Uncertainty modeling and analysis of surface area calculation based on a regular grid digital elevation model (DEM)

In the field of digital terrain analysis (DTA), the principle and method of uncertainty in surface area calculation (SAC) have not been deeply developed and need to be further studied. This paper considers the uncertainty of data sources from the digital elevation model (DEM) and SAC in DTA to perform the following investigations: (a) truncation error (TE) modeling and analysis, (b) modeling and analysis of SAC propagation error (PE) by using Monte-Carlo simulation techniques and spatial autocorrelation error to simulate DEM uncertainty. The simulation experiments show that (a) without the introduction of the DEM error, higher DEM resolution and lower terrain complexity lead to smaller TE and absolute error (AE); (b) with the introduction of the DEM error, the DEM resolution and terrain complexity influence the AE and standard deviation (SD) of the SAC, but the trends by which the two values change may be not consistent; and (c) the spatial distribution of the introduced random error determines the size and degree of the deviation between the calculated result and the true value of the surface area. This study provides insights regarding the principle and method of uncertainty in SACs in geographic information science (GIScience) and provides guidance to quantify SAC uncertainty.     

DEM误差对滑坡危险性评价模型的影响

基于数字高程模型(DEM)计算得到的坡度、坡向等地形属性是滑坡危险性评价模型的重要输入数据, DEM误差会导致地形属性计算结果不确定性, 进而影响滑坡危险性评价模型的结果。本文选择基于专家知识的滑坡危险性评价模型和逻辑斯第回归模型, 采用蒙特卡洛模拟方法, 研究DEM误差所导致的滑坡危险性评价模型结果不确定性。研究区位于长江中上游的重庆开县, 采用5 m分辨率的DEM, 以序贯高斯模拟方法模拟了不同大小(误差标准差为1 m、7.5 m、15 m)和空间自相关性(变程为0 m、30 m、60 m、120 m)的12 类DEM误差场参与滑坡危险性评价。每次模拟包括100 个实现, 通过对每次模拟分别计算滑坡危险性评价结果的标准差图层和分类一致性百分比图层, 用以评价结果不确定性。评价结果表明, 在不同的DEM精度下, 两个滑坡危险性评价模型所得结果的总体不确定性随空间自相关程度的变化趋势并不相同。当DEM空间自相关性程度不同时, 基于专家知识的滑坡危险性评价模型的评价结果总体不确定随着DEM误差增加而呈现不同的变化趋势, 而逻辑斯第回归模型的评价结果总体不确定性随着DEM误差大小增加而单调增加。从评价结果总体不确定性角度而言, 总体上逻辑斯第回归模型比基于专家知识的滑坡危险性评价模型更加依赖于DEM数据质量。     

An adaptive approach to selecting a flow‐partition exponent for a multiple‐flow‐direction algorithm

Most multiple‐flow‐direction algorithms (MFDs) use a flow‐partition coefficient (exponent) to determine the fractions draining to all downslope neighbours. The commonly used MFD often employs a fixed exponent over an entire watershed. The fixed coefficient strategy cannot effectively model the impact of local terrain conditions on the dispersion of local flow. This paper addresses this problem based on the idea that dispersion of local flow varies over space due to the spatial variation of local terrain conditions. Thus, the flow‐partition exponent of an MFD should also vary over space. We present an adaptive approach for determining the flow‐partition exponent based on local topographic attribute which controls local flow partitioning. In our approach, the influence of local terrain on flow partition is modelled by a flow‐partition function which is based on local maximum downslope gradient (we refer to this approach as MFD based on maximum downslope gradient, MFD‐md for short). With this new approach, a steep terrain which induces a convergent flow condition can be modelled using a large value for the flow‐partition exponent. Similarly, a gentle terrain can be modelled using a small value for the flow‐partition exponent. MFD‐md is quantitatively evaluated using four types of mathematical surfaces and their theoretical ‘true’ value of Specific Catchment Area (SCA). The Root Mean Square Error (RMSE) shows that the error of SCA computed by MFD‐md is lower than that of SCA computed by the widely used SFD and MFD algorithms. Application of the new approach using a real DEM of a watershed in Northeast China shows that the flow accumulation computed by MFD‐md is better adapted to terrain conditions based on visual judgement.     

