Goals

On completing this module, students are expected to be able to:

• explain the different components of the marine and terrestrial carbon cycle;
• recognize that atmospheric CO₂ has changed through time and how that variation has impacted climate;
• interpret how the carbon cycle impacts Earth's climate;
• project through modeling how the amount and rate of future carbon emission impact climate and the chemistry of the oceans.

Learning Outcomes

After completing this module, students should be able to answer the following questions:

• Why is the global carbon cycle important to climate change?
• How have humans perturbed the global carbon cycle?
• What are the changes in values of pCO₂ since (1) 1900 and (2) the late 1950s?
• What is the current pCO₂ value?
• What is the significance of the annual cycle in atmospheric CO₂ concentrations?
• What is the correlation of CO₂ concentrations with glacial cycles?
• Generally speaking, what are the volumes of the different carbon reservoirs?
• What is the role of photosynthesis and CO₂ fertilization?
• What is the role of respiration and permafrost?
• How does the air sea exchange work?
• What is marine carbonate chemistry?
• What are the biologic pump, upwelling, downwelling and sedimentation; explain their role in the marine carbon cycle.
• What are the main types of fossil fuels and their relative contribution to recent CO₂ increases?
• What are the big polluters (countries) in total amount and per capita?
• What are the volumes of carbon and their trajectories for the different emissions scenarios?
• What is the role of deforestation and soil erosion in pCO₂ changes?

Below is an overview of your assignments for this module. The list is intended to prepare you for the module and help you to plan your time.

Assignments

1. Lab 5: Carbon Cycle Modeling
2. Submit Module 5 Lab (Graded).
3. Take Module 5 Quiz.
4. Yellowdig Entry and Reply

In the late 1950s, Roger Revelle, an American oceanographer based at the Scripps Institution of Oceanography in La Jolla, California began to ring the alarm bells over the amount of CO₂ being emitted into the atmosphere. Revelle was very concerned about the greenhouse effect from this emission and was cautious because the carbon cycle was not then well understood. So, he decided that it would be wise to begin monitoring atmospheric concentrations of CO₂. In the late 1950s, Revelle and a colleague, Charles Keeling, began monitoring atmospheric CO₂ at an observatory on Mauna Loa, on the big island of Hawaii. Mauna Loa was chosen because its elevation and location away from industrial centers made it as close to a global signal as any other location. The record from Mauna Loa, one of the most classic plots in all of science, shown in the figure below, is a dramatic sign of global change that captured the attention of the whole world because it shows that this "experiment" we are conducting is apparently having a significant effect on the global carbon cycle. The climatological consequences of this change are potentially of great importance to the future of the global population. The CO₂ concentration recently crossed the 400 ppm mark for the first time in millions of years! In 2025, the level has risen above 429 ppm (see CO2.Earth Webite for most up to date estimate).

The record of CO₂ measured at Mauna Loa, Hawaii shows seasonal cycles superimposed on a longer-term rise in the yearly average (black line). The seasonal cycles are related to seasonal variations in photosynthesis and soil respiration in the Northern Hemisphere, where most of the land mass is located at present. The long-term trend is related to the addition of CO₂ to the atmosphere through the combustion of fossil fuels.

Click for a text description of the Mauna Loa CO2 levels graph.

This image is a line graph titled "Mauna Loa Observatory, Hawaii* Monthly Average Carbon Dioxide Concentration," displaying the monthly average CO₂ concentration from 1958 to 2024, with data from the Scripps CO₂ Program, last updated in May 2024. The caption below the graph explains the seasonal cycles and long-term trends observed in the data.

• Graph Type: Line graph
• Y-Axis: CO₂ concentration (parts per million, ppm)
  • Range: 310 ppm to 420 ppm
• X-Axis: Years (1958 to 2024)
• Data Representation:
  • CO₂ Concentration: Black line with data points
    • Starts at around 315 ppm in 1958
    • Shows a steady upward trend with seasonal oscillations
    • Reaches approximately 420 ppm by 2024
  • Maunakea Data: Blue points
    • Noted as "Maunakea data in blue," indicating specific measurements from Maunakea included in the dataset
• Trend:
  • The graph shows a clear long-term increase in CO₂ concentration, rising by about 100 ppm over the 66-year period
  • Seasonal cycles are evident, with annual fluctuations of a few ppm, peaking in spring and dipping in autumn due to Northern Hemisphere photosynthesis and soil respiration
• Additional Info:
  • Source: Scripps Institution of Oceanography, UC San Diego
  • Caption: "The record of CO2 measured at Mauna Loa, Hawaii shows seasonal cycles superimposed on a longer-term rise in the yearly average (black line). The seasonal cycles are related to seasonal variations in photosynthesis and soil respiration in the Northern Hemisphere, where most of the land mass is located at present. The long-term trend is related to the addition of CO2 to the atmosphere through the combustion of fossil fuels."

The graph visually demonstrates the steady rise in atmospheric CO₂ levels, driven by fossil fuel combustion, alongside seasonal variations linked to natural processes in the Northern Hemisphere.

Credit: C. D. Keeling, S. C. Piper, R. B. Bacastow, M. Wahlen, T. P. Whorf, M. Heimann, and H. A. Meijer, Exchanges of atmospheric CO2 and 13CO2 with the terrestrial biosphere and oceans from 1978 to 2000. I. Global aspects, SIO Reference Series, No. 01-06, Scripps Institution of Oceanography, San Diego, 88 pages, 2001.

As the Mauna Loa record and others like it from around the world accumulated, a diverse group of scientists began to appreciate Revelle's concern that we really did not know too much about the global carbon cycle that ultimately regulates how much of our CO₂ emissions stay in the atmosphere.

The importance of present-day changes in the carbon cycle, and the potential implications for climate change became much more apparent when scientists began to get results from studies of gas bubbles trapped in glacial ice. As we learned in Module 1, the bubbles are effectively samples of ancient atmospheres, and we can measure the concentration of CO₂ and other trace gases like methane in these bubbles, and then by counting the annual layers preserved in glacial ice, we can date these atmospheric samples, providing a record of how CO₂ changed over time in the past. The figure below shows the results of some of the ice core studies relevant for the recent past -- back to the year 900 A.D.

The recent history of atmospheric CO₂, derived from the Mauna Loa observations back to 1958, and ice core data back to 900, shows a dramatic increase beginning in the late 1800s, at the onset of the Industrial Revolution. At the same time, the carbon isotope composition (δ13C is the ratio of 13C to 12C in atmospheric CO₂) of the atmosphere declines, as would be expected from the combustion of fossil fuels, which have low values of δ13C. The inset shows a more detailed look at the last 150 years, where we can see that the rise in CO₂ coincides with the rise in the burning of fossil fuels.

Click for a text description of the CO2 history graph.

This image is a graph titled depicts the atmospheric CO₂ concentration and related data from approximately 900 to 2000. The graph combines data from ice core records and Mauna Loa observations, illustrating changes in CO₂ levels and carbon isotope composition (δ13C). The caption explains the data sources and the relationship between CO₂ rise, fossil fuel combustion, and δ13C decline.

• Graph Type: Multi-line plot with inset
• Axes:
  • X-Axis: Time (years, from 900 to 2000)
  • Y-Axis (Left): Not explicitly labeled, but represents CO₂ concentration (ppm) and δ13C (per mil)
  • Y-Axis (Right): Fossil fuel emissions (Gigatons of carbon per year, GtC/yr)
• Data Representation:
  • CO₂ Concentration (Ice Core): Blue line with white dots
    • From 900 to ~1800, remains stable around 280 ppm
    • Begins rising in the late 1800s, reaching ~300 ppm by 1900
  • CO₂ Concentration (Mauna Loa): Blue line
    • Starts in 1958 at ~315 ppm, rises steadily to ~370 ppm by 2000
  • δ13C (Ice Core and Observations): Green line
    • Stable around -6.5 per mil from 900 to 1800
    • Declines from the late 1800s, reaching ~ -8 per mil by 2000
  • Fossil Fuel Emissions (FF): Orange dashed line
    • Starts near 0 GtC/yr in 1800, rises sharply after 1850, reaching ~6 GtC/yr by 2000
• Inset:
  • Focuses on 1850–2000
  • Shows detailed trends:
    • CO₂ rises from ~280 ppm to ~370 ppm
    • δ13C declines from ~ -6.5 to ~ -8 per mil
    • Fossil fuel emissions increase from near 0 to ~6 GtC/yr
• Annotations:
  • Labels for "Ice core" and "FF" (fossil fuel) on data lines
  • "Mauna Loa" label on the modern CO₂ data
  • Indicates the onset of the Industrial Revolution (~1800) as the start of the CO₂ increase
• Caption:
  • "The recent history of atmospheric CO2, derived from the Mauna Loa observations back to 1958, and ice core data back to 900, shows a dramatic increase beginning in the late 1800s, at the onset of the Industrial Revolution. At the same time, the carbon isotope composition (δ13C is the ratio of 13C to 12C in atmospheric CO2) of the atmosphere declines, as would be expected from the combustion of fossil fuels, which have low values of δ13C. The inset shows a more detailed look at the last 150 years, where we can see that the rise in CO2 coincides with the rise in the burning of fossil fuels."

The graph visually demonstrates a stable CO₂ level for centuries until the Industrial Revolution, followed by a sharp increase in CO₂ and fossil fuel emissions, accompanied by a decline in δ13C, consistent with the impact of burning fossil fuels.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

The striking feature of these data is that there is an exponential rise in atmospheric CO₂ (and methane, another greenhouse gas) that connects with the more recent Mauna Loa record to produce a rather frightening trend. Also shown in the above figure is the record of fossil fuel emissions from around the world, which show a very similar exponential trend. Notice that these two data sets show an exponential rise that seems to begin at about the same time. What does this mean? Does it mean that there is a cause-and-effect relationship between emissions of CO₂ and atmospheric CO₂ levels? Although we should remember that science cannot prove things to be true beyond all doubt, it is highly likely that there is a cause-and-effect relationship -- it would be an extremely bizarre coincidence if the observed rise in atmospheric CO₂ and the emissions of CO₂ were unrelated.

How serious is our modification of the natural carbon cycle? Here, we need a slightly longer perspective from which to view our recent changes, so we return to the records from ice cores and look deeper and further back in time than we did in the figure we have been examining.

The record of atmospheric CO2 over the last 400,000 years shows that the recent rise in CO₂ is unlike anything we’ve seen in the past 400 kyr both in terms of the rate of increase and the levels to which it is rising. Before this recent rise, CO₂ fluctuated by about 80 ppm in connection with the ice ages (which as you can see have a regularity to their timing); this pattern has clearly been interrupted by the recent trend. The data shown here come from a variety of ice cores (blue, green, red, and cyan) and the Mauna Loa observatory (black).

Click for a text description of the carbon dioxide variations graph.

This image is a graph that depicts atmospheric CO₂ concentrations over the past 400,000 years, with an inset focusing on the last 2,000 years. The data combines ice core records and modern observations from the Mauna Loa Observatory, illustrating both long-term natural fluctuations and the recent dramatic rise in CO₂ levels. The caption emphasizes the unprecedented nature of the modern CO₂ increase compared to historical patterns.

• Graph Type: Line graph with inset
• Main Graph:
  • X-Axis: Time (thousands of years ago, from 400 kyr ago to present)
  • Y-Axis: CO₂ concentration (parts per million, ppm)
    • Range: 200 ppm to 300 ppm (main graph), up to 400 ppm (including recent data)
  • Data Representation:
    • Ice Core Data: Multiple colored lines (blue, green, red, cyan)
      • Shows cyclical fluctuations between ~180 ppm and ~280 ppm over 400,000 years
      • Cycles correspond to Ice Age cycles, with a periodicity of about 100,000 years
    • Recent Data: Black line
      • Sharp increase starting around 0 years ago (present), rising to ~400 ppm
  • Trend:
    • Regular oscillations tied to Ice Age cycles, with CO₂ varying by ~80 ppm
    • Abrupt rise in CO₂ in the last century, breaking the historical pattern
  • Annotation:
    • "Ice Age Cycles" label highlights the periodic fluctuations in CO₂
• Inset Graph (Top Left):
  • Title: "The Industrial Revolution Has Caused A Dramatic Rise in CO₂"
  • X-Axis: Year (AD, from 1000 to 2000)
  • Y-Axis: CO₂ concentration (ppm)
    • Range: 280 ppm to 400 ppm
  • Data Representation:
    • Colored lines (blue, green, red, cyan) for ice core data, stable at ~280 ppm until ~1800
    • Black line for Mauna Loa data, showing a steep rise from ~280 ppm in 1800 to ~400 ppm by 2000
  • Trend:
    • Stable CO₂ levels until the Industrial Revolution (~1800)
    • Rapid increase post-1800, accelerating in the 20th century
• Caption:
  • "The record of atmospheric CO2 over the last 400,000 years shows that the recent rise in CO2 is unlike anything we’ve seen in the past 400 kyr both in terms of the rate of increase and the levels to which it is rising. Before this recent rise, CO2 fluctuated by about 80 ppm in connection with the ice ages (which as you can see have a regularity to their timing); this pattern has clearly been interrupted by the recent trend. The data shown here come from a variety of ice cores (blue, green, red, and cyan) and the Mauna Loa observatory (black)."

The graph visually contrasts the stable, cyclical CO₂ variations tied to Ice Age cycles over 400,000 years with the unprecedented and rapid rise in CO₂ since the Industrial Revolution, reaching levels not seen in the historical record.

