The copula-based risk framework of Qiu et al. (2021) quantifies multiple, conditional, and systemic risk of the water supply–hydropower–environment (WHE) nexus in cascade reservoir multi-objective operation, but it is fitted to stationary historical conditions and does not treat external drivers. The open problem is to quantify how climate change and human activities — altered inflow statistics, changing demand patterns, land-use change and upstream withdrawals — alter the marginal distributions and multivariate dependence structure (copula parameters) of the WHE risk indicators, and thereby the joint exceedance probabilities, conditional risk surfaces, and conditional-entropy systemic-risk minima; and to embed such nonstationary inflow regimes and evolving anthropogenic demands into the multi-objective optimization–copula–entropy workflow so that nexus risk assessments adapt to future climate and socioeconomic scenarios.

Background

Cascade reservoir systems on large rivers (the original case study is the Xiluodu–Xiangjiaba–Three Gorges cascade of the upper Yangtze) are operated simultaneously for off-stream water supply, hydropower generation, and maintenance of the downstream river environment. These three functions are hydraulically coupled — water released for one purpose changes the water available for the others — and the water supply–hydropower–environment (WHE) nexus view treats their operation outcomes as interdependent random variables rather than independent objectives. In the framework of Qiu et al. (2021), a multi-objective optimization model produces Pareto-optimal operation solutions (operations that cannot improve one objective without worsening another), from which seasonal risk indicators are derived for each subsystem: seasonal water supply, seasonal accumulated hydropower generation, and a seasonal flow-regime alteration index for the downstream river habitat, with each subsystem summarized by a guarantee rate, i.e., the probability that its performance target is met. A copula — a function that couples the marginal (single-variable) distributions of several random variables into a valid joint distribution while keeping margins and dependence structure separate — is then fitted (a trivariate t-copula, whose elliptical tails allow stronger joint extremes than a Gaussian copula) to compute joint exceedance probabilities such as the chance that all three guarantee-rate thresholds are met simultaneously, and conditional probabilities such as the risk to the downstream habitat given specified water-supply and hydropower guarantee rates. Finally, conditional entropy — the Shannon entropy of one subsystem's outcome distribution conditioned on the outcomes of the others, a measure of residual uncertainty of a subsystem when its partners' states are known — is used to quantify the systemic risk of the nexus, and its minima identify guarantee-rate combinations where the system-level uncertainty is smallest. The analysis of Qiu et al. (2021) is stationary: the marginals are fixed parametric distributions fitted to historical operation outputs, the copula parameters are constant, and no climate or socioeconomic scenario enters the workflow. The effects of climate change and human activities — altered inflow statistics, changing demand patterns, land-use change, upstream withdrawals — on the fitted marginal laws, the copula parameters, and consequently on the multiple, conditional, and systemic risk assessments are not quantified in the published framework, and an extension of the workflow to nonstationary inflow regimes and evolving anthropogenic demands is absent from it. This gap matters because reservoir planning horizons span decades over which stationarity of hydrology and demand is no longer a defensible assumption: without a scenario-conditional treatment, the risk surfaces and entropy-based systemic-risk minima used to select guarantee-rate combinations may be systematically biased for future conditions. The statistical tools needed for the nonstationary component exist separately in hydrological frequency analysis — time-varying copulas for nonstationary flood coincidence risk (Feng et al., 2020) and dynamic Bayesian copulas for nonstationary multivariate risk (Sarhadi et al., 2016) — but they have not been coupled to multi-objective cascade reservoir operation or to conditional-entropy systemic-risk evaluation of the WHE nexus.

Problem Statement

How do climate change and human activities quantitatively alter the multivariate risk structure of the water supply–hydropower–environment nexus in cascade reservoir multi-objective operation? Concretely: (1) how do nonstationary inflow regimes (changed flood/non-flood season inflow statistics under climate change) and evolving anthropogenic drivers (changing water-demand patterns, land-use change, upstream withdrawals) alter the fitted marginal distributions of the seasonal WHE risk indicators and the copula parameters describing their dependence; (2) how do these changes propagate to the multiple-risk joint exceedance probabilities, the conditional risk surfaces, and the conditional-entropy-based systemic risk and its minima that the workflow of Qiu et al. (2021) computes under stationarity; and (3) how can such drivers be embedded into the multi-objective optimization–copula–entropy workflow so that the risk surfaces, joint probabilities, and entropy minima used to choose guarantee-rate combinations of water supply, hydropower generation, and environment are valid under future climate and socioeconomic scenarios rather than only the historical record?

Parts (1), (2) and (3) are each separately required, and no part subsumes another; the climate and human-activity drivers, scenario family, case-study setting and planning horizon to be treated are selected by the solver rather than prescribed here. The problem's target is the scenario-conditional extension of the workflow (3) together with at least one worked driver-to-risk quantification of how the fitted marginals, the copula parameters, the joint exceedance probabilities, the conditional risk surfaces and the conditional-entropy systemic-risk minima change under the selected drivers (1)–(2).

References

  1. Qiu, H., Chen, L., Zhou, J., He, Z., Zhang, H. (2021). Risk analysis of water supply-hydropower generation-environment nexus in the cascade reservoir operation. Journal of Cleaner Production, 283, 124239. DOI: 10.1016/j.jclepro.2020.124239. https://doi.org/10.1016/j.jclepro.2020.124239
  2. Wu, Z., Liu, D., Mei, Y., Guo, S., Xiong, L., Liu, P., Yin, J., Zeng, Y. (2022). Delayed feedback between adaptive reservoir operation and environmental awareness within water supply-hydropower generation-environment nexus. Journal of Cleaner Production, 345, 131181. DOI: 10.1016/j.jclepro.2022.131181. https://doi.org/10.1016/j.jclepro.2022.131181
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