Joint probability analysis of streamflow and sediment load based on hybrid copula

Area of Science:

• Hydrology
• Environmental Science
• Statistical Modeling

Background:

• Statistical analysis of streamflow and sediment is crucial for watershed management and water infrastructure design, particularly in silt-rich rivers.
• Understanding the complex dependency between streamflow and sediment is essential for accurate hydrological assessments.

Purpose of the Study:

• To propose a novel bivariate joint distribution framework using nonparametric kernel density estimation (KDE) and a hybrid copula function.
• To accurately describe the complex dependent structure between streamflow and sediment variables.
• To validate the proposed method in the Jinsha River Basin (JRB).

Main Methods:

• Utilized nonparametric KDE to fit the marginal distribution functions of streamflow and sediment.
• Developed a hybrid copula function by linearly combining Clayton, Frank, and Gumbel copulas.
• Compared the hybrid copula with five commonly used single copulas (Clayton, Frank, Gumbel, Gaussian, and t).

Main Results:

• Nonparametric KDE effectively estimated marginal distributions for streamflow and sediment, outperforming Gamma and GEV distributions.
• The hybrid copula function provided a more comprehensive representation of the streamflow-sediment dependency compared to single copulas.
• Return period precision increased by 7.41% using the hybrid copula compared to the best single copula.
• Synchronous and asynchronous probabilities of streamflow and sediment in JRB were determined as 0.553 and 0.447, respectively.

Conclusions:

• The proposed hybrid copula framework significantly improves the accuracy of streamflow and sediment statistical analysis.
• This study offers a valuable methodology for bivariate joint probability analysis in hydrological and environmental studies.
• The findings enhance the accuracy of statistical analysis for silt-rich rivers and inform integrated watershed management.