Climate Change: Evidence of Human Causes and Arguments for Emissions Reduction

Abstract

In a recent editorial, Raymond Spier expresses skepticism over claims that climate change is driven by human actions and that humanity should act to avoid climate change. This paper responds to this skepticism as part of a broader review of the science and ethics of climate change. While much remains uncertain about the climate, research indicates that observed temperature increases are human-driven. Although opinions vary regarding what should be done, prominent arguments against action are based on dubious factual and ethical positions. Thus, the skepticisms in the recent editorial are unwarranted. This does not diminish the general merits of skeptical intellectual inquiry.

Appendix: A Simple Climate Model

Climate science includes the use of mathematical and computational models in order to simulate the global climate system. These models are used to conduct computer-based experiments to explore the behavior of climate under different circumstances without needing to actually alter the physical atmosphere of Earth. The behavior of these models provides much insight about climate change and can also be used to rebut many points of climate skepticism. The following text describes a simple algebraic climate model that is based on the conservation of energy entering and leaving Earth. This model illustrates that greenhouse gases are necessary to warm the surface and thus rebuts a simple point of skepticism that would claim greenhouse gases are irrelevant to climate. Many more sophisticated points of skepticism can be rebutted with more sophisticated but qualitatively similar models, which means that this model is an effective starting point for understanding climate science.

To construct this model, we first consider only energy emitted from the sun and ignore atmospheric greenhouse gases. If we let R _E be the radius of Earth, then $\pi R_{E}^{2}$ is the cross-sectional area of Earth and $4\pi R_{E}^{2}$ is the area of Earth’s surface. We let S ₀ be the amount of solar energy reaching Earth per unit area and per unit time (technically known as the energy flux). We also let α be the fraction of incoming sunlight that gets reflected back to space, which means that $(1 - \alpha )$ is the fraction absorbed at the surface. The total amount of energy absorbed at the surface of Earth per unit time can therefore be written as $S_{0} (1 - \alpha )\pi R_{E}^{2}$. The surface of Earth also emits energy in the form of blackbody radiation that can be described in terms of energy per unit area per unit time as $\sigma T_{E}^{4}$, where σ = 5.67 × 10⁻⁸ J s⁻¹ m⁻² K⁻⁴ is the Stefan–Boltzmann constant and T _E is Earth’s surface temperature. This allows us to write $4\pi R_{E}^{2} \sigma T_{E}^{4}$ as the amount of energy per unit time emitted by the surface. In order to conserve total energy, the solar energy absorbed at the surface of Earth must equal the energy emitted by the surface. We can write this equation as

$$ S_{0} (1 - \alpha )\pi R_{E}^{2} = 4\pi R_{E}^{2} \sigma T_{E}^{4} , $$

(1)

where we use S ₀ = 1370 W m⁻² per day and α = 0.30 (i.e., 30% of incoming solar radiation is reflected back to space) as typical values for this period of Earth’s history. Solving Eq. 1 for T _E gives an equation for the surface temperature of Earth if the sun were the only energy source:

$$ T_{E} = \root{4}\of{{{{\frac{{S_{0} (1 - \alpha )}}{4\sigma }}}}}. $$

(2)

We can evaluate Eq. 2 using the values described above to find that T _E  = 255 K = − 18.15°C, which is below the freezing point of water. In other words, if the sun were the only source of energy (i.e., without greenhouse gases), the surface of Earth would be completely frozen and life as we know it could not exist.

Greenhouse gases are atmospheric particles that absorb some of the radiation coming from the surface and also emit energy downward to the ground and upward to space. We can extend our model to include greenhouse gases by representing the atmosphere as a layer above the surface that is transparent to sunlight but absorbs infrared radiation emitted by the surface. Let ε be the fraction of energy coming from the surface that is absorbed by the atmosphere (technically known as the absorptivity of the atmosphere) so that the energy per unit time absorbed by the atmosphere is $4\pi R_{E}^{2} \sigma T_{S}^{4} \varepsilon$. Here we have replaced the surface temperature by T _S to avoid confusion with T _E in Eq. 2. The atmosphere itself radiates at a blackbody with energy flux of $\sigma T_{A}^{4} ,$ where T _A is the temperature of the atmosphere. ε also represents the fraction of radiation that is emitted from an atmosphere (technically known as the emissivity of the atmosphere; the assumption that absorptivity equals emissivity is known as Kirchoff’s law of thermal radiation). This allows us to write the amount of energy per unit time emitted by the atmosphere as $4\pi R_{E}^{2} \sigma T_{A}^{4} \varepsilon$ both downward toward the surface and upward toward space. This term uses the same R _E as above because the radius of Earth and the radius of the atmosphere are nearly identical. In order to maintain conservation of energy, the energy absorbed by the atmosphere must equal the energy emitted by the atmosphere. In our model the atmosphere emits both upward and downward, i.e. in two directions, whereas the surface only emits in one direction. Therefore we can write this balance as

$$ 4\pi R_{E}^{2} \sigma T_{S}^{4} \varepsilon = 2\left( {4\pi R_{E}^{2} \sigma T_{A}^{4} \varepsilon } \right). $$

(3)

Solving Eq. 3 for T _s gives us:

$$ T_{S} = 2^{1/4} T_{A} . $$

(4)

This gives us a relationship between surface temperature and atmospheric temperature for our model. We can now consider the total energy budget at the surface due to the absorption of sunlight and atmospheric greenhouse radiation:

$$ S_{0} (1 - \alpha )\pi R_{E}^{2} + 4\pi R_{E}^{2} \sigma T_{A}^{4} \varepsilon = 4\pi R_{E}^{2} \sigma T_{S}^{4} . $$

(5)

Here the two terms on the left hand side of Eq. 5 respectively represent the amount of solar and greenhouse energy absorbed at the surface, while the term on the right hand side represents the emission of radiation from the surface of Earth. We can rearrange and simplify Eq. 5 as

$$ S_{0} (1 - \alpha ) = 4\sigma \left( {T_{S}^{4} - T_{A}^{4} \varepsilon } \right), $$

(6)

so that we can substitute the relationship from Eq. 4 and then solve for the surface temperature T _S to find

$$ T_{S} = \root{4}\of{{{{\frac{{S_{0} (1 - \alpha )}}{2\sigma (2 - \varepsilon )}}}}} $$

(7)

This equation for surface temperature depends on the emissivity (or absorptivity) of the atmosphere ε, which contrasts with the radiative equilibrium balance in Eq. 2 that neglects absorption by the atmosphere. The global mean annual surface temperature of Earth today is T _S  = 288 K = 14.85°C; this value can be calculated from either multi-annual global data sets or more sophisticated climate models. These present-day Earth conditions are described by Eq. 7 with a value of ε = 0.77 so that the magnitude of the greenhouse effect $\Updelta T_{g}$ in this model is $\Updelta T_{g} = T_{S} - T_{E} = 33{\text{ K}}$. In other words, the atmospheric greenhouse effect of Earth provides an additional thirty degrees of warming to the surface and prevents global glaciation.

This model treats all greenhouse gases identically, such that ε is proportional to the total amount of greenhouse absorbers. Under a global warming scenario, then, the model shows that surface warming should follow from an increase in atmospheric greenhouse gases because a greater value of ε corresponds to an increase in atmospheric absorption and acts to raise surface temperature in Eq. 7. Thus we see that greenhouse effect can be understood through the balance of energy absorbed and emitted by the climate system.