Accuracy assessment of lidar-derived digital elevation models

Despite the relatively high cost of airborne lidar-derived digital elevation models (DEMs), such products are usually presented without a satisfactory associated estimate of accuracy. For the most part, DEM accuracy estimates are typically provided by comparing lidar heights against a finite sample of check point coordinates from an independent source of higher accuracy, supposing a normal distribution of the derived height differences or errors. This paper proposes a new methodology to assess the vertical accuracy of lidar DEMs using confidence intervals constructed from a finite sample of errors computed at check points. A non-parametric approach has been tested where no particular error distribution is assumed, making the proposed methodology especially applicable to non-normal error distributions of the type usually found in DEMs derived from lidar. The performance of the proposed model was experimentally validated using Monte Carlo simulation on 18 vertical error data-sets. Fifteen of these data-sets were computed from original lidar data provided by the International Society for Photogrammetry and Remote Sensing Working Group III/3, using their respective filtered reference data as ground truth. The three remaining data-sets were provided by the Natural Environment Research Council's Airborne Research and Survey Facility lidar system, together with check points acquired using high precision kinematic GPS. The results proved promising, the proposed models reproducing the statistical behaviour of vertical errors of lidar using a favourable number of check points, even in the cases of data-sets with non-normally distributed residuals. This research can therefore be considered as a potentially important step towards improving the quality control of lidar-derived DEMs.     

High-Resolution Forecast Models of Water Vapor Over Mountains: Comparison With MERIS and Meteosat Data

Propagation delay due to variable tropospheric water vapor (WV) is one of the most intractable problems for radar interferometry, particularly over mountains. The WV field can be simulated by an atmospheric model, and the difference between the two fields is used to correct the radar interferogram. Here, we report our use of the U.K. Met Office Unified Model in a nested mode to produce high-resolution forecast fields for the 3-km-high Mount Etna volcano. The simulated precipitable-water field is validated against that retrieved from the Medium-Resolution Imaging Spectrometer (MERIS) radiometer on the Envisat satellite, which has a resolution of 300 m. Two case studies, one from winter (November 24, 2004) and one from summer (June 25, 2005), show that the mismatch between the model and the MERIS fields ( rms = 1.1 and 1.6 mm, respectively) is small. One of the main potential sources of error in the models is the timing of the WV field simulation. We show that long-wavelength upper tropospheric troughs of low WV could be identified in both the model output and Meteosat WV imagery for the November 24, 2004 case and used to choose the best time of model output.     

Best prediction in linear models with mixed integer/real unknowns: theory and application

In this contribution, we extend the existing theory of minimum mean squared error prediction (best prediction). This extention is motivated by the desire to be able to deal with models in which the parameter vectors have real-valued and/or integer-valued entries. New classes of predictors are introduced, based on the principle of equivariance. Equivariant prediction is developed for the real-parameter case, the integer-parameter case, and for the mixed integer/real case. The best predictors within these classes are identified, and they are shown to have a better performance than best linear (unbiased) prediction. This holds true for the mean squared error performance, as well as for the error variance performance. We show that, in the context of linear model prediction, best predictors and best estimators come in pairs. We take advantage of this property by also identifying the corresponding best estimators. All of the best equivariant estimators are shown to have a better precision than the best linear unbiased estimator. Although no restrictions are placed on the probability distributions of the random vectors, the Gaussian case is derived separately. The best predictors are also compared with least-squares predictors, in particular with the integer-based least-squares predictor introduced in Teunissen (J Geodesy, in press, 2006).     

Measuring tree stem diameters using intensity profiles from ground-based scanning lidar from a fixed viewpoint

This paper presents a method for using the intensity of returns from a scanning light detection and ranging (lidar) system from a single viewing point to identify the location and measure the diameter of tree stems within a forest. Such instruments are being used for rapid forest inventory and to provide consistent supporting information for airborne lidars. The intensity transect across a tree stem is found to be consistent with a simple model parameterised by the range and diameter of the trunk. The stem diameter is calculated by fitting the model to transect data. The angular span of the stem can also be estimated by using a simple threshold where intensity values are tested against the expected intensity for a stem of given diameter. This is useful when data are insufficient to fit the model or the stem is partially obscured. The process of identifying tree positions and trunk diameters is fully automated and is shown to be successful in identifying a high proportion of trees, including some that are partially obscured from view. The range and bearing to trees are in excellent agreement with field data. Trunk angular span and diameter estimations are well correlated with field measurements at the plot scale. The accuracy of diameter estimation is found to decrease with range from the scanning position and is also reduced for stems subtending small angles (less than twice the scanning resolution) to the instrument. A method for adjusting survey results to compensate for trees missed due to obscuration from the scanning point and the use of angle count methods is found to improve basal area estimates and achieve agreement within 4% of field measurements.     

