RegFDC-Cauca v1.0.0: Flow Duration Curve Regionalization via the Index-Flow Method with Long-Memory in Ungauged Basins of the Cauca River System, Colombia

An open computational framework integrating Ward D2 clustering, ARFIMA and leave-one-out cross-validation in R

Abstract

Context and motivation. The flow duration curve (FDC) is a fundamental tool for hydrological design, ecological flow assessment, and water resources planning. In the Cauca River basin (Colombia), the low density of stream gauges prevents direct FDC construction at many sites of interest. The index-flow method allows FDC estimation in ungauged catchments, but requires a regionalization that captures intra-regional climatic heterogeneity and a synthetic series generation that preserves the long-term persistence observed in Andean Colombian streamflow.
Objective. To present RegFDC-Cauca v1.0.0, an open-source R computational framework for FDC regionalization in ungauged catchments of the Cauca River hydrological system (Colombian Andes), using Ward D2 clustering with weighted metadata, Hurst exponent detection, and ARFIMA(0,d,0) synthetic series generation.
Methods. The framework applies three complementary methodological advances: (i) Ward D2 hierarchical clustering of physical catchment attributes weighted with qualitative metadata (hydrological regime and climatic sub-region); (ii) Hurst exponent H estimation via the scaled R/S method and automatic selection between ARFIMA(0,d,0) and AR(1); and (iii) a log-log mean discharge model with BIC predictor selection and Jensen-corrected prediction intervals.
Results. The framework is calibrated and validated on 20 gauged catchments of the Cauca system (drainage areas 290–18 900 km2, period 2015–2019). Ward D2 clustering identifies three sub-regions (cophenetic coefficient = 0.80, mean silhouette = 0.51). Leave-one-out (LOO) cross-validation of dimensionless FDCs yields NSE = 0.97, KGE = 0.96, and PBIAS = 0.3%, with MAPE < 5% over 0.05 ≤ F ≤ 0.85. All catchments exhibit H > 0.60 (median = 0.88), validating universal use of ARFIMA(0,d,0) across the Cauca system.
Conclusions. FDCs estimated for 8 ungauged catchments (C021–C028) include 90% prediction intervals derived from regional inter-catchment variability and mean discharge model uncertainty.