Nearly all energy that drives Earth’s surface climate begins as solar radiation. Its wavelength determines how it interacts with gases and surfaces, while Earth’s shape, rotation, and axial tilt determine where and when that energy arrives.

What the atmosphere contains

Dry air near the surface is dominated by permanent gases: about 78% nitrogen ($\mathrm{N_2}$), 21% oxygen ($\mathrm{O_2}$), and just under 1% argon. Their proportions vary little compared with variable gases such as water vapour, carbon dioxide, methane, and ozone.

A concentration in parts per million is a molecular ratio. A carbon-dioxide concentration of $408\ \mathrm{ppm}$ means about 408 carbon-dioxide molecules per million molecules of dry air. A trace gas can strongly affect climate or chemistry despite its small concentration because its molecular structure determines which wavelengths it absorbs and emits.

Important radiatively active gases include:

• water vapour ($\mathrm{H_2O}$), the most abundant greenhouse gas and highly variable in space and time;
• carbon dioxide ($\mathrm{CO_2}$) and methane ($\mathrm{CH_4}$), which absorb thermal infrared radiation;
• ozone ($\mathrm{O_3}$), which absorbs ultraviolet radiation in the stratosphere and infrared at other wavelengths;
• nitrous oxide ($\mathrm{N_2O}$) and manufactured halocarbons, which also absorb infrared radiation.

A greenhouse gas absorbs and emits thermal infrared radiation. It does not simply reflect heat back like a mirror.

Wavelength, frequency, and energy

Electromagnetic radiation travels as waves. Wavelength $\lambda$ and frequency $\nu$ are related by

$$c=\lambda\nu,$$

where $c$ is the speed of light. The energy of one photon is

$$E=h\nu=\frac{hc}{\lambda}.$$

Shorter wavelengths therefore have higher frequency and higher photon energy. From shortest to longest wavelength, the main bands are gamma rays, X-rays, ultraviolet, visible light, infrared, microwaves, and radio waves. Visible light spans roughly $0.4$ to $0.7\ \mu\mathrm{m}$; this is also approximately the range used in photosynthesis.

Climate science often groups radiation by source:

• Solar shortwave: mainly $0.15$–$3\ \mu\mathrm{m}$, including visible and near-infrared radiation.
• Terrestrial longwave: mainly $3$–$100\ \mu\mathrm{m}$, emitted by the cooler Earth–atmosphere system.

These categories do not describe the two ends of the entire electromagnetic spectrum. They separate the largely distinct emission bands of the Sun and Earth.

Hotter objects emit more and peak at shorter wavelengths

Every object above absolute zero emits electromagnetic radiation. Two laws explain the Sun–Earth contrast.

Wien’s displacement law

$$\lambda_{\max}=\frac{2898\ \mu\mathrm{m\,K}}{T},$$

where $T$ must be in kelvins. Convert from Celsius with

$$T(\mathrm{K})=T(^{\circ}\mathrm{C})+273.15.$$

For the Sun at about $5780\ \mathrm{K}$,

$$\lambda_{\max}\approx\frac{2898}{5780}\approx0.50\ \mu\mathrm{m}.$$

For Earth at about $288\ \mathrm{K}$,

$$\lambda_{\max}\approx\frac{2898}{288}\approx10\ \mu\mathrm{m}.$$

The hot Sun peaks in visible shortwave radiation; the cooler Earth peaks in thermal infrared.

Stefan–Boltzmann law

An ideal blackbody emits

$$E=\sigma T^4,$$

where $\sigma=5.670374\times10^{-8}\ \mathrm{W\,m^{-2}\,K^{-4}}$. The fourth power makes emission sensitive to absolute temperature. Raising a surface from $288$ to $289\ \mathrm{K}$ changes its emission by

$$\left(\frac{289}{288}\right)^4-1\approx0.014,$$

or about 1.4%. Wien’s law tells us where the spectrum peaks; Stefan–Boltzmann tells us the total emitted flux.

What happens when radiation meets matter

At any wavelength, incident radiation can be:

• transmitted through the material;
• reflected from it;
• absorbed and converted into internal energy;
• scattered, meaning redirected by molecules or particles;
• refracted, meaning bent as its speed changes between media.

