Abstract The chapter provides a comprehensive review of the hydrology of the Congo River Basin (CRB), emphasizing its physical features, current data and models, hydrological processes, environmental pressures, and the evolving scientific understanding. Water resources of the CRB support vital ecosystem and societal services that include agriculture, fisheries, hydropower, navigation, water supply, biodiversity conservation, and maintenance of vulnerable ecosystems such as peatlands and flooded forests that are crucial for carbon storage and climate resilience. The CRB hydrology is shaped by its diverse physiographical and geomorphological features, linked through a complex river network encompassing wetlands, lakes, and groundwater systems. Connectivity between headwaters, the Cuvette Centrale, and major tributaries (Kasai, Lualaba, Oubangui, and Sangha) plays a central regulatory role. Our current understanding of these processes remains very limited, which restricts our ability to implement policies for water security and address the impacts of change on physical systems and society. Increasing pressures from deforestation, mining, land use, and climate change threaten hydrological stability, livelihoods, and ecosystem resilience. Heightened vulnerability to hydro-climatic extremes, such as floods, droughts, and landslides, and biological risks like Ebola outbreaks raises concerns of an approaching hydro-ecological tipping point. The chapter calls for urgent investment in monitoring networks, remote sensing, data integration, and predictive modeling to support sustainable water resources management and development. Fifteen major hydrological research challenges are identified , underscoring the need for robust scientific investment. Beyond the CRB, findings will enhance global understanding of tropical forest hydrology and reinforce the basin’s critical role in the Earth System.

River bathymetry-the submerged channel topography invisible to conventional remote sensing and costly to survey at scale-remains unmapped for most of the world's rivers, critically constraining hydrodynamic flood modelling. The Surface Water and Ocean Topography (SWOT) satellite mission now delivers global Water Surface Elevation (WSE) observations, opening a path to infer riverbed elevation from space. Yet recovering bathymetry from WSE alone is fundamentally ill-posed: without additional constraints, infinitely many bed configurations produce identical surface responses. We present a Physics-Informed Neural Network (PINN) framework that mitigates this ill-posedness by assimilating multi-temporal SWOT overpass across diverse flow regimes, treating bed elevation as the sole unknown while prescribing Manning's roughness, discharge, and channel width. A dual-network architecture separates the time-invariant bed elevation from flow-dependent water depth, embedding Gradually Varied Flow (GVF) physics as a differentiable constraint. Synthetic experiments across 24 bed profiles achieve centimetre reconstruction accuracy for smooth morphologies, degrading for abrupt features at the identifiability limits of one-dimensional hydraulics. Validation on the Severn and Thames demonstrates that as few as 12 high-flow overpasses-roughly 10% of the available record-reproduce fulldataset accuracy, with Mean Absolute Errors (MAE) below 0.3 m relative to ground-truth surveys. Critically, reconstruction accuracy is governed primarily by hydraulic parameter uncertainty rather than SWOT observational limitations: Manning's roughness variations alone introduce errors of +2.4 m, an order of magnitude beyond those from sampling density or measurement noise (+0.8 m). This framework charts a course from sporadic field campaigns to continuous, satellite-driven bathymetric monitoring for operational flood forecasting.

Reliable interpretation of Earth observation data remains a fundamental challenge. Synthetic aperture radar (SAR) satellites have become central to global flood monitoring due to its all-weather imaging capability. Recent advances in supervised artificial intelligence (AI) have led to claims of robust cross-scene generalization in SAR-based flood delineation. Here we show that such claims are difficult to reconcile with the fundamental physics of radar scattering. Through scattering theory, semi-empirical analysis, and evaluation of publicly available AI flood-mapping models, we demonstrate that coherent scattering, wind-introduced surface roughening, and calibration drift prevent consistent separation of water and non-water signatures. These systematic errors persist across both single-scene classifiers and change-detection approaches. These findings suggest fundamental limitations of supervised learning in physics-governed observation systems.

Rivers impact the well-being of humans and the environment. As they increasingly face planetary-scale stressors, it is critically important to monitor and understand rivers at the global scale. As the only synoptic resource for global primary data on rivers, satellite remote sensing has recently begun to provide unprecedented opportunities for the monitoring, understanding, and prediction of global river behaviour. Despite these advances, the role of satellite remote sensing in global river science has still not been fully explored. New satellite systems and algorithms will enable substantial improvements in river measurements, provide new answers to long-standing or newly emerging scientific questions, and eventually update basic knowledge of rivers to advance global river science. In this Review we explore how remote sensing has been used to study the world’s rivers, examine challenges and opportunities for further advancing our understanding of rivers using existing and upcoming sensors, and identify possible solutions and future research directions. This Review synthesizes the transformative role of satellite remote sensing in reshaping global river science. It offers a strategic roadmap to overcome current challenges and update our fundamental understanding of Earth’s river systems.

