24.4.2 Energy Imbalance

Earth's Energy Imbalance (EEI)

The Earth's Energy Imbalance (EEI) is the net difference between the solar energy absorbed by the Earth system and the thermal (infrared) energy radiated back into space:

$\text{EEI}=E_{\text{absorbed}}-E_{\text{emitted}}$

EEI is measured in watts per square metre (${\text{W m}}^{-2}$). A positive EEI means Earth is accumulating energy — the planet is warming. A negative EEI would mean Earth is losing energy and cooling.

Current satellite measurements indicate a positive EEI of approximately $+0.3$ to $+0.9{\text{W m}}^{-2}$, confirming ongoing planetary warming.

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Cause of the Current Positive EEI

The primary driver of today's positive EEI is the enhanced Greenhouse Effect:

1. Greenhouse gases (GHGs) such as ${\text{CO}}_2$, ${\text{CH}}_4$, and ${\text{N}}_2\text{O}$ accumulate in the atmosphere due to human activity.
2. These gases are largely transparent to incoming shortwave solar radiation but absorb outgoing longwave infrared radiation.
3. The absorbed infrared energy is re-emitted in all directions, including back toward Earth's surface — trapping heat.
4. This reduces the rate at which Earth emits energy to space, creating a positive imbalance.

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Where Does the Excess Heat Go?

The excess energy stored due to positive EEI is distributed as follows:

The oceans dominate because water has a high specific heat capacity and the ocean volume is enormous. Ocean heat content (OHC) measurements are therefore the most reliable indicator of EEI.

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Radiative Forcing and Energy Balance

Radiative Forcing (RF) quantifies how much a factor (e.g., doubling ${\text{CO}}_2$) alters the energy balance at the top of the atmosphere:

• Positive RF → more energy in than out → warming
• Negative RF → more energy out than in → cooling

When incoming solar energy exceeds outgoing terrestrial radiation, Earth experiences positive radiative forcing and warms until a new equilibrium is reached at a higher temperature.

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Albedo Feedback and EEI

Earth's average albedo is approximately 0.30 (30% of incoming solar radiation is reflected). Changes in albedo alter EEI:

• Melting ice caps → lower albedo → more solar energy absorbed → increased positive EEI (positive feedback)
• Increased cloud cover → higher albedo → more solar energy reflected → reduced positive EEI (negative feedback)

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Atmospheric Cells and the Coriolis Effect

The unequal heating of Earth's surface (more solar energy absorbed at the equator than at the poles) drives large-scale atmospheric circulation organised into Hadley, Ferrel, and Polar cells.

Coriolis Effect

Because Earth rotates, moving air masses experience an apparent deflection known as the Coriolis effect, arising from the conservation of angular momentum:

$L=mvr=\text{constant}$

As an air parcel moves from the equator (large $r$) toward the poles (smaller $r$), its tangential speed $v$ must increase to conserve $L$, causing deflection:

• Northern Hemisphere: deflection to the right
• Southern Hemisphere: deflection to the left

The Coriolis parameter $f$ is given by:

$f=2\Omega \sin \varphi$

where $\Omega =7.27\times 10^{-5}{\text{rad s}}^{-1}$ is Earth's angular velocity and $\varphi$ is latitude.

Hadley Cell

• Warm, moist air rises at the equator, cools, and descends at ~30° latitude.
• Surface winds returning to the equator are deflected by the Coriolis effect to form the Trade Winds.

Ferrel and Polar Cells

• Ferrel cell (30°–60°): mid-latitude circulation driven partly by the Hadley and Polar cells.
• Polar cell (60°–90°): cold air sinks at the poles and flows equatorward, deflected to form Polar Easterlies.

These atmospheric cells redistribute heat from the equator toward the poles, moderating global temperature gradients and directly linking the energy budget to global climate patterns.

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Summary