grammar - Understanding ～かどうかだ

生きるか死ぬかの問題だった。

It was a question of life or death.
飲み水が、一週間分あるかどうかだった。
It was a question of whether or not there was a week's worth of water.

The only way I can make sense of this structure is to assume that 飲み水 is the subject of ある. I'm parsing it like this:

[問題は] [飲み水が、一週間分あるかどうか] [だった]

The comma, and the lack of the topic is making me think that 飲み水 should pair up with だった, but I can't make a meaningful parsing if that is the case.

I know it is common to omit the topic and I also know that commas don't serve the same grammatical purpose as they do in English. I'd just like to check that my understanding of this sentence is correct.

Answer

Conclusion first, the grammatical topic of the second sentence is not 問題(は). I know this is unusual, but in this case, adding 問題は at the beginning of the sentence will dramatically change the meaning of the original sentence!

1. 飲み水が一週間分あるかどうかだった。
   There was at most only a week's worth of drinking water. / There was drinking water that might or might not last for a week. / There was some drinking water, but I was not sure it would last even for a week.


2. 問題は飲み水が一週間分あるかどうかだった。
   The problem was whether or not there was a week's worth of drinking water.

I think you already know how the second interpretation works. ～かどうか forms an embedded question, "whether or not ～". I was initially unaware of this, but the second interpretation would also be perfectly valid in a certain context. For example, if he knows he will be rescued after a week, and if he has everything to survive other than drinking water, then the only problem left is whether or not there is enough water for the next seven days.

But the actual story is not like that, and that's why you asked this question, right? :) Perhaps he had no idea when he would be rescued; he might have to wait much longer than a week. Thus the correct interpretation is 1, and you must not add 問題は at the beginning for this sentence to work. You have to be able to interpret this sentence as-is, without adding 問題は.

So, how does the first sentence work?

～かどうかだ or ～かどうかです has a usage that is a bit different from "whether or not ～". This is a little colloquial and I don't know how to normally translate this, but the basic idea is something like "may or may not", "fifty-fifty chance", "not certain yet", "depends on chance", "on the borderline between success and failure", or such.

Some examples:

• ここから富士山は見えるかどうかです。
  From here, you can see Mt. Fuji if you are lucky. / Sometimes we can barely see Mt. Fuji from here. / There is a chance we can see Mt. Fuji from here.


• 彼は合格できるかどうかです。
  
  He is on the borderline between pass and fail.


• 急いでいるが、間に合うかどうかだ。
  I'm in a hurry, but I may or may not be able to arrive on time.

Sorry for the loose translation, but I hope you now understand how to interpret the original sentence without adding an imaginary topic.

Finally, if we do need to start this sentence with 問題は without largely changing the original meaning, we can say this:

問題は[飲み水が一週間分あるかどうかだということ]だった。
The problem was the fact that I had only a week's worth of drinking water (at most).

I simply enclosed the "かどうか" part with a nominalizer(?) だということ.

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(EDIT history: Rewrote almost everything, but my opinion is the same. I hope I have explained this issue better now.)