Deep learning methods have frequently outperformed conceptual hydrologic models in rainfall-runoff modelling. Attempts of investigating such deep learning models internally are being made, but the traceability of model states and processes and their interrelations to model input and output is not yet fully understood. Direct interpretability of mechanistic processes has always been considered an asset of conceptual models that helps to gain system understanding aside of predictability. We introduce hydrologic neural ordinary differential equation (ODE) models that perform as well as state-of-the-art deep learning methods in stream flow prediction while maintaining the ease of interpretability of conceptual hydrologic models. In neural ODEs, internal processes that are represented in differential equations, are substituted by neural networks. Therefore, neural ODE models enable the fusion of deep learning with mechanistic modelling. We demonstrate the basin-specific predictive performance for 569 catchments of the continental United States. For exemplary basins, we analyse the dynamics of states and processes learned by the model-internal neural networks. Finally, we discuss the potential of neural ODE models in hydrology.

Wastewater-based epidemiology (WBE) has been shown to coincide with, or anticipate, confirmed COVID-19 case numbers. During periods with high test positivity rates, however, case numbers may be underreported, whereas wastewater does not suffer from this limitation. Here we investigated how the dynamics of new COVID-19 infections estimated based on wastewater monitoring or confirmed cases compare to true COVID-19 incidence dynamics. We focused on the first pandemic wave in Switzerland (February to April, 2020), when test positivity ranged up to 26%. SARS-CoV-2 RNA loads were determined 2–4 times per week in three Swiss wastewater treatment plants (Lugano, Lausanne and Zurich). Wastewater and case data were combined with a shedding load distribution and an infection-to-case confirmation delay distribution, respectively, to estimate infection incidence dynamics. Finally, the estimates were compared to reference incidence dynamics determined by a validated compartmental model. Incidence dynamics estimated based on wastewater data were found to better track the timing and shape of the reference infection peak compared to estimates based on confirmed cases. In contrast, case confirmations provided a better estimate of the subsequent decline in infections. Under a regime of high-test positivity rates, WBE thus provides critical information that is complementary to clinical data to monitor the pandemic trajectory.

The exposure of ecologically critical invertebrate species to biologically active pharmaceuticals poses a serious risk to the aquatic ecosystem. Yet, the fate and toxic effects of pharmaceuticals on these nontarget aquatic invertebrates and the underlying mechanisms are poorly studied. Herein, we investigated the toxicokinetic (TK) processes (i.e., uptake, biotransformation, and elimination) of the pharmaceutical diclofenac and its biotransformation in the freshwater invertebrate Hyalella azteca. We further employed mass spectrometry-based metabolomics to assess the toxic effects of diclofenac on the metabolic functions of H. azteca exposed to environmentally relevant concentrations (10 and 100 μg/L). The TK results showed a quick uptake of diclofenac by H. azteca (maximum internal concentration of 1.9 μmol/kg) and rapid formation of the conjugate diclofenac taurine (maximum internal concentration of 80.6 μmol/kg), indicating over 40 times higher accumulation of diclofenac taurine than that of diclofenac in H. azteca. Depuration kinetics demonstrated that the elimination of diclofenac taurine was 64 times slower than diclofenac in H. azteca. Metabolomics results suggested that diclofenac inhibited prostaglandin synthesis and affected the carnitine shuttle pathway at environmentally relevant concentrations. These findings shed light on the significance of the TK process of diclofenac, especially the formation of diclofenac taurine, as well as the sublethal effects of diclofenac on the bulk metabolome of H. azteca. Combining the TK processes and metabolomics provides complementary insights and thus a better mechanistic understanding of the effects of diclofenac in aquatic invertebrates.

