Notes on Thinking and Wicked Problems: Systems Thinking in Earth Science

Overview

• The lecture introduces Thinking and Wicked Problems, focusing on applying systems thinking to Earth systems and to wicked problems in earth science.
• Two core concepts:
  • Systems thinking = use a holistic approach to understanding interactions and interdependencies among parts/elements/components of systems.
  • Wicked problems = problems with unclear definitions and solutions that are often competing, contradictory, unpredictable, or changing.
• The course aims to connect these ideas to real Earth system challenges, some of which are existential (e.g., sustaining life on Earth).
• Personal anecdote: the instructor’s sabbatical at Oxford and work in Morocco linking deep-time processes (plate tectonics) to climate, ecosystems, natural resources, human behavior, and natural disasters; illustrates the complexity beyond a simple linear chain.
• The Earth system is embedded with many feedbacks and emergent behaviors, so complex that whole-system properties can differ from a simple sum of parts.
• The learning structure emphasizes starting with goals, then revisiting them to check understanding and allow questions.

Goals and learning outcomes

• Goal 1: Understand the fundamental components of any system (e.g., a car, a bathtub, the Earth) and how specific Earth systems behave.
  • Apply these ideas to biogeochemical cycles (water cycle, rock cycle, carbon cycle, etc.).
• Goal 2: Become acquainted with the major Earth spheres and their interactions: geosphere, hydrosphere, atmosphere, biosphere.
• Goal 3: Introduce the concept of wicked problems and how systems thinking can be applied to them in Earth science.

Fundamental inputs and outputs of a system

• All systems have inputs and outputs, primarily in terms of matter and energy.
• Earth system inputs (energy): predominantly solar radiation (exogenic energy entering the system).
• Earth system outputs (energy): heat energy and reflected light (energy leaving the system).
• Earth also generates internal heat (via radioactive decay) within the geosphere, which is discussed later.
• Matter flow: The Earth is largely closed to matter exchange over long timescales, though there are occasional inputs/outputs (e.g., asteroids, dust, atmospheric escape, major impacts that eject material). Overall, net mass change is near zero most of the time, but not strictly zero.
• The geological record shows the Earth’s system has changed over 4.6 Ga (the Hadean Eon) with substantial external inputs early on (dust, planetesimal accretion, Moon formation, late heavy bombardment bringing water).
• The simplified summary: energy is an open input (solar) and energy can leave as heat/reflected energy; matter is mostly closed with exceptions in the early Earth and via catastrophic events.

The Earth system in time: a historical context

• Hadean Eon (≈ 4.6 to 4.0 × 10^9 years ago): intense accretion, early solar-system material input, Moon-forming impact, late bombardment that delivered much of Earth’s water.
• Over time, the system became more balanced in terms of matter, but not strictly closed; inputs/outputs fluctuated with impacts, atmospheric loss, and other processes.
• This historical context emphasizes that real systems are not ideal isolated/closed/open categories; they can shift between regimes depending on processes active at the time.

Types of systems: isolated, closed, open

• Isolated system (theoretical): no exchange of matter or energy with the surroundings.
  • Example (hypothetical): a perfectly insulated thermos with boiling water that remains boiling forever if perfectly isolated.
  • Not observed in practice; universe-wide isolation is debated.
• Closed system: exchanges energy but not matter.
  • Example: a pressure cooker with a closed valve; energy can enter/leave (as heat) but matter (water) is conserved inside.
  • In practice, perfect closed systems are hard to realize; leaks or phase changes can complicate this.
• Open system: exchanges both energy and matter with surroundings.
  • Example: a boiling pot of water on a stove, which loses heat and water vapor to the atmosphere.
• In Earth system context, real systems are open with respect to both energy and matter to varying degrees; reservoirs help us describe where energy/matter is stored and how it moves.

