The poles are cold because of solar geometry, seasonal darkness, and radiation—not because they are meaningfully farther from the Sun.

Why distance is not the cause

Earth is about 149.6 million km from the Sun, while its radius is only 6,371 km. The equator is therefore only about 0.004% closer to the Sun than a pole.

Seasonal distance also points the wrong way for the Northern Hemisphere:

• Earth is closest to the Sun near 3 January at perihelion, during northern winter;
• Earth is farthest from the Sun in early July at aphelion, during northern summer.

The small distance change exists, but it does not explain polar temperature or the seasons.

Solar angle and day length

The same beam of sunlight is spread over a larger surface area when it arrives at a shallow angle. At 60° from overhead, the beam covers about twice the ground area it would cover when arriving vertically. A low-angle beam also travels through more atmosphere, increasing scattering and absorption before it reaches the surface.

Earth's axis is tilted 23.5°. The tilt changes both solar angle and day length through the year:

• at the equator, the noon Sun can be nearly overhead;
• at 45°N, the noon Sun reaches about 68° above the horizon near the June solstice;
• at the North Pole, the Sun never rises more than 23.5° above the horizon.

The Arctic Circle is at 66.5°N = 90° − 23.5°. Poleward of it, at least one day each year has no sunrise and at least one has no sunset.

At 80°N, polar night lasts roughly four months. Summer has continuous daylight, but the Sun remains low in the sky.

The June paradox

On 21 June, the North Pole receives more daily solar energy at the top of the atmosphere than the equator:

• North Pole: about 524 W/m² averaged over the day;
• equator: about 385 W/m².

Twenty-four hours of low-angle sunlight can exceed twelve hours of high-angle sunlight. The Arctic still remains near 0 °C in summer because much of the energy is reflected or used to melt ice rather than raise surface temperature.

The annual average reverses the June result. Over a full year, the poles receive about 40% of the solar energy received at the equator because winter darkness dominates the average.

Energy in, energy out

Every object with a temperature emits infrared radiation. The warmer it is, the more energy it emits. Greenhouse gases and clouds absorb some outgoing infrared radiation and emit part of it back toward the surface.

Without this atmospheric return, Earth's average surface temperature would be about −18 °C rather than about +15 °C.

Clouds affect both sides of the energy balance:

• they reflect incoming sunlight, which cools the surface;
• they return outgoing infrared radiation, which warms the surface.

During much of the Arctic year there is little or no sunlight to reflect, so the longwave warming effect often dominates. In a short part of midsummer, the shortwave cooling effect can dominate instead.

Poleward heat transport

Globally and over long times, absorbed solar energy must balance radiation to space. The balance does not hold at every latitude:

• the tropics absorb more energy than they emit;
• the poles emit more energy than they absorb.

The atmosphere and ocean continuously transport the tropical surplus toward the poles. The transport peaks near 35° latitude at roughly 5 petawatts.

The atmosphere carries most of the total through storms and weather systems. The ocean carries less overall but concentrates heat in currents, including warm Atlantic water entering the Barents Sea.

The surface energy balance

For one square metre of surface, five terms account for the energy crossing the boundary:

1. Net shortwave: sunlight received minus sunlight reflected;
2. Net longwave: infrared emitted upward minus infrared returned by the atmosphere;
3. Sensible heat: heat exchanged with moving air;
4. Latent heat: energy carried by evaporation or condensation;
5. Heat from below: energy conducted or mixed upward from the ocean or ground.

Five terms in the surface energy balance

• Mirror: raises reflection and reduces net shortwave absorption.
• Blanket: slows heat moving upward from the ocean.
• Cap: suppresses evaporation and latent heat loss.
• Buffer: separates the ocean from direct wind stress.

If incoming energy exceeds outgoing energy, the surface warms or melts. If outgoing energy exceeds incoming energy, it cools or freezes.

Four roles of sea ice

Sea ice changes the surface boundary in four main ways.

1. Mirror

Ice and snow reflect much more sunlight than open water, mainly changing net shortwave energy in summer. §3 compares the surface albedos and calculates the resulting absorbed energy.

2. Blanket

Sea ice insulates the relatively warm ocean from cold winter air. With a 30 °C temperature difference, the lecture comparison gives:

• 10 cm of new ice: about 600 W/m² of conductive heat loss;
• 2 m of ice: about 30 W/m².

As ice thickens, heat escapes more slowly, so new ice grows more slowly. This is a negative feedback on ice thickness.

3. Cap

A continuous ice cover suppresses evaporation, reducing latent heat loss and the supply of moisture to the atmosphere. Open leads can produce fog, sea smoke, and snow downwind because water is exposed again.

4. Buffer

Ice separates the ocean from direct wind stress. Wind moves the ice instead of directly stirring the upper ocean, helping the water beneath remain layered.

Melting requires latent heat

Melting ice at 0 °C requires about 334,000 J/kg without changing its temperature. Using an ice density of about 917 kg/m³, melting one vertical metre over one square metre requires

$$(334{,}000\ \text{J/kg})(917\ \text{kg/m}^3) \approx 3.06\times10^8\ \text{J/m}^2.$$

If the surface absorbs a net 100 W/m² for one day,

$$(100\ \text{J/s/m}^2)(86{,}400\ \text{s}) =8.64\times10^6\ \text{J/m}^2.$$

The melt depth is therefore

$$\frac{8.64\times10^6}{3.06\times10^8} \approx 0.028\ \text{m},$$

or about 2.8 cm.

While ice remains at the surface, added energy can go into phase change rather than raising temperature. This keeps the melting surface near 0 °C.

Snow strengthens both main thermal effects

Fresh snow is more reflective than bare ice and much less thermally conductive. Typical thermal conductivity values used in class are:

• snow: about 0.1–0.4 W m⁻¹ K⁻¹;
• sea ice: about 2.0–2.2 W m⁻¹ K⁻¹.

A thin snow layer can therefore reduce heat loss and slow ice growth substantially.

Main chain

1. Shallow solar angles, atmospheric path length, and winter darkness reduce annual polar solar input.
2. The poles run an energy deficit while the tropics run a surplus.
3. The atmosphere and ocean transport heat poleward.
4. At the surface, five fluxes determine warming, cooling, freezing, or melting.
5. Sea ice changes each exchange by acting as a mirror, blanket, cap, and mechanical buffer.