Use Of Uncertainty Analysis Research Articles

Uncertainty quantification in the techno-economic analysis of emission reduction technologies: a tutorial case study on CO2 mineralization

The pathways toward net-zero greenhouse gas emissions by 2050 should be designed based on solid scientific evidence. Ex ante system analysis tools, such as techno-economic assessments (TEAs), are key instruments to guide decision-makers. As ex ante TEAs of CO2 mitigation technologies embody a high level of uncertainty, the informed use of uncertainty analysis becomes crucial for meaningful interpretation and communication of TEA outputs. To foster enhanced appreciation and the use of uncertainty analysis, we compare multiple uncertainty analysis methods for ex ante TEAs, using a case study on CO2 mineralization in the cement industry. We show that local sensitivity analysis tools such as one-way analysis, which are most often used by TEA practitioners, may not suffice for deriving reliable conclusions and provide guidance on how to apply global sensitivity analysis methods, such as variance-based indicators for TEAs in this field.

Sensitivity analysis for transit equilibrium assignment and applications to uncertainty analysis

Systematic uncertainty analysis can be used to quantitatively evaluate variation in model outputs and identify the critical sources of uncertainty to improve the reliability and stability of a system. To analyze the effects of uncertainties in transit networks that may be caused by probabilistic travel demand, congestion, or vehicle frequencies, this study develops a sensitivity-based uncertainty analysis approach as a post-analysis tool for equilibrium transit systems. The congestion effect is considered in the waiting time and in-vehicle travel time of a passengers’ route-choice model. The hyperpath concept is used to manage passengers’ riding strategies due to the common-line problem at transit stops. A hyperpath-based gradient projection (GP) solution algorithm is developed for the solution of the variational inequality formulation of the transit equilibrium assignment problem (TEAP). A restricted sensitivity analysis approach originally developed for road networks is re-developed for the TEAP in transit networks. An analytical sensitivity-based approach is derived to conduct uncertainty analysis for the TEAP, which enables the simultaneous propagation of uncertainties from different input sources to the model outputs. Numerical examples are provided for the following purposes. (1) To demonstrate three applications of the sensitivity analysis of the TEAP, namely the perturbed solution estimation problem, the critical parameter identification problem, and the paradox analysis problem. (2) To illustrate the use of uncertainty analysis of the TEAP, such as estimating the variance and confidence level of model outputs with respect to various model inputs/parameters as random variables, and ranking the importance of arcs using sensitivity-based uncertainty analysis. (3) To demonstrate the applicability of the proposed approach to real transit networks. The findings demonstrate not only the importance of the analytical sensitivity analysis development for the TEAP, but also for the practical applications of sensitivity and uncertainty analyses.

Toward Improved Guidelines for Uncertainty Analysis of Carbon Capture and Storage Techno-economic Studies

Uncertainty analysis is a key element of sound techno-economic analysis (TEA) of CO2 capture and storage (CCS) technologies and systems, and in the communication of TEA results. Many CCS technologies are novel concepts, that are still in the early (pre-commercial) stages of development. Therefore, uncertainties in their technology performance and cost are often substantial, making it imperative that they be characterized, and their impacts reported. Although uncertainty analysis itself is not novel, with some methods already frequently used by the CCS TEA community, a document that provides a comprehensive overview of methods and approaches, as well as guidance on their selection and use, is still lacking. Given its importance, we seek to fill this gap by providing a critical review of uncertainty analysis methods along with guidance on the selection and use of these methods for CCS TEAs, highlighting good practice and examples from the CCS literature. There are many opportunities to bring the use of uncertainty analysis to a higher level than currently practiced. This review of and guidance on available methods is intended to help accelerate continued methods development and their application to more robust and meaningful CCS performance and cost studies.

