scholarly journals Do direct and inverse uncertainty assessment methods present the same results?

2020 ◽  
Vol 22 (4) ◽  
pp. 842-855 ◽  
Author(s):  
Arman Ahmadi ◽  
Mohsen Nasseri
Keyword(s):  
Inverse Method ◽  
Hydrological Model ◽  
Direct Method ◽  
Parametric Uncertainty ◽  
Uncertainty Assessment ◽  
Water Systems ◽  
Hydrological Models ◽  
Posterior Distributions ◽  
Mathematical Operations ◽  
Research Show

Abstract Hydrological models are simplified imitations of natural and man-made water systems, and because of this simplification, always deal with inherent uncertainty. To develop more rigorous modeling procedures and to provide more reliable results, it is inevitable to consider and estimate this uncertainty. Although there are different approaches in the literature to assess the parametric uncertainty of hydrological models, their structures and results have rarely been compared systematically. In this research, two different approaches to analyze parametric uncertainty, namely direct and inverse methods are compared and contrasted. While the direct method employs a sampling simulation procedure to generate posterior distributions of parameters, the inverse method utilizes an optimization-based approach to optimize parameter sets of an interval-based hydrological model. Two different hydrological models and case studies are employed, and the models are set by two distinct mathematical operations of interval mathematics. Findings of this research show that while the choice of the interval mathematic method can affect the final results, generally, the inverse method cannot be counted on as a reliable tool to analyze the parametric uncertainty of hydrological models, and the direct method provides more accurate results.

scholarly journals Uncertainty Assessment of Urban Hydrological Modelling from a Multiple Objective Perspective

Water ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 1393 ◽  
Author(s):  
Bo Pang ◽  
Shulan Shi ◽  
Gang Zhao ◽  
Rong Shi ◽  
Dingzhi Peng ◽  
...  
Keyword(s):  
Flood Management ◽  
Uncertainty Assessment ◽  
Multiple Objective ◽  
Hydrological Models ◽  
Validation Period ◽  
Urban Flood ◽  
Calibration Period ◽  
Storm Water Management Model ◽  
Glue Method ◽  
Generalized Likelihood Uncertainty Estimation

The uncertainty assessment of urban hydrological models is important for understanding the reliability of the simulated results. To satisfy the demand for urban flood management, we assessed the uncertainty of urban hydrological models from a multiple-objective perspective. A multiple-criteria decision analysis method, namely, the Generalized Likelihood Uncertainty Estimation-Technique for Order Preference by Similarity to Ideal Solution (GLUE-TOPSIS) was proposed, wherein TOPSIS was adopted to measure the likelihood within the GLUE framework. Four criteria describing different urban stormwater characteristics were combined to test the acceptability of the parameter sets. The TOPSIS was used to calculate the aggregate employed in the calculation of the aggregate likelihood value. The proposed method was implemented in the Storm Water Management Model (SWMM), which was applied to the Dahongmen catchment in Beijing, China. The SWMM model was calibrated and validated based on the three and two flood events respectively downstream of the Dahongmen catchment. The results showed that the GLUE-TOPSIS provided a more precise uncertainty boundary compared with the single-objective GLUE method. The band widths were reduced by 7.30 m3/s in the calibration period, and by 7.56 m3/s in the validation period. The coverages increased by 20.3% in the calibration period, and by 3.2% in the validation period. The median estimates improved, with an increase of the Nash–Sutcliffe efficiency coefficients by 1.6% in the calibration period, and by 10.0% in the validation period. We conclude that the proposed GLUE-TOPSIS is a valid approach to assess the uncertainty of urban hydrological model from a multiple objective perspective, thereby improving the reliability of model results in urban catchment.

