scholarly journals Distribution-Based Calibration of a Stormwater Quality Model

Water ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 1027 ◽  
Author(s):  
Dominik Leutnant ◽  
Dirk Muschalla ◽  
Mathias Uhl
Keyword(s):  
Goodness Of Fit ◽  
Experimental Models ◽  
Model Parameters ◽  
Calibration Data ◽  
Stormwater Quality ◽  
Quality Model ◽  
Test Statistic ◽  
Quality Models ◽  
Parking Lot ◽  
Flat Roof

Stormwater quality models are usually calibrated using observed pollutographs. As current models still rely on simplified model concepts for pollutant accumulation and wash-off, calibration results for continuous pollutant concentrations are highly uncertain. In this paper, we introduce an innovative calibration approach based on total suspended solids (TSS) event load distribution. The approach is applied on stormwater quality models for a flat roof and a parking lot for which reliable distributions are available. Exponential functions are employed for both TSS buildup and wash-off. Model parameters are calibrated by means of an evolutionary algorithm to minimize the distance between a parameterized lognormal distribution function and the cumulated distribution of simulated TSS event loads. Since TSS event load characteristics are probabilistically considered, the approach especially respects the stochasticity of TSS buildup and wash-off and, therefore, improves conventional stormwater quality calibration concepts. The results show that both experimental models were calibrated with high goodness-of-fit (Kolmogorov–Smirnov test statistic: 0.05). However, it is shown that events with high TSS event loads (>0.8 percentile) are generally underestimated. While this leads to a relative deviation of −28% of total TSS loads for the parking lot, the error is compensated for the flat roof (+5%). Calibrated model parameters generally tend to generate wash-off proportional to runoff, which is indicated by mass-volume curves. The approach itself is, in general, applicable and creates a new opportunity to calibrate stormwater quality models especially when calibration data is limited.

Stormwater quality models: sensitivity to calibration data

2005 ◽  
Vol 52 (5) ◽  
pp. 61-68 ◽  
Author(s):  
M. Mourad ◽  
J.-L. Bertrand-Krajewski ◽  
G. Chebbo
Keyword(s):  
Suspended Solids ◽  
Calibration Data ◽  
Stormwater Quality ◽  
Local Data ◽  
Sewer System ◽  
Error Sources ◽  
Quality Models ◽  
Sewer Systems ◽  
Complex Models

Stormwater quality modelling is a useful tool in sewer systems management. Available models range from simple to detailed complex ones. The models need local data to be calibrated. In practice, calibration data are rather lacking. Only few measured events are commonly used. In this paper, the effect of the number and the variability of calibration data on models of various levels of complexity are investigated. The study is carried out on “Le Marais” catchment for suspended solids where 40 reliable measured events and good knowledge of the sewer system are available. The method used is based on resampling subsets of measured events among the 40 available ones. Three types of models were calibrated using subsets of events of different sizes and characteristics resampled among the 40 available ones. For each calibration, the model was validated against the remaining events to stand upon the quality of the model. It was found that the models are quite sensitive to calibration data, a problem neglected in practical studies. The use of more complex models does not necessarily improve modelling results since more problems and error sources are to be expected. The findings are specific to “Le Marais” catchment and the models used.

Stormwater quality modelling in combined sewers: calibration and uncertainty analysis

2005 ◽  
Vol 52 (3) ◽  
pp. 63-71 ◽  
Author(s):  
A. Kanso ◽  
G. Chebbo ◽  
B. Tassin
Keyword(s):  
Uncertainty Analysis ◽  
Initial Conditions ◽  
Storm Water ◽  
Stormwater Quality ◽  
Quality Model ◽  
Predictive Capacity ◽  
Large Variability ◽  
Quality Models ◽  
Markov Chain Method ◽  
Urban Stormwater Quality

Estimating the level of uncertainty in urban stormwater quality models is vital for their utilization. This paper presents the results of application of a Monte Carlo Markov Chain method based on the Bayesian theory for the calibration and uncertainty analysis of a storm water quality model commonly used in available software. The tested model uses a hydrologic/hydrodynamic scheme to estimate the accumulation, the erosion and the transport of pollutants on surfaces and in sewers. It was calibrated for four different initial conditions of in-sewer deposits. Calibration results showed large variability in the model's responses in function of the initial conditions. They demonstrated that the model's predictive capacity is very low.

