In urban rainfall-runoff, commonly applied statistical techniques for uncertainty quantification mostly ignore systematic output errors originating from simplified models and erroneous inputs. Consequently, the resulting predictive uncertainty is often unreliable. Our objective is to present two approaches which use stochastic processes to describe systematic deviations and to discuss their advantages and drawbacks for urban drainage modeling. The two methodologies are an external bias description (EBD) and an internal noise description (IND, also known as stochastic gray-box modeling). They emerge from different fields and have not yet been compared in environmental modeling. To compare the two approaches, we develop a unifying terminology, evaluate them theoretically, and apply them to conceptual rainfall-runoff modeling in the same drainage system. Our results show that both approaches can provide probabilistic predictions of wastewater discharge in a similarly reliable way, both for periods ranging from a few hours up to more than 1 week ahead of time. The EBD produces more accurate predictions on long horizons but relies on computationally heavy MCMC routines for parameter inferences. These properties make it more suitable for off-line applications. The IND can help in diagnosing the causes of output errors and is computationally inexpensive. It produces best results on short forecast horizons that are typical for online applications.

Commercial microwave links (MWLs) were suggested about a decade ago as a new source for quantitative precipitation estimates (QPEs). Meanwhile, the theory is well understood and rainfall monitoring with MWLs is on its way to being a mature technology, with several well-documented case studies, which investigate QPEs from multiple MWLs on the mesoscale. However, the potential of MWLs to observe microscale rainfall variability, which is important for urban hydrology, has not been investigated yet. In this paper, we assess the potential of MWLs to capture the spatio-temporal rainfall dynamics over small catchments of a few square kilometres. Specifically, we investigate the influence of different MWL topologies on areal rainfall estimation, which is important for experimental design or to a priori check the feasibility of using MWLs. In a dedicated case study in Prague, Czech Republic, we collected a unique dataset of 14 MWL signals with a temporal resolution of a few seconds and compared the QPEs from the MWLs to reference rainfall from multiple rain gauges. Our results show that, although QPEs from most MWLs are probably positively biased, they capture spatio-temporal rainfall variability on the microscale very well. Thus, they have great potential to improve runoff predictions. This is especially beneficial for heavy rainfall, which is usually decisive for urban drainage design.

The concentration of total suspended solids (TSS) in surface waters is a commonly used indicator of water quality impairments. Its accurate prediction remains, however, problematic because: i) TSS build-up, erosion, and wash-off are not easily identifiable; ii) calibrating a TSS model requires observations of sediment loads, which are rare, and streamflow observations to calculate concentrations; iii) predicted TSS usually deviate systematically from observations, an effect which is commonly neglected. Ignoring systematic errors during calibration can lead to overconfident (i.e. unreliable) uncertainty estimates during predictions. In this paper, we therefore investigate whether a statistical description of systematic model errors makes it possible to generate reliable predictions for TSS. In addition, we explore how the reliability of TSS predictions increases when streamflow data are additionally used in model calibration. A key aspect of our study is that we use a Bayesian multi-output calibration and a novel autoregressive error model, which describes the model predictive error as a sum of independent random noise and autocorrelated bias. Our results show that using a statistical description of model bias provides more reliable uncertainty estimates of TSS than before and including streamflow data into calibration makes TSS predictions more precise. For a case study of a small ungauged catchment, this improvement was as much as 15%. Our approach can be easily implemented for other water quality variables which are dependent on streamflow.

Oversimplified models and erroneous inputs play a significant role in impairing environmental predictions. To assess the contribution of these errors to model uncertainties is still challenging. Our objective is to understand the effect of model complexity on systematic modeling errors. Our method consists of formulating alternative models with increasing detail and flexibility and describing their systematic deviations by an autoregressive bias process. We test the approach in an urban catchment with five drainage models. Our results show that a single bias description produces reliable predictions for all models. The bias decreases with increasing model complexity and then stabilizes. The bias decline can be associated with reduced structural deficits, while the remaining bias is probably dominated by input errors. Combining a bias description with a multimodel comparison is an effective way to assess the influence of structural and rainfall errors on flow forecasts.

Successful management and control of wastewater and storm water systems requires accurate sewer flow measurements. Unfortunately, the harsh sewer environment and insufficient flow meter calibration often lead to inaccurate and biased data. In this paper, we improve sewer flow monitoring by creating redundant information on sewer velocity from natural wastewater tracers. Continuous water quality measurements upstream and downstream of a sewer section are used to estimate the travel time based on i) cross-correlation (XCORR) and ii) dynamic time warping (DTW). DTW is a modern data mining technique that warps two measured time series non-linearly in the time domain so that the dissimilarity between the two is minimized. It has not been applied in this context before. From numerical experiments we can show that DTW outperforms XCORR, because it provides more accurate velocity estimates, with an error of about 7% under typical conditions, at a higher temporal resolution. In addition, we can show that pre-processing of the data is important and that tracer reaction in the sewer reach is critical. As dispersion is generally small, the distance between the sensors is less influential if it is known precisely. Considering these findings, we tested the methods on a real-world sewer to check the performance of two different sewer flow meters based on temperature measurements. Here, we were able to detect that one of two flow meters was not performing satisfactorily under a variety of flow conditions. Although theoretical analyses show that XCORR and DTW velocity estimates contain systematic errors due to dispersion and reaction processes, these are usually small and do not limit the applicability of the approach.