Torsion of Noncylindrical Shafts of Circular Cross Section

1950 ◽  
Vol 17 (3) ◽  
pp. 275-282
Author(s):  
H. J. Reissner ◽  
G. J. Wennagel
Keyword(s):  
Cross Sections ◽  
Inverse Method ◽  
Direct Method ◽  
Circular Cross Section ◽  
Theory Of Elasticity ◽  
Elementary Functions ◽  
Single Term ◽  
Circumferential Displacement ◽  
Basic Differential Equation ◽  
Technical Interest

Abstract The theory of torsion of noncylindrical bodies of revolution, initiated by J. H. Michell and A. Föppl, is stated by a basic differential equation of the circumferential displacement and by a boundary condition of the shear stress along the generator surface. The solution of these two equations by the “direct” method of first assuming the boundary shape has not lent itself to closed solutions in terms of elementary functions, so that only approximation, infinite series, and experimental methods have been applied. A semi-inverse method analogous to Saint Venant’s semi-inverse method for cylindrical bodies has the disadvantage of the restriction to special boundary shapes but the advantage of exact solutions by means of elementary functions. By this method, bodies of conical, ellipsoidal, and hyperbolic boundary shapes have been obtained in a simple analysis. One class of integrals leading to other boundary shapes seems not to have been analyzed up to now, namely, the integrals in the form of a product of two functions of, respectively, axial (z) and radial (r) co-ordinates. A first suggestion of this possibility was given in Love’s treatise on the mathematical theory of elasticity. In the present paper, the classes of boundary shapes, displacements, and stress distributions are investigated analytically and numerically. The extent of the numerical investigation contains only the results of single-term integrals for full and hollow cross sections of technical interest. The detailed analysis of the boundary shapes, following from series integrals, presents essential mathematical obstacles. Overcoming these difficulties might lead to a multitude of solutions of interesting boundary shapes, and stress and strain distribution.

Stepwise improvement of hydrological models using satellite-based evaporation and total water storage estimations

2021 ◽  
Author(s):  
Markus Hrachowitz ◽  
Petra Hulsman ◽  
Hubert Savenije
Keyword(s):  
Model Calibration ◽  
Hydrological Model ◽  
Model Development ◽  
Water Storage ◽  
Spatiotemporal Variability ◽  
Model Structure ◽  
Hydrological Models ◽  
Total Water ◽  
Spatiotemporal Model ◽  
Multiple Variables

<p>Hydrological models are often calibrated with respect to flow observations at the basin outlet. As a result, flow predictions may seem reliable but this is not necessarily the case for the spatiotemporal variability of system-internal processes, especially in large river basins. Satellite observations contain valuable information not only for poorly gauged basins with limited ground observations and spatiotemporal model calibration, but also for stepwise model development. This study explored the value of satellite observations to improve our understanding of hydrological processes through stepwise model structure adaption and to calibrate models both temporally and spatially. More specifically, satellite-based evaporation and total water storage anomaly observations were used to diagnose model deficiencies and to subsequently improve the hydrological model structure and the selection of feasible parameter sets. A distributed, process based hydrological model was developed for the Luangwa river basin in Zambia and calibrated with respect to discharge as benchmark. This model was modified stepwise by testing five alternative hypotheses related to the process of upwelling groundwater in wetlands, which was assumed to be negligible in the benchmark model, and the spatial discretization of the groundwater reservoir. Each model hypothesis was calibrated with respect to 1) discharge and 2) multiple variables simultaneously including discharge and the spatiotemporal variability in the evaporation and total water storage anomalies. The benchmark model calibrated with respect to discharge reproduced this variable well, as also the basin-averaged evaporation and total water storage anomalies. However, the evaporation in wetland dominated areas and the spatial variability in the evaporation and total water storage anomalies were poorly modelled. The model improved the most when introducing upwelling groundwater flow from a distributed groundwater reservoir and calibrating it with respect to multiple variables simultaneously. This study showed satellite-based evaporation and total water storage anomaly observations provide valuable information for improved understanding of hydrological processes through stepwise model development and spatiotemporal model calibration.</p>

Effect of Gold Nanoparticles Size on Detection of Methylphosphonic Acid Hydrolysis Product of Nerve Agent

2021 ◽  
Vol 25 (7) ◽  
pp. 1-7
Author(s):  
Fellyzra Elvya Pojol ◽  
Buong Woei Chieng ◽  
Keat Khim Ong ◽  
Rashid Jahwarhar Izuan Abd ◽  
Mohd Junaedy Osman ◽  
...  
Keyword(s):  
Gold Nanoparticles ◽  
Inverse Method ◽  
Direct Method ◽  
Hydrolysis Product ◽  
Spherical Shape ◽  
Methylphosphonic Acid ◽  
Visible Spectroscopy ◽  
Transmission Electron ◽  
Citrate Reduction ◽  
Chloride Trihydrate

