PyBL: an open source Python package for fine-scale rainfall modelling with short records based upon a Bartlett Lewis model

Abstract

Bartlett-Lewis (BL) model is a stochastic model that represents rainfall based upon the theory of Poisson cluster point process. It had been used for daily and hourly stochastic rainfall time series modelling for over 30 years. It was however known to underestimate sub-hourly rainfall extremes until some recent advances, where this shortcoming has been overcome. It could therefore serve as an alternative to the existing rainfall frequency analysis methods based upon, for example, annual maxima time series. The implementation of the BL model is however a non-trivial task. The formulation of the BL model is of high complexity, and the calibration of the model parameters constitutes a nonlinear optimisation process with high numerical instability. This hinders the widespread use of the BL model. Another computational challenge of BL modelling lies in sampling. In particular, when using this type of rainfall generators, it often requires sampling a large number of long-term realisations. In this work, with the purpose of promoting BL model and of demonstrating its capacity in modelling sub-hourly rainfall (both standard and extreme statistics), we have initiated an open source Python library for the BL model: pyBL, where a set of data structures and algorithms are designed specifically for the BL model, making the fitting and sampling processes more efficient and lightweight in terms of memory. In particular, one of our designs is a lossless time series compression method that perfectly suits BL model and a set of algorithms and can calculate statistical properties without any decompression. Additionally, we have implemented user interfaces and packaging at various levels, making experimental adjustments and optimisation methods more flexible and concise. Finally, two scientific experiments resembling real-world scenarios were conducted here to demonstrate pyBL's capacity of modelling sub-hourly rainfall extremes with short records, as well as flexibility of utilising records at various resolutions and with various data lengths. We show that, with the help from the BL model, we can well model hourly and sub-hourly rainfall extremes with merely half data length required by the widely-used Annual Maxima method.