| Natural river networks show well-known self-similar characteristics. Such characteristics are
represented by various power-law relationships, e.g., between upstream length and drainage
area (exponent h) (Hack, 1957), and in the exceedance probability distribution of upstream
area (exponent É) (Rodriguez-Iturbe et al., 1992). It is empirically revealed that these
power-law exponents are within narrow ranges. Power-law is also found in the relationship
between drainage density (the total stream length divided by the total basin area) and
specified source area (the minimum drainage area to form a stream head) (exponent η)
(Moussa and Bocquillon, 1996).
Considering that above three scaling relationships all refer to fundamental measures of
’length’ and ’area’ of a given drainage basin, it is natural to hypothesize plausible
inter-relationship between these three scaling exponents. Indeed, Rigon et al. (1996)
demonstrated the relationship between É and h. In this study, we expand this to a more
general É-η-h relationship. We approach É-η relationship in an analytical manner while η-h
relationship is demonstrated for six study basins in Korea. Detailed analysis and implications
will be presented.
References
Hack, J. T. (1957). Studies of longitudinal river profiles in Virginia and Maryland. US,
Geological Survey Professional Paper, 294.
Moussa, R., & Bocquillon, C. (1996). Fractal analyses of tree-like channel networks from
digital elevation model data. Journal of Hydrology, 187(1), 157-172.
Rigon, R., Rodriguez-Iturbe, I., Maritan, A., Giacometti. A., Tarboton, D. G., & Rinaldo,
A. (1996). On Hack’s Law. Water Resources Research, 32(11), 3367-3374.
Rodríguez-Iturbe, I., Ijjasz-Vasquez, E. J., Bras, R. L., & Tarboton, D. G. (1992). Power
law distributions of discharge mass and energy in river basins. Water Resources Research,
28(4), 1089-1093. |