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Rethinking Deep Learning-Based Rainfall-runoff Modelling for Data-Rich Hydrology
(University of Waterloo, 2026-07-28) Yu, Qiutong
Sequential deep learning (DL) architectures, particularly Long Short-Term Memory (LSTM) networks, have become widely used in large-sample rainfall-runoff modelling. By training a single model across many basins using meteorological forcings and static basin attributes, these models can exploit cross-basin rainfall–runoff patterns and often achieve strong overall predictive performance. This modelling paradigm has developed alongside the increasing availability of large hydrological datasets. While previous DL-based hydrological studies mainly benefited from increasing the number of gauged basins for regional training, hydrological datasets have continued to expand the information available to DL models in other ways. Lake-river routing network products and catchment discretization provide finer spatial detail, long-term hydrometeorological archives extend historical coverage, and high-frequency forcing and streamflow records support sub-daily prediction. These developments create opportunities for DL-based rainfall–runoff modelling, but they also raise methodological questions about how expanded datasets should be represented, selected, and matched with suitable model architectures. This thesis investigates how DL-based rainfall-runoff modelling can be adapted to use hydrological datasets that provide finer spatial detail, longer historical coverage, and higher temporal resolutions, through three complementary studies on subbasin-scale modelling, recency-aware training, and model architecture for data-intensive settings. The first study examines how subbasin-scale spatial information can be incorporated into LSTM-based streamflow prediction. Regional LSTM models typically use basin-averaged forcings and attributes, treating each basin as a lumped response unit. This representation supports large-sample training, but it also reduces information on within-basin variability and drainage connectivity. To address this limitation, the study proposed the Spatially Recursive (SR) model, a hybrid framework that applies a regionally trained lumped LSTM at the subbasin scale and routes the resulting local streamflow predictions through a lake–river hydrological routing model. The method was evaluated in the Great Lakes region and compared with the original lumped LSTM. The SR model achieved comparable performance at trained locations and improved prediction in larger basins. These results show that lake–river routing network information and subbasin-level response units can help regional LSTM models use spatially detailed hydrological data more effectively. The second study investigates how long historical records should be used when many training basins are available. Reanalysis products and hydrometric archives provide decades of meteorological forcing and streamflow data, but the relevance of older observations depends on their similarity to the prediction period. Using hydrometeorological records from 1374 North American watersheds spanning 1950–2023, this study evaluates the effects of training-period length and data recency through backward-expanding, forward-expanding, and sliding-window experiments. The results show that recent records have greater value for LSTM training than distant historical records. Extending the training period with older data produced limited gains and sometimes reduced performance. The benefit of increasing the number of training watersheds also depended on data recency, especially for prediction in ungauged basins. Spatial diversity improved generalization most clearly when recent observations were included. Peak-flow analyses further showed that very short recent windows may provide insufficient exposure to rare high-flow events, indicating that recency-aware training still requires adequate temporal coverage. These findings suggest that large-sample training data should be selected by considering both spatial diversity and temporal relevance. The third study explores whether enhanced recurrent architecture can support large-sample hourly rainfall-runoff modelling. At hourly resolution, models must process longer input sequences and preserve relevant information across many more time steps than in daily modelling. To examine this issue, this study implemented MF-xLSTM, which combines a multi-frequency daily–hourly input structure with an xLSTM model backbone. The model was evaluated using hourly data from 430 Canadian basins and compared with LSTM-based benchmarks under the same multi-frequency input setting. MF-xLSTM achieved performance comparable to the LSTM benchmarks when predicting unseen periods and showed stronger overall accuracy in pseudo-ungauged basins. It also produced low-flow volume bias closer to zero, suggesting that xLSTM’s memory mechanisms may help retain information from earlier parts of long input sequences that are relevant to delayed storage release such as groundwater baseflow. These results indicate that xLSTM is a plausible model backbone for large-sample hourly rainfall–runoff modelling. Overall, this thesis demonstrates that the benefits of expanded hydrological datasets depend on how these data are used in model development. In a data-rich hydrological setting, simply adding more data does not necessarily lead to better generalization. Finer spatial data need to be represented in ways that preserve within-basin heterogeneity and drainage connectivity; long historical records need to be selected with attention to temporal relevance; and high-frequency observations require architectures capable of retaining information across longer sequences. This thesis provides evidence on how DL-based rainfall-runoff modelling can make more effective use of expanded hydrological datasets.