Modelling topographic potential for erosion and deposition using GIS

Abstract

Modelling of erosion and deposition in complex terrain within a geographical information system (GIS) requires a high resolution digital elevation model (DEM), reliable estimation of topographic parameters, and formulation of erosion models adequate for digital representation of spatially distributed parameters. Regularized spline with tension was integrated within a GIS for computation of DEMs and topographic parameters from digitized contours or other point elevation data. For construction of flow lines and computation of upslope contributing areas an algorithm based on vector-grid approach was developed. The spatial distribution of areas with topographic potential for erosion or deposition was then modelled using the approach based on the unit stream power and directional derivatives of surface representing the sediment transport capacity. The methods presented are illustrated on study areas in central Illinois and the Yakima Ridge, Washington.     

Quantifying local flow direction uncertainty

Absolute elevation error in digital elevation models (DEMs) can be within acceptable National Map Accuracy standards, but still have dramatic impacts on field-level estimates of surface water flow direction, particularly in level regions. We introduce and evaluate a new method for quantifying uncertainty in flow direction rasters derived from DEMs. The method utilizes flow direction values derived from finer resolution digital elevation data to estimate uncertainty, on a cell-by-cell basis, in flow directions derived from coarser digital elevation data. The result is a quantification and spatial distribution of flow direction uncertainty at both local and regional scales. We present an implementation of the method using a 10-m DEM and a reference 1-m lidar DEM. The method contributes to scientific understanding of DEM uncertainty propagation and modeling and can inform hydrological analyses in engineering, agriculture, and other disciplines that rely on simulations of surface water flow.     

Evaluation on the accuracy of digital elevation models

1 IntroductionDigital elevation model (DEM) is digital representation of relief. It is one of the most important components in the database of GIS. At present, DEM is playing a key role in the field of survey and mapping, remote sensing and almost all the terrain related geographical analyses. DEM can be grouped into regular grids (raster) and triangulated irregular networks (TIN). Both have their advantages and disadvantages in application. It is generally believed that grid DEM will …     

Evaluation on the accuracy of digital elevation models

There is a growing interest in investigating the accuracy of digital elevation model (DEM). However people usually have an unbalanced view on DEM errors. They emphasize DEM sampling errors, but ignore the impact of DEM resolution and terrain roughness on the accuracy of terrain representation. This research puts forward the concept of DEM terrain representation error (Et) and then investigates the generation, factors, measurement and simulation of DEM terrain representation errors. A multi-resolution and multi-relief comparative approach is used as the major methodology in this research. The experiment reveals a quantitative relationship between the error and the variation of resolution and terrain roughness at a global level. Root mean square error (RMS Et) is regressed against surface profile curvature (V) and DEM resolution (R) at 10 resolution levels. It is found that the RMS Et may be expressed as RMS Et = (0.0061 × V+ 0.0052) × R - 0.022 × V + 0.2415. This result may be very useful in forecasting DEM accuracy, as well as in determining the DEM resolution related to the accuracy requirement of particular application.     

Forthcoming events

Spatial data uncertainty models (SDUM) are necessary tools that quantify the reliability of results from geographical information system (GIS) applications. One technique used by SDUM is Monte Carlo simulation, a technique that quantifies spatial data and application uncertainty by determining the possible range of application results. A complete Monte Carlo SDUM for generalized continuous surfaces typically has three components: an error magnitude model, a spatial statistical model defining error shapes, and a heuristic that creates multiple realizations of error fields added to the generalized elevation map. This paper introduces a spatial statistical model that represents multiple statistics simultaneously and weighted against each other. This paper's case study builds a SDUM for a digital elevation model (DEM). The case study accounts for relevant shape patterns in elevation errors by reintroducing specific topological shapes, such as ridges and valleys, in appropriate localized positions. The spatial statistical model also minimizes topological artefacts, such as cells without outward drainage and inappropriate gradient distributions, which are frequent problems with random field-based SDUM. Multiple weighted spatial statistics enable two conflicting SDUM philosophies to co-exist. The two philosophies are ‘errors are only measured from higher quality data’ and ‘SDUM need to model reality’. This article uses an automatic parameter fitting random field model to initialize Monte Carlo input realizations followed by an inter-map cell-swapping heuristic to adjust the realizations to fit multiple spatial statistics. The inter-map cell-swapping heuristic allows spatial data uncertainty modelers to choose the appropriate probability model and weighted multiple spatial statistics which best represent errors caused by map generalization. This article also presents a lag-based measure to better represent gradient within a SDUM. This article covers the inter-map cell-swapping heuristic as well as both probability and spatial statistical models in detail.     

