Digital photogrammetry and kinematic GPS applied to the monitoring of Vulcano Island, Aeolian Arc, Italy

Digital photogrammetry and kinematic global positioning system (GPS) techniques are investigated and compared over a volcanic area as operational approaches to map the topography and monitor surface displacements. The use of terrestrial and airborne GPS to support the photogrammetric survey allowed for operational and processing time reduction without loss of accuracy. A digital elevation model (DEM) is obtained from the processing of the high-resolution digital imagery survey, which provides detailed information over a large area. The internal accuracy of the derived DEM has been verified by the comparison of two sets of data obtained from imagery acquired in different epochs; the observed root-mean-square error of residuals ranges from a few centimetres to 15 cm depending on the morphological features. Kinematic and pseudo-kinematic GPS surveys are performed to derive accurate 3-D coordinates at monumented benchmarks and accurate elevation profiles along footpaths. The average repeatability of the GPS measurements on benchmarks is 1 cm for measurement durations of 2–3 min. The standard deviation of interpolated vertical coordinates obtained at the crossings of kinematic GPS profiles is 4.3 cm. The high quality of these GPS coordinates justifies their use also for the validation of the photogrammetric DEM. A comparison of 6000 common points provides a standard deviation of residuals of 18 cm. The results show that the deformation pattern of a volcanic area can be rapidly and accurately monitored even in the absence of geodetic benchmarks. The integration of aerial photogrammetry with GPS kinematic surveys may be considered as an optimal approach for deriving high-resolution mapping products to be used in support of studies of volcanic dynamics.     

Exploring the sensitivity of coastal inundation modelling to DEM vertical error

As sea level is projected to rise throughout the twenty-first century due to climate change, there is a need to ensure that sea level rise (SLR) models accurately and defensibly represent future flood inundation levels to allow for effective coastal zone management. Digital elevation models (DEMs) are integral to SLR modelling, but are subject to error, including in their vertical resolution. Error in DEMs leads to uncertainty in the output of SLR inundation models, which if not considered, may result in poor coastal management decisions. However, DEM error is not usually described in detail by DEM suppliers; commonly only the RMSE is reported. This research explores the impact of stated vertical error in delineating zones of inundation in two locations along the Devon, United Kingdom, coastline (Exe and Otter Estuaries). We explore the consequences of needing to make assumptions about the distribution of error in the absence of detailed error data using a 1 m, publically available composite DEM with a maximum RMSE of 0.15 m, typical of recent LiDAR-derived DEMs. We compare uncertainty using two methods (i) the NOAA inundation uncertainty mapping method which assumes a normal distribution of error and (ii) a hydrologically correct bathtub method where the DEM is uniformly perturbed between the upper and lower bounds of a 95% linear error in 500 Monte Carlo Simulations (HBM+MCS). The NOAA method produced a broader zone of uncertainty (an increase of 134.9% on the HBM+MCS method), which is particularly evident in the flatter topography of the upper estuaries. The HBM+MCS method generates a narrower band of uncertainty for these flatter areas, but very similar extents where shorelines are steeper. The differences in inundation extents produced by the methods relate to a number of underpinning assumptions, and particularly, how the stated RMSE is interpreted and used to represent error in a practical sense. Unlike the NOAA method, the HBM+MCS model is computationally intensive, depending on the areas under consideration and the number of iterations. We therefore used the HBM+ MCS method to derive a regression relationship between elevation and inundation probability for the Exe Estuary. We then apply this to the adjacent Otter Estuary and show that it can defensibly reproduce zones of inundation uncertainty, avoiding the computationally intensive step of the HBM+MCS. The equation-derived zone of uncertainty was 112.1% larger than the HBM+MCS method, compared to the NOAA method which produced an uncertain area 423.9% larger. Each approach has advantages and disadvantages and requires value judgements to be made. Their use underscores the need for transparency in assumptions and communications of outputs. We urge DEM publishers to move beyond provision of a generalised RMSE and provide more detailed estimates of spatial error and complete metadata, including locations of ground control points and associated land cover.     

