Synthetic Design Hyetographs Under Non-Stationary Climate Conditions

A Microcanonical Multiplicative Cascade Model with GEV-GAMLSS Frequency Analysis and ENSO Covariate for the Colombian Andes

Abstract

Design hyetographs are essential inputs for urban drainage and flood control modelling. In data-scarce tropical regions, practitioners conventionally generate them from daily records under the stationarity assumption — a hypothesis increasingly contradicted by observed hydroclimatic trends in the Colombian Andes. This paper presents an integrated, reproducible five-stage framework that relaxes that assumption, implemented in the open-source R script MCM_Hyetographs v1.0.0 and demonstrated on a 71-year annual maximum daily precipitation record (1954–2024) from the Planta Río Cali station (CVC, Valle del Cauca, Colombia).

The framework operates as follows. First, a majority-vote ensemble of six complementary stationarity tests (Mann-Kendall, Pettitt change-point, sequential Sneyers, moving-window Mann-Kendall, White heteroscedasticity, and augmented Dickey-Fuller; decision rule ≥ 3/6) classifies the series as stationary or non-stationary. Second, frequency analysis fits either a stationary GEV by maximum likelihood or a non-stationary GEV-GAMLSS model with the Oceanic Niño Index (ONI) as a linear covariate in the location parameter, with model selection by AIC. Third, IDF curves are anchored on station GEV quantiles using the Bell (1969) formulation with a regional P(1h)/P(24h) ratio (r₆₀ = 0.40 for the Andean inter-valley zone). Fourth, sub-hourly temporal disaggregation
employs a Microcanonical Multiplicative Cascade (MCM) with Beta-distributed weights calibrated from available pluviograph records. Fifth, a Monte Carlo ensemble (n = 500) propagates disaggregation uncertainty, yielding design hyetographs at the Q10, Q50, and Q90 percentiles for nine return periods (2–500 years) formatted for direct HEC-HMS import.

Applied to the Planta Río Cali record, four of six stationarity tests return non-stationary votes, activating the GAMLSS model (AIC = 655.20 vs. 660.34 for the stationary GEV; ΔAIC = 5.14). The Pettitt test identifies a structural change-point in 2013 (p = 0.005). The estimated ONI slope (β̂₁ = −4.41 mm per ONI unit; 95% CI: [−8.62, −0.20]) indicates that El Niño suppresses extreme daily precipitation at this station, consistent with orographic dynamics on the western slopes of the Cauca Valley. The neutral-scenario 100-year 24-hour design depth is 127.6 mm. MCM Beta parameters (α̂ = 1.619, β̂ = 6.085) produce hyetographs peaking near t ≈ 2.25 h with a stable peak-to-total ratio of 28–31% across all return periods. The Q90/Q10 peak intensity ratio of approximately 2.4 — constant across return periods — explicitly quantifies the uncertainty inherent in daily-to-sub-hourly extrapolation, which is invisible to deterministic methods. The framework bridges statistical climatology and operational engineering practice, providing climate-informed design hyetographs with explicit uncertainty bands for application in data-scarce Andean and broader tropical regions.