Statistical species distribution models (SDMs) are widely used to quantify how taxa respond to environmental conditions and to predict their distribution. However, the application of SDMs to freshwater fish taxa is complicated by the active dispersal of fish taxa through river networks, and the species- and habitat-dependent observation process (i.e., the sampling method and effort) required to accurately sample their distributions. Many studies have applied presence-absence models (PAMs) to fish taxa, while more recent studies have proposed zero-inflated models (ZIMs) to account for count observations with many zeroes. However, relatively few studies have incorporated the observation process into the model structure, which would facilitate the combination of data from various monitoring programs that differ in their observation process. In this study, we use conceptual models to identify potentially dominant natural and anthropogenic environmental conditions with a direct, mechanistic effect on the distributions of freshwater fish taxa in Switzerland, a region with a large range of environmental conditions, from alpine streams that are mainly affected by hydromorphological alterations to lowland streams in densely populated areas with intensive agricultural land use. Moreover, numerous barriers impede fish migration along the entire river network. Using combined data from two fish monitoring programs in Switzerland, we applied an exhaustive cross-validation procedure to select a set of environmental variables with the highest (out-of-sample) predictive performance for the PAM and ZIM for fish density (individuals/m²) of the seven most prevalent fish taxa (Salmo spp., Cottus spp., Squalius spp., Barbatula spp., Barbus spp., Phoxinus spp., Gobio spp.). We used these variables to develop a PAM and ZIM for each taxon that accounts for differences in sampling methods and sampling effort. We quantified the quality of fit during calibration using all samples and predictive performance during 5-fold cross-validation of each model.
Results show that stream temperature and stream morphology within the accessible habitat commonly appear among the best predictive presence-absence models for multiple taxa. Spatial variables that account for migration barriers and quantify morphological conditions within the accessible habitat were selected for 6 out of 7 taxa. The selected PAMs performed well for all taxa with an intermediate prevalence (10–40%), with an explanatory power () of between 0.32 - 0.37 during calibration using all samples and only minor decreases in explanatory power during cross-validation (= 0.34 – 0.44). As expected, the PAM for the highly prevalent Salmo spp. (91%) failed to predict the few absence data points. By contrast, the ZIM model performed best for Salmo spp., with a standardized likelihood ratio of 1.56. For all other taxa besides Barbus spp. the ZIM models also had likelihood ratios above one, indicating a better predictive performance than the null model. We hope this study stimulates the development and application of fish species distribution models based on prior knowledge of causally linked environmental variables and incorporating observation errors to improve their predictive performance. This can facilitate learning from biomonitoring data to support management.

Black soldier fly larvae treatment is an emerging technology for the conversion of biowaste into potentially more sustainable and marketable high-value products, according to circular economy principles. Unknown or variable performance for different biowastes is currently one challenge that prohibits the global technology up-scaling. This study describes simulated midgut digestion for black soldier fly larvae to estimate biowaste conversion performance. Before simulation, the unknown biowaste residence time in the three midgut regions was determined on three diets varying in protein and non-fiber carbohydrate content. For the static in vitro model, diet residence times of 15 min, 45 min, and 90 min were used for the anterior, middle, and posterior midgut region, respectively. The model was validated by comparing the ranking of diets based on in vitro digestion products to the ranking found in in vivo feeding experiments. Four artificial diets and five biowastes were digested using the model, and diet digestibility and supernatant nutrient contents were determined. This approach was able to distinguish broadly the worst and best performing rearing diets. However, for some of the diets, the performance estimated based on in vitro results did not match with the results of the feeding experiments. Future studies should try to establish a stronger correlation by considering fly larvae nutrient requirements, hemicellulose digestion, and the diet/gut microbiota. In vitro digestion models could be a powerful tool for academia and industry to increase conversion performance of biowastes with black soldier fly larvae.

Ubiquitous sensing will create many opportunities and threats for urban water management, which are only poorly understood today. To identify the most relevant trends, we conducted a horizon scan regarding how ubiquitous sensing will shape the future of urban drainage and wastewater management. Our survey of the international urban water community received an active response from both the academics and the professionals from the water industry. The analysis of the responses demonstrates that emerging topics for urban water will often involve experts from different communities, including aquatic ecologists, urban water system engineers and managers, as well as information and communications technology professionals and computer scientists. Activities in topics that are identified as novel will either require (i) cross-disciplinary training, such as importing new developments from the IT sector, or (ii) research in new areas for urban water specialists, for example, to help solve open questions in aquatic ecology. These results are, therefore, a call for interdisciplinary research beyond our own discipline. They also demonstrate that the water management community is not yet prepared for the digital transformation, where we will experience a data demand, i.e. a “pull” of urban water data into external services. The results suggest that a lot remains to be done to harvest the upcoming opportunities. Horizon scanning should be repeated on a routine basis, under the umbrella of an experienced polling organization.

