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

Giudice, Dario Del; Löwe, Roland; Madsen, Henrik; Mikkelsen, Peter Steen; Rieckermann, Jörg

doi:10.1002/2014wr016678

Cited by 24 publications

(22 citation statements)

References 77 publications

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“…Physically based models usually require high computational power and time and a large number of parameters, but there are situations in which it is important to keep the complexity to better understand system mechanisms. They are also necessary to deal with system variability and allow one to include a stochastic component to represent uncertainty in parameter and input values (Del Giudice et al, 2015).…”

Section: Urban Hydrological Model Characterizationmentioning

confidence: 99%

Spatial and temporal variability of rainfall and their effects on hydrological response in urban areas – a review

Cristiano

Veldhuis

Giesen

2017

Hydrol. Earth Syst. Sci.

254

146

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Abstract. In urban areas, hydrological processes are characterized by high variability in space and time, making them sensitive to small-scale temporal and spatial rainfall variability. In the last decades new instruments, techniques, and methods have been developed to capture rainfall and hydrological processes at high resolution. Weather radars have been introduced to estimate high spatial and temporal rainfall variability. At the same time, new models have been proposed to reproduce hydrological response, based on smallscale representation of urban catchment spatial variability. Despite these efforts, interactions between rainfall variability, catchment heterogeneity, and hydrological response remain poorly understood. This paper presents a review of our current understanding of hydrological processes in urban environments as reported in the literature, focusing on their spatial and temporal variability aspects. We review recent findings on the effects of rainfall variability on hydrological response and identify gaps where knowledge needs to be further developed to improve our understanding of and capability to predict urban hydrological response.

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Section: Urban Hydrological Model Characterizationmentioning

confidence: 99%

Spatial and temporal variability of rainfall and their effects on hydrological response in urban areas – a review

Cristiano

Veldhuis

Giesen

2017

Hydrol. Earth Syst. Sci.

254

146

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“…This is done by calculating

\begin{matrix} f ({boldy}^{L_{2}} | {boldy}_{o}^{L_{1}}, {boldx}_{o}^{L_{1} \cup L_{2}}) \\ = \int f ({boldy}^{L_{2}} | θ, {bold-italicψ}_{y}, {bold-italicψ}_{x}, {boldy}_{o}^{L_{1}}, {boldx}_{o}^{L_{1} \cup L_{2}}) f (θ, {bold-italicψ}_{y}, {bold-italicψ}_{x} | {boldy}_{o}^{L_{1}}, {boldx}_{o}^{L_{1} \cup L_{2}}) d θ d {bold-italicψ}_{y} d {bold-italicψ}_{x}, \end{matrix}

where the superscripts L 1 and L 2 indicate that we may be interested in predictions for another time period (here: “layout,” L ), L 2 , than we have observations for, L 1 . As in most studies on inference and uncertainty analysis, we still assume input data to be available also in L 2 and thus operate in “prediction” or “hindcasting” mode [ Renard et al ., ; Del Giudice et al ., ].…”

Section: Methodsmentioning

confidence: 99%

“…This concept is akin to the one adopted by Del Giudice et al . []. Parsimonious linear models, using as input spatially aggregate rainfall, are effective tools to reproduce the discharge dynamics at the catchment outlet during storm events [ Coutu et al ., ; Sun and Bertrand‐Krajewski , ].…”

Section: Methodsmentioning

confidence: 99%

“…We estimated the prior marginal distributions of A , k , x gw , σ 1 , σ 2 , χ 1 , χ 2 , and σ E based on a least squares calibration employing measurements not used in the final analysis (data not shown). Having an interpretation related to the hydrological system ( A is connected to the volume of effective precipitation, k to the rapidity of the system response, x gw to the base flow, and σ 1 , σ 2 , χ 1 , χ 2 to the harmonic dynamics of wastewater) and measurement device ( σ E represents the imprecision of runoff observations), we refer to these constants as “physical parameters.” Regarding the priors of the bias error model (BD), we followed the guidelines provided in previous works [ Reichert and Schuwirth , ; Brynjarsdóttir and O'Hagan , ; Del Giudice et al ., ]. For σ B , the magnitude of the bias, we determined its prior standard deviation by analyzing the model discrepancy between the model forced with accurate rainfall and the measured discharge.…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Describing the catchment‐averaged precipitation as a stochastic process improves parameter and input estimation

Giudice

Albert

Rieckermann

et al. 2016

Water Resources Research

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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.

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“…It has a total area of 1300 ha and an area-velocity flow meter is located downstream of the catchment as seen in Figure 5. The area is part of a larger complex catchment area connected to the wastewater treatment plant in Avedøre, and is already well known from several research studies [36][37][38][39][40]. The drainage system is known to have problems with infiltrating water, which causes the hydraulic response of the system to be very different from wet to dry periods of the year, a phenomenon that is very difficult to model deterministically (see the explanations in Section 2.4).…”

Section: Case Studymentioning

confidence: 99%

Evaluation of Maximum a Posteriori Estimation as Data Assimilation Method for Forecasting Infiltration-Inflow Affected Urban Runoff with Radar Rainfall Input

Pedersen

Lund

Borup

et al. 2016

Water

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High quality on-line flow forecasts are useful for real-time operation of urban drainage systems and wastewater treatment plants. This requires computationally efficient models, which are continuously updated with observed data to provide good initial conditions for the forecasts. This paper presents a way of updating conceptual rainfall-runoff models using Maximum a Posteriori estimation to determine the most likely parameter constellation at the current point in time. This is done by combining information from prior parameter distributions and the model goodness of fit over a predefined period of time that precedes the forecast. The method is illustrated for an urban catchment, where flow forecasts of 0-4 h are generated by applying a lumped linear reservoir model with three cascading reservoirs. Radar rainfall observations are used as input to the model. The effects of different prior standard deviations and lengths of the auto-calibration period on the resulting flow forecast performance are evaluated. We were able to demonstrate that, if properly tuned, the method leads to a significant increase in forecasting performance compared to a model without continuous auto-calibration. Delayed responses and erratic behaviour in the parameter variations are, however, observed and the choice of prior distributions and length of auto-calibration period is not straightforward.

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

Cited by 24 publications

References 77 publications

Spatial and temporal variability of rainfall and their effects on hydrological response in urban areas – a review

Spatial and temporal variability of rainfall and their effects on hydrological response in urban areas – a review

Describing the catchment‐averaged precipitation as a stochastic process improves parameter and input estimation

Evaluation of Maximum a Posteriori Estimation as Data Assimilation Method for Forecasting Infiltration-Inflow Affected Urban Runoff with Radar Rainfall Input

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