Incorporating vegetation into visual exposure modelling in urban environments

Visual exposure modelling establishes the extent to which a nominated feature may be seen from a specified location. The advent of high-resolution light detection and ranging (LiDAR)-sourced elevation models has enabled visual exposure modelling to be applied in urban regions, for example, to calculate the field of view occupied by a landmark building when observed from a nearby street. Currently, visual exposure models access a single surface elevation model to establish the lines of sight (LoSs) between the observer and the landmark feature. This is a cause for concern in vegetated areas where trees are represented as solid protrusions in the surface model totally blocking the LoSs. Additionally, the observer's elevation, as read from the surface model, would be incorrectly set to the tree top height in those regions. The research presented here overcomes these issues by introducing a new visual exposure model, which accesses a bare earth terrain model, to establish the observer's true elevation even when passing through vegetated regions, a surface model for the city profile and an additional vegetation map. Where there is a difference between terrain and surface elevations, the vegetation map is consulted. In vegetated areas the LoS is permitted to continue its journey, either passing under the canopy with clear views or partially through it depending on foliage density, otherwise the LoS is terminated. This approach enables landmark visual exposure to be modelled more realistically, with consideration given to urban trees. The model's improvements are demonstrated through a number of real-world trials and compared to current visual exposure methods.     

基于Kriging的地形高程插值

将地形高程作为区域化变量,根据普通Kriging法由散乱的高程点进行地形高程插值,并采用Matlab软件开发专门的程序,实现研究区高程插值计算与结果可视化分析。以广州市南沙区10 km2范围内的200个高程点数据为例,分别运用球面模型、指数模型和高斯理论变差函数模型进行10 m×10 m格网插值,借助Matlab可视化分析插值结果及其精度,表明采用指数模型效果最好。     

Uncertainty propagation in wildland fire behaviour modelling

Rothermel's model is the most widely used fire behaviour model in wildland fire research and management. It is a complex model that considers 17 input variables describing fuel type, fuel moisture, terrain and wind. Uncertainties in the input variables can have a substantial impact on the resulting errors and have to be considered, especially when the results are used in spatial decision making. In this paper it is shown that the analysis of uncertainty propagation can be carried out with the Taylor series method. This method is computationally cheaper than Monte Carlo and offers easy-to-use, preliminary sensitivity estimations.     

Curricula,Course Outlines and Laboratory Exercises

Many modern hydrological models require data inputs provided by automated digital terrain analysis functions incorporated into GIS. These inputs include fields representing surface flow directions, up-slope contributing areas, and sub-catchment partitions. Existing raster-based terrain analysis tools, including both those in off-the-shelf GIS packages and those in the recent literature, were designed to work with digital elevation data in mountainous topography. For highly variable topography, which may include large flood plains, lakes, wetlands, and other relatively flat areas, existing tools cannot accommodate the variable signal-to-noise in the source elevation data without significant human intervention to handle special cases. A general model for calculating flow directions, up-slope contributing areas, and sub-catchment partitions that automatically adapts to the variable information content of grid-based elevation data sets is presented here. The model uses a combination of breadth-first search and global optimization to extract the maximum amount of signal from any location within the data. The model is demonstrated to work well in handling topography dominated by large flood plains, lakes and other flat areas without the need for a large number of empirical rules. An important contribution of the approach is the handling of explicit hydrologic features, which makes the spatial representation closely related to hydrological processes. The results have important implications for developing hydrological models that are tractable in large, heterogeneous watersheds using moderate resolution data.     

Influence of complex topography on global solar radiation in the Yangtze River Basin

Global solar radiation（GSR） is the most direct source and form of global energy, and calculation of its quantity is highly complex due to influences of local topography and terrain inter-shielding. Digital elevation model（DEM） data as a representation of the complex terrain and multiplicity condition produces a series of topographic factors（e.g. slope, aspect, etc.）. Based on 1 km resolution DEM data, meteorological observations and NOAA-AVHRR remote sensing data, a distributed model for the calculation of GSR over rugged terrain within the Yangtze River Basin has been developed. The overarching model permits calculation of astronomical solar radiation for rugged topography and comprises a distributed direct solar radiation model, a distributed diffuse radiation model and a distributed terrain reflectance radiation model. Using the developed model, a quantitative simulation of the GSR space distribution and visualization has been undertaken, with results subsequently analyzed with respect to locality and terrain. Analyses suggest that GSR magnitude is seasonally affected, while the degree of influence was found to increase in concurrence with increasing altitude. Moreover, GSR magnitude exhibited clear spatial variation with respect to the dominant local aspect; GSR values associated with the sunny southern slopes were significantly greater than those associated with shaded slopes. Error analysis indicates a mean absolute error of 12.983 MJm-2 and a mean relative error of 3.608%, while the results based on a site authentication procedure display an absolute error of 22.621 MJm-2 and a relative error of 4.626%.     

