CORE 6: Energy Balance

At radiative equilibrium Earth emits as much energy as it absorbs. Does it emit at the same wavelengths it absorbs?

No. It absorbs mostly shortwave sunlight (peak near 0.5 µm) and emits longwave infrared (peak near 10 µm), because Earth is far colder than the Sun and Wien's law shifts its peak to longer wavelengths.

Why is the average sunlight arriving at the top of Earth's atmosphere about S/4 (about 340 W/m²) rather than the full solar constant S?

Earth catches sunlight over a flat disk of area πR² but spreads it over a sphere of area 4πR². Put another way, half the planet is in night and the day side meets the light at a slant.

By the Stefan-Boltzmann law, what happens to a blackbody's emitted power if its absolute temperature doubles?

It rises 16 times, because emission grows with the fourth power of temperature in kelvin. This steep growth is why a warming planet sheds heat so much faster.

What does it mean that Earth's planetary albedo is about 0.3?

About 30 percent of incoming sunlight is reflected straight back to space by clouds, air, aerosols and bright surfaces, and the other 70 percent is absorbed and heats the planet. Clouds supply about two-thirds of that reflection.

Rank open ocean, forest, desert sand and fresh snow from lowest to highest albedo.

Open ocean, then forest, then desert sand, then fresh snow. Darker surfaces absorb more light, so water and dark tree canopies are lowest and bright sand and snow are highest.

Why does fresh snow reflect so much more sunlight than open ocean?

Snow is a heap of tiny ice grains, and light bounces from grain to grain and back out before it is absorbed. Water instead absorbs most of the light that enters it, so the ocean looks dark.

Asphalt and concrete sit in the same sunny parking lot. Which has the higher albedo, and which has the higher brightness temperature?

Concrete has the higher albedo because it is lighter colored. Asphalt is darker, so it absorbs more sunlight, gets hotter and shows the higher brightness temperature in thermal infrared.

A satellite pixel or a region is part snow and part bare soil. How do you find its overall albedo?

Take the area-weighted average, multiplying each surface's albedo by the fraction of area it covers and adding them up. A mix of surfaces reflects in proportion to how much of each is present.

Which common surface change increases absorbed sunlight the most: sea ice melting to open ocean, forest cut to cropland, or grassland turning to desert?

Sea ice melting to open ocean, because albedo falls from about 0.6 to about 0.06. Forest clearing and desertification actually raise albedo slightly.

How do the climate effects of losing sea ice and losing land ice differ?

Sea ice loss mainly lowers albedo, letting the ocean absorb more sunlight. Land ice loss mainly raises sea level, because sea ice is already floating and displaces its own weight of water.

The simple equilibrium temperature model sets absorbed sunlight S(1 − α)/4 equal to emitted σT⁴. What temperature does it give for Earth, and how does that compare with the real surface?

About 255 K (−18 °C), while the real surface averages about 288 K (15 °C). The model has no atmosphere, so the 33 K gap is the natural greenhouse effect.

Why does a 10 percent brighter Sun raise a planet's equilibrium temperature by only about 2.4 percent?

Temperature depends on the fourth root of absorbed sunlight, because emission rises as T⁴. A planet only has to warm a little to radiate a lot more, so temperature responds weakly to changes in input.

Venus's simple equilibrium temperature is only about 230 K, yet its surface is about 737 K. What explains the gap?

A runaway greenhouse effect, a positive feedback in which warming added greenhouse gas until the oceans boiled off, left a thick, mostly CO2 atmosphere that traps outgoing infrared. Its bright clouds give it a high albedo, so the heat comes from trapping, not extra sunlight.

What makes a gas a greenhouse gas, in terms of shortwave and longwave radiation?

It lets most incoming shortwave sunlight pass through but absorbs outgoing longwave infrared and re-emits it in all directions, partly back down toward the surface. Like a blanket, it adds no heat but slows its escape.

Earth's infrared escapes to space mostly from about 5 to 6 km up, where the air is about 255 K. Why is the surface warmer than that?

The air warms by about 6.5 °C per km going down (the lapse rate), so the surface ends up about 33 K warmer than the emitting level.

Adding CO2 makes the air more opaque to infrared. How does that reduce outgoing longwave radiation (OLR)?

The level from which infrared escapes rises into higher, colder air, and colder air emits less (σT⁴). OLR drops below absorbed sunlight, so Earth warms until OLR recovers.

In the one-layer greenhouse model, a layer transparent to sunlight absorbs all surface infrared. Why is the surface warmer than with no atmosphere?

The layer emits from both faces, sending as much energy down as it sends to space, so the surface receives sunlight plus back radiation. It must warm (to about 303 K) to emit twice what escapes, and each added layer warms it further.

On NASA's energy budget diagram the surface emits about 398 W/m² of longwave, more than all the sunlight arriving at the top of the atmosphere. How is that possible?

Greenhouse gases and clouds send about 340 W/m² of back radiation down to the surface, so the surface receives far more from the sky than from the Sun. It must emit a lot to stay in balance.

A CERES map shows 340 W/m² incoming, 100 W/m² reflected shortwave and 230 W/m² outgoing longwave. What is the net flux, and what does it mean?

