Assuming the area you are looking at is relatively small and flat you could:
Create a buffer using the "Buffer Tool" in Arcmap of a random distance. Best guess based on the information you have. In the attribute table assign a height value to the buffer (in metres / feet above sea level).
Convert this buffer to raster.
Subtract the newly created buffer from the DEM / Surface you have. All positive values will be the flood area and all values 0 and below will be below the surface.
You can run the reclassify tool on this new raster classifying all positive values as a class and all 0 and negative values as a class. This new reclassified raster will be an integer format, which can be converted back to polygon.
You can then edit the polygon to get rid of any islands or sections of the "flooded area" which are outside of your study area.
Edit 1- Viewshed Methodology
If you have access to Spatial or 3D Analyst you could try this method.
You could use the Viewshed Tool to delineate a view catchment (simulating a flooded area).
1) Take the centreline of the road and run the Densify Tool to create more vertices. The viewshed tools run off the vertex of a line and not the line itself.
2) In the Centreline Shapefile, add the following Fields - all "Double" and all caps. OFFSETA ; VERT1 ; VERT2.
OFFSETA - is the height from which the viewshed will be run, this will be the height in metres / feet above ground level of your flooded area.
VERT1 - is the vertical angle above the horizon from which the viewshed will run. Set this to 0. This will force the viewshed to follow a hypothetical flat plane (as a flood surface would).
VERT2 - is the angle below the horizon. Set this to -90.
Run the viewshed.
3) The output will be a Viewshed raster indicating those areas which hypothetically may be flooded based on your flood height. You can run the RECLASS and convert this raster to Polygon.
I am not sure how this will handle downstream elevations. Some editing may be needed for these areas.
Edit 2 - Cross Sectional Buffer
Another method to try would be to create cross sectional buffers through your road.
Run the ET GeoWizards tool called "Create Station Lines".
ET Geowizards can be downloaded from ET GeoWizards. Open ET and go to:
Miscellaneous -> Create Station Lines
- Select your roads layer as the Polyline,
- Choose an output Choose the distance along the road you
want to have a cross section / Station Line (10m)
- Choose the length of your Line (30m)
- Specify you want the station line on both sides of the road
With these new lines, create a buffer, use half the distance you specified in Step 2 above as the buffer distance. So ultimately you end up with a series of polygons running perpendicular to your road.
Run the intersect tool between the Station Lines and Road Layer, specify the output shape type in the intersect as "Point".
Run the S
patial Analyst -> Extract -> Multiple Values to Points using the intersect point file and your Surface as the inputs.
This will add the elevation data to the point file representing the intersect between the station line and the road centreline. Add 10cm to the value that was placed in the point file.
Perform a spatial join between the point and polygon buffers, to allow you to transfer the revised elevation information to the polygon.
Create a raster from the polygon layer, using the revised elevation as the raster value.
Use the raster calculator to subtract the original surface from your new raster. The positive values will be the flooded areas and the negative values will not be flooded.