复杂地形对长江流域太阳总辐射的影响(英文)

Global solar radiation(GSR) is the most direct source and form of global energy, and calculation of its quantity is highly complex due to influences of local topography and terrain inter-shielding. Digital elevation model(DEM) data as a representation of the complex terrain and multiplicity condition produces a series of topographic factors(e.g. slope, aspect, etc.). Based on 1 km resolution DEM data, meteorological observations and NOAA-AVHRR remote sensing data, a distributed model for the calculation of GSR over rugged terrain within the Yangtze River Basin has been developed. The overarching model permits calculation of astronomical solar radiation for rugged topography and comprises a distributed direct solar radiation model, a distributed diffuse radiation model and a distributed terrain reflectance radiation model. Using the developed model, a quantitative simulation of the GSR space distribution and visualization has been undertaken, with results subsequently analyzed with respect to locality and terrain. Analyses suggest that GSR magnitude is seasonally affected, while the degree of influence was found to increase in concurrence with increasing altitude. Moreover, GSR magnitude exhibited clear spatial variation with respect to the dominant local aspect; GSR values associated with the sunny southern slopes were significantly greater than those associated with shaded slopes. Error analysis indicates a mean absolute error of 12.983 MJm-2 and a mean relative error of 3.608%, while the results based on a site authentication procedure display an absolute error of 22.621 MJm-2 and a relative error of 4.626%.     

Uncertainty due to DEM error in landslide susceptibility mapping

Terrain attributes such as slope gradient and slope shape, computed from a gridded digital elevation model (DEM), are important input data for landslide susceptibility mapping. Errors in DEM can cause uncertainty in terrain attributes and thus influence landslide susceptibility mapping. Monte Carlo simulations have been used in this article to compare uncertainties due to DEM error in two representative landslide susceptibility mapping approaches: a recently developed expert knowledge and fuzzy logic-based approach to landslide susceptibility mapping (efLandslides), and a logistic regression approach that is representative of multivariate statistical approaches to landslide susceptibility mapping. The study area is located in the middle and upper reaches of the Yangtze River, China, and includes two adjacent areas with similar environmental conditions – one for efLandslides model development (approximately 250 km²) and the other for model extrapolation (approximately 4600 km²). Sequential Gaussian simulation was used to simulate DEM error fields at 25-m resolution with different magnitudes and spatial autocorrelation levels. Nine sets of simulations were generated. Each set included 100 realizations derived from a DEM error field specified by possible combinations of three standard deviation values (1, 7.5, and 15 m) for error magnitude and three range values (0, 60, and 120 m) for spatial autocorrelation. The overall uncertainties of both efLandslides and the logistic regression approach attributable to each model-simulated DEM error were evaluated based on a map of standard deviations of landslide susceptibility realizations. The uncertainty assessment showed that the overall uncertainty in efLandslides was less sensitive to DEM error than that in the logistic regression approach and that the overall uncertainties in both efLandslides and the logistic regression approach for the model-extrapolation area were generally lower than in the model-development area used in this study. Boxplots were produced by associating an independent validation set of 205 observed landslides in the model-extrapolation area with the resulting landslide susceptibility realizations. These boxplots showed that for all simulations, efLandslides produced more reasonable results than logistic regression.     

复杂地形下长江流域太阳总辐射的分布式模拟

利用长江流域气象站1960-2005年的观测资料(包括常规气象站点资料和辐射站点资料)、NOAA-AVHRR遥感数据(反演地表反照率),以1km×1km的数字高程模型(DEM)反映地形状况的主要数据,通过基于DEM数据的起伏地形下天文辐射模型和地形开阔度模型,分别建立了长江流域太阳直接辐射、散射辐射和地形反射辐射分布式模型,实现了长江流域太阳总辐射模拟,并对总辐射模拟结果进行了时空分布规律分析和对其受季节、纬度、地形因子(高度、坡度和坡向等)影响的局部规律分析,以及模拟结果的误差分析和站点验证分析。结果显示:太阳总辐射在季节上受影响的程度依次是春季>冬季>夏季>秋季;随着高度、坡度、纬度的增加,太阳总辐射受坡向影响的程度呈增强趋势,从坡向上看,向阳山坡(偏南坡)对太阳总辐射量明显高于背阴坡(偏北坡)。模拟的平均绝对误差为13.04177MJm^-2,相对误差平均值3.655%,用站点验证方法显示:模拟绝对误差为22.667MJm^-2,相对误差为4.867%。     

