Adding separate distance files to calculate total distance in ArcGIS

Question

I have two raster files:

1. A raster of distance-to-outlet for a creek. Value = 0 at creek outlet (white), and the maximum value is at the beginning of the creek (black).
2. A raster of Euclidean distances from the creek boundary. Distances are calculated from creek boundary (red-green).

I need to create a third file that adds the Euclidean distances to the creek distances. Essentially, I need to scale the Euclidean distances per the creek distances, so the final file represents "total distance" to each point within the study area.

Answer 1

One way is to convert the creek distances to integer format if they are not already integers. For more precision you can multiply them by some larger value (a "scale factor") and round; later you can divide by that same value.

Because the creek distances are integers, you can perform a Euclidean allocation (usually at the same time you compute the Euclidean distance). To each cell in the entire area, this associates the value of its nearest creek-distance cell. Divide the Euclidean allocation value by the scale factor used in the first step (if any) and add that to the Euclidean distance. You could take this opportunity to weight the two distances differently if you like, simply by changing the scale factor.