We present a novel stochastic model for quantifying gross solids (GS) physical disintegration under varying turbulent flow conditions and used a unique experimental setup for model calibration and validation. The stochastic deterioration model predicts faeces size evolution over time. It conceptually entails the two main processes of solid fragmentation, namely breakage and erosion. Model parameters were calibrated on synthetic faeces and validated with real human ones. A cylindrical reactor was used, where turbulent flow was forced by an array of water jets and the physical disintegration of the faeces was monitored using a high speed camera. Image analysis of breakage experiments obtained under backlight illumination allowed determination of the evolution of the solids’ size over time. The flow field in the reactor was characterised by particle image velocimetry (PIV) using tracer particles seeded into the water. We found different disintegration behaviours depending on turbulence intensity and water content of the solid. In conditions of low shear stress, dense solids hardly disintegrated. Generally, the model predictions mirrored the broad range in the solids disintegration rate imparted by the high variability in flow conditions and in solids characteristics. It is expected that, similar to our experiments, also in real sewer systems both flow conditions and solid characteristics are highly variable and the stochastic model can be tailored to capture this variability. We thus anticipate that the model can be integrated into existing sewer models predicting sewer flows and solids’ movement. From these, shear stress, flow velocities and transport of individual solids can be inferred. The integration of the present solids disintegration model may provide better predictions of hot-spots for solids accumulation and blockages in sewers.

Contaminants in sewer overflows can contribute to exceedances of environmental quality standards, thus the quantification of contaminants during rainfall events is of relevance. However, monitoring is challenged by i) high spatiotemporal variability of contaminants in events of hard-to-predict durations, and ii) a large number of remote sites, which would imply enormous efforts with traditional sampling equipment. Therefore, we evaluate the applicability of passive samplers (Empore styrene-divinylbenzene reverse phase sulfonated (SDB-RPS)) to monitor a set of 13 polar organic contaminants. We present calibration experiments at high temporal resolution to assess the rate limiting accumulation mechanisms for short events (<36 h), report parameters for typical sewer conditions and compare passive samplers with composite water samples in a field study (three locations, total 10 events). With sampling rates of 0.35–3.5 L/d for 1 h reference time, our calibration results indicate a high sensitivity of passive samplers to sample short, highly variable sewer overflows. The contaminant uptake kinetic shows a fast initial accumulation, which is not well represented with the typical first-order model. Our results indicate that mass transfer to passive samplers is either controlled by the water boundary layer and the sorbent, or by the sorbent alone. Overall, passive sampler concentration estimates are within a factor 0.4 to 3.1 in comparison to composite water samples in the field study. We conclude that passive samplers are a promising approach to monitor a large number of discharge sites although it cannot replace traditional stormwater quality sampling in some cases (e.g. exact load estimates, high temporal resolution). Passive samplers facilitate identifying and prioritizing locations that may require more detailed investigations.

The identification of appropriate sanitation systems is particularly challenging in developing urban areas where local needs are not met by conventional solutions. While structured decision-making frameworks such as Community-Led Urban Environmental Sanitation (CLUES) can help facilitate this process, they require a set of sanitation system options as input. Given the large number of possible combinations of sanitation technologies, the generation of a good set of sanitation system options is far from trivial.
This paper presents a procedure for generating a set of locally appropriate sanitation system options, which can then be used in a structured decision-making process. The systematic and partly automated procedure was designed (i) to enhance the reproducibility of option generation; (ii) to consider all types of conventional and novel technologies; (iii) to provide a set of sanitation systems that is technologically diverse; and (iv) to formally account for uncertainties linked to technology specifications and local conditions.
We applied the procedure to an emerging small town in Nepal. We assessed the appropriateness of 40 technologies and generated 17,955 appropriate system options. These were classified into 16 system templates including on-site, urine-diverting, biogas, and blackwater templates. From these, a subset of 36 most appropriate sanitation system options were selected, which included both conventional and novel options.
We performed a sensitivity analysis to evaluate the impact of different elements on the diversity and appropriateness of the set of selected sanitation system options. We found that the use of system templates is most important, followed by the use of a weighted multiplicative aggregation function to quantify local appropriateness. We also show that the optimal size of the set of selected sanitation system options is equal to or slightly greater than the number of system templates.
As novel technologies are developed and added to the already large portfolio technology options, the procedure presented in this work may become an essential tool for generating and exploring appropriate sanitation system options.

