SCIENCE · INVESTIGATE AND EXPLAIN

Compare prescribed planetary albedos

Separate fixed-temperature energy differences from equilibrium comparisons and feedback claims.

Learning outcome: Calculate an albedo perturbation and explain why manually selected albedos do not simulate a temperature response.

Starting recap

Percentage-point change becomes a fractional difference in the reflection formula. An imposed input is not an endogenous response.

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Try

Changing albedo from 30% to 35% reduces absorption by 17.0125 W/m² at fixed solar input.

Open the experiment

Predict

Does manually changing albedo demonstrate a complete temperature–albedo feedback loop?

Your prediction and reason

Experiment

Keep temperature at 255 K while comparing 30% and 35% albedo. Record flux changes, then compare the two equilibrium temperatures separately.

Balance absorbed sunlight and thermal radiation

Worked teaching model · synthetic values · Fixed Sun-normal irradiance 1361 W/m²; global mean incoming sunlight is one quarter of this. Albedo is the whole-planet reflected solar fraction. Outgoing thermal radiation is σT⁴ for an equivalent unit-emissivity emitter, with σ = 5.670374419 × 10⁻⁸ W m⁻² K⁻⁴. T is effective emitting temperature, not mean surface temperature. Albedo is prescribed independently of T. No heat capacity, time evolution, atmosphere/surface separation, greenhouse response or measured climate data is included.

Planetary albedo: 30 % Effective emitting temperature: 255 K

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Sunlight meets a disk of area πR²; the planet has surface area 4πR². Dividing total intercepted power by the whole surface area gives 1361/4 = 340.25 W/m². This is a global mean, not local noon sunlight. Reflected plus absorbed sunlight equals incoming sunlight; these are not three independent energy inputs.

Selected albedo and fixed 30% reference at the same emitting temperature
Quantity	Selected	30% reference
Planetary albedo	30%	30%
Global mean incoming solar flux	340.250 W/m²	340.250 W/m²
Reflected solar flux	102.075 W/m²	102.075 W/m²
Absorbed solar flux	238.175 W/m²	238.175 W/m²
Selected effective emitting temperature	255 K	255 K
Outgoing thermal flux	239.758 W/m²	239.758 W/m²
Signed net into modeled system	-1.583 W/m²	-1.583 W/m²
Continuous equilibrium effective temperature	254.578 K	254.578 K
Same equilibrium expressed in Celsius	-18.572 °C	-18.572 °C

Equilibrium shift relative to the 30% reference: 0.000 K. The equilibrium is solved continuously, while the temperature slider advances in 5 K steps. At 30% albedo, 255 K is close to—but not exactly—the 254.578 K balance point. A small displayed mismatch is not a measured planetary imbalance.

For albedo α (a fraction), absorbed flux = (1 − α)S/4 and equilibrium T = [(1 − α)S/(4σ)]^(1/4). Use kelvin in the fourth power; subtract 273.15 only afterward to report Celsius. Positive net means energy accumulation; negative net means energy loss. No heat capacity is supplied, so this model cannot give kelvin per year or a date when equilibrium is reached.

Effective emitting temperature is the equivalent temperature giving the outgoing flux σT⁴. It is not the mean surface temperature, nor generally an arithmetic mean of spatially varying emitting temperatures. This calculation does not separate surface and atmospheric radiation or represent the greenhouse mechanism. Changing prescribed albedo is a comparison, not a simulated feedback: temperature never changes albedo here.

Absorbed 238.175 W/m²; outgoing 239.758 W/m²; signed net -1.583 W/m². Net energy loss.

Continuous equilibrium effective temperature 254.578 K (-18.572 °C). The selected temperature is 255 K; a rounded slider value need not give exact balance. Net power identifies energy gain or loss, not a warming rate or surface-climate prediction.

Observation to attach to a capture

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Understand

Change one input and preserve the comparison

Start at albedo 30% and effective emitting temperature 255 K. Record incoming, reflected, absorbed and outgoing flux. Before raising albedo to 35%, predict which entries will change. The solar source is fixed, and the selected temperature is fixed, so incoming and outgoing flux should remain unchanged.

Reflection increases because the planet returns a larger fraction of incoming sunlight to space. Absorption decreases by the same amount. NASA’s energy-budget explanation describes planetary reflection as involving the atmosphere and surface. This slider represents their combined planetary effect; it does not identify a particular patch of ice, cloud layer or land-cover intervention.

The experiment is a comparison between prescribed albedos. No equation makes albedo respond to temperature. That distinction is essential when deciding whether the result demonstrates a feedback.

Calculate percentage-point changes

Moving from 30% to 35% is an increase of five percentage points. As a fraction, Δα = 0.05. Multiply by global mean incoming flux 340.25 W/m² to obtain a reflected-flux increase of 17.0125 W/m². Absorbed flux decreases from 238.175 to 221.1625 W/m².

This is not a 5% relative increase in albedo: 0.05/0.30 is about 16.7%. Keep percentage points and relative percentages distinct. For this energy ledger, the direct fractional difference 0.05 is the quantity the formula needs.

At the held temperature of 255 K, outgoing flux remains about 239.7576 W/m². The net therefore changes from about −1.5826 to −18.5951 W/m². These are rates of energy loss per area, not degrees of cooling. Holding temperature fixed is a controlled comparison, not an evolving planet being cooled by the program.

Compare the two equilibrium conditions

The equilibrium effective temperature also changes when albedo changes. At 30% it is about 254.5781 K; at 35% it is about 249.9050 K. The difference is approximately −4.6731 K. This compares two equilibrium solutions under the model assumptions, not a forecast of a transition occurring over a stated number of years.

You can predict the ratio without calculating σ again. Because Tₑ is proportional to the fourth root of absorbed flux, the new-to-old equilibrium ratio is (0.65/0.70) raised to the power 1/4. Solar irradiance and the radiation constant cancel. The ratio is less than one, consistent with reduced absorption.

Create a paper ledger for albedos 20%, 40% and 60%, keeping selected temperature fixed. Write predictions for reflected and absorbed flux before inspecting outputs. Then compare their equilibrium temperatures separately. Avoid mixing a fixed-temperature net comparison with a comparison in which each state has already reached its own equilibrium.

Decide whether a feedback was simulated

A feedback requires a response that returns to affect the original change. For an ice–albedo mechanism, for example, a temperature change would have to alter ice conditions, those conditions would alter planetary reflectivity, and the changed absorption would affect temperature. Those connecting responses are absent from this lab.

Manually moving an albedo slider can explore one radiative consequence of a hypothetical change. It cannot establish the size or timing of the real feedback, identify what caused an observed albedo change, or show how clouds respond. The lack of these responses in this model does not imply that they are unimportant physically.

In your explanation, name what was held constant and distinguish an imposed input from a response. A controlled calculation becomes more useful when its causal boundary is explicit.

Transfer to another albedo difference

At the same fixed solar input and selected temperature, compare albedos 10% and 25%. Calculate the change in absorbed flux and say whether this experiment alone establishes a temperature–albedo feedback.

Check the albedo-comparison transfer

Albedo rises by 0.15, so absorption decreases by 0.15 × 340.25 = 51.0375 W/m². Outgoing flux stays fixed when the selected temperature is fixed. The comparison does not simulate feedback because albedo is prescribed and does not respond to temperature.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Distinguish percentage points from relative percent and explain the missing response required for a feedback model.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

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Previous: Solve for an effective radiative equilibrium Next: Bound climate claims with energy evidence

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