Hydrologic drought prediction under climate change: Uncertainty modeling with Dempster-Shafer and Bayesian approaches

Representation and quantification of uncertainty in climate change impact studies are a difficult task. Several sources of uncertainty arise in studies of hydrologic impacts of climate change, such as those due to choice of general circulation models (GCMs), scenarios and downscaling methods. Recently, much work has focused on uncertainty quantification and modeling in regional climate change impacts. In this paper, an uncertainty modeling framework is evaluated, which uses a generalized uncertainty measure to combine GCM, scenario and downscaling uncertainties. The Dempster-Shafer (D-S) evidence theory is used for representing and combining uncertainty from various sources. A significant advantage of the D-S framework over the traditional probabilistic approach is that it allows for the allocation of a probability mass to sets or intervals, and can hence handle both aleatory or stochastic uncertainty, and epistemic or subjective uncertainty. This paper shows how the D-S theory can be used to represent beliefs in some hypotheses such as hydrologic drought or wet conditions, describe uncertainty and ignorance in the system, and give a quantitative measurement of belief and plausibility in results. The D-S approach has been used in this work for information synthesis using various evidence combination rules having different conflict modeling approaches. A case study is presented for hydrologic drought prediction using downscaled streamflow in the Mahanadi River at Hirakud in Orissa, India. Projections of n most likely monsoon streamflow sequences are obtained from a conditional random field (CRF) downscaling model, using an ensemble of three GCMs for three scenarios, which are converted to monsoon standardized streamflow index (SSFI-4) series. This range is used to specify the basic probability assignment (bpa) for a Dempster-Shafer structure, which represents uncertainty associated with each of the SSFI-4 classifications. These uncertainties are then combined across GCMs and scenarios using various evidence combination rules given by the D-S theory. A Bayesian approach is also presented for this case study, which models the uncertainty in projected frequencies of SSFI-4 classifications by deriving a posterior distribution for the frequency of each classification, using an ensemble of GCMs and scenarios. Results from the D-S and Bayesian approaches are compared, and relative merits of each approach are discussed. Both approaches show an increasing probability of extreme, severe and moderate droughts and decreasing probability of normal and wet conditions in Orissa as a result of climate change. (C) 2010 Elsevier Ltd. All rights reserved.

Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic

Uncertainties associated with the structural model and measured vibration data may lead to unreliable damage detection. In this paper, we show that geometric and measurement uncertainty cause considerable problem in damage assessment which can be alleviated by using a fuzzy logic-based approach for damage detection. Curvature damage factor (CDF) of a tapered cantilever beam are used as damage indicators. Monte Carlo simulation (MCS) is used to study the changes in the damage indicator due to uncertainty in the geometric properties of the beam. Variation in these CDF measures due to randomness in structural parameter, further contaminated with measurement noise, are used for developing and testing a fuzzy logic system (FLS). Results show that the method correctly identifies both single and multiple damages in the structure. For example, the FLS detects damage with an average accuracy of about 95 percent in a beam having geometric uncertainty of 1 percent COV and measurement noise of 10 percent in single damage scenario. For multiple damage case, the FLS identifies damages in the beam with an average accuracy of about 94 percent in the presence of above mentioned uncertainties. The paper brings together the disparate areas of probabilistic analysis and fuzzy logic to address uncertainty in structural damage detection.

Climate change impact assessment: Uncertainty modeling with imprecise probability

Hydrologic impacts of climate change are usually assessed by downscaling the General Circulation Model (GCM) output of large-scale climate variables to local-scale hydrologic variables. Such an assessment is characterized by uncertainty resulting from the ensembles of projections generated with multiple GCMs, which is known as intermodel or GCM uncertainty. Ensemble averaging with the assignment of weights to GCMs based on model evaluation is one of the methods to address such uncertainty and is used in the present study for regional-scale impact assessment. GCM outputs of large-scale climate variables are downscaled to subdivisional-scale monsoon rainfall. Weights are assigned to the GCMs on the basis of model performance and model convergence, which are evaluated with the Cumulative Distribution Functions (CDFs) generated from the downscaled GCM output (for both 20th Century [20C3M] and future scenarios) and observed data. Ensemble averaging approach, with the assignment of weights to GCMs, is characterized by the uncertainty caused by partial ignorance, which stems from nonavailability of the outputs of some of the GCMs for a few scenarios (in Intergovernmental Panel on Climate Change [IPCC] data distribution center for Assessment Report 4 [AR4]). This uncertainty is modeled with imprecise probability, i.e., the probability being represented as an interval gray number. Furthermore, the CDF generated with one GCM is entirely different from that with another and therefore the use of multiple GCMs results in a band of CDFs. Representing this band of CDFs with a single valued weighted mean CDF may be misleading. Such a band of CDFs can only be represented with an envelope that contains all the CDFs generated with a number of GCMs. Imprecise CDF represents such an envelope, which not only contains the CDFs generated with all the available GCMs but also to an extent accounts for the uncertainty resulting from the missing GCM output. This concept of imprecise probability is also validated in the present study. The imprecise CDFs of monsoon rainfall are derived for three 30-year time slices, 2020s, 2050s and 2080s, with A1B, A2 and B1 scenarios. The model is demonstrated with the prediction of monsoon rainfall in Orissa meteorological subdivision, which shows a possible decreasing trend in the future.