Accurate flood modeling is crucial for effective analysis and forecasting. Full-momentum hydrodynamic models often demand substantial computation, sometimes exceeding typical forecasting horizons. In contrast, low-complexity models, such as local inertial approximations, provide accurate results in subcritical flows but may exhibit limited skill in supercritical conditions. This paper explores two main aspects: (i) the impact of urban in frastructure on 2D hydrodynamic modeling without detailed sewer and drainage data, and (ii) the comprehensive spatio-temporal assessment of 2D local inertial modeling using three numerical schemes (original formulation, s-centered, and s-upwind) in a dam-break scenario on complex terrain. The HydroPol2D model is benchmarked against HEC-RAS 2D full momentum solver. We present one numerical validation study comparing the developed model with benchmark examples and three real-world scenarios. The first two are located in S & atilde;o Paulo, Brazil: a detention pond receiving a 1 in 100-year inflow hydrograph and a highly urbanized catchment subject to a rain-on-the-grid simulation with a 1 in 50-year Huff hyetograph. The latter, located in Pernambuco State, Brazil, provides the first comprehensive assessment of local-inertial model performance for simulating an instantaneous dam-break scenario. Model validation against the benchmark example yields results identical to those reported in the literature. Results demonstrate that the model accurately simulates drainage infrastructure via internal boundary conditions, representing drainage infrastructure, with peak errors of less than 5 % compared to HEC-RAS 2D. However, neglecting urban infrastructure leads to peak-discharge differences of up to 21 % and major hydrograph mismatches, while roughly doubling computation time. The dam-break testing scenario demonstrates good predictive performance for maximum flood depths (CSI = 0.92 for the original local inertial model (lim), 0.95 for s-centered, and 0.89 for s-upwind), though the model's lack of convective inertia results in faster flood wave propagation than the full momentum solver. Notably, HydroPol2D was 23 times faster than HEC-RAS 2D, making it well-suited for rapid simulation of dam breaks or to be used in ensemble forecasting systems, in addition to being capable of modeling urban drainage infrastructure, such as orifices, weirs, and pumps.

Abstract. Climate change is projected to impact tropical cyclone magnitude and frequency, with high magnitude events becoming more common. The destructive nature of event derived storm surges and associated coastal flooding necessitates risk management. However, the historic record is too short and too sparse to assess risk effectively, resulting in incomplete probability distributions of surge heights, particularly for distribution tails. Hydrodynamic simulation can fill these gaps, but the number of simulations required, both spatially and under diverse climates, coupled with their high computational cost, is prohibitive. To address this, we present an Artificial Neural Network storm surge emulator, deployed in the northwest Gulf of Mexico. This is trained on a database of hydrodynamic simulations, and outputs spatially coherent time series of surge. Our model achieves an R2 of 0.91, with a RMSE of 13 cm when compared to an independent test set of hydrodynamic simulations, while exhibiting a computational gain factor of over 1500. Our approach is novel in its use of feature engineering to improve performance. Here variables which are physically relevant to surge are derived from commonly used features, such as wind and pressure, allowing us to maintain a simple model architecture, while steering the model towards physically coherent learning. Shapley Values are utilised for model interpretation and demonstrate that the model is making physically justified inference. Success is demonstrated by comparing our feature engineered model to a control, which engages in minimal feature engineering. The control achieves an R2 of 0.71 and a RMSE of 23 cm only.

