Climate models are tools used in climate research. They are attempts to synthesize our theoretical and empirical knowledge of the climate system in a computer code. This chapter describes how climate models are constructed, and how they are evaluated, and it discusses some applications.

a) Construction

Climate models solve budget equations numerically on a computer. The equations are based on the conservation of energy, momentum, and mass (air, water, carbon, and other relevant elements, substances, and tracers). Typically they are solved in separate boxes that represent specific regions of Earth’s climate system components (Fig. 1). Along their boundaries the boxes exchange energy, momentum and mass. Exchange with the flow of water or air from one box to another is called advection. Prognostic variables such as temperature, specific humidity in the atmosphere, or salinity in the ocean, and three velocity components (zonal, meridional, and vertical) are calculated in each box. The momentum equations, which are used to calculate the velocities, are based on Newton’s laws of motion and they include effects of the rotating Earth such as the Coriolis force. The temperature equations are based on the laws of thermodynamics. Thus, climate models represent the fundamental laws of physics as applied to Earth’s climate system.

Figure 1: Schematic of a three-dimensional coupled climate model. From wikipedia.org.

The evolution of the prognostic variables in the interior boxes are solved one time step at a time (see chapter 4, equation B1.4). After the prognostic variables have been updated the fluxes between boxes (I and O) are calculated, which are used for the next time step. Then the prognostic variables are updated again using the fluxes, and so on. This procedure is called forward modeling because all model variables at the next time step are calculated only from the model variables at the previous time step and the boundary conditions without the use of observations. Boundary conditions such as the incident solar radiation at the top-of-the-atmosphere or concentrations of greenhouse gases are usually required as input to the calculations. These are also called radiative forcings. Other boundary conditions need to be applied at the lower boundary: the topography (mountains) and bathymetry (sea floor). To start a forward model simulation initial conditions need also to be provided. Those can be taken from observations or idealized distributions.

Climate models range from the simplest zero-dimensional (0D) Energy Balance Model (EBM) discussed in chapter 4 to the most complex three-dimensional General Circulation Models (GCMs). The range of models ordered with respect to complexity is called the hierarchy of climate models. The 0D-EBM can be expanded by solving the energy budget equation separately at different latitudinal bands. This is called the one-dimensional EBM (1D-EBM). The 1D-EBM is still vertically averaged but it includes energy exchange between latitudinal bands as discussed in chapter 6. Meridional energy transport in 1D-EBMs is typically treated as a diffusive process proportional to the temperature gradient, such that heat flows from warm to cold regions. 1D-EBMs typically treat the ocean and atmosphere as one box, so that one cannot distinguish between heat transport in the ocean and atmosphere.

One-dimensional models are also used for vertical energy transfer in the atmosphere. These are called radiative-convective models and they work similar to the models used to produce Fig. (6) in chapter 4. Radiative-convective models themselves range in complexity from line-by-line models, which calculate radiative transfer in the atmosphere at individual wavelengths, to models that average over a range of frequencies (band models). Line-by-line models are computationally expensive and cannot be used in three-dimensional GCMs, which use band models. Band models are calibrated and tested by comparison to line-by-line models. As discussed in chapter 4, radiative fluxes alone would cause a much warmer surface and much colder upper troposphere than observed. Therefore, radiative-convective models include convection, mostly by limiting the lapse rate to the observed or moist adiabatic rate.

Intermediate complexity models consist of 2D-EBMs, which are still vertically averaged but include zonal transport of energy and moisture (in this case they are called Energy-Moisture-Balance Models or EMBMs), zonally-averaged ocean models coupled to a 1D-EBM, and zonally averaged dynamical atmospheric models (resolving the Hadley circulation). Intermediate complexity models also often include biogeochemistry and land ice components. They are computationally relatively inexpensive and can be run for many thousands or even millions of years.

The first climate models developed in the 1960s were 1D-EBMs and simple GCMs of the atmosphere and ocean at very coarse resolution. Initially ocean and atmospheric models were developed separately and only later they were coupled. Coupling involves the exchange of heat and water fluxes and momentum at the surface. Current state-of-the-science coupled, three-dimensional GCMs also include sea ice and land surface processes such as snow cover, soil moisture and runoff of water through river drainage basins into the ocean. Many models also include dynamic vegetation with separate plant functional types such as trees and grasses. However, most current coupled GCMs that are used for future projections do not include interactive ice sheet components. This is because ice sheets have long equilibration (response) times of tens of thousands of years and therefore they need to be run for a much longer time than the other climate system components, which is currently not possible for most climate models.

The deep ocean has an equilibration time of about a thousand years. For future projections people are mostly interested in the next hundred or perhaps a few hundreds of years. For the most reliable and detailed projections on these timescales global climate modeling groups try to configure their models at the finest possible resolution. Currently the typical resolution is a few degrees (~200 km) in the horizontal directions and 20 to 30 vertical levels each in the atmosphere and ocean components. Finer resolution global models are being developed at various climate modeling centers around the world, but currently most climate projections of centennial and longer time scales are based on coarser resolution models (Fig. 2).

Figure 2: Illustrations of land surfaces (green and brown colors) and sea floor (blue) at fine (top; ~10 km) and coarse (botton; ~100 km) resolution. Note that the elevations and depths are strongly exaggerated with respect to horizontal distances. From ucar.edu.

Ice sheet models have finer spatial resolution (10s of kilometers) in order to resolve the narrow and steep ice sheet margin, but they have much larger time steps (1 year) than atmospheric (seconds) and ocean (minutes to hours) models because of the slow ice velocities (10-100 m/yr) compared to velocities of ocean currents (1-10 cm/s) or winds (1-10 m/s). The time step in a model depends on the velocity of the fluid and the grid-box size. The higher the velocity and the smaller the grid-box size the smaller the time step has to be to guarantee numerical stability. Finer resolution models therefore have to use smaller time steps, which is an additional burden on the computational resources. Another obstacle to move to higher resolution is the amount of data that accumulate. The highest resolution ocean model simulations currently require petabytes (10¹⁵ bytes = 1000 terrabytes) of storage for all the model output. Processing these huge amounts of data is a challenge.

One way to avoid increasing computational resources at higher resolution is to construct regional climate models for a specific region of interest, e.g. North America. However, the disadvantage of regional climate models is that boundary conditions at the margins of the model domain have to be prescribed. The resulting solution in the interior depends strongly on those boundary conditions, which often are taken from global climate models. Therefore, any bias from the global climate model at the boundary would be propagated by the regional model into the interior of the model domain. However, in the interior the regional climate model can account for details e.g. of the topography, that a global model cannot. Thus, although not a silver bullet, regional climate models are useful for simulating climate in more spatial detail than possible with global models.

Typically the resolution and grids of the atmospheric and ocean components are different. Therefore, surface fluxes and variables needed to calculate the fluxes need to be mapped from one grid to the other. This is often accomplished by a coupler, which is software that does interpolation, extrapolation, and conservative mapping. All calculations need to be numerically sound such that energy, water, and other properties are conserved. However, numerical schemes, e.g. for the transport from one box to the next, are associated with errors and artifacts.

Models that include biogeochemistry, such as the carbon cycle, and/or ice sheets are called Earth System Models. Earth System Models calculate atmospheric CO₂ concentrations interactively based on changes in land and ocean carbon stocks. They can be forced directly with emissions of anthropogenic carbon, whereas models without carbon cycles need to be forced with prescribed atmospheric CO₂ concentrations.

Due to the limited resolution of the models, processes at spatial scales below the grid box size cannot be directly simulated. For example, individual clouds or convective updrafts in the atmosphere are often only a few tens or hundred meters in size and therefore cannot be resolved in global atmospheric models. Similarly, turbulence and eddies in the ocean, which are important for the transport of heat and other properties, cannot be resolved by global ocean models. These processes must be parameterized. A parameterization is a mathematical description of the process that depends on the resolved variables, e.g. the mean temperature in the grid box, and one or more parameters. A simple example of a parameterization is the meridional heat flux F_m = -K∂T/∂y in a 1D-EBM, which can be parameterized as a diffusive process, where K>0 is the diffusivity, ∂T/∂y is the meridional temperature gradient and y represents latitude. This parameterization transports heat down-gradient (note the minus sign), which means from warmer to colder regions. In this case the parameter K can be determined from observations of meridional heat flux (Chapter 6, Fig. 4) and ∂T/∂y (Chapter 6, Fig. 1). Parameterizations can be derived from empirical relationships based on detailed measurements or high-resolution model results. The parameter values are usually not precisely known but they influence the results of the climate model. Therefore, parameterizations are a source of error and uncertainty in climate models. Parameters in the cloud parameterization of a model, for example, will impact its cloud feedback and therefore its climate sensitivity.

b) Evaluation

Climate models are evaluated by comparing their output to observations. Fig. 3 shows the multi model mean (the average of all models) from the most recent IPCC report (Flato et al., 2013). The model simulated surface temperature distribution is similar to the observations (Chapter 6, Fig. 1) with warm (20-30°C) temperatures in the tropics and cold (<0°C) temperatures near the poles and at high altitudes (Himalayas). The models also reproduce some of the observed zonal gradients such as the cooler temperatures in the eastern equatorial Pacific compared to the western Pacific warm pool and the warmer temperatures in the northeast Atlantic compared to the northwest Atlantic, which are caused by the upper ocean circulation. However, the models are not perfect as indicated by biases such as too cold temperatures in the northern North Atlantic and too warm temperatures in the southeast Atlantic and Pacific. The warm biases in the southeast Atlantic and Pacific are most likely caused by the coarse resolution ocean models that do not resolve well the narrow upwelling in these regions. A similar bias is seen in the California current in the northeast Pacific. Despite these biases the multi model mean agrees with the observed temperatures to within plus/minus one degree Celsius in most regions. Even the larger regional biases such as those mentioned above are relatively small compared to the ~60°C range of temperature variations on Earth. This indicates that the models reproduce observed surface temperatures relatively well.

Figure 3: Annual mean surface air temperature distribution from 1980-2005 as simulated by climate models (a) and their bias (b). The bias b = T_m – T_o is the difference between the model simulated temperature T_m and that estimated from observations T_o. From ipcc.ch.

Fig. 4 shows the multi model mean precipitation. The models reproduce the general pattern of the observations (Chapter 6, Fig. 8) such as more precipitation in the tropics and at mid-latitudes compared with less precipitation in the subtropics and at the poles. They also reproduce some of the observed zonal differences such as dryer conditions over the eastern parts of the subtropical ocean basins compared with wetter conditions further west. However, the models also display systematic biases such as the double Intertropical Convergence Zone (ITCZ) over the East Pacific and too dry conditions over the Amazon. The relative errors in precipitation are generally larger than those for temperature. This indicates that the models are better in simulating temperature than precipitation. This may not be surprising given that the simulation of precipitation depends strongly on parameterized processes such as convection and clouds.