Propagation of vertical and horizontal source data errors into a TIN with linear interpolation

Digital elevation models (DEMs) have been widely used for a range of applications and form the basis of many GIS-related tasks. An essential aspect of a DEM is its accuracy, which depends on a variety of factors, such as source data quality, interpolation methods, data sampling density and the surface topographical characteristics. In recent years, point measurements acquired directly from land surveying such as differential global positioning system and light detection and ranging have become increasingly popular. These topographical data points can be used as the source data for the creation of DEMs at a local or regional scale. The errors in point measurements can be estimated in some cases. The focus of this article is on how the errors in the source data propagate into DEMs. The interpolation method considered is a triangulated irregular network (TIN) with linear interpolation. Both horizontal and vertical errors in source data points are considered in this study. An analytical method is derived for the error propagation into any particular point of interest within a TIN model. The solution is validated using Monte Carlo simulations and survey data obtained from a terrestrial laser scanner.     

基于光学立体和InSAR的Grove山地区DEM建立和分析

本文分别利用光学立体和In SAR技术生成了东南极Grove山地区15 m分辨率的ASTER DEM和20 m分辨率的In SAR DEM。在利用ASTER立体像对生成DEM的过程中引入ICESat测高数据作为高程控制以减少错误匹配,提高DEM垂直精度;而在利用ERS tandem数据生成DEM后,选取ICESat测高数据对In SAR DEM进行倾斜面纠正,以消除基线不精确估计等带来的影响。通过与未作控制的ICESat测高数据进行比较,评价了两种DEM的精度并对误差进行了分析。同时,比较了两种DEM的差异,并分析了造成这些差异的原因,探讨了两种技术生成南极冰盖DEM的优势和不足。最后结合两DEM的优势,融合生成了Grove山地区高精度的DEM。     

Methodological sensitivity of morphometric estimates of coarse fluvial sediment transport

The estimation of fluvial sediment transport rate from measurements of morphological change has received growing recent interest. The revival of the ‘morphological method’ reflects continuing concern over traditional methods of rate determination but also the availability of new survey methods capable of high-precision, high-resolution topographic monitoring. Remote sensing of river channels through aerial digital photogrammetry is a potentially attractive alternative to labour intensive ground surveys. However, while photogrammetry presents the opportunity to acquire survey data over large areas, data precision and accuracy, particularly in the vertical dimension are lower than in traditional ground survey methods. This paper presents results of recent research in which digital elevation models (DEMs) have been developed for a reach of a large braided gravel-bed river in Scotland using both digital photogrammetry and high-resolution RTK GPS ground surveys. A statistical level of change detection is assessed by comparing surfaces with independent check points. The methodological sensitivity of the annual channel sediment budget (1999–2000) to the threshold is presented. Results suggest that while the remote survey methods employed here can be used to develop qualitatively convincing, moderate precision DEMs of channel topography (RMSE=±0.21 m), the remaining errors imply significant limits on reliable change detection which lead to important information losses. Tests at a 95% confidence interval for change detection show that over 60% of channel deposition and 40% of erosion may be obscured by the lower level of precision associated with photogrammetric monitoring when compared to ground survey measurements. This bias reflects the difficulty of detecting the topographic signature of widespread, but shallow deposition on bar tops.     