Reservoir performance under uncertainty in hydrologic impacts of climate change

Relatively few studies have addressed water management and adaptation measures in the face of changing water balances due to climate change. The current work studies climate change impact on a multipurpose reservoir performance and derives adaptive policies for possible futurescenarios. The method developed in this work is illustrated with a case study of Hirakud reservoir on the Mahanadi river in Orissa, India,which is a multipurpose reservoir serving flood control, irrigation and power generation. Climate change effects on annual hydropower generation and four performance indices (reliability with respect to three reservoir functions, viz. hydropower, irrigation and flood control, resiliency, vulnerability and deficit ratio with respect to hydropower) are studied. Outputs from three general circulation models (GCMs) for three scenarios each are downscaled to monsoon streamflow in the Mahanadi river for two future time slices, 2045-65 and 2075-95. Increased irrigation demands, rule curves dictated by increased need for flood storage and downscaled projections of streamflow from the ensemble of GCMs and scenarios are used for projecting future hydrologic scenarios. It is seen that hydropower generation and reliability with respect to hydropower and irrigation are likely to show a decrease in future in most scenarios, whereas the deficit ratio and vulnerability are likely to increase as a result of climate change if the standard operating policy (SOP) using current rule curves for flood protection is employed. An optimal monthly operating policy is then derived using stochastic dynamic programming (SDP) as an adaptive policy for mitigating impacts of climate change on reservoir operation. The objective of this policy is to maximize reliabilities with respect to multiple reservoir functions of hydropower, irrigation and flood control. In variations to this adaptive policy, increasingly more weightage is given to the purpose of maximizing reliability with respect to hydropower for two extreme scenarios. It is seen that by marginally sacrificing reliability with respect to irrigation and flood control, hydropower reliability and generation can be increased for future scenarios. This suggests that reservoir rules for flood control may have to be revised in basins where climate change projects an increasing probability of droughts. However, it is also seen that power generation is unable to be restored to current levels, due in part to the large projected increases in irrigation demand. This suggests that future water balance deficits may limit the success of adaptive policy options. (C) 2010 Elsevier Ltd. All rights reserved.

Effect of matrix cracking and material uncertainty on composite plates

A laminated composite plate model based on first order shear deformation theory is implemented using the finite element method.Matrix cracks are introduced into the finite element model by considering changes in the A, B and D matrices of composites. The effects of different boundary conditions, laminate types and ply angles on the behavior of composite plates with matrix cracks are studied.Finally, the effect of material property uncertainty, which is important for composite material on the composite plate, is investigated using Monte Carlo simulations. Probabilistic estimates of damage detection reliability in composite plates are made for static and dynamic measurements. It is found that the effect of uncertainty must be considered for accurate damage detection in composite structures. The estimates of variance obtained for observable system properties due to uncertainty can be used for developing more robust damage detection algorithms. (C) 2010 Elsevier Ltd. All rights reserved.

Guessing under source uncertainty with side information

We study the problem of guessing the realization of a finite alphabet source, when some side information is provided, in a setting where the only knowledge the guesser has about the source and the correlated side information is that the joint source is one among a family. We define a notion of redundancy, identify a quantity that measures this redundancy, and study its properties. We then identify good guessing strategies that minimize the supremum redundancy (over the family). The minimum value measures the richness of the uncertainty class.

