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Many ocean organisms live only at specific depths. For example, the coral Acropora palmata only grows within a few meters of the sea surface, where it can get the most sunlight.

Suppose you drill a core into a coral reef using a floating drill, and find some of this coral that's 10,000 years old at a depth of 100 meters below the surface. How could this happen? Either the sea level must have risen, or the island the coral is growing on must have sunk.

You can figure out whether the island has sunk by looking for very old corals of the same type. For example, if you find corals dating back to a previous warm period 120,000 years ago at or above sea level, you can be sure that the land isn't sinking very fast.

You can repeat this analysis for other corals that live at greater depth, you can repeat the analysis in coral reefs all around the world, and repeat it for other types of organisms that live near the water surface in colder climates, and you find a consistent pattern of sea level change over time.

> Is someone who denies the historic sea level graph equivalent to a Flat Earther?

There aren't many people who deny that sea level has changed. Most often climate change deniers use the past sea level graph to show that sea levels are not stable, and thus -- they say -- the current sea level rise is nothing special, and a natural process. Some people argue that the ages of the changes are wrong, and the sea level changes actually represent the biblical flood.

http://people.uncw.edu/grindlayn/GLY550/Fairbanks-Sealevel-1989.pdf

https://www.sciencedirect.com/science/article/abs/pii/S0012821X98001988

https://commons.wikimedia.org/wiki/File:Post-Glacial_Sea_Level.png

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There’s a lot of ways we can figure out ancient sea level. There’s three main ways and they are so the sized together to try and get a complete picture. two methods both come from ocean sediment cores. Using sediment codes you can do two things. Depending on the kind of sediment you find and how old it is, you can reconstruct ancient shorelines. There are usually big sediment deposits that get left behind when sea level dramatically shifts up or down, and these are nice indicators of an ancient shoreline. Sediment cores can also be used to estimate global sea level using oxygen isotopes. Oxygen isotopes fractionate due to natural processes in the water cycle, so depending on the ratio of oxygen 18 to 16, we can take a guess at how much ice was on the land surface. Since we assume the global amount of water is somewhat constant, if we know how much is locked up on land then we can calculate how much must have filled those ocean. Combined with geological models of ancient continent shapes you can arrive at a global sea level. You can also use biostratigraphy like u/agate_ said. Corals are great for this because they live in colonies that can be tens of thousands of years old, so they allow us to see for slight changes in depth and ocean chemistry in the relatively recent past.

Also no denying historic sea level is not equivalent to a flat earther. The major reason to me is that whenever we talk about the past in science we have to put huge asterisks next to everything. We can’t ever really be certain something that happened thousands to millions of years ago happened as we think it did. However we can observe the earth as it is right now, and thus that it isn’t flat.

If we're talking about sea level reconstructions further back than we have tide records (i.e., direct measurement of average sea level in multiple places globally) or the modern where we primarily rely on satellite altimetry data (e.g., Strassburg et al., 2014), then there are a wide array of methods used to reconstruct sea level. A non exhaustive list:

1. Dating packages of specific types of coral reefs. Particular species of corals can only live within a very narrow range near sea level. If sea level rises, the existing corals will die (from lack of light) and the colony will move upward building on top of the old corals. If sea level lowers, the existing corals will die (from exposure) and the colony will move downward and build on the flanks of the old corals. If you then date the different packages of corals you have a relative sea level record. To make this an absolute record of sea level, you need to know something about the rate of rock uplift of the area to which the corals are rooted. Dating of packages of corals that are now completely above sea level along tectonically active coast lines, like Papua New Guinea, can be used to construct sea level curves if the rate of rock uplift can be constrained through a variety of other means (e.g., extrapolation of geodetic rates, low temperature thermochronology, etc). There are varieties of studies that estimate portions of the sea level curve through these means (e.g., Cutler et al., 2003, Chappell, 2002).

2. Backstripping sediment records. Basically looking at the stratigraphic records of sedimentary basins and using the record of subsidence (after accounting for sediment compaction and subsidence driven by tectonics) to work out the relative height of different packages which are tied to different sedimentary environments that may be relevant for sea level (e.g., Sahagian et al., 1996, Kominz, 1995, Levy & Christie-Blick, 1991, etc.)

3. Sequence stratigraphy as interpreted from seismic records. This is a methodology really pioneered by the oil industry using large 2D and 3D seismic sections of marine. These rely on identifying packages (sequences) and finding the geometric relations between their boundaries, i.e., onlap, offlap, etc., which provide indications of relative sea level through time (e.g., Christie-Blick, 1991). These techniques have been used to produce large-scale global estimates of sea level (e.g., Vail et al., 1977, Haq et al., 1987, Haq & Al-Qahtani, 2005).

4. Similar to the prior one, sequence stratigraphy applied to continental sedimentary records as opposed to seismic stratigraphy (e.g., Sloss, 1963, Ronov, 1994, Haq & Schutter, 2008 etc.)

5. Proxy records for ocean temperature and ice sheet volume. Specifically, marine oxygen isotope records (i.e., primarily the ratio of two stable isotopes of oxygen, ^(16)O and ^(18)O) preserved in a variety of ways (e.g., in the shells of marine microrganisms) are sensitive to the global volume of ice stored on land because during periods where large ice sheets are building, the ice becomes preferentially enriched in light ^(16)O whereas the oceans become enriched in heavy ^(18)O (e.g., this explainer from NASA). Thus reconstructing this ratio within the ocean as preserved in marine organism shells (where the age of these organisms are known through dating the sediment within which they are deposited) allows us to reconstruct the relative volume of ice and thus the sea level (along with associated data on temperature, etc). There lots of studies building out parts of the global sea level record using multiple independent oxygen isotope records, models, and a variety of other data (e.g., Waelbrock et al., 2002, Siddall et al., 2003, Miller et al., 2011, Grant et al., 2012, Rohling et al., 2014, De Boer et al., 2017, etc.).

6. Recently, new methods have been proposed such as using paleogeographic reconstructions (which themselves represent huge syntheses of stratigraphic, paleomangetic, and paleontological data) to construct sea level curves (e.g., Marcilly et al., 2022).

7. Combinations of portions of above. Many of the above references in fact already combine more than one type of record or proxy to reconstruct a portion of sea level variations. Additionally, there are a variety of efforts to combine as many records as possible to identify disagreements and similarities in these records and to produce as accurate composites as possible (e.g., Miller et al., 2005, Miller et al., 2020).

In summary, if you browse through many of these, you'll see that there are ranges of uncertainty and sets of assumptions for any individual method and the methods do not always agree in detail for specific time periods. However, broadly when comparing the sea level curves derived from different approaches (and using them to refine each other), we find a good amount of coherence and agreement. Thus, while the absolute magnitude of past sea level as estimated from these approaches is likely not completely correct, we have high confidence in the broad patterns and order of magnitude values.

Corals only reflect one method for reconstructing past sea level, and while quite accurate recorders, their use is limited to the last few hundred thousand years (e.g., Woodroffe & Webster, 2014). For a complete answer, we must consider the varied array of methods used to reconstruct sea level over the phanerozoic, e.g., sequence stratigraphic techniques, stable isotopic records, etc.

You're right in general, but OP's question was in reference to the last 20,000 years, focusing on a Wikipedia figure whose data were primarily collected from corals and other shallow-water biological proxies.

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