You don't mention where you reside but your profile says Canada. Therefore you are in a frost zone. In good conscience I cannot endorse your construction proposal for a couple reasons.

1) Frost Heave - your fence and patio are not structural That means they respond to seasonal ground movement. Attaching your pergola to them with cause it to "twist" and pull apart.

2) Wind and Snow Load - these are the two influences nature will put upon a pergola. It must be securely anchored to a footing set below the frost line.

What to do? I recommend attaching a ledger board to your garage and setting footings beyond the existing patio. Or, replace fence post(s) with concrete footings and attach a pergola support to the footing using a post stand-off base, then get dual use of the pergola support by attaching the fence to it.

Hope this helps. I'm linking our pergola. It is free standing and we live in northern Illinois where the influences I mention are factors. The footings are 5 feet below the patio surface, 12" diameter.

Here is a link that might be useful: Pergola

fnmroberts: Do you find that the snow in your location tends to fall through the lattice, or build up on it?

kas

kaseki - Sort of both but alot sifts through with the wind, the rest melts fairly soon as it has south and west exposure to the sun. Never any sagging or need to clear.

Thanks. I'm thinking of a similar treatment to a simple un-ornamented pergola -- really more like an arbor without vegetation -- to provide some shade.

kas in NH