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It looks like my post is irrelevant then. I was assuming you wanted to make new dimension IDs so that it would be easier to avoid such mistakes like accidentally using same dimension ID for things that should be in separate dimensions. But from what I understand, that's not the problem, so you can just pick some ID and use it for your island. Dimensions don't have weathers, all they have is elements. However, if you set weather in the client-side script, it only changes for that player. If you change the weather for the player alongside putting that player in the dimension, from their perspective it will appear as if that dimension has a different weather. To achieve this, whenever you call setElementDimension, you can also call triggerClientEvent to trigger a custom event, which then you would use to call setWeather on the client-side script. For customizing weather-related properties, in addition to links that @FlorinSzasz posted, there are several other functions, such as setColorFilter and setFogDistance, that you would call on the client side.

Nice one! Awesome job!

You can't "create" new dimensions. But the element limit is 2^16 = 65536. And there are also 65536 dimensions - just enough to store each element into its own separate dimension. This allows you to create your own dimension system, based on the built-in one. In fact, I tried something like that a long time ago. A dimension system that used arbitrary values as dimension IDs, with each value being assigned a unique integer from 0 to 65535. You can use tables to track things like which elements each dimension contains and which custom dimension system ID corresponds to which built-in dimension system ID.