Part IV: Climate Systems

Global circulation, energy balance, ocean-atmosphere interactions, teleconnections, monsoons, and climate feedbacks

1. Earth's Energy Balance

The climate of Earth is fundamentally governed by the balance between incoming shortwave solar radiation and outgoing longwave terrestrial radiation. Understanding each component of this budget -- at the top of the atmosphere (TOA), within the atmosphere, and at the surface -- is the foundation of climate science.

1.1 Solar Radiation Input and the Solar Constant

The Sun, a G2V main-sequence star with a photospheric temperature of approximately 5778 K, emits radiation across the electromagnetic spectrum. The total solar irradiance (TSI), historically called the solar constant, is the flux of solar energy per unit area perpendicular to the beam at the mean Earth-Sun distance (1 AU = 1.496 x 10$^{8}$ km):

$S_0 \approx 1361 \text{ W/m}^2$

This value is not truly constant. It varies due to:

-- The 11-year Schwabe sunspot cycle: amplitude ~1 W/m$^2$ (~0.07%)

-- Orbital eccentricity: $\pm$3.4% annual variation (perihelion in January)

-- Longer Gleissberg and de Vries cycles: estimated ~0.2% over centuries

-- Measured continuously since 1978 by satellite radiometers (ERB, ACRIM, SORCE, TSIS)

Earth intercepts solar radiation across a disk of area $\pi R_E^2$ (where $R_E \approx 6371$ km), but its total surface area is $4\pi R_E^2$. The globally averaged incoming solar flux is therefore:

$\bar{Q}_{in} = \frac{S_0}{4} \approx 340 \text{ W/m}^2$

The factor of 4 arises from the ratio of the cross-sectional disk area to the full sphere surface area.

1.2 Planetary Albedo

Not all incoming solar radiation is absorbed by the Earth system. A fraction $\alpha$, called the planetary albedo (or Bond albedo), is reflected back to space without being absorbed. This reflection occurs at multiple levels:

$\alpha \approx 0.30$

Contributions to planetary albedo:

-- Clouds: ~0.15 (largest single contributor, especially marine stratocumulus)

-- Atmospheric Rayleigh and Mie scattering: ~0.06

-- Ice sheets and snow cover: ~0.06-0.08

-- Land surfaces (deserts, vegetation): ~0.02-0.04

-- Ocean surface (low albedo ~0.06, but large area): ~0.02

The absorbed solar radiation globally averaged is thus:

$\bar{Q}_{abs} = \frac{S_0(1 - \alpha)}{4} \approx 238 \text{ W/m}^2$

Surface albedo varies enormously by surface type. Fresh snow has an albedo of 0.80-0.90, sea ice 0.50-0.70, desert sand 0.30-0.40, grassland 0.15-0.25, forests 0.10-0.20, and open ocean only 0.06-0.10. This spatial heterogeneity is critical for feedbacks such as the ice-albedo mechanism discussed in Chapter 6.

1.3 Effective Radiating Temperature

At radiative equilibrium, the total absorbed solar energy must balance the total emitted longwave (thermal infrared) radiation. Treating Earth as a blackbody radiator using the Stefan-Boltzmann law:

$\frac{S_0(1 - \alpha)}{4} = \sigma T_e^4$

Solving for the effective temperature:

$T_e = \left[\frac{S_0(1 - \alpha)}{4\sigma}\right]^{1/4} \approx 255 \text{ K} \approx -18°\text{C}$

where $\sigma = 5.67 \times 10^{-8}$ W/(m$^2$K$^4$) is the Stefan-Boltzmann constant. This is the temperature at which the planet must radiate to balance absorbed sunlight.

For comparison, the effective temperatures of other terrestrial bodies:

-- Venus: $T_e \approx 230$ K (actual surface: 737 K due to massive greenhouse effect)

-- Mars: $T_e \approx 210$ K (actual surface: ~218 K, thin atmosphere, weak greenhouse)

-- Moon: $T_e \approx 270$ K (no atmosphere, no greenhouse effect)

1.4 Quantifying the Greenhouse Effect

Earth's observed mean surface temperature is $T_s \approx 288$ K (15 degrees C), which is 33 K warmer than the effective temperature $T_e \approx 255$ K. This 33 K enhancement is the greenhouse effect. It arises because the atmosphere is largely transparent to incoming shortwave solar radiation but strongly absorbs outgoing longwave radiation, re-emitting it both upward and downwardtoward the surface.

A simple single-layer greenhouse model illustrates this. Consider an atmosphere that is transparent to shortwave but has longwave emissivity $\epsilon$. The surface temperature becomes:

$T_s = T_e \left(\frac{2}{2 - \epsilon}\right)^{1/4}$

For $\epsilon = 1$ (perfectly absorbing atmosphere): $T_s = 2^{1/4} T_e \approx 303$ K. For $\epsilon \approx 0.77$, this yields the observed $T_s \approx 288$ K. A multi-layer model converges to the full radiative transfer solution.

The Greenhouse Effect in Numbers:

-- Surface emits ~396 W/m$^2$ (Stefan-Boltzmann at 288 K)

-- But only ~239 W/m$^2$ escapes to space from the TOA

-- The difference (~157 W/m$^2$) is the greenhouse trapping

-- Atmosphere radiates ~340 W/m$^2$ back down to the surface (back-radiation)

-- Net longwave loss from surface: 396 - 340 = 56 W/m$^2$

1.5 Top-of-Atmosphere Radiation Budget

The net radiation at the top of the atmosphere determines whether the planet is gaining or losing energy. Satellite missions such as CERES (Clouds and the Earth's Radiant Energy System) measure all three components:

$N = F_{SW}^{\downarrow} - F_{SW}^{\uparrow} - F_{LW}^{\uparrow}$

$F_{SW}^{\downarrow} \approx 340$ W/m$^2$: Incoming solar (shortwave)

$F_{SW}^{\uparrow} \approx 100$ W/m$^2$: Reflected solar (shortwave)

$F_{LW}^{\uparrow} \approx 239$ W/m$^2$: Outgoing longwave radiation (OLR)

Current imbalance: $N \approx +0.7$ to $+1.0$ W/m$^2$ (planet is accumulating energy)

This energy imbalance, though small compared to the total fluxes, drives ongoing global warming. Over 90% of the excess energy is absorbed by the oceans, measurable as increasing ocean heat content. The remaining energy melts ice, warms the land, and warms the atmosphere.

1.6 Surface Energy Balance

At the Earth's surface, the net radiative energy must be partitioned among non-radiative fluxes. The surface energy balance is:

$R_n = H + LE + G$

$R_n$: Net radiation at the surface (shortwave down minus up, plus longwave down minus up)

$H$: Sensible heat flux (turbulent transfer of heat to the atmosphere)

$LE$: Latent heat flux (energy used for evapotranspiration; $L \approx 2.5 \times 10^6$ J/kg)

$G$: Ground heat flux (conduction into the soil or ocean)

Expanding the net radiation term:

$R_n = (1 - \alpha_s) S^{\downarrow} + L^{\downarrow} - L^{\uparrow}$

where $\alpha_s$ is the surface albedo, $S^{\downarrow}$ is downwelling shortwave, and $L^{\downarrow}, L^{\uparrow}$ are the downwelling and upwelling longwave fluxes.

