An evaluation of the nonlinear/non-Gaussian filters for the sequential data assimilation

This paper aims to investigate several new nonlinear/non-Gaussian filters in the context of the sequential data assimilation. The unscented Kalman filter (UKF), the ensemble Kalman filter (EnKF), the sampling importance resampling particle filter (SIR-PF) and the unscented particle filter (UPF) are described in the state-space model framework in the Bayesian filtering background. We first evaluated those methods with a simple highly nonlinear Lorenz model and a scalar nonlinear non-Gaussian model to investigate the filter stability and the error sensitivity, and then their abilities in the one-dimensional estimation of the soil moisture content with the synthetic microwave brightness temperature assimilation experiment in the land surface model VIC-3L. All the results are compared with the EnKF. The advantages and disadvantages of each filter are discussed.The results in the Lorenz model showed that the particle filters are suitable for the large measurement interval assimilation and that the Kalman filters were suitable for the frequent measurement assimilation as well as small measurement uncertainties. The EnKF also showed its feasibility for the non-Gaussian noise. The performance of the SIR-PF was actually not as good as that of the UKF or the EnKF regarding a very small observation noise level compared with the uncertainties in the system. In the one-dimensional brightness temperature assimilation experiment, the UKF, the EnKF and the SIR-PF all proved to be flexible and reliable nonlinear filter algorithms for the low dimensional sequential land data assimilation application. For the high dimensional land surface system that takes the horizontal error correlations into account, the UKF is restricted by its computational demand in the covariance propagation; we must use the EnKF, the SIR-PF and other covariance reduction algorithms. The large computational cost prevents the UPF from being applied in practice.     

Progressive Latin Hypercube Sampling: An efficient approach for robust sampling-based analysis of environmental models

Efficient sampling strategies that scale with the size of the problem, computational budget, and users’ needs are essential for various sampling-based analyses, such as sensitivity and uncertainty analysis. In this study, we propose a new strategy, called Progressive Latin Hypercube Sampling (PLHS), which sequentially generates sample points while progressively preserving the distributional properties of interest (Latin hypercube properties, space-filling, etc.), as the sample size grows. Unlike Latin hypercube sampling, PLHS generates a series of smaller sub-sets (slices) such that (1) the first slice is Latin hypercube, (2) the progressive union of slices remains Latin hypercube and achieves maximum stratification in any one-dimensional projection, and as such (3) the entire sample set is Latin hypercube. The performance of PLHS is compared with benchmark sampling strategies across multiple case studies for Monte Carlo simulation, sensitivity and uncertainty analysis. Our results indicate that PLHS leads to improved efficiency, convergence, and robustness of sampling-based analyses.     

Parameter estimation and uncertainty analysis of the Spatial Agro Hydro Salinity Model (SAHYSMOD) in the semi-arid climate of Rechna Doab,Pakistan

Manual calibration of distributed models with many unknown parameters can result in problems of equifinality and high uncertainty. In this study, the Generalized Likelihood Uncertainty Estimation (GLUE) technique was used to address these issues through uncertainty and sensitivity analysis of a distributed watershed scale model (SAHYSMOD) for predicting changes in the groundwater levels of the Rechna Doab basin, Pakistan. The study proposes and then describes a stepwise methodology for SAHYSMOD uncertainty analysis that has not been explored in any study before. One thousand input data files created through Monte Carlo simulations were classified as behavior and non-behavior sets using threshold likelihood values. The model was calibrated (1983–1988) and validated (1998–2003) through satisfactory agreement between simulated and observed data. Acceptable values were observed in the statistical performance indices. Approximately 70% of the observed groundwater level values fell within uncertainty bounds. Groundwater pumping (Gw) and hydraulic conductivity (Kaq) were found to be highly sensitive parameters affecting groundwater recharge.     

Regression models for grouped survival data: Estimation and sensitivity analysis

In this study, regression models are evaluated for grouped survival data when the effect of censoring time is considered in the model and the regression structure is modeled through four link functions. The methodology for grouped survival data is based on life tables, and the times are grouped in k intervals so that ties are eliminated. Thus, the data modeling is performed by considering the discrete models of lifetime regression. The model parameters are estimated by using the maximum likelihood and jackknife methods. To detect influential observations in the proposed models, diagnostic measures based on case deletion, which are denominated global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to those measures, the local influence and the total influential estimate are also employed. Various simulation studies are performed and compared to the performance of the four link functions of the regression models for grouped survival data for different parameter settings, sample sizes and numbers of intervals. Finally, a data set is analyzed by using the proposed regression models.     

