A data-driven Dynamic Emulation Modelling approach for the management of large, distributed water resources systems

Water resources engineering and hydrology focus predominantly on physically-based models to characterize the dynamics of the physical, social and economic processes. Such a high fidelity models are usually computationally expensive and cannot be used in problems requiring hundreds or thousands of model runs to be satisfactory solved. Typical examples include optimal planning and management, data assimilation, and sensitivity analysis. An effective approach to overcome this limitation is to perform a top-down reduction of the physically-based model by identifying a simplified, computationally efficient emulator, constructed from and then used in place of the original physically-based model in highly resource-demanding tasks. In this work we propose a new data-driven Dynamic Emulation Modeling (DEMo) approach that combines the advantages of data-based modeling in representing complex, non-linear relationships, and preserves the state-space representation, which is both a precondition to infer an ex-post physically meaningful interpretation of the emulator and particularly effective in some applications (e. g. optimal management and data assimilation). The core mechanism of the proposed approach is a novel variable selection procedure based on a class of tree-based methods that is recursively applied to a data-set of input, state and output variables generated via simulation of the physically-based model. The approach embodies some very important properties: it is fully automated, independent on domain experts and system knowledge, and suitable for non-linear processes; it has a high potential in terms of complexity reduction; and, finally, it provides an ex-post interpretation of the emulator structure. The approach is demonstrated on a real-world case study concerning the optimal operation of a selective withdrawal reservoir suffering from algal blooms due to thermal stratification. The emulator, which is identified on a data-set generated with the 1D coupled hydrodynamic-ecological model DYRESM-CAEDYM, shows good performances in emulating the dynamic behaviour of the original model in characterizing the chlorophyll-a concentration in the euphotic layer.