Figure 4: As Fig. 3 but for annual mean precipitation.

Fig. 5 compares correlation coefficients of different variables. It confirms our previous conclusion that the models are better in simulating temperature than precipitation. It also shows that the models have very good skill in simulating Emitted Terrestrial Radiation at the top-of-the-atmosphere, whereas they are less good at simulating clouds. The current generation of climate models (CMIP5) are improved compared with the previous generation (CMIP3) particularly for precipitation. Another interesting feature also apparent in Fig. 5 is that the the multi model mean is almost always in better agreement with the observations than any one particular model. A similar phenomenon, which has been called the wisdom of the crowd, has been noted by Sir Francis Galton (1907), who analyzed villager’s guesses for the weight of an ox at an English livestock fair. He found that many guesses where too high or too low, but the mean of all guesses was almost exactly the correct weight of the animal.

FIgure 5: Correlation coefficient for the annual mean surface air temperature (TAS), outgoing longwave radiation (RLUT; in chapter 6 we called this variable emitted terrestrial radiation from the atmosphere: ETR_a), precipitation (PR), and the shortwave cloud radiative effect (SW CRE). The correlation coefficient -1 ≤ r ≤ 1 is a measure of pattern agreement. See this wikipedia.org page for a detailed definition of r. If two variables are unrelated r = 0, whereas if they are perfectly in linear agreement r = 1. Each short horizontal line is one model. The longer line is the multi model mean and the circles are the median. Results are shown for the current generation of climate models from the Climate Modeling Intercomparison Project 5 (CMIP5) and the previous generation (CMIP3). Green dots show correlation coefficients for alternative observational datasets indicating uncertainties in the observations. They represent the best the models could do given uncertainties in the observations. From ipcc.ch.

Fig. 6 shows that most models overestimate temperatures in the thermocline by about 1°C, presumably due to too much vertical diffusion. Again these errors are relatively small given the large range (~20°C) of deep ocean temperature variations. Model errors in salinity are larger near the surface than in the deep ocean. In the southern hemisphere subtropics near surface waters are too fresh, perhaps related to the double ITCZ bias and associated too wet conditions in the atmosphere there (Fig. 5).

Figure 6: Zonally averaged differences in temperature (A) and salinity (B) between the multi model mean and observations (color contours and white lines). Black lines indicate observed temperature and salinity from the World Ocean Atlas 2009. From ipcc.ch.

All climate models simulate an increasing ocean heat content over the last 40 years, consistent with observations. Some models simulate more and others less heat uptake. The multi model mean, however, is in good agreement with the observations. This indicates that the models are skillful not only in simulating the mean state of ocean temperatures but also its recent temporal evolution.

Figure 7: Changes in ocean heat content simulated by the CMIP5 models (thin lines), and their multi model mean (red thick line), compared to observations (black thick line). From ipcc.ch.

Historical and paleoclimate variations are also used to test and evaluate climate models as will be discussed next.

c) Applications

Some of the main applications of climate models are paleoclimate studies, detection and attribution studies, and future projections. Future projections will be discussed in the next chapter.

Paleoclimate model studies are not only useful for a better understanding of past climate changes and their impacts but they can also be used to evaluate the models. For example, model simulations of the Last Glacial Maximum (LGM) are broadly consistent with temperature reconstructions (see Chapter 3) that show global cooling of 4-5°C, polar amplification and larger changes over land than over the ocean. The models reproduce these basic features of the reconstructions, which indicates that they have skill simulating climates different from the present (Masson-Delmotte et al., 2013). On the other hand, there are also differences between model results and observations, e.g. in deep ocean circulation (Muglia et al., 2015), which indicates that model’s skills in those aspects are questionable.

Detection and attribution studies attempt to determine which observed climate changes are unusual (detection) and what are its causes (attribution). Climate models driven with only natural forcings show variations from one year to the next due to internal climate variability (e.g. El Niño) and short term cooling in response to large volcanic eruptions (Fig. 8). However, they do not show a long-term warming trend over the past century, in contrast to the observations. This suggests that the global warming observed since about the 1970’s is highly unusual and cannot be explained by internal climate variability (as represented in the models) nor by natural drivers. However, if anthropogenic forcings are included the models reproduce very well the observed long term trend. The multi model mean also reproduces well the observed short term coolings associated with large volcanic eruptions of the past 50 years.

Figure 8: Comparison of climate model simulations with observed surface temperature changes. Left panels show timeseries of globally averaged surface temperatures from the current generation of climate models (CMIP5; yellow thin lines show individual models, red thick line shows the multi model mean) and the previous generation (CMIP3; blue lines, mostly obscured by the overlain yellow lines). Two sets of simulations are show. Top panels show models forced with natural forcings only, bottom panels show models forced with both natural and human forcings. From ipcc.ch. This is a key figure.

Models driven with both natural and anthropogenic forcings reproduce well not only the observed global mean temperature changes but also its spatial distribution such as larger warming at high northern latitudes (polar amplification) and over land (land-sea contrast). These results represent evidence that human activities are the main reason for the observed warming during the past 50-60 years. The IPCC’s AR5 concludes that “it is extremely likely that human activities caused more than half of the observed increase in GMST from 1951 to 2010” (Bindhoff et al., 2013), where GMST stands for global mean surface temperature.

Due to the importance of CO₂ as a greenhouse gas the carbon cycle is a crucial part of the climate system. Since carbon exchanges with the biosphere, biological processes need to be considered in climate science. The carbon cycle is part of the broader biogeochemical cycles, which include other biologically important chemical elements such as nitrogen and oxygen.

a) The Natural Carbon Cycle

Carbon exchanges relatively rapidly between three large reservoirs: the ocean, the atmosphere, and the land (Fig. 1). Of those the ocean contains the most carbon: almost 40,000 Pg. Most of the carbon in the ocean is in the form of Dissolved Inorganic Carbon (DIC), and most DIC resides in the intermediate and deep layers because those depths make up most of its volume. Marine biota are important in transferring carbon from the surface to the deep ocean, but their biomass is very small because they consist mainly of microscopic algae called phytoplankton. Phytoplankton build the base of the ocean’s food web through photosynthesis. They have adapted to be tiny and light, so as not to sink to the sea floor. They need to stay near the sunlit surface to photosynthesize. Below about 100 m depth light levels get too low due to absorption by sea water. The deep ocean is therefore dark but organic matter sinks there from the surface in various forms, e.g. as fecal pellets of zooplankton. Below the surface, the sinking dead organic matter is respired by bacteria and returned into the inorganic carbon pool. This is called the biological pump because it removes carbon from the surface and atmosphere and sequesters it in the deep ocean, where it can stay for hundreds to thousands of years. Dissolved CO₂ gas in sea water is part of the DIC pool. It exchanges with the atmosphere about 80 Pg of carbon per year. Ocean-atmosphere gas exchange depends on the difference between surface ocean and atmospheric partial pressures (pCO₂; in this book we use pCO₂ and CO₂ concentration synonymously in units of parts per million or ppm) and therefore leads to a strong and relatively rapid coupling of the atmospheric CO₂ concentration to the surface ocean.

Figure 1: The Carbon Cycle. Numbers in boxes represent reservoir mass, also called carbon stocks, inventories, or storage in PgC (1 Pg = 10¹⁵g = 1 Gt). 2.1 PgC = 1 ppm atmospheric CO₂. Numbers next to arrows indicate fluxes in PgC/yr. Black numbers and arrows represent estimates of the natural (pre-industrial) carbon cycle. Red numbers and arrows indicate estimates of anthropogenic effects for 2000-2009. From Ciais et al. (2013). Image from ipcc.ch. See additional material at the end of this chapter for a figure showing the sizes of the reservoirs and fluxes in proportion to the size of the boxes and arrows.

The second biggest of the three rapidly exchanging carbon reservoirs is the land, which contains about 4,000 Pg of carbon. On land carbon is stored in living vegetation, in soils, and in permafrost. Since land plants don’t have the problem of sinking out of the light they can grow big and contain large amounts of carbon, such as trees. Therefore, much more carbon is stored in living biomass on land (~500 Pg) than in the ocean (~3 Pg). However, even more carbon is stored in soils and permafrost.

More than 100 Pg of carbon are removed from the atmosphere each year by photosynthesis of land plants and turned into organic matter. Organic matter cycles through the land food web and eventually gets into the soil carbon pool where it decomposes. Like in the ocean, bacteria and heterotrophic organisms on land respire organic carbon and turn it back into inorganic CO₂. Land carbon uptake and release does not depend strongly on atmospheric CO₂ concentrations. They depend more on water availability and temperature, respectively. Plant growth on land is strongly water limited and respiration rates strongly depend on temperature. However, CO₂ increases the water use efficiency of land plants because at higher CO₂ concentrations they don’t need to open the stomata as much as at lower CO₂ concentrations. Stomata are small openings in the cells that allow CO₂ to enter, but they also allow water to leave in a process called transpiration (see figure in box below). Thus, at higher CO₂ levels plants can grow more for the same amount of water usage.

The atmospheric carbon reservoir is relatively small compared to the ocean, which is ~40 times bigger, and the land, which is ~10 times bigger. However, the atmosphere is crucial in linking land and ocean through rapid exchanges.

Box 1: Photosynthesis and Respiration

Photosynthesis (Fig. B1.1) is the process by which autotrophic organisms (plants, algae, and many bacteria) produce organic matter and oxygen from CO₂ and water using light as an energy source.

Figure B1.1: Chemical Reaction for Photosynthesis. Carbon dioxide and water is converted to carbohydrates and oxygen. This process uses energy.

Respiration (Fig. B1.2) is the reverse process by which heterotrophic organisms (bacteria, fungi, animals, and humans) oxidize organic carbohydrates to derive their energy resulting in CO₂ and water.

Figure B1.2:Chemical Reaction for Respiration. Carbohydrates and oxygen are converted to CO₂ and water. This process releases energy.

In order to photosynthesize, land plants have to take up CO₂ from the air. They do this by opening little pores called stomata, through which not only CO₂ can enter, but also water and oxygen can leave the cell (Fig. B1.3).

Figure B1.3: Illustration of Gas Exchange Through Stomata in a Leaf.

b) Anthropogenic Carbon

Human effects on the global carbon cycle have been relatively limited before the industrial revolution, although some emissions from land-use change such as deforestation may have been going on for hundreds or thousands of years. During the last 100 years or so, however, rapid burning of fossil fuels such as coal, gas, and oil have caused a massive perturbation (Fig. 2). This perturbation is perhaps most evident in the atmosphere where CO₂ concentrations have increased by more than 40 %. In chapter 3 we have seen that current levels of atmospheric CO₂ have been unprecedented for the last 800,000 years, but reconstructions going back further in time indicate that the last time Earth’s atmosphere had about 400 ppm CO₂ is about 3 million years ago.