Consideration of Uncertainties in Analyzing Nuclear Power Facilities’ Fire Hazard

Paying increased attention to the safety of nuclear power facilities is a key element for their further development. An approach to analyzing their fire safety with due regard to the uncertainty factors associated with the parameters of applied models and with the fire breakout and development conditions is presented. The two-zone fire modeling code that takes into account the specific features of transportable (floating) nuclear power plants is used, and its basic characteristics are given. An original approach to a dynamic probabilistic safety assessment is applied, which is based on a global optimum search algorithm. This algorithm is used in this study for taking into account the uncertainties associated with combustion models, possible human actions, and change in the equipment’s operation modes. The proposed method incorporates a genetic algorithm for searching the global optimum, the main purpose of which is to find the most hazardous fire development scenarios in accordance with adaptive variation of parameters within their uncertainty boundaries. Application of the method is demonstrated for two versions of fire breakout in the process rooms of a transportable power unit equipped with a nuclear power installation. The basic parameters of the two-zone fire model and dynamic probabilistic safety assessment are given. The results of computations for the dynamic probabilistic safety assessment demonstrate the complex nature of interaction among different processes. The data from analyzing the influence of the main parameters are given, a comparison with the standard calculation version and with the use of uncertainty analysis is carried out, and the conditional probability of the worst scenario is estimated. Owing to the consideration of uncertainties and the search for the most dangerous scenarios, it became possible to establish the fire development scenarios that can lead to essentially more severe consequences than those determined in using the standard parameters of two-zone fire models.

Uncertainty analysis in the techno-economic assessment of CO2 capture and storage technologies. Critical review and guidelines for use

Uncertainty analysis is a key element of sound techno-economic analysis (TEA) of CO2 Capture and Storage (CCS) technologies and systems, and in the communication of TEA results. Many CCS technologies are relatively novel, with only few large-scale projects constructed and in operation to date. Therefore, uncertainties in technology performance and costs are often substantial, making it imperative that they be characterized and reported. Although uncertainty analysis itself is not novel, with some methods already frequently used by the CCS TEA community, a document that provides a comprehensive overview of methods and approaches, as well as guidance on their selection and use, is still lacking. Given its importance, we seek to fill this gap by providing a critical review of uncertainty analysis methods along with guidance on the selection and use of these methods for CCS TEAs, highlighting good practice and examples from the CCS literature. The paper starts by identifying the different audiences for CCS TEAs, the different modelling approaches available for CCS technology performance and cost analysis, and the different roles that uncertainty analysis may play. It then continues to discuss established, as well as emerging, uncertainty analysis methods and addresses how and when each method is best used, as well as common pitfalls. We argue that the most commonly used method of one-parameter-at-a-time ‘local’ sensitivity analysis may often be a suboptimal choice, and that other approaches may be more suitable or lead to more insight, especially since uncertainty analysis software is becoming more widespread and easier to use. Finally, the paper discusses the benefits of advanced uses of uncertainty analysis in, for instance, the design of CCS experiments or in the design and planning of CCS infrastructure. Sound uncertainty analysis has an important role to play in TEAs of CCS technologies and systems, and there are many opportunities to bring the use of uncertainty analysis to a higher level than currently practiced. This review of and guidance on available methods is intended to help accelerate continued methods development and their application to more robust and meaningful CCS performance and costing studies.

Data Quality Assessment of the Uncertainty Analysis Applied to the Greenhouse Gas Emissions of a Dairy Cow System

The results of an uncertainty analysis are achieved by the statistical information (standard error, type of probability distributions, and range of minimum and maximum) of the selected input parameters. However, there are limitations in identifying sufficient data samples for the selected input parameters for statistical information in the field of life cycle assessment (LCA). Therefore, there is a strong need for a consistent screening procedure to identify the input parameters for use in uncertainty analysis in the area of LCA. The conventional procedure for identifying input parameters for the uncertainty analysis method includes assessing the data quality using the pedigree method and the contribution analysis of the LCA results. This paper proposes a simplified procedure for ameliorating the existing data quality assessment method, which can lead to an efficient uncertainly analysis of LCA results. The proposed method has two salient features: (i) a simplified procedure based on contribution analysis followed by a data quality assessment for selecting the input parameters for the uncertainty analysis; and (ii) a quantitative data quality assessment method is proposed, based on the pedigree method, that adopts the analytic hierarchy process (AHP) method and quality function deployment (QFD). The effects of the uncertainty of the selected input parameters on the LCA results were assessed using the Monte Carlo simulation method. A case study of greenhouse gas (GHG) emissions from a dairy cow system was used to demonstrate the applicability of the proposed procedure.

