Deriving an emulation model of a rectangular-basin two-layer numerical model

In the last decades, rapid improvement in processor speed has encouraged the development of large, distributed, process-based models, which are implemented in more and more complex computer codes. However, despite the increased computing power, the use of such models is far from being inexpensive: obtaining output trajectories over a time horizon of few years can require many days of simulation. As a consequence, the application for planning and management purposes is still very limited. What-if analysis, for example, i.e. the evaluation of the behavior of a system against a set of possible scenarios, can be applied to process-based models only when the number of scenarios is very small, as each model simulation can be prohibitively time consuming. Furthermore, the integration of process-based models into an optimization scheme is, at the state of the art, essentially impracticable. In recent years, emulation modeling emerged as a promising technique to overcome these limitations. An emulation model is a simple, usually lumped model, which is identified from synthetic data generated via simulation of a computationally inefficient model, and that can be used in its place to run fast simulations and optimization. Emulation modeling is largely employed in aerospace and mechanical engineering and is an emerging issue in environmental modeling, especially in the field of air quality. Applications to water systems mainly concern modeling and control of diffuse pollution in groundwater and soils. In this paper, the application of emulation modeling techniques is extended to hydrodynamics, namely modeling of stratified lakes. The ultimate scope is to allow for an indirect use of large, distributed, process-based hydrodynamic models for optimization purposes, closing the gap between scientific-oriented research and decision-making practice. The applicability of the emulation modeling approach is tested over a simplified but rather realistic case study: a one-dimensional, nonlinear, two-layer model of a rectangular basin. The model is simulated to generate synthetic time series of the thermocline displacement from the equilibrium position, as a function of the wind action, in different conditions of stratification (i.e. layers density). These data are used to develop a very simple emulation model. Precisely, an AutoRegressive-eXogenous (ARX) emulation model is identified, with different parameter settings estimated for each stratification condition. Although very simple, the emulation model provides an accurate estimate of the selected output variable. Moreover, its parameters can be provided with a physically meaningful interpretation. These promising results motivate further research to extend the application of emulation modeling to more sophisticated hydrodynamics models and to use this approach for planning and management of water resources.