Analysis of uncertainty propagation through model parameters and structure

2010 ◽  
Vol 62 (6) ◽  
pp. 1230-1239 ◽  
Author(s):  
Abhijit Patil ◽  
Zhi-Qiang Deng
Keyword(s):  
Sensitivity Analysis ◽  
Standard Deviation ◽  
Dissolved Oxygen ◽  
Error Propagation ◽  
Uncertainty Propagation ◽  
Sensitivity Coefficient ◽  
Model Parameters ◽  
Hydrologic Simulation ◽  
Hspf Model ◽  
Forcing Function

Estimation of uncertainty propagation in watershed models is challenging but useful to total maximum daily load (TMDL) calculations. This paper presents an effective approach, involving the combined application of Rosenblueth method and sensitivity analysis, to the determination of uncertainty propagation through the parameters and structure of the HSPF (Hydrologic Simulation Program-FORTRAN) model. The sensitivity analysis indicates that the temperature is a major forcing function in the DO-BOD balance and controls the overall dissolved oxygen concentration. The mean and standard deviation from the descriptive statistics of dissolved oxygen data obtained using the HSPF model are compared to those estimated using Rosenblueth's method. The difference is defined as the error propagated from water temperature through dissolved oxygen. The error propagation, while considering the second order sensitivity coefficient in Rosenblueth's method, is observed to have a mean of 0.281 mg/l and a standard deviation of 0.099 mg/l. A relative low error propagation value is attributed to low skewness of dependent and independent variables. The results provide new insights into the uncertainty propagation in the HSPF model commonly used for TMDL development.

scholarly journals Advanced sensitivity analysis of the impact of the temporal distribution and intensity of rainfall on hydrograph parameters in urban catchments

2021 ◽  
Vol 25 (10) ◽  
pp. 5493-5516
Author(s):  
Francesco Fatone ◽  
Bartosz Szeląg ◽  
Adam Kiczko ◽  
Dariusz Majerek ◽  
Monika Majewska ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Logistic Regression ◽  
Temporal Distribution ◽  
Sensitivity Coefficient ◽  
Model Parameters ◽  
Hydrodynamic Models ◽  
Sensitivity Coefficients ◽  
Urban Catchments ◽  
Outflow Hydrograph ◽  
The Impact

Abstract. Knowledge of the variability of the hydrograph of outflow from urban catchments is highly important for measurements and evaluation of the operation of sewer networks. Currently, hydrodynamic models are most frequently used for hydrograph modeling. Since a large number of their parameters have to be identified, there may be problems at the calibration stage. Hence, sensitivity analysis is used to limit the number of parameters. However, the current sensitivity analytical methods ignore the effect of the temporal distribution and intensity of precipitation in a rainfall event on the catchment outflow hydrograph. This article presents a methodology of constructing a simulator of catchment outflow hydrograph parameters (volume and maximum flow). For this purpose, uncertainty analytical results obtained with the use of the GLUE (generalized likelihood uncertainty estimation) method were used. A novel analysis of the sensitivity of the hydrodynamic catchment models was also developed, which can be used in the analysis of the operation of stormwater networks and underground infrastructure facilities. Using the logistic regression method, an innovative sensitivity coefficient was proposed to study the impact of the variability of the parameters of the hydrodynamic model depending on the distribution of rainfall, the origin of rainfall (on the Chomicz scale), and the uncertainty of the estimated simulator coefficients on the parameters of the outflow hydrograph. The developed model enables the analysis of the impact of the identified SWMM (Storm Water Management Model) parameters on the runoff hydrograph, taking into account local rainfall conditions, which have not been analyzed thus far. Compared with the currently developed methods, the analyses included the impact of the uncertainty of the identified coefficients in the logistic regression model on the results of the sensitivity coefficient calculation. This aspect has not been taken into account in the sensitivity analytical methods thus far, although this approach evaluates the reliability of the simulation results. The results indicated a considerable influence of rainfall distribution and intensity on the sensitivity factors. The greater the intensity and rainfall were, the lower the impact of the identified hydrodynamic model parameters on the hydrograph parameters. Additionally, the calculations confirmed the significant impact of the uncertainty of the estimated coefficient in the simulator on the sensitivity coefficients. In the context of the sensitivity analysis, the obtained results have a significant effect on the interpretation of the relationships obtained. The approach presented in this study can be widely applied at the model calibration stage and for appropriate selection of hydrographs for identification and validation of model parameters. The results of the calculations obtained in this study indicate the suitability of including the origin of rainfall in the sensitivity analysis and calibration of hydrodynamic models, which results from the different sensitivities of models for normal, heavy, and torrential rain types. In this context, it is necessary to first divide the rainfall data by origin, for which analyses will be performed, including sensitivity analysis and calibration. Considering the obtained results of the calculations, at the stage of identifying the parameters of hydrodynamic models and their validation, precipitation conditions should be included because, for the precipitation caused by heavy rainfall, the values of the sensitivity coefficients were much lower than for torrential ones. Taking into account the values of the sensitivity coefficients obtained, the calibration of the models should not only cover episodes with high rainfall intensity, since this may lead to calculation errors at the stage of applying the model in practice (assessment of the stormwater system operating conditions, design of reservoirs and flow control devices, green infrastructure, etc.).

