Parametric emulation and inference in computationally expensive integrated urban water quality simulators

Water quality environmental assessment often requires the joint simulation of several subsystems (e.g. wastewater treatment processes, urban drainage and receiving water bodies). The complexity of these integrated catchment models grows fast, leading to potentially over-parameterised and computationally expensive models. The receiving water body physical and biochemical parameters are often a dominant source of uncertainty when simulating dissolved oxygen depletion processes. Thus, the use of system observations to refine prior knowledge (from experts or literature) is usually required. Unfortunately, simulating real-world scale water quality processes results in a significant computational burden, for which the use of sampling intensive applications (e.g. parametric inference) is severely hampered. Data-driven emulation aims at creating an interpolation map between the parametric and output multidimensional spaces of a dynamic simulator, thus providing a fast approximation of the model response. In this study a large-scale integrated urban water quality model is used to simulate dissolved oxygen depletion processes in a sensitive river. A polynomial expansion emulator was proposed to approximate the link between four and eight river physical and biochemical river parameters and the dynamics of river flow and dissolved oxygen concentration during one year (at hourly frequency). The emulator scheme was used to perform a sensitivity analysis and a formal parametric inference using local system observations. The effect of different likelihood assumptions (e.g. heteroscedasticity, normality and autocorrelation) during the inference of dissolved oxygen processes is also discussed. This study shows how the use of data-driven emulators can facilitate the integration of formal uncertainty analysis schemes in the hydrological and water quality modelling community.