STRUCTURAL UNCERTAINTY IN HYDROLOGICAL MODELS

<p>A hydrological model incurs three types of uncertainties: measurement, structural and parametric uncertainty. Measurement uncertainty exists due to errors in the measurements of rainfall and streamflow data. Structural uncertainty exists due to errors in the mathematical representation of hydrological processes. Parametric uncertainty is a consequence of limited data available to calibrate the model, and measurement and structural uncertainties.</p><p>Recently, separation of structural and measurement uncertainties was identified as one of the twenty-three unsolved problems in hydrology. The information about measurement and structural uncertainties is typically available in the form of residual time-series, that is, the difference between observed and simulated streamflow time-series. The residual time-series, however, provides only an aggregate measure of measurement and structural uncertainties. Thus, the measurement and structural uncertainties are inseparable without additional information. In this study, we used random forest (RF) algorithm to gather additional information about measurement uncertainties using hydrological data across several watersheds. Subsequently, the uncertainty bounds obtained by RF were compared against the uncertainty bounds obtained by two other methods: rating-curve analysis and recently proposed runoff-coefficient method. Rating curve analysis yields uncertainty in streamflow measurements only and the runoff-coefficient yields uncertainty in both rainfall and streamflow measurements. The results of the study are promising in terms of using data across different watersheds for the construction of measurement uncertainty bounds. The preliminary results of this study will be presented in the meeting.</p>

On constructing limits-of-acceptability in watershed hydrology using decision trees

Next generation of Geometrical Product Specifications (GPS) is the foundation of the technology standards and metrology specifications. Estimation of uncertainty in measurement according to next generation of GPS may improve the reliability of the measurement. A method to estimate the uncertainty in spatial straightness measurement is proposed according to the requirements of next generation of GPS standard system. Based on the transparent box model given in next generation of GPS, the calculation method of uncertainty in spatial straightness measurement is deduced. And the decision rule based on the compliance uncertainty is adopted to decide whether the axis can be accepted or not. The experiment indicates that this method may assure the integrity of the verification result and improve the reliability of measurement.

The paper deals with modeling and estimation of uncertainty in measurement of power quality (PQ) characteristics by using a virtual measurement instrument. The described virtual PQ analyzer is comprised of National Instruments (NI) analog input modules, NI data acquisition board, personal computer and software in LabVIEW™. The main sources of uncertainty are identified and evaluated. A Monte Carlo simulation is used for the model estimation and generation of the combined uncertainty of particular characteristics. Experimental measurement and statistical analysis of the results are made and compared with the simulation results. The experimental results have served for a verification of the model and the Monte Carlo simulation results.

Propagation of structural uncertainty in watershed hydrologic models

A statement of measurement uncertainty describes the quality of a clinical assay analysis result, and uncertainty models of clinical assays can be used to evaluate and optimize laboratory protocols designed to minimize the measurement uncertainty associated with an assay. In this study, we propose a methodology to lend systematic structure to the uncertainty modeling process. Clinical laboratory assays are typically classified based on the chemical reaction involved, and therefore, based on the assay analysis methodology. We use this fact to demonstrate that uncertainty models for assays within the same category are structurally identical in all respects except for the values of certain model parameters. This is accomplished by building uncertainty models for assays belonging to two categories--substrate assays based on optical absorbance analysis of endpoint reactions, and ion selective electrode (ISE) assays based on potentiometric measurements of electromotive force. Uncertainty models for the substrate assays and the ISE assays are built, and for each category, a general mathematical framework for the uncertainty model is developed. The parameters of the general framework that vary from assay to assay for each category are identified and listed. Estimates of measurement uncertainty from the models were compared with estimates of uncertainty from quality control data from the clinical laboratory. We demonstrate that building a general modeling framework for each assay category and plugging in parameter values for each assay is sufficient to generate uncertainty models for an assay within a given category.