Currently humans emit about 10 billion tons of carbon into the atmosphere per year mostly from fossil fuel burning (~90 %). However, deforestation continues to be a significant contribution (~10 %). Anthropogenic carbon emissions from fossil fuel burning have increased rapidly after World War Two. The ocean has taken up about 40 % (155/395) of all anthropogenic carbon emissions hitherto. 60 % (240/395) have stayed in the atmosphere, whereas the land comes out in a wash because of loss due to deforestation and gain due to recent regrowth.

Figure 2: Anthropogenic Carbon Sources and Sinks in Billion Metric Tons of Carbon Per Year (Gt C/yr) as a function of the year. Positive numbers show sources from fossil fuel burning and cement production (gray) and deforestation (yellow). Negative numbers show uptake by land (green), atmosphere (light blue), and ocean (dark blue). From Friedlingstein et al. (2019). Image from globalcarbonproject.org.

Anthropogenic carbon emissions have increased rapidly during the early 2000’s but in recent years they have flattened out (Fig. 3) mostly because of emissions from China showed a similar behavior (Fig. 4). About half of all carbon put into the atmosphere by humans since the industrial revolution (cumulative emissions) was done so in the last 30 years. Cumulative emissions are the grey and brown areas in Fig. 2. Together they amount to about 500 GtC or half a trillion metric tons. As we will see later cumulative carbon emissions determine the global temperature increase.

Figure 3: Estimates of carbon emissions from fossil fuel burning and cement production since 1990. From globalcarbonproject.org.

The effects of the financial and economic crisis is seen in the dip in global carbon emissions in 2009 caused by emission reductions in the US and Europe (Fig. 4), whereas emissions continued to increase in China until 2013 after which they stayed constant. A similar dip can be expected for the current economic slowdown due to the coronavirus pandemic.

Figure 4: Carbon emissions in GtC/yr (units in the figure labels are incorrect) from the top four fossil fuel emitters. From globalcarbonproject.org.

Human caused carbon emissions are mainly from burning of fossil fuels, whereas cement production contributes only about 6 % (Fig. 5). Burning of coal, oil, and gas have all increased substantially during the last 50 years. The increase in emissions from China during the first decade of the 21^st century was fueled mainly by coal burning.

Figure 5: Contributions to fossil fuel emissions in GtC/yr from coal, oil, and gas burning and cement production. From globalcarbonproject.org.

Among the four top emitters the US is the one with the largest emissions per person (Fig. 6). The average US American emits more than 4 metric tons of carbon into the air each year. This is more than twice the emissions per person in Europe or China, more than three times the average emissions world-wide, and about ten times the emissions from a person in India. The US is responsible for 25% of all carbon emitted in the past (cumulative emissions) although it makes up only 4% of the world’s population. Europe, which accounts for about 10% or the world’s population, has emitted more than 22% of all carbon. This figure shows other countries.

Figure 6: Carbon emissions per person in tC/yr. The width of the boxes represents the population. From globalcarbonproject.org.

How do we know that the rising CO₂ concentrations in the atmosphere are from human activities? There are several independent lines of evidence. The first comes from economic data. Since fossil fuels are traded internationally we know how much oil, coal, and gas a country imports and uses. The data shown in Figs. (2) through (6) are based on these estimates. The shaded area in Fig. (3) indicates the error bars of those estimates. Not all countries publish and make their data available, which leads to these uncertainties. However, they are relatively small such that the emissions are known to within about a 5 % error margin.

Box 2: Carbon Isotopes

Carbon exists as three isotopes. The most common carbon-12 (¹²C) with 6 protons and 6 neutrons, the rarer carbon-13 (¹³C) with an additional neutron, and carbon-14 (¹⁴C) or radiocarbon with two additional neutrons. ¹⁴C is radioactive and decays with a half-life of 5,730 years.

Figure B2.1: Illustration of the Atomic Structure of Carbon Isotopes. The nucleus consists of protons (red) and neutrons (green). It is surrounded by electrons (blue).

Plants and algae fractionate carbon isotopes by about 20 ‰ during photosynthesis such that they preferentially take up the light ¹²C. Pre-industrial δ¹³C values of atmospheric CO₂ were about -6.5 ‰. Thus plant and soil carbon have δ¹³C values of around -27 ‰.

Figure B2.2: Schematic Distribution of Carbon Isotopes in the Carbon Cycle Components.

The delta notation is analogous to that of oxygen isotopes discussed in chapter 3. δ¹³C = R/R_std – 1, where R = ¹³C/¹²C is the ratio of the heavy over the light isotope and R_std is that of a standard.

The second line of evidence is based on carbon isotope measurements. Fractionation during photosynthesis leads to plants and algae having very depleted δ¹³C values (see box Carbon Isotopes). Since fossil fuels are derived from ancient plants they are depleted in ¹³C isotopes as well. Thus the addition of carbon with a very depleted ¹³C signature to the atmosphere leads to a decrease in δ¹³C values of atmospheric CO₂. This is observed in measurements both from ambient air and air extracted from ice cores (Fig. 7).

Figure 7: Carbon isotope measurements of atmospheric CO2. Top: Ambient air data from Mauna Loa (black) and the South Pole (red). Bottom: ice core measurements.

The third line of evidence is based on oxygen measurements in air. Burning of fossil fuels has a similar chemical reaction equation that that of respiration. Carbohydrates react with oxygen to form CO₂ and water. Energy is released during this reaction. Thus, burning of carbohydrates consumes oxygen. By measuring the oxygen to nitrogen ratio in air the changes in atmospheric oxygen concentration can be detected even though they are small compared to the absolute oxygen concentrations (Fig. 8). These measurements are evidence of a massive combustion process happening on Earth right now.

Figure 8: Measurements of atmospheric oxygen to nitrogen ratios from Cape Grim, Tasmania. Similar measurements exist from other locations. Image from scrippso2.ucsd.edu.

We conclude that humans have caused a large perturbation to the natural carbon cycle mostly by the burning of fossil fuels, which has increased atmospheric CO₂ concentrations from 280 ppm to more than 400 ppm, to levels unprecedented in Earth’s history for about 3 million years. About 40 % of the anthropogenic carbon emitted so far has been taken up by the ocean, thus reducing the accumulation of CO₂ in the atmosphere.

c) Carbonate Chemistry and Ocean Acidification

CO₂ enters the ocean from the atmosphere through gas exchange if the partial pressure in the atmosphere is larger than the partial pressure in the ocean. It dissolves as CO₂ gas in water just like it is dissolved in your soda drink. If you look at an unopened bottle of soda, you do not see bubbles. The CO₂ molecules are emerged within a vast number of water molecules. The drink was bottled under pressure or under cold temperatures. Solubility of CO₂ like that of other gases such as oxygen depends on temperature. More gas can be dissolved in colder water (Fig. 9). This is the reason why as you warm up a soda drink it will lose CO₂. Because it is not liquid, CO₂ does not ‘evaporate’ into the air, but it outgasses. Evaporation implies a phase change, which does not occur in this case.

Figure 9: Solubility of CO2 in water. From engineeringtoolbox.com.

In the ocean CO₂ reacts with seawater to form carbonic acid (H₂CO₃), which dissociates into bicarbonate (HCO₃^–) and carbonate (CO₃^2-) ions:

(1)  

The sum of these three carbon species is called dissolved inorganic carbon (DIC = CO₂ + HCO₃^– + CO₃^2-) or total carbon. The equilibrium between the species depends on the pH. In the current ocean, pH is about 8.1, which leads to about 86.5 % of DIC being in the form of bicarbonate ions, 13.0 % in the form of carbonate ions, and only 0.5 % in the form of aqueous CO₂ (Fig. 10; Zeebe and Wolf-Gladrow, 2001).

Figure 10: Ratios of carbonate species concentrations as a function of the pH. Currently average seawater has a pH of about 8.1. Therefore most carbon in the ocean is in the form of bicarbonate. Addition of anthropogenic CO₂ decreases the pH. From wikipedia.org.

Dissociation of carbonic acid into bicarbonate (baking soda) produces a hydrogen ion H⁺, which increases the pH of the water. Most hydrogen ions, however, re-combine with carbonate ions to form additional bicarbonate ions. Nevertheless, adding CO₂ to seawater increases its hydrogen ion concentration (decreases its pH) and decreases the carbonate ion concentration. This process is called ocean acidification.

Observations show that the partial pressure of surface ocean water follows closely the trend in atmospheric CO₂ (Fig. 11) indicating the uptake of anthropogenic carbon. The measurements also demonstrate that the ocean’s pH decreases. Data from near Hawaii show that the pH has decreased by about 0.05 units from 1988 to 2011. Global estimates suggest a decrease by 0.2 units from preindustrial times. This corresponds to a ~30 % increase in hydrogen ions.

Figure 11: Measurements of seawater pCO₂ (blue) and pH (green) at ocean station Aloha near Hawaii together with the Mauna Loa record of atmospheric CO₂ (red). From pmel.noaa.gov.

The penetration of anthropogenic carbon into the ocean is largest in the North Atlantic, at mid-latitudes in the Southern Ocean and in the subtropical North Pacific (Fig. 12). As we will see below these are regions of convergence, subduction, or deep water formation.

Figure 12: Anthropogenic carbon in the ocean estimated from observations (Khatiwala et al., 2013). From rapid.ac.uk.

Anthropogenic CO₂ enters the ocean at the surface. Therefore most anthropogenic carbon is in the surface layers (Fig. 13). However, measurable amounts have penetrated most of the upper kilometer of the ocean. In some regions such as the North Atlantic and in the Southern Ocean anthropogenic carbon has entered levels below 2 km depth. These are regions in the ocean where surface waters sink to great depths taking anthropogenic carbon with them.

Figure 13: Latitude-depth sections of anthropogenic carbon in the Atlantic (A), Pacific (B), and Indian (C) oceans. Note that the depth scale is different in panel (A) from the other panels. Black lines denote two surfaces of constant potential density (expressed in σ_θ = density – 1000 kg m^-3). Movements in the ocean are preferentially along lines of constant potential density because it requires no change in energy (adiabatic). Grey outlines and numbers denote different intermediate and deep water masses and their anthropogenic carbon content in PgC. From pmel.noaa.gov.

Calcifying organisms such as corals, coccolithophores, foraminifera, and pteropods build shells and other body parts out of calcium carbonate (CaCO₃) by using calcium Ca²⁺ and carbonate CO₃^2- ions (Fig. 14).

Figure 14: Examples of Calcifying Organisms.

Top left:(inactive link as of 5/19/2021) Coccolithophores (phytoplankton).

Top right: A live foraminifera (zooplankton).

Bottom left: Corals (animals).

Bottom right: (inactive link as of 5/19/2021) A pteropod, a.k.a. sea butterfly.

