Shoufan Fang

Mapping Multiple Variables for Predicting Soil Loss by Geostatistical Methods with TM Images and a Slope Map

Soil erosion is widely predicted as a function of six input factors, including rainfall erosivity, soil eredibility, slope length, slope steepness, cover management, and support practice. Because of the multiple factors, their interactions, and their spatial and temporal variability, accurately mapping the factors and further soil loss is very difficult. This paper compares two geostatistical methods and a traditional stratification to map the factors and to estimate soil loss. Soil loss is estimated by integrating a sample ground data set, TM images, and a slope map. The geostatistical methods include collocated cokriging and a joint sequential co-simulation model. With both geostatistical methods, local estimates and variances at any location cohere the factors and soil loss are unknown can be computed. The results showed that the two geostatistical methods performed significantly better than traditional stratification in terms of overall and spatially explicit estimate. Furthermore, the cokriging led to higher accuracy of mean estimates than did the co-simulation, while the latter provided decision makers with reliable uncertainties of the local estimates as useful information to assess risk when making decisions based on the prediction maps.

Mapping and uncertainty of predictions based on multiple primary variables from joint co-simulation with Landsat TM image and polynomial regression

In the management of natural resources, multiple variables correlated with each other usually need to be mapped jointly. However, joint mapping and spatial uncertainty analyses are very difficult mainly because of interactions among variables and imperfection of existing methods. There is abundant evidence that considering interactions among variables and spatial information from neighbors can result in improved maps. This study presents a remote sensing-aided method for that purpose. The method is based on the integration of joint sequential co-simulation with Landsat TM image for mapping and polynomial regression for spatial uncertainty analysis. The method was applied to a case study in which ground cover (GC), canopy cover (CC), and vegetation height (VH) were jointly mapped to derive a map of the vegetation cover factor for predicting soil loss. The variance contributions from the variables, their interactions, and the spatial information from neighbors leading to uncertainty of predicted vegetation cover factor were assessed. The results showed that in addition to unbiased maps, this method reproduced the spatial variability of the variables and the spatial correlation among them, and successfully quantified the effect of variation from all the components on the prediction of the vegetation cover factor.

The Impact of Misclassification in Land Use Maps in the Prediction of Landscape Dynamics

Land use maps are widely used in modeling land use change, urban sprawl, and for other landscape related studies. A misclassification confusion matrix for land use maps is usually provided as a measure of their quality and uncertainty. However, this very important information is rarely considered in land use map based studies, especially in modeling landscape dynamics. Ignoring uncertainty of land use maps may cause models to provide unreliable predictions. This study is an attempt to investigate the impact of the accuracy of land use maps used as input for an urban sprawl model. In the study area, the regional confusion matrix has been localized using a topographical map. Based on the regional and local confusion matrices, several error levels have been defined. The results showed that a localized confusion matrix that reflected the characteristics of the study area had error rates that were much different than the regional confusion matrix. The predictions of the probability of urban sprawl based on the land use maps and defined error levels were quite different.

Improved generalized Fourier amplitude sensitivity test (FAST) for model assessment

The Fourier amplitude sensitivity test (FAST) can be used to calculate the relative variance contribution of model input parameters to the variance of predictions made with functional models. It is widely used in the analyses of complicated process modeling systems. This study provides an improved transformation procedure of the Fourier amplitude sensitivity test (FAST) for non-uniform distributions that can be used to represent the input parameters. Here it is proposed that the cumulative probability be used instead of probability density when transforming non-uniform distributions for FAST. This improvement will increase the accuracy of transformation by reducing errors, and makes the transformation more convenient to be used in practice. In an evaluation of the procedure, the improved procedure was demonstrated to have very high accuracy in comparison to the procedure that is currently widely in use.

A Methodology for Spatial Uncertainty Analysis Of Remote Sensing and GIS Products

When remote sensing and GIS products are generated, errors and uncertainties from collection, processing and analysis of image and ground data, and model development, accumulate and are propagated to the maps. The products thus possess many sources of uncertainties that vary spatially and temporally. Spatially identifying the sources of uncertainties, modeling their accumulation and propagation, and finally, quantifying them will be critical to control the quality of spatial data. This paper demonstrates a methodology and its applications for a case study in which uncertainty of predicted soil erosion is hierarchically partitioned into various primary components on a pixel-by-pixel basis. The methodology is based on a regionalized variable theory of variables. It integrates remote sensing aided co-simulation algorithms in geostatistics, and uncertainty and error budget methods in uncertainty analysis. The simulation algorithms generate realizations that can be used to calculate local estimates, and the variances and co-variances between them. Uncertainty and error budget methods partition the uncertainty of output into various input components and quantify their relative uncertainty contributions. The results can thus suggest the main uncertainty sources and their variation spatially, and further provide a rationale to reduce errors in map generation and application.