Influence of survey strategy and interpolation model on DEM quality

Accurate characterisation of morphology is critical to many studies in the field of geomorphology, particularly those dealing with changes over time. Digital elevation models (DEMs) are commonly used to represent morphology in three dimensions. The quality of the DEM is largely a function of the accuracy of individual survey points, field survey strategy, and the method of interpolation. Recommendations concerning field survey strategy and appropriate methods of interpolation are currently lacking. Furthermore, the majority of studies to date consider error to be uniform across a surface. This study quantifies survey strategy and interpolation error for a gravel bar on the River Nent, Blagill, Cumbria, UK. Five sampling strategies were compared: (i) cross section; (ii) bar outline only; (iii) bar and chute outline; (iv) bar and chute outline with spot heights; and (v) aerial LiDAR equivalent, derived from degraded terrestrial laser scan (TLS) data. Digital Elevation Models were then produced using five different common interpolation algorithms. Each resultant DEM was differentiated from a terrestrial laser scan of the gravel bar surface in order to define the spatial distribution of vertical and volumetric error. Overall triangulation with linear interpolation (TIN) or point kriging appeared to provide the best interpolators for the bar surface. Lowest error on average was found for the simulated aerial LiDAR survey strategy, regardless of interpolation technique. However, comparably low errors were also found for the bar-chute-spot sampling strategy when TINs or point kriging was used as the interpolator. The magnitude of the errors between survey strategy exceeded those found between interpolation technique for a specific survey strategy. Strong relationships between local surface topographic variation (as defined by the standard deviation of vertical elevations in a 0.2-m diameter moving window), and DEM errors were also found, with much greater errors found at slope breaks such as bank edges. A series of curves are presented that demonstrate these relationships for each interpolation and survey strategy. The simulated aerial LiDAR data set displayed the lowest errors across the flatter surfaces; however, sharp slope breaks are better modelled by the morphologically based survey strategy. The curves presented have general application to spatially distributed data of river beds and may be applied to standard deviation grids to predict spatial error within a surface, depending upon sampling strategy and interpolation algorithm.     

Sediment flux in a small gravel-bed stream: Response to channel remediation works

Abstract:  Sediment transfers in a short reach of the Kiwitea Stream, near Fielding, lower North Island, New Zealand, are assessed using morphological budgeting based on repeat digital elevation model (DEM) differencing. Field data were acquired using high-precision GPS in October 2004, May and November 2005. Two interpolation methods to construct DEMs were compared. Universal kriging and Triangulation with Linear Interpolation produced consistent results and mean errors of between 4 and 14 mm. DEM error increases where relief changes rapidly. Sediment transfers are derived only from the low-relief active channel and indicate a rapidly changing environment. Remediation works following 2004 flood impacts have reduced bank erosion. A highly mobile bed renders the channel system sensitive to small and frequent flood events.     

Effects of DEM resolution and source on soil erosion modelling: a case study using the WEPP model

Digital elevation models (DEMs) vary in resolution and accuracy by the production method. DEMs with different resolutions and accuracies can generate varied topographic and hydrological features, which can in turn affect predictions by soil erosion models, such as the WEPP (Water Erosion Prediction Project) model. This study investigates the effects of DEMs on deriving topographic and hydrological attributes, and on predicting watershed erosion using WEPP v2006.5. Six DEMs at three resolutions from three sources were prepared for two small forested watersheds located in northern Idaho, USA. These DEMs were used to calculate topographic and hydrological parameters that served as inputs to WEPP. The model results of sediment yields and runoffs were compared with field observations. For both watersheds, DEMs with different resolutions and sources generated varied watershed shapes and structures, which in turn led to different extracted hill slope and channel lengths and gradients, and produced substantially different erosion predictions by WEPP.     

A comparison of digital elevation models generated from different data sources

It can be challenging to accurately determine the topography of physically complex landscapes in remote areas. Ground-based surveys can be difficult, time consuming and may miss significant elements of the landscape. This study compares digital elevation models (DEMs) generated from three different data sources, of the physically complex Narran Lakes Ecosystem, a major floodplain wetland ecosystem in Australia. Topographic surfaces were generated from an airborne laser altimetry (LiDAR) survey, a ground-based differential GPS (DGPS) survey containing more than 20,000 points, and the 9″ DEM of Australia. The LiDAR- and DGPS-derived data generated a more thorough DEM than the 9″ DEM; however, LiDAR generated a surface topography that yielded significantly more detail than the DGPS survey, with no noticeable loss of elevational accuracy. Both the LiDAR- and the DGPS-derived DEMs compute the overall surface area and volume of the largest floodplain lake within the system to within 1% of each other. LiDAR is shown to be a highly accurate and robust technique for acquiring large quantities of topographic data, even in locations that are unsuitable for ground surveying and where the overall landscape is of exceptionally low relief. The results of this study highlight the potential for LiDAR surveys in the accurate determination of the topography of floodplain wetlands. These data can form an important component of water resource management decisions, particularly where environmental water allocations for these important ecosystems need to be determined.     

