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The case for anthropogenic global warming rests on a physically consistent combination of forcing, energy storage and observed response, rather than on the claim that every unusual event has the same cause. For this examination, the observational comparison is the evidence available around 2010, and the two forecast horizons are approximately 2060 and 2110. Separating the robust mechanisms from uncertain regional details is essential to a coherent attribution of recent climate change.

The greenhouse effect follows from radiative transfer. Sunlight supplies energy, while the Earth loses energy mainly through long-wave radiation. Carbon dioxide, methane and other greenhouse gases absorb and emit in parts of that outgoing spectrum. Increasing their concentrations alters the levels and temperatures from which radiation escapes, initially reducing the net loss of energy for a given surface state. The surface and atmosphere must then warm until outgoing radiation again balances the input. Strong absorption near the centres of some bands does not eliminate the influence of additional gas: absorption in the wings and the changing height of emission still matter. For scale, the approximate carbon dioxide forcing law $\Delta F\simeq 5.35\log (C/C_0)\mathrm{W}{\mathrm{m}}^{-2}$ gives about $3.7\mathrm{W}{\mathrm{m}}^{-2}$ for doubling. It describes a forcing, not the ultimate temperature response, which additionally involves climate feedbacks and ocean heat uptake.

Measured increases in atmospheric carbon dioxide are consistent with fossil-fuel combustion and changes in land use. The carbon isotope signature and atmospheric oxygen consumption provide independent evidence of the combustion source, while the ocean and land absorb part of the emitted carbon. Methane and other climatically active gases add to the forcing. Aerosols exert partially compensating effects, so net human forcing is smaller than the sum of the warming gases alone. Uncertainty in that compensation affects the quantitative rate of warming without removing the greenhouse mechanism.

A sustained rise in global temperature is accompanied by increased ocean heat content, glacier retreat and sea level rise. This combination is harder to explain as an artefact of a few surface thermometers than a temperature series in isolation: the ocean is a large energy reservoir, and thermal expansion and melting have independent observational consequences. Internal variations of ocean circulation can move heat between regions and alter warming over particular decades, but cannot indefinitely supply a positive global energy accumulation without a change in the energy budget. Solar changes and volcanic eruptions also influence climate, and must be included in attribution; they do not reproduce the full recent warming pattern and sustained heat gain. Volcanic aerosol episodes chiefly produce temporary cooling. Broad troposphere warming together with stratosphere cooling is another useful fingerprint: additional greenhouse gases and ozone changes have a different vertical response from simply increasing solar input. No one fingerprint is unique to one cause, but their joint agreement with greenhouse forcing strengthens the attribution.

Polar observations are especially informative because they connect atmosphere, ocean and ice. In the Arctic, reduced summer sea ice extent, thinning and loss of multi-year sea ice indicate a diminished ice reservoir. Warmer air, earlier melt and delayed freeze-up contribute, while wind and current changes redistribute ice and export thick floes. Pacific heat inflow and changes in Atlantic-origin waters supply oceanic routes to melting. The protection afforded by the cold halocline means that warmer Atlantic water does not automatically heat the ice: the intervening mixing and density stratification must be considered. The 2007 retreat illustrates how long-term thinning, anomalous winds and greater solar absorption can combine. It neither proves that weather variability has ceased nor provides a reason to ignore the longer-term energy imbalance.

Loss of grounded ice has a different global implication. Increased surface melt and runoff on Greenland, and changes in outlet-glacier discharge, transfer water from land to the ocean. In Antarctica, warming of the Peninsula and disintegration of some ice shelves demonstrate strong regional change. Warm ocean water reaching shelf cavities can thin floating shelves from below; loss of ice-shelf buttressing can then speed grounded-ice discharge. The floating shelf's disappearance is not itself equivalent to adding its whole volume to sea level. The important subsequent response is increased loss from grounded ice sheets. Increased snowfall can compensate some losses, so a mass budget must distinguish accumulation, melting and ice flow.

The two polar regions should not be assumed to behave identically. Around 2010, Antarctic sea-ice changes included strong regional contrasts and an overall satellite-era behaviour quite different from Arctic summer retreat. Winds, ozone-related atmospheric changes, freshwater effects and the circulation of the Southern Ocean influence the Antarctic pattern. A large cold continent surrounded by an ocean is physically different from an ocean surrounded by land, and vigorous Southern Ocean heat uptake can delay surface warming. A regional increase in Antarctic sea ice is therefore compatible with global ocean heat gain and losses from some grounded Antarctic ice; it still needs its own dynamical and thermodynamic explanation. Credible attribution accounts for these differences instead of requiring uniform warming everywhere.

Several mechanisms produce polar amplification. The ice-albedo feedback is the most direct: retreating snow and ice expose darker surfaces that absorb more sunlight, causing further warming and melt. Much of the extra energy over newly open Arctic water is stored during summer and released to the atmosphere in autumn and winter, when an ice-covered ocean would be better insulated. Consequently the largest near-surface atmospheric response need not occur in the season of greatest solar input. Sea-ice loss changes both reflection and the timing of ocean heat release.

