How far upstream would severe sea level rise (1m) noticably affect a large river? The projection for sea level rise due to global warming seem to hover about 1m by 2100, let's use this figure. How far upstream would this noticably affect a large river, e.g. the Rhine?

I think it is obvious that the Delta would be changed severely, while it is nigh impossible to say accuratly how exactly (I assume). Upstream, I think the following effects com into play: Less hydraulic head means less flow velocity, more sedimentation and a higher water level in the river bed (the river needs more cross section to achieve the same volume flow with less head). Are these assumptions correct so far?

Now the main question is how far upstream we would notice these changes in river behavior: Only at 1m above new sea level, or 10m, or 100m? Is this stronger determined by linear distance along the river, or by height above (new) sea level? 

I prefer the Rhine as an example because it's the closest large river. If someone has a good answer for another large river I'm happy too.
This is both a simple and complex answer.

The simple bit is that a 1m rise in sea level would impact the river to a point 1m higher than the current point (with a slight error margin dependent on flow rates etc)

The rise itself over the next 85 years will not push back along the river (as Michael mentioned) as it's not like a tidal bore such as the Severn Bore. 

The complex bit is that the 1m rise could be along an estuary, or across winding wetlands, or a wide delta or other feature, so the change to river flow could actually be quite catastrophic. And these effects could impact very far upstream, especially in the case of a river such as the Rhine, with a heavily populated floodplain. Wikipedia notes the last 50km of the Rhine are at 0m elevation, so that's an incredibly large possible impact area.