-to-one relationship between CO₂ and O₂ in the atmosphere/cycle, which is conceptually correct, but a line in the transcript incorrectly states that a molecule of CO₂ contains “one carbon atom and 12 oxygen atoms, six O₂ molecules.” The correct composition is CO₂ = one carbon atom and two oxygen atoms. The notes reflect the correct stoichiometry and mark the discrepancy.

• Global O₂ reservoir and its sensitivity:

  • The atmospheric oxygen pool is very large, around ~3.6\times 10^{7} \text{ teramoles} (i.e., 3.6\times 10^{7} \text{ Tmoles}).

  • The observed carbon dioxide increase (~$+56\%$ since pre-industrial) corresponds to a relatively small fractional change in atmospheric O₂ (about 0.07\%): that is, O₂ is less perturbed than CO₂ because it is a much larger reservoir.

  • This is why fossil-fuel combustion drives CO₂-related climate change without causing suffocation risks due to O₂ depletion.

System concepts: pools, fluxes, and steady-state vs perturbation

• Key idea: For biogeochemical cycles, consider both pool size and flux through the pool; both influence system sensitivity and response to perturbations.

• Some pools are large but fluxes are small (e.g., glaciers in the carbon/oxygen context, or ice in hydrology) while others are small but highly dynamic (e.g., atmospheric water vapor, etc.).

• Glaciers and snow: thawing increases freshwater input to rivers and oceans; it also contributes to sea-level rise and changes in water availability; the long-term storage in glaciers is redistributed into more active hydrological components.

• The concept of redistribution among phases (gas, liquid, and solid) and its effects on the Earth system:

  • Total water on Earth is conserved, but the distribution among gas, liquid, and ice changes with temperature and climate; this redistribution influences sea level and regional hydrology.

• Why these concepts matter for environmental change:

  • Understanding the size of a pool and the flux through it helps identify which components are most vulnerable or most influential in a changing climate.

• Simple takeaway: in system thinking, you look for (a) size of pools, (b) magnitude and direction of fluxes, (c) potential feedbacks and non-linearities, and (d) the role of time lags and distance (spatial separation) in producing delayed or cross-border effects.

Connecting to the carbon cycle and system thinking

• The carbon cycle is treated as a closed system with small external inputs and large internal exchanges among reservoirs (atmosphere, land, and ocean).

• The balance between photosynthesis (carbon uptake) and respiration/oxidation (carbon release) largely governs the atmospheric CO₂ pool, with human activities shifting this balance by adding substantial CO₂ to the atmosphere.

• The carbon cycle connects to the oxygen cycle via stoichiometric relationships (1:1 in uptake and release for net photosynthesis/respiration) but with scale differences due to the size of the reservoirs and the long-term storage in the ocean and biomass.

• Practical takeaway: a simple mass-balance approach can yield first-order insights into how much carbon has accumulated in the atmosphere and how that translates into CO₂ concentration, which then informs climate forcing considerations.

Measurement, interpretation, and time scales

• Seasonal pattern in CO₂: the North Hemisphere grows more plant biomass in spring/summer, producing a seasonal dip in atmospheric CO₂; in winter, respiration dominates, causing CO₂ to rise.

• Time lag concepts in the carbon system:

  • The peak atmospheric CO₂ concentration often lags behind the maximum rate of photosynthesis or net primary production because the system is dominated by respiration and decomposition during those times, and carbon takes time to accumulate/vent from different reservoirs.

  • This time lag is analogous to daily solar heating: the hottest time of the day is after noon because heat loss lags behind the peak energy input.

• Observational data and interpretation:

  • The Mauna Loa CO₂ record provides a long-running, hemispherically averaged view of atmospheric CO₂ and demonstrates the rise since pre-industrial times.

  • Ice cores extend the record into the past, enabling estimates of pre-industrial CO₂ levels (around 280 ppm) and enabling quantification of changes since the industrial revolution.

• Concrete numbers highlighted in the transcript:

  • Pre-industrial atmospheric CO₂ in terms of carbon: about 589\ \text{PgC}.

  • Current atmospheric carbon in CO₂ form: about 918\ \text{PgC}, corresponding to ~425\ \text{ppm} CO₂.

  • Carbon added since the industrial revolution: 329\ \text{PgC}, which is about a 56\% increase over the pre-industrial amount.

• Unit and calculation clarifications:

  • CO₂ concentration in air expressed in ppm is a mole-based fraction: for every 1,000,000 moles of gas, ~425 are CO₂ today.

  • Relationship between CO₂ moles and carbon mass uses that one mole CO₂ contains one mole of carbon; hence, mass of carbon is simply $n{CO2} \times 12\ \text{g/mol}$.

  • To convert to petagrams of carbon (PgC): divide grams by 10^{15}.

• Important numerical relationships used in the class:

  • Total atmospheric gas moles: N_{tot} \approx 1.8 \times 10^{20}\ \,\text{mol}.

  • Current atmospheric CO₂ moles (based on 425 ppm): n{CO2} \approx 7.65 \times 10^{16}\ \,\text{mol}.

  • Mass of carbon in atmosphere from CO₂: mC = n{CO_2} \times 12\ \text{g/mol} = 9.18\times 10^{17}\ \text{g} = 918\ \text{PgC}.