1.7 The Bowen Ratio

The Bowen ratio quantifies the partitioning of available energy between sensible and latent heat:

$\beta = \frac{H}{LE}$

Typical values of the Bowen ratio by surface type:

-- Tropical ocean: $\beta \approx 0.1$ (latent heat dominates)

-- Tropical rainforest: $\beta \approx 0.2\text{-}0.3$

-- Temperate grassland: $\beta \approx 0.5\text{-}1.0$

-- Semi-arid desert: $\beta \approx 5\text{-}10$ (sensible heat dominates)

-- Urban areas: $\beta > 2$ (impervious surfaces, limited evaporation)

The Bowen ratio is measured using eddy covariance towers or estimated from the Bowen ratio energy balance (BREB) method, which uses gradients of temperature and humidity above the surface. Land-use change (deforestation, urbanization) alters $\beta$ and thus local and regional climate.

2. General Circulation of the Atmosphere

The general circulation of the atmosphere is the large-scale, time-averaged pattern of atmospheric motion driven by differential solar heating between the equator and the poles, modified by Earth's rotation (Coriolis effect), land-sea contrasts, and orography. It is the primary mechanism by which the atmosphere transports heat, moisture, and angular momentum.

2.1 The Need for Meridional Energy Transport

The tropics (equatorward of ~38 degrees latitude) receive more solar radiation than they emit as longwave, creating an energy surplus. Polar regions have a deficit. Without poleward heat transport, the tropics would be ~14 K warmer and the poles ~25 K cooler than observed. The required poleward heat transport is:

-- Maximum total poleward transport: ~5.5 PW (petawatts, 10$^{15}$ W) at ~35 degrees latitude

-- Atmosphere contributes ~3.5 PW (~60% of total)

-- Ocean contributes ~2.0 PW (~40% of total)

-- Atmospheric transport mechanisms: mean meridional circulation (Hadley cell), transient eddies (storms), stationary waves

-- In the tropics, the Hadley cell dominates; in mid-latitudes, transient eddies dominate

The total northward heat transport by the atmosphere can be decomposed:

$\mathcal{H} = \int_0^{2\pi}\int_0^{p_s} \overline{v}\,\overline{(c_p T + gz + Lq + \tfrac{1}{2}|\mathbf{v}|^2)} \;\frac{a\cos\varphi}{g}\,dp\,d\lambda$

Total moist static energy transport -- the sum of sensible, potential, latent, and kinetic energy fluxes.

2.2 The Hadley Cell

The Hadley cell is the dominant thermally direct circulation in the tropics, extending from the equator to approximately 30 degrees latitude in each hemisphere. It was first proposed by George Hadley in 1735 to explain the trade winds.

Hadley Cell Structure (0 degrees - ~30 degrees)

Thermally direct circulation: Air rises near the equator at the Intertropical Convergence Zone (ITCZ) in deep cumulonimbus convection, flows poleward in the upper troposphere (10-15 km altitude), descends in the subtropics (~30 degrees), and returns equatorward at the surface as the trade winds.

-- Surface: Northeast trades (NH) and Southeast trades (SH)
-- Upper branch: Strong poleward and westerly flow due to angular momentum conservation
-- Subtropical subsidence creates high-pressure belts, deserts, and clear skies
-- Annual mean mass transport: ~10$^{10}$ kg/s per hemisphere
-- Strongest and widest in the winter hemisphere (cross-equatorial Hadley cell)

A key feature of the Hadley cell is angular momentum conservation. Air moving poleward from the equator conserves its angular momentum. If an air parcel starts at the equator with zero relative zonal velocity, conservation of angular momentum gives the zonal wind at latitude $\varphi$:

$u = \Omega a \cos\varphi \left[\frac{\cos\varphi_0}{\cos\varphi} - 1\right]$

where $\Omega = 7.292 \times 10^{-5}$ rad/s is Earth's angular velocity,$a \approx 6371$ km is Earth's radius, $\varphi_0$ is the starting latitude, and $\varphi$ is the current latitude.

For air starting at the equator ($\varphi_0 = 0$), reaching 30 degrees:

$u(30°) = \Omega a \cos 30° \left[\frac{1}{\cos 30°} - 1\right] \approx 134 \text{ m/s}$

This exceeds observed subtropical jet speeds (~40-70 m/s) because friction and eddy momentum fluxes act to decelerate the upper-level flow.

Held-Hou Model of Hadley Cell Extent

Held and Hou (1980) developed an influential axisymmetric theory for the width of the Hadley cell. By assuming angular momentum conservation aloft, thermal wind balance, and radiative-convective equilibrium outside the cell, they derived the poleward extent:

$\varphi_H = \left(\frac{5 g \Delta_h H}{3 \Omega^2 a^2}\right)^{1/2}$

$g$: gravitational acceleration (9.81 m/s$^2$)

$\Delta_h$: fractional equator-to-pole temperature difference $\approx (T_{eq} - T_{pole})/T_0$

$H$: tropopause height (~15 km in the tropics)

$\Omega$: Earth's rotation rate

$a$: Earth's radius

With typical values, $\varphi_H \approx 28°\text{-}32°$, consistent with observations. The theory predicts the Hadley cell widens with increased equator-to-pole temperature contrast or decreased rotation rate.

2.3 The Ferrel Cell

Ferrel Cell (30 degrees - 60 degrees)

Thermally indirect (eddy-driven) circulation: Unlike the Hadley and Polar cells, the Ferrel cell is not a direct thermal circulation. It is maintained by the convergence of eddy momentum and heat fluxes from baroclinic eddies (mid-latitude weather systems).

-- Surface: Prevailing westerlies (southwesterly in NH, northwesterly in SH)
-- Warm air descends at ~30 degrees and cold air rises at ~60 degrees -- thermally indirect
-- The mid-latitude storm tracks reside within this cell
-- Transient eddies (cyclones and anticyclones) are the primary agents of poleward heat transport here
-- Eliassen-Palm flux diagnostics show eddy driving of the mean Ferrel circulation

The transformed Eulerian-mean (TEM) framework reveals that the residual circulation in mid-latitudes is actually poleward and downward, consistent with diabatic cooling in the lower troposphere. The Eulerian-mean Ferrel cell is an artifact of the zonal averaging that masks the dominant eddy transport.

2.4 The Polar Cell

Polar Cell (60 degrees - 90 degrees)

Thermally direct, but weak: Intensely cold air sinks over the poles, flows equatorward as shallow polar easterlies, and rises at the polar front (~60 degrees).