About +10 W/m², found as incoming minus reflected minus OLR. Positive means the planet is gaining energy and will warm.

True or false: Earth's energy budget is exactly balanced at every moment.

False. Balance is only reached on average and over time. Right now CERES and ocean floats show Earth absorbing slightly more than it emits, an imbalance that roughly doubled to about 1 W/m² since the mid-2000s.

What does the CERES instrument (on Terra, Aqua, Suomi NPP and NOAA-20) measure?

Earth's radiation budget at the top of the atmosphere, meaning reflected sunlight (shortwave), outgoing longwave radiation and their net. It uses broadband channels to capture total energy rather than narrow bands for imaging.

How can you tell whether a CERES map shows reflected shortwave or outgoing longwave?

Look at the cloudy tropics and ice sheets. On a shortwave map they are bright (high reflection), while on a longwave map they are low because their cold cloud tops and cold ice emit little heat. Clear warm deserts are high on the longwave map.

On a CERES OLR map, the lowest values fall into three kinds of places. What are they, and why?

Polar ice sheets, high mountains like Tibet and rainy tropical regions like the Amazon, Congo and Indonesia. The first two are cold surfaces, and the tropics have tall thunderstorm clouds whose very cold tops emit little longwave.

On a CERES OLR map, why are clear deserts and subtropical oceans so high?

They are warm, and with few clouds their emission escapes straight to space. Emission rises steeply with temperature (σT⁴), so hot clear surfaces give the most OLR.

Why does the Greenland ice sheet have a negative net radiation even in summer?

Its high albedo reflects most incoming sunlight, so absorbed shortwave is smaller than the longwave it still emits. Bright ice loses more energy than it gains.

What is the main cause of the latitude pattern in top-of-atmosphere net radiation (energy surplus in the tropics, deficit at the poles)?

Earth's spherical shape. Sunlight hits the tropics nearly overhead but the poles at a low angle, spreading the same beam over more area.

In a GOES thermal infrared image, what do very cold brightness temperatures usually show?

High cloud tops from deep convection such as thunderstorms. Cloud tops get colder the higher they reach, so cold spots in thermal infrared mark tall storms.

What is radiative forcing, and what does a positive value mean?

It is a change in Earth's net energy balance (incoming minus outgoing, in W/m²) caused by something imposed on the climate, like greenhouse gases, aerosols, the Sun or a volcano. Positive forcing means Earth takes in more than it loses, so it warms.

An IPCC style bar chart shows W/m² bars since 1750 for CO2, methane, other gases, aerosols, land use and the Sun. How do you read it?

Each bar is a radiative forcing, with positive bars warming and negative bars cooling. CO2 is the largest warming term, aerosols are the main cooling term with the widest error bar, and the Sun's bar is tiny.

Why does CO2 forcing grow with the logarithm of concentration rather than in a straight line?

The center of CO2's main absorption band is already saturated, so extra CO2 can only absorb in the weaker band edges. Each doubling adds about the same forcing, about 3.7 W/m².

Why is a molecule of a CFC (chlorofluorocarbon) a far stronger greenhouse gas than a molecule of CO2?

CFCs absorb inside the 8 to 12 µm atmospheric window, where little else absorbs, and they are far from saturated. Each new CFC molecule blocks heat that would otherwise escape.

Water vapor causes about half of Earth's greenhouse effect. Why is it treated as a feedback, not a driver, of recent warming?

Its amount is set by temperature, since warmer air holds about 7 percent more vapor per °C and excess rains out within about 9 days. CO2 lasts for centuries and is added independently, so it drives the change and vapor amplifies it.

What is the difference between a climate forcing and a climate feedback?

A forcing is an outside push on the energy balance, like burning fuel adding CO2. A feedback is the climate's response to the temperature change that then amplifies or damps it, like sea ice melting because the planet warmed.

What does a positive climate feedback mean, and does positive mean good?

Positive means the response pushes in the same direction as the original change, amplifying it. It does not mean good, and positive feedbacks amplify cooling too, which is how small orbital changes grew into ice ages.

Explain the ice-albedo feedback as a chain and give its sign.

Warming melts snow and sea ice, exposing darker ocean or land, which lowers albedo, so more sunlight is absorbed, causing more warming and more melting. It reinforces the starting change, so it is positive.

Explain the water vapor feedback as a chain and give its sign.

Warming increases evaporation and lets air hold more water vapor, which absorbs more outgoing longwave, which adds warming and more vapor. It is the largest positive feedback.

What is the Planck feedback, and why is it the climate's main stabilizer?

A warmer Earth emits more infrared to space (σT⁴), which removes energy and limits further warming. It is negative and the strongest feedback, so it keeps the climate from running away.

Classify each as a positive or negative feedback: permafrost thaw, warmer oceans dissolving less CO2, CO2 fertilization of plants, and faster silicate rock weathering.

Permafrost thaw and less CO2 dissolving in warm water are positive, because both put more greenhouse gas in the air. CO2 fertilization and silicate weathering are negative, because both pull CO2 out of the air.

