On the planet I’m making, there was a big flood that happened and raised the sea level by 30 meters.
I want the planet to have a cold climate, so I can’t simply explain the flood by saying it was global warming (because then the planet would be too hot). Also, the temperature before this flood was -10°c but it warmed to 4°c because of a lower albedo
How would I explain it?
Volcanic activity can effectively melt large quantities of ice even though the climate is cold, and that molten water will cause floods.
Just look at Iceland: once a volcano starts erupting under the ice cap, large floods ensue.
Mýrdalsjökull is subject to large jökulhlaups when the subglacial volcano Katla erupts, roughly every 40 to 80 years. The eruption in 1755 is estimated to have had a peak discharge of 200,000 to 400,000 $m^3/s$.
Therefore you just need to take Iceland example and expand it on a larger scale: you have already extensive ice caps, since the planet is cold, so you just need to add large scale volcanic activity.
"I want the planet to have a cold climate, so I can’t simply explain the flood by saying it was global warming (because then the planet would be too hot)."
That's no problem. Just have it warm up from 'very cold' to merely 'cold'. When an ice age ends, the ice sheets melting can release large floods when meltwater is pent up behind ice dams that suddenly break. Consider the real-world example of meltwater pulse 1A which raised sea levels 16-25 metres. Although the globe was warming, it was still globally colder 14,000 years ago than it is today.
Although very abrupt climate change with jumps of 5-10 C can occur in a matter of a few years (e.g. The Younger Dryas), Meltwater Pulse 1A is thought to have taken about 400-500 years, so that may be a bit slow for your purposes.
If you want something a bit faster than that, I suggest volcanoes, earthquakes, landslides, tsunamis, meteorites, etc. Also have a look at the Zanclean flood, or the similar event postulated for the Black Sea, for another idea.
Salt Meteors or Meteorites
http://www.psrd.hawaii.edu/Nov99/PurpleSalt.html A large enough salt meteor or shower of salt meteorites spiked salinity levels within a large enough region and de-iced a large enough portion of the planet to cause global sea level rise of about 30 meters. After the sea level rose, and salinity concentration became diluted (or reason X, like the additional salt reacting to existing chemicals on the planet and causing them to fall out of suspension as sediment, etc.), then the water is able to freeze again.
Ice dam breaks.
https://www.youtube.com/watch?v=Zy_m_2zQFX4
I think this was done best in the movie Ice Age: the Meltdown. I like the squirrel and it should be in more movies. But it happened for real in our world. The Missoula floods were big ones. Lake Missoula was formed by melting glaciers and the water impounded behind an ice dam.
http://hugefloods.com/LakeMissoula.html
When the dam broke (probably because of a squirrel somehow) the water rushed across the land and seriously washed things away. Similar actions on the North American East coast formed the Hudson river valley. You can check out images or maps of these places for ideas about topography formed by megafloods.
That said, in our world it was not enough water to raise sea level 30 meters. But the principle is sound. If your world has small and shallow oceans relative to Earth, and a colossal amount of water locked into glaciers on one of your continents, a relative thaw and unfreezing of some of that water could wind up with a continent spanning meltwater lake, and then a big dump into the ocean. Several big dumps might be more realistic; that is apparently how the Missoula floods worked, although I read somewhere that the Hudson River Valley was carved over the course of a week.
That does not mean your world needs to get hot - a transient heating and melt for some reason will do. I like a volcanic eruption not for hot lava and heating (too local) but ashy eruptions that paint the glaciers black and alters their albedo. Or a Fortean rain from space of nitrogen and phosphorus that stimulates the snow algae... and alters glacier albedo.
This is roughly the same problem that creationists face in explaining the flood of Noah, therefore we can borrow some of their theories for this case.
Canopy Theory:
Some layer of water surrounded your planet and eventually became rain due to a disturbance. This could be a layer of water vapor maintained by same (possibly biotic?) phenomena, or a belt of water-ice that got disturbed by a passing body or caught by an expanding atmosphere.
Hydroplate Theory:
Water is fairly common in the universe, so it's not that outlandish that there could have been huge aquifers beneath the earth that eventually emptied themselves due to the movement of the tectonic plates.
Catastrophic Plate Tectonics
If your planet has oceans, all you need to do to flood it is have the ocean floor rise significantly and rapidly. The creationists have proposed somewhat plausible mechanisms for how this could happen.
Disclaimer: This answer was written with the intent to neither endorse nor condemn creationism, but merely to borrow inspiration from the thought given to the problem.
