S. et al. (2026) A four dimensional vine copula-based probabilistic framework for intra-seasonal design flood hydrograph generation

Identification

• Journal: Stochastic Environmental Research and Risk Assessment
• Year: 2026
• Date: 2026-04-01
• Authors: Shilpa L. S., Srinivasan K.
• DOI: 10.1007/s00477-026-03212-3

Research Groups

• Department of Civil Engineering, Indian Institute of Technology Madras, Chennai, India
• Kerala State Council for Science, Technology and Environment, Trivandrum, India

Short Summary

This study develops a four-dimensional vine copula-based probabilistic framework to generate intra-seasonal design flood hydrographs, capturing both flood magnitude and shape variability. Applied to the Nacimiento Dam, the framework provides robust, sub-seasonal design hydrographs for improved flood mitigation strategies.

Objective

• To develop an integrated, fully multivariate (four-dimensional vine copula-based) probabilistic framework for generating intra-seasonal design flood hydrographs that simultaneously capture intra-seasonal variability in flood magnitude (peak, volume, duration) and hydrograph shape (prior/posterior-peaked or multimodal).

Study Configuration

• Spatial Scale: Upstream reach of the Nacimiento Dam, Nacimiento River, California, USA (USGS 11148900, 35.79° N latitude and 121.09° W longitude, drainage area 419.58 km²).
• Temporal Scale: 35 years of hourly streamflow data from 1988 to 2023 (water year). Flood season segmented into three sub-seasons: pre-flood season (1 December - 8 January), main-flood season (9 January - 13 March), and post-flood season (14 March - 30 April).

Methodology and Data

• Models used:
  • Four-dimensional vine copulas (Canonical (C-vine) and Drawable (D-vine) structures) for multivariate dependence modeling.
  • Probability change point analysis for flood season segmentation.
  • Maximum Likelihood Estimation (MLE) for parameter estimation of distributions and copulas.
  • Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for model selection.
  • Ljung and Box test for autocorrelation.
  • Mann–Kendall (M–K) test and modified M–K test for trend analysis.
  • Hybrid modified continuous time Markov chain (MCTMC) model for synthetic streamflow generation.
  • Typical Flood Hydrograph (TFH) method for hydrograph construction, incorporating a shape factor (ratio of time to peak and duration).
  • Software: MATLAB (R2023b, 'fitmethis', 'lbqtest', 'MannKendall', 'MannKendall_Modified'), R (4.3.1, 'VineCopula', 'rvinecopulib').
• Data sources:
  • Observed hourly streamflow records (1988-2023) from the USGS National Water Information System for the Nacimiento River, upstream of Nacimiento Dam, California.
  • Synthetic hourly streamflow sequences (50 Monte Carlo simulations, generating 1750 annual maximum flood events) derived from the observed data using the MCTMC model.
  • Flood characteristics: flood peak (P), volume (V), time to peak (Tp), and duration (D).

Main Results

• The framework successfully segments the flood season into pre- (1 December - 8 January), main- (9 January - 13 March), and post- (14 March - 30 April) sub-seasons for the Nacimiento Dam site.
• The hybrid MCTMC model effectively generates synthetic hourly streamflow sequences, preserving the distributional characteristics of flood attributes and providing sufficient data for robust analysis.
• Four-dimensional vine copulas (C-vine and D-vine) effectively model complex multivariate dependence among flood peak, volume, time to peak, and duration, outperforming traditional bivariate or trivariate approaches.
• For a given univariate return period, 'AND' joint return periods (JRPs) are consistently higher than 'OR' JRPs, indicating that simultaneous exceedance of all four flood characteristics is less frequent.
• The choice of vine type (C-vine vs. D-vine) significantly impacts estimated design flood quantiles; for example, a 100-year flood event in the pre-flood season yielded an 'OR' JRP of 27 years and an 'AND' JRP of 548 years using a D-vine, compared to 28 years ('OR') and 245 years ('AND') using a C-vine.
• The introduction of a shape factor (Tp/D) allows for objective selection of normalized typical flood hydrographs, ensuring that design hydrographs reflect realistic intra-seasonal variability in shape (e.g., unimodal vs. multimodal, prior-peaked).
• The framework generates sub-seasonal design hydrographs that accurately reflect real-world flood behavior, demonstrating its utility for adaptive reservoir flood mitigation. For instance, a 100-year return period flood event in the pre-flood season was characterized by a peak discharge of 696.09 m³/s, a volume of 4.65 x 10⁷ m³, a time to peak of 29.61 hours, and a duration of 91.16 hours.

Contributions

• Proposes an integrated, fully multivariate (four-dimensional) probabilistic framework using vine copulas for intra-seasonal design flood hydrograph generation, extending beyond common bivariate or trivariate formulations.
• Introduces a novel objective shape factor (ratio of time to peak and duration) to link design flood characteristics with hydrograph morphology, overcoming arbitrary shape selection limitations.
• Demonstrates the ability of the framework to capture complex seasonal dynamics and higher-order dependence (d > 3) among flood peak, volume, duration, and time-to-peak.
• Provides a robust tool for generating shape-aware, sub-seasonal design hydrographs that reflect realistic variability, crucial for dynamic and adaptive reservoir flood-mitigation operations.
• Highlights the importance of considering hydrograph shape variability (e.g., multimodal responses) in design flood estimation, which is often overlooked by traditional methods.

Funding

The authors declare that no financial support was received for the research, authorship, or publication of this article.

Citation

@article{S2026four,
  author = {S., Shilpa L. and K., Srinivasan},
  title = {A four dimensional vine copula-based probabilistic framework for intra-seasonal design flood hydrograph generation},
  journal = {Stochastic Environmental Research and Risk Assessment},
  year = {2026},
  doi = {10.1007/s00477-026-03212-3},
  url = {https://doi.org/10.1007/s00477-026-03212-3}
}