Review: Current and emerging methods for catchment-scale modelling of recharge and evapotranspiration from shallow groundwater

A review is provided of the current and emerging methods for modelling catchment-scale recharge and evapotranspiration (ET) in shallow groundwater systems. With increasing availability of data, such as remotely sensed reflectance and land-surface temperature data, it is now possible to model groundwater recharge and ET with more physically realistic complexity and greater levels of confidence. The conceptual representation of recharge and ET in groundwater models is critical in areas with shallow groundwater. The depth dependence of recharge and vegetation water-use feedback requires additional calibration to fluxes as well as heads. Explicit definition of gross recharge vs. net recharge, and groundwater ET vs. unsaturated zone ET, in preparing model inputs and reporting model results is necessary to avoid double accounting in the water balance. Methods for modelling recharge and ET include (1) use of simple surface boundary conditions for groundwater flow models, (2) coupling saturated groundwater models with one-dimensional unsaturated-zone models, and (3) more complex fully-coupled surface-unsaturated-saturated conceptualisations. Model emulation provides a means for including complex model behaviours with lower computational effort. A precise ET surface input is essential for accurate model outputs, and the model conceptualisation depends on the spatial and temporal scales under investigation. Using remote sensing information for recharge and ET inputs in model calibration or in model–data fusion is an area for future research development. Improved use of uncertainty analysis to provide probability bounds for groundwater model outputs, understanding model sensitivity and parameter dependence, and guidance for further field-data acquisition are also areas for future research.

Uncertainty analysis as essential step in the establishment of the dynamic Design Space of primary drying during freeze-drying

Large molecules, such as biopharmaceuticals, are considered the key driver of growth for the pharmaceutical industry. Freeze-drying is the preferred way to stabilise these products when needed. However, it is an expensive, inefficient, time- and energy-consuming process. During freeze-drying, there are only two main process variables to be set, i.e. the shelf temperature and the chamber pressure, however preferably in a dynamic way. This manuscript focuses on the essential use of uncertainty analysis for the determination and experimental verification of the dynamic primary drying Design Space for pharmaceutical freeze-drying. Traditionally, the chamber pressure and shelf temperature are kept constant during primary drying, leading to less optimal process conditions. In this paper it is demonstrated how a mechanistic model of the primary drying step gives the opportunity to determine the optimal dynamic values for both process variables during processing, resulting in a dynamic Design Space with a well-known risk of failure. This allows running the primary drying process step as time efficient as possible, hereby guaranteeing that the temperature at the sublimation front does not exceed the collapse temperature. The Design Space is the multidimensional combination and interaction of input variables and process parameters leading to the expected product specifications with a controlled (i.e., high) probability. Therefore, inclusion of parameter uncertainty is an essential part in the definition of the Design Space, although it is often neglected. To quantitatively assess the inherent uncertainty on the parameters of the mechanistic model, an uncertainty analysis was performed to establish the borders of the dynamic Design Space, i.e. a time-varying shelf temperature and chamber pressure, associated with a specific risk of failure. A risk of failure acceptance level of 0.01%, i.e. a ‘zero-failure’ situation, results in an increased primary drying process time compared to the deterministic dynamic Design Space; however, the risk of failure is under control. Experimental verification revealed that only a risk of failure acceptance level of 0.01% yielded a guaranteed zero-defect quality end-product. The computed process settings with a risk of failure acceptance level of 0.01% resulted in a decrease of more than half of the primary drying time in comparison with a regular, conservative cycle with fixed settings.

Application of the generalized likelihood uncertainty estimation (GLUE) approach for assessing uncertainty in hydrological models: a review

The generalized likelihood uncertainty estimation (GLUE) technique is an innovative uncertainty method that is often employed with environmental simulation models. Over the past years, hydrological literature has seen a large increase in the number of papers dealing with uncertainty. There are now a lot of citations to their original paper which illustrates GLUE tremendous impact. GLUE’s popularity can be attributed to its simplicity and its applicability to nonlinear systems, including those for which a unique calibration is not apparent. The GLUE was introduced for use in uncertainty analysis of watershed models has now been extended well beyond rainfall-runoff watershed models. Given the widespread adoption of GLUE analyses for a broad range or problems, it is appropriate that the validity of the approach be examined with care. In this article, we present an overview of the application of GLUE for assessing uncertainty distribution in hydrological models particularly surface and subsurface hydrology and briefly describe algorithms for sampling of the prior parameter in hydrologic simulation models.

A stochastic recovery model of influenza pandemic effects on interdependent workforce systems.

