| Digital Terrain Analysis(DTA)is one of digital information processing technologies on terrain attribute calculation and feature extraction based on Digital Elevation Model(DEM).Over the past 40 years,it has been widely used in many fields,such as civil engineering,hydraulic engineering,and military communication and so on,which has produced significant social and economic benefits.Therefore,the theories,methods and applications of DTA have been a research focus in geography,geomorphology and geographic information science.Uncertainty,as one of the basic components of real world,is a concept that cannot be avoided.Uncertainty theories have been regarded as an important component of basic theory in many areas of different subjects,especially in the field of geographic information science(GISicence),uncertainty problem was regarded as one of the research cores in GISicence.As a hot issue in the field of GISicence,DTA has been studied by many scholars,and achieved rich results in past twenty years.According to previous studies,the uncertainty of DTA includes two aspects:one is the uncertainty of DEM data;the other is the uncertainty of DTA calculation methods.The uncertainties of DEM data mainly include the system errors caused by the acquisition of DEM source data and the errors of DEM interpretation algorithm.The uncertainties of DTA calculation methods are mainly caused by the error of calculation method itself,the propagation error of DEM data source error and DEM resolution and the level of terrain complexity,etc.The uncertainties of DEM data have been studied by many researchers.However,the study of the uncertainties of DTA calculation methods is relatively few,and the researches mainly concentrate on the uncertainties of the calculation of slope,slope length,profile curvature and so on.Consequently,this paper will focus on the uncertainties of DTA calculation methods.We select one surface area calculation method and two volume calculation methods of DTA as research object.Uncertainty modeling and analysis of these methods are studied based on regular grid DEM.The main contents of this paper are:1)The Selection and derivation of calculating methods on surface area and volume;2)The modelling and analysis of truncation error;3)The modelling and analysis of error propagationThrough the comparative analysis of the experimental results,we can obtain the following conclusions:1)The uncertainties of surface area calculation of DTA(1)In the case of no data source error,with the improvement of DEM resolution,the absolute error' value and truncation error'value of surface area calculation gradually decreases,while with the level of terrain complexity becoming high,the absolute error' value and truncation error' value of surface area calculation gradually increases.DEM resolution and the level of terrain complexity affect the accuracy of calculation on surface area and volume together,but the level of terrain complexity is more significant.(2)In the case of having data source error,for surface area calculation,when the level of terrain complexity or DEM resolution increases,the same RMSE of coordinate or elevation all leads the RMSE of surface area increasing through the error propagation of calculation method.However,due to different constraints of RMSE and absolute error,the trends between two errors show inconsistent.The increase of RMSE'value of coordinate or elevation does not mean that the absolute error' value will become larger.For RMSE is a kind of relative error,there are essential diferences between RMSE and absolute error.(3)In the case of having data source error,for surface area calculation,when the RMSE'value of elevation is relatively high,random elevation error has a great interference on the error caused by the level of terrain complexity,generating offsetting phenomenon.The offsetting phenomenon results in large changes of the relationship between the level of terrain complexity and the accuracy of surface area calculation.However,these will not happen when the RMSE'value of elevation is low.(4)In the case of having data source error,for the surface area calculation method adopted in this paper,when DEM resolution and the level of terrain complexity are the same,the spatial structure of the distribution of random errors determines the size of the calculations deviation compared to the theoretical true value.The size of the RMSE of the random error determines the degree of deviation from the theoretical true value;namely,determine the fluctuation range of the deviation value.2)The uncertainties of volume calculation of DTA(1)In the case of no data source error,when the TDR method is used to calculate volume,with the improvement of DEM resolution,the absolute error' value and the truncation error'value of volume calculation gradually decreases,while with the level of terrain complexity becoming high,the absolute error' value and truncation error'value of volume calculation gradually increases.When the SDR method is used to calculate volume,with the improvement of DEM resolution,the truncation error'value of volume calculation still gradually decreases,but the absolute error' value has a slight fluctuation due to over parametric fitting.When the SDR method is used to calculate volume,with the level of terrain complexity becoming high,the absolute error' value and truncation error'value of volume calculation also gradually increases.(2)In the case of having elevation error,SDR shows a weaker stability of volume calculation accuracy than TDR.Because in the case of having elevation error,the calculation accuracy of SDR has some changes compared to the calculation accuracy in error-free case,but the calculation accuracy of TDR has not changes regardless of whether having an error.(3)In the case of having data source error,for volume calculation,the absolute error' value of volume calculation does not all enlarge with the increase of RMSE'value of elevation.Whether using TDR method or SDR method,the absolute error all shows a strong fluctuation,which mainly caused by the spatial distribution of elevation error other than the spatial autocorrelation correlation of elevation error.The fluctuation is less restricted by the complexity of terrain,for each terrain,the fluctuation of absolute error have a greater randomness.Yet the fluctuation is obviously constrained by DEM resolution,with DEM resolution increasing,the fluctuation range of absolute error will be reduced significantly.(4)In the case of having data source error,when DEM resolution and elevation error are the same,the RMSE of volume calculation is not related to terrain complexity,but only has a relationship with DEM resolution.These conclusions can enrich uncertainty modelling and analysis related theories of DTA and has some practical guidance for surface and volume calculation.3)Comprehensive conclusionIn the actual accuracy assessment,the distinction between absolute error and relative error should be distinguished according to research problem.Relative errors can only reflect system internal accuracy.For system external accuracy,the absolute error should be used as the evaluation standard as far as possible.It can not blindly replace absolute error with relative error to evaluate the accuracy.It is easily cause the the final evaluation results to produce some errors. |
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