Multilevel Factorial Analysis Research Articles

Development of a multi-level factorial data assimilation approach for groundwater contaminant sources identification

The ensemble Kalman filter (EnKF) is recognized as a widely used approach for groundwater contamination sources (GCSs) parameters identification. The identification accuracy is affected by the quantification of sources of uncertainty (such as random disturbances on model inputs and measurements) in the assimilation process, but few studies have revealed the contributions of different sources of uncertainty on identification accuracy. To this end, this study developed an innovative multi-level factorial data assimilation (MFDA) approach, which integrates ensemble Kalman filtering and multi-level factorial analysis, to comprehensively reveal the impact of sources of uncertainty on the GCSs parameters identification accuracy for the first time. Not only did it explore the direct impact of individual sources of uncertainty on the GCSs parameters identification accuracy, more importantly, it also revealed the composite ones from multi-parameter interactions among these sources of uncertainty. The developed MFDA approach quantified the contributions of multiple sources of uncertainty, including model input data error (i.e. precipitation), model parameter error (i.e. hydraulic conductivity), contaminant concentration measurements error, and ensemble size. And the feasibility of the developed approach was verified by two hypothetical numerical case studies. The results indicated that: i) it was critically important to reduce the contamination concentration measurement errors to improve GCSs parameter identification accuracy. ii) model parameter and model input data were not sensitive to the identification accuracy. iii) the interaction between sources of uncertainty significantly affects the identification accuracy, which illustrated the interaction cannot be ignored in the identification process. Overall, this study highlights that the developed MFDA approach represents a promising solution for improving GCSs parameters identification accuracy.

Uncertainty quantization of meteorological input and model parameters for hydrological modelling using a Bayesian‐based integrated approach

AbstractThe traditional treatment of uncertainty in hydrological modelling primarily attributes it to model parameters, but rarely systematically considers meteorological input errors, especially in quantifying the impact of meteorological input errors on parameter uncertainty. This study developed a Bayesian‐based integrated approach to quantitatively investigate uncertainties in meteorological inputs (precipitation and temperature) and model parameters as well as the variation in parameter uncertainty due to meteorological input errors. Additionally, we analysed the propagation from these uncertainties to runoff response in snowmelt and non‐snowmelt periods. The applicability and advantages of this approach were presented by applying of the Soil and Water Assessment Tool to the Shitoukoumen Reservoir Catchment. Differential Evolution Adaptive Metropolis‐Markov Chain Monte Carlo was applied for the straightforward Bayesian inference the uncertainties of meteorological inputs and model parameters. On this basis, multilevel factorial analysis technology was used to quantitatively investigate the specific impact of the model parameters' individual and interactive effects due to meteorological input errors. Finally, the impact of meteorological input errors and model parameter uncertainty on the model performance were analysed and quantified systematically. The results showed that the meteorological input errors could affect the random characteristics of multiple model parameters. Moreover, meteorological input errors could further affect the model parameters' effects on annual average runoff. Overall, the above results have significant implications in enhancing hydrological model to simulate/predict runoff and understanding hydrological processes during different periods.

Multilevel factorial analysis for effects of SSPs and GCMs on regional climate change: a case study for the Yangtze River Basin

Multilevel factorial analysis for effects of SSPs and GCMs on regional climate change: a case study for the Yangtze River Basin

A factorial inexact copula stochastic programming (FICSP) approach for water-energy- food nexus system management