Characteristic words as fixed points of homomorphisms
(University of Waterloo, 1991-12) Shallit, J. O.
With each real number 0, 0 < 0 < 1, we can associate the so-called characteristic word w = w(0), defined by wn = [(n+1)0]-[n0], for n>1. We prove the following: if 0 has a purely periodic continued fraction expansion, then w(0) is a fixed point of a certain homomorphism y=y0.
Comparative stylistics in an integrated machine translation system
(University of Waterloo, 1991-10) Mah, K.
Comparative stylistics is a subfield of stylistics that attempts to account for the differences in style between languages. Rules of comparative stylistics are commonly presented, in textbooks of translation, as "rules-of-thumb", but if we hope to incorporate a knowledge of comparative stylistics into natural language understanding systems, we must take a more formal approach. In particular, we will develop a computational model of comparative stylistics for machine translation that could be used to guide translation and thereby improve the quality of the translated output. An implementation of this model would provide additional information to the machine translation system about the potential modulations to the translated text and their effects, enabling it to make a more informed decision. In this thesis, we develop a set of formal rules of syntactic French-English comparative stylistics to be used as a component of a model of comparative stylistics. As the foundation for the formal rules, we adapt theoretical rules of syntactic French-English comparative stylistics compiled by Guillemin-Flescher [1981] and the formal representation of syntactic style developed by DiMarco [1990]. A corpus of French sentences and their English translations is analyzed to convert the theoretical rues to a set of formal rules that builds on DiMarco's grammars of syntactic style. Thus, we present a formal grammar of French-English comparative stylistics. We also suggest a method for incorporating these rules into an existing machine translation system.
Abstraction in nonlinear planning
(University of Waterloo, 1991-12) Yang, Qiang; Tenenberg, Josh D.; Woods, Steve
We extend the hierarchical, precondition-elimination abstraction of Abstrips to nonlinear, least-commitment planners such as Tweak. Specifically, we show that the combined planning system, AbTweak, satisfies the monotonic property, whereby the existence of a lowest level solution the implies the existence of a highest level solution that is structurally similar to II. This property enables one to prune a considerable amount of the search space without loss of completeness. In addition, we develop a criteria for good abstraction hierarchies, and develop a novel, complete search strategy called Left, Wedge that is optimized for good abstraction hierarchies. We demonstrate the utility of both the monotonic property and the Left-Wedge strategy through a series of empirical tests.
On specialization constraints over complex objects
(University of Waterloo, 1991-12) Ito, M.; Weddell, G.; Coburn, N.
Most semantic data models and object-oriented data models allow entity and object classes to be organized according to a generalization taxonomy. In addition, range restrictions (or property typing) may be specified not only on properties associated with a given class, but also on properties inherited from superclasses. In this paper, we consider a more general form of specialization constraint in which range restrictions are associated with property value paths, instead of with the properties themselves. One consequence is that the constraints enable a form of molecular abstraction, in which the internals of more complicated objects can be defined in terms of a collection of more primitive classes. We consider the problem for two models. The first imposes no constraints on class membership for an object beyond those implied by sub-classing constraints. In this case, we present a sound and complete axiomatization for arbitrary specialization constraints, and efficient decision procedures for the corresponding membership problems. The second model is more typical and requires that each object is created with respect to a particular class. Membership problems in this case are shown to be NP-hard, and NP-complete if class schema include a "bottom" class. We exhibit polynomial-time decision procedures when a bottom class does exist and antecedent specialization constraints satisfy a bounded path length condition. We also consider a case concerning the second model in which class schema satisfy a lower semi-lattice condition. A sound and complete axiomatization for well-formed specialization constraints is presented, together with efficient decision procedures for the membership problem for well-formed constraints, and for determining if an arbitrary constraint is well-formed. We prove that the membership problem for arbitrary specialization constraints remains NP-complete, however, even for class schema satisfying the lower semi-lattice condition.