CivilAche

 The Geomorphological Instantaneous Unit Hydrograph (GIUH) links catchment runoff response to quantitative stream network geometry without requiring direct streamflow records. Based on Horton’s Laws of Drainage Network Composition, three morphological ratios are derived: ​Bifurcation Ratio: $R_b = \frac{N_\omega}{N_{\omega+1}}$ ​Length Ratio:  $R_l = \frac{\bar{L}_{\omega+1}}{\bar{L}_\omega}$ ​Area Ratio: $R_a = \frac{\bar{A}_{\omega+1}}{\bar{A}_\omega}$ ​Where $N_\omega,$ $\bar{L}_\omega,$ and $\bar{A}_\omega$ represent stream count, mean length, and mean area of order $\omega.$ Rodríguez-Iturbe’s GIUH formulation computes the peak discharge $(q_p)$ and time-to-peak $(t_p)$ of the unit hydrograph as: $q_p = \frac{1.31}{L_\Omega} \cdot R_a^{0.43} \cdot v \quad$  $\text{and}$  $\quad t_p = \frac{0.58 \cdot L_\Omega}{v} \cdot \left(\frac{R_b}{R_a}\right)^{0.55} \cdot R_l^{-0.38}$ ​Where $L_\Omega$ is the length of the highest-order stream $(\text{km})$ and $v$ is peak ...