Reservoirs, sources, and sinks

• Reservoirs: physical places where energy or matter resides (e.g., oceans as a reservoir of water).
• Sources: reservoirs where outgoing matter/energy exceeds incoming (net release to the system or to a downstream reservoir).
• Sinks: reservoirs where incoming matter/energy exceeds outgoing (net uptake or storage).
• Important nuance: physical entities can act as both sources and sinks depending on processes and time, and can be reservoirs as well.
• Examples:
  • Rainforest: can be a sink for carbon via photosynthesis, but under combustion or decay can become a source of CO₂.
  • Ocean: reservoir of heat and carbon, exchanging with atmosphere and land via circulation and gas exchange.
• Quantities measured in reservoirs include:
  • Depth/volume for water in a bathtub or rainforest carbon storage in biomass; and
  • Rates for flows (e.g., liters per second for water input/output).

A simple illustrative diagram: bathtub, tap, and drain

• Inputs: water from tap (input rate).
• Outputs: water through the drain (output rate).
• Reservoir: the bathtub (storage of water).
• State of the reservoir (sink vs source) depends on the balance of In vs Out and the cumulative net change in the reservoir.
• If In > Out, the bathtub fills (reservoir acting as a sink over time).
• If Out > In, the bathtub drains (reservoir acting as a source to downstream components).
• System type (open vs closed) depends on whether there is exchange with external reservoirs (e.g., the atmosphere, rainfall, groundwater, etc.).
• Expanded thought experiment: connecting the bathtub to a larger water cycle by including evaporation, atmosphere, rainfall, groundwater; demonstrates the water cycle as a complex open system with interlinked reservoirs.

Equilibrium and dynamic equilibrium

• Simple open systems tend toward a state of balance where input rates equal output rates: In = Out, leading to no long-term change in reservoir size (dM/dt = In − Out ≈ 0).
• Dynamic equilibrium: inputs and outputs may vary, but the system self-regulates to maintain a stable state over long time intervals; still has internal changes and processes but overall budgets stay balanced.
• Disequilibrium: when inputs outpace outputs over time, the reservoir grows; conversely, if outputs outpace inputs, the reservoir shrinks.
• This concept is foundational for understanding how Earth systems respond to forcing and perturbations over time.

Feedbacks: positive vs negative

• Feedbacks are processes where outputs influence future inputs, altering the system’s trajectory.
• Positive feedbacks: amplify changes; push the system away from equilibrium; can lead to rapid shifts or runaway processes.
  • Example: Milankovitch cycles causing cooling -> more snow/ice -> higher albedo -> more cooling -> more ice growth (and the reverse with warming and ice melt). Both directions can be positive feedbacks depending on the direction of change.
  • Snowball Earth: a proposed extreme example where ice growth and high albedo can rapidly drive Earth into global glaciation; subsequent deglaciation could occur rapidly as oceans absorb more heat and albedo decreases.
  • The Cryogenian glaciations (Snowball Earth era) are cited as dramatic evidence of rapid, large-scale climate shifts, though the timescale is discussed with a note about historical characterization (the lecture mentions 60 billion years in a digression; actual Snowball Earth events occurred ~720–660 million years ago, and durations are typically described as tens of millions of years).
• Negative feedbacks: dampen changes and tend to stabilize the system toward equilibrium.
  • Cloud feedback: warming can increase evaporation, potentially increasing cloud formation; depending on altitude and cloud properties, clouds can reflect solar radiation and cool, acting as a negative feedback; clouds can also trap heat, providing a complex interplay with warming (the net effect is context-dependent).
  • A clear analogy is the thermostat in a hot water heater: as water reaches a set temperature, the heater turns off; when water cools, it turns on again; this is a negative feedback that maintains near-constant temperature.
• Important caveat: many Earth-system feedbacks are complex and interdependent; the net effect of a given feedback can depend on multiple interacting processes (e.g., cloud properties, feedbacks involving water vapor and radiation, permafrost thawing releasing greenhouse gases).

