Modeling rainfall with a Bartlett–Lewis process: incorporating climate co-variate using a deep learning method
Authors: Chen Pei-Chun , Wang Li-Pen 
Published: February 2023

Stochastic rainfall modeling has been a useful tool to generate long rainfall time series for hydrological applications. One of the widely-used stochastic rainfall generators in the UK water industry to support drainage system design is the Bartlett-Lewis Rectangular Pulse model (BLRP). In practice, there are two main challenges that need to be addressed in the development of BLRP models: 1) capacity of preserving standard and extreme rainfall properties across a wide range of timescales, e.g. from sub-hourly to monthly; 2) ability to reflect the variations in the underlying climate/weather.For the first challenge, some breakthroughs have been achieved over the past few years. Onof and Wang (2020) reformulated the original BLRP model to overcome its deficiency in underestimating rainfall extremes at sub-hourly timescales. Kim and Onof (2020) further extended Onof and Wang&#8217;s work by introducing an additional parameter to enable reproducing rainfall properties across a wide range of timescales &#8211;from sub-hourly to monthly or longer.&#160;The second challenge is however yet to be addressed. The concept of weather analogs is often adopted in the literature to incorporate the impact of climate dynamics. A set of atmospheric variables, which are assumed to be able to well represent the underlying weather/climate condition, are selected and associated with the co-located local rainfall properties. Cross (2020), e.g., proposed a regression method to associate the monthly temperature with the parameters of the BLRP model. However, the concept of &#8216;calendar month&#8217; &#8211;a man-made period of time&#8211;&#160; was still used in this method, which hindered the capacity of resembling the natural variations in seasons between years. To better resemble nature, Dai (2021) proposed a moving-window approach Dynamic Time Warping (DTW) method. Dai&#8217;s method sliced the original rainfall time series with a 30-day width and 10-day step moving window to reduce the impact of artificial separation of seasons. In addition, the DTW was employed to provide a more robust metric than the eulerian distance for quantifying the similarity between any two climate conditions. Dai&#8217;s work suggests that an unconventional metric may be required to better identify weather/climate analogs.&#160;Hoffmann and Lessig (2022) proposed a deep-learning method, called AtmoDist, that transforms the original atmospheric variables into a number of high-dimensional features and computes the distance from the extracted features. The result showed that the AtmoDist outperforms the traditional distance in identifying weather analogs. In this research, we extend the moving-window DTW based analog method proposed in Dai (2021) by replacing the DTW with the AtmoDist. Similarly to Dai (2021), selected atmospheric variables from the ERA5 hourly data on pressure levels are used for model training and validation. The local rainfall properties derived from the periods of the identified weather analogs resulting from the AtmoDist and the DTW methods will be first compared to evaluate their ability to identify weather analogs. Then, the derived local rainfall properties will be used as input to the BLRP model. This will enable the quantification of the impact of large-scale atmospheric variations to the local rainfall properties.&#160;