Decreasing carbonate ion concentrations and pH will lower the saturation state of calcium carbonate, which will make it more difficult for organisms to build calcium carbonate shells. It will also more easily dissolve existing calcium carbonate. Many scientists are concerned that the currently ongoing changes in the carbonate chemistry of the ocean and those expected for the future, in case of continued anthropogenic carbon emissions, may have adverse consequences for the ocean’s ecosystem. The rates of change are likely much larger than anything experienced in the last millions of years, with unknown risks.

Experiments show that increased CO₂ or decreased pH can lead to malformed or partially dissolved coccoliths or pteropod shells. However, ocean acidification research is still in its infancy and consequences for many species and ecosystems are currently not known.

We have seen how global climate has changed and we’ve learned that some of these changes have been related to forcings and feedbacks such as atmospheric CO₂ concentrations and the seasonal distribution of solar irradiance. Now we want to proceed to understand quantitatively why climate is changing. To do this we will consider Earth’s energy budget, review what electromagnetic radiation is, how it interacts with matter, how it passes through the atmosphere, and how this creates the greenhouse effect. But first, we will briefly discuss the general budget equation because it is widely used by scientists and it will be used at different occasions throughout this book.

Box 1: Budget Equation

Scientists like to keep track of things: energy, water, carbon, anything really because it allows them to exploit conservation laws. In physics, for example, we have the law of energy conservation. It is the first law of thermodynamics and states that energy cannot be destroyed or created; it can only change between different forms or flow from one object to another. Similarly, the total amounts of water and carbon on earth are conserved although they may change forms or flow from one component to another one. To start, we need a well-defined quantity of interest. Let’s call that quantity X. It could be energy, water, carbon, or something else that obeys a conservation law. It can be restricted to a specific part or component of the climate system, e.g. water in the cryosphere. Mathematically a budget equation can be written as

(B1.1)  

where the differentials ∂ denote an infinitesimally small change, t is time, I is the input, and O is the output. The left-hand-side of this equation is the rate-of-change of X. In practice the differentials can be replaced by finite differences (Δ) such that we get

(B1.2)  

Finite differences can be easily calculated: ΔX = X₂ – X₁ and Δt = t₂ – t₁. Here X₁ corresponds to the quantity X at time t₁ and X₂ correspond to the quantity X at time t₂. Note that the inputs and outputs have units of the quantity X divided by time. They are often called fluxes.

Figure B1.1: Illustration of the budget equation. A box containing a conserved quantity X that does not include internal sources or sinks will change in time according to the external inputs minus the outputs.

Different boxes can be connected such that the output of one box becomes the input of another box.

A budget is in balance if the quantity X does not change in time. In this case ΔX = 0 and the input equals the output:

(B1.3)  

Let’s do a little example. Assume a student gets a monthly stipend of $1,000 and $400 from his/her parents. Those are the inputs to the student’s bank account in units of dollars per month I = $1,000/month + $400/month = $1,400/month. The outputs would be the student’s monthly expenses. Let’s say he/she pays $400 for tuition, $420 for rent, $390 for food, and $100 for books (not for this one though) such that O = $400/month + $420/month + $390/month + $100/month = $1,310/month. The rate-of-change of his/her bank account is ΔX/Δt = I – O = $1,400/month – $1,310/month = $90/month. The student saves $90 per month.

Equation B1.2 can be used to predict the quantity X at time t₂

(B1.4)  

from its value X₁ at time t₁ if the inputs and outputs are known. In climate modeling this method, called forward modeling, is used to predict quantities into the future one time step Δt at a time.

In our example, if the student starts at time t₁, let’s say in January, with X₁= $330 in his/her bank account then we can predict that in February he/she will have X₂ = $330 + ($1,400/month – $1,310/month)×(1 month) = $330 + $90 = $420. Note that in this case the time step Δt = 1 month.

a) Electromagnetic Radiation

Earth’s energy budget is determined by energy input from the sun (solar radiation) and energy loss to space by thermal or terrestrial radiation, which is emitted from Earth itself. Solar radiation has shorter wavelengths than terrestrial radiation because the sun is hotter than Earth. To understand this let’s consider the electromagnetic radiation spectrum (Fig. 1). Electromagnetic radiation are waves of electric and magnetic fields that can travel through vacuum and matter (e.g. air) at the speed of light (c). It is one way that energy can be transferred from one place to another. The wavelength of electromagnetic radiation (λ), which is the distance from one peak to the next, varies by more than 16 orders of magnitude. Visible light, which has wavelengths from about 400 nm (nanometers, 1 nm = 10^-9 m = one millionth of a millimeter) to about 700 nm, occupies only a small part of the entire spectrum of electromagnetic radiation. The frequency (ν) times the wavelength equals the speed of light c = νλ.

Albert Einstein showed in 1905 that electromagnetic radiation has particle properties. In modern quantum physics the light particle is called a photon. Each photon has a discrete amount of energy E = hv = hc/λ that corresponds to its wavelength, where h = 6.63×10^-34 Js is Planck’s constant. The shorter the wavelength the higher the energy. High energy photons at ultraviolet, X-ray, and gamma ray wavelengths can be harmful to biological organisms because they can destroy organic molecules such as DNA.

Figure 1: The Spectrum of Electromagnetic Radiation. Electromagnetic radiation ranges from radio-waves with wavelengths of hundreds of meters and more, to gamma rays, with wavelengths of 10^-12 m, which is as small as the size of an atomic nucleus.

Interaction of electromagnetic radiation with matter depends on the wavelength of the radiation. Molecules have different discrete energy states and they can transition from one state to another one by absorbing or emitting a photon at a wavelength that corresponds to that energy difference (Fig. 2). Absorption (capture) of a photon leads to a transition from a lower to a higher energy state. Note that once absorbed the photon is gone and its energy has been added to the molecule. Emission (release) of a photon leads to a transition from a higher to a lower state (reversing the direction of the arrows in the top panel of Fig. 2). Note that the emitted photon can have a different wavelength that the absorbed photon. If, e.g., a UV photon was absorbed and has caused the energy of the molecule to increase from the ground electronic state to the second excited state, the molecule can emit two visible photons, first one that leads to a transition from the second to the first excited electronic state, and then another that leads to a transition to the ground state.

Figure 2: Interactions of electromagnetic radiation with molecules. Top: Absorption of a high-energy photon with an ultraviolet or visible wavelength can lead to excited electronic states. Each excited electronic energy state has sub-states with different vibrational levels. Absorption of a lower energy, infrared photon can excite a vibrational level without changing the electronic state. Bottom: Absorption of low-energy photons at microwave or infrared wavelengths can lead to rotation or vibration of molecules, whereas high-energy photons at ultraviolet wavelengths can break apart molecules. From wag.caltech.edu.

In physics, a blackbody is an idealized object that can absorb and emit radiation at all frequencies. A blackbody emits radiation according to Planck’s law (Fig. 3). In classical physics experiments, a closed box covered on the inside with graphite is used to study its properties. It has only a small hole as an opening to measure the radiation that comes out of the box. Although a blackbody is an idealization many objects behave like a blackbody. Even fresh snow. Or the sun.

Figure 3: The intensity of blackbody radiation (arbitrary units) according to Planck’s law as a function of its wavelength (in nm in the top panel and μm (micrometers, 1 μm = 10^-6 m = 1,000 nm) in the bottom panel). The sun’s temperature is about 6,000 K, with a peak in the visible part of the spectrum. The blue curve in the top panel shows Wien’s law, which describes how the maximum moves towards larger wavelengths at colder temperatures. The bottom panel shows curves representative of sun’s (6,000 K) and Earth’s (303 K) temperatures. Note that the bottom panel uses a logarithmic x-axis and that the values for the sun (left scale) are about 6 orders of magnitude larger than those for Earth (right scale). Top image from periodni.com, bottom image from learningweather.psu.edu.

Integration of the Planck curve overall frequencies results in the Stefan-Boltzmann law

(1)  

which states that the total energy flux F in units of watts per square meter (Wm^-2) emitted from an object is proportional to the absolute temperature of the object T in units of Kelvin (K) to the power four. The Stefan Boltzmann constant is σ = 5.67×10^-8 Wm^-2K^-4 and ε is the emissivity (0 < ε < 1), a material-specific constant that allows for deviations from the ideal blackbody behavior (for which ε = 1). For ε = 1, F represents the area under the Planck curve. The emissivity for ice is 0.97, that for water is 0.96, and that for snow it is between 0.8 and 0.9. Thus, water and ice are almost perfect blackbodies, whereas for snow the approximation is less perfect but still good. Highly reflective materials such as polished silver (ε = 0.02) and aluminum foil (ε = 0.03) have low emissivities.

Equation (1) states that any object at a temperature larger than absolute zero emits energy. The energy emitted increases rapidly with temperature. E.g. a doubling of temperature will cause its radiative energy output to increase by a factor of 2⁴ = 16.

Temperature is the macroscopic expression of the molecular motions in a substance. In any substance such as the ideal gas depicted in Fig. 4 molecules are constantly in motion. They bump into each other and thus exchange energy. A single molecule is sometimes slow and at other times fast, but it is their average velocity that determines the temperature of a gas. More precisely, the temperature of an ideal gas T ~ E is proportional to the average kinetic energy of its molecules. The faster they move the higher the temperature. At absolute zero temperature T = 0 K all motions would cease.

Figure 4: Animation of molecular motions in an ideal gas. From en.wikipedia.org.

The lower panel in Fig. (3) shows blackbody curves for temperatures representative of the sun and Earth. Due to Earth’s lower temperature the peak in the radiation occurs at longer wavelengths around 10 μm in the infrared part of the spectrum. The sun’s radiation peaks around 0.5 μm in the visible part of the spectrum, but it also emits radiation at ultra-violet and near infrared wavelengths. Sunlight at the top-of-the-atmosphere is almost perfectly described by a blackbody curve (Fig. 5). Some solar radiation is absorbed by gases in the atmosphere but most is transmitted.

Figure 5. Solar radiation spectra for the incident sunlight at the top-of-the-atmosphere (yellow), at sea level (red), and a blackbody curve (grey). From en.wikipedia.org.

b) The Greenhouse Effect

Absorption by water vapor in the infrared and by ozone (O₃) in the ultraviolet and scattering of light remove 25-30% of solar radiation before it hits the surface (Fig. 6). For Earth’s radiation, on the other hand, total absorption is with 70-85% much larger. The most important absorbers in the infrared are water vapor and CO₂ whereas oxygen/ozone, methane, and nitrous oxide absorb smaller amounts. Gases that absorb infrared radiation are called greenhouse gases. There is only a relatively narrow window around 10 μm through which Earth’s atmosphere allows radiation to pass without much absorption. Thus, Earth’s atmosphere is mostly transparent to solar radiation, whereas it is mostly opaque to terrestrial radiation.

