The Nuts and Bolts of Climate Modelling
Buy the book
In this post from NET-ZERO:
What is Radiative Forcing? The extra energy trapped in the Earth system which is causing the planet’s surface to warm.
Why Do Fast Feedback Mechanisms Amplify Warming? How the combined response of water vapour, rising heat, melting ice and clouds amplifies CO2-led temperature increases.
How Will the Biosphere Respond to Increasing Temperatures? How the latest Earth System Models are attempting to capture changes to forests, fires, ice sheets, and ocean circulation currents to understand how this may further amplify temperature change or create dangerous tipping points for the Planet.
Radiative Forcing
The sun’s energy enters the Earth system with an average power of 340 Watts per square metre at any given time. Atmospheric gases, clouds, snow, ice, oceans, and the Earth’s surface reflect 30% (100 W per m2) of this incoming energy straight back into space and the remaining 240 W per square metre is absorbed by the atmosphere, land, and oceans.
The portion of the sun’s energy which is absorbed, is re-radiated and sent back towards space as lower energy, longer wavelength, infrared radiation. Greenhouse gases like CO2 in the atmosphere can absorb this outgoing infrared radiation and trap energy in the Earth system.
The only way the planet can rebalance the incoming and outgoing energy budget, is to heat the Earth’s surface and push more energy radiation back into space.
The initial change in energy flux entering Earth is called Radiative Forcing. It is measured in Watts per square metre (W/m2) - a positive value leads to warming, a negative value leads to cooling.
Diagram of the Greenhouse effect led by the relationship between CO2 concentrations and the height of the tropopause. (1) Pre-industrial CO2 concentrations of 280 ppm doubles to 560ppm. This increases absorption in the atmospheric window and increases the altitude of the emission level (where energy escapes to space). The higher, colder emission level emits less energy to space. (2) The new emission level is now out of balance emitting just 236 W/m2 to space versus incoming energy from the sun of 240W/m2 so net of 4W/m2 enters Earth, (3) The extra incoming energy warms the surface and atmosphere until the temperature of the emission level returns to 255K or -18⁰C and energy balance is restored. The surface temperature must warm by about 3⁰C to rebalance the energy flow and reach a new, warmer steady state if CO2 is doubled. Adapted from Andrew Dessler.
Climate Modelling Begins By Calculating Radiative Forcing Change
Climate models begin with underlying assumptions on how the sun’s cycle, greenhouse gases, and air pollution will change the amount of solar energy entering and leaving the atmosphere to calculate the change in Radiative Forcing (the extra trapped energy in watts per square metre) and use this to estimate the initial temperature change.
Solar Forcing: The sun has an 11 year sunspot cycle which changes the output by ±0.1%, impacting temperatures by ±0.1⁰C.
Greenhouse Gas Emissions: The initial concentration increases of carbon dioxide (CO2) and other greenhouse gases depend on predictions of future human emissions. Doubling CO2 concentrations (from pre-industrial times/pre-1900) to 560 ppm will increase the added radiative forcing by 3.7 watts per square metre.
Aerosols, dust, smoke and soot: Small particles suspended in the atmosphere are released from human activities such as burning fossil fuels or industry, alongside natural processes such as volcanic eruptions. Sulphur particles from volcanic eruptions reflect the sun and cool the atmosphere. Black carbon or soot from industrial activity is a strong warming influence as it absorbs the sun’s energy, helps to form clouds and covers reflective surfaces. However, unlike greenhouse gases, these don’t persist very long in the atmosphere. If we stopped emitting industrial sulphates this cooling effect would be gone within one to two years. The net impact of aerosols today is to lower radiative forcing by 0.9 watts per square metre.
Unsplash by Ritam Baishya
Next Climate Model Calculate Fast Ongoing Feedbacks
Next climate models must calculate the impact from fast feedback mechanisms which can either amplify or dampen the initial radiative forcing from sun, CO2, and aerosols. In turn this will amplify or dampen the initial temperature change.
Planck Feedback: The response of the Earth to emit more radiation as the planet warms. This is what brings greenhouse-gas-led energy imbalances back into check. Planck feedback offsets radiative forcing by 3.3 watts per square metre per 1⁰C warming. If the Planck feedback was the only response to greenhouse warming then the climate sensitivity (the temperature increase for double the CO2 concentration) would be just 1.1⁰C.
However, there are more fast feedback mechanisms and we can represent the impact of each based on a measure of amplifying feedback strength - a positive number amplifies the initial temperature change, a negative number dampens the initial temperature change.
