Are there any schema design changes that can take a design from 4NF into a different 4NF design

I would do something like this:

period_start_on date
period_duration interval
position        int -- position of this row in the year,
                    -- e.g. 1 for first Monday of Oct,
                    -- 2 for 2nd Monday, etc.
values ...
primary key(period_start_on, period_duration)
check(position >= 1 and position < 40)

Then if you want December only, you use WHERE period_duration = '1d' and period_start_on >= '2012-12-01' AND period_start_on < '2013-01-01'. If you want to compare two years, you JOIN using position:

SELECT y1.*, y2.*
FROM   the_table y1
  JOIN the_table y2 USING (position)
WHERE y1.period_start_on >= '2011-01-01' AND y1.period_start_on < '2012-01-01'
  AND y2.period_start_on >= '2012-01-01' AND y2.period_start_on < '2013-01-01'

Second normal form

If I understand you correctly, the combination of {date, compound_type, location, method} uniquely identifies {value, units}, and all four are needed in order to identify a unique sample ({date, location, method} isn't enough by itself, for example).

I'm going to write this as if I hadn't received an answer on my question about functional dependencies, since other people might be interested in an explanation of both possibilities.

If there are no partial dependencies

1) Assuming none of the non-prime attributes {value, unit} depend on part of the candidate keys {id} or {date, compound_type, location, method}, your table is in 2NF since, as Wikipedia puts it, "every non-prime attribute of the table is either dependent on the whole of a candidate key, or on another non-prime attribute."

If there are partial dependencies

2) One or both of the non-prime attributes {value, unit} depend on only parts of the candidate key {date, compound_type, location, method}. You've confirmed this is the case with {compund}->{unit}, so your table is not in 2NF.

In order to fix the violation of 2NF, I would suggest moving {unit} to the compound table, which I'm guessing would end up looking something like this: {id, name, unit}. Here, the candidate keys are {id} and {name}. Since there are no composite candidate keys, the table is automatically 2NF. It's also 3NF since there are no transitive dependencies, I.E. there's no attribute that's dependent on unit.

Third normal form

OK, that leaves us with the samples table looking like this: {id, date, compund_type, location, method, value}. The two candidate keys are {id} and {date, compund_type, location, method}, which leaves {value} as the single non-prime attribute. Assuming that there are no more 2NF violations (you can't use a subset of {date, compund_type, location, method} to uniquely determine value), we can check the table for violations against 3NF.

3NF states that every non-prime attribute (attributes that don't belong to a candidate key) must be directly dependent on every superkey. Since we only have one non-prime attribute, {value}, it's impossible for the table to violate 3NF, since there's no non-prime attribute for {value} to be dependent on, and no non-prime attribute that can depend on {value}.

I'm going to leave discussions about BCNF out of this for simplicity.

Surrogate key vs. natural key

As for your other questions: "is using an id(PK) column like I have above the best way to go with all of the repeating dates?" I think so. Semantically, the surrogate key id isn't necessary, but it does help keep things simple. I'm not sure how MySQL works underneath the hood, but in other DBMSs composite primary keys with non-integer data types can lead to unnecessary overhead for example when indexing. Another problem with composite keys is that it gets annoying to query them.

Imagine that you need to add information about which labs each sample was sent to. A sample can be sent to several labs and each lab can receive several samples, so you create a table to connect the two tables. Would you rather write this

SELECT *
FROM samples s
JOIN labs_samples ls ON 
    s.date = sl.date,
    s.compund_type = sl.compund_type,
    s.location = sl.location,
    s.method = sl.method

or this

SELECT *
FROM samples s
JOIN labs_samples ls ON s.id = ls.id

?