Figure 6: Radiation transmitted and absorbed by the cloud-free atmosphere. The left part of the figure shows the solar radiation and the right part shows Earth’s radiation. The blackbody curve at 5525 K (red curve in the top panel) represents the incident (downgoing) solar radiation at the top-of-the-atmosphere. The red filled area is the radiation transmitted through the atmosphere. The difference between the two (the white area between the red curve and the red area) is the amount absorbed by the atmosphere. For Earth’s radiation blackbody curves are shown for three temperatures (210, 260, and 310 K) and represent upgoing radiation from the surface. This is a key figure. From commons.wikimedia.org

Why is it that only certain gases in the atmosphere absorb infrared radiation? After all there is much more nitrogen (N₂) and oxygen (O₂) gas in the atmosphere than water vapor and CO₂ (Fig. 7). However, nitrogen and oxygen gas both consist of two atoms of the same element. Therefore, they do not have an electric dipole moment, which is critical for the interaction with electromagnetic radiation. Gas molecules that consist of different elements like water or CO₂, on the other hand, do have dipole moments and can interact with electromagnetic radiation. Since CO₂ is a linear and symmetric molecule it does not have a permanent dipole moment. However, during certain vibrational modes (Fig. 7) it attains a dipole moment and can absorb and emit infrared radiation. Detailed spectroscopic measurements of absorption coefficients show thousands of individual peaks in the spectra for water vapor and CO₂ caused by the interaction of vibrational with rotational modes and broadening of lines by collisions (e.g. Pierrehumbert, 2011). These data are used by detailed, line-by-line radiative transfer models to simulate atmospheric transmission, absorption, and emission of radiation at individual wavelengths.

Figure 7:

Left: Composition of the dry atmosphere. Water vapor, which is not included in the image, varies widely but on average makes up about 1 % of the troposphere.

Top right: Vibrational modes of CO₂. The black circles in the center represent the carbon atom, which carries a positive charge, whereas the oxygen atoms (white) carry negative charges. The asymmetric stretch mode (b) and the bend mode (c) lead to an electrical dipole moment, whereas the symmetrical stretch (a) does not. Modes (b) and (c) correspond to absorption peaks around 4 and 15 μm, respectively (Fig. 6).

Bottom right: Vibrational modes of H₂O. The red balls in the center represent the negatively charged oxygen atom, whereas the white balls represent the positively charged hydrogen atoms. Due to its angle, it has a permanent dipole moment and various modes of vibration and rotation.

Absorption (emission) of radiation by the atmosphere tends to increase (decrease) its temperature. At equilibrium the atmosphere will emit just as much energy as it absorbs, but it will emit radiation in all directions, half of which goes downward and increases the heat flux to the surface. This additional heat flux from the atmosphere warms the surface. This is the greenhouse effect.

An atmosphere in which only radiative heat fluxes are considered and that was perfectly transparent in the visible and perfectly absorbing in the infrared would result in a much warmer surface temperature than our current Earth (see Perfect Greenhouse Model box below). It can also be easily shown that adding more absorbing layers would further increase surface temperatures to T_s = (n + 1)^1/4T₁, where T₁ = 255 K is the temperature of the top-most of n layers. For two layers T_s = 335 K and the intermediate atmospheric layer’s temperature is T₂ = 303 K. This could be called the ‘Super Greenhouse Model’. Thus, even though no infrared radiation from the surface can escape to space already with one perfectly absorbing layer, adding more absorbing layers further increases surface temperatures because it insulates the surface further from the top, which will always be at 255 K. In atmospheric sciences, this process is called increasing the optical thickness of the atmosphere.

Box 3: Earth’s Energy Balance Model 2 (Perfect Greenhouse)

Since Earth’s atmosphere absorbs most terrestrial radiation emitted from the surface, we may want to modify our ‘Bare Rock’ Energy Balance Model by adding a perfectly absorbing atmosphere. As in the ‘Bare Rock’ model the energy balance at the top-of-the-atmosphere gives us the emission temperature of the planet, which we now interpret as the atmospheric temperature T_a = 255 K. We now have an additional equation for the atmospheric energy balance. At equilibrium, the total emitted terrestrial radiation from the atmosphere (two times ETR_a = σT_a⁴ since one ETR_a goes downward and one goes upward) must equal the absorbed radiation coming from the surface (ETR_s = σT_s⁴). This gives us a surface temperature of T_s = 2^1/4T_a = 303 K, which is too warm compared with the real world.

Figure B3.1: As Fig. B2.1 but for the ‘Perfect Greenhouse’ model.

c) Earth’s Energy Budget

In contrast to the ‘Perfect Greenhouse’ model, Earth’s atmosphere does absorb some solar radiation, it does transmit some infrared radiation, and, importantly, it is heated by non-radiative fluxes from the surface (Fig. 8). In fact, if only radiative fluxes (solar and terrestrial) are considered, surface temperatures turn out to be much warmer than they currently are and upper tropospheric temperatures are too cold (Manabe and Strickler, 1964). However, warming of the surface by absorbed solar and terrestrial radiation causes the air near the surface to warm and rise, causing convection. Convective motions cause both sensible and latent heat transfer from the surface to higher levels in the atmosphere. Most of this non-radiative heat transfer is in the form of latent heat. Evaporation cools the surface, whereas condensation warms the atmosphere aloft. Thus, the energy and water cycles on Earth are coupled.

Figure 8: Earth’s energy budget estimated from modern observations and models. Adapted from Trenberth et al. (2009).

The downward terrestrial radiation from the atmosphere is the largest input of heat to the surface. In fact, it is more than twice as large as the absorbed solar radiation. This illustrates the important effect of greenhouse gases and clouds on the surface energy budget. The greenhouse effect is like a blanket that keeps us warm at night by reducing the heat loss. Similarly, the glass of a greenhouse keeps temperatures from dropping at night.

Clouds are almost perfect absorbers and emitters of infrared radiation. Therefore, cloudy nights are usually warmer than clear-sky nights. The important effect of water vapor on the greenhouse effect can be experienced by camping in the desert. Night-time temperatures there often get very cold due to the reduced greenhouse effect in the dry, clear desert air.

d) Radiative Forcings, Feedback Processes, and Climate Sensitivity

We’ve seen how adding greenhouse gases to the atmosphere increases its optical thickness and further insulates the surface from the top, which will lead to warming of the surface. But how much will it warm for a given increase in CO₂ or another greenhouse gas? To answer this question and because we also want to consider other drivers of climate change we introduce the concepts of radiative forcing and feedbacks. These concepts are a way to separate different mechanisms that result in climate change. Radiative forcing is the initial response of radiative fluxes at the top-of-the-atmosphere. It can be defined as the change in the radiative balance at the top-of-the-atmosphere (the tropopause) for a given change in one specific process that affects those fluxes with everything else held constant. Examples for such a process are changes in greenhouse gas concentrations, aerosols, or solar irradiance.

A change in the radiative balance at the top-of-the-atmosphere will cause warming if the forcing is positive (more absorbed solar radiation or less emitted terrestrial radiation), and it will cause cooling if the forcing is negative (less absorbed solar or more emitted terrestrial to space). The amount of the resulting warming or cooling will not only depend on the strength of the forcing but also on feedback processes within the climate system. A climate feedback is a process that amplifies (positive feedback) or dampens (negative) the initial temperature response to a given forcing. E.g. as a response to increasing CO₂ concentrations surface temperatures will warm, which will cause more evaporation and increased water vapor in the atmosphere. Since water vapor is also a greenhouse gas, this will lead to additional warming. Thus, the water vapor feedback is positive. The warming or cooling resulting from one specific forcing and all feedback processes is called climate sensitivity. Let’s discuss some of the known radiative forcings and feedback processes in more detail.

Radiative Forcings

Detailed radiative transfer models can be used to calculate the radiative forcing for changes in atmospheric greenhouse gas concentrations. As shown in Fig. (9) for CO₂, the forcing turns out to depend logarithmically on its concentration (Ramaswamy et al., 2001)

(2)  

where C is the CO₂ concentration and C₀ is the CO₂ concentration of a reference state (e.g. the pre-industrial).

Figure 9: Radiative forcing (ΔF) in watts per square meter as a function of the atmospheric CO₂ concentration (C) relative to a reference value (C₀ ) according to eq. (2; black thick line). The black straight lines indicate the reference state C = C₀ (ΔF = 0). The green and red dashed lines indicate the current (2016) state relative to the pre-industrial C/C₀ = 400 ppm / 280 ppm = 1.4 (ΔF = 1.9 Wm^-2) and that for a doubling of CO₂ (ΔF_2x = 3.7 Wm^-2) respectively.

This means that the radiative effect of adding a certain amount of CO₂ to the atmosphere will be smaller the more CO₂ is already in the atmosphere. The reason for this is the saturation of peaks in the absorption spectrum (Fig. 6). E.g. in the center of the peak at 15 mm all radiation from the surface is already fully absorbed. Increasing CO₂ further only broadens the width of the peak.

Figure 10: Top: Atmospheric methane concentrations as a function of time. Top: Recent air measurements from Mauna Loa.

Bottom: Ice core, firn, and air measurements from Antarctica. Note that most methane sources are in the northern hemisphere, which leads to higher concentrations there compared with the southern hemisphere.

Methane (CH₄) is produced naturally in wetlands and by various human activities such as in the energy industry, in rice paddies, and by agriculture (e.g. cows). It is removed by chemical reaction with OH radicals and has a lifetime of about 10 years. Anthropogenic activities have increased atmospheric methane concentrations since the industrial revolution by more than a factor of two, from around 700 ppb to more than 1600 ppb currently (Fig. 10). On a per-molecule basis methane is a much more potent greenhouse gas than CO₂, perhaps in part because its main absorption peak around 8 mm is less saturated than the one for CO₂ (Fig. 6). However, since methane concentrations are more than two orders of magnitude smaller than CO₂ concentrations, its radiative forcing since the industrial revolution is 0.5 Wm^-2, which is less than that for CO₂. As we will see below CO₂ also has a much longer lifetime than methane and therefore it can accumulate over long timescales. Indeed, while recent measurements indicate a slowdown of methane growth rates in the atmosphere, CO₂ increases at ever higher rates (Fig. 8 in Chapter 2).

Aerosols are small particles suspended in the air. Natural processes that deliver aerosols into the atmosphere are dust storms and volcanic eruptions. Burning of oil and coal by humans also releases aerosols into the atmosphere. Aerosols have two main effects on Earth’s radiative balance. They directly reflect sunlight back to space (direct effect). They also act as cloud condensation nuclei such that they can cause more or brighter clouds, which also reflect more solar radiation back to space. Thus, both the direct and indirect effects of increased aerosols lead to cooling of the surface. Therefore, aerosol forcing is negative.

