I combine classical descriptive geomorphological studies with numerical ones and always try to supplement it with a compositional discipline involving mineralogy and/or petrography. The missing link between the various geoscientific disciplines is sedimentology (GMS). With this holistic approach you come close to a perfect terrain analysis that in case of material amenable to age dating can be used for relief generations and called and advanced level terrain analysis

DILL, H.G., BUZATU, A., KLEYER, C., BALABAN, S.-I., PÖLLMANN, H., and FÜSSL, M. (2022) A Natural GMS Laboratory (Granulometry-Morphometry- Situmetry): Geomorphological-Sedimentological-Mineralogical Terrain Analysis linked to Coarse-Grained Siliciclastic Sediments at the Basement-Foreland Boundary (SE Germany).- Minerals: 12, 1- 43.

DILL, H.G., BUZATU, A., KLEYER, C., BALABAN, S.-I., PÖLLMANN, H., and FÜSSL, M. (2022) A composite terrain-and provenance analysis tied to specific times of a basement-foreland drainage system and its gravel-sand-clay deposits, (Bohemian Massif, SE Germany).- Sedimentary Geology: 441, 106266 (30 pp).

DILL, H.G., BALABAN, S.-I., FÜSSL, M., PÖLLMANN, H.,, BUZATU, A., (2022) Morphostratigraphy of landform series from the Late Cretaceous to the Quaternary. The “3 + 1” model of the quadripartite watershed system at the NW edge of the Bohemian Massif.- Geomorphology: 419, 108489 (41 pp).

Glückauf

HGD

Creating longitudinal river profiles typically involves the following steps and materials:

Remember that the specific techniques and materials you use may vary based on the scale and complexity of your study area and the level of detail required for your research. Additionally, if you have access to a mentor or advisor, they can provide valuable guidance tailored to your specific research objectives.

Good Luck

A coarser description than Abolghasem Goorabi 's, but in order to simply get a plot. And it assumes the horizontal scale in example is in 'river miles / klometers', and you have a GIS. This intended to provide an illustration, not a rigorous geomorphology analysis. ( ... and just an observation, but how does one expect a quality answer when one does not describe the bounding box of the area of interest, your skills, or software being used .. the Earth is a big place, is this a wild life preserve or a continent, scale matters ).

• A vector dataset of the river courses, like 'HydroRIVERS" from https://www.hydrosheds.org/products/hydrorivers or a more detailed one for your area of interest. It may also be possible to download the river streamlines from OpenStreetMap.org.
• A raster Digital Elevation Model (DEM), like the ESA GLO-30 and GLO-90: worldwide coverage from https://spacedata.copernicus.eu/collections/copernicus-digital-elevation-model - these are usually delivered as tiles, so these will need to be mosaic-ed into a single raster.
• This data is usually in geographic coordinates ( latitude and longitude ) and needs to be converted to projected coordinate system ( miles or kilometers ) in a CRS appropriate for your Area of Interest.
• The 'mouth' of the system, the branch points of the tributaries, and the sources needs to be extracted - usually this is by default, but not always.
• The next step is to assemble the vector polylines of the river centerlines into separate continuous polylines from the source all the way to the mouth. This may require you to break and concatenate polylines from the original data, or even add segments if those are broken by lakes or reservoirs. ( yes, they will overlap each other as they go downstream to the 'mouth').
• For each of those continuous polylines, generate the river mile points from the mouth ( in QGIS https://www.northrivergeographic.com/qgis-points-along-line/ at some convenient interval (depending on relief and the resolution of your DEM raster, and will add both a accumulated distance and angle attribute field ) , but all GIS systems have a similar function.
• Add the elevations for each point set using a tool like QGIS's https://wiki.tuflow.com/QGIS_Extract_Ground_Elevation
• Export the sets of points to a tab or comma delimited text file, and plot each as an overlay using the Distance and Elevation attributes in the plotting application of your choice ... even Microsoft Excel can do this.

Again, this is probably sufficient for an illustration like the example you gave. The process will be similar no matter what GIS you use, or even the Spatial Library in a statistical package like R.

There are many other ways, to get the centerlines from sources to mouth, if one has a previously hydro-conditioned DEM, the stream lines can be generated by using just the sources and mouth points - but on other DEMs this can give erratic results because of local sinks, etc.