-- Surface: Polar easterlies (weak and shallow)
-- The polar front marks the boundary between polar and mid-latitude air masses
-- Much weaker and more intermittent than the Hadley cell
-- Polar vortex in the stratosphere sits above this cell
-- Arctic amplification is modifying this cell structure in the current climate

2.5 Jet Streams

Jet streams are narrow, fast-flowing air currents in the upper troposphere (typically 9-12 km altitude) with wind speeds of 30-70 m/s, occasionally exceeding 100 m/s. They arise from the thermal wind relationship between horizontal temperature gradients and vertical wind shear:

Thermal Wind Relation:

$\frac{\partial \mathbf{V}_g}{\partial \ln p} = \frac{R}{f}\mathbf{k} \times \nabla_p T$

Strong meridional temperature gradients produce strong vertical wind shear, resulting in jet-stream-level maxima.

Subtropical Jet (~30 degrees)

Located near the tropopause at the poleward edge of the Hadley cell, at about 200 hPa (~12 km). Driven by angular momentum transport from the tropics. Strongest in winter (~50-70 m/s in NH). Nearly continuous around the globe. Located above the subtropical surface high-pressure belt.

Polar Front Jet (~50-60 degrees)

Located at the polar front (boundary between Ferrel and Polar cells), at about 300 hPa (~9 km). Associated with the strongest baroclinicity. Highly meandering due to Rossby waves. Steers mid-latitude cyclones and fronts. Its position determines weather patterns for billions of people.

Additional jet features include the tropical easterly jet (upper-level easterlies over South Asia during the monsoon, ~150 hPa), the stratospheric polar night jet (strong wintertime westerlies in the stratosphere at 60 degrees), and low-level jets such as the Great Plains low-level jet (nocturnal southerly jet bringing moisture from the Gulf of Mexico, crucial for severe weather in the US).

Video: Global Atmospheric Circulation

Met Office explanation of global circulation patterns

Video: General Atmospheric Circulation

Detailed lecture on the general atmospheric circulation and its driving mechanisms

3. Ocean-Atmosphere Interactions

The ocean covers 71% of Earth's surface, stores over 1000 times more heat than the atmosphere, and transports approximately 2 PW of heat poleward. Ocean-atmosphere coupling is central to climate variability on timescales from weeks (tropical cyclone intensification) to millennia (thermohaline circulation adjustment).

3.1 The Ocean as a Climate Regulator

-- Heat capacity: The top 2.5 m of ocean has the same heat capacity as the entire atmosphere. The full ocean mixed layer (~50-200 m) has $\sim 100\times$ the thermal inertia of the atmosphere.

-- Thermal response times: Mixed layer adjusts on timescales of months to years; the deep ocean on centuries to millennia.

-- Carbon sink: The ocean absorbs ~25% of annual anthropogenic CO$_2$ emissions and ~93% of the excess heat from global warming.

-- Water cycle: ~85% of global evaporation occurs from the ocean surface, driving the atmospheric branch of the hydrological cycle.

-- Sea surface temperature (SST): The lower boundary condition for the atmosphere over oceans; SST patterns govern tropical convection, hurricane formation, and teleconnections.

3.2 Ekman Transport and the Ekman Spiral

When wind blows over the ocean surface, it drives a frictional current in the upper ocean. The Ekman spiral, derived by V. Walfrid Ekman in 1905, describes how this current rotates with depth due to the balance between the Coriolis force and frictional stress.

The surface current is deflected 45 degrees to the right of the wind in the Northern Hemisphere (left in SH). With increasing depth, the current continues to rotate and weaken exponentially. The depth at which the current has rotated 180 degrees from the surface direction and decayed to $e^{-\pi} \approx 4\%$of the surface speed is the Ekman depth:

$D_E = \frac{\pi}{\sqrt{2}}\sqrt{\frac{A_z}{f}} = \pi\sqrt{\frac{2A_z}{f}}$

$A_z$: vertical eddy viscosity coefficient (typically $10^{-2}\text{-}10^{-1}$ m$^2$s$^{-1}$)

$f = 2\Omega\sin\varphi$: Coriolis parameter

Typical Ekman depth: 20-200 m depending on latitude and wind conditions

The net Ekman transport (depth-integrated mass transport) is directed 90 degrees to the right of the wind stress in the NH (left in SH):

$\mathbf{M}_E = \frac{1}{f}\mathbf{k} \times \boldsymbol{\tau}_s$

where $\boldsymbol{\tau}_s$ is the surface wind stress vector and $f$ is the Coriolis parameter.

Ekman transport is critical for coastal upwelling (wind-driven divergence of surface water replaced by cold, nutrient-rich deep water) and for the formation of subtropical gyres through Ekman pumping. Convergent Ekman transport in subtropical gyres pushes surface water downward (Ekman pumping), while divergent transport in subpolar gyres draws water upward (Ekman suction).

3.3 Sverdrup Balance and Wind-Driven Circulation

The large-scale, wind-driven ocean circulation in the interior is described by the Sverdrup balance, which relates the depth-integrated meridional transport to the curl of the wind stress:

$\beta V = \frac{1}{\rho_0}\text{curl}_z(\boldsymbol{\tau}_s) = \frac{1}{\rho_0}\left(\frac{\partial \tau_y}{\partial x} - \frac{\partial \tau_x}{\partial y}\right)$

$\beta = df/dy = 2\Omega\cos\varphi / a$: meridional gradient of Coriolis parameter

$V$: depth-integrated meridional volume transport

$\rho_0$: reference ocean density (~1025 kg/m$^3$)

The Sverdrup transport determines the broad pattern of subtropical and subpolar gyres.

Western Boundary Currents

The Sverdrup balance alone cannot close the gyre circulation. Mass conservation requires a narrow, intense western boundary current -- explained by Stommel (1948) as a consequence of the $\beta$-effect. These currents include:

Gulf Stream (North Atlantic)

Transports ~30 Sv (30 x 10$^6$ m$^3$/s) of warm water northeastward. Speeds up to 2.5 m/s. Width ~100 km. Carries ~1.3 PW of heat poleward. Separates from the coast at Cape Hatteras.

Kuroshio (North Pacific)

Japanese counterpart to the Gulf Stream. Transports ~25 Sv. Flows northeastward along Japan. Important for Japan's mild climate and Pacific fisheries.

Agulhas (Indian Ocean)

Strongest western boundary current by transport (~70 Sv). Flows southwestward along southeast Africa. Agulhas retroflection and leakage connect Indian and Atlantic oceans.

Brazil Current (South Atlantic)

Flows southward along the Brazilian coast. Weaker than the Gulf Stream (~10-20 Sv). Converges with the cold Malvinas Current at the Brazil-Malvinas Confluence (~38 degrees S).

3.4 Thermohaline Circulation and the AMOC

The thermohaline circulation (THC) is the density-driven component of the global ocean circulation, sometimes called the "global conveyor belt." Density is controlled by both temperature (thermo-) and salinity (-haline):

$\rho = \rho_0[1 - \alpha_T(T - T_0) + \beta_S(S - S_0)]$

where $\alpha_T \approx 2 \times 10^{-4}$ K$^{-1}$ is the thermal expansion coefficient and $\beta_S \approx 7.6 \times 10^{-4}$ (PSU)$^{-1}$ is the haline contraction coefficient.