Abstract. Global river discharge observations are critical for climate and hydrological research, used for water resource management, risk mitigation, infrastructure and environment conservation, among many other areas. However, existing observations are limited in availability, accuracy and spatial extent, with uneven geographical distribution and high levels of uncertainty often recorded. The NASA SWOT mission provides the opportunity to fill this gap, providing water level observations for all rivers exceeding 100 m in width worldwide. Combined with the daily discharge model GRADES-hydroDL, we present a statistical method to produce a set of global virtual gauging stations with the same temporal resolution as the satellite observations. The high level of accuracy that the SWOT water surface elevation observations allows us to improve the dynamics of discharge estimation over the input discharge model. For our validation gauges, where we compared modelled discharge to observed values, 66 % of Pearson R values are larger than 0.9, showing the method’s skill at replicating temporal patterns in recorded flow. The median Root Mean Square Error, RMSE, of the input discharge set is 36.3 m3 s−1 larger than that of our proposed method, and the NSE 0.3 lower. However, our method fails to improve the bias; the median absolute normalised bias is 0.10 (10 %) higher in our model than the input model, indicating that while the inclusion of Earth Observation can greatly improve the discharge time series dynamics, the trade-off is an increased bias in the distribution. Nevertheless, as the record of SWOT observations increases in length, these results should improve and the margins of bias difference decrease. The result is a globally applicable reanalysis dataset of discharge, which will complement existing physically based models and ground observations, and can be widely used within global hydrological models.

2025 featured geographically concentrated flood anomalies shaped by shifting large-scale atmospheric circulation and ocean–atmosphere variability, with antecedent hydrologic conditions and topography amplifying impacts in several regions. The year ranked in the lower tier of the past two decades for flood exposure, totalling over US$ 28 billion in damages and 4,200 flood-related fatalities globally.

Traditional nadir altimeters struggle with coastal water surface elevation (WSE) measurement and fine-scale river-estuary interactions, due to land-water signal interference and their wide inter-track spacing. The wide-swath Surface Water and Ocean Topography (SWOT) mission, using a new Ka-band radar interferometer, aims to address these issues by delivering 2D WSE measurements with unprecedented spatial resolution, accuracy, and precision. However, the mission's effectiveness in coastal WSE retrieval and its error characteristics remain unverified. This study leverages gauge and airborne LiDAR data to validate SWOT's WSE in the Bristol Channel and Severn Estuary. Assuming error-free in situ data, SWOT ocean products exhibit a standard deviation of difference (STD) of 13 cm within a 3 km radius of tide gauges. Compared to LiDAR, SWOT's PIXC measurements have STD of 37 cm, improving to 14 cm over 100 m grids and 9 cm over 1 km2 areas. This meets the SWOT science requirement of 10 cm STD at 1 km2 scale and extends satellite-based WSE monitoring into complex coastal environments.

Urban flooding is one of the most damaging impacts of climate change. The two main causes of changes in rainfall-driven flooding are altered precipitation and changes in urbanisation. Yet attribution studies only focus on the former. Furthermore, very few event attribution studies examine subdaily rainfall extremes, the timescale at which such extremes are accelerating the most. Here, for the first time, we carry out an impact event attribution study examining the effects of both climate change and urbanisation on a flash-flooding event in the U.K. city of Leeds. By combining a convection-permitting climate model with a flood inundation model, we show that the extent of flooding in the urban area of Leeds was increased during this event in 2014 by 49% compared to the potential flooding that would have occurred if a similar rainfall event had taken place 30 years earlier. The increase from urbanisation (29%) is almost twice that from climate change (16%). Both factors combine nonlinearly to increase flood extent by more than the sum of their parts. Our results also show that urban flood risk could be significantly misrepresented if changes in rainfall intensity are used as a proxy for changes in pluvial flooding.

Modelling flood hazards at large scales – both uniform frequency hazard maps and event simulations whose frequency varies in space – is a relatively new scientific endeavour. Data and computation constraints have historically necessitated either a more local focus to modelling efforts, or the building of proof-of-concept global-scale models whose fidelity inhibits most practical applications. Here, we present a global climate-conditioned flood catastrophe model; the culmination of decades of research into scaling inundation modelling, the incorporation of climate change, and synthetic event generation. 30 m resolution global maps representing fluvial, pluvial, and coastal flooding for given return periods were simulated using a hydrodynamic model with sub-grid channels whose inputs were defined using regional flood frequency analyses. Change factors from climate model cascades were flexibly used to perturb the local flood frequency a given flood map represents. Separately, a 10,000-year-long set of synthetic events were simulated using a conditional multivariate statistical model fitted to global fluvial-pluvial-coastal reanalysis data. The empirical return period of a given event is used to sample the corresponding flood map return period in order to build a long synthetic series of floods. With a global exposure model built using a top-down approach – downscaling capital stock models to high-resolution satellite-derived land-use and building height data – and a global vulnerability model derived from an extensive review of modelling and engineering literature, we demonstrate the calibration and validation of the global risk model. We also show the software challenges overcome to run this model, as well as to enable end-users to flexibly calculate the flood risk of their own exposures in the Oasis Loss Modelling Framework.

