The basic approach of companies like Pool Chlor that use gas chlorine, sodium hypochlorite, or both, and that only do once-a-week visits is to use a high CYA level such as 100 ppm to minimize the loss of chlorine in sunlight and to raise the FC level high to around 14 ppm so that it will roughly last the week until the next visit. In the hot desert climates they service, the daily chlorine loss is around 15% so that after 7 days the FC drops to around 4.5 ppm (lower, if the pool is used frequently). This allows them to visit their client's pools once a week. The use of 50 ppm Borates is often done as well, but it's the FC/CYA ratio in the 5-15% range that is the main key to preventing algae growth (the borates act more as insurance and as a pH buffer). Even if nascent algae starts in the day or two before a visit, it gets killed off by the higher chlorine level when the chlorine is added.
Note that a once a week approach can lead to larger pH swings so that is one reason why additional pH buffering from Borates and/or a somewhat higher TA level are used. The use of a mix of gas chlorine with sodium hypochorite also lets one add the chlorine in a way that doesn't have the pH change as much upon addition (chlorine gas is very acidic while hypochlorite is basic upon addition). The higher TA can keep the pH more stable through the week with the pH rise from outgassing compensating for the drop in pH from chlorine usage/consumption. Replenishing the lost TA would be done as needed during the weekly visit.
Basically, they are just doing a similar, though a bit more sophisticated, managed maintenance that you are doing, but you take the approach of a more moderate CYA level and twice-a-week visits. Your in-between visit can, of course, be a very fast one that just measures the water chemistry and adds chlorine while the other (weekly) visit can be longer doing brushing of pool surfaces, for example. Your method is closer to what is done here at TFP by individual pool owners and provides a more consistent chlorine level. The pool owners with the weekly pool service peak at 14 ppm FC with 100 ppm CYA normally don't notice it, but for those who are most sensitive to chlorine what you are doing is less likely to be noticeable.
The pool service where I live (that I don't use, but I go to their store to buy 12.5% chlorinating liquid) services thousands of pools in the area and they generally use Trichlor tabs/pucks in either floating feeders or inline chlorinators, but they target 4.5 ppm FC and they sometimes shock the pool with chlorinating liquid during their weekly visit if there is visible algae or higher chlorine demand. They do not know about nor follow the FC/CYA relationship so do not change their target as the CYA level changes. When the CYA level reaches 100 ppm, they do partial drain/refill to lower the CYA level. With many pools using cartridge filters due to water restrictions in our area, they usually need to do this partial drain/refill at least once during a season. Winter rains dilute the water further in preparation for the start of the next season.
As for papers showing chlorine loss vs CYA level, there are several and none of them seem to tie well to what we see in real pools in details, though they do show consistent characteristics.
This paper from Wojtowicz shows information in Figure 1 from Monsanto that shows that even low levels of CYA such as 25 ppm make a huge difference compared to no CYA, but then they show that higher CYA to 50 ppm is a small difference and to 100 ppm and even smaller improvement. This is inconsistent with what we have seen in real pools and confirmed by
Mark's experiments that showed a greater than proportional increase in CYA protection going from 45 ppm to 80 ppm and also we have seen much higher losses when the CYA level is too low (30 ppm or lower, for example). The other information in the Wojtowicz paper shows that chlorine oxidation of CYA gives a chlorine demand, but it is higher than we see in most real pools (but then Wojtowicz used 138 ppm CYA for his tests and the loss rate would be proportional to the product of CYA and hypochlorite described in
this paper). See also
this paper of Wojtowicz in Figures 7 and 8 showing the loss of CYA over months from oxidation by hypochlorite where the "p = 0.01" curve does seem to be close to what is seen in most pools while the "p = 0.02" curve has only been reported in a much smaller number of pools on this forum.
As for your question of chlorine loss from sunlight, there are many different factors for chlorine loss so there isn't a single set of numbers to give you that would be precise. There is some chlorine loss from oxidation of pool cleaner bags, pool covers, cartridge filter material, metal and equipment that is all independent of bather load, but whose rate is related to temperature. The oxidation of organics in the pool including blown-in pollen, leaves and other material is also a factor as is bather waste (mostly urea, ammonia, creatinine and amino acids from sweat and urine). We don't have clear data on the temperature dependence, but it seems to be roughly a doubling of rate for every 13ºF so cooler pools have a lower base chlorine demand. We know that bather load is a relatively minor factor requiring around 4 grams of chlorine for every person-hour in a pool (competitive swimmers require roughly double this amount) so 2 person-hours in 15,000 gallons is 0.14 ppm FC. So all of these sources of chlorine demand need to be subtracted out and what is left is that lost from sunlight. You can roughly figure this out by subtracting out a 12-hour overnight chlorine loss from a 12-hour daytime chlorine loss and then double to get a 24-hour average sunlight loss. The following is a very rough estimate of the % FC loss per day at different CYA levels all assuming that the same FC/CYA ratio is maintained (but chlorine added just once for the day) and in a strong sunny environment at peak summer:
CYA ... % FC Loss ... FC Loss at 10% FC/CYA Start ... FC End
100 .... 15 ................... 1.5 .................................... 8.5 (8.5%) OK
80 ...... 20 ................... 1.6 .................................... 6.4 (8.0%) OK
50 ...... 40 ................... 2.0 .................................... 3.0 (6.0%) on the edge
30 ...... 60 ................... 1.8 .................................... 1.2 (4.0%) TOO LOW
20 ...... 75 ................... 1.5 .................................... 0.5 (2.5%) TOO LOW
0 ........ 99+ ................. N/A
The above is why those in the sunniest climates usually use higher CYA levels and have to add chlorine more frequently (also, the temperature of their pools tends to be higher which adds to daily chlorine losses). Now we have people with lower CYA levels that are able to maintain their pools, but in many cases they are in part shade or have pool covers that reduce some of the chlorine loss. Note that part of the reason for the higher % losses at lower CYA levels is from the absolute chlorine loss that is independent of the CYA level shown above because it is based on the active chlorine level which is constant since the same FC/CYA ratio is being used. So 0.5 to 0.7 ppm FC per day might be a daily non-sunlight loss and would make the loss from sunlight alone at 30 ppm CYA more like 40%.
Given that you start your pools with only 30 ppm CYA, what kind of losses in chlorine are you seeing? Are these uncovered pools exposed to strong sunlight all day during the summer? I'm surprised you are able to manage those pools only twice a week at that low CYA level. Also, for the pools with old plaster that get mustard algae, do these pools have borates or are these pools whose customers refuse to pay for borates? I'm just curious if the borates help against mustard algae at all -- we know they help against green algae.
It would be great to get some real experimental data to isolate the various loss rates -- improving the loss rate data for hypochlorite oxidation of CYA, for the general temperature dependence of chlorine oxidation of various substances normally found in the pool, and for chlorine loss from the UV in sunlight at different CYA levels and water depths (since there is a CYA shielding effect separate from the protection by binding to chlorine). In particular, getting a better understanding of how light interacts with chlorine bound to CYA would help explain the loss rates that are higher than would be predicted by loss from free hypochlorous acid and hypochlorite ion alone. Experiments getting spectral UV absorption data for the UV shielding effect would also be helpful.
