Treatment of precipitation uncertainty in rainfall-runoff modelling: a fuzzy set approach

Maskey, Shreedhar; Guinot, Vincent; Price, Roland K.

doi:10.1016/j.advwatres.2004.07.001

Cited by 109 publications

(65 citation statements)

References 17 publications

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“…Numerous approaches exist to quantify the resulting model uncertainties [48,49], including analytical methods [50], generalized likelihood uncertainty estimation (GLUE) [51,52], parameter estimation [53], approximation methods (e.g., first-order second-moment method), Melching [54], simulation and sampling-based methods [55], Bayesian methods [56], analytical methods, methods based on the analysis of model errors, methods based on fuzzy sets [57,58], etc. The selection of a suitable method depends on the knowledge of the river's hydraulics, the availability of data, and the modelling approach, as suggested in the code of practice by Pappenberger and Beven [59].…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Analysis of a Two-Dimensional Hydraulic Model

Oubennaceur

Chokmani

Nastev

et al. 2018

Water

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Abstract:A reliability approach referred to as the point estimate method (PEM) is presented to assess the uncertainty of a two-dimensional hydraulic model. PEM is a special case of numerical quadrature based on orthogonal polynomials, which evaluates the statistical moments of a performance function involving random variables. When applied to hydraulic problems, the variables are the inputs to the hydraulic model, and the first and second statistical moments refer to the mean and standard deviation of the model's output. In providing approximate estimates of the uncertainty, PEM appears considerably simpler and requires less information and fewer runs than standard Monte Carlo methods. An example of uncertainty assessment is shown for simulated water depths in a 46 km reach of the Richelieu River, Canada. The 2D hydraulic model, H2D2, was used to solve the shallow water equations. Standard deviations around the mean water depths were estimated by considering the uncertainties of three main input variables: flow rate, Manning's coefficient and topography. Results indicate that the mean standard deviation is <27 cm for the considered flow rates of 759, 824, 936, 1113 m 3 /s. Higher standard deviations were obtained upstream of the topographic shoal at the municipality of Saint-Jean-sur-Richelieu. The PEM method adds further value to the H2D2 model predictions as it indicates the magnitude and the spatial variation in uncertainties. The effort required to complete an uncertainty analysis using the PEM method is minimal and the resulting insight is meaningful. This knowledge should be incorporated into decision-making in the context of flood risk assessment.

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Section: Introductionmentioning

confidence: 99%

Uncertainty Analysis of a Two-Dimensional Hydraulic Model

Oubennaceur

Chokmani

Nastev

et al. 2018

Water

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“…For high temporal resolution in particular, uncertainty in the temporal and spatial distributions of rainfall can dominate over uncertainty in the magnitude of rainfall, as shown by Maskey et al (2004) for the Polish watershed Klodzko. Therefore, if rainfall properties are more accurately estimated it is likely that the streamflow estimations would improve, a conclusion supported by the works of Andréassian et al (2001), who tested the sensitivity of three lumped watershed models to imperfect knowledge of rainfall input.…”

Section: Introductionmentioning

confidence: 99%

“…One of the major sources of uncertainty in streamflow estimations by rainfall-runoff models is spatiotemporal uncertainty in catchment rainfall (Hromadka and McCuen, 1998;Maskey et al, 2004;Jones et al, 2006). For high temporal resolution in particular, uncertainty in the temporal and spatial distributions of rainfall can dominate over uncertainty in the magnitude of rainfall, as shown by Maskey et al (2004) for the Polish watershed Klodzko.…”

Section: Introductionmentioning

confidence: 99%

Impact of rainfall estimation uncertainty on streamflow estimations for catchments Wye and Tyne in the United Kingdom

Ekström

Jones

2008

Intl Journal of Climatology

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ABSTRACT:The main sources of uncertainty in rainfall-runoff models are found in the input variables where the largest impact on estimated streamflow is generally given by the catchment rainfall. Hence, by quantifying the uncertainty of catchment rainfall, it is possible to provide an estimate, albeit conservative, of streamflow estimation uncertainty. In this article, 42 series of catchment average rainfall were used to estimate monthly streamflow for two river catchments in the United Kingdom over a period of 8 years, these were as follows: a composite series based on weighted rain gauge series, a series based on interpolated gridded rainfall data and an ensemble of 40 series, based on simulated rainfall grids conditioned on observed rainfall statistics. This study shows that, on average, the uncertainty in monthly streamflow, as given from the mean range of monthly simulated data, were approximately 28 and 42% of the long-term mean for the two catchments respectively. By quantifying uncertainty in streamflow due to catchment rainfall uncertainty it was possible to identify contributions of other factors to the total streamflow estimation uncertainty. For example, streamflow uncertainty was, in this experiment, shown to respond also to the absolute magnitude of the streamflow, a consequence of the model being optimized for low flows.

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“…Fuzzy numbers have been used to propagate parametric uncertainty in the finite element analysis [36,37]. Furthermore, fuzzy numbers have been used to address uncertainty in the heat conduction problem [38], the rainfall-runoff model [39], the climate-pest model [40], the structural safety assessment [41], and the machining process [42]. Behind these diverse applications, one common theme is the recognition of the limits of probability theory in the handling of uncertainty information.…”

Section: Introductionmentioning

confidence: 99%

Interval Estimations of Building Heating Energy Consumption using the Degree-Day Method and Fuzzy Numbers

Cheng¹,

Li²

2018

Buildings

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Abstract:The purpose of this paper is to propagate the input uncertainties of the degree-day method to estimate the building heating energy consumption as numerical intervals. While it is common to use average or expected values (e.g., Typical Meteorological Year) to address the input uncertainties, this practice can only yield the best estimates as single-point values without informing the possible range of variations. After classifying two types of uncertainty as weather variability and imprecision in the degree-day method, this paper proposes the adoption of fuzzy numbers and their arithmetic as the theoretical approach to handle uncertainty. As the degree-day method mainly involves elementary arithmetic (e.g., addition and multiplication), fuzzy number arithmetic can be directly applied to formally process numerical intervals. The proposed method is demonstrated and verified via a building example in Canada, and the interval results are comparable to the variation of heating energy consumption based on the data of outdoor ambient temperatures in 52 years.

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Treatment of precipitation uncertainty in rainfall-runoff modelling: a fuzzy set approach

Cited by 109 publications

References 17 publications

Uncertainty Analysis of a Two-Dimensional Hydraulic Model

Uncertainty Analysis of a Two-Dimensional Hydraulic Model

Impact of rainfall estimation uncertainty on streamflow estimations for catchments Wye and Tyne in the United Kingdom

Interval Estimations of Building Heating Energy Consumption using the Degree-Day Method and Fuzzy Numbers

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