We used the observed exponents of depth and slope to predict the Manning friction exponent and to test it against field exponents from three studies.  Finally, we briefly sketch how the two anomalous scaling exponents could be estimated from the transport of suspended sediment load and the bed load.

Gupta, V. K. and O.J. Mesa. “Horton laws for hydraulic–geometric variables and their scaling exponents in self-similar Tokunaga river networks,” Nonlinear Processes Geophysics, 21, pp. 1007-1025, 2014.