As the person who answered the linked question, this seems different to me. That question revolves around a broken stick regression, trying to find the break location.
This is a problem where I think you are trying to find a break point in the variance? Worse, much of your data seems to be zero. So I think you want to deal with this differently. A simple variance, thus an implicit normal approximation may not really be appropriate.
I might look at this as two random process, each with homogeneous variance, around some constant level. There are some exact zeros in there that may or may not need to be dealt with in the model. But your goal here seems to be to locate the point where that variance changes? I might better think of viewing this as simply a pair of Poisson processes, and you want to see where the Poisson parameter changes.
Another option would be to view this as a poisson process, with a Poisson parameter that depends on specific humidity. Then you would be looking to find a form for that relationship. Use maximum likelihood techniques to estimate the coefficients in that function.
I can guess some possible ways to parameterize that function of humidity, but really, it would help most to actually have the data in hand to play with. With the data in hand, I would start by plotting a lot. Break it into bins. Decide if a Poisson process does indeed make sense, etc.
I'll look back in an hour or so in case I can help you.