Large explosive volcanic eruptions can lead to ash particles and gas such as sulfur dioxide (SO₂) ejected into the stratosphere, where they can be rapidly distributed over large areas (Fig. 11). In the stratosphere SO₂ is oxidized to form sulfuric acid aerosols. However, stratospheric aerosols eventually get mixed back into the troposphere and removed through precipitation or dry deposition. The lifetime of volcanic aerosols in the stratosphere is in the order of months to a few years. Estimates of the radiative forcing from volcanic eruptions depend on the eruption but varies from a few negative tenths of a watt per square meter to -3 or -4 Wm^-2 for the largest eruptions during the last 100 years (Fig. 12).

Figure 11: Effects of volcanic eruptions.

Top: Measurements of solar radiation transmitted at Hawaii’s Mauna Loa Observatory.

Center: Photograph of a rising Pinatubo ash plume.

Bottom: Photograph from Space Shuttle over South America taken on Aug. 8, 1991 showing the dispersion of the aerosols from the Pinatubo eruption in two layers in the stratosphere above the top of cumulonimbus clouds.

Anthropogenic aerosols are released from burning tropical forests and fossil fuels. The latter is the major component producing more sulfate aerosols currently than those naturally produced. Aerosol concentrations are higher in the northern hemisphere, where industrial activity is located. Radiative forcing estimates are uncertain but vary between about -0.5 to -1.5 Wm^-2 for both direct and indirect effects (Figs. 12, 13). Generally, estimates of aerosol forcings are more uncertain than those for greenhouse gases.

Solar irradiance varies with the 11-year sunspot cycle. Direct, satellite-based observations of total solar irradiance show variations of about 1 Wm^-2 between sunspot maxima and minima (Fig. 14). To estimate radiative forcing TSI needs to be divided by four, which results in about 0.25 Wm^-2. Longer-term estimates of TSI variations based on sunspot cycles indicate an increase from the Maunder Minimum (1645-1715) to the present by about 1 Wm^-2. The resulting forcing is again about 0.25 Wm^-2.

Comparisons of the different forcings indicate that long-term trends of the last 100 years or so are dominated by anthropogenic forcings. The negative forcings from increases in aerosols compensate somewhat the positive forcings from the increase in greenhouse gases. However, the net effect is still a positive forcing of about 2 Wm^-2. Volcanic forcings are episodic and the estimates of solar forcing are much smaller than those of anthropogenic forcings.

Figure 12: Radiative forcings as a function of time. From data.giss.nasa.gov.

Figure 13: Summary of radiative forcings. From IPCC (2013). Hatched bars denote low confidence and scientific understanding.

Figure 14: Total solar irradiance variations.

Top: measurements based on various satellites as a function of time.

Bottom: longer term reconstructions.

Feedback Processes

A feedback process is a modifier of climate change. It can be defined as a process that can amplify or dampen the response to the initial radiative forcing through a feedback loop. In a feedback loop the output of a process is used to modify the input (Fig. 15). By definition, a positive feedback amplifies and a negative feedback dampens the response. In our case, the input is the radiative forcing (ΔF) and the output is the global average temperature change (ΔT).

Imagine talking into a microphone. A positive feedback process works like the amplifier that makes your voice louder. It can lead to a runaway effect if no or only weak negative feedback processes are present. If you hold the microphone too close to the speaker, the runaway effect can result in a loud noise. Early in Earth’s history, between about 500 million and 1 billion years ago, Earth may have experienced a runaway effect into a completely ice and snow covered planet called ‘Snowball Earth’ caused by the ice-albedo feedback (see below). An example of a negative feedback process would be talking into a pillow. This makes your voice quieter. A negative feedback is stabilizing. It prevents a runaway effect. Both positive and negative feedback processes operate in the climate system. (Try to imagine talking into multiple pillows and microphones.) In the following we will discuss the most important ones.

Let’s assume we have an initial positive forcing (ΔF > 0) as illustrated in Fig. 15. As a response, temperatures in the troposphere will warm. Since the troposphere is well mixed, we can assume that the warming is uniform (ΔT_s = ΔT_a > 0). Thus, the upper troposphere will warm, which will lead to increased emitted terrestrial radiation (ΔETR_a > 0) to space. Increased heat loss opposes the forcing and leads to cooling. This is the Planck feedback, and it is negative. Equilibrium will be achieved if ΔETR_a = ΔF. Since ΔETR_a = ETR_a,f–ETR_a,i is the difference between the final ETR_a,f = σ(T_a + ΔT_a)⁴ and the initial ETR_a,i = 240 Wm^-2 as calculated above (e.g. Fig. B2.1), we can calculate the surface temperature change due to the forcing and the Planck feedback ΔT_pl = ΔT_a = [(ETR_a,i + ΔF)/σ]^1/4 – T_a. For a doubling of atmospheric CO₂  ΔF = 3.7 Wm^-2 this results in ΔT_pl = 1 K.

Thus, if only the Planck feedback was operating and everything else would be fixed, a doubling of CO₂ would result in a warming of about 1 K. However, warmer air and surface ocean temperatures will also lead to more evaporation. The amount of water vapor an air parcel can hold depends exponentially on its temperature. This relationship, which can be derived from classical thermodynamics, is called the Clausius-Clapeyron relation (Fig. 16). Since most of Earth is covered in oceans there is no lack of water available for evaporation. Therefore, it is likely that warmer air temperatures will lead to more water vapor in the atmosphere. Because water vapor is a strong greenhouse gas this will lead to an additional reduction in the amount of outgoing longwave radiation and therefore to more warming. Thus, the water vapor feedback is positive. If we assume again that the temperature change is uniform with height the troposphere will warm by an additional amount ΔT_wv due to the water vapor feedback (red line in Fig. 15).

Figure 16: The Clausius-Clapeyron relation describes the amount of water vapor (in g water per kg of moist air) that air at saturation can hold as a function of temperature. The water-holding capacity of air increases approximately exponentially with temperature such that a 1 degree C warming leads to a 7% increase in humidity. All points long the green line represent 100% relative humidity. The lower a point is below the green line the lower its relative humidity will be. E.g. a point half way between the green line and the zero line would have 50% relative humidity.

Increased amounts of water vapor in the atmosphere also imply increased vertical transport of water vapor and thus more latent heat release at higher altitudes where condensation occurs. This warms the air aloft ΔT_lr > 0. In contrast, at the surface increased evaporation leads to cooling ΔT_lr < 0. Thus, the lapse-rate, Γ = ΔT/Δz, which is the change in temperature with height in the atmosphere, is expected to decrease. Warming of the upper atmosphere will increase outgoing longwave radiation. Therefore, similarly to the Planck feedback, the lapse rate feedback is negative.

Since both the water vapor and the lapse rate feedback are caused by changes in the hydrologic cycle, they are coupled. This results in reduced uncertainties in climate models if the combined water vapor plus lapse rate feedback is considered rather than each feedback individually (Soden and Held, 2006).

Warming surface temperatures will also cause melting of snow and ice. This decreases the albedo and thus it increases the amount of absorbed solar radiation, which will lead to more warming. Thus, the ice-albedo feedback is positive. Our simple energy balance model 2 from above can be modified to include a temperature dependency of the albedo, which can exhibit a runaway transition to a snowball Earth and interesting hysteresis behavior. Hysteresis means that the state of a system does not only depend on its parameters but also on its history. Transitions between states can be rapid even if the forcing changes slowly.

Warming will also likely change clouds. However, no clearly understood mechanism has been identified so far that would make an unambiguous prediction how clouds would change in a warmer climate. Comprehensive climate models predict a large range of cloud feedbacks. Most of them are positive, but a negative feedback cannot be excluded at this point. The cloud feedback is the least well understood and the most uncertain element in climate models. It is also the source of the largest uncertainty for future climate projections.

Climate models can be used to quantify individual feedback parameters γ_i. They are calculated as the change in the radiative flux at the top-of-the-atmosphere ΔR_i divided by the change of the controlling variable Δx_i: γ_i = ΔR_i/Δx_i. E.g. to quantify the Planck feedback the controlling variable Δx_i = ΔT is atmospheric temperature. The atmospheric temperature is increased everywhere by ΔT = 1 K and then the radiative transfer model calculates ΔR at every grid point of the model, that is at all latitudes and longitudes, and then averages over the whole globe. This results in ΔR_pl and γ_pl = ΔR_pl/ΔT. All individual feedback parameters can be added to yield the total feedback γ = γ_pl + γ_wv + γ_lr + γ_ia + γ_cl. The total feedback has to be negative to avoid a runaway effect. The strongest, most precisely known feedback is the Planck feedback, which is about γ_pl = −3.2 Wm^-2K^-1.  Estimates for the other feedbacks are about γ_wv + γ_lr ≅ +1 Wm^-2K^-1 for the combined water vapor / lapse rate feedbacks, γ_ia = +0.3 Wm^-2K^-1 for ice-albedo feedback, and γ_cl = +0.8 Wm^-2K^-1 for the cloud feedback. This gives for the total feedback γ values from about −0.8 to about −1.6 Wm^-2. The total feedback parameter can be used to calculate the climate sensitivity.

Climate Sensitivity

The climate sensitivity ΔT_2× is usually defined as the global surface temperature change for a doubling of atmospheric CO₂ at equilibrium and it includes all fast feedbacks discussed above. Current best estimates are ΔT_2× ≅ 3 K, however it ranges from about 1.5 to about 4.5 K. This large uncertainty is mostly due to the large uncertainty of the cloud feedback. Sometimes the climate sensitivity S_C = −1/γ is reported in units of K/(Wm^-2). Since we know the forcing for a doubling of CO₂ ΔF_2× = 3.7 Wm^-2 quite well, one can be calculated from the other using S_C = ΔT_2×/ΔF_2×. For ΔT_2× ≅ 3 K, S_C ≅ 0.8 K/(Wm^-2), and γ ≅ 1.2 Wm^-2K^-1. Note that slow feedbacks associated with the growth and melting of ice sheets or changes in the carbon cycle are not included in these numbers. Since we would expect those feedbacks to be also positive we can expect an even higher climate sensitivity for longer timescales (hundredths to thousandths of years).

Our definitions of radiative forcings and feedbacks above are not clear cut. They are based on existing climate models and the processes included in them. For example changes in atmospheric CO₂ concentrations over long paleoclimate timescales can be thought of as a feedback rather than a forcing since the ultimate forcing of the ice age cycles are changes in the Earth’s orbital parameters and hence the seasonal distribution of solar radiation.