Credit: Robert A. Rohde (original PNG), User: Jklamo (SVG conversion) [CC BY-SA 3.0]

In addition to providing a record of the past concentration of CO₂ in the atmosphere, as we learned in Module 1, the ice cores also give us a temperature record. By studying the ratios of stable isotopes of oxygen that make up the glacial ice, we can estimate the temperature (in the region of the ice) at the time the snow fell (glacial ice is formed by the compression of snow as it gets buried to greater and greater depths). From these data, shown in the figure below, we can see the natural variations in atmospheric CO₂ and temperature that have occurred over the past 160,000 years (160 kyr).

Data from the Vostok (Antarctica) ice core for the past 160 kyr show the relationship between variations in heat-trapping gases CO₂ (carbon dioxide) and CH₄ (methane) concentrations in parts per million (ppm) and parts per billion (ppb) and the temperature at Vostok. Note that each curve has its own scale for the vertical axis, but they all share the same time scale. The dashed blue line at the end shows the very recent rise in CO₂ to the present day value of about 410 ppm, indicated by the arrow. The gas concentrations come from tiny bubbles trapped in the ice as it forms near the surface, while the temperature variations come from studying isotopes of oxygen and hydrogen in the ice itself. The ice cores thus provide us with an exceptional picture of atmospheric gas concentrations in the past and their relationship with temperature.

Click for a text description of the Vostak ice core graph.

This image is a multi-line graph depicting data from the Vostok (Antarctica) ice core over the past 160,000 years (160 kyr BP, or "before present"). The graph shows the relationship between atmospheric concentrations of two heat-trapping gases—carbon dioxide (CO₂) and methane (CH₄)—and the temperature at Vostok. The caption explains the data sources and the relationship between gas concentrations and temperature.

• Graph Type: Multi-line plot
• X-Axis: Time in thousands of years before present (kyr BP)
  • Range: 160 kyr BP to 0 kyr BP
• Y-Axes (three separate scales):
  • Left (Top): CH₄ concentration (parts per billion, ppb)
    • Range: 300 ppb to 800 ppb
  • Left (Middle): CO₂ concentration (parts per million, ppm)
    • Range: 180 ppm to 300 ppm
  • Left (Bottom): Vostok temperature (°C)
    • Range: -10°C to 0°C
  • Right: CO₂ concentration (ppm, for recent data)
    • Range: 200 ppm to 410 ppm
• Data Representation:
  • CH₄ Concentration: Green line
    • Fluctuates between ~350 ppb and ~700 ppb
    • Peaks around 140, 120, 100, 70, 10 kyr BP; dips between these peaks
    • Sharp rise near 0 kyr BP, reaching ~800 ppb
  • CO₂ Concentration: Blue line
    • Fluctuates between ~190 ppm and ~280 ppm
    • Peaks align with CH₄ peaks (140, 120, 100, 70, 10 kyr BP)
    • Dashed blue line at 0 kyr BP shows a recent rise to ~410 ppm (indicated by an arrow)
  • Vostok Temperature: Red line
    • Fluctuates between ~-8°C and ~-2°C
    • Peaks and dips closely correlate with CO₂ and CH₄, showing warmer periods at ~140, 120, 100, 70, 10 kyr BP
    • Sharp rise near 0 kyr BP, aligning with gas increases
• Trends:
  • Strong correlation between CO₂, CH₄, and temperature over 160 kyr
  • Cyclical patterns with peaks roughly every 20–30 kyr, corresponding to glacial-interglacial cycles
  • Recent data (dashed blue line) shows an unprecedented CO₂ rise to 410 ppm, far exceeding historical peaks
• Caption:
  • "Data from the Vostok (Antarctica) ice core for the past 160 kyr show the relationship between variations in heat-trapping gases CO2 (carbon dioxide) and CH4 (methane) concentrations in parts per million (ppm) and parts per billion (ppb) and the temperature at Vostok. Note that each curve has its own scale for the vertical axis, but they all share the same time scale. The dashed blue line at the end shows the very recent rise in CO2 to the present day value of about 410 ppm, indicated by the arrow. The gas concentrations come from tiny bubbles trapped in the ice as it forms near the surface, while the temperature variations come from studying isotopes of oxygen and hydrogen in the ice itself. The ice cores thus provide us with an exceptional picture of atmospheric gas concentrations in the past and their relationship with temperature."

The graph illustrates the tight coupling of CO₂, CH₄, and temperature over 160,000 years, with cyclical fluctuations tied to glacial cycles, and highlights the dramatic, unprecedented rise in CO₂ in recent times, as captured by the Vostok ice core data.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

In fact, looking at this much longer span of time enables us to clearly see that the present CO₂ concentration of the atmosphere is unprecedented in the last several hundreds of thousands of years. As geoscientists, we are interested in more than just the last few hundred kiloyears, and so we look back into the past using sediment cores retrieved from the deep sea. Geochemists studying these sediments have been able to reconstruct the approximate concentration of CO₂ in the atmosphere and the sea surface temperature (SST).

The longer history of atmospheric CO₂ as reconstructed from studies of deep-sea sediments. In the upper right, the blue region represents the upper and lower estimates back through time — you can see that it is difficult to be too precise going back this far in time — and you can see that the last time the midpoint of these estimates rose above the current level was around 2.5 Myr ago. This was a time when there was far less ice on Earth; the Arctic was apparently 15 to 20°C warmer than it is today, and sea level was about 20 meters higher than the present. As we go further back in time, we see that the atmospheric CO₂ concentration rises to very high levels. The Earth was a very different place before about 30 Myr ago — sea level was perhaps 100 m higher and there was practically no ice on Earth.

Click for a text description of the atmospheric CO2 concentration history graph.

This image is a graph depicting the long-term history of atmospheric CO₂ concentrations over the past 45 million years (Ma), reconstructed from deep-sea sediment studies. The graph includes an inset focusing on the last 5 million years to highlight recent trends. The caption provides context about the CO₂ levels, their implications for Earth's climate, and comparisons to past conditions.

• Graph Type: Area plot with inset
• Main Graph:
  • X-Axis: Time in millions of years ago (Ma)
    • Range: 45 Ma to 0 Ma (present)
  • Y-Axis: Atmospheric CO₂ concentration (parts per million, ppm)
    • Range: 0 ppm to 2500 ppm
  • Data Representation:
    • CO₂ Concentration: Green shaded area
      • Represents the range of estimated CO₂ concentrations
      • Peaks around 40 Ma at ~2000–2500 ppm
      • Declines gradually, with fluctuations, to ~300–500 ppm by 10 Ma
      • Drops significantly after 10 Ma, reaching ~300 ppm by 0 Ma
    • Trend:
      • High CO₂ levels (>1000 ppm) dominate before 30 Ma
      • Gradual decline with notable drops around 35 Ma and 10 Ma
      • Relatively stable at ~300–400 ppm in the last 5 Ma
• Inset Graph (Top Right):
  • X-Axis: Time in millions of years ago (Ma)
    • Range: 5 Ma to 0 Ma
  • Y-Axis: Atmospheric CO₂ concentration (ppm)
    • Range: 300 ppm to 450 ppm
  • Data Representation:
    • CO₂ Concentration: Blue shaded area
      • Shows upper and lower estimates of CO₂ concentration
      • Fluctuates between ~300 ppm and ~450 ppm
      • Midpoint rises above current levels (~410 ppm) around 2.5 Ma ago
    • Trend:
      • Less precise estimates due to data limitations
      • Indicates CO₂ levels were last above modern levels ~2.5 Ma ago
• Annotations:
  • Dashed line at ~2.5 Ma in the inset highlights when CO₂ was last above current levels
  • Sources cited: Pagani et al., 2005 (Science, 309, 600–603) for main graph; Pagani et al., 2010 (Nature Geoscience, 3, 27–30) for inset
• Caption:
  • "The longer history of atmospheric CO2 as reconstructed from studies of deep-sea sediments. In the upper right, the blue region represents the upper and lower estimates back through time — you can see that it is difficult to be too precise going back this far in time — and you can see that the last time the midpoint of these estimates rose above the current level was around 2.5 Myr ago. This was a time when there was far less ice on Earth; the Arctic was apparently 15 to 20°C warmer than it is today, and sea level was about 20 meters higher than the present. As we go further back in time, we see that the atmospheric CO2 concentration rises to very high levels. The Earth was a very different place before about 30 Myr ago — sea level was perhaps 100 m higher and there was practically no ice on Earth."

The graph illustrates the long-term decline in atmospheric CO₂ from extremely high levels (~2000–2500 ppm) 40 million years ago to modern levels (~410 ppm), with a significant drop after 30 Ma. The inset highlights that CO₂ was last above current levels ~2.5 Ma ago, a period with warmer climates and higher sea levels, underscoring the unique climatic conditions of earlier Earth.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

To find atmospheric CO₂ levels equivalent to the present, we have to go back 2.5 million years. This means that, to the extent that the state of the carbon cycle is closely linked to the condition of the global climate, we are pushing the system toward a climate that has not occurred any time within the last several million years -- not something to be taken lightly.

The farther back in time we go, the more difficult it is to figure out how CO₂ concentrations have changed, but that has not stopped some from attempting:

The history of atmospheric CO₂ over the last 550 Ma, based on modeling, shows extremely high levels about 100 Ma (million years ago) and before 350 Ma. Note that there are huge uncertainties associated with these estimates, but the mid-range of the estimates suggests that CO₂ levels were very high during this time period. Interestingly, these periods of high CO₂ more or less coincide with periods of high sea level, as can be seen in the lower panel.

Click for a text description of the model-derived history of atmospheric CO2 graph.

This image consists of two graphs illustrating the model-derived history of atmospheric CO₂ and its relationship to sea level over the past 550 million years (Ma). The upper graph shows CO₂ concentrations, and the lower graph shows approximate "Eustatic" sea level changes. The caption highlights the high CO₂ levels during specific periods and their correlation with high sea levels.

• Upper Graph:
  • Title: Model-Derived History of Atmospheric CO₂
  • X-Axis: Time (millions of years ago, Ma)
    • Range: 550 Ma to 0 Ma (present)
  • Y-Axis: Atmospheric CO₂ relative to present (RCO₂)
    • Range: 0 to 20 (times the present CO₂ level)
  • Secondary Y-Axis: Global average temperature (°C)
    • Range: 13.0°C to 9.1°C (calculated using equations of Varekamp, 1987)
  • Data Representation:
    • CO₂ Concentration: Gray shaded region
      • Represents the range of uncertainty in estimates
      • Peaks around 500 Ma and 100 Ma, reaching ~15–18 RCO₂ (15–18 times present levels)
      • Dips around 300 Ma and 50 Ma, dropping to ~2–4 RCO₂
      • Recent levels (0 Ma) are around 1 RCO₂ (present baseline)
    • Geological Periods: Labeled above the graph
      • Paleozoic (C, O, S, D, C, P)
      • Mesozoic (T, J, K)
      • Cenozoic
  • Trend:
    • High CO₂ levels (>10 RCO₂) before 350 Ma and around 100 Ma
    • Lower levels (~2–4 RCO₂) between 300 Ma and 50 Ma
    • Gradual decline toward present levels
  • Annotation:
    • "Shaded region indicates range of uncertainty"
    • Source: Data from Berner, 1991
• Lower Graph:
  • Title: Approximate "Eustatic" Sea Level
  • X-Axis: Time (millions of years ago, Ma)
    • Range: 550 Ma to 0 Ma (aligned with upper graph)
  • Y-Axis: Sea level (meters)
    • Range: Low to High (qualitative scale, not numerically labeled)
    • Approximate range: -200 m to 300 m relative to present
  • Data Representation:
    • Sea Level: Black line with shaded area
      • Peaks around 500 Ma and 100 Ma, reaching ~200–300 m above present
      • Dips around 300 Ma and 50 Ma, dropping to ~0 m or below
      • Present sea level marked as "today's sea level"
  • Trend:
    • High sea levels correlate with high CO₂ periods (before 350 Ma and ~100 Ma)
    • Lower sea levels align with lower CO₂ periods (~300 Ma and ~50 Ma)
• Caption:
  • "The history of atmospheric CO2 over the last 550 Ma, based on modeling, shows extremely high levels about 100 Ma (million years ago) and before 350 Ma. Note that there are huge uncertainties associated with these estimates, but the mid-range of the estimates suggests that CO2 levels were very high during this time period. Interestingly, these periods of high CO2 more or less coincide with periods of high sea level, as can be seen in the lower panel."

The image illustrates that atmospheric CO₂ was significantly higher (up to 15–18 times present levels) during the early Paleozoic (~500 Ma) and Cretaceous (~100 Ma), with large uncertainties. These high-CO₂ periods correspond closely with elevated sea levels, suggesting a link between CO₂ concentrations and global climate conditions over geological time.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

One thing that is clear is that further back in time, CO₂ levels have been much, much higher, and the average global temperatures have also been much higher. Why does the CO₂ concentration change so much? This is a big question whose answer involves many factors, but consider two that are relevant to what we'll learn about in this module. Photosynthesis only started in the Silurian (S on the timescale in the figure above), and photosynthesis is a major sink or absorber of atmospheric CO₂. Sea level was much higher during the two big peaks in CO₂ — this leaves less room for photosynthesis and it also decreases the planet's albedo, making it warmer. A warmer ocean cannot absorb atmospheric CO₂ and instead, it releases it to the atmosphere.

In conclusion, from this brief look at the record of fossil fuel emissions and atmospheric CO₂ concentrations, it is clear that we have cause for concern about the effects of the global CO₂ "experiment". Because of this concern, there is a tremendous effort underway to better understand the global carbon cycle. In the remainder of this module, we will explore the global carbon cycle by first examining the components and processes involved and then by constructing and experimenting with a variety of models. The models will be relevant to the dynamics of the carbon cycle over a period of several hundred years -- these will enable us to explore a variety of questions about how the system will behave in our lifetimes and a bit beyond.

