Deck cleaner is oxalic acid and water with a high price. Buy the powder and use your own water.
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Oxalic acid may not be the very best cleaner but it's also a safer bet to not harm the ($$$) wood. A lot of it will depend how dirty it is, if there's mildew and how much work and scrubbing you're willing to do? Buy the Oxalic acid powder and mix it with water yourself, it's significantly cheaper and like the post above deck cleaners can pretty much be the same thing; many expensive deck cleaners can also be bleach but costing many times more. Grew up as kid on sailboats, my job was to clean all the teak decking and trim on the boats and this is what we used.
The paragraph below was liberally taken from another site as I couldn't write it better:
"redwood or cedar deck surfaces can become grayed and appear weathered. Oxalic acid removes the tannin on the wood surface; as well as rust stains. The acid can also help neutralize the sodium hydroxide treatment if it was used previously by professional deck cleaning companies to clean and brighten decks (not sure this applies to you).
Oxalic acid's main benefit is aesthetic. It does not work well as a dirt remover, nor is it effective at killing mildew." This is partially true, Oxalic can clean some when using a good deck scrub brush and elbow grease (mostly because of a good brush and elbow greases). Your decks can look much cleaner using oxalic because the dark tannins are removed in the wood and elbow grease and brush removes dirt in the woods surface but it will not clean as well or remove mildew like Bleach with detergent. The results will depend a lot on how much elbow grease you're willing to do.
"Sodium hydroxide and chlorine bleach are the two chemicals most often used by professionals for deck cleaning. While they are more effective at deep cleaning than oxalic acid, they may cause surface damage to the wood over time. Chlorine bleach is excellent for wood brightening as well as killing mold and mildew (I see some in 2nd pic?), but must be combined with a detergent to clean well, and long term use of this harsh substance is hard on a deck's surface" Also have be careful with bleach as it can stain items and the paint around the deck and can leave bleach drip marks below as its dripping while drying.
As mentioned earlier about
being very careful with pressure washer is very sound advice, It can do an amazing job while not breaking a sweat and can reach deep but at the same time it can cause a fair amount of damage to the wood; especially on wood that's been soften by being in the shade and under tree's; this also applies when trying to sand. Keep pressure low, then use a good deck scrub brush on the whole deck with the chosen cleaner. Then apply oxalic the same way afterwards to neutralize. The above will do an amazing job to your deck wood, it will make your deck look fresh and bright; and totally ready for applying the protection coats you've chosen.
Good luck