Atlantic Meridional Overturning Circulation (AMOC):

-- Warm, salty surface water flows northward in the Atlantic
-- Loses heat to the atmosphere in the Nordic and Labrador Seas
-- Becomes dense enough to sink to depths of 2-4 km (deep water formation)
-- Returns southward as North Atlantic Deep Water (NADW) at depth
-- NADW spreads into the Southern, Indian, and Pacific Oceans
-- Eventually upwells and returns to the surface (overturning time ~1000 years)
-- Transports ~1.3 PW of heat northward at 26 degrees N (RAPID array measurement)
-- Overturning rate: ~17-18 Sv at 26 degrees N

AMOC and Climate Tipping Points:

The AMOC is considered one of the most important climate tipping elements. Freshwater input from melting ice sheets (Greenland), increased precipitation, and Arctic river runoff can reduce surface salinity, inhibiting deep water formation and potentially weakening or collapsing the AMOC. Paleoclimate records show AMOC slowdowns and shutdowns during Heinrich events and the Younger Dryas, associated with abrupt cooling of 5-10 K in the North Atlantic region within decades. Current observations suggest the AMOC has weakened by approximately 15% since the mid-20th century.

3.5 Air-Sea Heat Flux Components

The net heat flux at the ocean surface determines SST evolution:

$Q_{net} = Q_{SW} - Q_{LW} - Q_H - Q_E$

$Q_{SW}$: Net shortwave radiation absorbed (~170 W/m$^2$ global ocean average)

$Q_{LW}$: Net longwave radiation emitted (~50 W/m$^2$)

$Q_H$: Sensible heat flux (bulk formula: $Q_H = \rho_a c_p C_H U(T_s - T_a)$; ~10 W/m$^2$)

$Q_E$: Latent heat flux (bulk formula: $Q_E = \rho_a L_v C_E U(q_s - q_a)$; ~80 W/m$^2$)

$C_H, C_E \sim 10^{-3}$: bulk transfer coefficients; $U$: wind speed at 10 m

3.6 Ocean Mixed Layer Dynamics

The ocean mixed layer is the uppermost layer of the ocean where temperature and salinity are nearly uniform due to turbulent mixing by wind, waves, and convection. Its depth varies from ~20 m in summer tropics to over 500 m in winter subpolar regions.

The mixed layer temperature evolution follows:

$\rho_0 c_p h \frac{\partial T}{\partial t} = Q_{net} - \rho_0 c_p w_e \Delta T$

$h$: mixed layer depth

$Q_{net}$: net surface heat flux

$w_e$: entrainment velocity at the base of the mixed layer

$\Delta T$: temperature jump across the thermocline

Seasonal deepening occurs in autumn/winter via convective and mechanical mixing; shoaling occurs in spring when solar heating creates a shallow warm layer.

4. ENSO and Teleconnections

El Nino-Southern Oscillation (ENSO) is the dominant mode of interannual climate variability on Earth, involving coupled ocean-atmosphere feedbacks in the tropical Pacific Ocean. Its global teleconnections affect weather, agriculture, fisheries, disease, and economics for billions of people.

4.1 The Walker Circulation

Under normal (neutral) conditions, the Walker circulation is a zonal overturning cell along the equatorial Pacific, described by Sir Gilbert Walker in the 1920s:

-- Trade winds blow westward along the equator, piling warm water in the western Pacific (the "warm pool," SST > 28 degrees C)

-- Sea level is ~40-60 cm higher in the western Pacific than the eastern Pacific

-- The thermocline slopes from ~200 m deep in the west to ~50 m in the east

-- Upwelling of cold, nutrient-rich water occurs along the South American coast and equatorial eastern Pacific

-- Deep atmospheric convection and heavy rainfall occur over the warm pool (Indonesia, Maritime Continent)

-- Dry, subsiding air and high pressure prevail over the eastern Pacific

-- The upper-level return flow completes the circuit at 200 hPa

4.2 Bjerknes Feedback Mechanism

Jacob Bjerknes (1969) identified the fundamental positive feedback loop that amplifies ENSO anomalies. The Bjerknes feedback is a coupled ocean-atmosphere instability:

El Nino Development (Positive Feedback Loop):

1. Initial warm SST anomaly in the central/eastern equatorial Pacific

2. Reduced east-west SST gradient weakens the trade winds

3. Weaker trades reduce upwelling and reduce westward surface current

4. Warm water spreads further eastward (Kelvin wave propagation)

5. Further warming of SST in the central-east Pacific

6. Further weakening of the Walker circulation and trades

7. Cycle reinforces itself until limited by other processes

The termination and phase transition of ENSO involve delayed oceanic adjustment through equatorial ocean waves. The delayed oscillator theory (Suarez and Schopf, 1988; Battisti and Hirst, 1989) and the recharge-discharge oscillator(Jin, 1997) provide complementary explanations:

Delayed Oscillator: Westerly wind anomalies during El Nino excite downwelling Kelvin waves (propagating eastward, deepening the thermocline) and upwelling Rossby waves (propagating westward). The Rossby waves reflect off the western boundary as upwelling Kelvin waves, which return to the central Pacific after a delay of ~6-9 months and terminate the warm event.

Recharge-Discharge: During El Nino, anomalous Sverdrup transport drains (discharges) heat content from the equatorial band. The resulting shallow thermocline preconditions the system for La Nina.

4.3 El Nino and La Nina

El Nino (Warm Phase)

-- Trade winds weaken or reverse; warm water spreads eastward across the equatorial Pacific
-- SST anomalies of +1 to +3 degrees C in central/eastern Pacific (Nino 3.4 region)
-- Thermocline deepens in the east, shoals in the west
-- Suppressed upwelling off Peru and Ecuador collapses fisheries (anchovy collapse of 1972)
-- Convection shifts eastward: flooding in Peru/Ecuador, drought in Indonesia/Australia
-- Global impacts: warmer global mean temperature (+0.1-0.2 degrees C), reduced Atlantic hurricane activity, enhanced Pacific storms
-- Recurrence interval: 2-7 years; typical duration: 9-12 months
-- Extreme El Ninos: 1982-83, 1997-98, 2015-16

La Nina (Cold Phase)

-- Trade winds strengthen; enhanced upwelling in the eastern Pacific
-- SST anomalies of -1 to -2 degrees C in the eastern Pacific
-- Cold tongue extends further westward
-- Intensified Walker circulation
-- Enhanced rainfall over Indonesia, Maritime Continent, and northern Australia
-- Increased Atlantic hurricane activity
-- Often follows El Nino; can persist for 2-3 consecutive years
-- Global mean temperature slightly cooler than neutral years

4.4 ENSO Indices

Key ENSO Monitoring Indices:

-- Nino 3.4 SST Index: SST anomaly averaged over 5 degrees S-5 degrees N, 170 degrees W-120 degrees W. Most widely used. El Nino defined as 3-month running mean exceeding +0.5 degrees C for 5 consecutive overlapping seasons.