Citrate reduction of gold (III) chloride trihydrate (HAuCl4) is commonly used method to synthesise citrate-capped gold nanoparticles (cit-AuNPs). In this study, the sequence of reagents addition was modified (“inverse” method) to synthesise smaller size of cit-AuNPs than the standard Turkevich method (“direct” method). Ultraviolet-visible spectroscopy (UV-vis) and field emission transmission electron microscopy (FETEM) confirmed the formation of cit-AuNPs. The cit-AuNPs synthesized using “inverse” method are smaller in size (14.0 ± 3.03 nm) with uniform spherical shape compared to “direct” method (23.5 ± 7.52 nm). Smaller particles size of cit-AuNPs provide higher efficiency and sensitivity for detection of methylphosphonic acid (MPA) via colorimetric incorporated with image processing with a linear range from 2.5 to 12.5 mM and a low detection limit of 6.28 mM at shorter detection period (24 to 30 s).

scholarly journals The importance of hydrological uncertainty assessment methods in climate change impact studies

2014 ◽  
Vol 18 (8) ◽  
pp. 3301-3317 ◽  
Author(s):  
M. Honti ◽  
A. Scheidegger ◽  
C. Stamm
Keyword(s):  
Climate Change ◽  
Climate Change Impact ◽  
Hydrological Model ◽  
Uncertainty Assessment ◽  
Assessment Method ◽  
Calibration Data ◽  
Relative Importance ◽  
Impact Studies ◽  
Uncertainty Sources ◽  
Change Impact

Abstract. Climate change impact assessments have become more and more popular in hydrology since the middle 1980s with a recent boost after the publication of the IPCC AR4 report. From hundreds of impact studies a quasi-standard methodology has emerged, to a large extent shaped by the growing public demand for predicting how water resources management or flood protection should change in the coming decades. The "standard" workflow relies on a model cascade from global circulation model (GCM) predictions for selected IPCC scenarios to future catchment hydrology. Uncertainty is present at each level and propagates through the model cascade. There is an emerging consensus between many studies on the relative importance of the different uncertainty sources. The prevailing perception is that GCM uncertainty dominates hydrological impact studies. Our hypothesis was that the relative importance of climatic and hydrologic uncertainty is (among other factors) heavily influenced by the uncertainty assessment method. To test this we carried out a climate change impact assessment and estimated the relative importance of the uncertainty sources. The study was performed on two small catchments in the Swiss Plateau with a lumped conceptual rainfall runoff model. In the climatic part we applied the standard ensemble approach to quantify uncertainty but in hydrology we used formal Bayesian uncertainty assessment with two different likelihood functions. One was a time series error model that was able to deal with the complicated statistical properties of hydrological model residuals. The second was an approximate likelihood function for the flow quantiles. The results showed that the expected climatic impact on flow quantiles was small compared to prediction uncertainty. The choice of uncertainty assessment method actually determined what sources of uncertainty could be identified at all. This demonstrated that one could arrive at rather different conclusions about the causes behind predictive uncertainty for the same hydrological model and calibration data when considering different objective functions for calibration.

scholarly journals How good are hydrological models for gap-filling streamflow data?

2018 ◽  
Vol 22 (8) ◽  
pp. 4593-4604 ◽  
Author(s):  
Yongqiang Zhang ◽  
David Post
Keyword(s):  
Model Calibration ◽  
Hydrological Model ◽  
Hydrological Models ◽  
Hydrological Response ◽  
Gap Filling ◽  
Annual Streamflow ◽  
Response Variable ◽  
Benchmark Data ◽  
Streamflow Data ◽  
Streamflow Trend

Abstract. Gap-filling streamflow data is a critical step for most hydrological studies, such as streamflow trend, flood, and drought analysis and hydrological response variable estimates and predictions. However, there is a lack of quantitative evaluation of the gap-filled data accuracy in most hydrological studies. Here we show that when the missing data rate is less than 10 %, the gap-filled streamflow data obtained using calibrated hydrological models perform almost the same as the benchmark data (less than 1 % missing) when estimating annual trends for 217 unregulated catchments widely spread across Australia. Furthermore, the relative streamflow trend bias caused by the gap filling is not very large in very dry catchments where the hydrological model calibration is normally poor. Our results clearly demonstrate that the gap filling using hydrological modelling has little impact on the estimation of annual streamflow and its trends.

