I'm sure they know what they are doing but they have to tell you what they are doing in order for you to be able to interpret their data. Fortunately, in the case of all the important ions it is clear what they are doing. 'mg/L as CaCO3' is a means of expressing equivalence based based on the fact that 100 mg calcium carbonate dissolved with carbonic acid and with pH taken to pH 8.3 will require 100 mEq of acid to reduce that pH to 4.3. Because at pH 8.3 there will be 2 mEq bicarbonate ions from 100 mg of calcium carbonate the mEq of caclcium carbonate is simply obtained by dividing the mg by 50. Thus, for example, 200 mg/L calcium 'as Calcium carbonate' is 200/50 = 4 mEq/L. Multiplying this by 50 gives 4*50 = 200 mg/L. So the rule is take the number 'as CaCO3', divide by 50 and multiply by the equivalent weight of the ion. For your report
Ion As CaCO3 mEq/L EqWt mg/L
Ca 22.0 0.44 20 8.8
Mg 11.5 0.23 12.15 2.8
Na 62.7 1.25 23 28.8
K 3.8 .076 39.1 2.97
So far so good. With the anions it gets a little trickier. As, in their footnote, they indicate they are calculating the carbonic from the alkalinity they must be calculating the bicarbonate from the alkalinity too though they don't say this. The situation is complicated by the presence of phosphate (which contributes to alkalinity). If you know total phosphorous (what the test determines) and alkalinity then you can calculate bicarbonate and (carbonic and carbonate) quite easily. Another twist here that some labs recognize and some don't is that water itself (i.e. pure water) has a small amount of alkalinity of its own. If I assume that the bicarbonate number is correct (i.e. that they calculated it properly or measured it by ion chromatography) I can derive the alkalinity. The number would be 32.3 ppm as CaCO3. Note that this is close to the bicarbonate 'as CaCO3'. The assumption that the alkalinity is the same as the bicarbonate 'as CaCO3' is often made by the popular brewing spreadsheets and calculators so even with the uncertainty we are on pretty solid ground in assuming an alkalinity if about 32 ppm as CaCO3 and corresponding bicarbonate content of 38 mg/L.
For fluoride, chloride, bromide and sulfate the procedure is the same as for the cations because these are all the anions of strong acids:
F 2.20 .044 .84
Cl 28.7 .574 20.3
Br 0 0 - 0
NO3 .87 .017 1.1 (as Nitrate!)
SO4 41.3 .826 39.7
With phosphate and silicate the equivalent weight depends on the pH. In order to do the conversion we have to know what pH they used to compute the charge on the ions. Phosphate will be partially deprotonated, silicate will be very little deprotonated. Perhaps they used an equivalent weight of 1/3 the molecular weight for phosphate and 1/2 for silicate. Perhaps they didn't. As the phosphate is small it doesn't much matter nor does it for silica unless you are concerned about it gumming stuff up. If you want to know the silica you will have to check with these folks and ask them to translate to mg/L.
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