Outbreaks of infectious diseases, such as pandemics, can result in adverse consequences and major economic losses across various economic sectors. Based on findings from the 2009 A H1N1 pandemic in the National Capital Region (NCR), this paper presents a recovery analysis for workforce disruptions using economic input–output modeling. The model formulation takes into consideration the dynamic interdependencies across sectors in an economic system in addition to the inherent characteristics of the economic sectors. From a macroeconomic perspective, the risk of the influenza disaster can be modeled using two risk metrics. First, there is the level of inoperability, which represents the percentage difference between the ideal production level and the degraded production level. Second, the economic loss metric represents the financial value associated with the reduced output. The contribution of this work revolves around the modeling of uncertainties triggered by new perturbations to interdependent economic sectors within an influenza pandemic timeline. We model the level of inoperability of economic sectors throughout their recovery horizon from the initial outbreak of the disaster using a dynamic model. Moreover, we use the level of inoperability values to quantify the cumulative economic losses incurred by the sectors within the recovery horizon. Finally, we revisit the 2009 NCR pandemic scenario to demonstrate the use of uncertainty analysis in modeling the inoperability and economic loss behaviors due to time-varying perturbations and their associated ripple effects to interdependent economic sectors.

Exploring HVAC system sizing under uncertainty

In current practice, HVAC systems are sized based on standardized procedures that were mostly developed by ASHRAE. The standard approach only implicitly deals with uncertainty in peak system demand through the selection of an appropriate design day and the choice of a safety factor. Although this method works satisfactorily in most cases, it offers no support to a system designer who wants to track the risk associated with an undersized system. The opposite, i.e. avoiding that the system is needlessly oversized deserves even more attention given the fact that current practice of “defensive sizing” leads to oversized systems which leads to wasted capital investment and systems that operate far away from the optimum efficiency loads. This paper explores a new framework to guide the use of uncertainty analysis (UA) and sensitivity analysis (SA) in HVAC system sizing. UA will replace the safety factor with quantified margins based on comprehensive quantification of different sources of uncertainty. A probabilistic-based SA is then used to identify the important individual factors or groups of factors that contribute to uncertainty, providing means of risk management by applying better quality assurance methods or negotiating performance contracts.

Use of Uncertainty Analysis to Quantify the Impact of Measurement Error on an Estimate of Effect for Occupational Exposure to Tcdd-Contaminated Chemicals and Ischemic Heart Disease

Introduction Over the last few years novel advances in epidemiologic methods have refocused attention on causal relationships between exposure and disease, renouncing simple associations that often lack quantitative adjustment for study imperfections. Probabilistic uncertainty analysis is a mathematical technique for assessing how systematic error may affect study results. 1-7 Commonly employed in the fields of engineering and policy and risk analysis, 8-9 this method has not yet become established in epidemiology and has never been applied to dioxin research. Here, the impact of exposure and disease misclassification on the odds ratio (OR) for ischemic heart disease (IHD) mortality in a cohort of trichlorophenol (TCP) workers exposed to 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) is quantified using probabilistic uncertainty analysis to illustrate how this innovative method can be utilized in epidemiological dioxin studies.

Bearing Thermal Conductance Measurement Test Method and Experimental Design

Abstract Bearings are used in a number of spacecraft applications, ranging from minimal motion devices, such as pointing mechanisms, to high-speed components, such as control moment gyroscopes and reaction and momentum wheels. Terrestrial applications include pumps, axles, and tooling. Heat-transfer modes for rotational systems in a vacuum environment differ from their terrestrial counterpart. In space, with the absence of air, heat transfer consists of radiation from the rotating system and conductance through the bearings themselves. Depending on the application, conductance could dominate the effects on bearing temperatures and thermal gradients. Accurate thermal predictions are important because they can drive life and performance requirements. To accurately predict bearing temperatures, basic bearing thermal conductance data was needed. However, bearing thermal conductance tends to be the most significant unknown in a rotational system in the space environment. To address this shortcoming, this paper explores a new vacuum test rig designed to measure bearing conductance under simulated operational conditions. Experimental variables include control of the bearing rotational speed, applied axial load, and average bearing temperature and temperature gradient via an applied heat source/heat sink mechanism. All tests are conducted in vacuum. The experimental variables studied herein allowed parametric studies to be conducted under controlled thermal and mechanical conditions, permitting the exploration of the influences of those operational variables on bearing thermal conductance. This paper will describe the test method, the use of uncertainty analysis to design the experiment, and a verification study.

