That is crazily misleading.

For the initial construction, yes. Ongoing? No.

At a point in time, the amortized emissions become zero.

It's not misleading. The vegetation that is flooded decomposes anaerobically and releases methane. So there's an ongoing release over the years that it decomposes. They've measured these emissions at different dams over time, and the worst (where forest is flooded) results in nearly 2.5 times the GHG emissions as the worst coal plants.

For instance the Balbina hydroelectric reservoir in Brazil was responsible for 39000 tons of methane each year (https://www.researchgate.net/publication/252089237_CO2_emiss...)

That was a 2011 paper on a dam that was finished in 1989.

That is still misleading, grossly.

More happens in the water than just releases of methane - there's plant and animal life producing oxygen and consuming decomposing materials.

Plus 1989 is a brand new dam. The Hoover Dam was completed in 1936[1], and is expected to have a service life of at least 10,000 Years.[2]

10,000 years at a minimum. It will have paid dividends in renewable energies so many times over by then, that it's not even worth discussing.

Do you think the solar panels installed on your roof will last 10,000 years? Will they even last 10 years without needing replacement or repairs?

[1] https://en.wikipedia.org/wiki/Hoover_Dam

[2] https://delzottoproducts.com/2017/03/15/long-will-take-concr....

How is it misleading? Explain please.

What I see is a 250MW dam built in 1989, that produces in 2011 the equivalent GHGs of a 1000MW coal plant.

And at a point will not produce equivalent GHG's, which your coal plant will continue to do so.

The coal plant won't even be able to operate in 10,000 years, this dam will continue to do so.

Do you even read your own links? There's no way the dam will be operating in 10,000 years time.