Other than using a cover, I'm not sure what to suggest. You are already at 60 ppm CYA. A 6 ppm loss out of 11.5 ppm is about half and given that you only lost 0.5 ppm at night it would appear that this loss is due to sunlight. This is the peak time of year and even in northern latitudes the amount of solar radiation is quite high. The difference in northern latitudes is that this situation doesn't last very long.
I used to think that operating at a lower CYA level would save you chlorine. So running at 30 ppm CYA you would go from 7 to 3.5 ppm FC and only use 3.5 per day which is less. But now we have reports and experiments (in this thread) of CYA saving more chlorine even at the proportionately higher CYA levels. So that would say going to 80 ppm CYA or higher might help (the effect is non-linear) even maintaining the higher FC level. So I'm stumped and until we get a lot more data on true CYA protection of chlorine, I don't know what to say.
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