scholarly journals Effects of rainfall data resolution on watershed-scale model performance in predicting runoff

2014 ◽  
Vol 6 (2) ◽  
pp. 227-240 ◽  
Author(s):  
Huiliang Wang ◽  
Xuyong Li ◽  
Shaonan Hao
Keyword(s):  
Sensitivity Analysis ◽  
Temporal Resolution ◽  
Model Performance ◽  
Rainfall Data ◽  
Scale Model ◽  
Model Parameters ◽  
Model Accuracy ◽  
Hspf Model ◽  
Data Resolution ◽  
Dynamic Sensitivity Analysis

The hydrologic simulation program-FORTRAN (HSPF) model is widely used to develop management strategies for water resources, but its effectiveness is limited by predictive uncertainties associated with model input data. This study evaluated the effect of rainfall data resolution on the model performance when predicting runoff. We examined hourly, 3-hourly, 12-hourly, and 24-hourly temporal resolutions, and spatial resolutions from seven to one rain gauges. We used a statistical sensitivity analysis to test the effect of resolution on model accuracy, and a dynamic sensitivity analysis to test the effect on model parameters. Our results indicate that the model performance reduces when using a coarser rainfall resolution. The model used the corresponding parameters to absorb the effect of various resolution changes and reduced their impact on the runoff simulations. We used the paired-samples t-test to examine the significance of the rainfall data resolution to the model parameters, which revealed that the model accuracy was more sensitive to the temporal resolution. Our statistical analysis of the dispersion examined the parameter values. It showed that one parameter was sensitive to temporal resolution and three parameters were sensitive to spatial resolution. This study provided useful information for determining HSPF model parameters using rainfall data at different resolutions.

Performance Evaluation of a Standing Wave Thermoacoustic Refrigerator Using Normalized Sensitivity Coefficients

2020 ◽  
Vol 13 (3) ◽  
Author(s):  
Umar Nawaz Bhatti ◽  
Salem Bashmal
Keyword(s):  
Sensitivity Analysis ◽  
Standing Wave ◽  
Plate Thickness ◽  
Sensitivity Coefficient ◽  
Coefficient Of Performance ◽  
Model Parameters ◽  
Pressure Amplitude ◽  
Performance Parameters ◽  
Wide Range ◽  
Thermoacoustic Refrigerator

Abstract The sensitivity analysis using normalized sensitivity coefficient (NSC) can be used to identify important model parameters affecting the device performance by allowing one-to-one comparison. The results are highlighted in the form of order of magnitudes change in output for a unit change in input variable. In this study, the sensitivity analysis of a small capacity standing wave thermoacoustic refrigerator (SWTAR) has been performed using NSC. Specialized tool deltaec has been used to generate the results for the subsequent sensitivity analysis. Three key performance parameters, i.e., temperature difference achieved (ΔT), coefficient of performance (COP), and relative coefficient of performance (COPR) have been analyzed for perturbations in number of device variables, namely, oscillating pressure amplitude, two different stack material properties and four stack geometric parameters, i.e., stack length, stack center position, stack plate thickness, and half stack spacing. Sensitivity results are obtained for a wide range of mean operating pressures (Pm), mean operating temperature (Tm), and drive ratios (DRs). It has been found that performance parameters are most sensitive to the perturbations in oscillating pressure amplitude and least affected by the perturbations in the stack length. With respect to the oscillating pressure amplitude, maximum NSC of 24.12 has been reported for ΔT at mean pressure of 5 bar.