Water Vapour Feedback (Amplifies Radiative Change): Water vapour increases by 7% in the atmosphere for every 1⁰C increase in temperature and amplifies an initial CO2 led warming. Water vapour has the largest amplifying feedback strength of +0.6.
Lapse Rate Feedback (Dampens Radiative Change): The lapse rate is the rate at which the temperature of the atmosphere gets cooler as you travel higher. The extra heat energy from the initial warming evaporates more water from the Earth’s surface which moves up into the atmosphere by convection (latent heat). Once in the dry and cold atmosphere, the water turns back to liquid and releases the heat energy. The extra transfer of heat from the Earth’s surface to the colder atmosphere acts to reduce the temperature gradient of the atmosphere (the lapse rate) and so weakens the greenhouse effect. Lapse rate feedback acts to dampen the initial temperature increase with a strength of -0.3.
Cloud Feedbacks (Amplifies Radiative Change): Increasing temperature leads to more water in the atmosphere, increasing the number of clouds. Depending on their type and altitude, they can have either amplifying or dampening effects. Cloud tops higher up in the troposphere tend to warm the Earth as the cold water vapour traps more infrared energy. Low lying clouds tend to reflect more of the sun’s energy (due to warmer water vapour). Overall, clouds have a small amplifying impact but are one of the most uncertain elements of climate modelling. Cloud feedback is estimated at +0.25.
Sea Ice-Albedo Feedback (Amplifies Radiative Change): Increasing temperatures melt ice and reveal more sea. Ice reflects 75% of the energy which strikes its surface. The ocean reflects just 5%. Receding ice means less reflection and more absorption of the sun’s energy amplifying the initial temperature change. Ice is an amplifying feedback with strength +0.1.
So already summing up these feedbacks means an initial 1.1⁰C temperature increase from doubling CO2 concentrations will be amplified to about 3⁰C final warming.
Final Temperature = Initial Temperature Change ÷ (1 - Feedback Strength)
Temperature Rise Due to Initial Radiative Forcing increase (Planck) and Subsequent Fast Feedback Amplifying (+ve) and Dampening (-ve) Mechanisms
The simplified relationship between atmospheric CO2 concentration and temperature increase (since pre-industrial average 1850-1900). Approximation based on simplified radiative forcing relationship of 5.35 x ln (CO2 change) from Mhyre et al and using 0.8x Equilibrium Warming Factor to arrive at the mid-point of IPCC estimates.
Biosphere or Tipping Point Feedback
Once the fast feedbacks to the initial temperature change have been captured, Earth System Models attempt to capture the slower changes or abrupt changes to once stable parts of the Earth system:
Changes to the Land and Ocean Sink (Dampens CO2 change): The ocean has turned from a net carbon emitter to a net carbon absorber over the last 200 years, as the physical and biological ocean pumps responded to increasing CO2 concentrations in the atmosphere and attempt to rebalance the equilibrium (Le Chatelier’s principle). Vegetation on land has also increased the rate of growth and carbon uptake in response to higher CO2 concentrations (greening of Earth). The net result of these initial changes has been to remove an average of 55% of human CO2 emissions from the atmosphere. However, according to work by M. R. Raupach et al, the Atmospheric Sink is now starting to weaken. In 1959, 60% of human emissions were absorbed by land and oceans. By 2012, with temperatures nearly 0.8⁰C hotter, the land-ocean sink removed just 53% of excess human CO2 emissions. Warmer oceans hold less carbon, drought slows plant growth, and warmer soils increase microbial decay and respiration of carbon from soils. In other words, the fast carbon cycle (oceans and land) has a dampening response to CO2 increase, but rising temperatures are now starting to weaken the efficiency of this offset. A back-of-the-envelope calculation suggests if land and ocean uptake continues to weaken by ~10% for every 1⁰C initial warming (as it has done over the last 50 years) this will leave an extra 100 billion tonnes or 5 ppm more CO2 in the atmosphere (compared to the fraction of CO2 left in the atmosphere of the last 50 years).
