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Lentic waters integrate atmosphere and catchment processes, and thus ultimately capture climate signals. However, studies of climate warming effects on lentic waters usually do not sufficiently account for a change in heat flux from the catchment through altered inflow temperature and discharge under climate change. This is particularly relevant for reservoirs, which are highly impacted by catchment hydrology and may be affected by upstream reservoirs or pre‐dams. This study explicitly quantified how the catchment and pre‐dams modify the thermal response of Rappbode Reservoir, Germany's largest drinking water reservoir system, to climate change. We established a catchment‐lake modeling chain in the main reservoir and its two pre‐dams utilizing the lake model GOTM, the catchment model mHM, and the stream temperature model Air2stream, forced by an ensemble of climate projections under RCP2.6 and 8.5 warming scenarios. Results exhibited a warming of 0.27/0.15°C decade−1 for the surface/bottom temperatures of the main reservoir, with approximately 8%/24% of this warming attributed to the catchment warming, respectively. The catchment warming amplified the deep water warming more than at the surface, contrary to the atmospheric warming effect, and advanced stratification by about 1 week, while having a minor impact on stratification intensity. On the other hand, pre‐dams reduced the inflow temperature into the main reservoir in spring, and consequently lowered the hypolimnetic temperature and postponed stratification onset. This shielded the main reservoir from climate warming, although overall the contribution of pre‐dams was minimal. Altogether, our study highlights the importance of catchment alterations and seasonality when projecting reservoir warming, and provides insights into catchment‐reservoir coupling under climate change. Plain Language Summary Climate change is altering the temperature and mixing characteristics of lakes and reservoirs, with potentially detrimental effects on water quality. Water temperature and mixing are affected by the atmosphere, but also by the amount and temperature of the inflowing stream water. So far, most climate change studies have not fully accounted for the effect of streams on lakes and reservoirs. Thus, we linked different computer models to estimate future warming of a large drinking water reservoir in Germany, and separate the contribution of the atmosphere and inflowing streams. We found that warming of the reservoir water was 24% stronger when considering streams, and even more specifically for the deep water. This means that studies only accounting for atmospheric warming are underestimating climate impacts on reservoirs, including the negative impacts on oxygen levels. Small upstream dams, known as pre‐dams may also influence water temperature, potentially dampening the effect of inflow warming, although with weak effects because of their small size. Our results suggest that neglecting inflowing streams underestimates both the climate warming impacts on reservoirs and also the sensitivity of deep water, further biasing projections for ecological variables. Key Points Catchment heat flux amplifies reservoir bottom/surface warming by up to 24%/8% and advances stratification onset by ca. 1 week Contrary to the atmospheric warming effect, inflow warming affects reservoir deep water more than surface water Inflow temperature and seasonality need more attention when studying reservoir responses to climate change

A growing literature indicates that untreated wastewater from leaky sewers stands among major sources of pollution to water resources of urban systems. Despite that, the quantification and allocation of sewer exfiltration are often restricted to major pipe areas where inspection data are available. In large-scale urban models, the emission from sewer exfiltration is either neglected (particularly from private sewers) or represented by simplified fixed values, and as such its contribution to the overall urban emission remains questionable. This study proposes an extended model framework which incorporates sewer exfiltration pathway in the catchment model for a better justified pollution control and management of urban systems at a nationwide scale. Nutrient emission from urban areas is quantified by means of the Modelling of Nutrient Emissions in River Systems (MONERIS) model. Exfiltration is estimated for public and private sewers of different age groups in Germany using the verified methods at local to city scales, upscaling techniques, and expert knowledge. Results of this study suggest that the average exfiltration rate is likely to be less than 0.01 L/s per km, corresponding to approximately 1 mm/m/year of wastewater discharge to groundwater. Considering the source and age factors, the highest rate of exfiltration is defined in regions with significant proportions of public sewers older than 40 years. In regions where public sewers are mostly built after 1981, the leakage from private sewers can be up two times higher than such from public sewers. Overall, sewer exfiltration accounts for 9.8% and 17.2% of nitrate and phosphate loads from urban systems emitted to the environment, which increases to 11.2% and 19.5% in the case of no remediation scenario of projected defective sewer increases due to ageing effects. Our results provide a first harmonized quantification of potential leakage losses in urban wastewater systems at the nationwide scale and reveal the importance of rehabilitation planning of ageing sewer pipes in public and private sewer systems. The proposed model framework, which incorporates important factors for urban sewer managers, will allow further targeting the important data need for validating the approach at the regional and local scales in order to support better strategies for the long-term nutrient pollution control of large urban wastewater systems.

