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

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 computationally 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 in urban hydrology. 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 by means of 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 (due to input and structural errors), and measurement errors. In our case study, the best performing bias description was 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 directly reduce the causes of bias. More experience with the application of this framework will lead to a greater prior knowledge for a bias formulation. Furthermore, propagation of input uncertainty and improvement to the model structure are expected to reduce the bias

Rainfall input uncertainty is one of the major concerns in hydrological modeling. Unfortunately, during inference, input errors are usually neglected, which can lead to biased parameters and implausible predictions. Rainfall multipliers can reduce this problem but still fail when the observed input (precipitation) has a different temporal pattern from the true one or if the true nonzero input is not detected. In this study, we propose an improved input error model which is able to overcome these challenges and to assess and reduce input uncertainty. We formulate the average precipitation over the watershed as a stochastic input process (SIP) and, together with a model of the hydrosystem, include it in the likelihood function. During statistical inference, we use ''noisy'' input (rainfall) and output (runoff) data to learn about the ''true'' rainfall, model parameters, and runoff. We test the methodology with the rainfall-discharge dynamics of a small urban catchment. To assess its advantages, we compare SIP with simpler methods of describing uncertainty within statistical inference: (i) standard least squares (LS), (ii) bias description (BD), and (iii) rainfall multipliers (RM). We also compare two scenarios: accurate versus inaccurate forcing data. Results show that when inferring the input with SIP and using inaccurate forcing data, the whole-catchment precipitation can still be realistically estimated and thus physical parameters can be ''protected'' from the corrupting impact of input errors. While correcting the output rather than the input, BD inferred similarly unbiased parameters. This is not the case with LS and RM. During validation, SIP also delivers realistic uncertainty intervals for both rainfall and runoff. Thus, the technique presented is a significant step toward better quantifying input uncertainty in hydrological inference. As a next step, SIP will have to be combined with a technique addressing model structure uncertainty.

Anthropogenic eutrophication has led to the increased occurrence of hypoxia in inland and coastal waters around the globe. While low dissolved oxygen conditions are known to be driven primarily by nutrient loading and water column stratification, the relative importance of these factors and their associated time scales are not well understood. Here, we explore these questions for Lake Erie, a large temperate lake that experiences widespread annual summertime hypoxia. We leverage a three-decade data set of summertime hypoxic extent (1985-2015) and examine the role of seasonal and long-term nutrient loading, as well as hydrometeorological conditions. We find that a linear combination of decadal total phosphorus loading from tributaries and springtime air temperatures explains a high proportion of the interannual variability in average summertime hypoxic extent (R = 0.71). This result suggests that the lake responds primarily to long-term variations in phosphorus inputs, rather than springtime or annual loading as previously assumed, which is consistent with internal phosphorus loading from lake sediments likely being an important contributing mechanism. This result also demonstrates that springtime temperatures have a substantial impact on summertime hypoxia, likely by impacting the timing of onset of thermal stratification. These findings imply that management strategies based on reducing tributary phosphorus loading would take several years to reap full benefits, and that projected future increases in temperatures are likely to exacerbate hypoxia in Lake Erie and other temperate lakes.

The hypoxic zone in the northern Gulf of Mexico is among the most dramatic examples of impairments to aquatic ecosystems. Despite having attracted substantial attention, management of this environmental crisis remains challenging, partially due to limited monitoring to support model development and long‐term assessments. Here, we leverage new geostatistical estimates of hypoxia derived from nearly 150 monitoring cruises and a process‐based model to improve characterization of controlling mechanisms, historic trends, and future responses of hypoxia while rigorously quantifying uncertainty in a Bayesian framework. We find that November–March nitrogen loads are important controls of sediment oxygen demand, which appears to be the major oxygen sink. In comparison, only ~23% of oxygen in the near‐bottom region appears to be consumed by net water column respiration, which is driven by spring and summer loads. Hypoxia typically exceeds 15,600 km2 in June, peaks in July, and declines below 10,000 km2 in September. In contrast to some previous Gulf hindcasting studies, our simulations demonstrate that hypoxia was both severe and worsening prior to 1985, and has remained relatively stable since that time. Scenario analysis shows that halving nutrient loadings will reduce hypoxia by 37% with respect to 13,900 km2 (1985–2016 median), while a +2°C change in water temperature will cause a 26% hypoxic area increase due to enhanced sediment respiration and reduced oxygen solubility. These new results highlight the challenges of achieving hypoxia reduction targets, particularly under warming conditions, and should be considered in ecosystem management.

Keywords:Urban hydrology Modeling Sewer catchment Case study s u m m a r y A parsimonious model of flow capable of simulating flow in natural/engineered catchments and at WWTP (Wastewater Treatment Plant) inlets was developed. The model considers three interacting, dynamic storages that account for transfer of water within the system. One storage describes the ''flashy'' response of impervious surfaces, another pervious areas and finally one storage describes subsurface flow. The sewerage pipe network is considered as an impervious surface and is thus included in the impervious surface storage. In addition, the model assumes that water discharged from several CSOs (combined sewer overflows) can be accounted for using a single, characteristic CSO. The model was calibrated on, and validated for, the Vidy Bay WWTP, which receives effluent from Lausanne, Switzerland (population about 200,000), as well as for an overlapping urban river basin. The results indicate that a relatively simple approach is suitable for predicting the responses of interacting engineered and natural hydrosystems.

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