In this study, a factorial inexact copula stochastic programming (FICSP) method is developed for planning the regional-scale water-energy-food nexus (WEFN) system. The FICSP cannot only deal with uncertainties expressed as interval and random parameters, but also handle the interdependence among correlated random variables. Moreover, the multilevel factorial analysis embedded in FICSP is able to reflect the main and interactive effects among uncertain parameters. The IFCCP approach was then applied to planning the WEFN system for the City of Jinan, Shandong Province, China. A FICSP-WEFN model has been established under consideration of various restrictions related to water and land availability, food and vegetable demands and other environmental constraints. The obtained results indicated that the surface water and groundwater availabilities would be highly correlated with their marginals fitted through the Gaussian distribution and their dependence described by the Gaussian copula. Under limited water resources, the corn cultivation would be prioritized but the increase of water resources tends to increase the wheat cultivation and reduce corn planting. Under the advantageous conditions where sufficient water resources are available, the additional water resources tend to be allocated to wheat and vegetables whilst corn cultivation would not be changed. Moreover, the surface and recycled water would be first utilized for crop production, with the remaining water requirements satisfied by groundwater. The results from factorial analysis indicated that the system benefits would be increased under the demanding conditions through increasing the joint risk level and also the violation risk for surface water availability or decreasing the violation risk of groundwater availability. Nevertheless, the increase in the violation risks under the advantageous conditions would not necessarily lead to increased system benefit, implying that the crop cultivation patterns may be influenced by other restrictions rather than the water availability. In general, the developed FICSP method cannot only generate desired management strategies for WEFN system under consideration of joint risks, but also help track the factors that make dominant impacts on the WEFN management practices.

Development of a physics-informed data-driven model for gaining insights into hydrological processes in irrigated watersheds

• Process-based baseflow separation method can help trace the streamflow origins from the perspective of sub-hydrological processes. • Multilevel factorial analysis is applied to support the hydrological inference through stepwise clustered ensemble. • Hydrologicla inferences achieved from WFI method can lead to physically consistent results. Data-driven hydrological modeling has seen rapid development in recent years owing to its flexibility to approximate the complex relationships between driving forces and hydrological fluxes. However, traditional data-driven models typically cannot simultaneously capture the processes that pose both chronic and acute impacts on streamflow, thus impeding further inference. Therefore, this study presents a baseflow-filtered hydrological inference model to gain insights into hydrological processes in irrigated watersheds. The proposed model starts with separating the streamflow process into two sub-processes using a process-based baseflow separation method. Each sub-process is simulated through a new interpretable data-driven model. The resulting hydrological inferences facilitate the identification of the dominant factors influencing flows in saturated and unsaturated zones. The proposed model is applied to three irrigated watersheds, and the evaluation metrics show that the proposed model outperforms two conventional data-driven models. Our findings reveal that predictors associated with air temperature and long-term (i.e., monthly) irrigation are mainly responsible for characterizing baseflow dynamics, while precipitation and short-term (i.e., semi-weekly or weekly) irrigation are primarily responsible for describing overland flow and interflow dynamics. The fidelity of the derived hydrological inference is further demonstrated through sensitivity analysis. The results show that the relative importance of predictors not only reflects their significance on model performance, but also influence the changes on streamflow.

Development of a disaggregated multi-level factorial hydrologic data assimilation model

A disaggregated multi-level factorial hydrologic data assimilation model (FHDA) is proposed for exploring not only the direct effects from individual uncertainties but also, more importantly, the composite ones from multi-layer and multi-parameter interactions among multiple uncertainties in hydrologic data assimilation systems. Based on a disaggregated multi-level factorial analysis method, the proposed FHDA examined the contributions of multiple uncertainty sources, including data assimilation scheme, sample size, forcing data error, and observed data error. Three parameter assimilation schemes of data assimilation i.e., Ensemble Kalman Filter (EnKF), Standard Kernel Smoother (EnKFSKS), and Kernel Smoother with location shrinkage (EnKFKSLS) are tested. The results indicate that: i) the streamflow observations can be well tracked by 95% prediction intervals. ii) reducing streamflow observation error is the most efficient way to improve both deterministic and probabilistic predictions. iii) data assimilation scheme plays a vital role in hydrological predictions, especially for probabilistic ones (i.e., contributes 22% for the ensemble prediction uncertainty). Therefore, to improve the prediction accuracy, it is necessary to optimize the parameter assimilation schemes in hydrological data assimilation model.

