Author(s): Befekadu T. Woldegiorgis; Ann Van Grinensven; Fernando Pereira; Willy Bauwens
Linked Author(s): Fernando Pereira
Keywords: Water quality; Modelling; Analytical solution; Qual2e; Conceptual modelling
Abstract: The riverine system plays vital role in the ecological functioning. Efficient and reliable method of planning is a key for curbing the ever increasing water quality problems thereby maintaining a healthy aquatic environment and computer modelling plays a vital role in this regard. Most river water quality models have large simulation times because they are based on hydrodynamic simulators. This limits their applicability for operational purposes as well as planning activities involving long-term statistical information. For instance, imperfect nature of data monitoring and the approximate conceptualization of the reality are often causes for suspicion in model predictive capacity and hence, uncertainty analysis is required. Therefore, fast and accurate models are crucially complementary to the detailed models in operational and planning activities. Traditional QUAL2E model is widely in use for modelling river water quality processes and it can be considered as an approach with less parameters than detailed models while taking the pollutant interactions into account. This paper presents quasi-analytical solutions-based river water quality modelling approach that integrates ODEs of QUAL2E pollutant transformation in to dynamic CSTR method as an improvement over the numerical solution approaches used in conceptual water quality models. We compared it with the Euler method implemented in the widely applied SWAT model and explicit as well as implicit fourth order Rung-Kuta methods implemented in conceptual water quality models such as QUASAR and QUESTOR. The improvement mainly aimed at increasing model accuracy and solution stability with special emphasis for simulations during the low flow periods. We evaluated the behaviors of results from the Euler numerical solutions and the Runge Kuta4 numerical integration methods. It turned out that the numerical methods show serious instability because of overestimations of decay processes during large residence times as well as due to abrupt changes in the input concentrations. To overcome the instability we derived, based on simplifying assumptions, quasianalytical solutions of inhomogeneous first order differential equations resulting from the integration of the QUAL2E transformation formulations in to the CSTR-based mass balance equations. Finally, we tested the stability of the quasianalytical method for real simulations and hypothetical extreme low flow scenarios. The new quasi-analytical solution gives unconditionally stable solution even when advanced implicit fourth order Rung-Kuta schemes give unstable results. It also gives fairly comparable results with the reference RWQM while running 130, 000 times faster than it. Water quality processes are so critical during the low flow periods that it is fair to conclude that this approach is preferable to the numerical solutions of the ODEs of solute transformation. Besides the riverine system, this approach is well suited for water quality modelling in conveyance systems associated with large residence times like navigation canals. Furthermore, we demonstrated that the dynamic quasi-analytical CSTR solution of non-conservative pollutant modelling is analogous to the classical steady linear reservoir approach having variable and residence-time-dependent reservoir constant with proper input scaling down. In the context of decision support system, we believe that the implementation of this approach combined with conceptual water quantity modelling methods makes it vitally complementary to detailed models for planning and operation of wate r quality problems demanding fast and fairly accurate results.
Year: 2015