FSAUA: A framework for sensitivity analysis and uncertainty assessment in historical and forecasted land use maps

Land change modelers often create future maps using reference land use map. However, future land use maps may mislead decision-makers, who are often unaware of the sensitivity and the uncertainty in land use maps due to error in data. Since most metrics that communicate uncertainty require using reference land use data to calculate accuracy, the assessment of uncertainty becomes challenging when no reference land use map for future is available. This study aims to develop a new conceptual framework for sensitivity analysis and uncertainty assessment (FSAUA) which compares multiple maps under various data error scenarios. FSAUA performs sensitivity analyses in land use maps using a reference map and assess uncertainty in predicted maps. FSAUA was applied using three well-known land change models (ANN, CART and MARS) in Delhi, India. FSAUA was found to be a practical tool for communicating the uncertainty with end-users who develop reliable planning decisions.     

A probabilistic framework for comparison of dam breach parameters and outflow hydrograph generated by different empirical prediction methods

This study presents a probabilistic framework to simulate dam breach and evaluates the impact of using four empirical dam breach prediction methods on breach parameters (i.e., geometry and timing) and outflow hydrograph attributes (i.e., time to peak, hydrograph duration and peak). The methods that are assessed here include MacDonald and Langridge-Monopolis (1984), Von Thun and Gillette (1990), Froehlich (1995), 2008). Mean values and percentiles of breach parameters and outflow hydrograph attributes are compared for hypothetical overtopping failure of Burnett Dam in the state of North Carolina, USA. Furthermore, utilizing the probabilistic framework, the least and most uncertain methods alongside those giving the most critical value are identified for these parameters. The multivariate analysis also indicates that lone use of breach parameters is not necessarily sufficient to characterize outflow hydrograph attributes. However, timing characteristic of the breach is generally a more important driver than its geometric features.     

Parametric and nonparametric Bayesian model specification: A case study involving models for count data

In this paper we present the results of a simulation study to explore the ability of Bayesian parametric and nonparametric models to provide an adequate fit to count data of the type that would routinely be analyzed parametrically either through fixed-effects or random-effects Poisson models. The context of the study is a randomized controlled trial with two groups (treatment and control). Our nonparametric approach uses several modeling formulations based on Dirichlet process priors. We find that the nonparametric models are able to flexibly adapt to the data, to offer rich posterior inference, and to provide, in a variety of settings, more accurate predictive inference than parametric models.     

A detection problem: Sensitivity and uncertainty analysis of a land surface temperature approach to detecting dynamics of water use by groundwater-dependent vegetation

Sustainable management of groundwater-dependent vegetation (GDV) requires the accurate identification of GDVs, characterisation of their water use dynamics and an understanding of associated errors. This paper presents sensitivity and uncertainty analyses of one GDV mapping method which uses temperature differences between time-series of modelled and observed land surface temperature (LST) to detect groundwater use by vegetation in a subtropical woodland. Uncertainty in modelled LST was quantified using the Jacobian method with error variances obtained from literature. Groundwater use was inferred where modelled and observed LST were significantly different using a Student's t-test. Modelled LST was most sensitive to low-range wind speeds (<1.5 m s⁻¹), low-range vegetation height (<=0.5 m), and low-range leaf area index (<=0.5 m² m⁻²), limiting the detectability of groundwater use by vegetation under such conditions. The model-data approach was well-suited to detection of GDV because model-data errors were lowest for climatic conditions conducive to groundwater use.     

A General Probabilistic Framework for uncertainty and global sensitivity analysis of deterministic models: A hydrological case study

The present study proposes a General Probabilistic Framework (GPF) for uncertainty and global sensitivity analysis of deterministic models in which, in addition to scalar inputs, non-scalar and correlated inputs can be considered as well. The analysis is conducted with the variance-based approach of Sobol/Saltelli where first and total sensitivity indices are estimated. The results of the framework can be used in a loop for model improvement, parameter estimation or model simplification. The framework is applied to SWAP, a 1D hydrological model for the transport of water, solutes and heat in unsaturated and saturated soils. The sources of uncertainty are grouped in five main classes: model structure (soil discretization), input (weather data), time-varying (crop) parameters, scalar parameters (soil properties) and observations (measured soil moisture). For each source of uncertainty, different realizations are created based on direct monitoring activities. Uncertainty of evapotranspiration, soil moisture in the root zone and bottom fluxes below the root zone are considered in the analysis. The results show that the sources of uncertainty are different for each output considered and it is necessary to consider multiple output variables for a proper assessment of the model. Improvements on the performance of the model can be achieved reducing the uncertainty in the observations, in the soil parameters and in the weather data. Overall, the study shows the capability of the GPF to quantify the relative contribution of the different sources of uncertainty and to identify the priorities required to improve the performance of the model. The proposed framework can be extended to a wide variety of modelling applications, also when direct measurements of model output are not available.     