Development of a Stepwise‐Clustered Multi‐Catchment Hydrological Model for Quantifying Interactions in Regional Climate‐Runoff Relationships

AbstractThe concurrent variations of multi‐catchment runoffs exist widely in natural hydrological systems. Approaching such variations requires integrated analyses of not only the climate‐runoff relationships within individual catchments but also the distributive interactions among multiple catchments. In this study, a stepwise‐clustered multi‐catchment hydrological model (SCMW) is proposed to tackle the interactive relationships among multi‐catchment runoffs and their concurrent variations within a watershed system. Through multivariate inference based on Wilks likelihood ratio criterions and F tests, the proposed model can deal with both continuous and discrete variables as well as nonlinear relations among multiple variables without the assumptions of functional relationships. The proposed SCMW is applied to the Iskut‐Stikine Watershed, Canada. The effects of multiple uncertain factors are traced through multilevel factorial analysis. Overall, the accuracies of SCMW‐simulated mean and interval flows demonstrate that the developed method can well reproduce the distributive and interactive relationships between climatic variables and multi‐catchment runoffs. At the same time, the contributions of climate variables can be quantified; for example, it is found that near‐surface minimum temperature (at Below Johnson Station) can explain 25.6% concurrent variations of multi‐catchment runoffs, and vapor pressure (at Below Johnson Station) and precipitation (at Telegraph Creek Station) can explain 17.5% and 4.6% of such variations, respectively. The results of the multilevel factorial analysis indicate that the uncertainties in the simulated runoff levels are mainly from the modeling approach (43.3%); also, significant effects exist from interactions among multiple impact factors. The molding of concurrent variations of multi‐catchment runoffs through SCMW is helpful for improving simulation accuracy for watersheds with spatially heterogeneous climate‐runoff relationships.

Tracing Uncertainty Contributors in the Multi‐Hazard Risk Analysis for Compound Extremes

AbstractIn this study, an iterative factorial multimodel Bayesian copula (IFMBC) framework was developed for revealing uncertainties in risk inferences of compound extremes under the consideration of diverse model structures and parameter sets. Particularly, an iterative factorial analysis (IFA) method would be advanced in IFMBC to track the dominant contributors to the imprecise predictions of multi‐hazard risks. The developed IFMBC framework was applied for the risk assessment of compound floods at two estuarine systems (i.e., Washington and Philadelphia) in US. The results indicate that the most likely compound events, under predefined return periods, exhibit noticeable uncertainties. Those uncertainties also present multiple hotspots which may be attributed to different impacts from different factors. By applying the IFA method, the results suggest the copula structure would likely be ranked as one of the top 2 impact factors for predictions of failure probabilities (FPs) in the scenarios of AND, and Kendall, with its contributions higher than 30% for FP in Kendall (more than 40% at Washington) and more than 25% for FP in Kendall (larger than 40% at Philadelphia). In comparison, the copula structure may not pose a visible effect on the predictive uncertainty for FP in OR, with its contribution possibly less than 5% under long‐term service time periods. However, the marginal distributions would have higher effects on FP in OR than the effects on the other two FPs. Particularly, the marginal distribution for the extreme variable with high skewness and kurtosis values tends to be ranked as one of the most significant impact factors for FP in OR. Also, the overall impacts from parametric uncertainties in both marginal and dependence models cannot be neglected for the predictions of all three FPs with their contributions probably larger than 20% under a short service time period. Compared with the traditional multilevel factorial analysis, the IFA method can provide more reliable characterization for uncertainty contributors in multi‐hazard risk analyses, since the traditional method seems to significantly overestimate the contributions from parameter uncertainties.

Ensemble Drought Exposure Projection for Multifactorial Interactive Effects of Climate Change and Population Dynamics: Application to the Pearl River Basin