A modeling approach to simulate impact of climate change in lake water quality: phytoplankton growth rate assessment

1998 ◽  
Vol 37 (2) ◽  
pp. 177-185 ◽  
Author(s):  
Hany Hassan ◽  
Keisuke Hanaki ◽  
Tomonori Matsuo
Keyword(s):  
Climate Change ◽  
Water Quality ◽  
Growth Rate ◽  
Dissolved Oxygen ◽  
Lake Water ◽  
Phytoplankton Growth ◽  
Quality Data ◽  
Model Parameters ◽  
Lake Water Quality ◽  
Phytoplankton Growth Rate

Global climate change induced by increased concentrations of greenhouse gases (especially CO2) is expected to include changes in precipitation, wind speed, incoming solar radiation, and air temperature. These major climate variables directly influence water quality in lakes by altering changes in flow and water temperature balance. High concentration of nutrient enrichment and expected variability of climate can lead to periodic phytoplankton blooms and an alteration of the neutral trophic balance. As a result, dissolved oxygen levels, with low concentrations, can fluctuate widely and algal productivity may reach critical levels. In this work, we will present: 1) recent results of GCMs climate scenarios downscaling project that was held at the University of Derby, UK.; 2) current/future comparative results of a new mathematical lake eutrophication model (LEM) in which output of phytoplankton growth rate and dissolved oxygen will be presented for Suwa lake in Japan as a case study. The model parameters were calibrated for the period of 1973–1983 and validated for the period of 1983–1993. Meterologic, hydrologic, and lake water quality data of 1990 were selected for the assessment analysis. Statistical relationships between seven daily meteorological time series and three airflow indices were used as a means for downscaling daily outputs of Hadley Centre Climate Model (HadCM2SUL) to the station sub-grid scale.

scholarly journals A Sensitivity Analysis of the SPACSYS Model

Agriculture ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 624
Author(s):  
Yan Shan ◽  
Mingbin Huang ◽  
Paul Harris ◽  
Lianhai Wu
Keyword(s):  
Sensitivity Analysis ◽  
Wheat Yield ◽  
Climatic Conditions ◽  
Water Dynamics ◽  
Ecological Modelling ◽  
Soil Conditions ◽  
Model Parameters ◽  
Nutrient Inputs ◽  
Nutrient Pool ◽  
Wheat Field

A sensitivity analysis is critical for determining the relative importance of model parameters to their influence on the simulated outputs from a process-based model. In this study, a sensitivity analysis for the SPACSYS model, first published in Ecological Modelling (Wu, et al., 2007), was conducted with respect to changes in 61 input parameters and their influence on 27 output variables. Parameter sensitivity was conducted in a ‘one at a time’ manner and objectively assessed through a single statistical diagnostic (normalized root mean square deviation) which ranked parameters according to their influence of each output variable in turn. A winter wheat field experiment provided the case study data. Two sets of weather elements to represent different climatic conditions and four different soil types were specified, where results indicated little influence on these specifications for the identification of the most sensitive parameters. Soil conditions and management were found to affect the ranking of parameter sensitivities more strongly than weather conditions for the selected outputs. Parameters related to drainage were strongly influential for simulations of soil water dynamics, yield and biomass of wheat, runoff, and leaching from soil during individual and consecutive growing years. Wheat yield and biomass simulations were sensitive to the ‘ammonium immobilised fraction’ parameter that related to soil mineralization and immobilisation. Simulations of CO2 release from the soil and soil nutrient pool changes were most sensitive to external nutrient inputs and the process of denitrification, mineralization, and decomposition. This study provides important evidence of which SPACSYS parameters require the most care in their specification. Moving forward, this evidence can help direct efficient sampling and lab analyses for increased accuracy of such parameters. Results provide a useful reference for model users on which parameters are most influential for different simulation goals, which in turn provides better informed decision making for farmers and government policy alike.

