Approximate dynamic fault tree calculations for modelling water supply risks

Traditional fault tree analysis is not always sufficient when analysing complex systems. To overcome the limitations dynamic fault tree (DFT) analysis is suggested in the literature as well as different approaches for how to solve DFTs. For added value in fault tree analysis, approximate DFT calculations based on a Markovian approach are presented and evaluated here. The approximate DFT calculations are performed using standard Monte Carlo simulations and do not require simulations of the full Markov models, which simplifies model building and in particular calculations. It is shown how to extend the calculations of the traditional OR- and AND-gates, so that information is available on the failure probability, the failure rate and the mean downtime at all levels in the fault tree. Two additional logic gates are presented that make it possible to model a system’s ability to compensate for failures. This work was initiated to enable correct analyses of water supply risks. Drinking water systems are typically complex with an inherent ability to compensate for failures that is not easily modelled using traditional logic gates. The approximate DFT calculations are compared to results from simulations of theorresponding Markov models for three water supply examples. For the traditional OR- and AND-gates, and one gate modelling compensation, the errors in the results are small. For the other gate modelling compensation, the error increases with the number of compensating components. The errors are, however, in most cases acceptable with respect to uncertainties in input data. The approximate DFT calculations improve the capabilities of fault tree analysis of drinking water systems since they provide additional and important information and are simple and practically applicable

Dynamic Water Balance Modelling for Risk Assessment and Decision Support on MAR Potential in Botswana

Botswana experiences a water stressed situation due to the climate and a continuously increasing water demand. Managed Aquifer Recharge (MAR) is considered, among other measures, to improve the situation. To evaluate the possibility for increased water supply security, a probabilistic and dynamic water supply security model was developed. Statistically generated time series of source water availability are used in combination with the dynamic storages in dams and aquifers, and the possible supply is compared with the demand to simulate the magnitude and probability of water supply shortages. The model simulates the system and possible mitigation measures from 2013 to 2035 (23 years), using one-month time steps. The original system is not able to meet the demand, and the estimated volumetric supply reliability in the year 2035 is 0.51. An additional surface water dam (now implemented) will increase the reliability to 0.88 but there will still be a significant water shortage problem. Implementing large-scale MAR can further improve the reliability to at least 0.95. System properties limiting the effect of MAR are identified using the model and show how to further improve the effect of MAR. The case study results illustrate the importance and benefit of using an integrated approach, including time-dependence and future scenarios, when evaluating the need and potential of MAR

Uncertainty modelling in multi-criteria analysis of water safety measures

Water utilities must assess risks and make decisions on safety measures in order to obtain a safe and sustainable drinking water supply. The World Health Organization emphasises preparation of Water Safety Plans, in which risk ranking by means of risk matrices with discretised probability and consequence scales is commonly used. Risk ranking enables prioritisation of risks but there is currently no common and structured way of performing uncertainty analysis and using risk ranking for evaluating and comparing water safety measures. To enable a proper prioritisation of safety measures and an efficient use of available resources for risk reduction, two alternative models linking risk ranking and multi-criteria decision analysis (MCDA) are presented and evaluated. The two models specifically enable uncertainty modelling in MCDA and they differ in terms of how uncertainties in risk levels are considered. The need of formal handling of risk and uncertainty in MCDA is emphasised in the literature and the suggested models provide innovations that are not dependent on the application domain. In the case study application presented here, possible safety measures are evaluated based on the benefit of estimated risk reduction, the cost of implementation and the probability of not achieving an acceptable risk level. Additional criteria such as environmental impact and consumer trust may also be included when applying the models. The case study shows how safety measures can be ranked based on preference scores or cost-effectiveness and how measures not reducing the risk enough can be identified and disqualified. Furthermore, the probability of each safety measure being ranked highest can be calculated. The two models provide a stepwise procedure for prioritising safety measures and enable a formalised handling of uncertainties in input data and results

A probabilistic approach to soil layer and bedrock-level modelling for risk assessment of groundwater drawdown induced land subsidence

Sub-surface construction in urban areas generally involves drainage of groundwater, which can induce subsidence in soil deposits. Knowledge of where compressible sediments are located and how thick these are is essential for estimating subsidence risk. A probabilistic method for coupled bedrock-level and soil-layer modeling to detect compressible sediments is presented. The method is applied in an area in central Stockholm, where clay is the compressible sediment layer. First, a bedrock-level model was constructed from three sources of information: (a) geotechnical drillings reaching the bedrock; (b) drillings not reaching the bedrock; and (c) mapped bedrock outcrops. Input data for the probabilistic bedrock-level model was generated by a stepwise Kriging procedure. Second, a three layer soil model was constructed, including the following materials: (a) coarse grained post glacial and filling material below the ground surface; (b) glacial and post-glacial clays; and (c) coarse grained glaciofluvial and glacial till deposits above the bedrock. Layer thicknesses were transformed to proportions of the total soil thickness. Since Kriging requires data to be normally distributed, the proportions were transformed from proportions (P) to standard normal quantiles (z). In each iteration of a Monte-Carlo simulation, a spatial distribution of the bedrock level was simulated together with the transformed values for the soil-layer proportions. From the iterations, the probability density of the clay thickness (compressible sediments) at each grid cell was calculated. The results of the case study map the expected value (mean) and the 95th percentile of the probability of compressible sediments at specific locations. The resulting model is geologically realistic and validated through a cross-validation procedure in order to be in good agreement with a reference dataset. The case study showed that the method can efficiently handle large amounts of data and requires little manual adjustment. Moreover, the mapped results can provide useful decision support when planning risk-reducing measures and when communicating with stakeholders. Although this novel method is developed for risk assessment of groundwater drawdown induced subsidence, it is useful for other applications involving spatial soil strata modeling

