If you mean the slope of free water surface (hydraulic gradient), you can measure it by installing a series of river gauges (water level gauges) along the river. However, it doesn’t have a fix value. It may change with time and place to place. For example, the slope of free water surface is increased during floods.

As suggested by Dr. Hettiarachchi, water levels as well as gradients are not just a fixed value. If you can determine river facets (riffle, run, pool, glide), the top of the riffles control the channel gradient, but probably easiest to measure levels in pools, pool to pool, or series of pools over at least one sinuous bend. The channel distance is also measured. Since bankfull is also so important to channel forming processes, one may go from elevation top of point bar to top of point bar through at least a sinuous bend. Some might use GIS and estimate valley gradient, but this is problematic as the contour based DEMs are seldom accurate enough to estimate flood gradient of valley, and if the channel is entrenched, the valley surface is a terrace (abandoned floodplain), and not an active floodplain. Water surfaces can also vary somewhat, so if using a staff gauge, or hook gauge in stilling well, I usually try to get the average height of the fluctuation. In using the Rosgen methods in wading small streams for linear profile, we typically use a laser level with height detector on elevation rod, and we attempt to follow thalweg, measuring elevation of bottom, water surface level, level of bankfull indicator, level of floodplain If present, level of terrace for each measurement point. This information is plotted, graphed, etc. We calculate things like gradients associated with the facets, meander belts, etc. Rivermorph is a useful software to collect the various data of cross sections, linear profiles, banks, pebble or substrate counts, etc. if interested in getting his training or using his system. I have also used HEC RAS where a series of cross sections are used, and pieced together to estimate water levels, velocities, etc for varying flow rates. The more cross sections, the better the flow routing detail, but be sure to get at least the top of riffles and bottom of pools or should also be point bar location for cross sections as primary features. For cascades and turbulent waters, the water surface elevation may not be measurable due to turbulence and fluctuation.

Dear PhD. Annayat. As already answered by the masters before, there are several methods to perform this activity, each method with its specificities;

I would complement responses by stating that everything depends on the precision scale and for the purposes of applying this hydraulic gradient survey and river slope.

If you do not need precision and scale of much detail, you can perform a first tentative model or field preparation, modeling via DEM in GIS, using widely known hydrological algorithms implemented by TauDEM, GRASS, SAGA all available on free QGIS software (qgis.org).

Among the best free and widely available DEMs on the planet are ALOS PALSAR (https://www.eorc.jaxa.jp/ALOS/en/palsar_fnf/fnf_index.htm requires free registration) and TanDEMx (check availability) , with spatial resolutions of 12.5 meters and 1 meter (https://www.dlr.de/dlr/en/desktopdefault.aspx/tabid-10378/) respectively. TanDEM is a high resolution SAR with 20-55º Angle of View.

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Best Regards.