Unlocking deep insights into temperature-dependent rainfall simulation: are we approaching it optimally?
Authors: Chen Pei-Chun , Wang Li-Pen 
Published: March 2024

Statistically-based rainfall simulation has been a useful tool to generate long rainfall time series while preserving observed rainfall properties, commonly employed for hydrological applications such as drainage design. However, these models, typically constructed using historical gauge records, may overlook climate dynamics, failing to capture variations in underlying climate or weather conditions. Recent research works have aimed to address this limitation (Willems and Vrac, 2010; Kaczmarska et al., 2015; Cross et al., 2020; Ebers et al., 2023). For example, Cross et al. (2020) introduced a regression method linking monthly temperature to the parameters of a rainfall generator, while Ebers et al. (2023) proposed a temperature-dependent micro-canonical cascade model to enhance rainfall disaggregation for future climates. Many of these approaches adopt a temperature-dependent strategy due to the temperature dependence of the atmospheric precipitable water saturation value. Additionally, many of these methods involve using temperature in an 'aggregated' manner, associating the temperature averaged over a specific time duration (e.g., monthly or daily) with model parameters over the same duration. In this study, we aim to examine the soundness of this common approach, addressing two key research questions:&#160;Given the complex atmospheric processes governing precipitation, is relying solely on temperature as a covariate for statistical rainfall simulation adequate?
Is the current 'aggregated' approach the most optimal method for incorporating temperature as a covariate?
&#160;To address these two questions, we employed the deep-learning model AtmoDist, proposed by Hoffmann and Lessig (2022). This model effectively captures underlying climate dynamics by extracting relevant features from successive input atmospheric variables and deriving the time difference between them based on the extracted features. We trained the model using input atmospheric variables with two different temporal arrangements: aggregation and concatenation. Aggregation, similar to many existing temperature-dependent approaches, involves averaging (or summing) temperature over a given duration with no overlap. Concatenation, on the other hand, involves simply concatenating temperature into a sequence over a given duration, preserving the entire temperature profile.&#160;After successful training, we examined derived features and traced model weights to quantify the importance of each input atmospheric variable and to assess the impact of different temporal arrangements. For this experiment, we utilised four atmospheric variables (temperature, geopotential, u and v components of wind) from ERA5 hourly data spanning from 1940 to 2008. Results indicate that in an 'aggregated' arrangement, the model assigns similar weights to temperature and u and v components of wind. In a 'concatenation' arrangement, temperature plays a dominant role in capturing climate dynamics. These findings suggest that the common approach of solely using temperature as a covariate and in an 'aggregation' manner may not be the most optimal. Instead, Including additional variables or using temperature as a covariate in a 'concatenation' manner is recommended.