The atmospheric vertical structure also matters. In the tropics, convective adjustment often produces appreciable warming aloft, which increases radiative cooling. Stable polar boundary layers can concentrate warming near the surface, producing a different lapse-rate feedback and less compensating cooling from upper layers. Furthermore, the idealized Planck feedback scales as $4\sigma T^3$: colder emitting regions have a smaller increase of blackbody radiation per kelvin, although a quantitative atmospheric comparison needs full radiative transfer. Water-vapour and cloud changes modify both short-wave and long-wave fluxes, with cloud effects depending on season and surface properties. Changes in poleward heat and moisture transport provide further coupling. Thus polar amplification has several interacting causes; it is not simply the same local ice-albedo process repeated throughout the year.

Polar change affects the rest of the planet. Grounded-ice loss contributes to eustatic sea level change, while ocean warming contributes to thermosteric sea level change; together they increase coastal flooding and erosion risks. Redistribution of ice and freshwater changes density stratification and dense-water formation, potentially altering the Atlantic meridional overturning circulation and other oceanic heat and carbon transports. A weakening is physically plausible under warming and freshening, but an immediate complete shutdown is not a necessary prediction. Permafrost carbon feedback can release additional carbon dioxide and methane, increasing warming outside the Arctic. Habitat loss, changing primary production and altered food webs affect marine ecosystems and people, while a longer open-water season changes navigation, coastal exposure and resource access. These impacts are not exhausted by a single global-mean temperature number.

Forecasts require an emissions scenario as well as physical understanding. On the roughly fifty-year horizon, continued emissions imply further ocean and atmospheric warming, a longer Arctic melt season, less late-summer ice and a greater fraction of young seasonal ice. Mountain glaciers generally continue to lose mass, and sea level continues rising through thermal expansion and land-ice loss. Variability can interrupt a regional trend for several years, and the exact first nearly ice-free Arctic summer cannot be fixed from the 2007 minimum. Ocean heat storage and slow ice-sheet adjustment also mean that some further change is committed even if emissions are reduced.

By approximately 2110, sustained high emissions would imply a substantially warmer world, potentially several degrees above early twenty-first-century global temperatures, with stronger Arctic warming and likely recurrent nearly ice-free late summers. This is a seasonal prediction, not a claim that the entire Arctic Ocean must be ice-free in winter. Losses of grounded ice and thermal expansion would produce larger cumulative sea level rise, plausibly measured in several decimetres and potentially more if ice dynamics accelerate. The largest uncertainty is not whether adding heat expands water, but the future emissions trajectory and the response of major ice sheets. Complete loss of Greenland on this century-long horizon is not required by that prediction. With strong mitigation, substantially smaller late-century warming and ice loss are possible, although sea level can continue to rise beyond stabilization of surface temperature.

Anthropogenic forcing explains the broad warming signal; feedbacks amplify polar change, while emissions and ice dynamics govern future outcomes. This distinction permits both a firm physical conclusion and honest uncertainty about dates, regional details and the magnitude of rapid ice-sheet change.

A convective chimney is a localized, deeply mixed region within a stratified ocean, formed when surface buoyancy loss allows convection to penetrate far below the surrounding mixed layer. The chimney describes the mixed water column and its circulation; instantaneous downward transfer occurs through many smaller plumes, accompanied by compensating motion and lateral exchange, rather than through one permanently uniform downward pipe. Open-ocean convection occurs in the Labrador and Irminger Seas, the Greenland Sea, the northwestern Mediterranean, and episodically in the open Weddell Sea under a large polynya. Dense-water formation on a continental shelf is related but geometrically distinct from deep open-ocean chimney convection.

Observed Greenland Sea convective chimneys include compact, approximately circular, weakly stratified cores with temperature and salinity much more uniform vertically than in the ambient ocean. A mapped example was about $20\mathrm{km}$ across, extended to about $2500\mathrm{m}$ in winter, and rotated anticyclonically. In summer a fresh, low-density cap and shallower lateral intrusions could isolate the deep core, while winter buoyancy loss removed the cap and renewed deep contact. Such cores could persist through several seasons, so presence of a deep homogeneous core is not proof that vigorous convection is occurring continuously. These particular dimensions and seasonal structure come from successive hydrographic surveys of Greenland Sea chimneys.

Formation is favoured by the cyclonic Greenland gyre, which domes density surfaces and can reduce the depth of the stratified barrier. Cold, dry wind outbreaks produce strong sensible, latent and longwave heat loss. Where frazil ice and pancake ice form in the Odden ice tongue, ice growth removes relatively fresh material while brine rejection increases the density of the remaining water. Ice advection can keep exposing water for further freezing and separate local brine release from later freshwater return. This combination of preconditioning, cooling and sustained salt input can make a formerly buoyant surface layer dense enough to convect.

