Non-stationary flood frequency analysis in the Guachicono River (Colombian Andes): trend detection, GAMLSS modeling and design quantiles

A six-test stationarity battery, parametric bootstrap and non-stationary confidence intervals for hydrological design under climate change

Abstract

Background and motivation. Flood frequency analysis is the cornerstone of hydraulic infrastructure design. The classical paradigm assumes statistical stationarity of peak-discharge series, an assumption increasingly challenged by anthropogenic climate change and land-use modification. In the upper Guachicono River basin (Cauca, Colombia), an Andean river with 31 years of continuous record (1993–2023), the stationarity hypothesis cannot be taken for granted without rigorous scrutiny.
Objective. To present CFE-Colombia v1.0.0, an open-source R computational framework for non-stationary flood frequency analysis, integrating: (i) formal detection of trends and structural breaks via a battery of six complementary tests, (ii) multi-scale wavelet analysis with Monte Carlo simulation (n = 1 000), (iii) stationary fitting with AICc-based model selection and parametric bootstrap confidence intervals, and (iv) non-stationary modeling via GAMLSS with Cox-Snell residual validation.
Methods. The test battery comprises Mann-Kendall (MK), Pettitt, sequential Sneyers, moving-window MK, White (heteroscedasticity), and augmented Dickey-Fuller (ADF). The stationary analysis fits six distributions (GEV, Gumbel, Log-Normal, Pearson III, LP3, and Normal) with AICc selection. The non-stationary analysis evaluates six GAMLSS models with P-splines and Gumbel, Log-Normal, and Gamma families. Uncertainty is quantified via parametric bootstrap (B = 1 000) for GEV quantiles and residual bootstrap (B = 500) for GAMLSS quantiles.
Results. A significant increasing trend (τ = 0.316, Sen slope = 2.48 m3/s/yr, p = 0.013) and an abrupt structural break in 2010 (∆ = 37.5%, p = 0.020) were detected, classifying the series as non-stationary. The best GAMLSS model (M4: Log-Normal with time varying μ and σ via P-splines) yields AIC = 360.78 and adequate validation (KS p = 0.744, Filliben r = 0.976; edfμ = 4.59, df.fit = 9.80). For the year 2023, the 100-year design discharge is 542.9 m3/s (95% CI: 455.2–2 435.2 m3/s), compared with 1 160.8 m3/s from the stationary GEV model (−53.2%).
Conclusions. The integrated framework reveals a stationary/non-stationary crossover paradox at Tr ≈ 5–7 yr: the stationarity assumption dangerously underestimates frequent floods with short return periods (Tr ≤ 5 yr) by up to +37.7%, and significantly overestimates major floods with long return periods (Tr ≥ 10 yr) under current basin conditions. Ignoring non-stationarity produces systematically incorrect hydrological designs, with direct implications for the engineering safety of water infrastructure in the Colombian Macizo Colombiano region under accelerated land-use transformation and climate chang.