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.     

Evaluating the Potential of an Airborne Laser-scanning System for Measuring Volume Changes of Glaciers

Airborne laser scanning (ALS) is well suited for the production of digital elevation models (DEM), and can, in contrast to photographic methods, be used to acquire a DEM independently of surface texture and external light sources. ALS thus serves as a tool to generate DEMs of firn areas where photogram- metric methods often fail.
The potential of an integrated ALS system – comprising a laser scanner, precise differential global positioning system, and a gyro platform – for DEM generation of firn areas is currently being assessed. The Unteraargletscher, Bernese Alps, Switzerland, has been chosen as a test site. As part of a pilot project aimed at determining the mass balance distribution of that glacier without the use of in situ information, ALS measurements were conducted in autumn 1997. The DEM derived from laser measurements is extremely sensitive to the position and attitude of the aircraft. Currently the main work focuses on assessing and improving the system's accuracy by error modelling and by the development of error-correction algorithms.
Preliminary results from Unteraargletscher are presented, and the potential of this method for the generation of DEMs of firn areas is discussed.     

Special Issue on parallel processing in GIS

This paper explores three theoretical approaches for estimating the degree of correctness to which the accuracy figures of a gridded Digital Elevation Model (DEM) have been estimated depending on the number of checkpoints involved in the assessment process. The widely used average‐error statistic Mean Square Error (MSE) was selected for measuring the DEM accuracy. The work was focused on DEM uncertainty assessment using approximate confidence intervals. Those confidence intervals were constructed both from classical methods which assume a normal distribution of the error and from a new method based on a non‐parametric approach. The first two approaches studied, called Chi‐squared and Asymptotic Student t, consider a normal distribution of the residuals. That is especially true in the first case. The second case, due to the asymptotic properties of the t distribution, can perform reasonably well with even slightly non‐normal residuals if the sample size is large enough. The third approach developed in this article is a new method based on the theory of estimating functions which could be considered much more general than the previous two cases. It is based on a non‐parametric approach where no particular distribution is assumed. Thus, we can avoid the strong assumption of distribution normality accepted in previous work and in the majority of current standards of positional accuracy. The three approaches were tested using Monte Carlo simulation for several populations of residuals generated from originally sampled data. Those original grid DEMs, considered as ground data, were collected by means of digital photogrammetric methods from seven areas displaying differing morphology employing a 2 by 2 m sampling interval. The original grid DEMs were subsampled to generate new lower‐resolution DEMs. Each of these new DEMs was then interpolated to retrieve its original resolution using two different procedures. Height differences between original and interpolated grid DEMs were calculated to obtain residual populations. One interpolation procedure resulted in slightly non‐normal residual populations, whereas the other produced very non‐normal residuals with frequent outliers. Monte Carlo simulations allow us to report that the estimating function approach was the most robust and general of those tested. In fact, the other two approaches, especially the Chi‐squared method, were clearly affected by the degree of normality of the residual population distribution, producing less reliable results than the estimating functions approach. This last method shows good results when applied to the different datasets, even in the case of more leptokurtic populations. In the worst cases, no more than 64–128 checkpoints were required to construct an estimate of the global error of the DEM with 95% confidence. The approach therefore is an important step towards saving time and money in the evaluation of DEM accuracy using a single average‐error statistic. Nevertheless, we must take into account that MSE is essentially a single global measure of deviations, and thus incapable of characterizing the spatial variations of errors over the interpolated surface.     

