What is simple and grammatically correct?

Question

I have two constructions with the same meaning:

1. The estimation of these attributes is difficult by using traditional field measurements method, which is rather expensive and time-consuming.
2. The estimation of these attributes by using traditional field measurements method is difficult, rather expensive and time-consuming.

Which one would be clear and grammatically correct?

Answer 1

The prepositional phrase "by using the traditional field measurements method" belongs to "The estimation". In the first example, you have moved the predicate "is difficult" in-between them, so the prepositional phrase becomes stranded and the reader tries to parse the sentence as if it belonged to the predicate instead. In other words, the second sentence is parsed as:

 2. [The estimation [of X] [by Y]] [is difficult].

While the first sentence is parsed as:

 1.  [The estimation [of X]] [is difficult [by Y]].

And that's when the latter falls apart, because "to be difficult by condition" is ungrammatical; you have to use "to be difficult when condition" instead.

So, here are your actual choices:

1. The estimation of these attributes is difficult when using the traditional field measurements method, which is rather expensive and time-consuming.
2. The estimation of these attributes by using the traditional field measurements method is difficult, rather expensive and time-consuming.

Another point to note is, of course, that in (1) it is the method that is expensive and time-consuming, while in (2) it is the estimation. I suppose it doesn't make a real difference in your case (because the expenses and the time consumption propagate from the method used to the estimation process as a whole, so it makes sense either way), but in general this is something to keep an eye on.

Lastly, note that you were missing a definite article in both cases, which I silently corrected in my answer.

Answer 2

Stylistically I'd recommend tightening it up:

Estimating these attributes with the traditional field measurements method is difficult, time-consuming, and rather expensive.

The words "by using" can easily be replaced by "with" (or simply "by" or "using").

I included "the" before "traditional field measurements method" as there appears to be only one such method being referred to; if there are multiple methods you could omit "the" but pluralize "methods".

Estimating these attributes by traditional field measurements methods is difficult, time-consuming, and rather expensive.

It's unclear in the original context whether the modifier "rather" is intended to apply only to "expensive", or is intended to apply to both "expensive" and "time-consuming"; in the above sentences I assumed the former and worded it so as to be unambiguous. If you did intend "rather time-consuming and rather expensive", the only way I can think of to clearly and non-redundantly express that is:

Estimating these attributes using the traditional field measurements method is difficult, as well as rather expensive and time-consuming.