Energy budgets: systems, global and seasonal variations, transfers, diurnal changes

Atmospheric Processes and Global Climate Change (Cambridge 9696)

Learning objective

Explain how the Earth’s energy budget operates, describe the main global energy‑transfer systems, analyse seasonal and diurnal variations, and relate these processes to observed climate change.

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1. Energy‑budget systems

1.1 Required components (syllabus 2.1)

• Incoming short‑wave radiation (SW_in) – solar energy reaching the top of the atmosphere (TOA).
• Reflected short‑wave radiation (SW_ref) – fraction of SW_in reflected by clouds, aerosols, ice and the surface (planetary albedo α).
• Absorbed short‑wave radiation by the atmosphere (SW_atm) – energy absorbed by gases, clouds and aerosols before it reaches the surface.
• Absorbed short‑wave radiation by the surface (SW_surf) – energy that reaches and is absorbed by land or ocean.
• Outgoing long‑wave radiation (LW_out) – thermal infrared emitted by the Earth‑system to space.

1.2 Quantitative global energy budget (average values)

Component	Mean flux (W m⁻²)	How it is obtained / notes
Incoming short‑wave (SWin)	340	Solar constant S₀ ≈ 1361 W m⁻² ÷ 4 (geometric factor)
Reflected short‑wave (SWref)	102	α ≈ 0.30 → 0.30 × 340
Absorbed short‑wave by atmosphere (SWatm)	78	Absorption by water vapour, ozone, clouds, aerosols
Absorbed short‑wave by surface (SWsurf)	160	340 – 102 – 78
Outgoing long‑wave (LWout)	240	Balances net incoming energy (SWin – SWref)

1.3 Planetary energy‑budget flow diagram (syllabus requirement)

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2. Moisture cycle and weather processes (syllabus 2.2)

2.1 The water‑vapour cycle

• Evaporation – conversion of liquid water to vapour from oceans, lakes and wet surfaces.
• Transpiration – vapour released by plants; together with evaporation it is called evapotranspiration.
• Condensation – vapour cools and forms cloud droplets or ice crystals.
• Precipitation – water returns to the surface as rain, snow, sleet or hail.

2.2 Cloud types (relevant for energy transfer)

• Cumulus – low, puffy clouds; strong reflectors of short‑wave radiation.
• Stratus – layered clouds; moderate albedo, can produce drizzle.
• Cirrus – high, thin ice‑crystal clouds; relatively transparent to short‑wave but trap long‑wave radiation.

2.3 Main precipitation mechanisms (syllabus 2.2)

• Convective precipitation – intense, short‑lived showers produced by strong surface heating (common in the tropics and summer afternoons).
• Frontal (orographic) precipitation – occurs when moist air is forced to rise over a weather front or mountain range, cooling and condensing.
• Orographic precipitation – specifically associated with uplift over topography; leeward side often lies in a rain shadow.

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3. Global transfers of energy (syllabus 2.3 & 2.4)

3.1 Atmospheric circulation – the three‑cell model

• Hadley cell (0°–30°) – warm air rises at the ITCZ, moves pole‑ward aloft, cools and descends in the subtropics, driving the trade‑wind belts.
• Ferrel cell (30°–60°) – mid‑latitude “eddy” cell driven by the pole‑ward flow from the Hadley cell and equator‑ward flow from the Polar cell; produces the prevailing westerlies.
• Polar cell (60°–90°) – cold, dense air descends at the poles, flows equator‑ward at the surface, rises near 60° latitude.

3.2 Wind belts and jet streams

• Trade winds – easterlies in the low latitudes (≈ 10 km h⁻¹) associated with the surface branch of the Hadley cell.
• Westerlies – prevailing mid‑latitude winds (30°–60°) driven by the Ferrel cell.
• Polar easterlies – surface winds pole‑ward of 60°.
• Sub‑tropical jet – fast westerly jet near the top of the Hadley cell (~30° latitude, 30–50 m s⁻¹).
• Polar jet – stronger westerly jet near the pole‑ward edge of the Ferrel cell (~60° latitude).

3.3 Oceanic energy transport

• Surface currents – wind‑driven (e.g., Gulf Stream, Kuroshio) transport warm water pole‑ward.
• Thermohaline circulation – deep‑water formation in high‑latitude regions (North Atlantic, Southern Ocean) and a global “conveyor belt” that redistributes heat over centuries.
• Ekman transport – wind‑driven spiral causing surface water to move 90° to the right (NH) or left (SH), contributing to upwelling and heat redistribution.

3.4 Ocean‑atmosphere coupling (syllabus 2.4)

• El Niño Southern Oscillation (ENSO) – anomalous warming (El Niño) or cooling (La Niña) of equatorial Pacific SSTs modifies global wind patterns, SW distribution and LW emission.
• Monsoon systems – large seasonal land‑sea temperature contrast drives reversal of winds and massive latent‑heat fluxes (e.g., South‑Asian summer monsoon).

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4. Seasonal and diurnal variations (syllabus 3)

4.1 Seasonal (annual) variation

• Result of Earth’s axial tilt (23.5°) → changing solar declination throughout the year.
• High latitudes: large swings in day length and solar altitude → strong seasonal contrast in SW_in and albedo (snow‑cover feedback).
• Equatorial band: relatively constant SW_in; seasonal changes are mainly due to the north‑south migration of the ITCZ.
• Figure 2 – Insolation curves for 0°, 30° and 60° latitude (students should sketch).

