Originally Posted by mabrungard
The measurements peak during the winter months. The increase is due to road salting. Its typical for many surface water sources in the north.
That certainly used to be the case but governments have become much more sensitive to this and whereas one used to see piles of salt in road maintenance yards in the past one now typically sees those things that look like beehives with the salt piles inside. This keeps rain from washing salt into/onto the area near the maintenance yards and has, apparently cut down on the amount of NaCl making it into the environment from that source.
So lets see what the data in #6 tell us. The upper array of numbers are the correlation coefficients for the monthly data in the table. The data in Mjn are the months from June. For example, for May Mjn = 2 as it does for August. Low Mjn numbers represent warm weather months and higher numbers represent cold weather months. Reading across the first (Mjn) row we see that sodium (0.8296) and chloride (0.8509) are both strongly correlated with months from summer but alkalinity is even more so at 0.9210 and sulfate (0.7797) slightly less so. Potassium, Calcium and Magnesium are not strongly tied to (correlated with) the months from June but they are highly predictable from the straight month of the year. This can be seen from reading across the bottom line (Mo = straight month numbers: Jan =1, Feb = 2...) where we note that potassium and magnesium are strongly correlated with how far into the year we are but that calcium is strongly anti-correlated (less calcium in the fall than in the spring).
The numbers in the bottom table are measures of the quality of the correlations in the top table. For example at the intersection of calcium and chloride in the upper table we see a weak correlation (0.1587) between those two ions. In that bottom table we see, at that same intersection, the number 0.3156. This is the probability that we would see a correlation as high or higher than 0.1587 if calcium and chloride were in fact not correlated. A probability as high as 1/3 (one chance in 3) isn't very convincing and we accept that there may be no relationship between the calcium and chloride. The county apparently isn't using calcium chloride for road deicing. We have much more confidence in the correlation between sodium and chloride where r =0.7579 and the probability that they are uncorrelated is only 0.15%. The county could be using sodium chloride but correlation doesn't prove causation and they probably aren't using sodium bicarbonate which is supported by r = 0.8086 and only an 0.04% chance that those ions are in fact independent. Nor are they probably using sodium sulfate.
This exercise was kind of fun and suggests several hypotheses. There could be a common explanation for the increases in Na, Cl, SO4 and Alkalinity or there could be separate ones (road salting for Na and Cl and something else for alkalinity and sulfate) etc.