[27] CORE 6: Energy Balance

What is the solar constant (total solar irradiance) at Earth's distance from the Sun?

About 1361 W/m² (sunlight on a surface facing the Sun at the top of the atmosphere).

What is the global, annual average incoming solar flux at the top of Earth's atmosphere (TOA)?

About 340 W/m², which is S/4: the solar constant (1361 W/m²) divided by 4.

Why is Earth's average incoming sunlight S/4 instead of S?

Earth intercepts sunlight over a disk of area πR² but spreads it over its whole spherical surface, 4πR².

What is emissivity (ε) of a surface?

How efficiently it emits compared with a blackbody at the same temperature (0 to 1), so emission = εσT⁴.

By the Stefan-Boltzmann law, how much more power does a blackbody emit if its absolute temperature doubles?

16 times as much (2⁴), because emission grows with the fourth power of T.

Why is incoming solar radiation called shortwave and Earth's outgoing radiation longwave?

By Wien's law the hot Sun (~5800 K) peaks near 0.5 µm (visible), while cool Earth (~255-288 K) peaks near 10 µm (thermal IR).

How does the solar flux a planet receives depend on its distance d from its star?

It falls as 1/d² (inverse-square law), so doubling the distance cuts the flux to one quarter.

What does CERES measure?

Top-of-atmosphere reflected shortwave flux, outgoing longwave flux and their net, i.e., Earth's radiation budget.

Albedo is the fraction of what?

Of incoming solar (shortwave) radiation that a surface or planet reflects, from 0 (absorbs all) to 1 (reflects all).

What is Earth's average planetary albedo (the whole planet's reflectivity, also called Bond albedo)?

About 0.30 (measured values are about 0.29-0.30).

Rank by albedo, lowest to highest: fresh snow, asphalt, grassland, desert sand, dense forest.

Asphalt < dense forest < grassland < desert sand < fresh snow.

Why is the albedo of fresh snow so much higher than that of open ocean?

Snow's many tiny ice grains scatter visible light back out with little absorption, while water absorbs most light that enters it.

Which surface change gives the largest increase in absorbed sunlight: sea ice melting to open ocean, desert turning to grassland, or forest turning to cropland?

Sea ice melting to open ocean (albedo ~0.6 drops to ~0.06).

MODIS and CERES both relate to albedo. What is the difference?

MODIS maps surface albedo at about 500 m, while CERES measures top-of-atmosphere (planetary) reflected shortwave at coarse (~20 km) resolution.

What is the basic idea behind the planetary equilibrium temperature equation?

Energy absorbed from the star equals energy emitted by the planet, so the temperature stays steady.

In T = [S(1 - α)/(4σ)]^(1/4), what does the quantity S(1 - α)/4 represent?

The global average absorbed solar flux (about 238-240 W/m² for Earth).

What is Earth's effective (equilibrium, no-greenhouse) temperature?

About 255 K (-18 °C), using S = 1361 W/m² and α = 0.30.

Earth's mean surface (288 K) is about 33 K warmer than its effective temperature (255 K). What causes the difference?

The natural greenhouse effect: greenhouse gases absorb outgoing IR and re-emit part of it back down (the simple model has no atmosphere).

How does equilibrium temperature scale with the solar constant S?

T ∝ S^(1/4), so a 10% brighter Sun raises T by only about 2.4% (1.1^(1/4) ≈ 1.024).

Venus's effective temperature is only ~230 K, but its surface is ~737 K. What explains the difference?

A very strong greenhouse effect from its thick (~92 bar), ~96% CO2 atmosphere, left behind by a past runaway greenhouse.

What is the runaway greenhouse effect, and where did it likely occur?

Warming adds water vapor, which causes more warming, until the oceans evaporate and the planet cannot shed heat. It likely happened on Venus.

What does Kirchhoff's law say about absorptivity and emissivity?

At a given wavelength they are equal: a good absorber is a good emitter.

How do greenhouse gases warm a planet's surface?

They let most sunlight through but absorb outgoing thermal IR and re-emit it in all directions, partly back down to the surface.

