Environmental Modelling & Software 77 (2016) 19e31 Contents lists available at ScienceDirect Environmental Modelling & Software journal homepage: www.elsevier.com/locate/envsoft Computationally efficient modelling of tidal rivers using conceptual reservoir-type models * Pieter Meert a, b, , Fernando Pereira b, Patrick Willems a, c a Hydraulics Section, Department of Civil Engineering, KU Leuven, Kasteelpark Arenberg 40, Leuven, BE-3001, Belgium b Flanders Hydraulics Research, Antwerpen, BE-2140, Belgium c Department of Hydrology and Hydraulic Engineering, Vrije Universiteit Brussel, Brussel, BE-1050, Belgium article info abstract Article history: Conceptual reservoir-type models of river systems, that mimic the results of detailed hydrodynamic Received 13 July 2015 models, provide a powerful tool for numerous river management applications. Thanks to their compu- Received in revised form tationally efficient model structure they are very well suited for applications that require long term 7 October 2015 simulations or a large number of model iterations. However, one well-known problem is that conceptual Accepted 20 November 2015 models have difficulties to account for backwater effects. For this reason, their application to tidally Available online 12 December 2015 influenced river reaches so far was almost non-existent. This paper introduces an extension of an existing grey-box reservoir modelling technique to incorporate tidally influenced river reaches. The methodology Keywords: Tidal rivers is demonstrated for the downstream part of the rivers Zenne and Rupel in Belgium. Results show a minor Conceptual models loss of accuracy when the detailed model is replaced by the surrogate conceptual model. Also, the tidal Reservoir routing effects are well represented. Computationally efficient modelling © 2015 Elsevier Ltd. All rights reserved. 1. Introduction the Brussels Capital Region, etc. This has resulted in a large number of hydrodynamic models which are mostly limited to individual Over the last decades, water authorities all over the world have components of a catchment, that can hardly interact with each developed a large variety of detailed hydrodynamic models in other and are all computationally demanding. Furthermore, there support of their water management tasks. Despite this vast exists an overlap in the areas covered by these models, resulting in modelling capacity, the current tendency towards integrated areas that are modelled twice or more, by different model types and catchment modelling is impeded by a number of practical obsta- by different authorities, and which might provide different results cles. One of the main restrictions is that the natural catchments for the overlapping areas. may be managed by up to three or more different authorities, each In recent years, several generic modelling packages have been with their own responsibilities and modelling tools. The basin of developed to analyze the behavior of river basins under varying the river Zenne in Belgium, for example, is managed by the W&Z hydrological conditions and to assist decision makers in short-term authority for the navigable rivers in Flanders, the Flemish Envi- operations and long-term planning at basin scale, such as the Riv- ronment Agency (VMM) for the non-navigable rivers of first cate- erWare tool (Zagona et al., 2001), the spatially distributed LIS- gory in Flanders, the provinces and cities for the non-navigable FLOOD model (Van Der Knijff et al., 2010), the RIBASIM package rivers of higher category, the Direction generale operationelle de la (Deltares, 2010) and the Source Integrated Modelling System (IMS; Mobilite et des Voies hydrauliques (DGO2) for the rivers in Wal- Welsh et al., 2013). RiverWare, for example, is a river and reservoir lonia, the Brussels Environment Agency (BIM/IBGE) for the rivers in modelling tool that contains a library of pre-programmed physical the Brussels Capital Region, Aquafin for the urban drainage systems process algorithms to permit site-specific detailed modelling. IMS in the Flanders Region, Vivaqua for the urban drainage systems in is an Australian multidisciplinary modelling environment for catchments and river systems in transboundary basins. These generic packages use simplified river routing techniques, like the * Corresponding author. Hydraulics section, Department of Civil Engineering, KU Muskingum routing (Cunge, 1969) or Laurenson's non-linear Leuven, Kasteelpark Arenberg 40, Leuven, BE-3001, Belgium. routing with lag method (Laurenson, 1986), and can provide E-mail address: [email protected] (P. Meert). http://dx.doi.org/10.1016/j.envsoft.2015.11.010 1364-8152/© 2015 Elsevier Ltd. All rights reserved. 