-- Nino 3 region: 5 degrees S-5 degrees N, 150 degrees W-90 degrees W (eastern Pacific focus)

-- Nino 4 region: 5 degrees S-5 degrees N, 160 degrees E-150 degrees W (central Pacific focus)

-- Nino 1+2 region: 0 degrees-10 degrees S, 90 degrees W-80 degrees W (far eastern Pacific, coastal)

-- SOI (Southern Oscillation Index): Standardized sea-level pressure difference between Tahiti and Darwin, Australia. Negative SOI indicates El Nino.

-- ONI (Oceanic Nino Index): 3-month running mean of Nino 3.4 SST anomalies. Official NOAA index.

-- MEI (Multivariate ENSO Index): Combines sea-level pressure, surface wind, SST, surface air temperature, and cloudiness.

4.5 Equatorial Wave Dynamics

ENSO dynamics involve equatorial ocean waves that communicate signals across the Pacific basin. The key waves are Kelvin waves (eastward-propagating) and Rossby waves (westward-propagating). For Rossby waves in the atmosphere, the dispersion relation is:

$c = \frac{\omega}{k} = \bar{u} - \frac{\beta}{k^2 + l^2}$

$c$: zonal phase speed

$\bar{u}$: mean zonal wind

$\beta = df/dy$: meridional gradient of the Coriolis parameter

$k, l$: zonal and meridional wavenumbers

Rossby waves always propagate westward relative to the mean flow (since the $\beta$ term is always negative). They are the primary mechanism for ENSO teleconnections, transmitting tropical heating anomalies to the extratropics.

In the equatorial ocean, Kelvin waves propagate eastward at speeds of ~2.5 m/s (crossing the Pacific in ~2-3 months), while the first baroclinic Rossby wave propagates westward at ~0.8 m/s. The Rossby wave reflection off the western boundary produces an eastward-propagating Kelvin wave, providing the delayed negative feedback that enables ENSO oscillation.

4.6 Other Major Teleconnections

Beyond ENSO, several other modes of climate variability produce teleconnections that affect weather and climate across the globe:

North Atlantic Oscillation (NAO)

The NAO is a pressure seesaw between the Icelandic Low and the Azores (subtropical) High. It is the dominant mode of atmospheric variability in the North Atlantic sector, particularly in winter. Positive NAO: Stronger-than-normal Icelandic Low and Azores High; enhanced westerlies; mild, wet winters in northern Europe; cold, dry conditions in Greenland and Labrador; enhanced storm track. Negative NAO: Weakened pressure centers; reduced westerlies; cold European winters; more blocking events; reduced storminess. The NAO index is defined as the normalized pressure difference between Lisbon (or the Azores) and Reykjavik. It exhibits variability on timescales from days to decades, with partial predictability from ocean and stratospheric conditions.

Pacific-North American Pattern (PNA)

The PNA is a prominent mode of atmospheric variability over the North Pacific and North America, consisting of alternating high and low pressure anomalies from the tropical Pacific to eastern North America. Positive PNA: Amplified ridge over western North America and trough over eastern North America; warmer western Canada/Alaska, colder southeastern US; reduced Pacific Northwest precipitation. It is strongly influenced by ENSO: El Nino tends to force a positive PNA pattern via a Rossby wave train triggered by enhanced tropical Pacific convection.

Arctic Oscillation (AO) / Northern Annular Mode (NAM)

The AO (or NAM) is a hemispheric-scale pattern of sea-level pressure with opposing anomalies between the Arctic and mid-latitudes. It is closely related to the NAO but is defined over the entire hemisphere. Positive AO: Strong polar vortex, low Arctic pressure, higher mid-latitude pressure; cold air locked in the Arctic; milder mid-latitude winters. Negative AO: Weak polar vortex, higher Arctic pressure; cold Arctic outbreaks penetrate into mid-latitudes. Stratosphere-troposphere coupling through sudden stratospheric warmings (SSWs) can shift the AO to negative phase, persisting for weeks.

Pacific Decadal Oscillation (PDO)

The PDO is a long-lived (20-30 year) pattern of SST variability in the North Pacific, identified by Nathan Mantua in 1997. Warm (positive) PDO: Warm SST anomalies along the North American coast and cool anomalies in the central North Pacific; resembles an El Nino pattern projected onto the North Pacific. Cool (negative) PDO: Opposite pattern. The PDO modulates ENSO impacts: when PDO and ENSO are in phase, teleconnection signals are amplified. Major phase shifts occurred around 1925, 1947, and 1977. The PDO may be driven by a combination of ENSO forcing, stochastic atmospheric forcing, and ocean memory through the "re-emergence mechanism."

Atlantic Multidecadal Oscillation (AMO)

The AMO is a coherent pattern of multidecadal (50-70 year) variability in North Atlantic SSTs. Warm AMO phase: Enhanced Atlantic hurricane activity, increased Sahel rainfall, reduced Amazon rainfall, warmer European summers, weakened Indian monsoon (some studies). Cool AMO phase: Reduced hurricane activity, Sahel droughts (1970s-80s). The AMO is thought to be linked to AMOC variability, though external forcing (volcanic aerosols, anthropogenic aerosols) may also contribute. Phase shifts occurred around 1930 (cool to warm), 1965 (warm to cool), and 1995 (cool to warm).

Indian Ocean Dipole (IOD)

The IOD is a coupled ocean-atmosphere mode in the Indian Ocean, characterized by an east-west SST gradient. Positive IOD: Cool SST anomalies off Sumatra, warm anomalies in the western Indian Ocean; enhanced rainfall in East Africa, reduced rainfall in Indonesia and Australia; can compound El Nino droughts in Australia. Negative IOD: Opposite pattern; enhanced rainfall in Indonesia/Australia, drought in East Africa. The IOD index is defined as the SST anomaly difference between the western (50 degrees E-70 degrees E, 10 degrees S-10 degrees N) and eastern (90 degrees E-110 degrees E, 10 degrees S-0 degrees) tropical Indian Ocean. It sometimes develops independently of ENSO but is often triggered by ENSO events.

Madden-Julian Oscillation (MJO)

The MJO is the dominant mode of intraseasonal (30-60 day) variability in the tropics. It consists of a large-scale envelope of enhanced and suppressed convection that propagates eastward at ~5 m/s from the Indian Ocean across the Maritime Continent and into the western Pacific. The MJO modulates tropical cyclone activity (both Atlantic hurricanes and Pacific typhoons), monsoon onset and active/break cycles, ENSO triggering (westerly wind bursts), extratropical weather patterns, and the PNA/NAO. It is monitored using the Wheeler-Hendon Real-time Multivariate MJO (RMM) index, which defines 8 phases corresponding to the convective center's location. The MJO is a major source of predictability on the 2-4 week timescale.

Video: El Nino Explained

NOAA Climate.gov explanation of ENSO

5. Monsoons

Monsoons are seasonal reversals of wind direction and associated changes in precipitation, driven primarily by the differential heating of land and ocean. The word derives from the Arabic "mawsim" (season). Monsoons affect roughly two-thirds of the world's population and are critical for agriculture, water resources, and ecosystems across the tropics and subtropics.

