Abstract
It is a challenge to develop models that can represent the stochastic behaviour of rivers and basins. Currently used streamflow models were constructed under rigid hypotheses. Hence, these models are limited in their ability to represent nonlinear dependencies and/or unusual distributions. Copulas help overcome these limitations and are being employed widely for modelling hydrological data. For instance, pure copula-based models have been proposed to simulate univariate hydrological series. However, there have been few studies on the use of copulas to model multivariate inflow series. Thus, the aim of this study is to develop a pure copula-based model for simulating periodic multivariate streamflow scenarios, wherein temporal and spatial dependencies are considered. The model was employed in a set of 11 affluent natural energy series from Brazil. We used the model to simulate many scenarios and analyze them through statistical tests such as Levene’s test, the Kolmogorov-Smirnov test, Kupiec test, and t-test. In addition, we investigated the spatial and temporal dependence of the scenarios. Finally, the critical periods of the simulated scenarios were investigated. The results indicated that the proposed model is capable of simulating scenarios that preserve historical features observed in the original data.
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Notes
Computed from affluent natural streamflows and productibilities of hydropower reservoirs. It can be considered the energy generated from water inflow in a specific location.
The density of a d-dimensional copula is given by \(c(u_{1},...,u_{d})=\frac {\partial ^{d} C(u_{1},...,u_{d})}{\partial u_{1},...,\partial u_{d}}\).
See Aas et al. (2009) for more information.
See Mai and Scherer (2012) for a formal definition.
In Brazil, there are 12 Aggregated Reservoir. However, after a visual inspection, we noted that one RSVR is non-stationary; thus, it was not included.
To help plan the system from a computational perspective, the hydroeletric power plants that make up the system are represented in an aggregated form, through an aggregated reservoir.
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Acknowledgements
The authors would like to thank the National Council for Scientific and Technological Development (CNPq) of Brazil for support through the CNPq-PDJ program (grant number 150866/2017-8).
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de Almeida Pereira, G.A., Veiga, Á. Periodic Copula Autoregressive Model Designed to Multivariate Streamflow Time Series Modelling. Water Resour Manage 33, 3417–3431 (2019). https://doi.org/10.1007/s11269-019-02308-6
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DOI: https://doi.org/10.1007/s11269-019-02308-6