A common land and water management task is to determine where and by how much source loadings need to change to meet water quality limits in receiving environments. This paper addresses the problem of quantifying changes in loading when limits are specified in many locations in a large and spatially heterogeneous catchment, accounting for cumulative downstream impacts. Current approaches to this problem tend to use either scenario analysis or optimization, which suffer from difficulties of generating scenarios that meet the limits, or high complexity of optimization approaches. In contrast, we present a novel method in which simple catchment models, load limits, upstream/downstream spatial relationships and spatial allocation rules are combined to arrive at source load changes. The process iteratively establishes the critical location (river segment or lake) where the limits are most constraining, and then adjusts sources upstream of the critical location to meet the limit at that location. The method is demonstrated with application to New Zealand (268,000 km2) for nutrients and the microbial indicator E. coli, which was conducted to support policy development regarding water quality limits. The model provided useful insights, such as a source load excess (the need for source load reduction) even after mitigation measures are introduced in order to comply with E. coli limits. On the other hand, there was headroom (ability to increase source loading) for nutrients. The method enables assessment of the necessary source load reductions to achieve water quality limits over broad areas such as large catchments or whole regions.

Recent advancements in catchment hydrology (such as understanding catchment similarity, accessing new data sources, and refining methods for parameter constraints) make it possible to apply catchment models for ungauged basins over large domains. Here we present a cutting-edge case study applying catchment-modelling techniques with evaluation against river flow at the global scale for the first time. The modelling procedure was challenging but doable, and even the first model version showed better performance than traditional gridded global models of river flow. We used the open-source code of the HYPE model and applied it for >130 000 catchments (with an average resolution of 1000 km2), delineated to cover the Earth's landmass (except Antarctica). The catchments were characterized using 20 open databases on physiographical variables, to account for spatial and temporal variability of the global freshwater resources, based on exchange with the atmosphere (e.g. precipitation and evapotranspiration) and related budgets in all compartments of the land (e.g. soil, rivers, lakes, glaciers, and floodplains), including water stocks, residence times, and the pathways between various compartments. Global parameter values were estimated using a stepwise approach for groups of parameters regulating specific processes and catchment characteristics in representative gauged catchments. Daily and monthly time series (>10 years) from 5338 gauges of river flow across the globe were used for model evaluation (half for calibration and half for independent validation), resulting in a median monthly KGE of 0.4. However, the World-Wide HYPE (WWH) model shows large variation in model performance, both between geographical domains and between various flow signatures. The model performs best (KGE >0.6) in the eastern USA, Europe, South-East Asia, and Japan, as well as in parts of Russia, Canada, and South America. The model shows overall good potential to capture flow signatures of monthly high flows, spatial variability of high flows, duration of low flows, and constancy of daily flow. Nevertheless, there remains large potential for model improvements, and we suggest both redoing the parameter estimation and reconsidering parts of the model structure for the next WWH version. This first model version clearly indicates challenges in large-scale modelling, usefulness of open data, and current gaps in process understanding. However, we also found that catchment modelling techniques can contribute to advance global hydrological predictions. Setting up a global catchment model has to be a long-term commitment as it demands many iterations; this paper shows a first version, which will be subjected to continuous model refinements in the future. WWH is currently shared with regional/local modellers to appreciate local knowledge.

Hydrological catchment models are important tools that are commonly used as the basis for water resource management planning. In the 1960s and 1970s, the development of several relatively simple models to simulate catchment runoff started, and a number of so-called conceptual (or bucket-type) models were suggested. In these models, the complex and heterogeneous hydrological processes in a catchment are represented by a limited number of storage elements and the fluxes between them. While computer limitations were a major motivation for such relatively simple models in the early days, some of these models are still used frequently despite the vast increase in computational opportunities. The HBV (Hydrologiska Byråns Vattenbalansavdelning) model, which was first applied about 50 years ago in Sweden, is a typical example of a conceptual catchment model and has gained large popularity since its inception. During several model intercomparisons, the HBV model performed well despite (or because of) its relatively simple model structure. Here, the history of model development, from thoughtful considerations of different model structures to modelling studies using hundreds of catchments and cloud computing facilities, is described. Furthermore, the wide range of model applications is discussed. The aim is to provide an understanding of the background of model development and a basis for addressing the balance between model complexity and data availability that will also face hydrologists in the coming decades.

The concept of time of concentration in the analysis of catchment responses dates back over 150 years to the introduction of the rational method. Since then it has been used in a variety of ways in the formulation of both unit hydrograph and distributed catchment models. It is normally discussed in terms of the velocity of flow of a water particle from the furthest part of a catchment to the outlet. This is also the basis for the definition in the International Glossary of Hydrology. While conceptually simple, this definition is, however, wrong when applied to catchment responses where, in terms of how surface and subsurface flows produce hydrographs, it is more correct to discuss and teach the concept based on celerities and time to equilibrium. While this has been recognized since the 1960s, some recent papers and texts remain confused over the definition and use of the time of concentration concept. The paper sets out the history of its use and clarifies its relationship with time to equilibrium but suggests that both terms are not really useful in explaining hydrological responses. An Appendix is included that quantifies the differences between the definitions of response times for subsurface and surface flows under simple assumptions that might be useful in teaching.

