This thesis describes the application of machine learning to hydrology problems in the face of imminent and long term climate change, in particular through the lens of data minimalism. First, we note that with the dawn of the Anthropocene the world's climate is changing, primarily due to human activity. That change is having and will continue to have profound effects on climatic, geological, and biological systems, including the world's hydrological systems with which we are concerned. We further note that there are large swathes of the world where there is insufficient data for the development of traditional empirical models, so a new approach is required, one that can generalise from the data we do have.

The opening chapters begin with a treatment of the relevant features and a strategy for compressing the dimensionality to create a model that does not rely on internal measurements from a hydrological system to make predictions about streamflow. We then take this framework and examine the performance of different machine learning model architectures within it and note that whilst some machine learning methods offer greater flexibility, simplicity, and performance, this is subordinate to the feature engineering.

With the modelling approach established for a single hydrological system, we extend the framework in order to be able to better generalise to unseen hydrological systems; by introducing additional features that describe the physical nature of the catchment, such as its topography and geology and again noting that these might be assessed externally, along with proxy variables to estimate anthropogenic interaction with the natural system. In doing so, we create a framework that is able to generate usable predictions for even the most problematic of systems, such as those where human activity has resulted in severe ecosystem degradation.

If flooding is of concern then so too should be extreme phenomena that result in the causal precipitative events; and thus our attention turns toward the application of machine learning to storm prediction. Our experimental approach offers a brief guide through a history of networks for computer vision tasks, as any gridded data is analogous to an image, before developing a multi-task approach for identifying cyclonic activity, locating it within a domain, and then predicting its likely precipitative impact, thus connecting it to flood risk.

In attempting to improve certain frameworks for their better application to the problems at hand, namely those concerned with time histories, antecedent dependencies, or hidden states, we modify and extend the Neural Process framework, examining the structure of the encoder and decoder networks within. Whilst we achieve state of the art performance with the first foray, using Recurrent Neural Networks as encoder and decoder, our second, using Temporal Convolutional Neural Networks, was less successful but does not diminish our belief in the viability of the general approach.

Finally, we examine the application of the methods described in this thesis to the problem of future scenario impact modelling using climate projections; although ubiquitous methods of correcting the systematic bias within climate models were used, we believe that a new approach is required, one where climate projections are used to force a generative machine learning weather model that is then used to force impact models. This approach has the potential to be more realistic and more powerful, rapidly generating thousands of scenarios of impact under a given climate projection to create informed statistical distributions of impact.