What is the atmospheric lapse rate?

The rate at which temperature falls with height in the troposphere, about 6.5 °C per km on average.

From about what altitude does Earth's infrared escape to space on average, and what is the temperature there?

About 5-6 km up (mid-troposphere), where the air is about 255 K, Earth's effective temperature.

If Earth effectively radiates to space from ~5-6 km at 255 K, why is the surface warmer?

Temperature increases going down toward the surface (about 6.5 K per km), so the surface is about 33 K warmer than the emitting level.

How does adding CO2 reduce Earth's outgoing longwave radiation, in terms of emission height?

More CO2 makes the air more opaque to IR, so the level from which IR escapes rises into colder air, and colder air emits less (σT⁴).

What happens to outgoing longwave radiation right after CO2 increases, and then over time?

It drops at first, so Earth absorbs more than it emits, then recovers as the planet warms until it again equals absorbed sunlight.

Albedo and greenhouse gases both change the energy balance. Which side of the budget does each act on?

Albedo acts on incoming shortwave (how much is reflected), and greenhouse gases act on outgoing longwave (how much is trapped).

What are the assumptions of the one-layer (single-layer) greenhouse model?

One atmospheric layer that is transparent to sunlight, absorbs all surface longwave, and emits σT⁴ both up and down.

What is the global average outgoing longwave radiation (OLR, the thermal IR Earth emits to space)?

About 239-240 W/m², balancing the ~240 W/m² of absorbed sunlight.

What is back radiation in the energy budget, and how large is it?

Longwave emitted downward by greenhouse gases and clouds to the surface, about 333-340 W/m².

What is the latent heat flux in the surface energy budget?

Energy carried up by evaporation and transpiration, released in the atmosphere when the vapor condenses.

What is the sensible heat flux?

Heat carried from the surface to the air by conduction and convection (thermals) because the surface is warmer than the air.

How do you compute the net top-of-atmosphere flux from CERES incoming, reflected and outgoing values, and what does a positive result mean?

Net = incoming solar - reflected shortwave - OLR. Positive means the planet is gaining energy (warming).

What is Earth's current energy imbalance (absorbed minus emitted at the top of the atmosphere)?

About +1 W/m² in recent years, tiny next to the 340 W/m² of incoming sunlight but enough to keep warming the planet.

Where does about 90% of the excess heat from Earth's energy imbalance go?

Into the ocean.

Which two observing systems together measure Earth's energy imbalance?

CERES (top-of-atmosphere radiation) and Argo robotic floats (ocean heat content down to 2000 m).

Which region has the largest annual net radiation surplus at the top of the atmosphere?

The tropics (the poles have a deficit).

What is the primary cause of the latitude variation in top-of-atmosphere net radiation?

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

On a CERES OLR map, how do deep convective (thunderstorm) clouds and low stratus (flat, sheet-like) clouds compare?

Deep convective clouds show very low OLR (cold tops), while low stratus shows OLR close to clear sky (warm tops).

Radiative forcing is a change in what?

In Earth's net radiative energy balance (incoming minus outgoing flux) caused by an imposed change such as greenhouse gases, aerosols or the Sun.

An IPCC (UN climate science panel) bar chart shows W/m² values for CO2, CH4, N2O, aerosols and land use since 1750. What quantity does it show?

Radiative forcing by each driver (positive bars warm, negative bars cool).

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

A forcing is an externally imposed change in the energy balance, while a feedback is a response to temperature change that amplifies or damps it.

What is the radiative forcing from a doubling of CO2?

About 3.7 W/m² (5.35 × ln 2).

Why does CO2 forcing depend on the logarithm of concentration?

The center of CO2's 15 µm band is already saturated (opaque), so extra CO2 absorbs mainly in the weaker band wings.

What is the sign of the radiative forcing from sulfate aerosols, and how does it work?

Negative (cooling): they scatter sunlight to space, raising albedo, and brighten clouds.

What is the sign of the radiative forcing from black carbon (soot)?

Positive (warming): it absorbs sunlight and darkens snow and ice.