Generalized Diagonal Band Copulas with Two-Sided Generating Densities

Copulas are joint continuous distributions with uniform marginals and have been proposed to capture probabilistic dependence between random variables. Maximum-entropy copulas introduced by Bedford and Meeuwissen (Bedford, T., A. M. H. Meeuwissen. 1997. Minimally informative distributions with given rank correlations for use in uncertainty analysis. J. Statist. Comput. Simulation 57(1–4) 143–175) provide the option of making minimally informative assumptions given a degree-of-dependence constraint between two random variables. Unfortunately, their distribution functions are not available in a closed form, and their application requires the use of numerical methods. In this paper, we study a subfamily of generalized diagonal band (GDB) copulas, separately introduced by Ferguson (Ferguson, T. F. 1995. A class of symmetric bivariate uniform distributions. Statist. Papers 36(1) 31–40) and Bojarski (Bojarski, J. 2001. A new class of band copulas—Distributions with uniform marginals. Technical report, Institute of Mathematics, Technical University of Zielona Góra, Zielona Góra, Poland). Similar to Archimedean copulas, GDB copula construction requires a generator function. Bojarski's GDB copula generator functions are symmetric probability density functions. In this paper, symmetric members of a two-sided framework of distributions introduced by van Dorp and Kotz (van Dorp, J. R., S. Kotz. 2003. Generalizations of two-sided power distributions and their convolution. Comm. Statist.: Theory and Methods 32(9) 1703–1723) shall be considered. This flexible setup allows for derivations of GDB copula properties resulting in novel convenient expressions. A straightforward elicitation procedure for the GDB copula dependence parameter is proposed. Closed-form expressions for specific examples in the subfamily of GDB copulas are presented, which enhance their transparency and facilitate their application. These examples closely approximate the entropy of maximum-entropy copulas. Application of GDB copulas is illustrated via a value-of-information decision analysis example.

The use of uncertainty analysis as a food waste estimation tool

Food waste going to landfill is a significant environmental issue with 33% of all food we buy simply being thrown away. Not only is this extremely wasteful but rotting food produces gases that are harmful to the environment and contributes to global warming. The UK government is committed to reducing the amount of household waste directly being disposed of at landfills by 10.1 million tonnes over 20 years from 2000 (Waste Composition Analysis: Guidance for Local Authorities, Defra, 2004). As part of this the Waste Reduction Action Programme was set up to fund and facilitate innovative solutions to reduce waste to landfill. Part of that process was to assess bids by solution providers with regards the effectiveness of the technologies that they were offering. This was found to be a non-trivial task, with multiple input parameters and large variations in data. Establishing which parameters have the greatest effect on food waste estimation was therefore essential in any decision-making process. However, the large number of unknowns, assumptions and parameters makes this understanding both difficult and time consuming. A branch of mathematics known as uncertainty analysis can be used to analyse these types of situations quickly and effectively and is easily adapted to understanding of food waste estimation. This paper outlines the techniques used to develop an internet-based decision-making tool and demonstrates the methodology used with simple case studies.

Intensity modulated proton therapy and its sensitivity to treatment uncertainties 1: the potential effects of calculational uncertainties

The effects of calculational uncertainties on 3D and distal edge tracking (DET) intensity modulated proton therapy (IMPT) treatment plans have been investigated. Dose calculation uncertainties have been assessed by comparing analytical and Monte Carlo dose calculations, and potential range uncertainties by recalculating plans with all CT values modified by ±3%. Analysis of the volume of PTV agreeing to within ±3% between the two calculations shows that the 3D approach provides significantly improved agreement (87.1 versus 80.3% of points for the 3D and DET approaches, respectively). For the DET approach, doses in the CTV have also been found to globally change by 5% as a result of 3% changes in CT value. When varying the intra-field gradients of the plans a similar trend is seen, but with the more complex plans also being found to be more sensitive to both uncertainties. In conclusion, the DET approach has been found to be relatively sensitive to the calculational errors investigated here. In contrast, the 3D approach appears to be quite robust, unless strong internal gradients are present. Nevertheless, the routine use of uncertainty analysis is advised when assessing all forms of IMPT plans.

