Climate change is projected to impact tropical cyclone magnitude and frequency, with high magnitude events becoming more common. The destructive nature of event derived storm surges and associated coastal flooding necessitates risk management. However, the historic record is too short and too sparse to assess risk effectively, resulting in incomplete probability distributions of surge heights, particularly for distribution tails. Hydrodynamic simulation can fill these gaps, but the number of simulations required, both spatially and under diverse climates, coupled with their high computational cost, is prohibitive. To address this, we present an Artificial Neural Network storm surge emulator, deployed in the northwest Gulf of Mexico. This is trained on a database of hydrodynamic simulations, and outputs spatially coherent time series of surge. Our model achieves an R² of 0.91, with a RMSE of 13 cm when compared to an independent test set of hydrodynamic simulations, while exhibiting a computational gain factor of over 1500. Our approach is novel in its use of feature engineering to improve performance. Here variables which are physically relevant to surge are derived from commonly used features, such as wind and pressure, allowing us to maintain a simple model architecture, while steering the model towards physically coherent learning. Shapley Values are utilised for model interpretation and demonstrate that the model is making physically justified inference. Success is demonstrated by comparing our feature engineered model to a control, which engages in minimal feature engineering. The control achieves an R² of 0.71 and a RMSE of 23 cm only.