River Quality Models for Consent Setting in England and Wales

1989 ◽  
Vol 21 (8-9) ◽  
pp. 1015-1024 ◽  
Author(s):  
C. P. Crockett ◽  
R. W. Crabtree ◽  
I. D. Cluckie
Keyword(s):  
River System ◽  
Quality Model ◽  
Catchment Scale ◽  
Quality Models ◽  
England And Wales ◽  
Future Developments ◽  
Statistical Framework ◽  
River Quality ◽  
National Approach

In England and Wales the placing of effluent discharge consents within a statistical framework has led to the development of a new hybrid type of river quality model. Such catchment scale consent models have a stochastic component for the generation of model inputs and a deterministic component to route them through the river system. This paper reviews and compares the existing approaches for consent modelling used by various Water Authorities. A number of possible future developments are suggested including the potential need for a national approach to the review and setting of long term consents.

Preliminary uncertainty analysis – a prerequisite for assessing the predictive uncertainty of hydrologic models

1996 ◽  
Vol 33 (2) ◽  
pp. 79-90 ◽  
Author(s):  
Jian Hua Lei ◽  
Wolfgang Schilling
Keyword(s):  
Uncertainty Analysis ◽  
Model Parameters ◽  
Observation Data ◽  
Calibration Data ◽  
Model Output ◽  
Predictive Uncertainty ◽  
Runoff Volume ◽  
Output Uncertainty ◽  
Sensitive Parameters ◽  
Calculated Model

Physically-based urban rainfall-runoff models are mostly applied without parameter calibration. Given some preliminary estimates of the uncertainty of the model parameters the associated model output uncertainty can be calculated. Monte-Carlo simulation followed by multi-linear regression is used for this analysis. The calculated model output uncertainty can be compared to the uncertainty estimated by comparing model output and observed data. Based on this comparison systematic or spurious errors can be detected in the observation data, the validity of the model structure can be confirmed, and the most sensitive parameters can be identified. If the calculated model output uncertainty is unacceptably large the most sensitive parameters should be calibrated to reduce the uncertainty. Observation data for which systematic and/or spurious errors have been detected should be discarded from the calibration data. This procedure is referred to as preliminary uncertainty analysis; it is illustrated with an example. The HYSTEM program is applied to predict the runoff volume from an experimental catchment with a total area of 68 ha and an impervious area of 20 ha. Based on the preliminary uncertainty analysis, for 7 of 10 events the measured runoff volume is within the calculated uncertainty range, i.e. less than or equal to the calculated model predictive uncertainty. The remaining 3 events include most likely systematic or spurious errors in the observation data (either in the rainfall or the runoff measurements). These events are then discarded from further analysis. After calibrating the model the predictive uncertainty of the model is estimated.

scholarly journals Copula-based software metrics aggregation

2021 ◽  
Author(s):  
Maria Ulan ◽  
Welf Löwe ◽  
Morgan Ericsson ◽  
Anna Wingkvist
Keyword(s):  
Open Source Software ◽  
Software Metrics ◽  
Information Quality ◽  
Empirical Studies ◽  
Probabilistic Approach ◽  
Software Systems ◽  
Quality Model ◽  
Quality Models ◽  
Joint Distributions ◽  
Abstract Notion

AbstractA quality model is a conceptual decomposition of an abstract notion of quality into relevant, possibly conflicting characteristics and further into measurable metrics. For quality assessment and decision making, metrics values are aggregated to characteristics and ultimately to quality scores. Aggregation has often been problematic as quality models do not provide the semantics of aggregation. This makes it hard to formally reason about metrics, characteristics, and quality. We argue that aggregation needs to be interpretable and mathematically well defined in order to assess, to compare, and to improve quality. To address this challenge, we propose a probabilistic approach to aggregation and define quality scores based on joint distributions of absolute metrics values. To evaluate the proposed approach and its implementation under realistic conditions, we conduct empirical studies on bug prediction of ca. 5000 software classes, maintainability of ca. 15000 open-source software systems, and on the information quality of ca. 100000 real-world technical documents. We found that our approach is feasible, accurate, and scalable in performance.

scholarly journals A Hypothesis Test for the Goodness-of-Fit of the Marginal Distribution of a Time Series with Application to Stablecoin Data

2021 ◽  
Vol 5 (1) ◽  
pp. 10
Author(s):  
Mark Levene
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Marginal Distribution ◽  
Hypothesis Test ◽  
Data Sets ◽  
Test Statistic ◽  
Sample Test ◽  
Kolmogorov Smirnov ◽  
Heavy Tailed ◽  
Jensen Shannon Divergence