20 P. Meert et al. / Environmental Modelling & Software 77 (2016) 19e31 powerful solutions to overcome the above mentioned obstacles. suited for the aims of the research in this paper, since they start Simulations with these model packages are usually performed at from premises that constrain the conditions on which they are daily (or even larger) time step, making them suitable for long-term applicable. Problems arise for example in predicting water levels in catchment water balance calculations, but less suitable for river parts that show an important interaction between the tidal modelling individual flood events, which requires smaller time influence downstream and the fresh water discharges upstream. steps and a higher spatial resolution of calculation nodes. In order Furthermore, the accuracy of the simulation results of the above to meet these drawbacks, this paper makes use of conceptual mentioned models and methods can be rather poor, limiting their models, that emulate the results of the detailed models, based on a use in practice. Another important limitation is the fact that none of concatenation of reservoir-type model elements. The conceptual them ensures an explicit conservation of the water mass in the models considered here can be regarded as physically-inspired or system, which impedes an accurate incorporation of (variable) grey-box models, since they have a structure that is based on a human interactions on the water system, like for example hydraulic simplified representation of reality (Knight and Shamseldin, 2006). structures that regulate flood control areas or pumping stations The explicit calculation scheme of these models allows for very that control the water level in polders and land reclamation areas. short calculation times, making them useful not only for integrated The modelling approach presented in this paper is based on the catchment modelling, but also for other applications that require mass balance equation and can therefore address the problems long-term simulations or a large number of model runs, as in discussed here. In addition, the approach is ‘open’ enough, so that it forecasting, real-time control, sensitivity analyses, etc. is compatible with other (existing) reservoir routing techniques So far, conceptual models have mostly been applied to the free and independent of the type of hydrodynamic model that is used flowing, upstream parts of river systems, where no influences are for the detailed simulations. present of the backwaters induced by downstream water level This paper first describes the study area and the available data of boundary conditions (e.g. Wolfs et al., 2015; Van den Zegel et al., the rivers Zenne and Rupel in Belgium. Next, the existing concep- 2014; Vaze et al., 2011; Kozar et al., 2010). The application of con- tual modelling approach and the extension of this technique to ceptual models to tidally influenced river reaches was therefore incorporate the tidally influenced parts of the river system are almost non-existent. This paper presents an extension of the discussed. This is followed by an overview of how the detailed methodology presented in the paper by Wolfs et al. (2015), that is hydrodynamic model is transformed into a lumped conceptual applicable to the tidally influenced parts of a river system and that model. Finally, the simulation results of the presented approach are is also compatible with the existing conceptual modelling compared with the results of a hydrodynamic model to show the approach. This will allow to construct conceptual reservoir-type accuracy of the conceptual model. models for a complete river system, and make these models use- ful for integrated catchment modelling applications. 2. Study area and available data A large variety of computationally efficient modelling tech- niques to simulate the tidal propagation in estuaries and tidal rivers The river Zenne catchment is part of the international Scheldt exists. The techniques vary in quite a number of aspects: applica- basin that flows to the North Sea and is located in the central part of bility of boundary conditions, the number of processes accounted Belgium (see Fig. 1). The basin has a total area of 1162 km2, which is for, accuracy of the model results, etc. Empirical or black box divided over three administrative regions: the Walloon Region models are the most elementary type of models: they attempt to (574 km2), the Brussels-Capital Region (162 km2) and the Flemish find a relation between a model input x and the model outputs or Region (426 km2). The upstream part of the river (before entering physical quantities y, without accounting for the underlying phys- the city of Brussels) has a natural meandering course. In Brussels ical processes. Surface analysis methods (e.g. Barcena et al., 2012) and further downstream the river has been canalized: straight- can be mentioned as examples of these straightforward empirical ening of the meanders, re-profiling of the river bed and a vaulting models. An important premise of these models is that a unique over approximately 8.3 km. The river basin is crossed by a canal that relation must exist between model inputs and outputs. Data driven connects the cities of Brussels and Charleroi with the Scheldt river models like artificial neural networks have become widely used in and the North Sea. The canal and the river form a very complex all fields of hydrology and have recently also been applied in system that is highly influenced by human interactions and activ- simulating tidal propagation (e.g.