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

Relating Net Nitrogen Input in the Mississippi River Basin to Nitrate Flux in the Lower Mississippi River: A Comparison of Approaches

A quantitative understanding of the relationship between terrestrial N inputs and riverine N flux can help guide conservation, policy, and adaptive management efforts aimed at preserving or restoring water quality. The objective of this study was to compare recently published approaches for relating terrestrial N inputs to the Mississippi River basin (MRB) with measured nitrate flux in the lower Mississippi River. Nitrogen inputs to and outputs from the MRB (1951 to 1996) were estimated from state-level annual agricultural production statistics and NOy (inorganic oxides of N) deposition estimates for 20 states that comprise 90% of the MRB. A model with water yield and gross N inputs accounted for 85% of the variation in observed annual nitrate flux in the lower Mississippi River, from 1960 to 1998, but tended to underestimate high nitrate flux and overestimate low nitrate flux. A model that used water yield and net anthropogenic nitrogen inputs (NANI) accounted for 95% of the variation in riverine N flux. The NANI approach accounted for N harvested in crops and assumed that crop harvest in excess of the nutritional needs of the humans and livestock in the basin would be exported from the basin. The U.S. White House Committee on Natural Resources and Environment (CENR) developed a more comprehensive N budget that included estimates of ammonia volatilization, denitrification, and exchanges with soil organic matter. The residual N in the CENR budget was weakly and negatively correlated with observed riverine nitrate flux. The CENR estimates of soil N mineralization and immobilization suggested that there were large (2000 kg N ha-1) net losses of soil organic N between 1951 and 1996. When the CENR N budget was modified by assuming that soil organic N levels have been relatively constant after 1950, and ammonia volatilization losses are redeposited within the basin, the trend of residual N closely matched temporal variation in NANI and was positively correlated with riverine nitrate flux in the lower Mississippi River. Based on results from applying these three modeling approaches, we conclude that although the NANI approach does not address several processes that influence the N cycle, it appears to focus on the terms that can be estimated with reasonable certainty and that are correlated with riverine N flux