From Sparse Measurements to Robust Inference: A Bootstrap Framework for Solute and Particulate Export Mechanisms Assessment in River Catchments

Quantifying solute and particulate export from river catchments is particularly challenging when concentration measurements are sparse, irregular, or limited to low‑frequency monitoring schemes. In such conditions, traditional regression‑based approaches used to interpret concentration–discharge (C–Q) relationships often fail to capture the full range of hydrological and hydrochemical variability. Here we present a bootstrap‑based methodology designed to robustly infer export mechanisms and associated uncertainties using minimal observational data.

The approach combines daily discharge series (Q) with available concentration measurements (C), explicitly separating rising and falling limbs of the hydrograph to account for hysteresis effects and asymmetric mobilization dynamics. In each bootstrap iteration (N≈1000), entire (Q, C) pairs are resampled and the C–Q relationship is fitted. For each parameter set, cumulative load duration curves (Mp%, p = 1–99) are computed, enabling the derivation of confidence intervals for both regression parameters and export‑pattern metrics.

The method yields a full empirical distribution of Mp%, allowing process‑based inference even in catchments with very limited measurements. Results demonstrate that bootstrap‑derived parameter distributions reliably distinguish dilution vs. mobilization patterns, identify “hot moments” of export, and quantify hysteresis strength. Percentile‑based confidence intervals effectively communicate uncertainty without assuming parametric error structures, making the framework well-suited for diverse catchment types and monitoring strategies.

This work shows that bootstrap resampling provides a powerful, model‑agnostic tool for moving “from pattern to process” in data‑scarce environments. The methodology enables more defensible interpretation of C–Q behaviours, supports targeted design of water‑quality monitoring networks, and provides transferable insights for ungauged or poorly sampled catchments.