If not a geologist or geomorphologist, consider this book as a possibly helpful reference. https://www.amazon.com/Incised-Channels-Morphology-Dynamics-Control/dp/1887201645

If imagery is is helpful to locate some former channels, old sloughs and oxbows, meander scrows, remnant channel deposits, your most accurate remote tool will probably be LiDAR ( light detection and ranging). At landscape levels, you may find elevation and channel details that may even not be noticeable in field surveys or aerial photos, unless you know what you might be looking for. Most geologists and geomorphologists would use equipment to sample and detail the layering within sediment cores. There are various ways to date sediments also to help validate observations. If you have locations with observed flood elevations, sometimes this can be very useful. But when floods include excess sediment loading from landslides with aggravation, avulsion that quickly entrenches and abandoned channel meanders, these abrupt changes can be difficult to evaluate without sediment cores and/or deeply exposed banks.

It is true that river locations within their valley can make significant changes through time. Channel burial often signals a low gradient, braided system. With LiDAR, you may find remnant meander scrolls. There may be many buried channels as the channels shift and relocate through time.

If if you have historic writings and enscriptions, archeologists have various tools that may help find remnants of buried villages. Reconstructing river locations through time appears difficult task, with substantial uncertainty in costing out research needs if all available is a few inscriptions.

You could use three different approaches, separately or together (best way):

1) Field work trying to find clues about this river such as terraces, slope changes, lithology, paleostreams.....

2) High resolution Lidar elevation models, aerial and satellite images. To search for these clues remotely and with a bigger perspective

3) Free cost digital elevation models (ASTER...) and satellite images such as Sentinel 2 or Landsat. In the last one you can also check if there was some clue or pattern between 1972 until present. Furthermore this kind of paleochannel sometime accumulate more humidity, thus you can also check this by creating different indexes with this free satellite images.

I hope this will help you

In my humble opinion, previously to write your proposal you should check the area with the free resources cited above.

I agree with the previous recommendations, but I would add a study of the upper basins, in the maps with contour lines, to define those of greater extension that would assure in case of an extraordinary rainfall an extensive flood. This way you can focus on the most likely areas. In Googlearth it is noted that the entire region under study, is completely occupied and cultivated, with paddies and small villages, and numerous beach resort. All this modifications can create a lot of interference to the remote sensors. An interesting detail is the coastal dynamics that tend to occlude the outputs of water courses. It is one more element that helps the occurrence of a major flood.

Thanks Ivan Lizaga, what indexes do you suggest?

You could try NDWI but maybe the topography suggest the area where could it be located thus focalise your efforts in that area. I don't know a lot about your study area, but try to use the index in wet - medium -dry periods to observe if exist some anomalies. Furthermore, flow accumulation tool of many of the GIS softwares could be usefull to detect the ancient fluvial/alluvial terraces.

Thank a lot Ivan Lizaga

If you are interested, here are some images from google earth that show some area in my research area.