> 涵養量と消耗量の差は氷床の「質量収支」で、その期間に氷床の大きさ (質量) がどれだけ変化した **かの** 指標となる。

> もうすぐ一年に一回の小説コンテストが「八重堂」で開かれるの。それで以前と同じように何人 **かの** 作家先生を審査員に招待するつもりだったの。

Whenever you use a question word like どれだけ、何、etc. You seem to need that か
particle, but what is the role of the の particle here? Is 何人か人 also
grammatically correct?

Im also confused on how to translate the first texts use of a "question inside
a statement". Thank you!
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grammar particles particle-の
What is the meaning of か+の in these two sentences?
This の is simply the AのB structure where A is a property of B. Question
phrases can work like nouns. In your first example B is 指標 ("an indicator")
and A is describing what kind of indicator it is: 氷床の大きさがどれだけ変化したか ("how much
the size of the ice sheet changed")

> その期間に氷床の大きさ (質量) がどれだけ変化したかの指標  
>  An indicator of how much the size (mass) of the ice sheet changed in that
> period.

Your second example is a bit different. We don't really have a question phrase
here. 何人か is just a word meaning "several/some people", so 何人かの作家 is
"several/some" authors.

**I'm less sure about the following part. Some confirmation from someone more
knowledgeable would be useful:** 何人か人 is not grammatically correct in the
sense that 何人か is no longer modifying 人. However 何人か can act adverbially, so
if you wrote 何人か作家先生を招待する then 何人か would not be associated with 作家先生 but with
招待する and you would have "invite authors severally" which is weird in English
but I think is perfectly acceptable Japanese.
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My understanding is that Japanese does not distinguish direct and indirect
questions. The grammatical model that I've found works best, is to treat か as
a _nominalizer_. Given a (completed) predicate X, Xか functions like a noun
meaning "the proposition that X is true", or "the question of X". (in this
way, e.g. 問題 would bear the same relationship to interrogative か that 事 or やつ
does to nominalizing の.)

Let's try applying that model. We have a main clause (for lack of a better
term; the part following a conjunctive で)

> その期間に氷床の大きさ (質量) がどれだけ変化したかの指標となる

Thus, その期間に氷床の大きさ (質量) fills the が position of the predicate どれだけ変化した ("it
changed by some amount"). Adding か to that predicate nominalizes it: "the
amount by which it changed", where "it" can be filled in with a translation of
その期間に氷床の大きさ (質量) (left as an exercise).

Since we now have a noun, the subsequent の cannot be a nominalizer, but is
instead the usual [categorizing
の](https://japanese.stackexchange.com/questions/2770). A "the amount by which
it changed"-categorized 指標 ("indicator"), then, is an "indicator of how much
it changed".

This then feeds to a quotative と and the verb なる. Thus, "Being a
涵養量と消耗量の差は氷床の「質量収支」, it became an indicator of how much that 期間に氷床の大きさ (質量)
changed".

Unless the が-marked part actually belongs to なる, in which case I guess we end
up with "Since it is a 涵養量と消耗量の差は氷床の「質量収支」, that 期間に氷床の大きさ (質量) became an
indicator of the amount of change." But I think that would use に rather than
the quotative と. That part is a bit above my level, it seems.
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