How is energy transferred from Earth's surface to the atmosphere?

Conduction, convection, radiation and also evaporation.

Conduction is when two bodies are in physical contact with one another. If there's a thermal gradient between the two bodies (they're different temperatures), heat will generally be transferred from the warmer body to the cooler body until equilibrium is reached. The rate at which this happens depends largely on the thermal conductivity of the two bodies - higher means quicker; also how well they are contacted. In this case the two bodies are the earth's surface (land or surface water) and the layer of air immediately next to it.

Convection is related to conduction, and happens in air because it is a gas. When you heat part of a gas (by conduction for example), it expands and becomes less dense. This makes it tend to rise, as it becomes buoyant, similar to a cork being buoyant in a bowl of water. Cooler air from the surrounding area moves in to replace the heated air which rose and the cycle continues. Meanwhile the heated air at some height, cools, transferring thermal energy to the atmosphere.

Radiation (electromagnetic) - typically infra red, also transfers energy stored in the surface to the atmosphere. Whilst being transparent to ultraviolet radiation (one of the main forms of light coming from the sun), carbon dioxide, water vapour and methane which naturally occur in the atmosphere trap or absorb infra red radiation, once again being a way in which energy in the earth's surface gets transferred to the atmosphere.

Finally, Evaporation takes what is known as latent (hidden) heat from a body of surface water (could be a stream, canal, river, lake or ocean) and transfers it to the atmosphere. Evaporation is an energy intensive process (it is endothermic), meaning you have to put heat in for it to happen. That heat can come from that which is already present in the earth's surface (mainly as a result of sunlight hitting it). When water evaporates, into vapour, it takes this heat into the atmosphere. When it gets high enough to cool, the water 'condenses out' into droplets and it rains. Condensation is the reverse of evaporation - it releases heat, in this case, into the atmosphere.

Energy incident to the earth's surface is primarily sunlight, in wavelengths for which the atmosphere is transparent.

If the sunlight is reflected off snow, ice, or at acute angles from water surfaces, it is still at those short incident wavelengths, and is transmitted back into space through the transparent atmosphere.

If it is absorbed in the ocean which of course accounts for nearly 80% of the earth's surface , the energy stored in the ocean increases, primarily near the surface where most of the energy is captured. In equilibrium, that energy increases the energy of water molecules that leads to evaporation. It is evaporation to the atmosphere that accounts for most of the energy transferred from the oceans, so the atmospheric energy is comprised of the sum of moisture and its gases.

On solid earth surfaces that are covered in growing material, photosynthesis absorbs most of the incident sunlight, converting that energy to the chemistry of plant growth (plus evaporation to regulate the plant temperature). The fraction of wavelengths not absorbed are in the spectrum we call 'green', and that is what we see as the predominant colour of plants.

Sand, rock, dry dirt and the like are heated by sunlight so that they transfer energy to the atmosphere by both radiation and convection. The radiation portion we do not see but feel as heat is in the longer wavelength, 'infrared' portion of the spectrum. It is in this range of wavelengths that we encounter the 'greenhouse effect'. It is only those wavelengths that are important to the CO2 contribution to the greenhouse effect. Thus we can reduce that portion of the greenhouse effect by reducing atmospheric CO2 (and methane etc), and/or we can reduce the fraction of the solid surface radiation by minimizing surfaces that can be elevated to high enough temperatures by the sun.

Convection needs only small differences in temperature and thus air density to start this vertical mixing. The temperature of such air currents are never high enough to radiate the infrared wavelengths retained by our common greenhouse gases, so have little impact on net sun energy retention. 

It is easiest to understand the impact of maintaining and increasing forests. Of course we could also reduce paving and roofing the earth's surface, all of which can reach IR radiation temperatures. A lesser understood impact is to reduce our depletion of groundwater. The latter threatens increasing desertification, and as moisture becomes less available at the surface, growth fails and we get more hot dirt. 

Energy is transferred between the earth's surface and the atmosphere via conduction, convection, and radiation. Conduction is the process by which heat energy is transmitted through contact with neighboring molecules.

mostly through convection(bulk motion of the air), and to outer space it is mainly through radiation.

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