AbstractWith a changing climate, drought has become a common natural disaster. In our study, population exposure to drought over the Pearl River Basin (PRB) under climate change is investigated. Drought frequency is evaluated through the Standardized Precipitation Evapotranspiration Index (SPEI). The data needed for SPEI calculation are obtained based on the ensemble of multiple global climate model (GCM) outputs. Population exposure to drought for the future is assessed by combining drought frequency under two emission scenarios (RCP4.5 and RCP8.5) with three downscaled population scenarios (SSP1, SSP2, and SSP3). Moreover, the main contribution (and their interactions) of GCM, RCP, and SSP to the sources of uncertainty on population exposure projections is explored through multilevel factorial analysis. Results indicate that the temperature and precipitation would continually increase for the future, and the increase in drought frequency is more substantial during the 2080s than in the 2050s. Meanwhile, population exposure to drought accounts for 21.60% of the total population in 1976–2005 over the PRB area. During the 2050s, it would decrease to 11.98–12.28% under RCP4.5 and 14.15–14.40% under RCP8.5, respectively. By the 2080s, population exposure would slightly reduce under RCP4.5 and increase to 28.86–29.44% under RCP8.5. GCM is the primary uncertainty source of drought exposure in the 2050s, with contribution rates of 72.41%, 57.47%, 51.10%, and 78.71% to the four responses. In comparison, by the 2080s, RCP is the primary contributing factor, with contribution rates of 53.91%, 44.92%, 64.20%, and 48.00%, respectively.

Optimisation of Bee Pollen Extraction to Maximise Extractable Antioxidant Constituents.

This paper presents the findings of a comprehensive review on common bee pollen processing methods which can impact extraction efficiency and lead to differences in measured total phenolic content (TPC) and radical scavenging activity based on 2,2-diphenyl-1-picrylhydrazyl (DPPH) and ferric reducing antioxidant power (FRAP) data. This hampers the comparative analysis of bee pollen from different floral sources and geographical locations. Based on the review, an in-depth investigation was carried out to identify the most efficient process to maximise the extraction of components for measurement of TPC, DPPH and FRAP antioxidant activity for two bee pollen samples from western Australia (Jarrah and Marri pollen). Optimisation by Design of Experiment with Multilevel Factorial Analysis (Categorical) modelling was performed. The independent variables included pollen pulverisation, the extraction solvent (70% aqueous ethanol, ethanol, methanol and water) and the extraction process (agitation, maceration, reflux and sonication). The data demonstrate that non-pulverised bee pollen extracted with 70% aqueous ethanol using the agitation extraction method constitute the optimal conditions to maximise the extraction of phenolics and antioxidant principles in these bee pollen samples.

Multi-level factorial analysis for ensemble data-driven hydrological prediction

Assessing the impacts of climate change on hydrologic regimes through hydrologic modeling is challenged by data uncertainty, predictor-selection uncertainty, and model uncertainty as well as their interrelationships. In this study, a Multi-level factorial ensemble data-driven hydrological model (MFEDHM) is developed to quantify the interactive, individual, and integrative impacts of multiple boundary conditions (e.g., climate conditions) on hydrological processes, and revealing the spatial heterogeneity of these impacts under various uncertainties and non-predictor impacts. In the MFEDHM, multi-level factorial analysis is integrated with ensemble prediction (i.e., Bayesian Model Averaging) and data-driven hydrological model. The MFEDHM is applied to quantitatively analyze the rainfall-runoff relationships of 16 catchments over China. Results reveal that the multilevel factorial analysis can accurately reveal both individual and interactive impacts of climate variables on hydrologic processes, and the impacts of non-climatic factors. As the most important finding of this study, climate-change impacts on hydrology show significant spatial heterogeneities over China. For instance, contemporaneous climatic conditions dominate (57%-64%) runoff changes and variations in Southern China, while precedent climate conditions pose significant impacts (20%-67%) on runoffs in Northern China; the overall influence of non-predictor factors (anthropogenic) on runoffs may decrease by 0.07% for the catchment-area increment of 10000 km2 and ranges from 4% to 27% over China. The development of the MFEDHM can enhance the reliability of ensemble hydrologic prediction, and provide scientific support for climate-change impacts assessment and adaptation under complexities.

