Modelling rainfall with a Bartlett-Lewis process: pyBL (v1.0.0), a Python software package and an application with short records

Abstract

The Bartlett-Lewis (BL) model is a stochastic framework for representing rainfall based upon Poisson cluster point process theory. This model has been used for over 30 years in the stochastic modelling of daily and hourly rainfall time series. Historically, the BL model was known to underestimate sub-daily rainfall extremes, but recent advancements have addressed this issue, making it a viable alternative to traditional rainfall frequency analysis methods, such as those based on annual maxima time series. Despite its potential, calibrating the BL model is a not a trivial task. The model's formulation is complex, and calibrating it involves a nonlinear optimisation process that can be numerically unstable, which has limited its broader application. To promote the use of the BL model and demonstrate its capabilities in modelling sub-hourly rainfall - both standard and extreme statistics - we have developed an open-source Python package called pyBL. This paper details the design of the BL model and summarises the key features of the pyBL package. It includes a brief explanation of how to use the package in selected user scenarios. In addition, we report on scientific experiments that resemble real-world situations to showcase pyBL's ability to model sub-hourly rainfall extremes with short records and its flexibility in utilising records of various timescales and lengths.