How are disaster effects calculated into GDP?
GDP is just a partial measure of flow. There are lots of changes to the stock of a nation, its capital, that are not captured by GDP.

Destruction of assets in natural disasters isn't recognised as a loss in GDP. It gets worse: the rebuilding would actually be a positive on GDP. NB any loss in economic output from, say, destruction of factories, would appear as a negative on GDP - the loss of the factory's output.

Changes in natural capital aren't captured either.

GDP is just a measure of volume of transactions. It gets misused as a proxy for economic wellbeing. That's not the indicator's fault, it's the fault of those who misuse it.