Dario Del Giudice

Model bias and complexity - Understanding the effects of structural deficits and input errors on runoff predictions

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. We investigate how a random bias process behaves as a function of model complexity.We analyze 5 model structures to simulate a stormwater system.The reduction of systematic deviations is associated with decreasing structural deficits.In this study the remaining bias is likely to be dominated by input errors.The method provides sound probabilistic predictions in a relatively efficient way.

Modeling of facade leaching in urban catchments

Building facades are protected from microbial attack by incorporation of biocides within them. Flow over facades leaches these biocides and transports them to the urban environment. A parsimonious water quantity/quality model applicable for engineered urban watersheds was developed to compute biocide release from facades and their transport at the urban basin scale. The model couples two lumped submodels applicable at the basin scale, and a local model of biocide leaching at the facade scale. For the facade leaching, an existing model applicable at the individual wall scale was utilized. The two lumped models describe urban hydrodynamics and leachate transport. The integrated model allows prediction of biocide concentrations in urban rivers. It was applied to a 15 km2 urban hydrosystem in western Switzerland, the Vuachere river basin, to study three facade biocides (terbutryn, carbendazim, diuron). The water quality simulated by the model matched well most of the pollutographs at the outlet of the Vuachere watershed. The model was then used to estimate possible ecotoxicological impacts of facade leachates. To this end, exceedance probabilities and cumulative pollutant loads from the catchment were estimated. Results showed that the considered biocides rarely exceeded the relevant predicted no-effect concentrations for the riverine system. Despite the heterogeneities and complexity of (engineered) urban catchments, the model application demonstrated that a computationally ‘‘light’’ model can be employed to simulate the hydrograph and pollutograph response within them. It thus allows catchment-scale assessment of the potential ecotoxicological impact of biocides on receiving waters.

Comparison of two stochastic techniques for reliable urban runoff prediction by modeling systematic errors

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.

Dynamic time warping improves sewer flow monitoring.

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.

Long-Term Phosphorus Loading and Springtime Temperatures Explain Interannual Variability of Hypoxia in a Large Temperate Lake

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 (R2 = 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.

On the practical usefulness of least squares for assessing uncertainty in hydrologic and water quality predictions

Abstract Sophisticated methods for uncertainty quantification have been proposed for overcoming the pitfalls of simple statistical inference in hydrology. The implementation of such methods is conceptually and computationally challenging, however, especially for large-scale models. Here, we explore whether there are circumstances in which simple approaches, such as least squares, produce comparably accurate and reliable predictions. We do so using three case studies, with two involving a small sewer catchment with limited calibration data, and one an agricultural river basin with rich calibration data. We also review additional published case studies. We find that least squares performs similarly to more sophisticated approaches such as a Bayesian autoregressive error model in terms of both accuracy and reliability if calibration periods are long or if the input data and the model have minimal bias. Overall, we find that, when mindfully applied, simple statistical methods such as least squares can still be useful for uncertainty quantification.

Accelerating Bayesian inference in hydrological modeling with a mechanistic emulator

Abstract As in many fields of dynamic modeling, the long runtime of hydrological models hinders Bayesian inference of model parameters from data. By replacing a model with an approximation of its output as a function of input and/or parameters, emulation allows us to complete this task by trading-off accuracy for speed. We combine (i) the use of a mechanistic emulator, (ii) low-discrepancy sampling of the parameter space, and (iii) iterative refinement of the design data set, to perform Bayesian inference with a very small design data set constructed with 128 model runs in a parameter space of up to eight dimensions. In our didactic example we use a model implemented with the hydrological simulator SWMM that allows us to compare our inference results against those derived with the full model. This comparison demonstrates that iterative improvements lead to reasonable results with a very small design data set.