Uncertainty quantification and partition for multivariate risk inferences through a factorial multimodel Bayesian copula (FMBC) system

In this study, a factorial multimodel Bayesian copula (FMBC) method is proposed to investigate various uncertainties in the copula-based multivariate risk models and further track the major contributors to the imprecise predictions for different risk indices. In FMBC, the copula models with different marginals and dependence structures will be firstly established with the parameter uncertainties being quantified by the adaptive Metropolis algorithm. A multilevel factorial analysis approach is then adopted to characterize the individual and interactive effects of marginals, copula functions and the associated parameter uncertainties on different risk indices. Moreover, a copula-based dependent sampling algorithm is proposed in the factorial analysis process to generate parameter samples under consideration of their correlation. The applicability of the FMBC approach is demonstrated through the multivariate flood risk analysis at two gauging stations in Wei River basin. The results indicate that extensive fluctuation exists in the inferences of multivariate return periods resulting from different marginal and dependence structures as well as the associated parameter uncertainties. For risk indices of the failure probabilities in AND and Kendall, their predictive variability can be mainly attributed to the uncertainties in model parameters and copula structure, with their total contribution more than 75%. In comparison, the failure probability in OR would be mainly influenced by the parameter uncertainty and also marginal structures, with their total contribution more than 80%. The copula structure would not have a visible effect on the failure probability in OR, with its contribution less than 5% for most scenarios. The obtained results can provide scientific support for reliable hydrological risk inferences within a multivariate context.

Effectiveness of a Shell and Helically Coiled Tube Heat Exchanger Operated With Gold Nanofluids at Low Concentration: A Multi-Level Factorial Analysis

Abstract This work assesses the thermal performance of gold nanofluid as a cooling liquid in a shell and helically coiled tube (SHCT) heat exchanger (HE) built at the bench scale. Tests planned under a multi-level factorial experimental design were carried out to evaluate the effects of the volumetric fraction of the gold nanoparticles, the volumetric flowrate of the working fluid, and the inlet temperature of the hot fluid (water) on the SHCT heat exchanger effectiveness. Spherical gold nanoparticles with a mean diameter of 14 ± 2 nm were produced using Turkevich’s method to be used at two concentrations of approximately 10−5 vol%. The heat transfer tests were performed at volumetric flowrates of 20, 30, and 40 l/h for both working fluids using heated water at inlet temperatures of 40, 50, and 60 °C. Results showed that the less concentrated nanofluids were comparatively more efficient, suggesting the presence of a range of gold concentration values for improving the heat transfer effectiveness.

Characterizing Impact Factors on the Performance of Data Assimilation for Hydroclimatic Predictions through Multilevel Factorial Analysis

In this study, the multi-level factorial analysis approach is employed to characterize the major impact factors on the performances of different data assimilation schemes. Four data assimilation methods, including EnKF and PF methods, and two integrated data assimilation methods are adopted for real-time hydrological prediction through a conceptual rainfall-runoff model in a catchment of Jing River. Different uncertainty scenarios for model inputs and outputs, as well as streamflow observations are tested through the multilevel factorial analysis to track the dominant impacts factors on the performances of data assimilation approaches. The multi-level factorial results suggest that, for different data assimilation schemes, the impacts from stochastic perturbations in model inputs, outputs and streamflow observations are different and some of them may be statistically insignificant. But the impact for one factor is generally dependent upon the others and scenarios with extreme stochastic perturbations (low or high) may more likely result in a good performance for all data assimilation schemes.

Stepwise clustering future meteorological drought projection and multi-level factorial analysis under climate change: A case study of the Pearl River Basin, China