Background: Estimation of measurement uncertainty (MU) has been extensively addressed in documents from standard authorities. In microbiology, bacterial counts are log transformed to get a more normal distribution. Unfortunately, the difference between using original and log-transformed data appears to not have been investigated even in publications focusing on MU estimation. Method: Statistical formulae inferencing and estimation of MU using real bacterial enumeration datasets. Results: Both mean and SD calculated from original data carry the same scale and unit as the original data. However, the mean of log-transformed data becomes a geometric mean in log, and the SD becomes the logarithm of a ratio. Furthermore, calculation of RSD obtained by dividing the SD by the mean is meaningless and misleading for log-transformed data. The ratio, the antilog of the SD of log-transformed data, copes with multiplicative and divisive relationships to geometric mean (without log), instead of the arithmetic mean. The ratio can be converted to an analog ratio, which is similar or almost identical to the RSD of the untransformed data, especially when the within-subject variation is small. When MU is estimated from multiple samples with different measurands, the calculated RSD of original data is independent of the mean and can be pooled; however, for log-transformed data, the SD can be combined to estimate the common uncertainty. Conclusions: Calculation and use of RSD of log-transformed data are meaningless and misleading. Procedures outlining the estimation and interpretation of MU from log-transformed data require re-evaluation.

Natural gas is a mixture that contains hydrocarbons and other compounds, such as CO2 and N2. Natural gas composition is commonly measured by gas chromatography, and this measurement is important for the calculation of some thermodynamic properties that determine its commercial value. The estimation of uncertainty in chromatographic measurement is essential for an adequate presentation of the results and a necessary tool for supporting decision making. Various approaches have been proposed for the uncertainty estimation in chromatographic measurement. The present work is an evaluation of three approaches of uncertainty estimation, where two of them (guide to the expression of uncertainty in measurement method and prediction method) were compared with the Monte Carlo method, which has a wider scope of application. The aforementioned methods for uncertainty estimation were applied to gas chromatography assays of three different samples of natural gas. The results indicated that the prediction method and the guide to the expression of uncertainty in measurement method (in the simple version used) are not adequate to calculate the uncertainty in chromatography measurement, because uncertainty estimations obtained by those approaches are in general lower than those given by the Monte Carlo method.

Improved Geometrical Product Specifications (GPS) is an internationally accepted standards system. It is the foundation of the technology standards and metrology specifications. Uncertainty is one of the most important concepts in improved GPS. In the improved GPS standards system, uncertainty is used as an economic tool to enable optimum allocation of resources amongst specification, manufacturing and verification. Estimation of uncertainty in measurement according to improved GPS can improve the reliability of the measurement. A method to estimate the uncertainty in straightness measurement is proposed according to the requirements of improved GPS standard system. Based on the mini-zone method and the transparent box model, the calculation equation of uncertainty in straightness measurement is deduced. The experiment indicates that this method may assure the integrity of the verification result and improve the reliability of measurement.

This study explores the decomposition of predictive uncertainty in hydrological modeling into its contributing sources. This is pursued by developing data‐based probability models describing uncertainties in rainfall and runoff data and incorporating them into the Bayesian total error analysis methodology (BATEA). A case study based on the Yzeron catchment (France) and the conceptual rainfall‐runoff model GR4J is presented. It exploits a calibration period where dense rain gauge data are available to characterize the uncertainty in the catchment average rainfall using geostatistical conditional simulation. The inclusion of information about rainfall and runoff data uncertainties overcomes ill‐posedness problems and enables simultaneous estimation of forcing and structural errors as part of the Bayesian inference. This yields more reliable predictions than approaches that ignore or lump different sources of uncertainty in a simplistic way (e.g., standard least squares). It is shown that independently derived data quality estimates are needed to decompose the total uncertainty in the runoff predictions into the individual contributions of rainfall, runoff, and structural errors. In this case study, the total predictive uncertainty appears dominated by structural errors. Although further research is needed to interpret and verify this decomposition, it can provide strategic guidance for investments in environmental data collection and/or modeling improvement. More generally, this study demonstrates the power of the Bayesian paradigm to improve the reliability of environmental modeling using independent estimates of sampling and instrumental data uncertainties.