Accurate long-term forecasting of spatiotemporal dynamics remains a fundamental challenge across scientific and engineering domains. Existing machine learning methods often neglect governing physical laws and fail to quantify inherent uncertainties in spatiotemporal predictions. To address these challenges, we introduce a physics-consistent neural operator (PCNO) that enforces physical constraints by projecting surrogate model outputs onto function spaces satisfying predefined laws. A physics-consistent projection layer within PCNO efficiently computes mass and momentum conservation in Fourier space. Building upon deterministic predictions, we further propose a diffusion model-enhanced PCNO (DiffPCNO), which leverages a consistency model to quantify and mitigate uncertainties, thereby improving the accuracy and reliability of forecasts. PCNO and DiffPCNO achieve high-fidelity spatiotemporal predictions while preserving physical consistency and uncertainty across diverse systems and spatial resolutions, ranging from turbulent flow modeling to real-world flood/atmospheric forecasting. Our two-stage framework provides a robust and versatile approach for accurate, physically grounded, and uncertainty-aware spatiotemporal forecasting.

Over the last fifteen years, hydrodynamic modelling has, like so many branches of hydrology, made the leap from local to global scales. Where once we may have applied our models to single river reaches a few 10s of kilometres in length, we can now build and execute models at ~30m spatial resolution over the entire terrestrial land surface. In turn, this has allowed us to address scientific and practical questions that were hitherto impossible to answer. For example, global inundation modelling can help us understand and quantify large scale hydrological and biogeochemical cycles and many questions in flood risk management, for example decisions about future government spending on flood defences, analysing the solvency of flood insurance portfolios under extreme conditions, or determining climate change impacts, require predictions of flood risk at national, continental, or even global scales.This paper therefore discusses the scientific developments that were needed to make this local-to-global transition possible and outlines what the latest generation of global inundation models now can (and cannot) do. Finally, the paper looks at current limits to inundation modelling in terms of boundary conditions, flood defence data and model validation and considers the prospects for further improvements in model skill using the data from recently launched and forthcoming satellite missions such as SWOT and NISAR.

Over the last few decades flood risk management has become increasingly reliant on simulation of flood inundation from physical models of river-floodplain systems. Information from these models takes the form of flood extent and depth maps, and can directly influence decisions in sectors such as humanitarian response, insurance and urban planning. However, it is expensive to create accurate models, due to input data requirements, resulting in relatively low-quality simulations along most rivers. One of the major issues is river bathymetry (the land below the water surface) because this cannot be measured remotely and at a large scale.One way to overcome this issue would be to develop ‘inverse’ models that estimate bathymetry from water surfaces, which are much more observable. In the past, suitable water height measurements have been a limiting factor, however, the Surface Water and Ocean Topography mission will for the first time measure all global river water surfaces wider than ~50 m. This paper develops methods to estimate river bathymetry from SWOT data, evaluating the SWOT height observations and river bathymetry estimates for a small (40-70m wide) UK river. SWOT data is sufficiently accurate to estimate bathymetry that when used for flood modelling could simulate flood extents and depths with similar accuracy to a traditional model based on local river survey data.

The increasing frequency and intensity of heavy rainfall events driven by climate change poses challenges for flood risk management. In this study, we use a high-resolution, convection-permitting ensemble from the UK climate projections local dataset to explore how the spatiotemporal characteristics of heavy rainfall events may evolve across the UK. Adopting an event-based framework, we analyse 5 km hourly rainfall data from 12 ensemble members and compare changes in future rainfall events to those derived from applying intensity-based scaling factors alone. This comparison allows us to identify aspects of rainfall change that are not captured by shifts in intensity distributions. Our results show that short-duration winter events become increasingly localised, with peak intensities increasing by up to 47%, amplifying flash flood potential. In summer, rainfall events exhibit expanded spatial extents—expanding by 25%–40%—magnifying total precipitation volumes. While we find small changes in the number of clustered events (i.e. heavy rainfall events that occur within a 21 day window), there are large changes to the contribution these have to seasonal precipitation, particularly in summer (7%–11% in the baseline to 11%–16% in future period). These findings highlight new insights into how heavy rainfall may change under future climate conditions, identifying aspects of change beyond intensity increases alone that are relevant for informing current practice for flood risk estimation.