Climate change has significant impacts on the Pearl River Basin, and the regional ecological environment and human production may face severe challenges in the future due to changes in temperature and precipitation, as well as their derivative disasters (e.g., drought). Therefore, a full understanding of the possible impacts of climate change on Pearl River Basin is desired. In this study, the potential changes in temperature, precipitation, and drought conditions were projected through a stepwise clustering projection (SCP) model driven by multiple GCMs under two different RCPs. The developed model could facilitate specifying the inherently complex relationship between predictors and predictands, and its performance was proven to be great by comparing the observations and model simulations. A multi-level factorial analysis was employed to explore the major contributing factors to the variations in projecting drought conditions. The results suggested that the Pearl River Basin would suffer significant increasing trends in Tmean (i.e., 0.25–0.34 °C per decade under RCP4.5 and 0.42–0.60 °C per decade under RCP8.5), and the annual mean precipitation would increase under both RCPs. The drought events lasting for 1–2 months would be decreased by 7.7%, lasting for 3–4 months would be increased by 4.3%, and lasting for more than five months would be increased by 3.4% under RCP4.5, respectively. While they changed to 6.1%, 1.4%, and 4.7% under RCP8.5, respectively. More medium and long-term drought events with higher drought severity would occur. GCM has dominant influences on four different responses of drought duration, accounting for 50.20%, 52.61%, 56.71%, and 56.24% of total variabilities, respectively. Meanwhile, the effects explained by GCM*RCP interactions cannot be neglected, with an average contribution rate of 44.37%, 37.86%, 37.66%, and 35.83%, respectively.

Quantifying uncertainties in temperature projections: A factorial-analysis-based multi-ensemble downscaling (FAMED) method

In this study, a factorial-analysis-based multi-ensemble downscaling (FAMED) method is developed through incorporating multi-level factorial analysis and multiple statistical methods within a general framework. FAMED can effectively downscale climate variables as an ensemble from a global scale to a local scale, as well as disclose the individual and interactive effects of global climate model (GCM), emission scenario (ES), statistical downscaling method (SDM) on climate projection responses. Then, FAMED is applied to the City of Nur Sultan (the capital of Kazakhstan) for projecting the future changes of daily maximum, mean and minimum temperatures (Tmax, Tmean and Tmin). The mean, extreme and trend indices of temperature projections under 60 simulation chains with five GCMs, three ESs and four SDMs are examined for the period of 2021–2100. Major findings are: (i) ensemble simulations under the sixty simulation chains show that Nur Sultan would experience a warming trend (0.00046–0.00566 °C/month of Tmax, 0.00049–0.00540 °C/month of Tmean, and 0.00056–0.00542 °C/month of Tmin) in 2021–2100; (ii) comparing with the base period (1979–2004), monthly maximum, mean and minimum temperatures would increase by 3.25–7.41 °C, 1.96–5.87 °C, 2.10–6.00 °C in the future period (2075–2100); (iii) GCM is the main factor affecting the mean values of temperature projections (its contribution >65%), ES is the primary factor for the trend of temperature projections (its contribution >80%), and both GCM and SDM have important effects on the extreme values of temperature projections (the total contribution >70%); (iv) among all GCMs and SDMs, IPSL-CM5A-LR and stepwise cluster analysis (SCA) have the best performances in the model validation, demonstrating that the two tools are applicable to other cities and regions in Central Asia.

Assessment of parameter uncertainty for non-point source pollution mechanism modeling: A Bayesian-based approach

Uncertainty assessment of parameters associated with non-point source pollution mechanism modeling are crucial for improving the effectiveness of pollution controlling. In this study, an approach based on Bayesian inference and integrated Markov chain Monte Carlo and multilevel factorial analysis has been developed, and it can not only apply straightforward Bayesian inference to assess parameter uncertainties, but also quantitatively investigate the main and interactive effects of multiple parameters on the model response variables by measuring the specific variations of model outputs. Its applicability and advantages are presented through the application of the Soil and Water Assessment Tool to Shitoukoumen Reservoir Catchment in northeast China. This study investigated the uncertainties of a set of sensitive parameters and their multilevel effects on model response variables, including average annual runoff (AAR), average annual sediment (AAS) and average annual total nitrogen (AAN). Results revealed that (i) soil conservation service runoff curve number for moisture condition II (CN2) had a positive effect on all response variables; (ii) available water capacity of the soil layer (SOL_AWC) had a negative effect on all response variables; (iii) the universal soil loss equation support practice (USLE_P) had a positive effect on AAS and AAN, and little effect on AAR; while the nitrate percolation coefficient (NPERCO) had a positive effect on AAN, and little effect on AAS and AAR; and (iv) the interactions amongst parameters had obvious interdependent effects on the model response variables, for example, the interaction between CN2 and SOL_AWC had a major impact on AAR. The above findings can improve the simulating and predicting capabilities of non-point source pollution mechanism model. Overall, this study highlights that the proposed approach represents a promising solution for uncertainty assessment of model parameters in non-point source pollution mechanism modeling.