The global carbon cycle is a whole system of processes that transfers carbon in various forms through the Earth’s different parts. The carbon that is in the atmosphere in the form of CO₂ and CH₄ (methane) doesn’t stay in the atmosphere for long — it moves from there to other places and takes different forms. Plants use the CO₂ from the atmosphere in photosynthesis to make carbohydrates and other organic molecules, and from there it may return to the atmosphere as CO₂, or it may enter the soil as still different compounds that contain carbon. Some carbon is deposited in sedimentary rocks from the oceans, and much later, this carbon may be released to the atmosphere. So, carbon moves around — it flows — from place to place.

Because CO₂ is such an important greenhouse gas, the way the carbon cycle works is central to the operation of the global climate system. Later in this module, we will work with a computer model of the carbon cycle to do experiments that will help us understand how it works, but it will help to begin with an overview of the carbon cycle from the systems perspective.

What is meant by a systems perspective? It just means that we focus on the places where carbon resides (the reservoirs, in systems terminology), how it moves from reservoir to reservoir, how much of it moves from place to place, and what controls those movements. This same perspective is behind the simple climate model we worked on in Module 3.

First, let’s consider the main reservoirs of carbon. These can be seen in the diagram below, where each box represents a different reservoir, and remember that in each of them, the carbon may be in very different forms. Note a GT or gigaton is a billion metric tons or 10¹⁵ grams which is a whole lot of carbon!

The global carbon cycle, showing the different reservoirs for carbon

Click for a text description of the global carbon cycle diagram.

This image is a diagram illustrating the major reservoirs of carbon in the global carbon cycle, quantified in gigatons (GT) of carbon. The diagram uses color-coded boxes to represent different carbon storage compartments on Earth, arranged to show their relative sizes and roles in the carbon cycle.

• Diagram Type: Block diagram
• Components (Reservoirs with Carbon Stocks):
  • Atmosphere:
    • 750 GT
    • Represented by a light blue horizontal box at the top
  • Land Biota:
    • 610 GT
    • Green box, positioned below the atmosphere
  • Surface Oceans:
    • 970 GT
    • Light blue box, positioned to the right of Land Biota
  • Ocean Biota:
    • 3 GT
    • Small green box, positioned to the right of Surface Oceans
  • Soil:
    • 1580 GT
    • Orange box, positioned below Land Biota
  • Deep Oceans:
    • 38,000 GT
    • Large light blue box, positioned below Surface Oceans
  • Mantle:
    • "Huge amount" (not quantified)
    • Green box, positioned below Soil
  • Sedimentary Rocks:
    • 1,000,000 GT
    • Purple box, positioned below Deep Oceans
• Visual Layout:
  • The boxes are arranged in a grid-like pattern, with sizes roughly proportional to the carbon stored in each reservoir
  • The Atmosphere, Land Biota, Surface Oceans, and Ocean Biota are at the top, indicating their relatively smaller but active roles
  • Soil and Deep Oceans are larger, reflecting their significant carbon storage
  • Sedimentary Rocks is the largest box, emphasizing its massive carbon reservoir
  • The Mantle is noted as having a "huge amount," but no specific value is given, suggesting its vast but less accessible carbon pool

The diagram provides a clear visual summary of the distribution of carbon across Earth's major reservoirs, highlighting the dominance of sedimentary rocks and deep oceans in long-term carbon storage, while the atmosphere, biota, and surface oceans play more dynamic roles in the carbon cycle.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

The mantle reservoir is huge and somewhat removed from the other reservoirs, thus we will not really bother with it. Among the other reservoirs, you can see that there is a huge range in the sizes. The ocean biota contain a very small amount of carbon relatively speaking, while sedimentary rocks contain a vast quantity (in the form of calcite — CaCO₃ — that forms limestones, and coal, petroleum, etc.).

Now, let’s look at the system with the flows included, as arrows connecting the reservoirs:

The global carbon cycle, showing the different reservoirs for carbon and the exchanges between reservoirs in GT per year

Click for a text description of the global carbon cycle flows diagram.

This image is a diagram of the global carbon cycle, focusing on the major reservoirs of carbon and the flows between them, with an emphasis on human-related activities. The diagram uses color-coded boxes to represent carbon reservoirs and arrows to indicate carbon flows, with red arrows highlighting flows altered by human activities and green arrows showing natural temperature-sensitive flows.

• Diagram Type: Block diagram with flow arrows
• Reservoirs (in Gigatons of carbon, GT):
  • Atmosphere: 750 GT (light blue box, top)
  • Land Biota: 610 GT (green box, middle left)
  • Surface Oceans: 970 GT (light blue box, middle right)
  • Ocean Biota: 3 GT (green box, top right)
  • Soil: 1580 GT (orange box, below Land Biota)
  • Deep Oceans: 38,000 GT (light blue box, below Surface Oceans)
  • Mantle: "Huge amount" (green box, bottom left)
  • Sedimentary Rocks: 1,000,000 GT (purple box, bottom right)
• Flows:
  • Red Arrows (human-related activities):
    • From Sedimentary Rocks to Atmosphere: Labeled "Fossil Fuel Burning," indicating carbon release from burning fossil fuels
    • From Land Biota to Atmosphere: Represents deforestation and land-use changes releasing carbon
    • From Soil to Atmosphere: Likely indicates carbon release from soil disturbance (e.g., agriculture)
  • Green Arrows (labeled with "T," temperature-sensitive flows):
    • Between Atmosphere and Land Biota: Photosynthesis and respiration, sensitive to temperature changes
    • Between Atmosphere and Surface Oceans: CO₂ exchange, affected by temperature
    • Between Surface Oceans and Deep Oceans: Carbon transfer via ocean circulation, temperature-dependent
• Annotations:
  • Text at top: "Red arrows are flows that are related to human activities, Green T = Flows sensitive to temperature"
  • The diagram emphasizes human impacts (fossil fuel burning, deforestation) and natural processes influenced by temperature (e.g., photosynthesis, ocean CO₂ uptake)

The diagram visually summarizes the global carbon cycle, highlighting the significant role of human activities in increasing atmospheric carbon through fossil fuel burning and land-use changes, alongside natural temperature-sensitive carbon exchanges between the atmosphere, land, and oceans.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

The black arrows represent natural processes of carbon transfer, while the red arrows represent changes humans are responsible for. The magnitudes of the flows are shown in units of gigatons of carbon per year. The diagram as constructed here represents a steady state if we just consider the black arrows; the flows going into each reservoir are equal to the flows going out of the reservoir — in other words, there is a balance. We will step through this system, talking about the processes involved in the flows, but first, let’s try to learn something from the numbers themselves in this diagram.

First, just a bit more on the notion of steady state. The diagram below illustrates some simple systems, one of which is not in a steady state, and the others of which are.

Diagram illustrating concepts of Steady State and Not in Steady State

Click for a text description of the Steady state vs. Non-steady state diagram.

This image is a simple diagram consisting of three green rectangular boxes stacked vertically against a black background. Each box contains the number "20" in black text centered within it.

• Diagram Type: Stacked rectangular blocks
• Components:
  • Three green rectangles, each identical in size and color
  • Each rectangle has the number "20" displayed in the center
• Layout:
  • The boxes are aligned vertically, evenly spaced, with small gaps between them
  • The black background provides high contrast, making the green boxes and white text stand out

The image lacks additional context, labels, or annotations, so its specific meaning or purpose is unclear. It could represent a count, a value, or a placeholder in a larger diagram or presentation.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

In the first example, A, more (10 units per time) is subtracted from the reservoir than is added (5 units per time), and so over time, the amount in the reservoir will decline — it will not remain constant, or steady. In each time step, it will lose 5 units of whatever the material is. In the other two (B,C), the amount added is the same as the amount subtracted, so these reservoirs will be in a steady state. If you look at example C, you see that the sum of inflows (5+5) is equal to the outflow (10).

When a system is in a steady state, we can say something about the average time something will spend in the reservoir — this is called the residence time for the reservoir. Here is a simple example — if there are 40,000 students at Penn State, and 10,000 students enter each year and 10,000 students graduate each year, then the system is in a steady state. The residence time is the total number of students divided by either the number entering or graduating each year — this give 4 years as the average residence time. Here is a figure to explain the idea further:

Diagram illustrating concept of Residence Time

Click for a text description of the Residence time diagram.

This image is a simple diagram featuring a single green rectangular box against a black background. The box contains the number "20" in black text centered within it.

• Diagram Type: Single rectangular block
• Components:
  • One green rectangle
  • The number "20" displayed in the center of the rectangle
• Layout:
  • The green box is positioned centrally within the black background
  • The black background provides high contrast, making the green rectangle and black text stand out

The image lacks additional context, labels, or annotations, so its specific meaning or purpose is unclear. It could represent a count, a value, or a placeholder in a larger diagram or presentation.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

The concept of residence time is a useful one in studying any kind of system because it tells us something about how quickly material is moving through a system, and more important, it tells us how quickly some part of the system, or the system as a whole, can respond to changes. If something has a short residence time, it can respond quickly to changes, whereas if it has a long residence time, it responds very slowly. Mathematically, the residence time is the same as something called the response time which, as the name implies, is a measure of how much time it takes for the system to respond to a change. The word "respond" in this context means "return to a steady state."

Although the residence time and the response time are often the same value, they represent different ideas. As we said earlier, the residence time is a measure of the average length of time something spends in a reservoir — like the average length of time a carbon atom spends in the atmosphere. The response time, instead, is a measure of how quickly something returns to steady state after some disturbance that knocks it out of steady state. So, response time is only meaningful in cases where a system has a tendency to remain in a steady state.

Now, let’s turn to the carbon cycle and consider some of the flows in and out of the reservoirs. What is the residence time for the atmosphere? To get this, we take the amount in the reservoir (750 GT) and divide it by the sum of the inflows or the outflows. Let’s take the outflows: 100 GT C/yr for photosynthesis + 90 GT C/yr going into the oceans. The residence time is thus:

$$750 G T / 190 G T y r - 1 = \mathrm{3.9\; years}$$

This is a pretty short residence time. Now, let’s look at the deep ocean (which is the vast majority of the oceans) — its residence time is:

$$38000 G T / 10 G T y r - 1 = 3 , 800 \mathrm{years}$$

We use 10 for the inflow/outflow value because we use the net of the water flux into and out of the deep ocean. The result, 3,800 years, is much longer than the atmosphere, and what this means is that the carbon cycle has some parts that respond quickly, but other parts that respond very slowly, and the very slow parts tend to put a damper on how quickly the other parts can change. In other words, if we suddenly inject carbon dioxide into the atmosphere, you might think that the short residence time of the atmosphere means that the excess CO₂ can be removed very quickly, but because these reservoirs are linked together, it turns out that the deep ocean must return to its steady state before the atmosphere can get back to its steady state.

We're going to take a step backwards for a second and think about a much simpler system, but one that has some things in common with the global carbon cycle. First, however, we need to recognize that the natural carbon cycle is something that always varies a bit, but it has some important feedbacks in it that tend to make it stable or steady. And then, along come humans, burning an impressive amount of fossil fuel and creating a new flow in the carbon cycle. To get a sense of how a system with a tendency to remain in a steady state might respond to a new flow, we turn to a simpler model.

Our simple model is a water tub with a drain and two faucets.

STELLA model diagram of a water tub filled by a "natural" faucet and an "extra" faucet, which could be considered to represent humans altering a natural system. Water is removed by a drain, whose rate is dependent on how much water is in the tub (more water in the tub means that more water leaves through the drain. The converter k is the rate constant for the drain, equivalent to a percentage of the total water in the tub.

Click for a text description of the STELLA model diagram.

This image is a diagram titled "WATER TUB," illustrating a simplified model of a water tub system with inflows and outflows, analogous to a dynamic system reaching a steady state. The diagram uses arrows and labels to show the flow of water into and out of the tub, with a caption explaining the specific model parameters and outcomes.

• Diagram Type: Flow diagram
• Components:
  • Water Tub: A central rectangular box labeled "WATER TUB," representing the reservoir of water.
  • Inflows:
    • Natural Faucet: An arrow labeled "natural faucet" entering the tub from the left, representing a constant water inflow.
    • Extra Faucet: Another arrow labeled "extra faucet" entering the tub from the left, contributing additional inflow.
    • Faucet Total: A circular node labeled "faucet total" where the natural and extra faucet inflows combine before entering the tub.
  • Outflow:
    • Drain: An arrow labeled "drain" exiting the tub to the right, leading to a circular node with a "k" (likely a rate constant) and then to a cloud-like symbol, indicating water leaving the system.
  • Feedback:
    • A red dashed arrow loops from the drain back to the tub, suggesting the drain rate is dependent on the amount of water in the tub.
• Annotations:
  • The diagram does not include numerical values or scales directly on the components, but the caption provides specific parameters.
• Caption:
  • "This graph shows the model results from a case where the initial amount of water in the tub was 10 liters and the faucet rate was 3 liters per time unit. The initial drain flow rate is just 10% of the starting amount of water -- 1 liter per time unit -- so the amount of water in the tub increases until it reaches 30 liters, at which point the drain flow rate is 3 liters per time unit, the same as the faucet rate. When the faucet (inflow) rate is equal to the drain (outflow) rate, the system is in a steady state. The figure also shows how the response time is defined for this kind of a system that evolves into a steady state."