4.2 Diurnal (day‑night) variation

• Daytime: surface gains energy (SW_surf); night‑time: surface loses energy via LW_out.
• Factors controlling diurnal temperature range (DTR)
  • Heat capacity – water (high) → small DTR; land (low) → large DTR.
  • Cloud cover – clouds reflect SW (cooling day) and trap LW (warming night) → reduced DTR.
  • Atmospheric moisture – latent‑heat fluxes moderate temperature swings.
• Figure 3 – Typical diurnal temperature curves over a desert, a temperate land area and the open ocean.

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5. Mechanisms of energy transfer in the atmosphere (syllabus 4)

1. Radiation – transfer of energy by electromagnetic waves; dominant source (solar) and sink (infrared) of the climate system.
2. Conduction – molecular heat transfer; important only in the thin layer of air directly in contact with the ground or sea surface.
3. Convection – bulk movement of air parcels; creates vertical transport of heat, drives cloud formation and large‑scale circulation.
4. Latent‑heat transfer – energy absorbed/released during phase changes of water. $$Q_{\text{latent}} = L_{v}\,\dot{m}$$ where $L_{v}\approx2.5\times10^{6}\,\text{J kg}^{-1}$ and $\dot{m}$ is the mass flux of water vapour.

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6. Energy‑balance equation, feedbacks and climate‑change evidence (syllabus 5)

6.1 Radiative balance at the top of the atmosphere

$$\Delta F \;=\; \frac{S_{0}}{4}\,(1-\alpha) \;-\; \epsilon\,\sigma\,T_{s}^{4}$$

• $S_{0}$ = solar constant (≈ 1361 W m⁻²)
• $\alpha$ = planetary albedo
• $\epsilon$ = effective emissivity of the Earth‑system (reduced by greenhouse gases)
• $\sigma$ = Stefan‑Boltzmann constant (5.67 × 10⁻⁸ W m⁻² K⁻⁴)
• $T_{s}$ = surface temperature (K)

Positive $\Delta F$ → net energy gain (warming); negative $\Delta F$ → net loss (cooling).

6.2 Key climate feedbacks (syllabus focus)

• Ice‑albedo feedback – melt → lower α → more SW absorbed → further warming.
• Water‑vapour feedback – warmer air holds more moisture → stronger greenhouse trapping → additional warming.
• Cloud feedback – low clouds increase albedo (cooling); high clouds trap LW (warming). Net effect remains an active research area.

6.3 Evidence of recent climate change (required for syllabus 2.3)

• Instrumental records – global mean surface temperature has risen ~1.1 °C since pre‑industrial times (1880‑2020); sea‑level rise ≈ 20 cm; decreasing Arctic sea‑ice extent.
• Proxy data – ice‑core δ¹⁸O and CO₂ concentrations, tree‑ring widths, sediment cores all indicate warmer temperatures and higher greenhouse‑gas levels in the late‑20th century compared with the Holocene average.
• Other indicators – glacier retreat worldwide, shift in species’ ranges, increased frequency of extreme weather events.

6.4 Greenhouse gases – properties and radiative forcing

Gas	Typical atmospheric concentration (2023)	Global‑warming potential (100 yr)	Atmospheric lifetime	Radiative‑forcing formula (CO₂‑equivalent)
CO₂	≈ 420 ppm	1 (reference)	≈ 100 yr (very long)	ΔF = 5.35 ln(C/C₀)
CH₄	≈ 1.9 ppm	≈ 28	≈ 12 yr
N₂O	≈ 0.33 ppm	≈ 265	≈ 114 yr
F‑gases (e.g., CFC‑12)	≈ 0.5 ppb	≫ 10 000	Centuries

6.5 Anthropogenic forcing and system response

Human activities increase concentrations of the gases above, reducing the effective emissivity ($\epsilon$) and producing a positive radiative forcing (ΔF > 0). The resulting energy imbalance drives:

• Higher equilibrium surface temperature.
• Amplification of feedbacks (ice‑albedo, water‑vapour).
• Potential changes to the Hadley cell extent, jet‑stream position and thermohaline circulation strength.

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7. Summary points (quick revision)

• The Earth’s climate is a balance between incoming short‑wave and outgoing long‑wave radiation.
• Energy‑budget components: SW_in, SW_ref, SW_atm, SW_surf, LW_out.
• Global redistribution of energy occurs via the three‑cell atmospheric circulation, wind belts, jet streams, surface currents and the thermohaline conveyor.
• Seasonal variation is driven by axial tilt; diurnal variation is controlled by heat capacity, cloud cover and atmospheric moisture.
• Radiation, conduction, convection and latent heat are the four mechanisms that move energy within the atmosphere.
• Key feedbacks – ice‑albedo, water‑vapour, clouds – can accelerate or moderate warming.
• Robust evidence (instrumental and proxy) shows the climate is warming; greenhouse‑gas properties (GWP, lifetime) explain the magnitude of anthropogenic forcing.
• Quantifying the energy budget provides the foundation for assessing and predicting climate change.

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Suggested diagrams (to be drawn by students)

1. Figure 1 – Planetary energy‑budget flow chart (SW_in, SW_ref, SW_atm, SW_surf, LW_out with greenhouse‑gas trapping).
2. Figure 2 – Seasonal insolation curves for 0°, 30° and 60° latitude.
3. Figure 3 – Diurnal temperature profiles over desert, temperate land and ocean.
4. Figure 4 – Three‑cell atmospheric model showing Hadley, Ferrel and Polar cells, ITCZ, trade winds, westerlies and jet streams.
5. Figure 5 – World map of major surface ocean currents and the thermohaline conveyor belt.
6. Figure 6 – Schematic of the water‑vapour cycle with arrows for evaporation, transpiration, condensation and the three precipitation mechanisms.
7. Figure 7 – Bar chart of major greenhouse gases with concentrations, GWP and atmospheric lifetimes.