What is the net effect of low, thick clouds (stratus, stratocumulus) on climate?

Net cooling (a negative radiative effect).

Why do low, thick clouds cool the climate?

They reflect much sunlight (high albedo), but their warm tops emit almost as much IR as the surface, so they trap little.

What is the net effect of high, thin clouds (cirrus) on climate?

Net warming (a positive radiative effect).

Why do high, thin cirrus clouds warm the climate?

They let most sunlight through but absorb surface IR and emit to space from very cold tops, so they trap heat.

What is the global net cloud radiative effect measured by CERES?

About -20 W/m²: clouds cool Earth overall.

How is the cloud radiative effect computed from CERES data?

All-sky top-of-atmosphere net flux minus clear-sky net flux.

What two properties control a cloud's albedo?

Its optical thickness (amount of liquid water or ice) and the number and size of its droplets.

What is the aerosol direct effect?

Aerosols scatter sunlight back to space (cooling) or absorb it (warming the air layer).

What is the aerosol indirect effect?

Aerosols act as cloud condensation nuclei (CCN, the particles water condenses on), changing cloud brightness and lifetime.

(Twomey effect, step 1) More aerosols enter air that is forming a cloud. What happens to the number of cloud droplets?

It increases, because there are more cloud condensation nuclei for water to condense on.

(Twomey effect, step 2) A cloud has more droplets but the same total amount of water. How do the droplets change?

They are smaller.

(Twomey effect, step 3) A cloud now has many small droplets instead of fewer large ones. How does its albedo change?

It increases (more total droplet surface scatters more sunlight).

(Twomey effect, step 4) Clouds become brighter from added aerosols. What is the climate result?

More sunlight is reflected to space: cooling (negative forcing).

What is the Albrecht (cloud lifetime) aerosol effect?

Smaller droplets from added aerosols suppress drizzle, so clouds last longer and cover more area (more cooling).

An aerosol's single-scattering albedo is near 1. What does that mean for its climate effect?

It mostly scatters sunlight, so it cools (like sulfate). Low values mean an absorbing, warming aerosol (like black carbon).

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

Lowers it (it darkens the bright clouds), a warming effect.

How should you structure a written answer explaining a feedback loop?

As a chain: initial change, then process, then result, and state whether the result reinforces (positive) or opposes (negative) the initial change.

(Planck feedback, step 1) Earth's surface and atmosphere warm. How does the infrared they emit to space change?

It increases with the fourth power of temperature (σT⁴).

(Planck feedback, step 2) Warming makes Earth emit more infrared to space. How does that affect further warming?

More energy is lost, which limits further warming: a negative feedback.

(Water vapor feedback, step 1) Earth warms. What happens to the amount of water vapor in the air?

It increases, about 7% per °C (Clausius-Clapeyron: warmer air can hold more vapor).

(Water vapor feedback, step 2) Warming adds water vapor to the air. What does the extra vapor do?

It absorbs more outgoing longwave, adding greenhouse warming, which adds more vapor: a positive feedback.

What is the largest positive feedback in climate models?

The water vapor feedback (about +1.8 W/m² per K), which roughly doubles the warming from CO2 alone.

(Ice-albedo feedback, step 1) Global temperatures rise. What happens to snow and sea ice?

They melt and shrink.

(Ice-albedo feedback, step 2) Snow and sea ice shrink. What replaces them, and how does albedo change?

Darker ocean (~0.06) or land replaces bright ice (~0.5-0.9), so albedo drops.

(Ice-albedo feedback, step 3) Albedo drops as ice is replaced by dark ocean. What happens to absorbed sunlight?

More sunlight is absorbed.

(Ice-albedo feedback, step 4) More sunlight is absorbed where the ice melted. What follows?

More warming, which melts more ice, so the loop repeats.

What is the overall sign of the cloud feedback, and how certain is it?

Likely positive (about +0.4 W/m² per K), but it is the most uncertain feedback.

How do changes in low and high clouds with warming give a positive cloud feedback?

Fewer low clouds (less reflection) and higher high clouds with colder tops (more trapping) both add warming.