Constraining uncertainty in regional hydrologic impacts of climate change: Nonstationarity in downscaling

Regional impacts of climate change remain subject to large uncertainties accumulating from various sources, including those due to choice of general circulation models (GCMs), scenarios, and downscaling methods. Objective constraints to reduce the uncertainty in regional predictions have proven elusive. In most studies to date the nature of the downscaling relationship (DSR) used for such regional predictions has been assumed to remain unchanged in a future climate. However,studies have shown that climate change may manifest in terms of changes in frequencies of occurrence of the leading modes of variability, and hence, stationarity of DSRs is not really a valid assumption in regional climate impact assessment. This work presents an uncertainty modeling framework where, in addition to GCM and scenario uncertainty, uncertainty in the nature of the DSR is explored by linking downscaling with changes in frequencies of such modes of natural variability. Future projections of the regional hydrologic variable obtained by training a conditional random field (CRF) model on each natural cluster are combined using the weighted Dempster-Shafer (D-S) theory of evidence combination. Each projection is weighted with the future projected frequency of occurrence of that cluster (''cluster linking'') and scaled by the GCM performance with respect to the associated cluster for the present period (''frequency scaling''). The D-S theory was chosen for its ability to express beliefs in some hypotheses, describe uncertainty and ignorance in the system, and give a quantitative measurement of belief and plausibility in results. The methodology is tested for predicting monsoon streamflow of the Mahanadi River at Hirakud Reservoir in Orissa, India. The results show an increasing probability of extreme, severe, and moderate droughts due to limate change. Significantly improved agreement between GCM predictions owing to cluster linking and frequency scaling is seen, suggesting that by linking regional impacts to natural regime frequencies, uncertainty in regional predictions can be realistically quantified. Additionally, by using a measure of GCM performance in simulating natural regimes, this uncertainty can be effectively constrained.

A method for Estimating the Degree of Uncertainty With Respect to Life Cycle Assessment During Design

Life cycle assessment (LCA) is used to estimate a product's environmental impact. Using LCA during the earlier stages of design may produce erroneous results since information available on the product's lifecycle is typically incomplete at these stages. The resulting uncertainty must be accounted for in the decision-making process. This paper proposes a method for estimating the environmental impact of a product's life cycle and the associated degree of uncertainty of that impact using information generated during the design process. Total impact is estimated based on aggregation of individual product life cycle processes impacts. Uncertainty estimation is based on assessing the mismatch between the information required and the information available about the product life cycle in each uncertainty category, as well as their integration. The method is evaluated using pre-defined scenarios with varying uncertainty. DOI: 10.1115/1.4002163]

Estimation of soil hydraulic properties and their uncertainty: comparison between laboratory and field experiment

Often the soil hydraulic parameters are obtained by the inversion of measured data (e.g. soil moisture, pressure head, and cumulative infiltration, etc.). However, the inverse problem in unsaturated zone is ill-posed due to various reasons, and hence the parameters become non-unique. The presence of multiple soil layers brings the additional complexities in the inverse modelling. The generalized likelihood uncertainty estimate (GLUE) is a useful approach to estimate the parameters and their uncertainty when dealing with soil moisture dynamics which is a highly non-linear problem. Because the estimated parameters depend on the modelling scale, inverse modelling carried out on laboratory data and field data may provide independent estimates. The objective of this paper is to compare the parameters and their uncertainty estimated through experiments in the laboratory and in the field and to assess which of the soil hydraulic parameters are independent of the experiment. The first two layers in the field site are characterized by Loamy sand and Loamy. The mean soil moisture and pressure head at three depths are measured with an interval of half hour for a period of 1 week using the evaporation method for the laboratory experiment, whereas soil moisture at three different depths (60, 110, and 200 cm) is measured with an interval of 1 h for 2 years for the field experiment. A one-dimensional soil moisture model on the basis of the finite difference method was used. The calibration and validation are approximately for 1 year each. The model performance was found to be good with root mean square error (RMSE) varying from 2 to 4 cm(3) cm(-3). It is found from the two experiments that mean and uncertainty in the saturated soil moisture (theta(s)) and shape parameter (n) of van Genuchten equations are similar for both the soil types. Copyright (C) 2010 John Wiley & Sons, Ltd.