Analytical methods for error propagation in planar space–time prisms

The space–time prism demarcates all locations in space–time that a mobile object or person can occupy during an episode of potential or unobserved movement. The prism is central to time geography as a measure of potential mobility and to mobile object databases as a measure of location possibilities given sampling error. This paper develops an analytical approach to assessing error propagation in space–time prisms and prism–prism intersections. We analyze the geometry of the prisms to derive a core set of geometric problems involving the intersection of circles and ellipses. Analytical error propagation techniques such as the Taylor linearization method based on the first-order partial derivatives are not available since explicit functions describing the intersections and their derivatives are unwieldy. However, since we have implicit functions describing prism geometry, we modify this approach using an implicit function theorem that provides the required first-order partials without the explicit expressions. We describe the general method as well as details for the two spatial dimensions case and provide example calculations.     

Reviewers of the Journal of Geodesy for Volume 79

Acknowledgement for Referees

Reviewers of the Journal of Geodesy for Volume 79     

Effect of signal contamination in matched-filter detection of the signal on a cluttered background

To derive a matched filter for detecting a weak target signal in a hyperspectral image, an estimate of the band-to-band covariance of the target-free background scene is required. We investigate the effects of including some of the target signal in the background scene. Although the covariance is contaminated by the presence of a target signal (there is increased variance in the direction of the target signature), we find that the matched filter is not necessarily affected. In fact, if the variation in plume strength is strictly uncorrelated with the variation in background spectra, the matched filter and its signal-to-clutter ratio (SCR) performance will not be impaired. While there is little a priori reason to expect significant correlation between the plume and the background, there usually is some residual correlation, and this correlation leads to a suppressing effect that limits the SCR obtainable even for strong plumes. These effects are described and quantified analytically, and the crucial role of this correlation is illustrated with some numerical examples using simulated plumes superimposed on real hyperspectral imagery. In one example, we observe an order-of-magnitude loss in SCR for a matched filter based on the contaminated covariance.     

Plate kinematics of Nubia–Somalia using a combined DORIS and GPS solution

We have used up to 12 years of data to assess DORIS performance for geodynamics applications. We first examine the noise characteristics of the DORIS time-series of weekly station coordinates to derive realistic estimates of velocity uncertainties. We find that a combination of white and flicker noise best explains the DORIS time-series noise characteristics. Second, weekly solutions produced by the Institut Géographique National/Jet Propulsion Laboratory (IGN/JPL) DORIS Analysis Centre are combined to derive a global velocity field. This solution is combined with two independent GPS solutions, including 11 sites on Nubia and 5 on the Somalia plate. The combination indicates that DORIS horizontal velocities have an average accuracy of 3 mm/year, with best-determined sites having velocity accuracy better than 1 mm/year (one-sigma levels). Using our combined velocity field, we derive an updated plate kinematics model with a focus on the Nubia–Somalia area. Including DORIS data improves the precision of the angular velocity vector for Nubia by 15%. Our proposed model provides robust bounds on the maximum opening rates along the East African Rift (4.7–6.7 mm/year). It indicates opening rates 15 and 7% slower than values predicted by NUVEL-1A for the southern Atlantic Ocean and Indian Ocean, respectively. These differences are likely to arise from the fact that NUVEL-1A considered Africa as a single non-deforming plate, while here we use a more refined approach.     

Study of the optimum time span for distinguishing <Emphasis Type="Italic">Avena ludoviciana</Emphasis> from wheat crop based on their spectral reflectance characteristics

The study to establish the optimum time span for distinguishing Avena ludoviciana from wheat crop based on their spectral signatures was carried out at Student’s Research Farm, Department of Agronomy during 2006–07 and 2007–08. The experimental sites during both the seasons were sandy loam in texture, with normal soil reaction and electrical conductivity, low in organic carbon and available nitrogen and medium in available phosphorus and potassium. The experiment was laid out in randomized block design with four replications and consisting of twelve treatments comprising 0, 10, 15, 25, 50, 75, 100, 125, 150, 200, 250 plants m⁻² and a pure Avena ludoviciana plot (T_max). The results revealed that in all the treatments irrespective of wheat and weeds, the red reflectance (%) value decreased from 34 to 95 DAS (days after sowing) in 2006–07 and 45 DAS to 100 DAS during 2007–08, and thereafter a sharp increase was observed in all the treatments. This trend might be due to increased chlorophyll index after 34 DAS as red reflectance was reduced by chlorophyll absorption. Among all the treatments, T_max (Pure Avena ludoviciana plot) had the highest red reflectance and T₀ (Pure wheat plot) had a lowest value of red reflectance during both the years. The highest value of IR reflectance was obtained at 95 DAS (2006–07) and 70 DAS (2007–08) in all the treatments. IR reflectance of wheat crop ranged between 24.61 and 61.21 per cent during 2006–07 and 27.33 and 67.3 per cent during 2007–08. However, IR reflectance values declined after 95 DAS and 70 DAS up to harvesting during 2006–07 and 2007–08. This lower reflectance may have been due to the onset of senescence. The highest RR and NDVI values were recorded under pure wheat treatment and minimum under pure weed plots. This may be due to dark green colour and better vigor of the wheat as compared to Avena ludoviciana. It was observed that by using RR and NDVI, pure wheat can be distinguished from pure populations of Avena ludoviciana after 34 DAS and different levels of weed populations can be discriminated amongst themselves from 68 DAS up to 107 DAS during both the years of investigation.