The diagram visually represents a dynamic system where water accumulates in the tub until the inflow (3 liters per time unit from the faucet) equals the outflow (drain rate, which increases to 3 liters per time unit when the tub reaches 30 liters), achieving a steady state. The red dashed feedback loop indicates that the drain rate depends on the water volume, illustrating the system's response time to reach equilibrium.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

One faucet represents the natural addition of water to the tub, while the other represents a new flow. The tub has a drain in it, and it takes out 10% of the water in a given time interval (the value of k is 0.1 and the drain flow is just the amount in the tub times k). When you first open the model, the extra faucet is set to zero, and if you run the model you will see that it is in a steady state — the faucet and drain are equal, so the amount in the reservoir remains constant. What happens to the system if you increase the faucet flow using the upper knob to the right of the graph? If the faucet flow increases, then at first it will be greater than the drain and the amount in the tub will increase; but as faucet flow increases, so will the drain flow, and it will eventually become equal to the faucet flow and the system will return to steady state, but one with more water in the tub. Give it a try, and see what happens. At steady state, you can write a simple equation that says:

$$F = k \ast W$$

It turns out that the response time for this system is just 1/k. In this example model, k = 0.1 so the response time is 10 time units (the units depend on how the flows are given — liters per second or minute). This response time is not the length of time required for the system to get into a steady state — it is the time required to accomplish 63%, or the change to the new steady state. Why 63%? There is some math behind this choice, but in essence, it is just a convention that helps us avoid the problem of picking the time when steady state is achieved, which is difficult since it does so asymptotically. The figure below shows how this looks. In the graphs below, the blue line for the water tub is hidden beneath the red curve of the drain — these have different scales on the left hand side, but they are the same exact shape, so one plots over the other.

This graph shows the model results from a case where the initial amount of water in the tub was 10 liters and the faucet rate was 3 liters per time unit. The initial drain flow rate is just 10% of the starting amount of water -- 1 liter per time unit -- so the amount of water in the tub increases until it reaches 30 liters, at which point the drain flow rate is 3 liters per time unit, the same as the faucet rate. When the faucet (inflow) rate is equal to the drain (outflow) rate, the system is in a steady state. The figure also shows how the response time is defined for this kind of a system that evolves into a steady state.

Click for a text description of the first bathtub model graph.

This image is a screenshot from a "Bathtub Model" simulation, depicting the dynamics of water accumulation in a tub based on inflow and outflow rates. The interface includes a graph showing the model's output, a diagram of the system, and controls for running the simulation. The caption is not provided, so I will describe the image based on its visual content.

• Interface Title: Bathtub Model
• Components:
  • Graph (Center):
    • Title: Model Diagram
    • X-Axis: Time (unitless, range: 0 to 60)
    • Y-Axis: Volume of water in the tub (liters)
      • Range: 0 to 30 liters
    • Data Representation:
      • Red line labeled "WATER_TUB": Shows water volume starting at 10 liters, rising to a steady state of ~30 liters around time 45
      • Pink dashed line labeled "% change": Indicates the percentage of total change in water volume, reaching ~63% around time 15 (labeled "Response Time")
      • Horizontal pink line at 30 liters marks the steady-state volume
  • System Diagram (Top Right):
    • Elements:
      • Natural Faucet: A control knob set to 3.0 liters per time unit (range: 0 to 5)
      • Faucet Total: A node combining inflows, set to 3.0 liters per time unit
      • Drain: A control knob labeled "k" set to 0.10 (range: 0 to 1), representing the drain rate constant
    • Connections:
      • Arrows show water flow from Natural Faucet to Faucet Total to WATER_TUB
      • Feedback loop from WATER_TUB to Drain, indicating the drain rate depends on the tub's water volume
  • Extra Faucet (Top Left):
    • A pink square with a grid, labeled "extra faucet," set to 0.0 liters per time unit (range: 0 to 2)
  • Controls (Bottom):
    • Buttons labeled "Run" and "Stop" for controlling the simulation
    • Page indicator: "Page 1"
  • Additional Settings (Left):
    • WATER_TUB initial value: 10 liters (range: 0 to 30)
    • Time step: 0.25 (range: 0 to 2)
    • Response Time: 3 (not adjustable)

The image illustrates a dynamic system where water enters the tub at a constant rate (3 liters per time unit) and drains at a rate proportional to the water volume (k = 0.1). The graph shows the water volume increasing from 10 liters to a steady state of 30 liters, with the response time (time to reach ~63% of the total change) marked at approximately 15 time units. The simulation interface allows users to adjust parameters like faucet rates and observe the system's behavior.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

I changed the faucet here to 3, and the water in the tub rose until it reached a value of 30, where the drain value then became equal to the faucet value and the system reached a new steady state. As shown by the blue arrow above, this takes 10 time units to accomplish 63% of the change.

So, this is a system that has negative feedback (the drain) that drives it to a steady state, which means that regardless of the values of the faucet or the drain constant, k, the system will find a steady state.

Now, look at what happens if we turn on a new faucet — add a new flow to a system that is in a steady state. In the figure below, you see what happens if we turn the extra faucet on for a bit and then turn it off.

This graph shows the model results from a case where the initial amount of water in the tub was 10 liters and the faucet rate was 1 liter per time unit. The extra faucet is initially zero, but it jumps to 0.8 liters per time unit and then drops back down to zero. The total faucet rate shown in this graph is the sum of the two faucets. The water in the tub spikes a bit later than the faucet rate -- this time difference is called the lag time of the system.

Click for a text description of the second bathtub model graph.

The screen presents a "Bathtub Model" simulation interface, designed to illustrate water flow dynamics in a bathtub over time. The interface includes a title "Bathtub Model" with a "Model Diagram" button at the top. A central graph features a time axis (0 to 60 units) and a volume axis (0 to 18,000 units), displaying a pink "1: WATER_TUB" curve peaking at 16,000 units around 15 time units and an orange "2: drain" curve peaking slightly later, both declining to zero. A pink "extra faucet" diagram with a faucet symbol pointing to a square labeled "1" is on the left. On the right, dials for "faucet_total" (5.0, range 0-10) and "k" (0.10, range 0-1.00) are shown. At the bottom, "RUN" and "STOP" buttons and a "Page 1" label complete the layout.

• Bathtub Model Interface
  • Title: Bathtub Model
  • Button: Model Diagram
• Graph
  • X-axis: Time (0 to 60 units)
  • Y-axis: Volume (0 to 18,000 units)
  • Curves:
    • Pink curve: Labeled "1: WATER_TUB"
      • Peaks at ~16,000 units at 15 time units
      • Declines to zero
    • Orange curve: Labeled "2: drain"
      • Peaks slightly after pink curve
      • Declines to zero
• Left Diagram
  • Label: extra faucet
  • Content: Flowchart with faucet symbol pointing to a square labeled "1"
  • Color: Pink
• Right Dials
  • Faucet_total
    • Value: 5.0
    • Range: 0 to 10
  • k
    • Value: 0.10
    • Range: 0 to 1.00
• Bottom Controls
  • Buttons: RUN, STOP
  • Label: Page 1

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

The system gets thrown out of its steady state temporarily, but returns to the original steady state when the extra faucet is turned back off. Note that there is a lag time here — the water tub peaks about 5 time units after the faucet peaks (this is the sum of the two faucets). If we were to decrease k, then the response time would lengthen, and the lag time would also lengthen. Think of this spike in the extra faucet as being equivalent to a short-term addition of CO₂ into the atmosphere. But what if we turn the extra faucet on and then leave it on for some time at a steady rate? This might be equivalent to us adding CO₂ to the atmosphere and then keeping those emissions constant (sometimes referred to as the "stabilization" of emissions). We can simulate this scenario with our simple model, and the results are shown below.

This graph shows the model results from a case where the initial amount of water in the tub was 10 liters and the natural faucet rate was 1 liter per time unit. The extra faucet is initially zero, but it jumps to 2 liters per time unit and then remains at that level. The total faucet rate shown in this graph is the sum of the two faucets. The water in the tub increases slowly until it reaches 30 liters, at which point the drain flow is equal to the sum of the two faucet flows and the system is in a new steady state.

Click for a text description of the third bathtub model graph.

The screen displays a "Bathtub Model" simulation interface for visualizing water flow dynamics, updated with new parameters compared to the previous image. The title "Bathtub Model" is at the top with a "Model Diagram" button. A central graph plots time on the x-axis (0 to 60 units) and volume on the y-axis (0 to 40,000 units), showing a pink curve labeled "1: WATER_TUB" that rises steadily to around 30,000 units by 60 time units, and an orange curve labeled "2: drain" that increases more gradually to about 5,000 units. On the left, a pink "extra faucet" diagram shows a faucet symbol pointing to a square labeled "1." On the right, dials show "faucet_total" at 5.0 (range 0-10) and "k" at 0.50 (range 0-1.00). At the bottom, "RUN" and "STOP" buttons are present, with the interface labeled "Page 1."

• Bathtub Model Interface
  • Title: Bathtub Model
  • Button: Model Diagram
• Graph
  • X-axis: Time (0 to 60 units)
  • Y-axis: Volume (0 to 40,000 units)
  • Curves:
    • Pink curve: Labeled "1: WATER_TUB"
      • Rises steadily to ~30,000 units by 60 time units
    • Orange curve: Labeled "2: drain"
      • Increases gradually to ~5,000 units by 60 time units
• Left Diagram
  • Label: extra faucet
  • Content: Flowchart with faucet symbol pointing to a square labeled "1"
  • Color: Pink
• Right Dials
  • Faucet_total
    • Value: 5.0
    • Range: 0 to 10
  • k
    • Value: 0.50
    • Range: 0 to 1.00
• Bottom Controls
  • Buttons: RUN, STOP
  • Label: Page 1

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

What you see is that the system responds by increasing the water in the tub until a new steady state is reached. The length of time needed to achieve the new steady state is determined by the response time of the system, which again, is governed by the magnitude of the drain constant, k.

In the real carbon cycle, this response time is measured in tens of thousands of years. For example, remember that the residence time of the deep ocean is about 3,800 years. The response time of the whole carbon cycle must be much longer than this because CO₂ emissions are cycled through more than just the deep ocean. Unfortunately, you can't add up the residence time of the individual reservoirs to get the response time of the whole carbon cycle which is really what we want to know, the system is much more complex than this. The natural carbon cycle will find a new steady state (it will "stabilize") in response to our carbon emissions, but it will take many thousands of years to do so. In the meantime, the system will continue to change as it makes this adjustment.

Carbon moves through the terrestrial realm through five main processes, which are represented as blue arrows in the figure below:

Carbon Flow in Terrestrial Reservoirs

Click for a text description of the Carbon Flow in Terrestrial Reservoirs image.

The image illustrates the carbon cycle in a terrestrial ecosystem. It features a forest with trees and grass above a soil layer. Arrows indicate carbon movement:

• Photosynthesis: An arrow from the sun to the trees shows plants absorbing carbon dioxide during photosynthesis.
• Plant Respiration: An arrow from the trees upward indicates carbon dioxide release through plant respiration.
• Litterfall: An arrow from the trees to the ground shows carbon transfer via falling leaves and organic matter.
• Soil Respiration: An arrow from the soil upward represents carbon dioxide release from soil microbes breaking down organic matter.
• Run-off: An arrow from the soil outward illustrates carbon loss through water run-off.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

We will briefly explore these processes, beginning with photosynthesis.

This figure illustrates in a schematic way what goes on in a leaf through the processes of photosynthesis and respiration. Photosynthesis is the combination of carbon dioxide and water, with solar energy, to create carbohydrates, giving off oxygen to the atmosphere as a by-product. The carbohydrates are used during respiration, which is the reverse chemical reaction, to produce energy that the plant needs to grow. During respiration, carbon dioxide is released back into the atmosphere, but this is roughly half of what is taken up from the atmosphere in photosynthesis. Similarly, more oxygen is given off during photosynthesis than is used up in respiration.

Click for a text description of the photosynthesis and respiration image.

The image illustrates the carbon cycle in a terrestrial ecosystem. It features a forest with trees and grass above a soil layer. Arrows indicate carbon movement:

• Photosynthesis: An arrow from the sun to the trees shows plants absorbing carbon dioxide during photosynthesis.
• Plant Respiration: An arrow from the trees upward indicates carbon dioxide release through plant respiration.
• Litterfall: An arrow from the trees to the ground shows carbon transfer via falling leaves and organic matter.
• Soil Respiration: An arrow from the soil upward represents carbon dioxide release from soil microbes breaking down organic matter.
• Run-off: An arrow from the soil outward illustrates carbon loss through water run-off.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

Since its origin over 3 billion years ago, photosynthesis has been one of the most important processes on Earth, helping to make our planet habitable, in stark contrast to the other planets. The basic idea is that plants capture light energy and use it to split water molecules and then combine the products with carbon dioxide to make carbohydrates, which are used for fuel and construction of plants; oxygen which is crucial to making Earth habitable, is a by-product of this reaction, which is summarized as:

The Photosynthesis Reaction

Click for a text description of the Photosynthesis Reaction image.

The image depicts the chemical equation for photosynthesis. It consists of four labeled boxes in a horizontal sequence, representing the reactants and products:

• The first box, labeled "6CO₂" in gray, represents carbon dioxide.
• The second box, labeled "6H₂O" in light blue, represents water.
• The third box, labeled "C₆H₁₂O₆" in pink, represents sugar (glucose), with the word "Light" in yellow above it, indicating the requirement of light energy.
• The fourth box, labeled "6O₂" in light green, represents oxygen.

The equation shows that six molecules of carbon dioxide (6CO₂) and six molecules of water (6H₂O), in the presence of light, produce one molecule of glucose (C₆H₁₂O₆) and six molecules of oxygen (6O₂).