What is equilibrium climate sensitivity (ECS)?

The eventual global surface warming from doubled CO2 once the climate, with its fast feedbacks, reaches a new equilibrium.

What shape does an exponential growth curve have, and what is special about its rate?

It steepens steadily: the rate of increase is proportional to the current value.

What shape does a logarithmic curve have?

It keeps rising but flattens: the slope keeps shrinking.

How do you tell linear, piecewise-linear, exponential and logarithmic curves apart on a graph?

Straight line, straight segments with kinks, a curve that keeps steepening, and a curve that keeps flattening.

What does an exponential approach to equilibrium look like on a temperature graph?

Fast change at first, then slower and slower, leveling off toward the equilibrium value.

What does Newton's law of cooling say?

An object's rate of temperature change is proportional to its temperature difference from its surroundings.

What is the time constant τ of an exponential approach, and how does it relate to the rate constant k?

τ = 1/k, the e-folding time: the time for the remaining difference to shrink by a factor of e.

In a simple energy balance model, how does a larger heat capacity change the approach to equilibrium?

It lengthens the time constant, so temperature approaches the same final value more slowly.

What is committed warming?

Extra warming that still happens after forcing stops rising, because the ocean has not yet caught up to equilibrium.

(CO2 to new equilibrium, step 1) CO2 rises. What is the first change in Earth's radiation?

Outgoing longwave drops, because emission to space now comes from higher, colder levels.

(CO2 to new equilibrium, step 2) Outgoing longwave drops while absorbed sunlight is unchanged. What appears at the top of the atmosphere?

A positive energy imbalance (positive radiative forcing).

(CO2 to new equilibrium, step 4) The surface and atmosphere warm. What happens to outgoing longwave and to the imbalance?

Outgoing longwave rises (σT⁴), shrinking the imbalance, so warming slows.

(CO2 to new equilibrium, step 5) When does warming stop after a one-time step increase in CO2?

When outgoing longwave again equals absorbed sunlight: a new, warmer equilibrium, approached roughly exponentially.

To find the average rate of change of a gas from a record with a seasonal wiggle (like the Keeling curve of CO2 at Mauna Loa), which line should you read?

The deseasonalized trend line: (end value - start value) / (number of years).

Where is average methane concentration higher, Barrow (Alaska) or the South Pole, and why?

Barrow, by roughly 100 ppb or more, because most methane sources (wetlands, fossil fuels, agriculture) are in the Northern Hemisphere.

If warming melts ice and Earth settles at a new equilibrium with lower albedo, how does global average OLR compare with today?

Higher, because more sunlight is absorbed and at equilibrium OLR must equal absorbed sunlight.

On a CERES OLR map of a much warmer world, where would OLR rise most, and why?

Over the Arctic and other high latitudes, which warm fastest (Arctic amplification, sea ice loss), and a warmer surface emits more longwave (σT⁴).

What does InSAR (interferometric synthetic aperture radar) measure?

Ground deformation as small as millimeters (subsidence, earthquake slip, volcano swelling, glacier flow), from the phase difference between two SAR images of the same spot.

Why can InSAR detect ground motion far smaller than its pixel size?

It measures the phase of the returned wave, not just its timing. Each full color fringe means about half a wavelength of motion toward or away from the radar (a few cm for C-band).

What causes speckle, the grainy salt-and-pepper look of radar images?

Constructive and destructive interference of echoes from the many scatterers inside each pixel.

Why do radar images show speckle while ordinary sunlit optical images do not?

Radar sends coherent waves (one frequency, fixed phase), so echoes inside a pixel interfere randomly. Sunlight is incoherent, so its reflections simply add.

Converting top-of-atmosphere (TOA) reflectance to surface reflectance removes what?

The atmosphere's effects: scattering (haze, path radiance) and absorption by gases, leaving what the ground itself reflects.

Over dark targets such as water, why is TOA reflectance in the blue band higher than the true surface reflectance?

Rayleigh scattering by air adds path radiance (scattered light that never touched the surface) on the way to the senso