water Article Efficient Reservoir Modelling for Flood Regulation in the Ebro River (Spain) Isabel Echeverribar 1,2, * , Pablo Vallés 1 , Juan Mairal 1 and Pilar García-Navarro 1   Citation: Echeverribar, I.; Vallés, P.; Mairal, J.; García-Navarro, P. Efficient Reservoir Modelling for Flood Regulation in the Ebro River (Spain). Water 2021, 13, 3160. https:// doi.org/10.3390/w13223160 Academic Editors: Anargiros I. Delis and Ioannis K. Nikolos Received: 22 September 2021 Accepted: 12 October 2021 Published: 9 November 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Fluid Mechanics, Universidad Zaragoza, I3A, Maria de Luna s/n, 50018 Zaragoza, Spain; 736453@unizar.es (P.V.); mairalascaso@unizar.es (J.M.); pigar@unizar.es (P.G.-N.) 2 Hydronia Europe, Pº Castellana 95-15, 28046 Madrid, Spain * Correspondence: echeverribar@unizar.es Abstract: The vast majority of reservoirs, although built for irrigation and water supply purposes, are also used as regulation tools during floods in river basins. Thus, the selection of the most suitable model when facing the simulation of a flood wave in a combination of river reach and reservoir is not direct and frequently some analysis of the proper system of equations and the number of solved flow velocity components is needed. In this work, a stretch of the Ebro River (Spain), which is the biggest river in Spain, is simulated solving the Shallow Water Equations (SWE). The simulation model covers the area of river between the city of Zaragoza and the Mequinenza dam. The domain encompasses 721.92 km 2 with 221 km of river bed, of which the last 75 km belong to the Mequinenza reservoir. The results obtained from a one-dimensional (1D) model are validated comparing with those provided by a two-dimensional (2D) model based on the same numerical scheme and with measurements. The 1D modelling loses the detail of the floodplain, but nevertheless the computational consumption is much lower compared to the 2D model with a permissible loss of accuracy. Additionally, the particular nature of this reservoir might turn the 1D model into a more suitable option. An alternative technique is applied in order to model the reservoir globally by means of a volume balance (0D) model, coupled to the 1D model of the river (1D-0D model). The results obtained are similar to those provided by the full 1D model with an improvement on computational time. Finally, an automatic regulation is implemented by means of a Proportional-Integral-Derivative (PID) algorithm and tested in both the full 1D model and the 1D-0D model. The results show that the coupled model behaves correctly even when controlled by the automatic algorithm. Keywords: reservoir model; numerical simulation; shallow water equations; PID regulation 1. Introduction As extreme phenomena, flood events raise concern among governments, institutions and general society. The European Union has been developing plans and directives during the last decades focusing on the control of their impact [1]. River overflows cause the flooding of adjacent lands, urbanised areas and other infrastructures. Additionally, floods can also take human lives, as reported by the UN [2], specially in areas with poor prevention plans and a lack of predictive tools. Frequently, dams and reservoirs are present in river basins as hydraulic elements with different functions. Not only to ensure enough water supply for agricultural activities or energy production, but also as hydraulic structures for discharge adjustment and control during flood events. Basin authorities manage their operation focusing on available space in the reservoir, maximum acceptable downstream discharges, and peak arrival times. In this context, the development of predictive tools that provide information about the temporal and spatial evolution of water level and discharge along a river during flood events can help to quantify the damage caused and has been widely addressed in last decades [3]. Some works are focused on urban areas coupling their overland models Water 2021, 13, 3160. https://doi.org/10.3390/w13223160 https://www.mdpi.com/journal/water