Observations of a hydrologic system response are needed to accurately model system behaviour. Nevertheless, often very few monitoring stations are operated because collecting such reference data adequately and accurately is laborious and costly. It has been recently suggested to use observations not only from dedicated flow meters but also from simpler sensors, such as level or event detectors, which are available more frequently but only provide censored information. Binary observations can be considered as extreme censoring. It is still unclear, however, how to use censored observations most effectively to learn about model parameters. To this end, we suggest a formal likelihood function that incorporates censored observations, while accounting for model structure deficits and uncertainty in input data. Using this likelihood function, the parameter inference is performed within the Bayesian framework. We demonstrate the implementation of our methodology on a case study of an urban catchment, where we estimate the parameters of a hydrodynamic rainfall-runoff model from binary observations of combined sewer overflows. Our results show, first, that censored observations make it possible to learn about model parameters, with an average decrease of 45% in parameter standard deviation from prior to posterior. Second, the inference substantially improves model predictions, providing higher Nash-Sutcliffe efficiency. Third, the gain in information largely depends on the experimental design, i.e. sensor placement. Given the advent of Internet of Things, we foresee that the plethora of censored data promised to be available can be used for parameter estimation within a formal Bayesian framework.

To estimate drug consumption more reliably, wastewater-based epidemiology would benefit from a better understanding of drug residue stability during in-sewer transport. We conducted batch experiments with real, fresh wastewater and sewer biofilms. Experimental conditions mimic small to medium-sized gravity sewers with a relevant ratio of biofilm surface area to wastewater volume (33 m² m^–3). The influences of biological, chemical, and physical processes on the transformation of 30 illicit drug and pharmaceutical residues were quantified. Rates varied among locations and over time. Three substances were not stable—that is, >20% transformation, mainly due to biological processes—at least for one type of tested biofilm for a residence time ≤2 h: amphetamine, 6-acetylcodeine, and 6-monoacetylmorphine. Cocaine, ecgonine methyl ester, norcocaine, cocaethylene, and mephedrone were mainly transformed by chemical hydrolysis and, hence, also unstable in sewers. In contrast, ketamine, norketamine, O-desmethyltramadol, diclofenac, carbamazepine, and methoxetamine were not substantially affected by in-sewer processes under all tested conditions and residence times up to 12 h. Our transformation rates include careful quantification of uncertainty and can be used to identify situations in which specific compounds are not stable. This will improve accuracy and uncertainty estimates of drug consumption when applied to the back-calculation.

This review describes and compares statistical failure models for water distribution pipes in a systematic way and from a unified perspective. The way the comparison is structured provides the information needed by scientists and practitioners to choose a suitable failure model for their specific needs.
The models are presented in a novel framework consisting of: 1) Clarification of model assumptions. The models originally formulated in different mathematical forms are all presented as failure rate. This enables to see differences and similarities across the models. Furthermore, we present a new conceptual failure rate that an optimal model would represent and to which the failure rate of each model can be compared. 2) Specification of the detailed data assumptions required for unbiased model calibration covering the structure and completeness of the data. 3) Presentation of the different types of probabilistic predictions available for each model.
Nine different models and their variations or further developments are presented in this review. For every model an overview of its applications published in scientific journals and the available software implementations is provided.
The unified view provides guidance to model selection. Furthermore, the model comparison presented herein enables to identify areas where further research is needed.

Predictions of the expected number of failures of water distribution network pipes are important to develop an optimal management strategy. A number of probabilistic pipe failure models have been proposed in the literature for this purpose. They have to be calibrated on failure records. However, common data management practices mean that replaced pipes are often absent from available data sets. This leads to a 'survival selection bias', as pipes with frequent failures are more likely to be absent from the data.
To address this problem, we propose a formal statistical approach to extend the likelihood function of a pipe failure model by a replacement model. Frequentist maximum likelihood estimation or Bayesian inference can then be applied for parameter estimation. This approach is general and is not limited to a particular failure or replacement model.
We implemented this approach with a Weibull-exponential failure model and a simple constant probability replacement model. Based on this distribution assumptions, we illustrated our concept with two examples. First, we used simulated data to show how replacement causes a 'survival selection bias' and how to successfully correct for it. A second example with real data illustrates how a model can be extended to consider covariables.