SRTM resample with short distance‐low nugget kriging

The shuttle radar topography mission (SRTM), was flow on the space shuttle Endeavour in February 2000, with the objective of acquiring a digital elevation model of all land between 60° north latitude and 56° south latitude, using interferometric synthetic aperture radar (InSAR) techniques. The SRTM data are distributed at horizontal resolution of 1 arc‐second (～30 m) for areas within the USA and at 3 arc‐second (～90 m) resolution for the rest of the world. A resolution of 90 m can be considered suitable for the small or medium‐scale analysis, but it is too coarse for more detailed purposes. One alternative is to interpolate the SRTM data at a finer resolution; it will not increase the level of detail of the original digital elevation model (DEM), but it will lead to a surface where there is the coherence of angular properties (i.e. slope, aspect) between neighbouring pixels, which is an important characteristic when dealing with terrain analysis. This work intents to show how the proper adjustment of variogram and kriging parameters, namely the nugget effect and the maximum distance within which values are used in interpolation, can be set to achieve quality results on resampling SRTM data from 3” to 1”. We present for a test area in western USA, which includes different adjustment schemes (changes in nugget effect value and in the interpolation radius) and comparisons with the original 1” model of the area, with the national elevation dataset (NED) DEMs, and with other interpolation methods (splines and inverse distance weighted (IDW)). The basic concepts for using kriging to resample terrain data are: (i) working only with the immediate neighbourhood of the predicted point, due to the high spatial correlation of the topographic surface and omnidirectional behaviour of variogram in short distances; (ii) adding a very small random variation to the coordinates of the points prior to interpolation, to avoid punctual artifacts generated by predicted points with the same location than original data points and; (iii) using a small value of nugget effect, to avoid smoothing that can obliterate terrain features. Drainages derived from the surfaces interpolated by kriging and by splines have a good agreement with streams derived from the 1” NED, with correct identification of watersheds, even though a few differences occur in the positions of some rivers in flat areas. Although the 1” surfaces resampled by kriging and splines are very similar, we consider the results produced by kriging as superior, since the spline‐interpolated surface still presented some noise and linear artifacts, which were removed by kriging.     

Terrain complexity and uncertainties in grid‐based digital terrain analysis

The objective of this research is to study the relationship between terrain complexity and terrain analysis results from grid‐based digital elevation models (DEMs). The impact of terrain complexity represented by terrain steepness and orientation on derived parameters such as slope and aspect has been analysed. Experiments have been conducted to quantify the uncertainties created by digital terrain analysis algorithms. The test results show that (a) the RMSE of derived slope and aspect is negatively correlated with slope steepness; (b) the RMSE of derived aspect is more sensitive to terrain complexity than that of derived slope; and (c) the uncertainties in derived slope and aspect tend to be found in flatter areas, and decrease with increasing terrain complexity. The study shows that although primary surface parameters can be well defined mathematically, the implementation of those mathematical models in a GIS environment may generate considerable uncertainties related to terrain complexity. In general, when terrain is rugged with steep slopes, the uncertainty of derived parameters is quite minimal. While in flatter areas, the DEM‐based derivatives, particularly the aspect, may contain a great amount of uncertainty, causing significant limitation in applying the analytical results.     

考虑多大气参数不确定性的地面太阳短波辐射估算误差数学期望

以香港地面站观测的AOD与WVC数据为参照,首先分析了MISR/AOD和MODIS/WVC产品的不确定性描述方法,然后在考虑二者联合不确定性的影响下,推导了辐射传输方程法估算地面太阳短波辐射的相对误差分布函数。通过统计2005―2013年香港MISR/AOD和MODIS/WVC反演值的分布情况,得出两者的联合概率密度函数,然后将AOD和WVC的联合概率密度函数作为权重函数与相对误差分布函数积分,得到对辐射传输方程法估算地面太阳短波辐射的相对误差数学期望。结果表明,夏季在太阳天顶角为0°时,使用MISR/AOD和MODIS/WVC产品估算地面太阳短波辐射的相对误差期望为3.17%,并且有90%的把握使估算结果相对误差＜3.53%;不同季节不同太阳天顶角下、不同置信水平下,地面太阳短波辐射估算的相对误差大小,可为不同应用研究提供基础数据,为评估亚热带地面太阳短波辐射估算结果是否符合应用需求提供依据。     

论DEM地形分析中的尺度问题

DEM及其地形分析具有强烈的尺度依赖特征。本文以黄高原地区的研究为例,结合地学建模和地学模拟的需求,重点讨论DEM地形分析中的尺度问题。文中从DEM建立与应用出发,首先建立了DEM地形分析中的尺度概念体系,剖析了各类尺度之间的关系,其次讨论了尺度所引起的各种地形分析效应问题,最后探讨了DEM地形分析中的尺度转换类型和方法。