Credit: Davi Bice © Penn State University is licensed under CC BY-NC-SA 4.0

This process takes places in the chloroplasts located in the interiors of leaves. Here, chlorophyll absorbs solar energy in the red and blue parts of the spectrum. This energy is then used to split a water molecule into hydrogen and oxygen; in the process, the plants gain chemical energy that is used in a companion process that converts carbon dioxide into carbohydrates represented by C₆H₁₂O₆ in the above equation.

The rate of consumption of CO₂ by photosynthesis is mainly a function of water availability, temperature, the concentration of CO₂ in the atmosphere, and key nutrients such as nitrogen. The importance of water in plant growth is obvious from looking at the equation above. Temperature is an important factor in many life processes, and photosynthesis is no exception. As a general rule, the rates of most metabolic processes increase with temperature, but there is usually an upper limit where the high temperatures begin to destroy important enzymes, or otherwise inhibit life functions. The fact that photosynthesis depends on the concentration of CO₂ is not obvious, but it is very important. Plants take in their CO₂ through small openings about 10 microns in diameter called stomata, which the plant can control like valves, opening and closing to adjust the rate of transfer. The more they let in, the faster the rate of photosynthesis and the faster the growth — but if they open their stomata wide to let in a lot of CO₂, they can lose a lot of water, which is not so good. However, if there is a greater concentration of CO₂ in the atmosphere, then the plants will get a good dose of CO₂ by opening their stomata just a little bit, allowing them to conserve water. What this amounts to is increased efficiency of growth at higher levels of CO₂. We call this effect CO₂ fertilization, and it is an important way in which plants are our friends in helping to minimize the rise of CO₂ in the atmosphere. You can see this effect in the graph below, which shows the theoretical relationship between the CO₂ concentration in the atmosphere and the uptake of carbon from photosynthesis by land plants, summed up for the whole globe.

This figure shows how the rate of photosynthesis increases as the concentration of CO₂ in the atmosphere increases — this is known as the CO₂-fertilization effect. But notice that at high concentrations (right hand side of the graph), the red curve flattens out, meaning that the photosynthesis rate does not increase forever — it has a limit.

Click for a text description of the rate of photosynthesis graph.

The image is a graph depicting the relationship between atmospheric CO₂ concentration and global carbon uptake. The x-axis represents "Atmospheric CO2 Concentration (ppm)," ranging from 0 to 1000 ppm. The y-axis represents "Global Uptake of Carbon (GtC/yr)," ranging from 0 to 180 GtC/yr. A red curve shows that as CO₂ concentration increases, carbon uptake rises sharply at first, then gradually levels off, approaching around 160 GtC/yr at 1000 ppm.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

The following video explains photosynthesis in great detail:

Video: Photosynthesis (12:26)

If the video does not play above, click here to be directed to the Photosynthesis video on YouTube.

If we think of photosynthesis as the process of making fuel (carbohydrates), then respiration can be thought of as the process of burning that fuel — using it for maintenance and growth. This process can be described in the form of a reaction, just like photosynthesis. The chemical reaction is just the reverse of photosynthesis.

Through respiration, plants (and animals) release water, carbon dioxide, and they use up oxygen. Do the carbon flows involved in respiration and photosynthesis balance each other, as the equations seem to imply? The answer is no — otherwise, how could organisms grow?

Experiments on a variety of plants indicate that the ratio of photosynthesis to respiration is generally about 2 to 1. When plants are young, and growing rapidly, but with not much biomass to maintain, this ratio is even higher; in older, larger plants, this ratio is lower since more carbon needs to go towards maintenance.

Litter Fall

Dead plant material enters the soil in two ways -- it falls on the surface as litter, and it is contributed below the surface from roots. The relative importance of these two pathways into the soil varies according to the plants in an ecosystem, but it appears that the two are commonly about equal, which may seem a bit surprising since loss of organic carbon from root systems is a process that we generally don't see. The flow of carbon associated with litter fall is roughly the difference between the photosynthetic uptake of carbon and the return of carbon through plant respiration. If this were not the case, then the size of the global land biota reservoir would be growing or declining, and although some regions are growing, others are shrinking, and they nearly balance out.

Leaf litter in an Australian forest

Credit: Wikipedia CC BY-SA 3.0 (Creative Commons)

Respiration (sometimes called decay) also occurs within the soil, as microorganisms consume the dead plant material. In terms of a chemical formula, this process is the same as described above for plant respiration (the reverse of photosynthesis).

There is an unseen but fascinating universe of microbes living within the soil, and they are the key means by which nutrients such as carbon and nitrogen are cycled through the soil system. A great diversity of microorganisms live in the soil, and they are capable of consuming tremendous quantities of organic material. Much of the organic material added to the litter (the accumulated material at the surface of the soil) or within the root zone each year is almost completely consumed by microbes; thus there is a reservoir of carbon with a very fast turnover time — on the order of 1 to 3 years in many cases. The by-products of this microbial consumption are CO₂, H₂O, and a variety of other compounds, and are collectively known as humus (not the same as Hummus, the Mediterranean chickpea purée!). Humus is a much less palatable compound, as far as microbes are concerned, and is not decomposed very quickly. After it is produced at shallow levels within the soil, it generally moves downward and accumulates in regions of the soil with high clay content. Part of the reason it accumulates in the lower parts of the soil is that there tends to be less oxygen in that environment, and the lack of oxygen makes it even more difficult for microbes to work on this humus and decompose it further. But eventually, due to various processes (animals burrowing, people plowing, etc.) that stir the soil, this humus moves back up to where there is more oxygen, and then the microbes will eventually destroy the humus and release some more CO₂. This humus then constitutes another, longer-lived reservoir of carbon in the soil. Carbon 14 (¹⁴C) dates on some of this soil humus give ages of several hundred to a thousand years old. Taken together, the fast and slow decomposition processes, both driven by microbes, lead to an average carbon residence time of around 20 to 30 years for most soils. The data used in our global carbon cycle model lead to a residence time of about 26 years for the global soil carbon reservoir.

These microbes (considered in terms of their respiratory output) are very sensitive to the organic carbon content of the soil as well as the temperature and water content, respiring faster at higher carbon concentrations, higher temperatures and in moister conditions.

Permafrost - an unknown

In recent years, increasing attention has been directed at permafrost soil carbon, since the polar regions are warming much faster than the rest of the globe. Permafrost is soil that has been frozen for at least two years. As the permafrost melts, carbon that was added to these soils by processes like litter fall will become available for soil microbes to respire and release to the atmosphere. In fact, it is almost surely happening already, but given that much of the permafrost is still frozen, we have probably not seen the real manifestation of this source of carbon. Estimates are variable, but a figure like 1000 to 1500 Gt of carbon reflects the current thinking; this is a huge amount of carbon and has the potential to significantly alter the future of atmospheric CO₂ levels. As the permafrost begins to melt, some estimates are that it will contribute something in the range of 2-5 Gt C/yr, which is large compared to the human-related changes. Of course, some of this released carbon will be offset by new carbon sequestered into these formerly frozen soils, but initially, the system will not be in equilibrium and these regions can be expected to be a net source of CO₂ to our atmosphere.

Permafrost in Sweden (cracks are due to thawing)

Credit: Source: Wikipedia CC BY-SA 3.0 (Creative Commons)

Runoff

Although most of the carbon loss from the soil reservoir occurs through respiration, some carbon is transported away by water running off over the soil surface. This runoff is eventually transported to the oceans by rivers. The actual magnitude of this flow is a bit uncertain, although it does appear to be quite small. The most recent estimates place it at 0.6 Gt C/yr.

Here are the terrestrial flow processes once again, but this time with the estimated magnitudes of flows included. Most of these are very large flows, and they have a seasonality to them — photosynthesis is obviously big in the growing season, but it is small in the winter. If land masses and land plants were equally divided in the northern and southern hemispheres, this seasonality would cancel out, but in today's world, a large majority of land and plants are in the Northern Hemisphere, so around July, photosynthesis is very strong. In fact, this on and off aspect of photosynthesis is the primary reason for the seasonal changes in atmospheric CO₂ concentrations seen in the Mauna Loa record.

Carbon Flow in Terrestrial Reservoirs showing Fluxes

Click for a text description of the Carbon Flow image.

This image illustrates the terrestrial carbon cycle in a forest ecosystem. At the top left, there is a bright yellow sun with the word "estria" written on it, emitting three yellow, wavy arrows downward to represent sunlight. Below the sun, a row of green trees with brown trunks stands on a grassy surface, with a brown soil layer beneath. Blue arrows indicate the movement of carbon through various processes:

• A blue arrow curves from the sunlight down to the trees, representing carbon absorption through photosynthesis.
• Another blue arrow points upward from the trees into the air, labeled "49 GtC/yr," indicating carbon dioxide release through plant respiration.
• A blue arrow curves from the trees downward to the ground, labeled "litterfall," showing carbon transfer via fallen leaves and organic matter.
• A blue arrow rises from the soil into the air, labeled "49 GtC/yr," representing carbon dioxide release through soil respiration.
• A blue arrow extends horizontally from the soil to the right, indicating carbon loss through run-off.

The word "SOIL" is written in black within the brown soil layer. The background is solid black, emphasizing the elements of the carbon cycle.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

Processes of Carbon Flow in the Oceanic Realm

Far less obvious to us than the terrestrial processes we just discussed, the cycling of carbon in the oceans is tremendously important to the global carbon cycle. For example, the oceans absorb a large portion of the CO₂ emitted through anthropogenic activities. As with the terrestrial part of the global carbon cycle, we will explore here the various processes involved in transferring carbon in and out of the oceans.

Below, we see a general depiction of the flows involved in the oceanic realm, along with the flow magnitudes.

Pathways and fluxes of carbon exchange in the oceans

Click for a text description of the Ocean carbon flows image.

This image illustrates the oceanic carbon cycle, focusing on carbon flow in marine environments. At the top center, a bright yellow sun labeled "FLOW" emits three yellow, wavy arrows downward, representing sunlight. Below the sun, the ocean is depicted in layers, with labels and red arrows showing carbon movement:

• The top layer, labeled "SURFACE WATERS" in black, is a light blue section. A red arrow labeled "10 GtC/yr marine biota" points within this layer, indicating carbon uptake by marine life.
• A red arrow labeled "ere" points from the surface waters into the atmosphere above, showing carbon dioxide exchange.
• A red arrow labeled "92.2 GtC/yr downwelling" points downward from the surface waters to the deeper layers, representing carbon sinking.
• Below the surface waters is a darker blue layer labeled "DEEP WATERS" in black. A red arrow labeled "105.6 GtC/yr bio-pump" points downward within this layer, showing the biological pump moving carbon deeper.
• A red arrow labeled "90.6 GtC/yr upwelling" points upward from the deep waters back to the surface waters, indicating carbon rising through upwelling.
• At the bottom, a brown layer labeled "OCEAN SEDIMENT" in black represents the ocean floor. A red arrow labeled "0.6 GtC/yr sedimentation" points downward from the deep waters into the sediment, showing carbon deposition.
• On the right side, two red arrows extend from the deep waters and surface waters into the atmosphere, indicating carbon release back to the air.

The background is solid black, highlighting the ocean layers and carbon flow processes. All text is in black, and the arrows are red, providing clear contrast.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

Carbon dioxide can be dissolved in seawater, just as it can be dissolved in a can of soda. It can also be released from seawater, just as the CO₂ from soda can also be released. This transfer of gas back and forth between a liquid and the atmosphere is an extremely important process in the global carbon cycle, since the oceans are such an enormous reservoir with the potential to store and release significant quantities of CO₂.

The exchange of a gas like CO₂ between the air and seawater is governed by the differences in concentrations, as shown in the figure below, where the solid red line represents the concentration (increasing to the right) in the air and in the ocean. The dashed line indicates what the concentration might look like after some exchange of CO₂ occurs — lower concentration in the atmosphere, and higher in the oceans. But note that the change in concentration is less in the ocean than in the atmosphere, which is a result of some chemistry we will explore in just a bit.

Air-Sea CO₂ Exchange

Click here to see a text description of the Air-Sea CO2 Exchange image

This image illustrates the movement of gases between two layers of seawater. The image is divided into two horizontal sections, both depicting seawater but with different properties, against a solid black background.

• The top section has the text "SEAWATER (stagnant)" in black on the left and is a light blue layer. At the top of this section, a yellow triangular shape points downward, representing a source of gases.
• The bottom section has the text "SEAWATER (mixed)" in black on the left and is a slightly darker cyan layer.
• A red dashed line runs diagonally from the top right of the stagnant layer to the bottom left of the mixed layer, indicating the boundary between the two layers.
• A black arrow with the text "O₂" points downward from the yellow triangle, passing through the stagnant layer, across the red dashed line, and into the mixed layer, showing oxygen moving from the stagnant to the mixed seawater.
• Another black arrow with the text "pCO₂" points downward alongside the O₂ arrow, following the same path, indicating the partial pressure of carbon dioxide also moving from the stagnant to the mixed layer.

The image uses contrasting colors and clear labels to highlight the gas exchange between the two seawater layers. A text description at the bottom says: Here, the atmosphere has a higher concentration (pCO2) than the ocean, so it will flow into the ocean; this will decrease the concentration in the atmosphere and raise it in the ocean. If the concentration gradient goes the other way–higher in the water than the air–the flow of CO2 goes up into the air.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

As depicted in the figure above, the concentrations in the air and the sea are relatively constant (spatially, not temporally) since these two media undergo rapid and turbulent mixing that would tend to even out any systematic variations. The exception to this is a thin layer of water, just 20 to 40 microns thick (a micron is one thousandth of a millimeter), which, because of the surface tension of the water, is unable to mix well. This stagnant film is the barrier across which the diffusion has to occur. The rate of gas transfer is a function of the concentration difference and the thickness of the stagnant film of water (which thins when the winds are strong).

