# Method for estimating discharge, hydraulic depth, and mean velocity in rivers through spatial interpolation of at-a-station hydraulic geometry in data- scarce regions

## TL;DR

A new method called SHGI estimates river discharge, depth, and velocity using river width data in areas with limited hydrological monitoring.

## Contribution

SHGI introduces spatial interpolation of hydraulic geometry parameters to estimate river flow metrics in data-scarce regions.

## Key findings

- SHGI ensures spatial continuity by incorporating upstream distance in parameter interpolation.
- The method preserves compositional constraints of hydraulic geometry parameters during interpolation.
- Validation in contrasting river basins confirmed SHGI's robustness and accuracy.

## Abstract

Reliable discharge estimation is essential for water resource management, yet many regions lack sufficient hydrological stations. To address this limitation, we propose the Spatial Hydraulic Geometry Interpolation (SHGI) method, which estimates discharge (Q), hydraulic depth (D), and mean velocity (V) from river width (W) obtained via surveys or satellite imagery. SHGI integrates hydraulic geometry theory with multiquadric radial basis interpolation, applied to the Meta and Atrato river basins in Colombia. Parameters of at‑station hydraulic geometry (coefficients a, c, k and exponents b, f, m) were derived using least squares and transformed into log‑ratio space to preserve their compositional constraints. Interpolation along upstream distance ensures spatial continuity, and closure operations guarantee internal consistency. Validation against observed data in basins with contrasting geomorphology and data density confirmed the method’s robustness.

The principal contributions of SHGI are:•Longitudinal continuity: explicit incorporation of upstream distance to interpolate parameters consistently along channels and tributaries.•Compositional integrity: preservation of the multiplicative and additive constraints of hydraulic geometry parameters during interpolation.•Estimation under data scarcity: enabling calculation of Q, D, and V at ungauged sites using only river width.

Longitudinal continuity: explicit incorporation of upstream distance to interpolate parameters consistently along channels and tributaries.

Compositional integrity: preservation of the multiplicative and additive constraints of hydraulic geometry parameters during interpolation.

Estimation under data scarcity: enabling calculation of Q, D, and V at ungauged sites using only river width.

Image, graphical abstract