Intensive hierarchical optimal water allocation with uncertainties based on Non-stationary Transformers

Ensuring water supply reliability as well as improving the quality of water environment is a challenging task, especially in cities with water shortage. Non-stationarity and variability in streamflow and water demand compound this challenge. This study first develops Non-stationary Transformer models to explore the stationarity in streamflow forecasting and, uncertainties of both water availability (WA) and water demand (WD). Compared with traditional transformers, Non-stationary Transformers can improve data predictability and maintain model capability simultaneously. Not only the uncertain range of streamflow forecast but also optimal allocation schemes have been enhanced by Non-stationary Transformers, especially the NS-Informer model. The uncertainties from WA and WD forecasts are all simulated by bootstrap. Then, the impacts of WA as well as WD uncertainties on the hierarchical optimal allocation of PTSOA (Process-based three-layer synergetic optimal allocation) model are assessed. It would be at most 1.34 $\times$ 10⁷m³ of water saved under the scenario considering uncertainties from WA and WD, compared to the scenario only considering one uncertain source in the optimal allocation. The results show that considering more sources of uncertainties has the potential to make model allocation schemes more intensive.