scholarly journals Global Sensitivity Analysis of a Homogenized Constrained Mixture Model of Arterial Growth and Remodeling

2021 ◽  
Author(s):  
Sebastian Brandstaeter ◽  
Sebastian L. Fuchs ◽  
Jonas Biehler ◽  
Roland C. Aydin ◽  
Wolfgang A. Wall ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Model Parameters ◽  
Computational Studies ◽  
Growth And Remodeling ◽  
Global Sensitivity ◽  
Output Variability ◽  
Constrained Mixture ◽  
The One ◽  
Influential Parameters

AbstractGrowth and remodeling in arterial tissue have attracted considerable attention over the last decade. Mathematical models have been proposed, and computational studies with these have helped to understand the role of the different model parameters. So far it remains, however, poorly understood how much of the model output variability can be attributed to the individual input parameters and their interactions. To clarify this, we propose herein a global sensitivity analysis, based on Sobol indices, for a homogenized constrained mixture model of aortic growth and remodeling. In two representative examples, we found that 54–80% of the long term output variability resulted from only three model parameters. In our study, the two most influential parameters were the one characterizing the ability of the tissue to increase collagen production under increased stress and the one characterizing the collagen half-life time. The third most influential parameter was the one characterizing the strain-stiffening of collagen under large deformation. Our results suggest that in future computational studies it may - at least in scenarios similar to the ones studied herein - suffice to use population average values for the other parameters. Moreover, our results suggest that developing methods to measure the said three most influential parameters may be an important step towards reliable patient-specific predictions of the enlargement of abdominal aortic aneurysms in clinical practice.

scholarly journals Gaussian Processes Proxy Model with Latent Variable Models and Variogram-Based Sensitivity Analysis for Assisted History Matching

Energies ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 4290
Author(s):  
Dongmei Zhang ◽  
Yuyang Zhang ◽  
Bohou Jiang ◽  
Xinwei Jiang ◽  
Zhijiang Kang
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Processes ◽  
Latent Variable ◽  
History Matching ◽  
Latent Variable Models ◽  
High Dimensional ◽  
Model Parameters ◽  
Variable Model ◽  
Assisted History Matching ◽  
Proxy Models

Reservoir history matching is a well-known inverse problem for production prediction where enormous uncertain reservoir parameters of a reservoir numerical model are optimized by minimizing the misfit between the simulated and history production data. Gaussian Process (GP) has shown promising performance for assisted history matching due to the efficient nonparametric and nonlinear model with few model parameters to be tuned automatically. Recently introduced Gaussian Processes proxy models and Variogram Analysis of Response Surface-based sensitivity analysis (GP-VARS) uses forward and inverse Gaussian Processes (GP) based proxy models with the VARS-based sensitivity analysis to optimize the high-dimensional reservoir parameters. However, the inverse GP solution (GPIS) in GP-VARS are unsatisfactory especially for enormous reservoir parameters where the mapping from low-dimensional misfits to high-dimensional uncertain reservoir parameters could be poorly modeled by GP. To improve the performance of GP-VARS, in this paper we propose the Gaussian Processes proxy models with Latent Variable Models and VARS-based sensitivity analysis (GPLVM-VARS) where Gaussian Processes Latent Variable Model (GPLVM)-based inverse solution (GPLVMIS) instead of GP-based GPIS is provided with the inputs and outputs of GPIS reversed. The experimental results demonstrate the effectiveness of the proposed GPLVM-VARS in terms of accuracy and complexity. The source code of the proposed GPLVM-VARS is available at https://github.com/XinweiJiang/GPLVM-VARS.

scholarly journals Cost-effectiveness of TAS-102 plus bevacizumab versus TAS-102 monotherapy in patients with metastatic colorectal cancer