Small Island Developing States are a group of 57 island nations and territories which are some of the most at-risk places to the impacts of climate change globally, particularly from changes in hydrometeorological hazards such as flooding. Despite this, little research has quantified present day flood hazard and population exposure in small islands, let alone how this may change as global temperatures continue to rise. Until now, this was due to the insufficient data to produce high-resolution flood hazard and population exposure estimates for a wide range of possible scenarios at such a large scale. Following the release of Fathom’s Global Flood Model 3.0, in this work we combine global flood hazard estimates for coastal, fluvial, and pluvial flood hazard at ~30m flood model resolution to estimate present day population exposure to flooding across all 57 small islands. We also investigate how flood hazard and population exposure changes under three climate scenarios: two plausible climate change scenarios (SSP1-2.6 and SSP2-4.5), and a plausible worst-case climate scenario (SSP5-8.5). We assess how present day flood hazard and exposure differs across the island typologies, and how these are projected to change under the different climate change scenarios. We also compare population exposure with vulnerability metrics to explore how population exposure to flooding and vulnerability interact. The results of this analysis aim to improve understanding regarding the range of plausible estimates of current and future population exposure to flooding in Small Island Developing States. These results will help inform adaptation to more extreme flood risk in Small Island Developing States under current and future climate change.

Extreme precipitation is projected to intensify and occur more frequently under climate change. However, the effect of global warming on the spatial and temporal structure of extreme rainfall events at the local scale is uncertain. In the UK, the current method for estimating changes in flood hazard under climate change involves applying a simple multiplicative uplift to spatially uniform catchment rainfall. This approach neglects spatio-temporal characteristics of rainfall, which are known to be important for flood hazards. The UCKP Local Convection Permitting Model (CPM) has for the first time provided the capacity to assess these characteristics of rainfall at the local scale. Here, we use an ensemble of 2.2km hourly convection-permitting transient projections from UKCP Local to identify changes in the spatial and temporal characteristics of precipitation extremes over 100-years (1981-2080) across the UK. The analysis uses an ‘event-based’ approach, exploring seasonal changes in the peak intensity, total rainfall, and duration of events, but also changes in the spatial extent and temporal clustering of events through time. We identify ~13000 extreme rainfall events across the UK over the 100-year period. Event peaks are identified using a seasonal and time-varying threshold (99th percentile) on hourly rainfall rates, and event start and stop times are extracted using a lower threshold (20th percentile). We identify seasonal differences in how spatial extents of rainfall extremes will change, with winter and spring events growing, but summer and autumn events reducing in areal coverage. We also identify changes in the sub-seasonal timing of rainfall extremes, with events becoming more clustered, particularly during the winter months. Understanding changes in the spatial and temporal characteristics of rainfall events is critical as they may compound with increases in rainfall intensity, exacerbating the impacts of flooding.

Insurers and risk managers for critical infrastructure such as transport of power networks typically do not account for flooding and extreme winds happening at the same time in their quantitative risk assessments. We explore this potentially critical underestimation of risk from these co-occurring hazards through studying events using the regional 12 km resolution UK Climate Projections for a 1981-1999 baseline and projections of 2061-2079 (RCP8.5). We create a new wintertime (Oct-Mar) set of 3,427 wind events to match an existing set of fluvial flow extremes and design innovative multi-event episodes (Δt of 1-180 days long) that reflect how periods of adverse weather affect society (e.g. through damage). We show that the probability of co-occurring wind-flow episodes in Great Britain (GB) is underestimated 2-4 times if events are assumed independent. Significantly, this underestimation is greater both as severity increases and episode length reduces, highlighting the importance of considering risk from closely consecutive (Δt 3 days) and the most severe storms. In the future (2061-2079), joint wind-flow extremes are twice as likely as during 1981-1999. Statistical modelling demonstrates that changes may significantly exceed thermodynamic expectations of higher river flows in a wetter future climate. The largest co-occurrence increases happen in mid-winter (DJF) with changes in the north Atlantic jet stream an important driver; we find the jet is strengthened and squeezed into a southward-shifted latitude window (45-50°N) giving typical future conditions that match instances of high flows and joint extremes impacting GB today. This strongly implies that the driving large-scale driving conditions (e.g. jet stream state) for a multi-impact ‘perfect storm’ will vary by country; understanding regional drivers of weather hazards over climate timescales is vital to inform risk mitigation and planning (e.g. diversification, mutual aid across Europe).