In general, this flow depends on the concentration of CO₂ in the atmosphere and the oceans, but it gets a little complicated because the concentration of CO₂ in seawater depends on a number of other factors. To understand this process, and to see why the atmosphere's concentration changes more than the ocean, we need to have some sense of what happens to CO₂ once it gets dissolved in seawater.

Carbonate Chemistry of Seawater

When CO₂ from the atmosphere comes into contact with seawater, it can become dissolved into the water where it undergoes chemical reactions to form a series of products, as described in the following:

1. CO₂ (dissolved gas) + H₂O <=> H₂CO₃ (carbonic acid)
2. H₂CO₃ (carbonic acid) <=> H+ + HCO₃^- (hydrogen ion + bicarbonate)
3. HCO₃- <=> H⁺ + CO₃^-2 (hydrogen ion + carbonate)

The amount of CO₂ as dissolved gas is what controls the concentration of CO₂ shown in the figure above. This concentration depends strongly on the temperature — it is low in cold water and it is high in warm water, which means that the colder parts of the ocean absorb CO₂ from the atmosphere and the warm parts of the ocean release CO₂ into the atmosphere.

All of these reactions mean that in seawater, you can find all of these different forms or species of inorganic carbon co-existing, dissolved in seawater. In reality, though, bicarbonate (HCO₃^-) is the dominant form of inorganic carbon; carbonate (CO₃^2-) and dissolved CO₂ are important, but secondary (see figure below).

Relationship between carbon species and pH

Click here to see a text description of the Relationship between carbon species and pH graph.

The image is a graph titled "Relationship between Carbon Species and pH." It shows the fraction of Dissolved Inorganic Carbon (DIC) on the y-axis (ranging from 0.0 to 1.0) versus the pH of water on the x-axis (ranging from 4 to 12). Three curves represent different carbon species:

• A red curve labeled "dissolved CO₂" peaks around pH 5 and decreases sharply as pH increases.
• A green curve labeled "HCO₃^-" rises from pH 4, peaks around pH 8, and then declines.
• A blue curve labeled "CO₃^2-" starts near zero at pH 4, increases steadily, and dominates at pH values above 10.

A vertical dashed line at pH 8.04, labeled "modern seawater," intersects the curves. Below the graph, text reads: "pH = 7.04. The relative proportions of the different carbon species depends on the alkalinity and the total DIC; these proportions in turn determine the pH. Salinity and temperature also exert some control on the proportions of carbon species. In the oceans today, most of the carbon is in the form of HCO₃⁻, with relatively small amounts of CO₃^2- and dissolved CO₂. (after Homen, 1992)". A text description in the image says: The relative proportions of the different carbon species depends on the alkalinity and the total DIC; these proportions in turn determine the pH. Salinity and temperature also exert some control on the proportions of carbon species. In the oceans today, most of the carbon is in the form of HCO3-, with relatively small amounts of CO3 (2-) and dissolved CO2.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

In the above equations (1-3), the double-headed arrows mean that the reactions can go in both directions, and generally do, until some balance of the different compounds is achieved -- a chemical equilibrium.

Notice that in the equations above, the hydrogen ion appears in a number of places — the concentration of H+ in seawater is what determines the pH of the water, or in other words, its acidity. Remember that low pH means more acidic conditions. It turns out that the ratio of bicarbonate (HCO₃) to carbonate (CO₃) is proportional to the pH; at lower pH conditions, more of the carbon is in the form of bicarbonate than carbonate, and the result is that the fraction of dissolved CO₂ gas also goes up, and this tends to cause CO₂ gas to move from the seawater into the atmosphere. As we will see in Module 7, higher acidity (lower pH) also has important implications for organisms that live in the sea.

Obviously, the ratio of these two forms of carbon is important, so we need to ask what controls this. Without getting into the chemistry too much, the ratio depends on two main things, and it depends on these things because they determine the electrical charge balance in the water — the charges from all the positive and negative ions dissolved in the water have to add up to zero, and you can see that if you have more carbonate (minus 2 charge) than bicarbonate (minus 1 charge), you have more total negative charge. So, the 2 important factors here are:

1. the total amount of positive charge in the oceans that has to be canceled by the carbonate and bicarbonate — called the alkalinity;
2. the total amount of dissolved inorganic carbon in the oceans (DIC for short).

If the alkalinity is high, then more of the DIC has to take the form of carbonate (minus 2 charge), and a result is that the pH is higher, meaning less acidic. If the total DIC is large, then to get the charges to balance, more of the DIC has to be in the form of bicarbonate (minus 1 charge), which leads to lower pH and more acidic conditions.

Let’s return now to the figure that showed the exchange of CO₂ between the atmosphere and ocean and the question about why the ocean’s CO₂ concentration changed less than the atmosphere. The reason for this is the carbon chemistry reactions that shift some of the CO₂ dissolved gas into the forms of bicarbonate and carbonate — this reduces the amount of carbon in the form of dissolved CO₂ gas, so the concentration of dissolved CO₂ does not increase as much as it would if these reactions did not take place.

As you can see, the chemistry of carbon in seawater is relatively complex, but it turns out to be extremely important in governing the way the global carbon cycle operates and explains why the oceans can swallow up so much atmospheric CO₂ without having their own CO₂ concentrations rise very much.

Summary of Carbonate Chemistry

Let's see if we can summarize this carbonate chemistry — it is important to have a good grasp of this if we are to understand how the global carbon cycle works.

• Carbon can exist in three main inorganic forms in seawater — CO₂, HCO₃^-, and CO₃^2-, and there is a rapidly-achieved equilibrium between these species.
• The ratio of HCO₃^- to CO₃^2- along with the water temperature determines the CO2 concentration of seawater and also the pH.
• The temperature of the water also controls how much CO₂ occurs in the form of dissolved gas, thus affecting the concentration of CO₂ gas in seawater.
• The alkalinity of seawater represents the positively-charged ions that need to be countered by negatively-charged carbonate and bicarbonate ions.
• The concentration of the total dissolved inorganic carbon (DIC), along with the alkalinity, determines the ratio of HCO₃^- to CO₃^2-, and thus the CO₂ concentration of seawater. If we increase DIC without changing the alkalinity, then more carbon must be in the form of HCO₃^-, which increases both pH and the CO₂ concentration of seawater.
• The CO₂ concentration of seawater, relative to the atmospheric CO₂, determines whether the oceans absorb or release CO₂. Currently, the cold parts of the oceans absorb atmospheric CO₂ and the warm regions of the oceans add CO₂ to the atmosphere.
• The ability of carbon to switch back and forth between these three forms means that only a portion of the CO₂ absorbed by the oceans will remain as CO₂.

In the real world, there are important variations in the gas transfer between the ocean and atmosphere. This can be seen in the figure below, which represents a kind of snapshot of this transfer across the globe. The units here are grams of C per m² per year, and each box is about 1e6 m². The red, orange, and yellow colors represent places where the oceans are giving up CO₂ to the atmosphere; the blue and purple areas are places where the oceans are sucking up atmospheric CO₂. Summing these up, we find that the oceans are taking up around 92-93 Gt C/yr and they are releasing about 90 Gt C/yr — for a net flow of 2-3 Gt C/yr into the oceans — this represents something like 25-30% of the carbon we are adding to the atmosphere by burning fossil fuels. This exchange is variable in space and time, but a few general features can be pointed out. In general, the colder parts of the oceans absorb CO₂ and the warmer parts release CO₂ into the atmosphere. This makes sense because CO₂ is more soluble in colder water.

Flux of CO₂ across the Air-Sea Interface in 2000

Click for a text description of the Flux of CO2 across the Air-Sea Interface in 2000 map.

The image is a world map titled "Mean Annual Air-Sea Flux for 2000 [REV Jun 09] (NCEP II wind, 3,040K, T=-26)." It shows the net flux of carbon (in grams C m² yr^-1) between the atmosphere and the ocean for the year 2000. The map uses a color gradient to represent flux values, with a scale at the bottom ranging from -108 (deep blue) to +108 (deep red), passing through green (around 0).

• The map is overlaid with a grid of latitude and longitude lines, with latitude marked from 80°N to 80°S and longitude from 180°W to 180°E.
• Oceans are colored based on carbon flux:
  • Areas in deep blue (e.g., parts of the North Atlantic, Southern Ocean) indicate strong carbon uptake by the ocean (negative flux, up to -108 g C m² yr^-1).
  • Areas in red (e.g., equatorial Pacific, parts of the Indian Ocean) indicate carbon release to the atmosphere (positive flux, up to +108 g C m² yr^-1).
  • Green areas (e.g., parts of the mid-latitudes) indicate near-neutral flux (close to 0 g C m² yr^-1).
• Landmasses, such as North and South America, Africa, and Australia, are shown in gray.
• A timestamp in the bottom left corner reads "2000-Jan 2 14:37:51."

The map visually highlights regions where the ocean acts as a carbon sink or source, with significant uptake in high-latitude regions and outgassing in equatorial zones.

Credit: Columbia University Lamont-Doherty Earth Observatory

The surface waters of the world’s oceans are home to a great number of organisms that include photosynthesizing phytoplankton at the base of the food chain. These plants (and cyanobacteria) utilize CO₂ gas dissolved in seawater and turn it into organic matter, and just like land plants, phytoplankton also respires, returning CO₂ to the surface waters.

At the same time, many planktonic organisms extract dissolved carbonate ions from seawater and turn them into CaCO₃ (calcium carbonate) shells. When these planktonic organisms die, their soft parts are mainly consumed and decomposed very quickly, before they can settle out into the deeper waters of the oceans. This decomposition thus returns carbon, in the form of CO₂, to seawater.

Shells produced by coccolithophores, the dominant group of calcifying plankton

Credit: Tim Bralower © Penn State University is licensed under CC BY-NC-SA 4.0

However, some of the organic remains and the inorganic calcium carbonate shells will sink down into the deep oceans, thus transferring carbon from the shallow surface waters into the huge reservoir of the deep oceans. This transfer is often referred to as the biologic pump, and it causes the concentration of CO₂ gas, and also DIC in the surface waters to be less than that of the deeper waters. This can be seen in the figure below, which shows the vertical distribution of DIC (and also alkalinity) in a profile view for some of the major regions of the world's oceans.

Graph of Profiles of Alkalinity and DIC in the World's Oceans

Click here to see a text description.

The image, titled "Profiles of Alkalinity and DIC (ΣCO2) in the World’s Oceans," presents two graphs illustrating the vertical distribution of alkalinity and dissolved inorganic carbon (DIC or ΣCO2) across different ocean regions, sourced from Holmes (1992). The left graph plots alkalinity (μEq/kg) from 2250 to 2450 against depth (0 to 5 km), while the right graph plots ΣCO2 (μmol/kg) from 2000 to 2400 against the same depth range. Five ocean regions—North Atlantic (N.Atl), South Atlantic (S.Atl), North Pacific (N.Pac), South Pacific (S.Pac), and Antarctic—are represented by distinct colored lines (red, orange, blue, green, and purple, respectively). The accompanying caption explains that surface waters are depleted in alkalinity and DIC due to the biological pump, which exports carbon to the deep ocean. In deeper waters, the dissolution of marine biota releases Ca²⁺ ions, increasing alkalinity, while organic carbon decomposition elevates DIC levels, ultimately depleting surface ocean alkalinity.

Outlined Readout:

• Title: Profiles of Alkalinity and DIC (ΣCO2) in the World’s Oceans
  • Source: Holmes (1992)
• Graph 1: Alkalinity
  • X-axis: Alkalinity (μEq/kg), 2250 to 2450
  • Y-axis: Depth (km), 0 to 5
  • Regions:
    • North Atlantic (N.Atl): Red line
    • South Atlantic (S.Atl): Orange line
    • North Pacific (N.Pac): Blue line
    • South Pacific (S.Pac): Green line
    • Antarctic (Antarctica): Purple line
• Graph 2: ΣCO2 (DIC)
  • X-axis: ΣCO2 (μmol/kg), 2000 to 2400
  • Y-axis: Depth (km), 0 to 5
  • Regions:
    • North Atlantic (N.Atl): Red line
    • South Atlantic (S.Atl): Orange line
    • North Pacific (N.Pac): Blue line
    • South Pacific (S.Pac): Green line
    • Antarctic (Antarctica): Purple line
• Caption:
  • Purpose: Represents typical inorganic carbon profiles
  • Surface Waters:
    • Depleted in alkalinity and DIC
    • Cause: Biological pump exports carbon to deep ocean
  • Deep Waters:
    • Marine biota dissolve, releasing Ca²⁺ ions
    • Effect: Increases alkalinity
    • Organic carbon decomposition adds to DIC
  • Overall Effect: Depletes surface ocean alkalinity

Credit: David Bice ;© Penn State University is licensed under CC BY-NC-SA 4.0

Why is the alkalinity reduced in the surface waters? For the same reason that DIC is depleted. Planktonic organisms make shells of CaCO₃, and when these sink to the seafloor, they carry Ca²⁺ ions with them, thus reducing the alkalinity. Much of this CaCO₃ is later dissolved when it reaches deeper parts of the oceans, which explains the higher alkalinity values in the deep waters, as seen in the figure above. By controlling the concentration of CO₂ gas dissolved in the surface waters, the planktonic organisms exert a strong influence on the concentration of CO₂ in the atmosphere. For instance, if the biologic pump were turned off, atmospheric CO₂ would rise to about 500 ppm (relative to the current 408 ppm); if the pump were operating at maximum strength (i.e., complete utilization of nutrients), atmospheric CO₂ would drop to a low of 140 ppm. Clearly, this biologic pump is an important process.