Examples of feedbacks in the real Earth system

• Greenhouse gas forcing and feedbacks:
  • Forcing: increased greenhouse gases cause warming.
  • Positive feedbacks: warming reduces ice cover -> lowers albedo -> more solar absorption -> further warming; warming increases atmospheric water vapor (a greenhouse gas) -> additional warming; thawing permafrost releases CO₂ and CH₄, which further amplify warming.
  • Negative/compensating feedbacks: increased cloud cover from higher evaporation can reflect more sunlight and cool the surface, partially offsetting warming; but clouds can also trap heat, so the net effect depends on cloud type, altitude, and geographic distribution.
• Other examples discussed:
  • Ice-albedo feedback in polar regions (positive feedback).
  • The Amazon rainforest as a major carbon sink and a regulator of regional hydrology; deforestation can lead to reduced rainfall and potential tipping-point transitions, discussed below.

Forcing trajectories: linear, nonlinear, and threshold responses

• Forcing refers to an external driver applied to a system (e.g., increased greenhouse gas concentrations, deforestation).
• Three typical response trajectories:
  • Linear response: state changes in direct proportion to forcing; R ∝ F, where R is the response and F the forcing. The slope depends on the system’s properties (e.g., bathtub with a large cross-section vs. a narrow tube).
  • Nonlinear response: the response changes disproportionately with forcing (e.g., small increases in forcing lead to large responses); the trajectory is curved (green curve in the lecture).
  • Thresholded response (tipping point): a big, abrupt change occurs once forcing crosses a threshold; the response then shifts to a new regime; this can be irreversible on human timescales (e.g., collapse of ice shelves, Amazon rainforest dieback).
• Examples discussed:
  • Sea-level rise and ice-melt as a nonlinear response to warming (potentially exponential-like increase as ice melts accelerate).
  • Thresholds like the West Antarctic Ice Shelf collapse, which could cause rapid, metre-scale sea-level rise within years to decades once destabilized.
  • Deforestation-driven rainfall decline and forest dieback in the Amazon, potentially crossing a threshold that converts rainforest to savannah, altering regional and global climate and carbon balance.
• These trajectory types emphasize that many Earth-system responses are not simply proportional to forcing; nonlinearities and tipping points are common in complex systems.

Emergence: system-level properties beyond components

• Emergence refers to new behaviors or properties at the system level that cannot be predicted by examining components in isolation.
• Classic examples cited:
  • Life: emerging from simple chemical processes into living systems.
  • Consciousness: properties arising from neural networks that are not obvious from individual neurons.
  • Murmurations of birds: coordinated flocking behavior emerging from simple interaction rules among individuals.
  • Earthen architecture in Morocco as an emergent product of long-term processes (cultural, environmental, material choices).
• Emergence is a key feature of complex systems and is a topic to be explored further in upcoming discussions.

The Earth system, spheres, and interactions

• Spheres and their roles:
  • Geosphere: solid Earth, rocks, minerals, landforms, internal heat, tectonics.
  • Hydrosphere: all water on Earth (oceans, rivers, groundwater, etc.).
  • Atmosphere: air; climate, weather, greenhouse effect, and energy exchange.
  • Biosphere: living organisms and their interactions with other spheres.
• Interactions among spheres drive biogeochemical cycles (water, carbon, rock cycles) and influence climate, resource availability, and natural hazards.

Wicked problems in earth science and ethical/practical implications

• Wicked problems arise when definitions are unclear and solutions are contested, complex, and evolving.
• In Earth science, wicked problems include existential questions about sustaining life on Earth, climate change, resource management, and resilience to natural disasters.
• Practical implications include the need for:
  • Cross-disciplinary approaches (geology, ecology, climatology, anthropology, policy).
  • Emphasis on uncertainty, probabilistic reasoning, and adaptive management.
  • Ethical considerations about intergenerational equity, global responsibility, and the precautionary principle.

Connections to biogeochemical cycles and Earth-system processes

• Core cycles covered or referenced:
  • Water cycle (hydrologic cycle)
  • Rock cycle
  • Carbon cycle
• The course emphasizes applying systems thinking to these cycles, noting reservoirs, fluxes, and feedbacks.
• The solar energy input and its interactions with albedo (reflectivity) and greenhouse effects are central drivers of climate and habitability.
• The role of life and ecosystems as dynamic reservoirs (e.g., rainforests as carbon sinks/sources) and as modulators of atmospheric composition and hydrology.