Estimation of sensitivity coefficients of nonlinear model input parameters which have a multinormal distribution

This paper considers the estimation of sensitivity coefficients based on sequential random sampling when the input parameters of a nonlinear model are correlated and have a multinormal distribution. Due to the difficulties in generating sequential random samples for correlated model inputs and the properties of response surface models, sampling-based (simulation- and experiment-based) methods could not be used to estimate sensitivity coefficients of correlated model inputs. For this reason, an algorithm based on multi-expressions of multinormal distribution has been developed and used to generate sequential random samples for estimation of sensitivity coefficients. The multi-expression approach has very high accuracy in generating multinormal random samples. The estimated sensitivity coefficients based on sequential random samples changed when sample size changed. Most estimates converged with a sample size of 5000. Model structure mainly determined the speed of convergence. Both correlation among input parameters and model structure influenced the estimates of sensitivity coefficients. The sensitivity coefficients were compared to global partial derivatives that were computed using numerical integration.

A Bayesian approach for estimating the parameters of a forest process model based on long-term growth data

Process-based models are increasingly being used to model growth dynamics of forest ecosystems. Ideally, estimates of the parameters for these types of models should be obtained through physiological experiments. However, in many situations there is little or no experimental data available to parameterize such models. This paper presents some results of an ongoing study on alternative methods to estimate physiological parameters that are not readily available. The specific focus of this paper is the use of a Bayesian approach based on rejection sampling for estimating physiological parameters using observed state variables of process-based models for forest growth. The method is computationally intensive and can be used to estimate model parameters and their multi-dimensional distributions. The method is used to estimate some of the physiological parameters of a process-based growth model for Norway spruce [Picea abies (L.) Karst.] in Denmark. The estimated one-, two-, and three-dimensional distributions of the parameters of the process-based growth model are given.

Prediction of multinomial probability of land use change using a bisection decomposition and logistic regression

Land use change is an important research area in landscape ecology and urban development. Prediction of land use change (urban development) provides critical information for making the right policies and management plans in order to maintain and improve ecosystem and city functions. Logistic regression is a widely used method to predict binomial probabilities of land use change when just two responses (change and no-change) are considered. However, in practice, more than two types of change are encountered and multinomial probabilities are therefore needed. The existing methods for predicting multinomial probabilities have limits in building multinomial probability models and are often based on improper assumptions. This is due to the lack of proper methodology and inadequate software. In this study, a procedure has been developed for building models to predict the multinomial probabilities of land use change and urban development. The foundation of this procedure consists of a special bisection decomposition system for the decomposition of multiple-class systems to bi-class systems, conditional probability inference, and logistic regression for binomial probability models. A case study of urban development has been conducted to evaluate this procedure. The evaluation results demonstrated that different samples and bisection decomposition systems led to very similar quality and performance in the developed multinomial probability models, which indicates the high stability of the proposed procedure for this case study.

Mapping vegetation cover change using geostatistical methods and bitemporal Landsat TM images

Accurately mapping change in vegetation cover is difficult due to the need for permanent plots to collect field data of the change; errors from georeference, coregistration, and data analysis; a small coefficient of correlation between remote sensing and field data; and limitations of existing methods. In this study, four cosimulation procedures, two collocated cokriging procedures, and two regression procedures were compared. The results showed that with the same cosimulation or collocated cokriging methods, two postestimation procedures led to more accurate estimates than the corresponding two preestimation procedures. Among three postestimation procedures with the same image data, cosimulation resulted in the most accurate estimates and reliable variances, then regression modeling and collocated cokriging. Thus, cosimulation algorithms can be recommended for this purpose. Moreover, the accuracy by a joint cosimulation procedure of 1989 and 1992 vegetation cover was similar to that by a separate cosimulation procedure; however, the joint cosimulation overestimated the average change. In addition, adding more Thematic Mapper images increased the accuracy of mapping for the cosimulation procedures, and the increase was slight for the regression procedures.

Partitioning Spatial Model Uncertainty Based on Joint Spatial Simulation

In this study, an uncertainty analysis procedure for joint sequential simulation of multiple attributes of spatially explicit models used in geographical informational systems 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 cell by cell basis. In the partitioning, the correlation of neighboring cells 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 output and model input parameters. It was also shown for the case study that: (1) the uncertainty of soil erodibility of a cell is mainly propagated from its own soil properties; (2) the interactions of soil properties of neighboring cells could reduce uncertainty of soil erodibility; (3) it is sufficient for uncertainty analysis to include the nearest three neighboring cell groups; and (4) the largest uncertainty contributors vary by soil properties and location.