Construction And Quality Evaluation Of Slope And Apsect Based On Orthogonal Curves

The slope and aspect have been emphasized as two critically important indices describing the morphological characteristics of terrain.These two indices became vital terrain factors that were widely-used in various research,such as soil erosion,landslide monitoring,hydrological research,land use,soil and water conservation planning,etc.However,it is a difficult problem that how to obtain the ‘truth data' for these two factors.Usually,the value of these two factors can be acquired by mathematical simulation or field measurement,while how to conduct the field measurement and asses the data quality is still rarely investigated.The experiments were conduct at a slope surface located in the loess plateau.Based on the maximum grade line,there are a total of 144 elevation data were sampled using digitizing collection method.These data were then used to do three explorations:(1)analyst of changes of measured slope,(2)the influence of microtopography on the calculation of maximum drop slope,and(3)the comparisons of the measured slope and aspect,respectively,using the finite difference of slope degree by the Digital Elevation Model(DEM).The results showed that the measured slope and aspect was greatly impacted by several factors,such as the terrain factor,locating of the maximum grade line,the measured method,calculation models,etc.Therefore,this study proposed an Orthogonal Curves Slope and Aspect Model(OCSAM).The experiments were conducted on three explorations,model calibration,model validation,and the application of the OCSAM model.The main results are as follows.First,the maximum slope and aspect were greatly influenced by terrain factor.Also,the calculations were mainly impacted by the location of the maximum grade line.Additionally,the measurement of the maximum grade line was conducted using different methods that were upper tangent,down secant,fitted line,and compass slope.The results showed that the upper tangent and the compass slope were greatly impacted by microtopography,while the down secant and the fitted line were not significantly impacted by microtopography.Comparisons of the finite difference of slope and aspect based on DEM revealed that the slope was more accurate than the aspect.The results also showed that the mean value of difference between the simple difference and measured slope and aspect performed better to other difference method,but its dispersion degree is obvious,which shows that the random error of the simple difference method is greatly influenced by various errors.Second,OCSAM was developed based on Gauss synthesized surface.The comparisons between the morphology of the orthogonal curves and the theorical curves(TC)illustrated that using the cubic spline curves could reduce the error from orthogonal curves.Also,the difference between the orthogonal curves slope and aspect and theorical value increased with the increase of sampling interval.Especially,the difference greatly increased when the sampling interval was larger than 25 m.The results also showed that calculation was not significantly impacted by the error of sampling plane,while it was greatly influenced by the error of elevation.The results implied that the influence of elevation on the calculation of slope and aspect is greatly increasing in the flat terrain with smaller sampling intervals,the slope is more sensitive than the aspect.Third,the OCSAM effectively performed in field work at the coarser resolution because that it was not greatly impacted by the terrain and vegetation.The results demonstrated that the orthogonal curves slope and aspect were significantly influenced by cellsize,slope were reduced when resolution drop,apsect tend to be single with resolution reduction Specifically.Also,the difference of orientation has little effect on the slope and aspect,which was about 0.1°.Under the same observation condition,the orthogonal curves slope and the slope of the maximum grade line had positive correlation of approximate 1:1,while dispersion degree increased with increasing the slope.The orthogonal curves aspect using the 16-node had a similarity value of 64.58% comparing to the aspect of the maximum grade line.Furthermore,the comparisons between the finite difference based on DEM and the OCSAM showed that the slope difference resulted from the random error.The mean value of slope difference is the best matching with simple difference,the second is second order finite difference.But the variation range of slope difference is the worst with simple difference,the second is second order finite difference,the next is Frame difference,third order finite difference,third order finite difference weighted by reciprocal of squared distance and third order finite difference weighted by reciprocal of distance performed best.The orthogonal curves aspect using the 16-node had a similarity value of 75.69% comparing to the aspect of finite difference based on DEM.Last,the results showed that the error of elevation from DEM data was influenced on each other.The error of elevation increased with the grid size increased,the slope and aspect based on DEM was significantly impacted by the error of elevation.Also,the results showed that with increasing of grid size,different finite difference methods had different performances that(1)the third-order finite difference method performed better than other methods,(2)the simple finite difference method performed worst than any other,(3)With the increase of grid size,the influence of elevation error on slope and aspect was becoming lower,and the slope and aspect was more impacted by the terrain factor,(4)The aspect is more affected by the elevation error than the slope.especially in the flat terrain area,and(5)the influenced of the slope and aspect on the coordinate system transformation showed a law of periodic sine of 90°.Further,when evaluating the DEM quality based on OCSAM model,the aspect can be used to assess the sequence error of elevation data,the slope can be used to assess the elevation error of DEM.Overall,the OCSAM can not only solve the elevation error checking issue,but also can assess tthe sequence error of elevation data to maintain the consistency and integrity of the DEM data.