Alkalinity is very important, because when it is reduced, species that make shells out of CaCO₃ will dissolve. Today, the most sensitive species are those that make shells out of a form of CaCO₃ called aragonite which is more susceptible to dissolution than calcite, the other form of CaCO₃. Coral is an aragonite group that is very susceptible as we will see in Module 7.

What controls the strength of this biologic pump? The photosynthesizing plankton require nutrients in addition to CO₂ in order to thrive; specifically, they require nitrogen and phosphorus. Most of these plants need P, N, and C in a ratio of 1:16:125, and since at present the ratio of P to N in ocean water is about 1:16, both P and N limit the growth of these phytoplankton. Photosynthetic activity of plankton can be mapped out by satellites tuned to record differences in water color due to the presence of chlorophyll. This distribution is shown in the figure below.

The Distribution of Photosynthesis in the Oceans. Green, yellow and red shows higher levels, and dark blue shows lower levels

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

If the nutrients in seawater were being utilized to the maximum extent possible, there would be practically no P and N dissolved in seawater. But in fact, as shown by the figure below, the concentration of P tells us that the biologic pump is not operating at maximum efficiency. In the map below, the purple regions represent regions with no phosphate in the surface water of the oceans, meaning that there is simply a lack of nutrients, or that all the nutrients are utilized. In particular, it is the cold, polar regions that are not utilizing all of the available nutrients. This may be due in part to the temperature, but it may also be related to a paucity of iron, a minor nutrient that is apparently lacking in the colder regions, especially in the Southern Ocean ringing Antarctica.

Dissolved phosphate concentration in the oceans

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

In addition to nutrients, the strength of this biological pump is sensitive to the pH of the ocean water. The organisms in the oceans are adapted to a pH of around 8.3 or 8.4, but as we discussed earlier, if the oceans take up too much CO₂ too quickly, the pH will decrease and move it outside the optimum range for the organisms in the oceans. Thus, lower pH levels (i.e., higher acidity) will probably mean a reduction in the strength of the biological pump, which will, in turn, limit the oceans ability to absorb more carbon.

Downwelling

As mentioned above, downwelling (sinking of dense water) transfers cold and/or salty surface waters into the deep interior of the oceans, and as a result, carbon is transferred as well. The magnitude of the flow is thus a function of the volume of water flowing and the average concentration of carbon in the cold surface waters, which is itself a function of the total amount of carbon stored in this reservoir, assuming that the size of the reservoir is not changing appreciably over the few hundred years that this model is intended to be used for.

Downwelling occurs primarily near the poles, where surface waters are strongly cooled by contact with the air. This cooling leads to a density increase. The formation of ice from seawater at the margins of Antarctica increases the salinity of the seawater there, adding to the density of the water. This dense water then sinks and flows through the deep oceans, effectively mixing them on a timescale of about 1000 years or so (the Atlantic Ocean mixes somewhat faster, which helps explain the smaller ΣCO₂ and alkalinity gradients seen in the figure above).

Upwelling

Upwelling is just the opposite of downwelling, and as deep waters rise to the surface, they bring with them carbon, nutrients, and alkalinity. The total transfer of carbon is thus a function of the volume of water involved in this flow and the amount of carbon stored in the deep ocean reservoir. Upwelling occurs in areas of the oceans where winds and surface currents diverge, moving the surface waters away from a region; in response, deep waters rise up to fill the "void". Upwelling occurs along the equator, where there is a strong divergence, and also along the margins of some continents, such as the west coast of South America. This upwelling water also brings with it nutrients such as nitrogen and phosphorus, making these waters highly productive.

Note that the amount of carbon transferred by this flow is greater than the downwelling flow. This is not because the volume of flow is different in these two processes, but rather because the concentration of carbon in the deep waters of the ocean is greater than that in the shallow surface waters, due in part to the operation of the biologic pump mentioned above.

Sedimentation

Some of the carbon, both organic and inorganic (i.e., calcium carbonate shells) produced by marine biota and transferred to the deep oceans settles out onto the sea floor and accumulates there, eventually forming sedimentary rocks. The magnitude of this flow is small — about 0.6 Gt C/yr — relative to the total amount transferred by sinking from the surface waters — 10 Gt C/yr. The reason for this difference is primarily because the deep waters of the oceans dissolve calcium carbonate shell materials; below about 4 km, the water is so corrosive that virtually no calcium carbonate material can accumulate on the seafloor. In addition, some of the organic carbon is consumed by organisms living in the deep waters and within the sedimentary material lining the sea floor. This consumption results in the release of CO₂ into the bottom waters and thus decreases the amount of carbon that is removed from the ocean through this process. It is worth noting that the process of organic carbon consumption on the seafloor is another microbial process and is very similar to the soil respiration flow described earlier. Since the microbes living on the seafloor require oxygen to efficiently accomplish this task, the supply of oxygen to the seafloor by deep currents is an important part of this process.

White Cliffs of Dover, sedimentary rocks about 100 million years old formed entirely of CaCO3

Credit: Wikipedia CC BY-SA 3.0 (Creative Commons)

Volcanism and Metamorphism

When sedimentary rocks deposited on oceanic crust are subducted at a trench where two tectonic plates of Earth’s surface converge, they may melt or undergo metamorphism; in either case, the carbon stored in calcium carbonate -- limestone -- is liberated in the form of CO₂, which ultimately is released at the surface. The CO₂ may come out when a volcano erupts, or it may slowly diffuse out from the interior via hot springs, but in both cases, it represents a transfer of carbon from the reservoir of sedimentary rocks to the atmosphere. The magnitude of this flow is quite small and is adjusted here to a value of 0.6 Gt C/yr in order to create a model in steady state. This flow is defined as a constant in the model, although in reality, it will vary according to the timing of large volcanic eruptions. An extremely large volcanic eruption may emit carbon at a rate of around 0.2 Gt C/yr for a year or two, creating a minor fluctuation.

Processes of Carbon Flow in the Human Realm

Humans have exerted an enormous influence on the global carbon cycle, largely through deforestation and fossil fuel burning. In this section, we explore how these processes have led to changes in the dynamics of carbon in the atmosphere.

Fossil Fuel Burning

Another pathway for carbon to move from the sedimentary rock reservoir to the atmosphere is through the burning of fossil fuels by humans. Fossil fuels include petroleum, natural gas, and coal, all of which are produced by slow transformation of organic carbon deposited in sedimentary rocks — essentially the fossilized remains of marine and land plants. In general, this transformation takes many millions of years; most of the oil and gas we now extract from sedimentary rocks is on the order of 70-100 million years old. New fossil fuels take a very long time to form, and we are using them up much, much faster than they are being formed, meaning that if we keep using fossil fuels at the rate we are today, we will run out! This run out date depends on new discoveries and our ability to extract fuels more efficiently by processes like fracking, but we will be close to running out late this century.

These fossil fuels are primarily composed of carbon and hydrogen. For instance, methane, the main component of natural gas, has a chemical formula of CH₄; petroleum is a more complex compound, but it, too, involves carbon and hydrogen (along with nitrogen, sulfur, and other impurities). The combustion of fossil fuels involves the use of oxygen and the release of carbon dioxide and water, as represented by the following description of burning natural gas:

$$C H_4+ 2 O_2=> C O_2+ 2 H_{2}O$$

Beginning with the onset of the industrial revolution at the end of the last century, humans have been burning increasing quantities of fossil fuels as our primary energy source.

Pollution (including greenhouse gas emission from a factory in China)

Credit: Wikipedia CC BY-SA 3.0 (Creative Commons)

Smog hanging over Los Angeles.

Credit: Wikipedia CC BY-SA 3.0 (Creative Commons)

As a consequence, the amount of CO₂ emitted from this burning has undergone an exponential rise that follows the exponential rise in the human population. The magnitude of this flow is currently about 9 Gt C/yr. This number also includes the CO₂ generated in the production of cement, where limestone is burned, liberating CO₂.

Increase in the emission of carbon from fossil fuels since 1800

Click for a text description of the Global carbon emissions graph.

The image is a line graph illustrating the growth trends of five distinct data series over an unspecified time period. Each series is represented by a different colored line: blue, green, red, cyan, and gray. The x-axis represents time, though specific dates or intervals are not labeled, while the y-axis represents the data values, increasing from bottom to top, without specific numerical labels. All series show a general upward trend, with the blue, green, and red lines displaying the most significant growth, marked by sharp increases and noticeable volatility. In contrast, the cyan and gray lines exhibit more gradual growth with minimal fluctuations. A legend in the top left corner identifies the colors for each series, though the series themselves are not named. The graph features a black background with white grid lines for reference.

Outlined Readout:

• Graph: Line graph of five data series
• X-axis: Time (unspecified dates or intervals)
• Y-axis: Data values (increasing, no specific numerical labels)
• Data Series:
  • Blue line: Significant growth, sharp increases, volatile
  • Green line: Significant growth, sharp increases, volatile
  • Red line: Significant growth, sharp increases, volatile
  • Cyan line: Gradual growth, minimal fluctuations
  • Gray line: Gradual growth, minimal fluctuations
• Legend: Located in top left corner, identifies colors for each series (no specific names provided)
• Trends:
  • General upward trend for all series
  • Blue, green, red lines: Most significant growth with volatility
  • Cyan, gray lines: More modest growth, less fluctuation
• Design:
  • Background: Black
  • Grid lines: White, for reference

Credit: Wikipedia CC BY-SA 3.0 (Creative Commons)

As you can see in the graph above, this flow has changed considerably over time, as human population has increased and as our economies have become more industrialized with a big thirst for the energy provided from the combustion of fossil fuels. The model we will work within the lab activity for this module includes this history, beginning in 1880 and going up to 2010; beyond 2010 is the realm of future projections, which can be altered to explore the consequences of choices we might make or not make in the future. Part of the new energy economy that is key to our future is the use of so-called renewable energy sources, including wind, solar and geothermal energy, that emit little or no carbon. There are some interesting map view representations of this history of fossil fuel carbon emissions in the video below:

Video: Annual Fossil-Fuel CO2 Emissions (2:03) (No Narration)

Per capita emission of greenhouse gas by country in 2000

Credit: Source: Wikipedia / CC BY-SA 3.0 (Creative Commons)

Land-Use Changes - Forest Burning and Soil Disruption

The other form of human alteration of the global carbon cycle is through forest cutting and burning and the disruption of soils associated with agriculture. When deforestation occurs, most of the plant matter is either left to decompose on the ground, or it is burned, the latter being the more common occurrence. This process reduces the size (the mass) of the land biota reservoir, and the burning adds carbon to the atmosphere. Land-use changes other than deforestation can also add carbon to the atmosphere. Agriculture, for instance, involves tilling the soil, which leads to very rapid decomposition and oxidation of soil organic matter. This means that in terms of a system, we are talking about two separate flows here — one draining the land biota reservoir, the other draining the soil reservoir; both flows transfer carbon to the atmosphere. Current estimates place the total addition to the atmosphere from forest burning and soil disruption at around 2-3 Gt C/yr; estimates divide this into 70% to 50% forest burning, with soil disruption making up the remainder. Deforestation is a particular problem in the Amazon, as we will see in Module 9.

Deforestation

The actual history of this alteration to the natural carbon cycle is not well-constrained — not nearly as well known as the fossil fuel burning history — but we include a reasonable history that reflects patterns of land settlement and forest clearing.

The goals of this lab are to:

1. Simulate the fate of CO₂ added to the atmosphere;
2. Interpret what happens when we increase the rate of fossil fuel burning;
3. Evaluate how the rate of carbon addition affects the maximum temperature and minimum pH attained under fossil fuel burning;
4. Simulate the impact of the different emission scenarios on global temperature;
5. Evaluate how permafrost melting amplifies warming under the different emission scenarios.

Please make sure that you read the Introduction to the lab. Skipping it will result in a lot of confusion and a lower score on the assignment.

Introduction

In the lab activity for this module, we will be working with a STELLA model of the global carbon cycle that is attached to the climate model we used in Module 3. This model incorporates the processes of carbon transfer in the terrestrial and oceanic realms discussed in the previous sections; it also includes the history (from 1880 to 2010) of human impacts on the carbon cycle in the form of emissions from burning fossil fuels, burning forests, and disrupting the soil. The model is initially set up to represent the carbon cycle in a steady state just before the industrial revolution, at which point human alterations to the carbon cycle began in earnest. We will use this model to explore different carbon emissions scenarios for the future, to see how the climate and carbon cycle might respond.

Here is what the model looks like, in a very simple, stripped-down form:

Pre-Industrial Carbon Cycle

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

In this figure, you can see the initial amounts of carbon in each reservoir in GT and the annual flows of carbon between reservoirs in GT C/yr. A couple of things should be pointed out about this model. In some cases, flows have been combined into things called bi-flows that have arrows on each end; this means that carbon can flow either way. There is a bi-flow connecting the atmosphere and surface ocean that represents the two-way transfer of ocean-atmosphere exchange. There is another bi-flow connecting the surface and deep ocean that represents upwelling and downwelling combined into one.

The real model is quite a bit more complex-looking, as can be seen below:

Land use changes represent the combined effects of soil distribution, deforestation, etc., for the last 100 years, extrapolated into the future 200 years at the year 2000 level.

