Find in Library

<p>Self-similar structures of river networks have been quantified as having diverse scaling laws. Among these, we investigated a power function relationship between the apparent drainage density <span class="inline-formula"><i>ρ</i>_a</span> and the pruning area <span class="inline-formula"><i>A</i>_p</span>, with an exponent <span class="inline-formula"><i>η</i></span>. We analytically derived the relationship between <span class="inline-formula"><i>η</i></span> and other known scaling exponents of fractal river networks. The analysis of 14 real river networks covering a diverse range of climate conditions and free-flow connectivity levels supports our derivation. We further linked <span class="inline-formula"><i>η</i></span> with non-integer fractal dimensions found for river networks. Synthesis of our findings through the lens of fractal dimensions provides an insight that the exponent <span class="inline-formula"><i>η</i></span> has fundamental roots in the fractal dimension of the whole river network organization.</p>