Practical notes on study resources and course logistics

• Official textbook: an open online textbook linked from the course outline/Learning platform; intended to provide background on processes discussed.
• The discussion underscores accessibility and affordability of open resources compared with traditional costly textbooks.
• The course emphasizes real-world relevance, engineering relevance, and the need to connect theory with practical observations and systems thinking skills.
• The instructor notes that lecture notes from previous years may not exactly align with the first half of the course content, and suggests contacting the course coordinator for note access when needed.

Quick recap of key takeaways

• Systems thinking = holistic view of interdependencies and interactions among system components.
• Wicked problems require careful framing, due to unclear definitions and changing solutions.
• Earth system operates with energy input mainly from the sun, and energy output as heat and reflected light; matter exchange is primarily closed on long timescales with notable exceptions.
• Systems can be isolated, closed, or open; reservoirs store matter/energy; sources and sinks describe net flow directions;
• Equilibrium (and dynamic equilibrium) is the typical end-state for many open systems, but disequilibrium and emergent phenomena are common in Earth systems.
• Feedbacks (positive and negative) shape how systems respond to forcing; many feedbacks are complex and intertwined.
• Forcing can lead to linear, nonlinear, or threshold (tipping-point) responses; tipping points imply abrupt, potentially irreversible changes.
• Emergence describes high-level system properties that are not evident from components alone (e.g., life, consciousness, bird murmurations).
• The course links these ideas to biogeochemical cycles and to the four Earth spheres, highlighting the relevance to real-world problems and policy.

Key equations and formal representations (LaTeX)

• Mass or energy balance (reservoir dynamics):
  $\frac{dM}{dt} = ext{In} - ext{Out}$
• Simple equilibrium condition:
  $ext{In} = ext{Out} \ \frac{dM}{dt} = 0$
• Linear response (simplified):
  $R = kF$
  where R is the response, F is the forcing, and k is a system-dependent proportionality constant.
• Nonlinear response (illustrative):
  R = a F^n \, (n>1)
• Threshold (tipping point) response (conceptual):
  $R(F) = \begin{cases} R<em>0, & F < F^* \ R</em>0 + ext{jump}, &amp; F \&amp; ext{≥ } F^* \ \ ext{(irreversible in many cases)} \ \ \ \ \ \ \ \ \end{cases}$
• Energy balance sketch (conceptual):
  $ext{Net Radiative Balance} = ext{Solar Input} - ext{Outgoing Heat/Reflected Light}$
• Albedo effect (qualitative relation):
  ext{Albedo}
  ightarrow ext{Reflects Solar Energy}
  ightarrow ext{Cooling (negative feedback when dominant)}

References and suggested next steps

• Open-access textbook linked in the course outline for foundational background on the processes discussed (processes like plate tectonics, Biogeochemical cycles, and Earth-system interactions).
• Course coordinator (Kate Pedley) for access to lecture notes and additional resources; Judith as a previous instructor contact if needed.
• Consider exploring more on Milankovitch cycles, Snowball Earth hypothesis, and the Amazon rainforest’s role in regional and global climate dynamics as deeper case studies in subsequent lectures.

Real-world relevance and ethical considerations

• Understanding feedbacks and tipping points is crucial for assessing climate risk, resilience, and policy decisions.
• Emergence and interdisciplinary connections underscore that simple cause-and-effect explanations are insufficient for many Earth-system problems; policy and engineering must integrate complex, uncertain, and evolving knowledge.
• The open-resource emphasis aligns with broader trends toward accessible education and informed public discourse on environmental challenges.

Quick prompts to test understanding (practice questions)

• Define a reservoir, a source, and a sink in the context of the Earth system.
• Give an example of a positive feedback in the climate system and explain why it is positive.
• What is the difference between a dynamic equilibrium and a true equilibrium?
• Explain how a tipping point differs from a linear or nonlinear response with an example.
• Describe how emergent properties can arise in an Earth-system context and provide two examples.