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Kiyoaki Sugiura ◽  
Yuki Seo ◽  
Takayuki Takahashi ◽  
Hideyuki Tokura ◽  
Yasuhiro Ito ◽  
...  
Keyword(s):  
Colorectal Cancer ◽  
Health Care ◽  
Sensitivity Analysis ◽  
Cost Effectiveness ◽  
Combination Therapy ◽  
Metastatic Colorectal Cancer ◽  
Cost Effective ◽  
Model Parameters ◽  
Combination Regimen ◽  
The Cost

Abstract Background TAS-102 plus bevacizumab is an anticipated combination regimen for patients who have metastatic colorectal cancer. However, evidence supporting its use for this indication is limited. We compared the cost-effectiveness of TAS-102 plus bevacizumab combination therapy with TAS-102 monotherapy for patients with chemorefractory metastatic colorectal cancer. Method Markov decision modeling using treatment costs, disease-free survival, and overall survival was performed to examine the cost-effectiveness of TAS-102 plus bevacizumab combination therapy and TAS-102 monotherapy. The Japanese health care payer’s perspective was adopted. The outcomes were modeled on the basis of published literature. The incremental cost-effectiveness ratio (ICER) between the two treatment regimens was the primary outcome. Sensitivity analysis was performed and the effect of uncertainty on the model parameters were investigated. Results TAS-102 plus bevacizumab had an ICER of $21,534 per quality-adjusted life-year (QALY) gained compared with TAS-102 monotherapy. Sensitivity analysis demonstrated that TAS-102 monotherapy was more cost-effective than TAS-102 and bevacizumab combination therapy at a willingness-to-pay of under $50,000 per QALY gained. Conclusions TAS-102 and bevacizumab combination therapy is a cost-effective option for patients who have metastatic colorectal cancer in the Japanese health care system.

Sobol′ Sensitivity Analysis Using a Neural Network Model of a LB-LOCA in the ZION Nuclear Power Plant With CATHARE-2 V2.5 Code

2013 ◽  
Author(s):  
Fabrice Fouet ◽  
Pierre Probst
Keyword(s):  
Neural Network ◽  
Sensitivity Analysis ◽  
Nuclear Power ◽  
Uncertainty Propagation ◽  
Correlation Coefficients ◽  
Computer Code ◽  
Numerical Application ◽  
Loss Of Coolant Accident ◽  
Input Parameters ◽  
Artificial Neural Network Ann

In nuclear safety, the Best-Estimate (BE) codes may be used in safety demonstration and licensing, provided that uncertainties are added to the relevant output parameters before comparing them with the acceptance criteria. The uncertainty of output parameters, which comes mainly from the lack of knowledge of the input parameters, is evaluated by estimating the 95% percentile with a high degree of confidence. IRSN, technical support of the French Safety Authority, developed a method of uncertainty propagation. This method has been tested with the BE code used is CATHARE-2 V2.5 in order to evaluate the Peak Cladding Temperature (PCT) of the fuel during a Large Break Loss Of Coolant Accident (LB-LOCA) event, starting from a large number of input parameters. A sensitivity analysis is needed in order to limit the number of input parameters and to quantify the influence of each one on the response variability of the numerical model. Generally, the Global Sensitivity Analysis (GSA) is done with linear correlation coefficients. This paper presents a new approach to perform a more accurate GSA to determine and to classify the main uncertain parameters: the Sobol′ methodology. The GSA requires simulating many sets of parameters to propagate uncertainties correctly, which makes of it a time-consuming approach. Therefore, it is natural to replace the complex computer code by an approximate mathematical model, called response surface or surrogate model. We have tested Artificial Neural Network (ANN) methodology for its construction and the Sobol′ methodology for the GSA. The paper presents a numerical application of the previously described methodology on the ZION reactor, a Westinghouse 4-loop PWR, which has been retained for the BEMUSE international problem [8]. The output is the first maximum PCT of the fuel which depends on 54 input parameters. This application outlined that the methodology could be applied to high-dimensional complex problems.

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