Forest Wildfires and Peat Fires (Amplifying CO2 Change): Increasing temperatures dry out wood and peat which increases the risk of fires. Forest wildfires burn an average of 3.5 million square km per year (95% are caused by humans, 5% are due to lightning) compared to 0.15 square km deliberately burnt by humans for agriculture. However, natural forests grow back and recapture the carbon, farmland doesn’t. Since 1979 wildfires have increased by 20% or 0.5 million square km as the planet has warmed by 0.7⁰C. If the burnt area continues to expand faster than it can regrow then the carbon remains in the atmosphere. Forests hold 250 billion tonnes of carbon (900 billion tonnes CO2 ) over 40 million square km of land. A back-of-the-envelope calculation suggests that every 1⁰C initial warming will add up to 3%, 30 billion tonnes or 2 ppm of CO2 into the atmosphere. Peat fires and drying wetlands may be an even bigger problem as peat holds 550 billion tonnes of carbon (2,000 billion tonnes CO2) and may lose up to 10% of carbon, 200 billion tonnes or 10 ppm of CO2 per 1⁰C initial warming.
Rapid Release of Greenhouse Gases (Amplifies CO2e Concentrations): Tundra or permafrost is frozen soil which covers 19 million square km of the northern hemisphere. The Tundra holds 1.7 trillion tonnes of frozen carbon with more than 800 billion tonnes of carbon in the top three metres. If this frozen soil melts, the trapped gas is released into the atmosphere. The IPCC estimates up to 37-81% decline in the top 3.5 metres of permafrost at high northern latitudes this century unless we act on climate change. Work by Kevin Schaefer et al. estimates that a moderate warming scenario could add another 100 billion tonnes of carbon (or 370 billion tonnes of CO2 ) into the atmosphere by 2100. Furthermore, a small fraction may be methane (3%) which could double the total warming potential of the release because methane is a 28 times more potent greenhouse gas than CO2 over 100 years. A quick back-of-the-envelope calculation based on this trend could mean an additional 400 billion tonnes or 20 ppm CO2 in the atmosphere per 1⁰C initial warming. The tundra could prove to be one of the biggest carbon feedback mechanisms.
Ice Sheet Albedo (Amplifies Radiative Change): Glaciers around the world are already rapidly shrinking and will be more than half gone by the end of this century. The complete melting of all glaciers will add 0.4 metres to global sea level. The land based ice sheets of Greenland and West Antarctica are also melting but are much thicker and will take centuries to disappear. Total melting of the Greenland Ice Sheet (GIS) and Western Antarctic Ice Sheet (WAIS) would each add six metres to global sea levels – this change may prove irreversible at temperature increases above 2-4⁰C. The remainder of Antarctic ice could raise sea levels by another 60 metres but would take millennia to melt.
Amazon Rainforest Dieback (Amplifies CO2 concentrations): The Amazon rainforest generates around half of its heavy rainfall through evapotranspiration from the forest itself. Evaporation from warm damp soils and transpiration from leaves drives water into the atmosphere, creating clouds and more rainfall. However, rising temperatures may reduce rainfall, rising CO2 reduces transpiration and deforestation shrinks the forest. Combined, this process could trigger a sudden dieback (above 3⁰C), and rainforests would turn to more sparse savannah releasing CO2 in to the atmosphere from the rotting forest vegetation and soils.
Atlantic Meridional Overturning Circulation (Changing weather patterns): Melting Arctic sea ice and Greenland ice sheets release warmer, fresh water into the Arctic sea, reducing the saltiness and warming the upper ocean at high latitudes. This could weaken or divert ocean circulation currents such as the Gulf Stream which are driven by warmer, less dense tropical waters mixing with colder, denser Arctic waters. This would cool Western Europe and severely change global weather patterns. The IPCC has found some evidence this is already happening and asserts it is highly likely to weaken over this century and cannot rule out a complete collapse under high warming scenarios. Around 13,000 years ago, just before the climate settled into the current stable range, the Younger Dryas event cooled Greenland by 4-10⁰C but warmed the southern hemisphere in a matter of decades. Given the speed and variability climate scientists believe this was caused by a weakening of the Atlantic Meridional Overturning Circulation (AMOC).
Transient temperature increase forecasts based on peak population and peak consumption by 2060. Approximations use simplified radiative forcing relationship of 5.35 x ln (CO2 change) from Mhyre et al., bottom dashed line shows basic transient temperature increase calculation. Top dashed line includes extra CO2 in the atmosphere from melting tundra, peat and forest fires and a weakening land-ocean sink as the planet warms (sensitivities referenced in preceding text).
Scientists can now model radiative forcing and the key fast feedback mechanisms of water vapour, evaporation, clouds, ice, and aerosols in General Circulation Models. Work continues to fully integrate the remaining biosphere feedback mechanisms such as the carbon cycle response, fires, and melting permafrost into Earth System Models.