Operational management and prediction of water quantity and quality often requires a spatially meaningful simulation of environmental flows and storages at the catchment scale. In this study, the performance of a fully distributed conceptual hydrologic model was evaluated based on the HBV (Hydrologiska Byråns Vattenbalansavdelning) and TACD (Tracer Aided Catchment model – Distributed) model concept in the meso-scale Fyrisån catchment in the Central Swedish lowlands. For a more spatially explicit representation of runoff generation processes of small landscape elements such as wetlands, a new sub-grid parameterization scheme was implemented in the model. In addition, a simple flow distribution and lake retention routine was introduced to better conceptualize the flow routing. During intensive model evaluation and comparison the model underwent conventional split-sample and proxy-basin tests. In this process, shortcomings of the model in the transferability of parameter sets and in the spatial representation of runoff generating processes were found. It was also demonstrated how a detailed comparison with a lumped benchmark model and the additional use of synoptic stream flow measurements allowed further insights into the model performance. It could be concluded that such a thorough model assessment can help to detect shortcomings in the spatial representation of the model and help facilitate model development.

Standard epidemiological models for COVID-19 employ variants of compartment (SIR or susceptible–infectious–recovered) models at local scales, implicitly assuming spatially uniform local mixing. Here, we examine the effect of employing more geographically detailed diffusion models based on known spatial features of interpersonal networks, most particularly the presence of a long-tailed but monotone decline in the probability of interaction with distance, on disease diffusion. Based on simulations of unrestricted COVID-19 diffusion in 19 US cities, we conclude that heterogeneity in population distribution can have large impacts on local pandemic timing and severity, even when aggregate behavior at larger scales mirrors a classic SIR-like pattern. Impacts observed include severe local outbreaks with long lag time relative to the aggregate infection curve, and the presence of numerous areas whose disease trajectories correlate poorly with those of neighboring areas. A simple catchment model for hospital demand illustrates potential implications for health care utilization, with substantial disparities in the timing and extremity of impacts even without distancing interventions. Likewise, analysis of social exposure to others who are morbid or deceased shows considerable variation in how the epidemic can appear to individuals on the ground, potentially affecting risk assessment and compliance with mitigation measures. These results demonstrate the potential for spatial network structure to generate highly nonuniform diffusion behavior even at the scale of cities, and suggest the importance of incorporating such structure when designing models to inform health care planning, predict community outcomes, or identify potential disparities.

Flowing stream networks dynamically extend and retract, both seasonally and in response to precipitation events. These network dynamics can dramatically alter the drainage density and thus the length of subsurface flow pathways to flowing streams. We mapped flowing stream networks in a small Swiss headwater catchment during different wetness conditions and estimated their effects on the distribution of travel times to the catchment outlet. For each point in the catchment, we determined the subsurface transport distance to the flowing stream based on the surface topography and determined the surface transport distance along the flowing stream to the outlet. We combined the distributions of these travel distances with assumed surface and subsurface flow velocities to estimate the distribution of travel times to the outlet. These calculations show that the extension and retraction of the stream network can substantially change the mean travel time and the shape of the travel time distribution. During wet conditions with a fully extended flowing stream network, the travel time distribution was strongly skewed to short travel times, but as the network retracted during dry conditions, the distribution of the travel times became more uniform. Stream network dynamics are widely ignored in catchment models, but our results show that they need to be taken into account when modeling solute transport and interpreting travel time distributions.

Decades of hydrograph separation studies have estimated the proportions of recent precipitation in streamflow using end-member mixing of chemical or isotopic tracers. Here I propose an ensemble approach to hydrograph separation that uses regressions between tracer fluctuations in precipitation and discharge to estimate the average fraction of new water (e.g., same-day or same-week precipitation) in streamflow across an ensemble of time steps. The points comprising this ensemble can be selected to isolate conditions of particular interest, making it possible to study how the new water fraction varies as a function of catchment and storm characteristics. Even when new water fractions are highly variable over time, one can show mathematically (and confirm with benchmark tests) that ensemble hydrograph separation will accurately estimate their average. Because ensemble hydrograph separation is based on correlations between tracer fluctuations rather than on tracer mass balances, it does not require that the end-member signatures are constant over time, or that all the end-members are sampled or even known, and it is relatively unaffected by evaporative isotopic fractionation. Ensemble hydrograph separation can also be extended to a multiple regression that estimates the average (or “marginal”) transit time distribution (TTD) directly from observational data. This approach can estimate both “backward” transit time distributions (the fraction of streamflow that originated as rainfall at different lag times) and “forward” transit time distributions (the fraction of rainfall that will become future streamflow at different lag times), with and without volume-weighting, up to a user-determined maximum time lag. The approach makes no assumption about the shapes of the transit time distributions, nor does it assume that they are time-invariant, and it does not require continuous time series of tracer measurements. Benchmark tests with a nonlinear, nonstationary catchment model confirm that ensemble hydrograph separation reliably quantifies both new water fractions and transit time distributions across widely varying catchment behaviors, using either daily or weekly tracer concentrations as input. Numerical experiments with the benchmark model also illustrate how ensemble hydrograph separation can be used to quantify the effects of rainfall intensity, flow regime, and antecedent wetness on new water fractions and transit time distributions.