Study On The Changes Of Slope Statistical Distribution With Resolution And Terrain Complexity

Slope steepness(slope)is one of the main quantitative topographic variables,and its research is of great significance for land use,remote sensing and geographic information science.Slope calculation based on DEM has become a method for many geographical models to obtain slope data.Slope is affected by DEM resolution and terrain complexity.But at present,there is not enough understanding of slope change mechanism in the study of slope distribution changing with DEM resolution,and the research on slope distribution changing with terrain complexity is not systematic.The slope has been analyzed as a whole in these two aspects.Starting from the elevation gradient(p and q)which is the basic terms of slope,different elevation gradient algorithms are compared,and the basic statistical characteristics of elevation gradient are studied.Then a series of sample areas with different terrain complexity are selected and a series of DEM with different resolution from10m to 200m are generated.And the change of elevation gradient,variance of the gradient(?_g)and slope with resolution and its components and terrain complexity are analyzed.Finally,the effects of DEM resolution and terrain complexity are compared.The main innovations of this study are as follows:first,the theory of harmonic analysis is introduced to provide a new method for the evaluation of algorithm accuracy;second,the root of slope attenuation with the decrease of resolution is the attenuation of p and q and variance of the gradient(?_g)with resolution,which is the deep reason of slope change.This study is of great significance for more scientific and accurate calculation of slope and slope related composite terrain parameters in digital terrain analysis,providing more accurate slope data for geoscience model,and promoting the understanding of relationship between slope and terrain development.The main research results are as follows:(1)The Evans-Young(EY)algorithm is optimal algorithm:From the spatial pattern and uncertainty results,the EY algorithm has the smoothest surface,the least noise,the strongest anti noise ability and the smallest error.The result of harmonic analysis show that from low frequency to 200c/u,the EY algorithm is good because of its stability and anti-noise ability and the Sb algorithm is good because of its precision.When the frequency reaches 700c/u,the Sb algorithm is the only good choice.There are four basic statistical characteristics of elevation gradient which are p and q are normal distribution;the average values of p and q are equal to zero;p and q are independent from each other;and the variances of p and q are equal.The geomorphological basis of the four characteristics of elevation gradient is the alternate distribution of ridges and valleys caused by geomorphic cycle,and the random characteristics of elevation distribution and geomorphic development.(2)As the DEM resolution becomes coarser,elevation gradient and variance of the gradient(?_g)attenuates which is the root of slope attenuation:As the resolution becomes coarser,the image of elevation gradient becomes smoother,the entropy decreases,and more and more information is lost;the range and variance of p and q decrease,the distribution becomes concentrated and variance of the gradient(?_g)decreases.The attenuation of elevation gradient and variance of the gradient(?_g)is the root of slope attenuation and the driving factor of slope scale effect.The change law of elevation gradient and variance of the gradient(?_g)with the increase of smoothness are similar with that with the lower resolution or with that with the increase of sampling spacing.The difference is that the p and q results of all smoothing effect are close to those of all resolutions,while the data of all sampling effect are attenuated severely,the information is seriously lost,and the range and variance are small.Variance of the gradient(?_g)results of all smoothing effect are close to those of all resolutions,while variance of the gradient(?_g)of all sampling effect are attenuated and small.The influence of resolution on elevation gradient and variance of the gradient(?_g)mainly comes from the effect of smoothing,and sampling has a certain effect,but it is not the main factor.(3)The change law of slope with the resolution becomes coarser is consistent with the terrain complexity simplifies:With resolution becomes coarser,the slope image becomes smoother,and the entropy decreases,the information is lost;the average value and variance of slope are all decreased;all slope tends to be gentle,the curves change from"short"and"fat"to"high"and"thin",the range of slope value is also decreased.With resolution becomes coarser,when the cumulative frequency reaches 99.9%,the slope value becomes smaller and smaller on cumulative frequency curves.The change law of slope with the increase of smoothness are similar with that with the lower resolution or with that with the increase of sampling spacing.The difference is that the slope results of all smoothing effect are close to those of all resolutions,while much information is lost of all sampling effect data,and the mean and variance are small.The influence of resolution on slope mainly comes from the effect of smoothing,and the sampling is not the main factor.The change of p and q,variance of the gradient(?_g)and slope with terrain complexity simplifies is similar to that with resolution becomes coarser.In the same region,in the terrain expression sequence of DEM resolution from fine to coarser,it is similar to geomorphic development from the mature to old stage,and the terrain changes from complex to simple in the terrain change sequence.They have the same geomorphological basis and can be regarded as a process of spatial and temporal generation.