scholarly journals Fuzzy committees of specialized rainfall-runoff models: further enhancements and tests

2013 ◽  
Vol 17 (11) ◽  
pp. 4441-4451 ◽  
Author(s):  
N. Kayastha ◽  
J. Ye ◽  
F. Fenicia ◽  
V. Kuzmin ◽  
D. P. Solomatine
Keyword(s):  
Hydrological Model ◽  
Weighting Function ◽  
Hydrological Models ◽  
Membership Functions ◽  
Rainfall Runoff ◽  
Objective Functions ◽  
Hydrological Regimes

Abstract. Often a single hydrological model cannot capture the details of a complex rainfall–runoff relationship, and a possibility here is building specialized models to be responsible for a particular aspect of this relationship and combining them to form a committee model. This study extends earlier work of using fuzzy committees to combine hydrological models calibrated for different hydrological regimes – by considering the suitability of the different weighting function for objective functions and different class of membership functions used to combine the specialized models and compare them with the single optimal models.

scholarly journals Reducing parametric uncertainty in limit-cycle oscillation computational models

2017 ◽  
Vol 121 (1241) ◽  
pp. 940-969 ◽  
Author(s):  
R. Hayes ◽  
R. Dwight ◽  
S. Marques
Keyword(s):  
Limit Cycle ◽  
Computational Models ◽  
Structural Parameters ◽  
Parametric Uncertainty ◽  
Limit Cycle Oscillation ◽  
Posterior Distributions ◽  
Input Parameters ◽  
Data Points ◽  
Cycle Oscillation ◽  
True Values

ABSTRACTThe assimilation of discrete data points with model predictions can be used to achieve a reduction in the uncertainty of the model input parameters, which generate accurate predictions. The problem investigated here involves the prediction of limit-cycle oscillations using a High-Dimensional Harmonic Balance (HDHB) method. The efficiency of the HDHB method is exploited to enable calibration of structural input parameters using a Bayesian inference technique. Markov-chain Monte Carlo is employed to sample the posterior distributions. Parameter estimation is carried out on a pitch/plunge aerofoil and two Goland wing configurations. In all cases, significant refinement was achieved in the distribution of possible structural parameters allowing better predictions of their true deterministic values. Additionally, a comparison of two approaches to extract the true values from the posterior distributions is presented.

scholarly journals Comparative performance evaluation of self-adaptive differential evolution with GA, SCE and DE algorithms for the automatic calibration of a computationally intensive distributed hydrological model

2020 ◽  
Author(s):  
Saswata Nandi ◽  
M. Janga Reddy
Keyword(s):  
Differential Evolution ◽  
Hydrological Model ◽  
Automatic Calibration ◽  
Hydrological Models ◽  
Distributed Hydrological Model ◽  
Infiltration Capacity ◽  
Vic Model ◽  
Adaptive Differential Evolution ◽  
Computationally Intensive ◽  
Self Adaptive

Abstract Recently, physically-based hydrological models have been gaining much popularity in various activities of water resources planning and management, such as assessment of basin water availability, floods, droughts, and reservoir operation. Every hydrological model contains some parameters that must be tuned to the catchment being studied to obtain reliable estimates from the model. This study evaluated the performance of different evolutionary algorithms, namely genetic algorithm (GA), shuffled complex evolution (SCE), differential evolution (DE), and self-adaptive differential evolution (SaDE) algorithm for the parameter calibration of a computationally intensive distributed hydrological model, variable infiltration capacity (VIC) model. The methodology applied and tested for a case study of the upper Tungabhadra River basin in India, and the performance of the algorithms is evaluated in terms of reliability, variability, efficacy measures in a limited number of function evaluations, their ability for achieving global convergence, and also by their capability to produce a skillful simulation of streamflows. The results of the study indicated that SaDE facilitates an effective calibration of the VIC model with higher reliability and faster convergence to optimal solutions as compared to the other methods. Moreover, due to the simplicity of the SaDE, it provides easy implementation and flexibility for the automatic calibration of complex hydrological models.

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