Characterizing errors in digital elevation models and estimating the financial costs of accuracy

Digital topographic models are the foundation of more advanced modeling applications and ultimately inform planning and decision making in many fields. Despite this, the error associated with these models and derived attributes is commonly overlooked. Little attention has been given in the scientific literature to the benefits gained from having less error in a model or to the corresponding cost associated with reducing model error by choosing one product over another. To address these gaps in knowledge we evaluated the error associated with five digital elevation models (DEMs) and derived attributes of slope and aspect relative to the same attributes derived from LiDAR data. We also estimated the acquisition and processing costs per square kilometer of the five test models and the LiDAR models. We used three measures to characterize model error: (1) root mean square error, (2) mean error (and standard deviation), and (3) area of significant elevation error. We applied these measures to DEM products that are used extensively across a range of applications for planning and managing natural resources. We depicted the relationship between model accuracy (the inverse of error) and cost in two ways. One was accuracy/cost ratio for each model. The other used separate data on accuracy and cost to better guide potential users in choosing between models or deciding on necessary expenditure on models. The main conclusion of our work was that accounting for error in DEMs can inform choice of models and the need for financial outlays.     

Digital photogrammetry for air-photo-based construction of a digital elevation model over snow-covered areas ‐ Blamannsisen,Norway

Digital elevation models (DEMs) have been constructed over snow-covered and glaciated areas from 11 air photos optimized during production using a semi-automatic contrast-adjusting method called dodging. Construction of the DEMs from the air photos was accomplished using IMAGINE OrthoMAX software. In general, the results of the DEM construction are promising. Analytical and visual comparisons of GPS field data and published maps with the constructed DEMs indicate a high degree of agreement, with an average difference better than 2.8 m for most of the area. Errors and spurious data cells appear to have been minimized throughout most of the DEMs. One height anomaly, an erroneous peak with a height of between c. 250 m and 1200 m above the actual elevation, persistently appeared in one of the DEMs, despite numerous attempts to address the issue. Enhancements during the air-photo scanning process, such as sharpening and applying a tone curve, have been found to have a beneficial effect in reducing such erroneous results.     

联合ERS-1和ICESAT卫星测高数据构建南极冰盖DEM

南极冰盖DEM在南极研究中具有十分重要的作用,而构建南极冰盖DEM的主要数据源来自于卫星测高。在已有的测高卫星数据中,ERS-1/GM和ICESAT在空间分辨率和精度方面存在互补的关系,综合利用这两类数据,是获得南极冰盖高分辨率高精度DEM的前提。本文采用了数据联合的方法,利用ERS-1和ICESAT测高数据来构建南极冰盖DEM。采用ICESAT离散数据和RAMP/DEM v2对综合DEM进行精度评估,结果表明综合DEM高程精度在4 m左右。     

Assessing fitness for use: the expected value of spatial data sets

This paper proposes and illustrates a decision analytical approach to compare the value of alternative spatial data sets. In contrast to other work addressing value of information, its focus is on value of control. This is a useful concept when choosing the best data set for decision making under uncertainty due to error in the reported data. Application of the concept requires probabilistic accuracy measures and a loss function representing the cost of incorrect judgement about some target property. This is illustrated by an assessment of the suitability of two digital elevation models (DEMs) for determining the volume of sand required for building a container port. To demonstrate flexibility of the approach, accuracy assessment was based on both a random and a systematic sample of error data, using design-based estimation and model-based prediction, that is geostatistics. Analysis results included the expected loss for each combination of DEM and sampling strategy. These indicated that both DEMs were equally suitable for the intended use. Operational practicability of the method is highly dependent on the willingness of database producers to give access to sample information similar to the quick looks provided to potential users of remote sensing imagery.     

Derivation of topographic variables from a digital elevation model given by a spheroidal trapezoidal grid

Digital elevation models (DEMs) given by spheroidal trapezoidal grids are more appropriate for large regional, sub-continental, continental and global geological and soil studies than square-spaced DEMs. Here we develop a method for derivation of topographic variables, specifically horizontal (k) and vertical h (k) landsurface curvatures, from spheroidal trapezoidal-spaced DEMs. First, we v derive equations for calculation of partial derivatives of elevation with DEMs of this sort. Second, we produce formulae for estimation of the method accuracy in terms of root mean square errors of partial derivatives of elevation, as well as k h and k (m and m respectively). We design the method for the case that the v kh k v Earth's shape can be ignored, that is, for DEM grid sizes of no more than 225 km. We test the method by the example of fault recognition using a DEM of a part of Central Eurasia. A comparative analysis of test results and factual geological data demonstrates that the method actually works in regions marked by complicated topographic and tectonic conditions. Upon increasing DEM grid size, one can produce generalised maps of k and k. Spatial distributions of m and m h v kh k v depend directly on the distribution of elevation RMSE. Areas with high values of m are marked by low values of m, and vice versa, areas with high values kh k v of m are marked by low values of m. Data on m and m should be utilised k v kh kh k v to control and improve applications of k and k to geological studies. The method h v developed opens up new avenues for carrying out some 'conventional' raster operations directly on geographical co-ordinates.     

