Water Resources Management

, Volume 32, Issue 12, pp 3801–3820 | Cite as

Two-Dimension Monthly River Flow Simulation Using Hierarchical Network-Copula Conditional Models

  • Wenzhuo Wang
  • Zengchuan DongEmail author
  • Wei Si
  • Yu Zhang
  • Wei Xu


River flow simulation is required on water resources planning and management. This paper proposes hierarchical network-copula conditional models to generate two-dimension monthly streamflow matrix aiming at simulating flow both on time and space. HNCCMs develop the simulation generator driven by both temporal and spatial covariates conditioned upon values of a set of parameters and hyper parameters which can be addressed from the three-layer hierarchical system. In the first layer, streamflow time series of the station at the most upstream is generated using bivariate Archimedean copulas and river flow space series in each month at stations down a river in sequence is simulated by nested copulas in the second layer. Last, the seasonal characters of the temporal parameters and covariates are detected as well as the spatial ones are detected using the neural network by fitting them into functions to contribute to the downscaling of space series. A case study for the model is carried on the Yellow River of China. This case (1) detects temporal and spatial relationships which illustrate the capacity of catching the seasonal characterize and spatial trend, (2) generates a river flow time series at Huayuankou station as well as (3) simulates a flow space sequence in January picking out best fitted building blocks for the cascade of bivariate copulas, and finally (4) synthesizes two-dimension simulation of monthly river flow. The result illustrates the essentially pragmatic nature of HNCCMs on simulation for this spatiotemporal monthly streamflow which is nonlinear and complex both on time and space.


Two-dimension monthly river flow simulation Spatial and temporal covariates Bivariate Archimedean copulas Resilient back-propagation network 



The project was financially supported by the National Key Research Program of China (Grant No. 2016YFC0401306), the applied technology research program (2016-005-HHS-KJ-X).

Compliance with Ethical Standards

Conflict of Interest



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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Wenzhuo Wang
    • 1
  • Zengchuan Dong
    • 1
    Email author
  • Wei Si
    • 1
  • Yu Zhang
    • 1
  • Wei Xu
    • 1
  1. 1.College of Water Resources and HydrologyHohai UniversityNanjingChina

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