Hydrodynamic models are useful tools for urban water management. Unfortunately, it is still challenging to obtain accurate results and plausible uncertainty estimates when using these models. In particular, with the currently applied statistical techniques, flow predictions are usually overconfident and biased. In this study, we present a flexible and relatively efficient methodology (i) to obtain more reliable hydrological simulations in terms of coverage of validation data by the uncertainty bands and (ii) to separate prediction uncertainty into its components. Our approach acknowledges that urban drainage predictions are biased. This is mostly due to input errors and structural deficits of the model. We address this issue by describing model bias in a Bayesian framework. The bias becomes an autoregressive term additional to white measurement noise, the only error type accounted for in traditional uncertainty analysis. To allow for bigger discrepancies during wet weather, we make the variance of bias dependent on the input (rainfall) or/and output (runoff) of the system. Specifically, we present a structured approach to select, among five variants, the optimal bias description for a given urban or natural case study. We tested the methodology in a small monitored stormwater system described with a parsimonious model. Our results clearly show that flow simulations are much more reliable when bias is accounted for than when it is neglected. Furthermore, our probabilistic predictions can discriminate between three uncertainty contributions: parametric uncertainty, bias, and measurement errors. In our case study, the best performing bias description is the output-dependent bias using a log-sinh transformation of data and model results. The limitations of the framework presented are some ambiguity due to the subjective choice of priors for bias parameters and its inability to address the causes of model discrepancies. Further research should focus on quantifying and reducing the causes of bias by improving the model structure and propagating input uncertainty.

Data from a new experimental setup deployed in Dübendorf (Switzerland) are used to quantify and model the magnitude and dynamics of the wet-antenna attenuation (WAA) affecting a 1.85-km commercial microwave link at 38 GHz. The results show that the WAA exhibits the following properties: 1) It is bounded by a maximum value of about 2.3 dB; 2) it increases exponentially toward 2.3 dB during the first 5-20 min of rainfall; and 3) it decreases exponentially as soon as the rain stops. A new dynamic WAA model that reproduces these three features and can be calibrated using solely link measurements is proposed. Its performance is evaluated at different temporal resolutions and compared with other wet-antenna models from the literature. The results show that the dynamic model outperforms all other models and significantly reduces the uncertainty of the retrieved path-averaged rain rates.

Accurate rain rate measurements are essential for many hydrological applications. Although rain gauge remains the reference instrument for the measurement of rain rate, the strong spatial and temporal variability of rainfall makes it difficult to spot faulty rain gauges. Due to the poor spatial representativeness of the point rainfall measurements, this is particularly difficult where their density is low. Taking advantage of the high density of telecommunication microwave links in urban areas, a consistency check is proposed to identify faulty rain gauges using nearby microwave links. The methodology is tested on a data set from operational rain gauges and microwave links, in Zürich (Switzerland). The malfunctioning of rain gauges leading to errors in the occurrence of dry/rainy periods are well identified. In addition, the gross errors affecting quantitative rain gauge measurements during rainy periods, such as blocking at a constant value, random noise and systematic bias, can be detected. The proposed approach can be implemented in real time.

Traditionally, design and optimisation of urban drainage systems was mainly driven by cost efficiency, surface flood prevention, and later by emission reduction. More recent procedures explicitly include ecological conditions of the receiving water in the definition of acceptable pollutant discharges via sewer system and treatment plant outlets. An ambient Water Quality based impact Assessment (WQA) principle therefore requires an integrative system optimisation. However, a broad range of mostly national WQA protocols exist across Europe varying in structure and complexity, assessment concept, spatial and temporal scope and handling of uncertainty. This variety inherently implies a considerable risk of subjectivity in the impact assessment with highly variable outcomes. The present review identifies differences and similarities of WQA protocols in use and discusses their strengths and weaknesses through: (i) a systematic comparison of WQA protocols by selected attributes, (ii) a review of real-life cases reported in the literature and expert interviews, and (iii) an illustration of our main findings by applying selected WQA in an instructive example. The review discusses differences in structure and concept, which are mainly identified for simplistic WQA protocols. The application of selected protocols to an example case shows a wide variety of numerical results and conclusive decisions. It is found that existing protocols target different questions within the decision making process, which users should be more aware of. Generally, to make assessments more reliable, further fundamental research is required to fully understand the relationship between stressors and stream ecosystem responses which will make assessments more reliable. Technically, tools suggested in WQA protocols show severe deficiencies and an uncertainty assessment should be mandatory.