Standard uncertainty in each measurement result explicit or implicit

The International vocabulary of metrology – Basic and general concepts and associated terms (VIM3, 2.26 measurement uncertainty, JCGM 200:2012) defines uncertainty of measurement as a non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand, based on the information obtained from performing the measurement. Clinical Laboratory Standards Institute (CLSI) has published a very detailed guideline with a description of sources contributing to measurement uncertainty as well as different approaches for the calculation (Expression of measurement uncertainty in laboratory medicine; Approved Guideline, CLSI C51-A 2012). Many other national and international recommendations and original scientific papers about measurement uncertainty estimation have been published. In Croatia, the estimation of measurement uncertainty is obligatory for accredited medical laboratories. However, since national recommendations are currently not available, each of these laboratories uses a different approach in measurement uncertainty estimation. The main purpose of this document is to describe the minimal requirements for measurement uncertainty estimation. In such way, it will contribute to the harmonization of measurement uncertainty estimation, evaluation and reporting across laboratories in Croatia. This recommendation is issued by the joint Working group for uncertainty of measurement of the Croatian Society for Medical Biochemistry and Laboratory Medicine and Croatian Chamber of Medical Biochemists. The document is based mainly on the recommendations of Australasian Association of Clinical Biochemists (AACB) Uncertainty of Measurement Working Group and is intended for all medical biochemistry laboratories in Croatia.

Measurement uncertainty is a qualitative measure of measurand in addition to precision and accuracy. Estimation of uncertainty in measurement is one of the most important characteristics for demonstration of competence for testing and calibration laboratories accredited on ISO/ IEC 17025 standards. To ensure the metrological traceability, to have confidence in measurements and to produce valid results, laboratory must estimate uncertainty from all significant sources. Consequently, measurement uncertainty can have impact on decision rules, statement of conformity and risk associated while making decisions with reference to a standard or specification. This paper presents a concise guideline for estimation of measurement uncertainty for testing and calibration laboratories with focus on electrical whether accredited on ISO/ IEC 17025:2017 standards or planned to be achieve accreditation in future. Non-accredited electrical testing and calibration laboratories may adopt the procedure/ process to enhance acceptability, to ensure confidence in measurement results and as a part of good laboratory practices. Finally, authors presented their way of budgeting measurement uncertainty as an example which is being implemented in electrical testing laboratory.

Uncertainty modelling in measurement represents a crucial task since the final result of a measurement process cannot be expressed by a single value, but by a distribution of values over an interval within which the measurements lie with a given confidence level. A classical Type-1 fuzzy set could be the natural choice for uncertainty model, since a Membership Function (MF) intrinsically embeds the concepts of confidence interval and confidence level. Moreover, from computational aspects, working on fuzzy sets is much more easily than a Montecarlo simulation, that is actually the recommended approach. However, both the approaches need reliable and specific assumptions on the probability distribution of the input variables. So, in many practical cases, a Type-2 fuzzy set is needed in order to overcome this problem. In this paper, we will provide a full description of how a Type-2 MF can be built in order to model the uncertainty of a variable and how to evaluate uncertainty propagation through a generic function. A practical example of this representation will be also provided and compared with a Montecarlo simulation.

Clinicians request a large part of measurements of biological quantities that clinical laboratories perform for diagnostic, prognostic or diseases monitoring purposes. Thus, laboratories need to provide patient’s results as reliable as possible. Metrological concepts like measurement uncertainty and metrological traceability allow to know the accuracy of these results and guarantee their comparability over time and space. Such is the importance of these two parameters that the estimation of measurement uncertainty and the knowledge of metrological traceability is required for clinical laboratories accredited by ISO 15189:2012. Despite there are many publications or guidelines to estimate the measurement uncertainty in clinical laboratories, it is not entirely clear what information and which formulae they should use to calculate it. On the other hand, unfortunately, there are a small number of clinical laboratories that know and describe the metrological traceability of their results, even though they are aware of the lack of comparability that currently exists for patient’s results. Thus, to try to facilitate the task of clinical laboratories, this review aims to provide a proposal to estimate the measurement uncertainty. Also, different suggestions are shown to describe the metrological traceability. Measurement uncertainty estimation is partially based on the ISO/TS 20914:2019 guideline, and the metrological traceability described using the ISO 17511:2020. Different biological quantities routinely measured in clinical laboratories are used to exemplify the proposal and suggestions.