One of the common assumptions made in climate science is that at the top of the atmosphere the energy in is equal to the energy out in equilibrium. There is absolutely nothing wrong with that assumption, provided that the it is realistically considered. Ein = Eout over some time period. Ein never has to exactly equal Eout at any given moment in time. In fact, Ein probably does not equal Eout very often. It is a tool. If measure Ein and it is greater than Eout then there is an imbalance, more energy is remaining in the system than being released.
I modified the standard Ein=Eout assumption to Ein=Eout +S-W, where S is entropy and W is work. Depending on what you define as work or entropy, this is a more correct form to consider. Work in my opinion is the atmospheric lapse rate, ocean temperature differential that powers the winds etc. If the Earth were a billiard ball in space, Ein=Eout would be perfect. Earth is not a billiard ball so it deserves a more realistic consideration.
A rather large reason that it is a little disrespectful to consider the Earth a billiard ball is because it has fairly large oceans. Using the same logic as the Ein=Eout at the top of the atmosphere, I can consider that the oceans are a system that over some time period also meet the Ein=Eout requirements. This is not received very well by many. It is perfectly valid though since the Earth appears to have had oceans for a long time and not in any immediate danger of losing those oceans. This assumption also should be treated with the same respect as the TOA Ein=Eout assumption.
So if both the oceans and the Top of the atmosphere have equilibrium conditions over some period of time and it is unlikely that the time periods are the same, what good is using the equilibrium assumption for both systems? Well, in between the oceans and the top of the atmosphere are things inside the atmosphere and outside the oceans. That is where the -W goes and the +S passes through.
Over a long enough time scale, the oceans have an equilibrium condition and the top of the atmosphere also has an equilibrium condition. The in between the oceans and atmosphere may never and likely has not ever had an equilibrium condition. Mountains erode, land erodes, new land forms, lakes form, rivers form they also fade. The oceans rise and the oceans fall as ice builds and fades on land, but the oceans are a constant for the majority of the surface of the Earth. By using the assumption of equilibrium for both the oceans and the top of the atmosphere, you can consider an equilibrium model that recognizes the chaos, but doesn't just dive right into it.
Now if the oceans gain more energy over some time period, the assumption implies they will get rid of the energy in the same amount over some time period. The atmosphere can only get rid of energy by radiation according to Greenhouse Theory. The oceans can release energy is a large number of ways, one is by losing mass. That is right sports fans, evaporation does not have to return to the ocean immediately as condensation. Ice formed near the poles can stack up on the land and not return for some time. Ice formed can sublime to the atmosphere. As long as that water and ice returns over some time period, the oceans will have some equilibrium.
That is not too hard for most to comprehend, but how is that possibly an equilibrium? If the oceans derive most of their energy from the sun passing through the top of the atmosphere, and they transfer some of that energy to land, then the TOA Ein would not equal Eout while that was going on.
Just for grins, if say the oceans transferred billions and billions of tons of water to the polar regions as ice, Since each gram of that water would have to release 334 Joules of energy in that phase change, then the atmosphere would receive a large portion of billions and billions and billions of Joules of energy. As the ice melted, it would have to absorb all that energy again either from the oceans of the atmosphere. There would be no true equilibrium for either the oceans or the TOA while that was happening. If you find the right time period where the oceans found equilibrium, you would likely find the time period that the TOA found equilibrium.
That is a temperature reconstruction for the past 60,000 years for data collected at Lake Tanganyika in Africa near the equator. That may be too short of time for there to have been either a true ocean or TOA equilibrium . That 2.5C range though near the Equator where the majority of the energy is absorbed from the sun by the oceans, does provide a reasonable guess as to what equilibrium may be. Comparing an idealized equilibrium at the top of the atmosphere to an idealized equilibrium in the oceans, is just a way to reduce the uncertainty in each. See, there is no reason to assume that Ein=Eout at the top of the atmosphere over the past 120 years either is there, when the Earth has been changing for millions of years :) If for the entire period the temperature was below average the oceans released energy, how long you reckon it would take for the oceans to regain that energy?