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

The complications here arise from the fact that most of the flows are expressed by rather complicated equations. Most of the flows have small red arrows attached to them; these show you what things affect the flow rate. Think of the circle in the middle of the flow pipe as being a valve on a water pipe that controls how much water moves through the pipe. In many cases, the red arrows come from the reservoir that is being drained by the flow; this means that the outflow is dependent on how much is in the reservoir — when you have more in a reservoir, the outflow is often greater, and in essence, the outflow is a percentage of how much is in the reservoir.

Note that the atmosphere reservoir is connected to a converter called pCO₂ atm — this is the concentration of CO₂ in the atmosphere and the units are in parts per million or ppm, the same units that CO₂ concentrations are typically given in. In this model, the initial amount of carbon in the atmosphere gives a pCO₂ value of 280 ppm (and by now, it is just over 400 ppm). The pCO₂ atm converter is in turn connected to the same climate model we used in Module 3, where it determines the strength of the greenhouse effect. The climate model calculates the temperature at each moment in time and then passes that information back to the carbon cycle model in the form of a converter called global temp change, which is the change in global temperature relative to the starting temperature — this is like a temperature anomaly.

The global temp change converter is then attached to a couple of other converters that attach to the photosynthesis flow and the soil respiration flow. Both of these flows are sensitive to temperature and the temperature combines with something called a temperature sensitivity. You can see something above called the Tsens sr — this is the temperature sensitivity for soil respiration. Both photosynthesis and soil respiration are sensitive to the temperature; they increase with temperature. Global temp change is also connected to the surface temperature of the oceans (T surf) via a "ghosted" version of the converter — a dashed line version that helps eliminate so many long connecting arrows running all over the diagram.

The photosynthesis flow has lots of converters associated with it since it is dependent on numerous factors, but the main things are temperature and the atmospheric CO₂ concentration.

The model also includes a whole set of connected converters in the upper right that do all of the calculations related to the carbon chemistry in the oceans; this is where the pH or acidity of the surface ocean is calculated.

At the very top right of the model, there is a converter called Observed Atm CO₂ that contains the observed history of atmospheric CO₂ concentration since 1880. This is in the model so that we can test how good the model is. If our carbon cycle model is good, then it should calculate a pCO₂ that closely matches the observed record.

The model includes the history of carbon emissions from burning fossils fuels shown in the previous section; it also includes a history of land use changes that impact the carbon cycle. These land use changes are broken up into tree burning (that accompanies deforestation) and soil disruption (related to farming); they are then additions to the flow of carbon from the land biota and soil back into the atmosphere. These human alterations to the carbon cycle are shown in the model by clicking on the pink graph icons labeled ffb and land use changes on the right side of the model, as shown below.

As before, the model we will work runs on a browser; here is a link to the model. When you follow the link, you should see a screen like this (note the model has changed but the functions are similar):

Model for Module 5 Lab

Credit: David Bice © Penn State University is licensed under CC BY-NC-SA 4.0

You can think of this as the control panel for the model, where you can run it, stop it, make changes, and look at the results in the form of different graphs. You can access the different graphs by clicking on the triangular tab at the lower left of the graph window. The controls here consist of a set of switches you can turn on or off — these will determine which of 3 different emissions scenarios are applied to the model. The three buttons on the right-hand side show what the 3 emissions scenarios look like. The video below explains how to work the switches. There is also a switch that can be used to either include or exclude the carbon emissions to the atmosphere from human-related land-use changes such as deforestation and soil disruption, but we will not mess around with this switch — just leave it in the "on" or up position as it is in the diagram above.

This initial model is set up to run from 1880 to 2100. Later, we will work with a model that runs farther into the future.

This is the interface to the carbon cycle model that we will be working with in this module. If we click on this button here, we would see a view of what the carbon cycle looks like that's implemented in this model. It's a complicated thing, but it's a very realistic carbon cycle model that's going to allow us to explore, in a pretty realistic way, what will happen to atmospheric CO₂ and to other aspects of the carbon cycle as we change the burning of fossil fuels and the human effect on this particular system. This carbon cycle model here is attached to a little climate model, that you can see the edge of it over here, that's the same one that we worked with in Module 3. And so, the carbon cycle model will control the atmospheric CO₂ concentration here, and then that will feed into the climate model here and control the greenhouse effect. And then the temperature, determined by the climate model, will then come back and affect different parts of the carbon cycle model here.

Credit: Timothy Bralower

So, let me show you how to work this model. If you run it just the way you first open it, you'll see it calculates the global temperature change over time. So, zero is the temperature at 1880, but this is temperature relative to that time. And then, the temperature rises as we go to the year 2000 and 2100. Now, these switches down in here control different histories or scenarios of fossil fuel burnings. The business-as-usual emission scenario is what we ran first. So, when this switch is on, it uses that business-as-usual scenario, and it looks like this, where the carbon emissions just go up and up and up with no change all the way to 2100.

If we click this off, and leave this switch off, it's going to implement a scenario in which the fossil fuel burning just levels off. So, after the year 2010, it just levels off like this. So, we hold emissions constant, and we can see what happens to the temperature in the rest of the system in that case. If we turn this switch on, like that, it will implement this scenario here. It's a very unrealistic one, where after 2010, we drop quickly down to zero fossil fuel burning for the rest of time. So, this is a really dramatic case, just to see how the system will respond to that change.

Now, you can graph different parts of the system. Here, we can look at the atmospheric CO₂ concentration. Here, we can look at the ocean pH. Here, we can look at where the carbon goes, what fraction of it stays in the atmosphere, what fraction goes into the biosphere, and what fraction goes into the oceans. This shows us the details of the fossil fuel burning history that we applied in that case. This plots both the atmospheric CO₂ concentration and the fossil fuel burning history together, so you can see how they compare. This shows the values of carbon and all the different reservoirs in the carbon cycle model. This is the cumulative amount of carbon that we've released over time, so it just gets bigger and bigger and bigger. This is not the annual amount, but the cumulative.

Now, this is an interesting one to look at because it goes from 1880 to 2010, so the period of time that we know something about. And it plots in red the actual observed atmospheric CO₂ level and in blue the CO₂ level that the model calculates. And so, you can see that those two are very close throughout this whole time. And so, that means that our carbon cycle model, coupled with the climate model, is giving us a result that matches a historical record. And so, we say we have a good model, and we can essentially trust what it tells us in terms of projections off into the future.

Lab 3: Climate Modeling

Download this lab workbook as a Word document: Practice Lab Module 5. (Please download required files below.)

Please use Chrome for this lab.

Answer the questions in the workbook. Then, when you are ready, complete the Module 5 Lab 5 Practice Submission. Make sure you have the model ready to run, as we will be asking additional questions as indicated below. Once you are ready you can take the Module 5 Lab 5 GradedSubmission in a timed environment.

STEP 1. Please Note: The STELLA model in shown in the video below, which explains the controls.

Video: Carbon Cycle Intro (4:15)

To begin with, we will use this model of the carbon cycle (which is coupled to the same climate model we used in Module 3) to learn a few basic things about how the model responds to different scenarios of carbon emissions from fossil fuel burning (FFB). Note, the A2 scenario is also known as “Business-as-Usual” (BAU) in which we make no efforts to limit carbon emissions. Be sure to watch the video that introduces this model and explains how to use the switches to change the FFB scenarios. To get the right answers, it is imperative that you have switches in the correct positions. If in doubt, try reloading the model (reloading the web page) and restoring all devices.

Before running the model, try to guess what will happen to global temperature change under the two reduced emissions scenarios — in one of them (the leveling off scenario), the emissions are held constant after 2010, and in the other (the halt scenario), they drop to zero after 2010.

1. Which scenario has the largest impact on temperature in 2100?
   1. BAU
   2. FFB Hal
   3. FFB leveling off
2. Will the global temperature keep rising through 2100 in the BAU scenario?
   1. Yes
   2. No

Now run all three emissions scenarios (keep the land use switch in the on position) in the following sequence:
A2 (BAU), then FFB Leveling Off, followed by FFB Halt.

3. Focus on A2 (BAU) — what happens to the global temperature change when there is no attempt to lower emissions?
   1. Temperature keeps rising till 2200
   2. Temperature rises then starts falling at about 2170
   3. Temperature levels off after 100 years
4. Now turn to the FFB Level Off scenario — what happens to the global temperature change when the FFB emissions leveling begins about 2030?
   1. The rate of temperature rise slows very slightly beginning at 2040
   2. The rate of temperature rise keeps increasing through 2100 before decreasing
   3. Temperature levels off at 2030

STEP 2. Please Note: The model in the videos below may look slightly different than the model (linked below) that you will use to complete Step 2. Both models, however, function the same.

Now we turn to a version of the model that has three emissions scenarios from the IPCC.

Video: Carbon Cycle (4:39)

Again, the A2 scenario is also known as “Business-as-Usual” in which we make no efforts to limit carbon emissions; the A1B scenario is one of modest reductions in emissions; the B1 scenario is one of more drastic reductions. Run all three emission scenarios (A2, A1B, and B1) with the permafrost switch off and the land use switch on, then answer the following questions.

Temperature (Page 1 of the graph pad)

5. Which scenario produces the smallest warming in 2100?
6. Which scenario produces the largest warming in 2100?
7. What is the temperature difference between the A2 and A1B scenarios? (answer to 2.d.p)

Atmospheric CO (pCO2 atm on Page 2 of the graph pad)

8. Which emission scenario has the smallest impact on drawing down CO2?
9. When does the rate of CO increase in A2/BAU start to decrease? Hint: Look at the slope of the curve

pH (Page 3 of the graph pad)

pH is a measure of the acidity of the ocean — it is related to the amount of CO2 dissolved in the oceans. More CO2 in the oceans lowers the pH, which means the water is more acidic (a phenomenon known as Ocean Acidification). We will see in Module 7 that the key variable controlling the precipitation of reefs and other organisms that make shells of CaCO is a variable called saturation, which is indirectly related to the pH. Let’s assume for the next four questions that coral framework precipitation in a species of coral declines at a pH of 8.0 and that it can no longer form any below a pH of 7.8 (again this is hypothetical since saturation is key).

10. Select all the emission scenarios that result in a slow-down in shell precipitation at any time during the model run (i.e., pH drops below 8.0).
11. Will coral reefs survive under A1B?
12. Will coral reefs begin to recover in the period observed under A1B?

STEP 3.

Now, we will see what impact permafrost melting might have on the carbon cycle and climate. First, hit the “refresh” button on the browser to return the model to its original state. Run the A2 scenario with the PF switch in the off position, and then run it again with the PF switch turned on.

13. How much additional warming is caused by 2100 in the A1B scenario by the permafrost melting?
14. How much does the pCO2 atm increase by 2100 as a result of the permafrost melting?
15. Does permafrost melting impact the survival of corals under A1B?

End of Module Recap:

In this module, you should have grasped the following concepts:

• Carbon flows through the Earth system by a combination of biological, chemical, and physical mechanisms.
• The global carbon cycle is a critical part of the climate system since it controls the concentration of CO₂ in the atmosphere, and CO₂ is, because of its long residence time in the atmosphere, the main greenhouse gas "driver" of climate change.
• The carbon cycle is complicated by the fact that it has fast and slow parts to it, with the deep ocean exerting a lot of inertia that limits rapid changes; it also has a variety of positive and negative feedback mechanisms in which the flow rates depend on temperature. Finally, it has a number of important human components to it — burning fossil fuels, deforestation, and soil disruption.
• The global carbon cycle is probably never in a steady-state, but it has negative feedback mechanisms that drive it toward a steady state. The response time of the system is very long, measured in tens of thousands of years, due to the vast, sluggish deep ocean part of the system. Some parts of the system can respond (partially) to changes very quickly, as evidenced by the seasonal variations in atmospheric CO₂ seen in the Mauna Loa record.
• The human alterations to the carbon cycle are significant — we now add more than 10 times as much carbon to the atmosphere as volcanoes. Roughly half of this fossil fuel carbon has remained in the atmosphere, with the rest being taken up by the oceans and land plants.
• Land plants respond to higher CO₂concentrations in the atmosphere by increasing their efficiency, which enables them to take up increased amounts of CO₂ from the atmosphere, but this effect has a saturation point — an atmospheric CO₂ level where the uptake of CO₂ does not increase any more.
• The oceans are also an important part of the uptake of carbon, aided by chemical reactions that convert CO₂ gas into carbonate ions in solutions that are then exported to the deep ocean through the sinking of calcium carbonate shells, a process called the biological pump.
• The chemical reactions associated with the uptake of CO₂ by the oceans also influence the acidity of the oceans. If the oceans take up too much atmospheric CO₂, the acidity will increase — this acidification of the oceans is made worse if the rate of carbon emissions goes up. If the oceans become too acidic, it may have a detrimental impact on biological productivity in the oceans and thus the biological pump may be weakened, which will limit the amount of carbon the oceans can absorb.
• The various IPCC emissions scenarios all lead to increased temperatures in the next century — even if we reduce the rate of emissions from current levels, the atmospheric CO₂ concentration will increase, and thus the temperature will increase.
• There are some important unknowns in the carbon cycle, including how soil respiration will respond to temperature — if it is very sensitive, then at higher temperatures the soil reservoir will become a source of carbon rather than a sink. Furthermore, warming in the high latitudes of the northern hemisphere may lead to important emissions of carbon from permafrost. Permafrost is, in fact, currently melting, and the soil trapped in these frozen soils could increase the global warming of the next century by an additional degree C.

Assignments

You should have read the contents of this module carefully, completed and submitted any labs, the Yellowdig Entry and Reply, and taken the Module Quiz. If you have not done so already, please do so before moving on to the next module. Incomplete assignments will negatively impact your final grade.

Labs

• Lab 5: Carbon Cycle Modeling