Improving model structure and reducing parameter uncertainty in conceptual water balance models through the use of auxiliary data

The use of uncertainty analysis is gaining considerable attention in catchment hydrological modeling. In particular, the choice of appropriate model structure, identifiability of parameter values, and the reduction of model predictive uncertainty are deemed as essential elements of hydrological modeling. The chosen model structure must be parsimonious, and the parameters used must either be derivable from field‐measured data or inferred unambiguously from analysis of catchment response data. In this paper, a long‐term water balance model for the Susannah Brook catchment in Western Australia has been pursued using the “downward approach,” which is a systematic approach to determine the model with the minimum level of complexity, with parameter values that, in theory, are derivable from existing physiographic data relating to the catchment. Through analysis of rainfall‐runoff response at three different timescales and exploring the climate, soil, and vegetation controls on the water balance response at these timescales, an initial model structure was formulated, and a priori model parameter values were estimated. Further investigation with the use of auxiliary data such as deuterium concentration in the streamflow exposed inadequacies in the chosen model structure. Two more model structures were then proposed and investigated through formulating alternative hypotheses regarding the underlying causes of observed variability, including those suggested by observed deuterium composition in the streamflows and observed groundwater level dynamics. Along the way, the resulting models were systematically evaluated in three dimensions: ability to reproduce observations, predictive uncertainty, and physical realism. The final model, which included an efficient but detailed representation of unsaturated zone time delay, was found to be superior on all three counts, i.e., improved performance, reduced predictive uncertainty, and improved physical realism. These improvements can be directly attributed to the use of the auxiliary data (deuterium composition and groundwater level dynamics), which identified weaknesses in previous model structures, and the multiple wetting front model of water movement in the unsaturated zone, which captured more effectively the time delay in the unsaturated zone.

Determination of uncertainty in parameters extracted from single spectroscopic measurements

The ability to quantify uncertainty in information extracted from spectroscopic measurements is important in numerous fields. The traditional approach of repetitive measurements may be impractical or impossible in some measurements scenarios, while chi-squared analysis does not provide insight into the sources of uncertainty. As such, a need exists for analytical expressions for estimating uncertainty and, by extension, minimum detectable concentrations or diagnostic parameters, that can be applied to a single noisy measurement. This work builds on established concepts from estimation theory, such as the Cramer-Rao lower bound on estimator covariance, to present an analytical formula for estimating uncertainty expressed as a simple function of measurement noise, signal strength, and spectral overlap. This formalism can be used to evaluate and improve instrument performance, particularly important for rapid-acquisition biomedical spectroscopy systems. We demonstrate the experimental utility of this expression in assessing concentration uncertainties from spectral measurements of aqueous solutions and diagnostic parameter uncertainties extracted from spectral measurements of human artery tissue. The measured uncertainty, calculated from many independent measurements, is found to be in good agreement with the analytical formula applied to a single spectrum. These results are intended to encourage the widespread use of uncertainty analysis in the biomedical optics community.

The use of uncertainty analysis for the design of container closures

AbstractUnderstanding how easy packaging is to open is becoming a major area of interest for the packaging industry. Designing packaging to meet the direct needs of the consumer has been termed ‘inclusive design’. However, there are differing parameters that may affect the ease of opening a product. This paper outlines how the use of uncertainty analysis coupled with ‘inclusive design’ techniques can help manufacturers understand which parameters are important for product ‘openability’. Copyright © 2006 John Wiley & Sons, Ltd.

Field determination of the spatial variation of resistance to flow along a steep Alpine stream

Accurate field data have been collected along the Febbraro River (central Italian Alps) during quasi-steady, low-flow conditions to investigate the spatial variations of hydraulic and geomorphologic quantities potentially affecting resistance to flow. Detailed uncertainty analysis and weighted least-squares fitting of simple power function relationships to field-derived data are carried out to identify possible interdependencies between observed variables. Mean flow velocity is found to depend on water-surface slope, bed material particle size, and upstream drainage area, whereas its dependence on hydraulic depth appears less susceptible to quantification. Upstream drainage area is found to explain the variations of hydraulic depth, water-surface slope, Gauckler–Strickler conductance coefficient, and (although less significantly) flow discharge. Specifically, a highly significant positive dependence of the Gauckler–Strickler conductance coefficient on the upstream drainage area is found to exist, although anomalies in the variations of hydraulic depth and flow discharge are observed along the stream. The combined use of uncertainty analysis, hydraulic equations, and geomorphological relationships allows a possible characterization of resistance to flow along a steep Alpine stream and, perhaps more importantly, provides useful guidelines for future investigative efforts. Copyright  2006 John Wiley & Sons, Ltd.