Conversely, a fresh surface cap supplied by Arctic freshwater and ice melt strengthens density stratification. Warmer atmospheric outbreaks reduce surface heat loss and ice production; circulation changes affecting the cold northwesterly winds and the Odden can reduce the brine source. Atlantic advection supplies both heat and salt, with competing effects on density, so temperature alone is not an adequate diagnostic. The historical decline in Odden ice formation and changes in wind regimes offer a mechanism for less favourable chimney production around the period considered, but ice-driven formation is a physical hypothesis, not evidence that every observed chimney requires ice or that every local change follows a single climate index. The Greenland Sea salt-flux model explicitly includes ice production and advection.

For the brine rejection mechanism, let ${\dot{h}}_i>0$ be ice growth and let $s_w,s_i$ be water and ice salt mass fractions. Newly formed ice removes mass ${\rho }_i{\dot{h}}_i$ per area per time. Compared with removing water at concentration $s_w$, it leaves an excess salt flux in the liquid ofThe units are $\mathrm{kg}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$. With the exam's approximation $s=10^{-3}S$ for salinity $S$ in psu, the corresponding mixed-layer salinity tendency is, to first order,If ${\beta }_S=(1/{\rho }_w)(\partial \rho /\partial S)>0$, the surface buoyancy input is negative, with scale $-g{\beta }_S({\rho }_i/{\rho }_w){\dot{h}}_i(S_w-S_i)$. The enhanced density produces downward saline plumes that deepen mixing if this buoyancy loss overcomes the available density stratification. This explains why exporting new ice while retaining its rejected salt can strengthen overturning, whereas later local melt reverses the freshwater effect.

For the numerical comparison, the cover gives the specific heat capacity of ice, not of seawater. A seawater value must therefore be supplied explicitly. Take $c_{p,w}=4000\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$ and use the stipulated ${\rho }_w=1025\mathrm{kg}{\mathrm{m}}^{-3}$. A $100\mathrm{m}$ column has initial water mass per areaCooling it by $1.8\mathrm{K}$ removesThe specified thermal density relation givesThis assumes the whole column mixes and neglects entrainment and advected heat. Using the supplied ice heat capacity $2100$ for liquid seawater would change $Q$ incorrectly.

At the freezing point the same heat extraction produces a pure-ice mass per areaHere $f_i$ is the fraction of the original water mass removed into ice. With the explicit ice-density approximation ${\rho }_i=900\mathrm{kg}{\mathrm{m}}^{-3}$, the resulting ice thickness isThe water-equivalent thickness uses a reference water density: with fresh water at $1000\mathrm{kg}{\mathrm{m}}^{-3}$, it is $m_i/1000=\boxed{2.196\mathrm{m}\simeq 2.2\mathrm{m}}$. The depth of the original seawater removed is instead $m_i/1025=\boxed{2.143\mathrm{m}}$. These three quantities are different; $2.2\mathrm{m}$ is not the physical ice thickness for the stated density approximation.

Let the initial salinity be $S_0$. Complete exclusion of salt from the ice leaves all the initial salt in a liquid mass $M_1=M_0-m_i$. Conservation of salt during freezing givesThe initial salinity is not printed, so a unique numerical salinity increase requires another explicit assumption. For $S_0=35\mathrm{psu}$,The total density increase after cooling followed by freezing is then about $0.9464\mathrm{kg}{\mathrm{m}}^{-3}$. The factor $1/(1-f_i)$ is required because salt concentration refers to the remaining liquid mass. Using ice thickness divided by the original water depth as the removed mass fraction would violate this accounting.

For this assumed salinity, the freezing-to-cooling density efficiency shows that equal heat extraction at freezing produces about $0.7664/0.18=\boxed{4.26}$ times the density increase of the initial cooling. At low temperature the thermal expansion response is weak, whereas brine rejection changes salinity efficiently. This supports strong freezing-driven convection where water is already near its freezing point. It does not mean freezing always creates deep chimneys: the initial density stratification, freshwater supply, mixing depth and later melting remain decisive. The freezing point itself decreases as salinity rises; keeping it at $-1.8^{\circ }\mathrm{C}$ is the exam's approximation. Allowing that small additional cooling and a temperature-dependent equation of state would require a refined heat budget.

Important other sites of freezing-enhanced downward transfer include the Ross and Weddell Antarctic shelves and their coastal polynyas, Adélie Land and Cape Darnley, Arctic shelves such as the Barents and Kara Seas, and the Sea of Okhotsk. On shelves the saline dense water can cascade down a continental slope and feed deeper waters; the same salt-removal balance operates without requiring an isolated open-ocean chimney. A later direct observational example is bottom-water formation associated with Cape Darnley sea-ice production.

Atmospheric warming of the Greenland Sea can reduce surface cooling and ice formation, while increased freshwater input can inhibit convection. If these changes weaken the Atlantic meridional overturning circulation and its northward heat transport, their ocean-mediated tendency is relative cooling, or reduced warming, of northwestern Europe compared with otherwise identical atmospheric warming. This is not a prediction of net European cooling under all emissions scenarios, nor does one chimney determine the whole overturning circulation: other convection regions, winds, freshwater pathways and coupled ocean adjustment also matter. The physical conclusion is the sign of the heat-transport response, not a specified century-scale temperature decrement.