Modelling convective cell lifecycle with a copula-based approach

The utilisation of spatial-temporal rainfall generators for urban drainage design or operational planning has largely increased for better reflecting the hydrological response of the catchment. However, a significant challenge that persists within these models is their inadequate representation convective storms. More specifically, the overall variation in spatial and temporal rainfall modelling comprises those resulting from advection and evolution. Most of the generators however neglect the modelling of cell evolution. This deficiency poses difficulties to precise convective storm simulations, consequently leading to potential underestimations of flood risk.

In addressing the challenge of modelling convective storms, this study proposes a statistical-based algorithm that enables the generation of convective cell lifecycles accounting for the evolution of cell properties. To develop the algorithm, we first chose an area of approximately 431 km², centred at Birmingham city, as our study area. A total of 176 effective convective storm events, spanning from 2005-2017, were then identified using ground rain gauge records within the study area. We then utilised the enhanced TITAN storm tracking algorithm, proposed by Munoz et al (2018), to extract convective cell lifecycles for the selected events. Finally, a total of 116,287 lifecycles, comprising 354,855 individual cells, were retrieved, with an average of 660 per storm event.

We then investigated these cell lifecycles in three stages. The initial stage was to statistically characterise individual properties of convective cells, including rainfall intensity, spatial extent, and movement velocity. Following this, an investigation of the inter-correlations among these cell properties was conducted. Similar to the findings outlined in the literature, strong correlations could be found between cells’ intensity and their lifespans and between cells’ intensity and their spatial extents. The final stage focused on examining the evolution of these cell properties during their lifetimes. An interesting finding here is that the growth and decay rates of these cell properties are in fact correlated with cell properties themselves. This observation points to the need to incorporate this correlation structure into the process of sampling convective cells.

To resolve the complex correlation structure within convective cell evolution, we employed the Copula method, which is innovatively applied to statistically model the complex multi-variate interrelations among the characteristics of convective cells. The vine-copula approach, in particular, can well-reproduce the interrelations present in the dataset. The development of a novel copula-based algorithm for modeling convective cell lifecycles marks a key advancement, offering the potential for enhanced precision in spatial-temporal rainfall generators (McRobie et al., 2013), in depicting regional convective rainfall patterns.