I looked at your pic su-liam and noticed that those rivers were looking like they were climbing up the hill a little but a little more time staring at it and I thought that if you pulled all the rivers closer to you then they would match better. So at that angle then a vertical displacement might account for that.

In terms of Me-Dem Monks models it based on reference maps and some attempt is made to get it hydrologically correct but Tolkien never thought much about geology and geography when he made it. It was a map very plot driven. But even so it can be made to sort of work. The problem for me is that if I get my app to find fluid flow over it then the gradient is way to shallow to compute sensibly. As you said programs can take a long while. If the gradient is sufficient then it finds those streams quicker. So monks modeled the river channels using the vector app and these lines were thicker than they ought to have been in most cases. There was a requirement to match the reference maps even if that's not perfect physics. So I made an app where within a mask you could set the flow direction up. When water hits the positive mask then it starts traveling along the direction set with a kick so it sort of forces rivers into those channels. There is a gradient map export which can show where the terrain is too shallow to properly calculate it. Also because the general terrain is still moderately coarse even at 20K pix square then you can get areas where its vector math flat like at basins and saddle points. Water pools up there especially if there is no significant exit channel to go out. You get a shallow mound of water ! The idea was to model Middle Earth with full fluid flow but it never happened and I think its too difficult. We can botch it but I don't think I can do anything thats too sensible to create proper rivers and tributaries on it.

With hindsight I think the numeric approach is still the best for a home PC but eventually with enough processing power calculating math surfaces for the water could allow you to short cut all the numeric flow and just cut straight to the equilibrium fluid solution to the terrain. I don't think I would want to program that in my spare time tho. Monks and I would both like to model in the rain where as you interact with the terrain in real time then it shows hydrological effects updated in real time. Then maybe it could be done.

I think making a hydrological correct terrain from real or fake DEM date is not much difference since all our models are so fake anyway. I can take real DEM data and erode it into something which is not life like. The real world is too complex to model so that it would equalize all the parameters from real DEM data and get you to an equilibrium quickly. Its probably fair to say that it might be a little quicker than bad fake data tho - but its not all that cut and dried what is good DEM data. Maybe someone should program an AI genetic algo process to work out models which fit real world DEMs and use that model on fake DEMs to get them knocked into shape.