A probabilistic approach to soil layer and bedrock-level modelling for risk assessment of groundwater drawdown induced land subsidence

Sub-surface construction in urban areas generally involves drainage of groundwater, which can induce subsidence in soil deposits. Knowledge of where compressible sediments are located and how thick these are is essential for estimating subsidence risk. A probabilistic method for coupled bedrock-level and soil-layer modeling to detect compressible sediments is presented. The method is applied in an area in central Stockholm, where clay is the compressible sediment layer. First, a bedrock-level model was constructed from three sources of information: (a) geotechnical drillings reaching the bedrock; (b) drillings not reaching the bedrock; and (c) mapped bedrock outcrops. Input data for the probabilistic bedrock-level model was generated by a stepwise Kriging procedure. Second, a three layer soil model was constructed, including the following materials: (a) coarse grained post glacial and filling material below the ground surface; (b) glacial and post-glacial clays; and (c) coarse grained glaciofluvial and glacial till deposits above the bedrock. Layer thicknesses were transformed to proportions of the total soil thickness. Since Kriging requires data to be normally distributed, the proportions were transformed from proportions (P) to standard normal quantiles (z). In each iteration of a Monte-Carlo simulation, a spatial distribution of the bedrock level was simulated together with the transformed values for the soil-layer proportions. From the iterations, the probability density of the clay thickness (compressible sediments) at each grid cell was calculated. The results of the case study map the expected value (mean) and the 95th percentile of the probability of compressible sediments at specific locations. The resulting model is geologically realistic and validated through a cross-validation procedure in order to be in good agreement with a reference dataset. The case study showed that the method can efficiently handle large amounts of data and requires little manual adjustment. Moreover, the mapped results can provide useful decision support when planning risk-reducing measures and when communicating with stakeholders. Although this novel method is developed for risk assessment of groundwater drawdown induced subsidence, it is useful for other applications involving spatial soil strata modeling

Economic valuation of hydrogeological information when managing groundwater drawdown

A procedure is presented for valuation of information analysis (VOIA) to determine the need for additional information when assessing the effect of several design alternatives to manage future disturbances in hydrogeological systems. When planning for groundwater extraction and drawdown in areas where risks—such as land subsidence, wells running dry and drainage of streams and wetlands—are present, the need for risk-reducing safety measures must be carefully evaluated and managed. The heterogeneity of the subsurface calls for an assessment of trade-offs between the benefits of additional information to reduce the risk of erroneous decisions and the cost of collecting this information. A method is suggested that combines existing procedures for inverse probabilistic groundwater modelling with a novel method for VOIA. The method results in (1) a prior analysis where uncertainties regarding the efficiency of safety measures are estimated, and (2) a pre-posterior analysis, where the benefits of expected uncertainty reduction deriving from additional information are compared with the costs for obtaining this information. In comparison with existing approaches for VOIA, the method can assess multiple design alternatives, use hydrogeological parameters as proxies for failure, and produce spatially distributed VOIA maps. The method is demonstrated for a case study of a planned tunnel in Stockholm, Sweden, where additional investigations produce a low number of benefits as a result of low failure rates for the studied alternatives and a cause-effect chain where the resulting failure probability is more dependent on interactions within the whole system rather than on specific features

Using soil function evaluation in multi-criteria decision analysis for sustainability appraisal of remediation alternatives

Soil contamination is one of the major threats constraining proper functioning of the soil and thus provision of ecosystem services. Remedial actions typically only address the chemical soil quality by reducing total contaminant concentrations to acceptable levels guided by land use. However, emerging regulatory requirements on soil protection demand a holistic view on soil assessment in remediation projects thus accounting for a variety of soil functions. Such a view would require not only that the contamination concentrations are assessed and attended to, but also that other aspects are taking into account, thus addressing also physical and biological as well as other chemical soil quality indicators (SQIs). This study outlines how soil function assessment can be a part of a holistic sustainability appraisal of remediation alternatives using multi-criteria decision analysis (MCDA). The paper presents a method for practitioners for evaluating the effects of remediation alternatives on selected ecological soil functions using a suggested minimum data set (MDS) containing physical, biological and chemical SQIs. The measured SQls are transformed into sub-scores by the use of scoring curves, which allows interpretation and the integration of soil quality data into the MCDA framework. The method is demonstrated at a study site (Marieberg, Sweden) and the results give an example of how soil analyses using the suggested MDS can be used for soil function assessment and subsequent input to the MCDA framework

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data