The only plausible ways I can think of that don't also create sea level rise from global warming is to have some large amount of ice or water trapped above sea level and suddenly released. There are parallels to both in Earth's geologic history, though on a smaller scale.
For an ice-based flood, imagine a polar continent where the ice sheets are even more delicately-balanced than Antartica's are. Some event such as an earthquake or volcano breaks the keystone of that balance, causing a catastrophic collapse. On Earth, a collapse of the West Antarctic ice sheet could cause a sea level rise of about 4 meters: https://news.harvard.edu/gazette/story/2021/04/study-says-antarctic-ice-sheet-melt-to-lift-sea-level-higher-than-thought/ Just increase the size of the collapsing sheet as needed for your world.
For a land-based flood, imagine we have a large, closed basin at some elevation above sea level, something like the Great Basin of western North America, but larger & deeper. This collects water over the ages (perhaps it's not in the rain shadow of the Sierra & Cascades), until it finally over-tops the rim. The rock at that point is fairly weak, and erodes, emptying the basin in weeks or months. This actually did happen, though not on a large enough scale to affect global sea levels: https://en.wikipedia.org/wiki/Bonneville_flood The catastrophic filling of the Mediterranean & Black Sea basins are similar, though they would have lowered global sea levels - an anti-flood, if you will.
or even simpler:
It's a cold(er) climate but there is still liquid water. So frozen water entering the planet would become liquid, generally. So, you just need a giant ice meteor that evaporates into, basically, really thick, clouds as it enters the atmosphere. This gives you mass amounts of suspended water (briefly) as it begins a slowly circulating global-level thunder/rain storm for the next 4(99?) years
Baby geologist here. You don't need a flood. You don't need anything exceptional. As ice ages develop, sea level goes up.
Well, let me actually clarify a bit--the coastlines go up. There's less water in the oceans--it's all turning to ice through the precipitation cycle--but the shores still go back up the coast anyways.
Why? Well, because rock's a fluid on geologic timescales. Imagine you're in a boat, and then somebody puts a bunch of stuff in it: the boat's going to settle. In this case, the continents are a boat floating in a sea of rock, and all the ice developing is the stuff. We call this state isostasy, and when you add ice to the continents, you disrupt it.
That's right, baby, it's isostatic depression. When you cover the planet in ice, the continents sink into the earth a bit & the coastlines go up, by up to 200 m during the last ice age.
The opposite is also why sea levels are still falling on Canada shorelines today--North America is still rebounding after all the ice came off a short 10s of 1000s of years ago.
EDIT: Surprised to see downvotes without comments. Added some sources for you skeptics.
A nearby supernova inside a cloud of dust.
The supernova released an immense amount of heat and light, but this energy was trapped by the dust cloud that surrounded it, heating the dust cloud to many thousands of degrees.
For a year or two, there was a moon-apparent-diameter "second sun" in the sky, that gave of immense amounts of infrared heat, heating the planet surface by 10-15 degrees C.
This has caused a mass melting of the polar caps, ice sheets and glaciers, thus raising the sealevel by a lot.
After several months, maybe a year, the cloud cools below visible, and within 5 years it stops emitting any significant infrared heat, thus allowing the planet to slowly regain its old thermal equilibrium. The planet is a cold planet again. However it will take millenia for the water to be deposited into new icecaps, icesheets and glaciers.
The fun is over.
For now.. In about 5000 years, the shockwave of that dust cloud that got clobbered by the supernova will reach the planet, and then all hell breaks loose.
Assumptions:
A relatively small ice shelf on a coastline is holding back a continent's worth of glaciers from sliding into the ocean.
Picture a massive polar continent covered in ice sheets and glaciers (Antarctica but bigger, maybe). The geology of the continent is such that a majority of the glacier flow all converges to a coastline that has a significant ice sheet in the water that effectively "dams" the glacial flow. Or perhaps there are multiple convergence points, that are all dammed in a similar way.
The minor warming of your planet has been just enough to allow the ice sheet dam (or dams) to weaken and break away from the continent as massive icebergs. These icebergs themselves will not cause an increase is sea level since they were already floating on the ocean. However, without those dams in place, the continental glaciers are now free to dump their contents of centuries (millennia?) of accumulated ice and snow into the oceans, which will cause a rise in sea level.
The timeframe of this may be not be swift enough for your story as the pace of this flow of ice into the ocean will be, by definition, glacial. It could be a contributing factor though.