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (ESJS) and the Kolmogorov–Smirnov two-sample test statistic (KS2), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed α-stable distributions with 1<α<2 at the 95% confidence level. Moreover, ESJS is more powerful than KS2 on these data sets, since the widths of the derived confidence intervals for KS2 are, proportionately, much larger than those of ESJS.

scholarly journals Relative Performance of 1-D Versus 3-D Hydrodynamic, Water-Quality Models for Predicting Water Temperature and Oxygen in a Shallow, Eutrophic, Managed Reservoir

Water ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 88
Author(s):  
Xiamei Man ◽  
Chengwang Lei ◽  
Cayelan C. Carey ◽  
John C. Little
Keyword(s):  
Water Quality ◽  
Water Temperature ◽  
Water Quality Model ◽  
Relative Performance ◽  
Bubble Plume ◽  
Quality Model ◽  
Quality Models ◽  
Management Interventions ◽  
Water Quality Models ◽  
D Model

Many researchers use one-dimensional (1-D) and three-dimensional (3-D) coupled hydrodynamic and water-quality models to simulate water quality dynamics, but direct comparison of their relative performance is rare. Such comparisons may quantify their relative advantages, which can inform best practices. In this study, we compare two 1-year simulations in a shallow, eutrophic, managed reservoir using a community-developed 1-D model and a 3-D model coupled with the same water-quality model library based on multiple evaluation criteria. In addition, a verified bubble plume model is coupled with the 1-D and 3-D models to simulate the water temperature in four epilimnion mixing periods to further quantify the relative performance of the 1-D and 3-D models. Based on the present investigation, adopting a 1-D water-quality model to calibrate a 3-D model is time-efficient and can produce reasonable results; 3-D models are recommended for simulating thermal stratification and management interventions, whereas 1-D models may be more appropriate for simpler model setups, especially if field data needed for 3-D modeling are lacking.

scholarly journals Construction of a quality model for machine learning systems

2021 ◽  
Author(s):  
Julien Siebert ◽  
Lisa Joeckel ◽  
Jens Heidrich ◽  
Adam Trendowicz ◽  
Koji Nakamichi ◽  
...  
Keyword(s):  
Machine Learning ◽  
Lessons Learned ◽  
Training Data ◽  
Use Case ◽  
Construction Process ◽  
Quality Model ◽  
Quality Models ◽  
Quality Properties ◽  
Reference Quality ◽  
Industrial Use

AbstractNowadays, systems containing components based on machine learning (ML) methods are becoming more widespread. In order to ensure the intended behavior of a software system, there are standards that define necessary qualities of the system and its components (such as ISO/IEC 25010). Due to the different nature of ML, we have to re-interpret existing qualities for ML systems or add new ones (such as trustworthiness). We have to be very precise about which quality property is relevant for which entity of interest (such as completeness of training data or correctness of trained model), and how to objectively evaluate adherence to quality requirements. In this article, we present how to systematically construct quality models for ML systems based on an industrial use case. This quality model enables practitioners to specify and assess qualities for ML systems objectively. In addition to the overall construction process described, the main outcomes include a meta-model for specifying quality models for ML systems, reference elements regarding relevant views, entities, quality properties, and measures for ML systems based on existing research, an example instantiation of a quality model for a concrete industrial use case, and lessons learned from applying the construction process. We found that it is crucial to follow a systematic process in order to come up with measurable quality properties that can be evaluated in practice. In the future, we want to learn how the term quality differs between different types of ML systems and come up with reference quality models for evaluating qualities of ML systems.

A test for fuzzy exponentiality based on Kullback-Leibler information

2021 ◽  
pp. 1-8
Author(s):  
Lingtao Kong
Keyword(s):  
Biological Sciences ◽  
Monte Carlo ◽  
Goodness Of Fit ◽  
Experimental Studies ◽  
Real Data ◽  
Test Statistics ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Higher Power ◽  
Leibler Information

The exponential distribution has been widely used in engineering, social and biological sciences. In this paper, we propose a new goodness-of-fit test for fuzzy exponentiality using α-pessimistic value. The test statistics is established based on Kullback-Leibler information. By using Monte Carlo method, we obtain the empirical critical points of the test statistic at four different significant levels. To evaluate the performance of the proposed test, we compare it with four commonly used tests through some simulations. Experimental studies show that the proposed test has higher power than other tests in most cases. In particular, for the uniform and linear failure rate alternatives, our method has the best performance. A real data example is investigated to show the application of our test.

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