5.1 Physical Mechanisms

The fundamental driver of monsoons is the land-sea thermal contrast. Land surfaces heat and cool much faster than the ocean due to their lower heat capacity, leading to seasonal pressure gradients that reverse the low-level winds:

-- Summer (wet) monsoon: Land heats rapidly, creating a thermal low. Moist oceanic air is drawn onshore, producing heavy rainfall. The upper-level flow diverges over the heated continent.

-- Winter (dry) monsoon: Land cools rapidly, creating a thermal high. Dry continental air flows offshore, producing dry conditions over the continent.

However, the monsoon is far more complex than a simple land-sea breeze scaled up. Additional factors include:

-- ITCZ migration: The seasonal migration of the ITCZ toward the summer hemisphere is the single most important large-scale control. Over the Indian Ocean, the ITCZ shifts from ~5 degrees S in January to ~20 degrees N in July.

-- Moisture-convection feedback: Latent heat release in deep convection intensifies the thermal low and strengthens the onshore flow.

-- Orographic effects: Mountain ranges (Himalayas, Western Ghats, Ethiopian Highlands) force uplift and block cold continental air.

-- Elevated heat source: The Tibetan Plateau (average elevation ~4500 m) acts as an elevated heat source in summer, dramatically strengthening the South Asian monsoon upper-level anticyclone.

-- SST patterns: Indian Ocean SST, the Indian Ocean Dipole, and ENSO strongly modulate monsoon intensity.

5.2 South Asian (Indian) Monsoon

The Indian Summer Monsoon (June-September)

The Indian monsoon is the most studied monsoon system, affecting over 1.5 billion people:

-- Onset: Typically arrives over Kerala (southwest India) around June 1 (plus or minus 7 days), advancing northwestward over ~6 weeks to cover all of India by mid-July.

-- Rainfall: Provides ~80% of India's annual rainfall. All-India seasonal mean: ~850 mm (June-September).

-- Wind reversal: Southwest winds (Somali Jet / Findlater Jet) at low levels bring moisture from the Arabian Sea. The Somali Jet reaches speeds of 30-40 m/s at ~1.5 km altitude -- the strongest low-level jet on Earth.

-- Upper-level: Tropical Easterly Jet (TEJ) at ~150 hPa over peninsular India (~40 m/s), driven by the tropospheric temperature gradient between the Tibetan Plateau and the southern Indian Ocean.

-- Active and break cycles: Intraseasonal oscillations (10-20 day and 30-60 day, related to the MJO) produce alternating periods of heavy rain (active phases) and dry spells (break phases).

-- Withdrawal: Begins from northwest India in early September, retreating southeastward. Complete withdrawal from southern India by mid-October.

-- Interannual variability: Coefficient of variation ~10%. Droughts often associated with El Nino; excess rainfall with La Nina, though the correlation weakened after the late 1970s.

5.3 East Asian Monsoon

East Asian Monsoon System

The East Asian monsoon affects China, Japan, Korea, and Southeast Asia:

-- Summer monsoon: Southeasterly winds from the Pacific bring moisture. The rain belt ("Mei-yu" in China, "Baiu" in Japan, "Changma" in Korea) migrates northward from May to August in a stepwise fashion.

-- Winter monsoon: Strong northwesterly cold surges from the Siberian High bring bitterly cold, dry air to eastern China, Korea, and Japan. Winter monsoon winds are typically stronger than summer monsoon winds.

-- Distinct from the Indian monsoon: The East Asian monsoon is more influenced by frontal activity (the Mei-yu front is a quasi-stationary front), the Western Pacific Subtropical High, and mid-latitude baroclinic disturbances.

-- Tropical cyclones: Late summer/autumn typhoons contribute significantly to East Asian rainfall, especially in the Philippines, Taiwan, and coastal China.

5.4 West African Monsoon

West African Monsoon

The West African monsoon governs the Sahel, the most climate-sensitive region on Earth:

-- Onset: Abrupt northward jump of the rain belt from the Guinea Coast (~5 degrees N) to the Sahel (~10-15 degrees N) in late June/early July.

-- African Easterly Jet (AEJ): A mid-tropospheric (~600 hPa) easterly jet at ~15 degrees N, driven by the temperature gradient between the hot Sahara and cooler Gulf of Guinea. It organizes mesoscale convective systems and African easterly waves.

-- African easterly waves: Synoptic-scale disturbances (period ~3-5 days) propagating westward in the AEJ. These are the seedlings of many Atlantic tropical cyclones.

-- Tropical Easterly Jet (TEJ): Upper-level easterlies at ~200 hPa provide divergence aloft, supporting deep convection.

-- Sahel drought: The catastrophic multi-decadal Sahel drought (1960s-1980s) was linked to cooling of the North Atlantic (negative AMO), warming of the South Atlantic, and global SST changes.

5.5 ITCZ Migration and Global Monsoons

The Intertropical Convergence Zone (ITCZ) is the ascending branch of the Hadley cell where trade winds from the two hemispheres converge. Its seasonal migration is the organizing principle for all monsoon systems:

-- Over the oceans, the ITCZ migrates only ~5-10 degrees seasonally (ocean thermal inertia limits displacement)

-- Over the continents, the ITCZ migrates much more (~20-30 degrees), driven by strong land-sea heating contrasts

-- The annual mean position of the ITCZ is at ~6 degrees N (not the equator) because the Northern Hemisphere has more land mass and the AMOC transports heat northward across the equator

-- The "energetic framework" for ITCZ position relates it to the atmospheric energy flux equator: the ITCZ lies in the hemisphere that is relatively warmer

-- Other major monsoon systems: North American Monsoon (southwestern US/Mexico), South American Monsoon (Amazon basin), Australian-Indonesian Monsoon, Southern African Monsoon

The concept of a global monsoon has gained traction, viewing regional monsoons as local expressions of a single global-scale seasonal oscillation in precipitation associated with the ITCZ and its solsticial excursions.

6. Climate Feedbacks

Climate feedbacks are processes that amplify (positive feedback) or dampen (negative feedback) the response to an initial radiative forcing. They are the central reason why climate sensitivity is uncertain and why the climate system's response to CO$_2$doubling is ~3 degrees C rather than the ~1.2 degrees C expected from the Planck response alone.

6.1 Formal Feedback Framework

Consider an initial radiative forcing $\Delta F$ (e.g., from doubling CO$_2$). In the absence of feedbacks, the system adjusts through increased longwave emission (the Planck response) until a new equilibrium is reached:

$\Delta T_0 = \frac{\Delta F}{\lambda_0}$

where $\lambda_0 = 4\sigma T_e^3 \approx 3.2$ W/(m$^2$K) is the Planck feedback parameter. For $\Delta F_{2\times CO_2} \approx 3.7$ W/m$^2$: $\Delta T_0 \approx 1.2$ degrees C.

