A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> Error Propagation in GIS Analysis <s> A method has been developed to investigate the sensitivity of the solutions of large sets of coupled nonlinear rate equations to uncertainties in the rate coefficients. This method is based on varying all the rate coefficients simultaneously through the introduction of a parameter in such a way that the output concentrations become periodic functions of this parameter at any given time t. The concentrations of the chemical species are then Fourier analyzed at time t. We show via an application of Weyl's ergodic theorem that a subset of the Fourier coefficients is related to 〈∂ci/∂kl〉, the rate of change of the concentration of species i with respect to the rate constant for reaction l averaged over the uncertainties of all the other rate coefficients. Thus a large Fourier coefficient corresponds to a large sensitivity, and a small Fourier coefficient corresponds to a small sensitivity. The amount of numerical integration required to calculate these Fourier coefficients is considerably less than that requi... <s> BIB001 </s> A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> Error Propagation in GIS Analysis <s> Abstract Different error budgets were approximated for a Weibull based growth projection system used to develop short- and long-term management plans for even-aged loblolly pine plantations. These budgets were developed as part of a ‘total quality’ program for a medium sized forest products corporation in the United States. The purpose of the assessment was to learn in a systematic and comprehensive fashion about the strengths and weaknesses of the overall system, as well as its components. More than twenty sources of error were considered in the development of the budgets through time. It was found in general that the predictions made with the projection system did not meet the precision standards required by the corporation. <s> BIB002 </s> A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> Error Propagation in GIS Analysis <s> Definition and identification of an error model for quantitative spatial attributes identification of the error model - a case study error propagation with local GIS operations - theory error propagation with local GIS operations - applications error propagation with global GIS operations - the use of multidimensional simulation implementation of error propagation techniques in GIS. <s> BIB003
Error propagation in spatial analysis is defined as the process whereby error is propagated from the original dataset to the resulting dataset generated by a spatial operation. The two approaches for modelling error propagation in spatial analyses are the analytical approach such as error propagation law in statistics and simulation approach such as Monte Carlo simulation for either raster based or vector based spatial analysis environment (Abbaspour at al. 2003) . When a spatial dataset is generated, errors and uncertainties starting from data collection, processing, analysis of data and model development, get accumulated and propagated to the final output maps. Thus the data products possess many sources of uncertainties varying spatially and temporally. To control and maintain the quality of a spatial data, it is crucial to spatially identify the sources of uncertainties, model their accumulations and propagation and finally to quantify them.  systematically discussed the sources and classification of the errors and uncertainties and suggested priorities for error quantification. Several methods were used for assessing the sources of uncertainty, including Monte Carlo methods BIB003 Openshaw,1992) , Fourier Amplitude Sensitivity Test [FAST] BIB001 , Taylor Series BIB002 , Polynomial Regression  ) and Sobol's method  . If uncertainty analysis is ignored, there might be incorrect predictions and analyses that are fatally flaw. A sensitivity analysis can be applied for studying propagation of attribute uncertainty in a spatial analysis. If errors of input data are unknown, a sensitivity analysis can be applied to study the relationships between input and output errors in a function transformation. One limitation of a sensitivity analysis is that it cannot give the mathematical expression of attribute uncertainty propagation analytically.  reviewed methods and applications of sensitivity analysis for attribute uncertainties analysis. Basically for each source layer in a GIS operation the uncertainty which is present in the data will be propagated through the operation becomes the input of another.