A factorial Bayesian copula framework for partitioning uncertainties in multivariate risk inference

In this study, a factorial Bayesian copula (FBC) method is proposed to quantify parameter uncertainties in copula-based models and then reveal their impacts on hydrologic risk inferences within a multivariate context. In detail, Bayesian inference and factorial analysis are integrated into copula-based multivariate risk models to (1) quantify parameter uncertainties, (ii) reveal their individual and interactive effects, and (iii) identify their detailed contributions to uncertain risk inferences. Streamflow observations at Xiangxi and Wei River basins is China are used to illustrate the applicability of FBC. The results indicate that imprecise parameters in marginal distributions and the dependence structure would lead to extensive uncertainties in predictive joint return periods and failure probabilities. Also, individual and interactive effects of parameters are well revealed through multilevel factorial analysis, and the detailed contributions of one parameter to different failure probabilities under different service time scenarios are identified.

A Bayesian-based multilevel factorial analysis method for analyzing parameter uncertainty of hydrological model

In this study, a Bayesian-based multilevel factorial analysis (BMFA) method is developed to assess parameter uncertainties and their effects on hydrological model responses. In BMFA, Differential Evolution Adaptive Metropolis (DREAM) algorithm is employed to approximate the posterior distributions of model parameters with Bayesian inference; factorial analysis (FA) technique is used for measuring the specific variations of hydrological responses in terms of posterior distributions to investigate the individual and interactive effects of parameters on model outputs. BMFA is then applied to a case study of the Jinghe River watershed in the Loess Plateau of China to display its validity and applicability. The uncertainties of four sensitive parameters, including soil conservation service runoff curve number to moisture condition II (CN2), soil hydraulic conductivity (SOL_K), plant available water capacity (SOL_AWC), and soil depth (SOL_Z), are investigated. Results reveal that (i) CN2 has positive effect on peak flow, implying that the concentrated rainfall during rainy season can cause infiltration-excess surface flow, which is an considerable contributor to peak flow in this watershed; (ii) SOL_K has positive effect on average flow, implying that the widely distributed cambisols can lead to medium percolation capacity; (iii) the interaction between SOL_AWC and SOL_Z has noticeable effect on the peak flow and their effects are dependent upon each other, which discloses that soil depth can significant influence the processes of plant uptake of soil water in this watershed. Based on the above findings, the significant parameters and the relationship among uncertain parameters can be specified, such that hydrological model’s capability for simulating/predicting water resources of the Jinghe River watershed can be improved.

Factorial-Based Inexact Stochastic Fuzzy Chance Constraint Programming Framework for Municipal Solid Waste Management with GHG Emission Trading: Analysis of Multilevel Parametric Interactions

This study proposes a factorial inexact stochastic fuzzy chance constraint programming framework for dealing with uncertainties in municipal solid waste management under consideration of greenhouse gas (GHG) emission trading. It can reflect uncertainties expressed as fuzzy, interval, and random variables and generate desired management strategies for minimizing the integrated cost for solid waste disposal and purchasing GHG emission credit. Moreover, multilevel factorial analysis is conducted to reveal the main and interactive effects of uncertain parameters. The results show that effective waste allocation schemes can be obtained to meet the waste disposal demands and GHG emission requirements under different α-cut levels. The changes in the fuzzy confidence level have impacts on the waste allocation schemes, especially for the waste flow to the incinerator. The disposal cost differs across the three levels of 0.3, 0.5, and 0.7 for incinerator capacity constraint when the fuzzy confidence level of composting capacity constraint is equal to 0.5, implying the existence of the interaction between uncertainties in the incinerator and composting facility. Comparison between the waste management practices with and without considering GHG emission requirements indicates that the purchase of GHG emission credits would contribute about 10 % to the total cost, which would not be influenced significantly by the α-cut level.