Measurements with modern instruments (the instrumental record) are available only for roughly the past century. This is insufficient to describe the full natural variability of the climate system, which makes attribution of observed changes difficult. We want to know if the changes observed in the recent past are unusual compared to pre-industrial climate variability. If they are it is more likely that they are anthropogenic, if not they could well be natural. Paleoclimate research is also important for a fundamental understanding of how the climate system works. Some paleoclimate changes, e.g. the ice age cycles, were much larger than those during the instrumental record. Thus, we can learn much from paleoclimate data about the impacts of large climate changes.

a) Methods

Paleoclimate research is able to extend the instrumental record back in time much further than the instrumental record and has delivered a fascinating history of past climate changes. Most paleoclimate evidence is indirect and based on proxies for climate variables. This evidence is less precise than measurements with modern instruments because of the additional uncertainty in the relation between the proxy and the climate variable. Examples for proxies are pollen (Fig. 1) found in lake sediments that can be used to reconstruct past vegetation cover, which in turn can be related to temperature and precipitation. Similarly, different species of planktic foraminifera prefer different temperatures. Some live in colder waters others prefer warmer waters. Their fossil shells accumulate in sediments, which can be retrieved with a coring device employed from a research vessel. Shells deeper in the sediment are older. If shells of cold-loving foraminfera are found at a site where currently warm-loving species live, it suggests that near surface temperatures in the past have been colder. Mathematical methods have been developed to quantify the temperature changes from the species composition. Other proxies are chemical such as the ratio of magnesium to calcium (Mg/Ca), which is related to temperature, or isotopes of oxygen or carbon in the calcium carbonate shells of foraminifera, which can be used to reconstruct temperature, salinity, ice volume and carbon cycling. Benthic foraminifera live on or in the ocean’s sediments and thus provide useful information on deep ocean properties. Here is an excellent interactive post about paleoclimate proxies.

Figure 1: Electron microscope pictures of fossil foraminifera (top, two planktic foraminifera on top and one benthic foraminifera on the bottom) and pollen (bottom).

Proxies are found in different archives such as tree-rings, ice-cores, corals, ocean or lake sediment cores that cover different time periods at a range of temporal resolutions (Fig. 2). The resolution of a record can be quantified as the time difference  Δ t = t ₂ – t ₁ between two adjacent samples t ₁ and t ₂ . The smaller  Δ t the higher the resolution. Written historical accounts can be used to reconstruct past climatic conditions at very high temporal resolution – some ancient documents contain daily weather entries – back to about 1,000 years, but there are only a limited number of such records available. Tree-rings, corals and speleothems (cave deposits such as stalactites and stalagmites) provide reconstructions at annual to decadal resolution ( Δ t ~ years to decades) back many thousands of years. Ice cores have typically decadal to centennial resolution going back almost a million years for Antarctica and about 100,000 years for Greenland. Ocean sediment cores cover millions of years in the past but usually at low temporal resolution of centennial to millennial timescales ( Δ t ~ 100s to 1,000s of years).

Figure 2: Layered paleoclimate archives. Varves are layered sea or lake sediments.

Several methods are used to date samples to construct chronologies of paleoclimate records. Tree-rings are annual layers, which can be counted. Patterns of thin and thick rings can be matched from one tree to another, older one (Fig. 3). This way a large number of trees can be used to create a long layer-counted chronology. Layer counting can also be used in other archives with annual layers such as ice cores or lake sediments. Most ocean sediments don’t have annual layers because of bioturbation, which is the mixing of sediments by worms and other organisms that live in the sediment. When organic material is present radiocarbon dating can be used to determine the age of a sample. Radiocarbon (¹⁴C) decays exponentially with a half-life of 5,730 years. Thus, the lower the ratio of radiocarbon to regular carbon (¹⁴C/¹²C) in a sample, the older it is. This ratio can be measured precisely with a mass spectrometer. However, this method can only be used until about 40,000 years before the present because older material has unmeasurably small amounts of ¹⁴C.

Figure 3: Long tree ring chronologies can be constructed by matching overlapping patterns of different trees.

b) The Last Two Millennia

Historical accounts such as pictures of the frozen Thames (Fig. 4) document a period of relatively cold conditions during the 16^th to 19^th centuries in Europe called the Little Ice Age. Conversely, relatively warm conditions during the 9^th to 13^th centuries, called the Medieval Warm Period, may have allowed Vikings to colonize Greenland and travel to North America.

Figure 4: Left: Picture of the frozen Thames from 1683-84 by Thomas Wyke. Right: Ruins of Hvalsey Church from the Greenland settlements of the Norse.

Two recent reconstructions of global temperatures, however, indicate that the Medieval Warm Period was not a global phenomenon (Fig. 5). These reconstructions also suggest that there was a long term cooling trend during the past 2,000 years that culminated in the Little Ice Age, which was terminated by a relatively rapid warming during the 20^th century. According to the PAGES 2k reconstruction global average temperature during the three decades from 1971 to 2000 was warmer than at any other 30-year period in the last 1,400 years. This suggests that the recent warming is unusual. The rate of change during the last ~100 years also seems to be unusually fast compared with the previous 2,000 years. The two independent reconstructions agree well in the cooling trend over the past 1,000 years, but the PAGES 2k reconstruction suggests slightly warmer conditions during the first millennium CE ( Common Era ). The Marcott et al. (2013) dataset is based mostly on lower resolution ocean sediment cores and is therefore smoothed compared to the higher resolution PAGES 2k dataset, which includes mostly land data such as pollen and tree rings.

Figure 5: Global multi-proxy temperature reconstructions from the PAGES 2k project based on 7 continental scale regional reconstructions (green) compared with an independent reconstruction that includes the whole Holocene (Marcott et al., 2013; blue with shaded error range; see also Fig. 7) and the instrumental record (red). The PAGES 2k reconstruction represents 30-year averages. It includes many more data than the lower resolution Marcott et al. (2013) reconstruction, particularly for the last 1,000 years. Thus the error range of the PAGES 2k reconstruction is presumably much smaller than that indicated by the blue shading. From RealClimate.

c) The Holocene

Fig. 6 shows the full Holocene (the last 10,000 years) reconstruction of global average temperatures from Marcott et al. (2013). It suggests that the long term cooling trend of the last 2,000 years is part of a longer trend that extends back in time to the middle Holocene around 4,000 BC. The early Holocene from around 8,000 BC to 4,000 BC was relatively warm, similarly to recent decades. (This is debated in the scientific community; a recent paper suggest that it wasn’t warmer during the early Holocene and that biases in proxies related to seasonality are to blame. If this is true, the current warming will be unprecedented for more than 10,000 years, perhaps more than 100,000 years or longer.) The rate of temperature change appears to be much smaller compared with the last 100 years, but the relatively low resolution of the reconstruction leads to smoothing and does not allow a fair comparison with the instrumental record on 100 year timescales.

Figure 6: Holocene global surface temperature reconstruction from Marcott et al. (2013, blue) with shaded error ranges together with the instrumental record (red) as a function of time in years CE. From RealClimate.

Now let’s have a look at CO₂. Is the observed increase in atmospheric CO₂ during the last 60 years unusual compared to the pre-industrial Holocene? Ice cores can be used to answer this question. When snow accumulates on an ice sheet it compresses to firn and later to ice due to the pressure of the overlaying snow (Fig. 7). During this compaction process small bubbles of air are trapped within the ice. In the lab the air can be extracted from the ice, e.g. by mechanically crushing the ice, and its CO₂ concentration, and other greenhouse gases, can be measured.

Figure 7: Ice cores have been drilled in different locations in Antarctica (top left) using drilling devices like the one depicted here (top center). Air gets trapped in the ice through compaction of snow and firn (top right). These air bubbles in the ice are visible by eye (bottom left) and in the microscope (bottom center). Sometimes dark ash layers are found in ice cores, which can help to date the ice (bottom right).

Ice cores from Greenland are not suitable for CO ₂ reconstructions because they are contaminated by impurities (e.g. dust) that can lead to CO ₂ production in the ice. However, Antarctic ice is so pure that it provides excellent records of past atmospheric CO ₂ concentrations. Different ice cores have been drilled in Antarctica (Fig. 7). The measurements from the youngest ice and firn match up very well with the direct measurements of modern air from Mauna Loa (Fig. 8). Also, the measurements from different ice cores agree with each other (different colored symbols in Fig. 8). This indicates that Antarctic ice cores faithfully record past atmospheric CO ₂ concentrations. The results show that atmospheric CO ₂ concentrations have been relatively constant between about 260 and 280 ppm during the Holocene (the last 10,000 years). It was only during the last 200 years that CO ₂ concentrations started to increase. Thus, we have answered the question posed above and conclude that the CO ₂ increase during the last 200 years is very unusual and has not happened before during the last 10,000 years. We also know that burning of fossil fuels has increased dramatically after the industrial revolution (1760-1840). In the carbon cycle chapter below, more evidence will be presented that demonstrates that the subsequently observed CO ₂ increase was indeed due to human activities such as the burning of fossil fuels.

Figure 8: Ice core CO₂ measurements of ancient air. The different colors indicate different ice cores. The inset zooms into the last 200 years and includes in red the modern air measurements from Mauna Loa (see Fig. 8 in Chapter 2). Note that the ice core measurements agree well with the modern data where they overlap. From IPCC (2007).

Other greenhouse gases have also been measured in air extracted from ice cores. Methane (CH₄) and nitrous oxide (N₂O) show a very similar behavior to CO₂, such that their concentrations were relatively constant throughout the Holocene around 700 ppb and 260 ppb, respectively, and increased dramatically during the last 200 years to values around 1,700 and 310 ppb, respectively (IPCC, 2007).

d) The Ice Ages

Fig. 6 already hints at a cold period before the Holocene. Indeed we now know that for a long time Earth had been in an ice age, or glacial state, before the current warm period of the Holocene begun. But it was only in the 19^th century that scientists realized that Earth has experienced ice ages on a global scale. This discovery was made by Louis Agassiz, a Swiss geologist, who hypothesized that not only Alpine glaciers were advanced but also large ice sheets moved south from northern Europe and America leaving glacial landforms behind (Fig. 9). For a fascinating and more detailed account of this discovery the reader is referred to Imbrie and Imbrie (1979).

Figure 9: Glacial Landforms. Top: Polished bedrock with striations indicate a glacier was moving over it. The glacier incorporates rocks into its base and by pushing them over the underlying bedrock creates grooves. This example is from Mount Rainier National Park. Bottom left: Moraines (this example is from Svalbard) are glacial deposits formed at the side (lateral moraines) or end (terminal moraines) of a moving glacier. Bottom right: Erratic boulders like this one from Scotland, many miles from a possible bedrock source, have been attributed by Louis Agassiz to the action of ice-age glaciers.

During the height of the last ice age, the Last Glacial Maximum (LGM) roughly 20,000 years ago, large additional ice sheets covered parts of North America and northern Europe (Fig. 10). The Laurentide Ice Sheet was more than 3 km thick and covered all of what is now Canada and part of the northern United States reaching as far south as New York City, Chicago, and Seattle. The Eurasian (or Fennoscandian) Ice Sheet covered all of Scandinavia, much of the British isles, the Baltic Sea, and surrounding land areas from northeastern Germany to northwestern Russia. Mountain glaciers also descended further down valleys and often into the low lands.

Figure 10: Reconstructions of ice sheets (contour lines show 500 m elevation differences) and surface temperature differences from modern (color scale in K) for the Last Glacial Maximum. From PAGES news.

