Is there any way you could assign a numerical value to clarity of sound? For example, if you wanted to see how clarity of sound was affected by environmental factors (being outside, for example), over distance, or with other factors, is there any way to evaluate clarity and have the method remain the same over multiple trials?
You should look into feature extraction from audio signals. Audio is being analyzed, as a result you get numerical values that more or less correspond to the perceived qualities of the sound. The values are called descriptors, and you will probably find the result you are looking for by combining some of them. You could then observe the impact of environmental factors on sounds by observing the combination of descriptor-values.
MPEG-7 Audio  proposes a set of descriptors to classify audio .
In the case of clarity you could try spectral centroid and spectral spread, they formalize the perception of brightness. These are rather simple descriptors. I recommend to use a MaxMSP implementation, i.e. by Alex Harker . If you want to take it further I recommend having look into high-level audio descriptors like ordered-chaotic and tonal-noisy .
Welcome to SD. Yes you could, but if you want to go past just a subjective grading (ie you just guess at how clear a sound is and note it down for the file) then the system can become complex very quickly.
You should check out the book The Tuning of the World by R. Murray Schafer, where he proposes a classification system for recordings, summarised nicely here:
There have been many suggestions for more comprehensive systems since, and this is a whole research area in itself. You could take what you like from this or adopt a system. I don't honestly know if there is a standard people follow (anyone?). The book is a good read anyway.
You cannot define the "clarity" of a sound in absolute terms. If I stand next to you and gargle The Star Spangled Banner, did you just hear a "lo-fi" version of the national anthem, or a true-to-life rendition of the national anthem as heard bubbling up through liquid held in equilibrium in a human throat by the force of air being exhaled?
If you define clarity, then all of a sudden your experiment becomes very easy to design. If I want to test the "clarity" of a stereo system, the question I am really asking is "how accurately does this stereo reproduce recorded sound? So, I'll record a real-life sound using the highest-quality microphone I can get my hands on (Recording A), and then create Recording B in the exact same recording environment, but by replacing the original sound source with a stereo loudspeaker, playing back Recording A. Then, I can compare recordings A and B to derive some measure of clarity.