A Markov switching algorithm is introduced to classify attenuation measurements from telecommunication microwave links into dry and rainy periods. It is based on a simple state-space model and has the advantage of not relying on empirically estimated threshold parameters. The algorithm is applied to data collected using a new and original experimental set-up in the vicinity of Zürich, Switzerland. The false dry and false rain detection rates of the algorithm are evaluated and compared to 3 other algorithms from the literature. The results show that, on average, the Markov switching model outperforms the other algorithms. It is also shown that the classification performance can be further improved if redundant information from multiple channels is used.

Urbanization and the resulting land-use change strongly affect the water cycle and runoff-processes in watersheds. Unfortunately, small urban watersheds, which are most affected by urban sprawl, are mostly ungauged. This makes it intrinsically difficult to assess the consequences of urbanization. Most of all, it is unclear how to reliably assess the predictive uncertainty given the structural deficits of the applied models. In this study, we therefore investigate the uncertainty of flood predictions in ungauged urban basins from structurally uncertain rainfall-runoff models. To this end, we suggest a procedure to explicitly account for input uncertainty and model structure deficits using Bayesian statistics with a continuous-time autoregressive error model. In addition, we propose a concise procedure to derive prior parameter distributions from base data and successfully apply the methodology to an urban catchment in Warsaw, Poland. Based on our results, we are able to demonstrate that the autoregressive error model greatly helps to meet the statistical assumptions and to compute reliable prediction intervals. In our study, we found that predicted peak flows were up to 7 times higher than observations. This was reduced to 5 times with Bayesian updating, using only few discharge measurements. In addition, our analysis suggests that imprecise rainfall information and model structure deficits contribute mostly to the total prediction uncertainty. In the future, flood predictions in ungauged basins will become more important due to ongoing urbanization as well as anthropogenic and climatic changes. Thus, providing reliable measures of uncertainty is crucial to support decision making.

The analysis of sewage for urinary biomarkers of illicit drugs is a promising and complementary approach for estimating the use of these substances in the general population. For the first time, this approach was simultaneously applied in 19 European cities, making it possible to directly compare illicit drug loads in Europe over a 1-week period. An inter-laboratory comparison study was performed to evaluate the analytical performance of the participating laboratories. Raw 24-hour composite sewage samples were collected from 19 European cities during a single week in March 2011 and analyzed for the urinary biomarkers of cocaine, amphetamine, ecstasy, methamphetamine and cannabis using in-house optimized and validated analytical methods. The load of each substance used in each city was back-calculated from the measured concentrations. The data show distinct temporal and spatial patterns in drug use across Europe. Cocaine use was higher in Western and Central Europe and lower in Northern and Eastern Europe. The extrapolated total daily use of cocaine in Europe during the study period was equivalent to 356. kg/day. High per capita ecstasy loads were observed in Dutch cities, as well as in Antwerp and London. In general, cocaine and ecstasy loads were significantly elevated during the weekend compared to weekdays. Per-capita loads of methamphetamine were highest in Helsinki and Turku, Oslo and Budweis, while the per capita loads of cannabis were similar throughout Europe. This study shows that a standardized analysis for illicit drug urinary biomarkers in sewage can be applied to estimate and compare the use of these substances at local and international scales. This approach has the potential to deliver important information on drug markets (supply indicator).

Inflow and Infiltration (I/I) into sewer systems is generally unwanted, because, among other things, it decreases the performance of wastewater treatment plants and increases combined sewage overflows. As sewer rehabilitation to reduce I/I is very expensive, water managers not only need methods to accurately measure I/I, but also they need sound approaches to assess the actual performance of implemented rehabilitation measures. However, such performance assessment is rarely performed. On the one hand, it is challenging to adequately take into account the variability of influential factors, such as hydro-meteorological conditions. On the other hand, it is currently not clear how experimental data can indeed support robust evidence for reduced I/I. In this paper, we therefore statistically assess the performance of rehabilitation measures to reduce I/I. This is possible by using observations in a suitable reference catchment as a control group and assessing the significance of the observed effect by regression analysis, which is well established in other disciplines. We successfully demonstrate the usefulness of the approach in a case study, where rehabilitation reduced groundwater infiltration by 23.9%. A reduction of stormwater inflow of 35.7%, however, was not statistically significant. Investigations into the experimental design of monitoring campaigns confirmed that the variability of the data as well as the number of observations collected before the rehabilitation impact the detection limit of the effect. This implies that it is difficult to improve the data quality after the rehabilitation has been implemented. Therefore, future practical applications should consider a careful experimental design. Further developments could employ more sophisticated monitoring methods, such as stable environmental isotopes, to directly observe the individual infiltration components. In addition, water managers should develop strategies to effectively communicate statistically not significant I/I reduction ratios to decision makers.

