An environmental system is a set of connected parts linked by flows of matter or energy. A forest, lake, drainage basin, and the whole Earth can each be treated as a system. The first step is always to say what lies inside the boundary, because that choice determines what counts as an input, an output, or an internal transfer.

Earth’s spheres are useful boundaries, not separate worlds

The atmosphere is the envelope of gases around Earth. The hydrosphere includes water as liquid, ice, and vapour. The lithosphere is the rigid crust and uppermost mantle, including the rock and soil beneath a catchment. The biosphere contains living organisms and the communities they form.

These spheres overlap and exchange matter and energy. Rain moves water from atmosphere to hydrosphere, infiltration carries it into soil and rock, roots move it into the biosphere, and evapotranspiration returns it to the atmosphere. The categories are analytical tools: ice can be separated as a cryosphere when frozen-water processes matter, or included in the hydrosphere when a broader water budget is enough.

Open, closed, and isolated systems

A system’s classification describes what can cross its boundary:

A smaller system can be open even when it sits inside a larger, nearly closed one. River discharge is an output from a drainage basin but an internal transfer within the global water cycle. The label therefore makes sense only after the boundary and timescale are stated.

Inside an open system, incoming material can be transformed, stored, and exported. A forest receives sunlight, carbon dioxide, water, and nutrients. Photosynthesis turns some of those inputs into biomass; soils and vegetation store carbon and nutrients; respiration, heat, dissolved material, litter, and harvested wood leave different parts of the system. A large stock does not automatically mean the forest is a net sink. That depends on whether inputs exceed outputs over the stated interval.

A budget links flows to storage

For a chosen conserved quantity,

$$\Delta S = I-O,$$

where $I$ is total input, $O$ is total output, and $\Delta S$ is the change in storage over the budget period. In rate form,

$$\frac{dS}{dt}=\sum I-\sum O.$$

If the budget follows one chemical species or one form of energy, internal production, consumption, and conversion terms may also be needed. Those processes can change that particular store even when total mass or energy remains conserved.

The terms must use compatible units. A nutrient budget might use $\mathrm{kg\,yr^{-1}}$, a catchment water budget might use $\mathrm{mm\,yr^{-1}}$, and an energy budget uses $\mathrm{W\,m^{-2}}$.

• If $I=O$, storage is steady even though material may be moving through the system continuously.
• If $I>O$, storage grows.
• If $I<O$, storage declines.

A steady state is therefore not inactivity. A lake can receive and release large water flows while its average level stays nearly constant. Many texts call this a dynamic equilibrium because active opposing processes balance at the system level.

The course slides use dynamic equilibrium in a different, specific way: inputs and outputs are unequal, so $\Delta S\ne0$, while the system fluctuates around a rising or falling trend. Atmospheric carbon dioxide is the example. Its seasonal cycle sits on a rising long-term mean because additions to the atmospheric store exceed removals. In strict budget language this is a non-steady trend, so distinguish the course label from the more common balance-based meaning.

Function and scale

A system’s structure is the arrangement of its components and connections. Its function is what those components and flows do: move water, store carbon, recycle nutrients, provide habitat, or transfer heat. Environmental systems can perform several functions at once, and changing one connection can affect many outputs.

Scale determines which processes look important. Turbulent eddies can last seconds over metres; thunderstorms last hours over tens of kilometres; hurricanes last days over hundreds of kilometres; planetary circulation and climate patterns extend over continents and years to decades. Larger spatial processes usually have longer characteristic times, but scales also interact: turbulence shapes clouds, while planetary circulation organizes the environment in which storms form.

A claim about equilibrium or trend must match the observation scale. A seasonal cycle is not a long-term trend, a local storm is not a climate shift, and a stable global average can hide large regional changes.

Feedback means a response returns to affect its cause

A feedback loop begins when a change produces a response that then changes the original process.

• A negative feedback opposes the initial change and tends to stabilize the system.
• A positive feedback reinforces the initial change and tends to move the system farther in the same direction.

“Positive” and “negative” describe the direction of the response, not whether the outcome is good or bad. A positive feedback can amplify cooling as well as warming, and a negative feedback can limit a change without cancelling it.

Permafrost gives an amplifying example:

$$\text{warming} \rightarrow \text{more permafrost thaw} \rightarrow \text{more microbial decomposition and greenhouse-gas release} \rightarrow \text{more warming}.$$

The loop strengthens the initial warming, but the word feedback does not by itself prove an infinite or unstoppable runaway. Its strength depends on how much carbon becomes available, which gases are released, and how other parts of the climate system respond.

Stable and unstable equilibria

Imagine a ball in a landscape of troughs and peaks. The ball represents the system’s current state.

• At the bottom of a stable trough, a small disturbance moves the ball uphill, but restoring negative feedbacks bring it back.
• At an unstable peak, even a small displacement sends the ball away toward one side or the other.
• The depth and width of a trough represent the system’s resilience: how much disturbance it can absorb without leaving that state.

The landscape is conceptual, not literal topography. External pressures can move the ball, but they can also reshape or tilt the landscape, making the current basin shallower and its threshold easier to cross.

Environmental variation takes several forms:

A temporary excursion is not automatically a regime shift. The defining change is that a new set of structures and feedbacks maintains the new state.

Thresholds and alternate stable states

Some systems can occupy more than one stable state under broadly similar external conditions. A shallow lake may be clear with abundant submerged plants, or turbid and dominated by cyanobacteria. Grassland can remain grass-dominated because grasses capture soil moisture and recurring fires kill young woody plants. A shrub–tree state can also maintain itself once woody cover changes shade, fuel, water use, and fire behaviour.

A threshold separates the basins of attraction. In the grassland example:

1. moderate grazing changes biomass while the grass-maintaining feedbacks still restore the system;
2. persistent overgrazing weakens grass cover, while fire suppression lets young woody plants survive;
3. with enough rainfall, shrub and tree cover increases;
4. once the threshold is crossed, feedbacks that favour woody vegetation can carry the system into a second stable state.

This is a regime shift, not just ordinary variation within grassland. Reversing the original pressure may not immediately restore the old state because the return threshold can differ from the forward threshold. That path dependence is called hysteresis.

A tipping point is the critical level of forcing or system condition at which a small additional change can trigger a disproportionately large transition. The forcing may build gradually even when the response is abrupt. The transition itself may still unfold over years or centuries, so “tipping” does not always mean instantaneous change.

Applying the framework to Earth systems

Potential tipping elements include ice sheets, permafrost, forests, coral reefs, monsoon systems, and large ocean-circulation components. Their evidence, timescale, reversibility, and threshold uncertainty differ. They should not be treated as a single countdown.

The Atlantic Meridional Overturning Circulation, for example, depends on temperature, salinity, density, wind, and mixing. Freshening and warming can weaken high-latitude sinking, but the AMOC is not identical to the Gulf Stream, and a change in one component does not imply the abrupt movie-style shutdown of the entire North Atlantic circulation.

The systems framework asks the useful questions directly:

• What is inside the boundary?
• What are the important stocks, inputs, outputs, and internal transfers?
• Which scale and time interval matter?
• Which feedbacks stabilize the current state, and which amplify change?
• Is the system fluctuating, trending, or approaching a threshold?
• How could human actions move the state or reshape the stability landscape?