Because so much more water was locked up as ice on land, sea level was 120 m lower during the LGM than it is today. Imagine your favorite beach of today. There was no water there at the LGM. Explore with NOAA’s interactive bathymetry viewer how much further it would have been to the water during the LGM at your favorite beach.

The LGM is a well-studied time period in paleoclimate research, and we have a wealth of data available. Ice cores show lower concentrations of atmospheric greenhouse gases such as CO₂ (180 ppm vs 280 ppm during the late pre-anthropogenic Holocene; Fig. 11) and methane. Vegetation reconstructions show that forests were replaced by tundra and grasslands over large parts of the mid- to high latitudes (Prentice et al., 2011). We also know from ice and ocean sediment cores that the air was dustier. Temperature proxies show colder temperatures almost everywhere (Fig. 10). However, temperature changes were not the same everywhere. Temperature changes over large parts of the tropical and subtropical oceans were rather small. Globally-averaged sea surface temperatures have been estimated to be only 2°C cooler than the present (MARGO, 2009). Land areas in the tropics experienced moderate cooling of about 3°C (Bartlein et al., 2011). The largest cooling of more than 8°C occurred over land at mid-to-high latitudes and over Antarctica (Fig. 11). Globally averaged surface air temperature has been estimated to be 4°C colder during the LGM (Annan and Hargreaves, 2013). More recent, yet unpublished studies suggest 5°C indicating some uncertainty in these estimates. These authors also suggest that on average the cooling over land was 3 times larger than over the oceans. The land-sea contrast and polar amplification are similar to what we’ve seen in observed warming over the past century (Fig. 2 in Chapter 2). This suggests that those are robust properties of the climate system.

Box 1: Oxygen Isotopes

Isotopes are variations of the same element with a different number of neutrons, which leads to a different mass (Fig. B1). Since different isotopes of the same element have the same number of electrons (yellow circles in Fig. B1) they react chemically identically or very similar.

Figure B1: Oxygen’s most common (99.8%) isotope oxygen-16 (¹⁶O) has 8 protons (red) and 8 neutrons (blue) such that its mass is 16 atomic units. Oxygen-18 (¹⁸O) has two additional neutrons, which makes it (18 – 16)/16 = 12.5% heavier than ¹⁶O. It is also much rarer (0.2%) than ¹⁶O. From Montessori Muddle.

Water molecules (H₂O) with ¹⁸O are (20 – 18)/18 = 11% heavier than those with ¹⁶O. The mass of a molecule affects how likely it will participate in a phase change such as evaporation or condensation. Water molecules at a certain temperature in the water phase have a distribution of kinetic energy . Some are a little faster, others are a little slower. Only the fastest will be able to leave the water phase and make it to the vapor phase (air). (Here is a nice youtube video explaining this in a little bit more detail.) Because the mass of a heavy water molecule is larger, its velocity, on average, must be smaller in order to have the same kinetic energy. Therefore, the heavier isotopes will remain in the liquid phase more often than the lighter isotopes. This process is called fractionation. It leads to an accumulation of heavy water isotopes in the ocean and relatively more light water isotopes in the air.

Here is an analogy. Imagine a number of black and white soccer balls are lined up at the center line of a soccer field. The black balls are slightly heavier than the white balls. Now a player will shoot the balls, one after another, alternatively black and white, towards the goal. When he/she is done you count the balls that made it across the goal line. Will there be more black or white balls? Yes, indeed, more white balls, because they are lighter and they fly farther due to larger velocities put in by the player who exerts about the same amount of energy for each shot. In this analogy the white balls are the light isotopes.

Isotopes are usually expressed as delta values such as , where R = ¹⁸O/¹⁶O is the heavy over light ratio of a sample, relative to that of a standard R_std. Fig. B2 illustrates how fractionation during evaporation and condensation affects the isotope values of water, vapor, and ice in the global hydrological cycle.

Figure B2: Typical δ¹⁸O values (in permil). Surface ocean water has δ¹⁸O values of around zero. Due to fractionation during evaporation less heavy isotopes make it into the air, which leads to negative delta values of around -10 ‰. Condensation prefers the heavy isotopes for reasons analogous to evaporation. In this example the first precipitation thus has a δ¹⁸O value of about -2 ‰, the remaining water vapor will be further depleted in ¹⁸O relative to ¹⁶O thus that its δ¹⁸O value is approximately -20 ‰. Any subsequent precipitation event further depletes ¹⁸O. This process is known as Rayleigh distillation and leads to very low δ¹⁸O values of less than -30 ‰ for snow falling onto ice sheets. Thus, ice has very negative δ¹⁸O of between -30 and -55 ‰. Deep ocean values today are about +3 to +4 ‰. During the LGM, as more water was locked up in ice sheets, the remaining ocean water became heavier in δ¹⁸O by about 2 ‰. We know this because foraminifera build their calcium carbonate (CaCO₃) shells using the surrounding sea water. Thus they incorporate the oxygen isotopic composition of the water into their shells which are preserved in the sediments and can be measured in the lab.

We conclude that paleoclimate data from the LGM show that Earth was dramatically different from today, with large ice sheets, low sea level, and different vegetation. These changes happened even though the global average temperatures changed only by 4-5°C. This is comparable to changes projected for some future scenarios.

Geologic evidence such as that shown in Fig. 9 is abundant only for the last major glaciation because each glacial advance erases evidence from previous glaciations. However, because of our friends, the foraminifera, we know many details of previous glaciations. How can that be? Foraminifera live in the ocean. Well, as explained in the box, the δ¹⁸O of sea water records the amount of ice volume and thus sea level. Since foraminifera record the δ¹⁸O of sea water in their shells, we can amazingly reconstruct past ice volume from tiny shells found in mud on the ocean floor.

Fig. 11 shows that there were about 9 glacial-interglacial cycles during the past 800,000 years. Most of the time sea level was lower than today, during some of the glacial maxima by more than 120 m. Ice core records show that glacial periods were always associated with low atmospheric CO₂ concentrations and low temperatures in Antarctica. CO₂ concentrations varied between about 180 ppm during glacial maxima and 280 ppm during interglacials. The correlation between these completely independent datasets, one from Antarctic ice cores, the other from deep sea foraminifera, is astounding. It demonstrates that climate and the carbon cycle are tightly interlinked. High CO₂ concentrations are always associated with warm temperatures, high sea level, and low ice volume. This indicates the importance of atmospheric CO₂ concentrations for climate but it also suggests that climate impacts the carbon cycle and causes changes in CO₂.

Figure 11: Glacial-interglacial Cycles. Top: Antarctic temperature anomaly (relative to the most recent pre-industrial time) estimated from deuterium ratios measured in the ice (Jouzel et al., 2007). Deuterium (D) is the heavy hydrogen isotope ²H. In H₂O it works similar to the heavy oxygen isotope as a local temperature proxy. Center: Atmospheric CO₂ concentrations from ice cores (Lüthi et al., 2008). Bottom: Global sea level changes (ΔSL = [δ¹⁸O – 3.2 ‰]×[-120 m / 1.69 ‰]) estimated from oxygen isotopes (δ¹⁸O) measured in benthic foraminifera from deep-sea sediments (Lisiecki and Raymo, 2004). This is a key figure.

Closer inspection of leads and lags shows that during the last deglaciation CO₂ and Antarctic temperature lead global temperature, which suggests that CO₂ is an important forcing mechanism for the warming (Shakun et al., 2012). But we also know that climate affects the carbon cycle. For example, CO₂ is more soluble in colder water, which causes the ice age ocean to take up additional carbon from the atmosphere. Another likely reason for the lower glacial CO₂ concentrations in the atmosphere is iron fertilization. The colder glacial atmosphere was also dustier. Dust contains iron and thus iron delivery to currently iron limited regions such as the Southern Ocean was increased during the ice age. This intensified phytoplankton growth and the biological pump, which describes processes of sinking and sequestering of carbon in the deep ocean. Our recent research indicates that about half (~45 ppm) of the glacial-interglacial CO₂ variations can be explained by temperature and another 25-35 ppm by iron fertilization (Khatiwala et al., 2019). However, this topic is not settled and subject to ongoing research. More about how climate can affect CO₂ will be discussed in the carbon cycle chapter. For now let’s just conclude that climate and the carbon cycle are tightly linked.

But what causes glacial-interglacial cycles? They are caused by changes in Earth’s orbit around the sun, which affects the seasonal distribution of incoming solar radiation. This theory was first proposed in 1938 by Serbian astronomer Milutin Milankovich, who calculated variations in Earth’s orbital parameters and linked those to past ice ages. Earth’s orbit can be described by three parameters (Fig. 12). The eccentricity E is the deviation from a perfectly circular orbit. Earth’s orbit is a slight ellipse although it is close to circular. E varies on ~100,000 year cycles between zero and 0.06. The tilt T, or obliquity, describes the angle between Earth’s axis of rotation and the ecliptic, which is the plane of Earth’s orbit around the sun. It is currently T = 23.5° but it varies between 24.5° and 22.5° on a 40,000 year cycle. Precession P is the wobble of Earth’s axis, like the wobble of a top. Currently we’re closest to the sun in January, which corresponds to the axis tilted towards the left in Fig. 12. P varies on a 23,000 year cycle and is strongly modulated by eccentricity. These variations are caused by gravitational forces from the other planets, particularly Jupiter and Saturn.

Figure 12: Milankovitch Cycles. Top: Earth’s orbit around the sun is determined by eccentricity (E), tilt (T) or obliquity, and precession (P). Bottom: Variation of Earth’s orbital parameters through time. Negative numbers towards the left show the past and positive numbers show the future.

Milankovich’s theory is that summer insolation in the northern hemisphere controls the waxing and waning of the ice sheets. When summer insolation is high, all snow from the previous winter will melt away. When summer insolation is low, some snow survives and during the next winter more snow accumulates. In this way, an ice sheet can grow. The northern hemisphere is important because that is where the major land masses are, where additional ice sheets can grow. The Antarctic ice sheet did not fundamentally change during the ice ages, although it grew somewhat bigger during the ice ages and shrunk a bit during interglacials and the Patagonian ice sheet was much smaller than those in the north.

The Milankovich theory was essentially confirmed by spectral analysis of deep sea δ¹⁸O data, which shows all the predicted periodicities (Hays et al., 1976). However, exactly when and why ice ages start and end remain active topics of research.

While the Milankovich theory explains the cyclicity and timing of glacial-interglacial cycles it does not explain their amplitudes (how much global average temperatures have changed). Simulations with gobal climate models show that the amplitude of glacial-interglacial temperature changes can only be reproduced if CO₂ changes are accounted for (e.g. Shakun et al., 2012). This leads us to conclude that CO₂ changes are an important (feedback) factor in determining glacial-interglacial temperature changes although the ultimate cause of the ice age cycles are Earth’s orbital cycles.