Test temporal change in standard deviation

Very dear geeks :cool:!

I am new in this forum. I am a french post-doc in marine ecology and I am especially interested in trophic relationships.

I am currently analyzing time series. I have to admit that time series are definitely one of my strongest Achilles heels, I am actually afraid of them :eek:

Anyway, lets go to the point. My question is the following: How to test that standard deviation (sd) change over the time in a time serie.

Lets take an example. one investigated the depth of lagoon water. 10 locations sampled each month for 10 years. To investigate the temporal change in average depth, I used a GAM. But imagine that all the locations are not changing the same way. Thus, the SD may change over time as well (see my drawing, sorry it is a bit blurry). Both time series have the same trend in their mean but definitely not in their sd. In the second plot, the sd is small at the beginning of the survey and larger at the end.
How should I test that sd change over time?

I think that regime shift detection may be a solution to test change in sd but this method split the time interval. Honestly I don't know whether this method is the best solution. What do you think? I tried to find info about that on the web but can't find anything that suit to my situation :confused:

Thank you so much in advance for any help!!