Effect of uncertainty on helicopter performance predictions

The effect of uncertainties on performance predictions of a helicopter is studied in this article. The aeroelastic parameters such as the air density, blade profile drag coefficient, main rotor angular velocity, main rotor radius, and blade chord are considered as uncertain variables. The propagation of these uncertainties in the performance parameters such as thrust coefficient, figure of merit, induced velocity, and power required are studied using Monte Carlo simulation and the first-order reliability method. The Rankine-Froude momentum theory is used for performance prediction in hover, axial climb, and forward flight. The propagation of uncertainty causes large deviations from the baseline deterministic predictions, which undoubtedly affect both the achievable performance and the safety of the helicopter. The numerical results in this article provide useful bounds on helicopter power requirements.

Composite material and piezoelectric coefficient uncertainty effects on structural health monitoring using feedback control gains as damage indicators

This article addresses uncertainty effect on the health monitoring of a smart structure using control gain shifts as damage indicators. A finite element model of the smart composite plate with surface-bonded piezoelectric sensors and actuators is formulated using first-order shear deformation theory and a matrix crack model is integrated into the finite element model. A constant gain velocity/position feedback control algorithm is used to provide active damping to the structure. Numerical results show that the response of the structure is changed due to matrix cracks and this change can be compensated by actively tuning the feedback controller. This change in control gain can be used as a damage indicator for structural health monitoring. Monte Carlo simulation is conducted to study the effect of material uncertainty on the damage indicator by considering composite material properties and piezoelectric coefficients as independent random variables. It is found that the change in position feedback control gain is a robust damage indicator.

Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f is an element of L-1 (G) has lacunary Fourier series and f vanishes on a non empty open subset of G, then we prove that f vanishes identically. This result can be viewed as a qualitative uncertainty principle.

Predictive uncertainty of chaotic daily streamflow using ensemble wavelet networks approach

Perfect or even mediocre weather predictions over a long period are almost impossible because of the ultimate growth of a small initial error into a significant one. Even though the sensitivity of initial conditions limits the predictability in chaotic systems, an ensemble of prediction from different possible initial conditions and also a prediction algorithm capable of resolving the fine structure of the chaotic attractor can reduce the prediction uncertainty to some extent. All of the traditional chaotic prediction methods in hydrology are based on single optimum initial condition local models which can model the sudden divergence of the trajectories with different local functions. Conceptually, global models are ineffective in modeling the highly unstable structure of the chaotic attractor. This paper focuses on an ensemble prediction approach by reconstructing the phase space using different combinations of chaotic parameters, i.e., embedding dimension and delay time to quantify the uncertainty in initial conditions. The ensemble approach is implemented through a local learning wavelet network model with a global feed-forward neural network structure for the phase space prediction of chaotic streamflow series. Quantification of uncertainties in future predictions are done by creating an ensemble of predictions with wavelet network using a range of plausible embedding dimensions and delay times. The ensemble approach is proved to be 50% more efficient than the single prediction for both local approximation and wavelet network approaches. The wavelet network approach has proved to be 30%-50% more superior to the local approximation approach. Compared to the traditional local approximation approach with single initial condition, the total predictive uncertainty in the streamflow is reduced when modeled with ensemble wavelet networks for different lead times. Localization property of wavelets, utilizing different dilation and translation parameters, helps in capturing most of the statistical properties of the observed data. The need for taking into account all plausible initial conditions and also bringing together the characteristics of both local and global approaches to model the unstable yet ordered chaotic attractor of a hydrologic series is clearly demonstrated.

GNSS Signal Detection Under Noise Uncertainty

High sensitivity detection techniques are required for indoor navigation using Global Navigation Satellite System (GNSS) receivers, and typically, a combination of coherent and non- coherent integration is used as the test statistic for detection. The coherent integration exploits the deterministic part of the signal and is limited due to the residual frequency error, navigation data bits and user dynamics, which are not known apriori. So, non- coherent integration, which involves squaring of the coherent integration output, is used to improve the detection sensitivity. Due to this squaring, it is robust against the artifacts introduced due to data bits and/or frequency error. However, it is susceptible to uncertainty in the noise variance, and this can lead to fundamental sensitivity limits in detecting weak signals. In this work, the performance of the conventional non-coherent integration-based GNSS signal detection is studied in the presence of noise uncertainty. It is shown that the performance of the current state of the art GNSS receivers is close to the theoretical SNR limit for reliable detection at moderate levels of noise uncertainty. Alternate robust post-coherent detectors are also analyzed, and are shown to alleviate the noise uncertainty problem. Monte-Carlo simulations are used to confirm the theoretical predictions.