Scaling techniques for extreme rainfall estimation at the local-to-global scale

Extreme rainfall is one of the major causes of flooding disasters, threatening both human safety and economic security. Additionally, flood intensity and frequency are projected to increase globally under climate change, making accurate estimation of rainfall intensity across different return periods and durations essential for flood risk mitigation and infrastructure design. However, estimating rainfall intensity and return period remains challenging, particularly in data-sparse regions, due to unevenly distributed gauges and the limitations of current data and models. Regional models provide detailed results but are difficult to transfer across regions, while global models offer broad coverage but lack spatial-temporal resolution and durations/return periods flexibility. Scale invariance offers a promising tool to bridge these gaps, yet little research has explored its global distribution or effective application in extreme rainfall estimation. The overarching objective of this thesis is to enhance the capability to estimate extreme rainfall scaling at a global scale, thereby providing intensity'duration'frequency (IDF) relationships with high spatial and temporal resolution, especially in data-sparse regions. This thesis estimates sub-daily rainfall intensity from daily rainfall data using scale invariance. The scale invariant method works with globally available data by linking a scaling parameter to geographical factors like latitude, longitude, altitude, distance to coast, as well as climatic factors such as rainfall patterns and climate types. The analysis uses several machine learning methods, including Simple Linear Regression, Decision Tree, Random Forest, and Adaboost. This framework is first tested in a UK case study with rich data, where regional scaling distributions and IDF curves are reproduced. It is then extended to a global scale to produce worldwide scaling parameter maps, capable of estimating intensities under both present and future climate. Sensitivity analyses assess the impacts of data gaps, annual maximum series (AMS) window length, and climate variability, while comparisons with peer-reviewed IDF studies are used to validate model accuracy and practical applicability. Results reveal clear spatial patterns in the global scaling parameter, with less negative values in wetter, more rainfall-consistent regions and more negative values in drier, less frequent rainfall regions. In this context, more negative values indicate a steeper contrast in intensity between short- and long-duration rainfall extremes, whereas less negative values reflect more uniform scaling across durations. Climate types and geographic variables emerge as dominant controls of distribution. The model accurately reproduces IDF curves across diverse sites worldwide (e.g., UK, Chile, India, USA, Austria), demonstrates robustness to data gaps, and shows limited sensitivity to climate variability. Recommendations are also provided on AMS window lengths suited to different climate types to balance uncertainty and local rainfall representativeness. Between 2071 and 2100 (under Representative Concentration Pathway 8.5), intensities of 4-hour events with 30-year return periods are projected to increase by 20-62% according to results from 8 illustrative sites globally from this model. This thesis presents the first global model that combines scale-invariant theory with machine learning to estimate a local scaling parameter and rainfall intensities from geographical and climatic predictors. It extends the theory of scale invariance by linking it to large-scale environmental drivers and validating sub-daily and daily relationships worldwide. Practically, the model offers an innovative tool to generate IDF curves under both present and future climate conditions with improved spatial and temporal consistency. The results can reduce biases associated with region-specific models and provide intensity estimates for hydraulic models used in flood simulations and economic loss assessments. Estimates of extreme rainfall can inform the design of protective measures for critical infrastructure such as schools, hospitals, drainage systems, and reservoirs, while also supporting large-scale assessments of vulnerability to surface flooding to inform stakeholders.