UNCERTAINTY ANALYSIS OF A PIPE MODEL BASED ON CORRELATED DISTRIBUTIONS

Traditionally, uncertainty analysis of complex simulation models has been conducted based on the assumption of that the components of the model are independent. In practice, correlation is universal in ecosystems. This study applied Bayesian estimation and rejection sampling to generate correlated random samples for an uncertainty analysis of a process based forest growth model, a pipe model. Comparison of error budgets built using independent and correlated distributions shows that correlated distributions are very important to provide reasonable and realistic simulation and uncertainty analysis

AN UNCERTAINTY ANALYSIS PROCEDURE FOR SPATIALLY JOINT SIMULATIONS OF MULTIPLE ATTRIBUTES

In this study, an uncertainty analysis procedure for joint sequential simulation of multiple attributes of spatially explicit models was developed based on regression analysis. This procedure utilizes information obtained from joint sequential simulation to establish the relationship between model uncertainty and variation of model inputs. Using this procedure, model variance can be partitioned by model input parameters on a pixel by pixel basis. In the partitioning, the correlation of neighboring pixels is accounted for. With traditional uncertainty analysis methods, this is not possible. In a case study, spatial variation of soil erodibility from a joint sequential simulation of soil properties was analyzed. The results showed that the regression approach is a very effective method in the analysis of the relationship between variation of the model and model input parameters. It was also shown for the case study that (1) uncertainty of soil erodibility of a pixel is mainly propagated from its own soil properties, (2) soil properties of neighboring pixels contribute negative uncertainty to soil erodibility, (3) it is sufficient for uncertainty analysis to include the nearest three neighboring pixel groups, and (4) the largest uncertainty contributors vary by soil properties and location

SPATIAL VARIABILITY IN AGGREGATION BASED ON GEOSTATISTICAL ANALYSIS

This study derived the equations for computing the spatial variability in the aggregation of original maps of continuous attributes. The derivation of the equations is based on traditional statistical and geostatistical principles. The derived equations can be used to compute the variance, covariance, and spatial (auto-/cross-) covariance of the aggregated pixels and sub-areas in a given study area. Using the derived equations, the total uncertainty within a study area will not change after aggregation. For a case study, it has been shown that aggregation will reduce the values of variance/covariance and spatial covariance of the aggregated individual pixels. It was also verified that the original semivariogram models should not be used for the aggregated maps to compute spatial covariances. It is suggested to use the original scales in geostatistical analyses to produce maps and then produce courser scaled maps through aggregation

Uncertainty Analysis of Biological Nonlinear Models Based on Bayesian Estimation

120 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.The general goal of this study is to develop an uncertainty analysis procedure based on realistic distribution for nonlinear models, especially biological models. Parameter estimation, random number generation, and uncertainty analysis are closely related in Monte Carlo simulation based model assessment. All three aspects are discussed in this study. Because of the complexity of models and inflexibility of estimation methods, existing estimation methods can not properly estimate the parameters of nonlinear biological models. Assessment of these models is based on unrealistic independent distribution of the parameters. Model assessment may provide incorrect information when parameter distribution is not realistic. In this study, Bayesian estimation with rejection sampling has been extended to estimate the parameters of nonlinear models. This estimation method can estimate marginal distributions and correlation among all parameters of nonlinear models. A sampling algorithm, Conditional Independent Sampling, has been developed to increase sampling efficiency and to increase the accuracy of the generated random samples. An uncertainty analysis method based on improved Monte Carlo has also been developed to fit the characteristics of the correlated joint distribution in establishing error budgets. The model assessment based on this method is very close to that based on crude Monte Carlo. The error budgets based on realistic correlated distribution are much more reasonable compared to those based on assumed independent distribution. The capability and flexibility of these alternative methods have been demonstrated by applications.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD