Automated modelling of urban runoff based on domain knowledge and equation discovery

Modelling tools are widely used to analyse the urban drainage systems and to simulate the effects of future urban development and stormwater control measures. Usually, these tools use only one mathematical model (predetermined by the modeller) at a time to describe a single hydrological process within the urban catchment. When there are alternative mathematical models for describing the same hydrological process, their suitability needs to be investigated separately, which makes the modelling task even more complex, time consuming and open for human errors. Furthermore, models have to be calibrated to achieve a better fit between measured and simulated runoff. Calibration can be performed either manually, by using a trial-and-error approach, or by employing search techniques and parameter optimization tools. To overcome the drawbacks associated with manual selection and calibration of models, automated modelling based on equation discovery was used in this study to a) find the most suitable mathematical model among multiple alternatives for describing every (environmental) process modelled and b) to calibrate the model parameters against measured data. First, knowledge on urban runoff modelling was formalized into a new library of modelling components, compliant with the equation discovery tool ProBMoT (Process Based Modelling Tool). Next, a conceptual model of the experimental urban sub-catchment within the city of Ljubljana, Slovenia, was defined. ProBMoT was used to find the structure and parameters' values of alternative rainfall-runoff models, according to the defined conceptual model that provide optimal fit against pipe flow measurements. Three alternative methods were used to describe infiltration: the SCS CN method, the Variable UK runoff equation, and the UK Water Industry Research equation. The proposed automated model discovery approach for finding the optimal rainfall-runoff model proved to be very efficient. Nine rainfall-runoff models were created with very good performance. The best performance was achieved by the models that used a combination of two different infiltration methods, i.e. the SCS CN infiltration method for the pervious area and one of the other two infiltration methods for the impervious area.

Automated summary

In this study, an automated model discovery approach based on equation discovery was used to find the optimal rainfall-runoff model for urban drainage systems. The method proved to be efficient and resulted in nine models with very good performance, with the best performance achieved by combining two different infiltration methods.