Backyard turning black after storms
This is a common problem. It could either be mildew, or be caused as a reaction from tannin in the wood. Given that you have black residue on rocks, it may be mildew. If the rocks/stones are near the deck/pergola, it may be just stained water dripping on to them and then staining them.
If you suspect that the black residue is due to a reaction from tannins in the wood, you may need to apply a sealant to the wood used in your deck and pergola. If it appears to be mildew, you can clean the deck and pergola (I recommend 50% water, 50% vinegar), and then apply a fungicide (some are specific to mildew) and then a sealant.
This article suggests using bleach to kill and clean the mildew, but the water-vinger solution is just as effective, and less toxic to other forms of life (humans included).