Historic reconstruction of reservoir topography using contour line interpolation and structure from motion photogrammetry

The geometry of impounded surfaces is a key tool to reservoir storage management and projection. Yet topographic data and bathymetric surveys of average-aged reservoirs may be absent for many regions worldwide. This paper examines the potential of contour line interpolation (TOPO) and Structure from Motion (SfM) photogrammetry to reconstruct the topography of existing reservoirs prior to dam closure. The study centres on the Paso de las Piedras reservoir, Argentina, and assesses the accuracy and reliability of TOPO- and SfM- derived digital elevation models (DEMs) using different grid resolutions. All DEMs were of acceptable quality. However, different interpolation techniques produced different types of error, which increased (or decreased) with increasing (or decreasing) grid resolution as a function of their nature, and relative to the terrain complexity. In terms of DEM reliability to reproduce area–elevation relationships, processing-related disagreements between DEMs were markedly influenced by topography. Even though they produce intrinsic errors, it is concluded that both TOPO and SfM techniques hold great potential to reconstruct the bathymetry of existing reservoirs. For areas exhibiting similar terrain complexity, the implementation of one or another technique will depend ultimately on the need for preserving accurate elevation (TOPO) or topographic detail (SfM).     

The impact of resolution on the accuracy of hydrologic data derived from DEMs

Hydrologic data derived from digital elevation models (DEM) has been regarded as an effective method in the spatial analysis of geographical information systems (GIS). However, both DEM resolution and terrain complexity has impacts on the accuracy of hydrologic derivatives. In this study, a multi-resolution and multi-relief comparative approach was used as a major methodology to investigate the accuracy of hydrologic data derived from DEMs. The experiment reveals that DEM terrain representation error affects the accuracy of DEM hydrological derivatives (drainage networks and watershed etc.). Coarser DEM resolutions can usually cause worse results. However, uncertain result commonly exists in this calculation. The derivative errors can be found closely related with DEM vertical resolution and terrain roughness. DEM vertical resolution can be found closely related with the accuracy of DEM hydrological derivatives, especially in the smooth plain area. If the mean slope is less than 4 degrees, the derived hydrologic data are usually unreliable. This result may be helpful in estimating the accuracy of the hydrologic derivatives and determining the DEM resolution that is appropriate to the accuracy requirement of a particular user. By applying a threshold value to subset the cells of a higher accumulation flow, a stream network of a specific network density can be extracted. Some very important geomorphologic characteristics, e.g., shallow and deep gullies, can be separately extracted by means of adjusting the threshold value. However, such a flow accumulationbased processing method can not correctly derive those streams that pass through the working area because it is hard to accumulate enough flow direction values to express the stream channels at the stream's entrance area. Consequently, errors will definitely occur at the stream’s entrance area. In addition, erroneous derivatives can also be found in deriving some particular rivers, e.g., perched (hanging up) rivers, anastomosing rivers and braided rivers. Therefore, more work should be done to develop and perfect the algorithms.     

The impact of resolution on the accuracy of hydrologic data derived from DEMs

1 Introduction Automated extraction of drainage features from DEMs is an effective alternative to the tedious manual mapping from topographic maps. The derived hydrologic characteristics include stream-channel networks, delineation of catchment boundaries, catchment area, catchment length, stream-channel long profiles and stream order etc. Other important characteristics of river catchments, such as the stream-channel density, stream-channel bifurcation ratios, stream-channel order, number…