With feedbacks, each feedback process $i$ has a feedback parameter $\lambda_i$ (units of W/(m$^2$K)), quantifying how much the TOA radiation budget changes per degree of surface warming due to that process. The total feedback parameter is the sum:

$\lambda_{total} = \lambda_0 - \sum_i \lambda_i$

Note the sign convention: positive $\lambda_i$ means positive (amplifying) feedback, reducing$\lambda_{total}$ and increasing the temperature response.

The equilibrium temperature change including all feedbacks is:

$\Delta T = \frac{\Delta F}{\lambda_0(1 - \sum f_i)}$

where $f_i = \lambda_i / \lambda_0$ is the feedback factor (dimensionless) for process $i$.

The feedback gain factor is $G = 1/(1 - \sum f_i)$.

If $\sum f_i < 1$: Finite amplification (stable climate).

If $\sum f_i \to 1$: Gain diverges -- runaway feedback (extremely unlikely for Earth).

If $\sum f_i > 1$: System unstable (does not apply to Earth's current climate).

Current best estimate: $\sum f_i \approx 0.5\text{-}0.65$, giving $G \approx 2\text{-}3$.

6.2 Water Vapor Feedback (Strongest Positive)

Water Vapor Feedback: $\lambda_{WV} \approx +1.8$ W/(m$^2$K)

Water vapor is Earth's most important greenhouse gas and its atmospheric concentration is strongly controlled by temperature through the Clausius-Clapeyron relation:

$\frac{de_s}{dT} = \frac{L_v e_s}{R_v T^2} \quad \Rightarrow \quad e_s \propto e^{-L_v/(R_v T)}$

Saturation vapor pressure increases by approximately 7% per Kelvin of warming.

As the climate warms:

-- The atmosphere can hold more water vapor

-- Observations confirm that specific humidity increases at ~7%/K (following Clausius-Clapeyron), while relative humidity remains approximately constant

-- More water vapor enhances the greenhouse effect, causing further warming

-- This feedback approximately doubles the Planck-only response

-- Well-understood physically; satellite observations (AIRS, AMSU) confirm the response

-- The water vapor and lapse rate feedbacks are physically coupled and are sometimes analyzed together: $\lambda_{WV+LR} \approx +1.2$ W/(m$^2$K)

6.3 Ice-Albedo Feedback

Ice-Albedo Feedback: $\lambda_{ice} \approx +0.3$ W/(m$^2$K)

A classic positive feedback with a simple physical mechanism:

1. Warming causes ice and snow to melt

2. Exposed darker surfaces (ocean, soil, vegetation) have much lower albedo

3. More solar radiation is absorbed

4. Further warming occurs, melting more ice

Key observations and quantification:

-- Arctic sea ice has lost ~50% of its September extent since 1979

-- Sea ice albedo: 0.5-0.7; open ocean albedo: 0.06-0.10

-- Arctic amplification (Arctic warming at 2-4 times the global rate) is partly driven by this feedback

-- Snow-albedo feedback operates over land: fresh snow albedo ~0.85, bare ground ~0.15-0.25

-- Strongest during spring and autumn when insolation is significant and ice is near its melting point

-- In Snowball Earth episodes, this feedback may have driven glaciation to the equator

6.4 Cloud Feedbacks (Most Uncertain)

Cloud Feedback: $\lambda_{cloud} \approx +0.3 \text{ to } +0.9$ W/(m$^2$K)

Clouds exert two competing radiative effects:

-- Shortwave (albedo) effect: Clouds reflect sunlight, cooling the surface (~-50 W/m$^2$ global mean)

-- Longwave (greenhouse) effect: Clouds trap outgoing IR radiation, warming the surface (~+30 W/m$^2$ global mean)

-- Net cloud radiative effect: approximately -20 W/m$^2$ (net cooling in the current climate)

The sign of the cloud feedback depends on how clouds change with warming:

-- High clouds (cirrus): Predicted to rise (Fixed Anvil Temperature hypothesis) without changing temperature, reducing OLR -- positive feedback.

-- Low clouds (marine stratocumulus): These produce strong SW cooling. If they decrease with warming, the feedback is strongly positive. This is the single largest source of uncertainty in climate sensitivity.

-- Cloud phase: Shift from ice to liquid clouds increases cloud optical depth and lifetime -- potentially negative feedback.

-- Cloud amount vs. optical properties: Different GCMs disagree on the sign and magnitude of low cloud changes.

IPCC AR6 assessed the net cloud feedback as likely positive (+0.45 W/(m$^2$K) best estimate), narrowing the uncertainty compared to AR5 thanks to advances in process understanding, high-resolution modeling, and observational constraints.

6.5 Lapse Rate Feedback

Lapse Rate Feedback: $\lambda_{LR} \approx -0.6$ W/(m$^2$K) (globally net negative)

The lapse rate feedback describes how the vertical profile of warming affects OLR:

-- Tropics: The moist adiabatic lapse rate decreases with warming, meaning the upper troposphere warms faster than the surface. This increases OLR relative to surface warming -- negative feedback.

-- High latitudes: Surface-based inversions mean warming is concentrated near the surface, with less warming aloft. This reduces OLR increase -- positive feedback (Arctic amplification).

-- Globally averaged, the tropical effect dominates, making this a net negative feedback.

-- Physically coupled to water vapor feedback: as the lapse rate decreases, more moisture is carried aloft. The combined water vapor + lapse rate feedback is more robust than either alone.

-- Combined $\lambda_{WV+LR} \approx +1.2$ W/(m$^2$K) is the best-constrained and most certain amplifying feedback.

6.6 Additional Feedback Processes

Vegetation-Albedo Feedback (+)

Warming allows forests to expand into tundra and grasslands, replacing high-albedo snow-covered surfaces with dark forest canopy. This reduces albedo, amplifying warming. Important during deglaciation: the retreat of ice sheets was amplified by the northward expansion of boreal forests.

Carbon Cycle Feedbacks (+)

Warming reduces the efficiency of oceanic CO$_2$ uptake (CO$_2$ solubility decreases with temperature), releases CO$_2$ and CH$_4$ from thawing permafrost, stresses terrestrial carbon sinks (increased drought, fire, mortality), and potentially releases methane from ocean clathrates. These processes are positive feedbacks operating on longer timescales (decades to centuries). The permafrost feedback alone could add 0.05-0.5 degrees C of additional warming by 2100.

Planck Feedback (-)

The most fundamental negative feedback: as the planet warms, it emits more longwave radiation (Stefan-Boltzmann law: $F \propto T^4$). This is the restoring mechanism that prevents runaway warming. $\lambda_0 \approx 3.2$ W/(m$^2$K) sets the baseline no-feedback sensitivity.