A framework for propagation of uncertainty contributed by parameterization,input data,model structure,and calibration/validation data in watershed modeling

Failure to consider major sources of uncertainty may bias model predictions in simulating watershed behavior. A framework entitled the Integrated Parameter Estimation and Uncertainty Analysis Tool (IPEAT), was developed utilizing Bayesian inferences, an input error model and modified goodness-of-fit statistics to incorporate uncertainty in parameter, model structure, input data, and calibration/validation data in watershed modeling. Applications of the framework at the Eagle Creek Watershed in Indiana shows that watershed behavior was more realistically represented when the four uncertainty sources were considered jointly without having to embed watershed behavior constraints in auto-calibration. Accounting for the major sources of uncertainty associated with watershed modeling produces more realistic predictions, improves the quality of calibrated solutions, and consequently reduces predictive uncertainty. IPEAT is an innovative tool to investigate and explore the significance of uncertainty sources, which enhances watershed modeling by improved characterization and assessment of predictive uncertainty.     

A new derivative based importance criterion for groups of variables and its link with the global sensitivity indices

A new derivative based criterion τy for groups of input variables is presented. It is shown that there is a link between global sensitivity indices and the new derivative based measure. It is proved that small values of derivative based measures imply small values of total sensitivity indices. However, for highly nonlinear functions the ranking of important variables using derivative based importance measures can be different from that based on the global sensitivity indices. The computational costs of evaluating global sensitivity indices and derivative based measures, are compared and some important tests are considered.     

Accounting for surface–groundwater interactions and their uncertainty in river and groundwater models: A case study in the Namoi River,Australia

Surface–groundwater (SW–GW) interactions constitute a critical proportion of the surface and groundwater balance especially during dry conditions. Conjunctive management of surface and groundwater requires an explicit account of the exchange flux between surface and groundwater when modelling the two systems. This paper presents a case study in the predominantly gaining Boggabri–Narrabri reach of the Namoi River located in eastern Australia. The first component of the study uses the Upper Namoi numerical groundwater model to demonstrate the importance of incorporating SW–GW interactions into river management models. The second component demonstrates the advantages of incorporating groundwater processes in the Namoi River model.Results of the numerical groundwater modelling component highlighted the contrasting groundwater dynamics close to, and away from the Namoi River where lower declines were noted in a near-field well due to water replenishment sourced from river depletion. The contribution of pumping activities to river depletion was highlighted in the results of the uncertainty analysis, which showed that the SW–GW exchange flux is the most sensitive to pumping rate during dry conditions. The uncertainty analysis also showed that after a drought period, the 95% prediction interval becomes larger than the simulated flux, which implies an increasing probability of losing river conditions. The future prospect of a gaining Boggabri–Narrabri reach turning into losing was confirmed with a hypothetical extended drought scenario during which persistent expansion of groundwater pumping was assumed. The river modelling component showed that accounting for SW–GW interactions improved the predictions of low flows, and resulted in a more realistic calibration of the Namoi River model.Incorporating SW–GW interactions into river models allows explicit representation of groundwater processes that provides a mechanism to account for the impacts of additional aquifer stresses that may be introduced beyond the calibration period of the river model. Conventional river models that neglect the effects of such future stresses suffer from the phenomenon of non-stationarity and hence have inferior low flow predictions past the calibration period of the river model. The collective knowledge acquired from the two modelling exercises conducted in this study leads to a better understanding of SW–GW interactions in the Namoi River thus leading to improved water management especially during low flow conditions.     

A step toward STEP-compatible engineering data management: the data models of product structure and engineering changes

In an iterative design process, there is a large amount of engineering data to be processed. Well-managed engineering data can ensure the competitiveness of companies in the competitive market. It has been recognized that a product data model is the basis for establishing engineering database. To fully support the complete product data representation in its life cycle, an international product data representation and exchange standard, STEP, is applied to model the representation of a product. In this paper, the architecture of an engineering data management (EDM) system is described, which consists of an integrated product database. There are six STEP-compatible data models constructed to demonstrate the integratibility of EDM system using common data modeling format. These data models are product definition, product structure, shape representation, engineering change, approval, and production scheduling. These data models are defined according to the integrated resources of STEP/ISO 10303 (Parts 41-44), which support a complete product information representation and a standard data format. Thus, application systems, such as CAD/CAM and MRP systems, can interact with the EDM system by accessing the database based on the STEP data exchange standard.