For a given wavelength,

$$\tau_\lambda+\alpha_\lambda+a_\lambda=1,$$

where $\tau$ is transmissivity, $\alpha$ reflectivity, and $a$ absorptivity. These properties depend on wavelength. The atmosphere transmits much visible light, ozone absorbs much ultraviolet radiation, and greenhouse gases absorb selected thermal-infrared bands. Short visible wavelengths are scattered more efficiently by small air molecules, which helps make the daytime sky blue.

From the solar constant to the global mean

The solar constant is the incoming solar flux on a surface perpendicular to the rays at Earth’s mean orbital distance. It is about

$$S_0\approx1361\ \mathrm{W\,m^{-2}}.$$

Earth intercepts sunlight over a circular disk of area $\pi R^2$, but that energy is spread over a spherical area $4\pi R^2$. The global, day–night average at the top of the atmosphere is therefore

$$\overline{S}=S_0\frac{\pi R^2}{4\pi R^2}=\frac{S_0}{4}\approx340\ \mathrm{W\,m^{-2}}.$$

The night side explains only half of the factor of four. Curvature across the sunlit hemisphere supplies the other half. The result is a top-of-atmosphere average, not the amount absorbed at the ground.

Earth’s orbit and axial orientation also vary over tens of thousands of years. Eccentricity, obliquity, and precession redistribute insolation by latitude and season, but they do not explain the recent rapid warming and they are not the cause of the annual seasons.

Solar altitude and day length make the seasons

Earth’s axis is tilted about $23.5^\circ$ from the line perpendicular to its orbital plane. It keeps nearly the same orientation in space as Earth revolves around the Sun. This produces two linked seasonal effects:

1. the Sun climbs higher above the horizon in the summer hemisphere, concentrating the beam over less surface area;
2. daylight lasts longer, extending the time over which energy arrives.

Earth–Sun distance is not the cause. Earth is closest to the Sun in early January, during Northern Hemisphere winter, and farthest in early July.

The subsolar point is where the Sun is directly overhead. Its latitude is the solar declination $\delta$, which moves from $23.5^\circ\mathrm{N}$ at the June solstice to $23.5^\circ\mathrm{S}$ at the December solstice. At local solar noon,

$$h=90^\circ-\left|\phi-\delta\right|,$$

where $h$ is solar altitude and $\phi$ is latitude.

At an equinox, $\delta=0^\circ$ and day length is close to 12 hours everywhere. At the June solstice, the Arctic Circle has about 24 hours of daylight while the Antarctic Circle has about 24 hours of darkness; December reverses the pattern. Near the equator, day length and noon solar altitude vary comparatively little through the year.

A low solar altitude weakens surface intensity for two reasons. The same beam is spread across a larger horizontal area, and it passes through a longer atmospheric path, allowing more absorption and scattering. Warm summers therefore come from both a stronger beam and longer days.

Atmospheric layers follow the temperature profile

Atmospheric layers are defined by how temperature changes with height, not by equal altitude bands.

The troposphere is deeper over the warm tropics and shallower near the poles. Its average environmental lapse rate is about

$$6.5\,^{\circ}\mathrm{C\,km^{-1}}.$$

This is an average observed profile, not a fixed law. The real atmosphere can cool faster or slower with height, or warm upward in a temperature inversion. It is also distinct from the dry and moist adiabatic lapse rates followed by moving air parcels.

Ozone creates the stratospheric inversion

Stratospheric ozone absorbs ultraviolet radiation and converts part of that energy into molecular motion. Heating is strongest above the bottom of the stratosphere, so temperature rises with altitude there. The ozonosphere is an ozone-rich region within the stratosphere, not a separate temperature-defined layer.

The Antarctic ozone hole is severe seasonal thinning, not an empty opening. Manufactured chlorine- and bromine-containing compounds accelerated ozone destruction. The Montreal Protocol reduced the production of major ozone-depleting substances, allowing gradual recovery. That history shows how atmospheric composition, radiation, chemistry, and international policy can be linked in one environmental system.

The ionosphere is also not a separate stacked layer. It is a broad region of charged particles that overlaps the upper mesosphere and thermosphere. Charged solar particles exciting atmospheric gases within this region produce auroras. Temperatures can be very high because individual particles carry large kinetic energy, even though the air is too sparse to contain much heat per unit volume.