Wastewater production, like many other engineered and environmental processes, is inherent stochastic in nature and requires the use of complex stochastic models, for example, to predict realistic patterns of down-the-drain chemicals or pharmaceuticals and personal care products. Up until now, a formal method of statistical inference has been lacking for many of those models, where explicit likelihood functions were intractable. In this Article, we investigate Approximate Bayesian Computation (ABC) methods to infer important parameters of stochastic environmental models. ABC methods have been recently suggested to perform model-based inference in a Bayesian setting when model likelihoods are analytically or computationally intractable and have not been applied to environmental systems analysis or water quality modeling before. In a case study, we investigate the performance of three different algorithms to infer the number of wastewater pulses contained in three high-resolution data series of benzotriazole and total nitrogen loads in sewers. We find that all algorithms perform well and that the uncertainty in the inferred number of corresponding wastewater pulses varies between 6% and 28%. In our case, the results are more sensitive to substance characteristics than to catchment properties. Although the application of ABC methods requires careful tuning and attention to detail, they have a great general potential to update stochastic model parameters with monitoring data and improve their predictive capabilities.

To check the effectiveness of campaigns preventing drug abuse or indicating local effects of efforts against drug trafficking, it is beneficial to know consumed amounts of substances in a high spatial and temporal resolution. The analysis of drugs of abuse in wastewater (WW) has the potential to provide this information. In this study, the reliability of WW drug consumption estimates is assessed and a novel method presented to calculate the total uncertainty in observed WW cocaine (COC) and benzoylecgonine (BE) loads. Specifically, uncertainties resulting from discharge measurements, chemical analysis and the applied sampling scheme were addressed and three approaches presented. These consist of (i) a generic model-based procedure to investigate the influence of the sampling scheme on the uncertainty of observed or expected drug loads, (ii) a comparative analysis of two analytical methods (high performance liquid chromatography–tandem mass spectrometry and gas chromatography–mass spectrometry), including an extended cross-validation by influent profiling over several days, and (iii) monitoring COC and BE concentrations in WW of the largest Swiss sewage treatment plants. In addition, the COC and BE loads observed in the sewage treatment plant of the city of Berne were used to back-calculate the COC consumption. The estimated mean daily consumed amount was 107 ± 21 g of pure COC, corresponding to 321 g of street-grade COC.

This paper gives a full review of the importance of sewer leakage, which has received increased attention throughout the last decades. Despite the intensive interdisciplinary research that has been invested, its magnitude is still unclear and a comprehensive solution for the assessment of sewer exfiltration does not seem to be at hand. However, given that mechanisms of exfiltration and the factors influencing its extent are similar all over the world, it seems possible to develop a generic leakage approach. Several methods for modelling sewer leakage are reviewed and the available measuring techniques are critically evaluated. Based on this evaluation, we suggest a unifying framework to facilitate focused model building. Specifically, we identify open research questions and propose to (i) standardise measurement results to enable better understanding, (ii) perform more long-term experiments under realistic field conditions, and (iii) assess the uncertainty of measurement and model results so that findings are not over-interpreted.

In this paper, 60 tracer experiments in 37 different sewer reaches have been analyzed for longitudinal dispersion under dry weather flow conditions. It was found that dispersion coefficients of sewers are two to three orders of magnitude smaller than those measured in rivers and do not differ much from system to system. Suitable equations were identified to predict reasonable dispersion coefficients in sewer reaches with uniform geometry and stable flow conditions, For engineering applications that require a high degree of accuracy the performance of tracer measurements is recommended.

A novel method is presented to estimate exfiltration from sewer systems using artificial tracers. The method relies upon use of an upstream indicator signal and a downstream reference signal to eliminate the dependence of exfiltration estimates on the accuracy of discharge measurement. An experimental design, a data analysis procedure, and an uncertainty assessment process are described and illustrated by a case study. In a 2-km reach of unknown condition, exfiltration was estimated at 9.9 ± 2.7%. Uncertainty in this estimate was primarily due to the use of sodium chloride (NaCl) as the tracer substance. NaCl is measured using conductivity, which is present at nonnegligible levels in wastewater, thus confounding accurate identification of tracer peaks. As estimates of exfiltration should have as low a measurement error as possible, future development of the method will concentrate on improved experimental design and tracer selection. Although the method is not intended to replace traditional CCTV inspections, it can provide additional information to urban water managers for rational rehabilitation planning.