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00:59Uncertainty: Overview
In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
00:59Propagation of Uncertainty from Random Error
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
01:10Propagation of Uncertainty from Systematic Error
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
01:12Modeling and Similitude
Scaled modeling is a fundamental technique in engineering, enabling the study of large and complex systems by creating smaller, manageable replicas that recreate critical characteristics of the original. In hydrology and civil infrastructure, for example, scaled models of dams help analyze water flow, turbulence, and pressure. This method allows for accurate predictions of real-world behavior within a controlled environment, significantly reducing the cost and time involved in full-scale...
01:30Typical Model Studies
Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
01:21Design Example: Creating a Hydraulic Model of a Dam Spillway
Scaled hydraulic models of dam spillways provide a practical way to replicate and study the intricate flow dynamics of these structures. Often built to a 1:15 ratio, these models allow for observing critical water behavior, such as velocity distribution, flow patterns, and energy dissipation.
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Uncertainty in hydrogeological modelling
1Department of Hydraulics and Environmental Engineering, Universidad Politécnica de Valencia, Spain.
Ciba Foundation Symposium
|January 1, 1997
Summary
Predicting groundwater contaminant flow requires accurate parameter values. Stochastic methods and the self-calibrated method improve predictions by incorporating all available data, reducing uncertainty in hydrogeological models.
Area of Science:
- Hydrogeology
- Environmental Science
- Geosciences
Background:
- Hydrogeological models are essential for predicting groundwater flow and contaminant transport.
- Parameter values like transmissivity and hydraulic conductivity are often sparse, leading to uncertainty in model predictions.
- Parameter uncertainty significantly impacts flow and transport predictions, necessitating robust uncertainty modeling.
Purpose of the Study:
- To address the challenge of parameter uncertainty in hydrogeological modeling.
- To enhance the accuracy and precision of groundwater flow and contaminant transport predictions.
- To introduce and evaluate advanced techniques for conditioning parameter realizations.
Main Methods:
- Stochastic simulation for generating multiple spatial parameter realizations.
- Conditioning parameter realizations using direct and indirect information.
- Application of the self-calibrated method for conductivity realization, incorporating conductivity, piezometric head, and geophysical data.
Main Results:
- Stochastic simulation generates frequency distributions of response variables (e.g., flow velocities, arrival times, concentrations).
- Conditioning parameter realizations to all available information improves the accuracy of uncertainty models.
- The self-calibrated method provides a technique for generating conductivity realizations conditioned to multiple data types.
Conclusions:
- Accurate parameter estimation is critical for reliable groundwater flow and contaminant fate predictions.
- Stochastic methods and data conditioning are vital for quantifying and reducing parameter uncertainty.
- The self-calibrated method represents a significant advancement in hydrogeological modeling for improved risk assessment.