In "amount of data, collected ~", which is modified by 'collected~'? amount or data?

Question

The fast-growing, tremendous amount of data, collected and stored in large and numerous data repositories, has far exceeded our human ability for comprehension without powerful tools.

(from Data Mining by Jiawei Han and Micheline Kamber)

1. Which one does the phrase "collected and stored in large and numerous data repositories" modify? 'amount' or 'data'?
2. Which does "without powerful tools" modify?
   Is this included in the noun phrase heading 'comprehension', like [comprehension without powerful tools]?
   or Does this modify 'ability'?
   or Does this modify the whole sentence?(In this case, how can we paraphrase it? 'because/while/as/when/if we have no powerful tools'???)

*Additional questions related to 1)

If I change the sentence into 'The fast-growing, tremendous amounts of money, which are/is collected and stored in large and numerous repositories, have far exceeded our capacity.' which one between 'are' and 'is' is correct?

According to sentences from 'Collins dictionary'('Funds are amounts of money that are available to be spent, especially money that is given to an organization or person for a particular purpose.' and 'A fund is an amount of money that is collected or saved for a particular purpose.'), it would be 'are'.

'amounts of money that are' and 'amount of money that is' indicate that the agreement is based not on 'money' but on 'amounts or amount'.

Doesn't this show that the modifiers in 'The fast-growing, tremendous amounts of money, which are/is collected and stored in large and numerous repositories, have far exceeded our capacity.' and 'The fast-growing, tremendous amount of data, collected and stored in large and numerous data repositories, has far exceeded our human ability for comprehension without powerful tools.' modifies first modify 'amount', not 'money or data'?

Answer 1

1. Which one does the phrase "collected and stored in large and numerous data repositories" modify? 'amount' or 'data'?

The phrase:

collected and stored in large and numerous data repositories

modifies data, not amount.

We can demonstrate this by simplifying the sentence, it has the same meaning phrased as:

The data, collected and stored in large and numerous data repositories,...

And if we try it the other way around:

The fast-growing, tremendous amount, collected and stored in large and numerous data repositories,...

The phrase implies the subject:

The fast-growing, tremendous amount [of data], collected and stored in large and numerous data repositories,...

2. Which does "without powerful tools" modify?

The phrase:

without powerful tools

modifies comprehension, or ability for comprehension.

You could phrase it like so:

... data repositories, has far exceeded our comprehension without powerful tools..

or:

... data repositories, has far exceeded our ability for comprehension without powerful tools.

But you could not, in my opinion, phrase it like so:

... data repositories, has far exceeded our ability without powerful tools.

As it leaves ambiguous what kind of ability is being mentioned.

As an additional exercise, you could rephrase it as:

... data repositories, has far exceeded our ability to comprehend without powerful tools.

Where I would nest the phrase like so:

... data repositories, has far exceeded our ability to (comprehend without powerful tools).

That being said, I think you could also interpret it as

... data repositories, has far exceeded our (ability to comprehend) without powerful tools.

Answer 2

The fast-growing, tremendous amount of data, collected and stored in large and numerous data repositories, has far exceeded our human ability for comprehension without powerful tools.

1. The modified term has to be "the fast-growing, tremendous amount of data"; this is so in my opinion, because what has been collected is not just data in an indefinite quantity, but a tremendous amount of it, and at that, this tremendous amount is fast-growing.

2. The modified term can be either "our human ability for comprehension" or "comprehension"; it is not clear which.