6.7 Equilibrium Climate Sensitivity

Equilibrium Climate Sensitivity (ECS) is defined as the equilibrium global mean surface temperature change resulting from a sustained doubling of atmospheric CO$_2$ concentration (from 280 to 560 ppm):

$\text{ECS} = \frac{\Delta F_{2\times CO_2}}{\lambda_{total}} = \frac{3.7 \text{ W/m}^2}{\lambda_0 - \sum_i \lambda_i}$

IPCC AR6 assessed ECS using multiple lines of evidence:

-- Process understanding and feedback analysis

-- Historical warming and ocean heat uptake observations

-- Paleoclimate constraints (Last Glacial Maximum, Pliocene, PETM)

-- Climate model ensembles (CMIP6)

Best estimate: ECS = 3.0 degrees C (likely range: 2.5-4.0 degrees C, very likely range: 2.0-5.0 degrees C)

Summary of Feedback Contributions (approximate):

-- Planck (negative): $\lambda_0 \approx -3.2$ W/(m$^2$K) [defines the baseline]

-- Water vapor (positive): $\lambda_{WV} \approx +1.8$ W/(m$^2$K)

-- Lapse rate (negative): $\lambda_{LR} \approx -0.6$ W/(m$^2$K)

-- Ice-albedo (positive): $\lambda_{ice} \approx +0.3$ W/(m$^2$K)

-- Cloud (positive, uncertain): $\lambda_{cloud} \approx +0.3 \text{ to } +0.9$ W/(m$^2$K)

-- No-feedback warming (Planck only): ~1.2 degrees C per CO$_2$ doubling

-- With feedbacks: ~3 degrees C per CO$_2$ doubling (factor of ~2.5 amplification)

Related sensitivity metrics include the Transient Climate Response (TCR), the warming at the time of CO$_2$ doubling under a 1%/year increase scenario (best estimate: 1.8 degrees C, likely range: 1.4-2.2 degrees C), and the Earth System Sensitivity (ESS), which includes slow feedbacks (ice sheets, vegetation, carbon cycle) and may be 1.5-2 times the ECS on millennial timescales.

7. Climate Modeling

7.1 Hierarchy of Climate Models

Climate models span a hierarchy from simple conceptual models to comprehensive Earth system models. Each level in the hierarchy is suited to different questions:

Energy Balance Models (EBMs)

The simplest class. Zero-dimensional EBMs balance global mean incoming solar with outgoing longwave radiation. One-dimensional EBMs resolve latitude and include meridional heat transport parameterized as diffusion. Budyko (1969) and Sellers (1969) independently showed EBMs with ice-albedo feedback exhibit multiple equilibria (including a "Snowball Earth" state). The 1-D EBM equation:

$C \frac{\partial T}{\partial t} = S_0 s(\varphi)(1-\alpha) - [A + BT] + D\nabla^2 T$

where $s(\varphi)$ is the distribution of insolation, $A + BT$ parameterizes OLR, and $D\nabla^2 T$ represents meridional diffusion of heat.

Radiative-Convective Models (RCMs)

One-dimensional column models that resolve the vertical structure of the atmosphere. They solve the radiative transfer equation including absorption and emission by greenhouse gases, and parameterize convective adjustment when the lapse rate exceeds the adiabatic lapse rate. Manabe and Wetherald (1967) used an RCM to make the first quantitative estimate of climate sensitivity to CO$_2$ doubling (~2.3 degrees C). Modern single-column models are still used for testing radiation and convection schemes before inclusion in full GCMs.

General Circulation Models (GCMs)

Three-dimensional models that solve the primitive equations of atmospheric and/or oceanic motion on a global grid. Atmosphere GCMs (AGCMs) coupled with Ocean GCMs (OGCMs) form Atmosphere-Ocean GCMs (AOGCMs). Typical horizontal resolution: 50-100 km (CMIP6 generation). They resolve synoptic-scale weather systems but must parameterize sub-grid processes (convection, turbulence, cloud microphysics, gravity wave drag). CMIP (Coupled Model Intercomparison Project) coordinates multi-model experiments for IPCC assessments.

Earth System Models (ESMs)

GCMs extended with interactive biogeochemistry, including the terrestrial and ocean carbon cycles, dynamic vegetation, atmospheric chemistry and aerosols, interactive ice sheets, and permafrost dynamics. ESMs are the primary tools for IPCC climate projections. Major ESMs include CESM (NCAR), GFDL-ESM (NOAA), UKESM (Met Office), MPI-ESM (Max Planck), IPSL-CM (IPSL), and EC-Earth (European consortium).

7.2 Model Components and Coupling

A modern Earth System Model couples multiple component models:

Atmosphere

-- Primitive equations (hydrostatic or non-hydrostatic)
-- Radiation scheme (SW and LW)
-- Convection parameterization
-- Cloud microphysics
-- Boundary layer turbulence
-- Gravity wave drag

Ocean

-- Navier-Stokes equations (Boussinesq, hydrostatic)
-- Thermohaline circulation
-- Mixed layer and mesoscale eddy parameterization
-- Sea ice thermodynamics and dynamics
-- Marine biogeochemistry

Land Surface

-- Surface energy and water balance
-- Soil thermal and hydrological processes
-- Dynamic vegetation
-- Snow cover and permafrost
-- Terrestrial carbon fluxes

Cryosphere

-- Ice sheet dynamics (Greenland, Antarctica)
-- Glacier mass balance
-- Permafrost carbon
-- Sea ice rheology and transport

Video: How Climate Models Work

NASA Goddard explanation of climate modeling

Summary

Part IV provided a comprehensive treatment of the fundamental components and processes of Earth's climate system:

-- Earth's energy balance: solar constant, planetary albedo, effective temperature (255 K), greenhouse effect (+33 K), TOA budget, and surface energy balance with Bowen ratio partitioning
-- General circulation: Hadley cell dynamics and angular momentum conservation, Held-Hou theory, Ferrel and Polar cells, subtropical and polar front jet streams, meridional heat transport
-- Ocean-atmosphere interactions: Ekman transport and spiral, Sverdrup balance, western boundary currents, thermohaline circulation (AMOC), air-sea heat fluxes, and mixed layer dynamics
-- ENSO and teleconnections: Walker circulation, Bjerknes feedback, delayed oscillator and recharge-discharge theories, ENSO indices, Rossby wave teleconnections, and detailed treatment of NAO, PNA, AO, PDO, AMO, IOD, and MJO
-- Monsoons: land-sea thermal contrast, ITCZ migration, Indian summer monsoon (onset, Somali Jet, active/break cycles), East Asian monsoon (Mei-yu), and West African monsoon (AEJ, Sahel drought)
-- Climate feedbacks: formal feedback framework, water vapor (strongest positive), ice-albedo, cloud (most uncertain), lapse rate, vegetation, and carbon cycle feedbacks; equilibrium climate sensitivity (ECS ~ 3 degrees C)
-- Climate modeling: energy balance models, radiative-convective models, GCMs, and Earth system models

The next parts will cover weather analysis and forecasting (Part V), paleoclimatology and past climates (Part VI), extreme weather events (Part VII), and the science of anthropogenic climate change (Part VIII).

NPTEL: Introduction to Atmospheric Science

Lectures from the NPTEL Introduction to Atmospheric Science course on the Earth system, including oceans, the hydrological cycle, and the carbon cycle.