• Key conceptual link: the carbon-to-oxygen coupling implies that carbon cycle dynamics are accompanied by oxygen fluxes, with a rough one-to-one relationship between uptake and release in the short term, though the reservoirs (O₂ vs. CO₂) differ greatly in size and turnover times.

• Bottom line on policy and societal relevance (transition to governance and policy context):

  • Time lags (in time and space) complicate governance and policy responses; benefits of reductions in emissions today may take decades to fully manifest in climate indicators.

  • International governance challenges arise when different countries have competing interests (e.g., plastics production vs. global pollution mitigation). The UN Plastics Treaty negotiations illustrate how global policy must reconcile economic and environmental objectives across diverse stakeholders.

Policy, governance, and practical implications (lag concepts applied)

• Time lag in governance: benefits of emission reductions or policy changes may not be visible for years or decades, influencing political incentives.

• Space lag: pollution or environmental impacts can cross borders (e.g., acid rain, transboundary pollution), requiring international cooperation and policy alignment.

• Plastics and market dynamics: disagreements between countries over plastic production, waste management, and economic considerations complicate treaty negotiations; the negotiation process involves balancing environmental protection with economic interests (oil/resource-rich economies vs. importing countries with pollution burdens).

• Research opportunities and programs:

  • Background: a funded 15-month continuous research program focused on chemistry, data science, and environmental topics; positions include cross-disciplinary opportunities involving environmental science, chemistry, data science, and sustainability.

  • Projects emphasize micro- and nanoplastics, environmental sampling methods, and potential health applications; cross-disciplinary collaborations or minors may be available.

  • Typical commitment: 40 hours/week in summer, 10+ hours/week in fall/spring, and full-time again in the following summer.

• Classroom and student engagement notes:

  • The class uses Poll Everywhere to engage students, gather demographics, and foster discussion about diverse backgrounds in environmental science and engineering.

  • Emphasis on hands-on connections between theory and real-world environmental challenges (urban forests, redlining, stormwater, throughfall and stem flow, and urban hydrology).

Summary of practical formulas and units to memorize

• Turnover time (steady state):
  T = \frac{V}{F{in}} = \frac{V}{F{out}}

• For atmospheric carbon in CO₂ form:

  • CO₂ moles from concentration:
    n{CO2} = N_{tot} \times \frac{\text{CO₂ ppm}}{10^6}

  • Mass of carbon in atmosphere:
    mC = n{CO2} \times MC \quad (M_C = 12\ \text{g/mol})

  • PgC conversion: 1\ \text{PgC} = 10^{15}\ \text{g}

• Carbon mass in atmosphere (example values):

  • Pre-industrial: 589\ \text{PgC}

  • Today: approximately 918\ \text{PgC}

  • Added since industrial revolution: 329\ \text{PgC}

  • Percentage increase: \%\Delta = \frac{329}{589} \approx 56\%

• Molar mass and composition reminders:

  • CO₂ molar mass: M{CO2} = 44\ \text{g/mol}

  • Carbon molar mass: M_C = 12\ \text{g/mol}

  • Composition check: carbon in CO₂ is 1 mole of C per 1 mole of CO₂ (stoichiometric one-to-one in terms of carbon content).

• Population and reservoir scale references:

  • Atmospheric O₂ reservoir: on the order of 3.6\times 10^{7}\ \text{Tmoles} (teramoles).

  • One Petamole equals 1000 Teramoles: 1\text{Pm} = 10^{15}\ \text{mol} = 1000\ \text{Tm}.

  • Total atmospheric gas moles: N_{tot} \approx 1.8\times 10^{20}.

Final takeaways to study for the exam

• Steady-state vs perturbation: how to compute turnover time and interpret fluxes in a simple reservoir model; recognize when a system is not in steady state and what a perturbation (e.g., warming) does to fluxes and pool sizes.

• The hydrological cycle accelerates with warming: more evaporation, more rainfall, and variable regional river flow depending on the local balance between precipitation and evaporation.

• In the carbon cycle, anthropogenic emissions have significantly increased the atmospheric CO₂ pool, with a robust, quantitative backbone: about 329 PgC added since the industrial revolution, corresponding to roughly a 56% increase from the pre-industrial atmospheric carbon pool.

• The ocean, land, and atmosphere form interconnected pools with one-to-one stoichiometric links between the carbon and oxygen fluxes in photosynthesis and respiration, but the reservoirs differ greatly in size and turnover times.

• Time lag and distance effects complicate governance and policy: regional and cross-border impacts require international cooperation and long-term planning; policy instruments must account for delayed benefits and spatially diffuse effects.

• Real-world application and data literacy: use simple mass-balance calculations to sanity-check large-scale Earth-system numbers; use long-running observation records (e.g., Mauna Loa CO₂) to ground, interpret, and validate theoretical models.

Notable examples and talking points mentioned in the session

• Everyday intuition: relate evaporation to heating water on a stove (as energy increases, evaporation rises); relate seasonal CO₂ cycles to plant growth and respiration.

• Georgia/Savannah humidity example: high humidity can coincide with strong rainfall but not necessarily with increased river flow due to rapid evaporation—illustrates regional complexity.

• Urban forestry and hydrology example: canopy interception, throughfall, stem flow, and their effects on hydrographs and urban flood dynamics; the role of trees in mitigating flood peaks and water chemistry in urban environments.

• Plastics governance context: differences in national interests during international negotiations (UN plastics treaty) illustrating the complexity of governance in a globally connected system.