What is the Bjerknes feedback in the Pacific, and what is its sign?

Weaker trade winds let warm water spread east, which weakens the east-west temperature contrast that drives the winds, which weakens them further. It is a positive feedback that grows El Niño events.

In Daisyworld, a planet covered with white and black daisies warms. How do the daisies respond, and what kind of feedback is it?

White daisies spread and black daisies shrink, because white daisies stay cooler in the heat. The planet's albedo rises and pushes temperature back down, which is a negative feedback.

Why has the Arctic warmed about three to four times faster than the global average?

Mainly the sea ice-albedo feedback, because melting ice exposes dark ocean that absorbs more sunlight, helped by the Arctic lapse rate feedback that keeps warming trapped near the surface.

Why do low, thick clouds such as stratocumulus cool the climate?

They are bright, so they reflect a lot of sunlight, but their tops are warm, so they emit almost as much infrared as the surface and trap little. Ocean stratocumulus decks are the biggest cloud coolers.

Why do high, thin cirrus clouds and contrails warm the climate?

They let most sunlight through but absorb the surface's infrared and emit to space from very cold tops, so they trap heat. Their weak reflection loses to strong trapping.

Why do clouds tend to keep days cooler but nights warmer?

By day their main effect is reflecting sunlight, which cools the surface. At night there is no sunlight to reflect, so their only effect is trapping infrared and sending some back down, which warms.

CERES compares all-sky and clear-sky fluxes to find the cloud radiative effect. Do clouds warm or cool Earth overall, and where is the exception?

Overall they cool, by about 20 W/m², because reflected sunlight outweighs trapped heat. Over bright ice sheets and deserts they add little reflection but still trap heat, so there they warm.

How does a large volcanic eruption cool the climate, and for how long?

It injects SO2 into the stratosphere, which forms reflective sulfate droplets that raise albedo. Surface cooling of about 0.5 °C lasts 1 to 3 years until the droplets settle out.

How do sulfate aerosols and black carbon (soot) differ in their direct effect on climate?

Sulfate mostly scatters sunlight back to space, so it cools. Black carbon absorbs sunlight, heating the air and darkening snow it lands on, so it warms.

What is the Twomey effect, the way aerosols brighten clouds?

Aerosols act as seeds for droplets, so more aerosols make more droplets. With the same water, the droplets are smaller and have more total surface, so the cloud reflects more sunlight and cools the climate.

A dark smoke layer sits above a bright low cloud deck. Does it raise or lower the scene's albedo?

It lowers it, because the absorbing smoke darkens the bright cloud below, which warms. A scattering aerosol over dark ocean does the opposite and brightens the scene, so the sign depends on aerosol type and height.

Global SO2 emissions have fallen since the mid-2000s. Did this cool or warm the planet?

It added warming. Fewer sulfate aerosols mean fewer reflective particles and less cloud brightening, so more sunlight reaches the surface.

How do warming from greenhouse gases and warming from a brighter Sun differ in the stratosphere?

Greenhouse gases warm the lower atmosphere but cool the stratosphere, because more CO2 up there radiates more heat to space. A brighter Sun would warm both layers, so a cooling stratosphere points to greenhouse gases.

What is equilibrium climate sensitivity (ECS), and why is the transient response smaller?

ECS is the eventual warming from doubled CO2 once fast feedbacks have acted, about 3 °C. The transient response is smaller, about 1.8 °C, because the ocean is still absorbing heat when CO2 reaches double.

CO2 jumps once and then stays fixed. Describe how Earth's temperature responds over time.

OLR drops, creating a positive imbalance, and the surface warms. As it warms OLR rises (σT⁴) and the imbalance shrinks, so warming slows and levels off at a new equilibrium, an exponential approach.

In a simple energy balance model, how does a larger heat capacity (such as a deeper ocean layer) change the warming curve?

It lengthens the time constant, so the temperature reaches the same final value more slowly. Like a wide tub under the same faucet, it takes longer to fill.

What is committed warming?

Warming that keeps happening after forcing stops rising, because the ocean's large heat capacity delays the surface reaching equilibrium. Earth is still catching up to forcing already in place.

On a graph of temperature against time, how do you tell linear, piecewise-linear, exponential growth, exponential approach and logarithmic curves apart?

Linear is one straight line, piecewise-linear is straight segments joined at kinks, exponential growth keeps steepening, exponential approach is steep then flattens toward a final value, and logarithmic keeps rising but flattens without a set limit.

What does Newton's law of cooling say, and why does a hot desert cool fastest right after sunset?

The rate of temperature change is proportional to the difference from the surroundings. Just after sunset the gap is largest, so cooling is fastest, then it slows as the surface nears the surrounding temperature.

In an exponential approach, what does the time constant τ tell you?

It is the time for the remaining gap to shrink by a factor of e. After one τ the object is about 63 percent of the way to its final value, and after three τ about 95 percent.

On a graph of cumulative heat gained by Earth over time, what does the slope show, and what does an upward bend mean?

The slope is the heating rate, which equals Earth's energy imbalance. An upward bend means the heating rate is increasing, so the imbalance is growing