Using gravity and topography-implied anomalies to assess data requirements for precise geoid computation

Many regions around the world require improved gravimetric data bases to support very accurate geoid modeling for the modernization of height systems using GPS. We present a simple yet effective method to assess gravity data requirements, particularly the necessary resolution, for a desired precision in geoid computation. The approach is based on simulating high-resolution gravimetry using a topography-correlated model that is adjusted to be consistent with an existing network of gravity data. Analysis of these adjusted, simulated data through Stokes’s integral indicates where existing gravity data must be supplemented by new surveys in order to achieve an acceptable level of omission error in the geoid undulation. The simulated model can equally be used to analyze commission error, as well as model error and data inconsistencies to a limited extent. The proposed method is applied to South Korea and shows clearly where existing gravity data are too scarce for precise geoid computation.     

Evaluation of the geometric stability and the accuracy potential of digital cameras — Comparing mechanical stabilisation versus parameterisation

Recent tests on the geometric stability of several digital cameras that were not designed for photogrammetric applications have shown that the accomplished accuracies in object space are either limited or that the accuracy potential is not exploited to the fullest extent. A total of 72 calibrations were calculated with four different software products for eleven digital camera models with different hardware setups, some with mechanical fixation of one or more parts. The calibration procedure was chosen in accord to a German guideline for evaluation of optical 3D measuring systems [VDI/VDE, VDI/VDE 2634 Part 1, 2002. Optical 3D Measuring Systems–Imaging Systems with Point-by-point Probing. Beuth Verlag, Berlin]. All images were taken with ringflashes which was considered a standard method for close-range photogrammetry. In cases where the flash was mounted to the lens, the force exerted on the lens tube and the camera mount greatly reduced the accomplished accuracy. Mounting the ringflash to the camera instead resulted in a large improvement of accuracy in object space. For standard calibration best accuracies in object space were accomplished with a Canon EOS 5D and a 35 mm Canon lens where the focusing tube was fixed with epoxy (47  μm maximum absolute length measurement error in object space). The fixation of the Canon lens was fairly easy and inexpensive resulting in a sevenfold increase in accuracy compared with the same lens type without modification. A similar accuracy was accomplished with a Nikon D3 when mounting the ringflash to the camera instead of the lens (52  μm maximum absolute length measurement error in object space). Parameterisation of geometric instabilities by introduction of an image variant interior orientation in the calibration process improved results for most cameras. In this case, a modified Alpa 12 WA yielded the best results (29  μm maximum absolute length measurement error in object space). Extending the parameter model with FiBun software to model not only an image variant interior orientation, but also deformations in the sensor domain of the cameras, showed significant improvements only for a small group of cameras. The Nikon D3 camera yielded the best overall accuracy (25  μm maximum absolute length measurement error in object space) with this calibration procedure indicating at the same time the presence of image invariant error in the sensor domain. Overall, calibration results showed that digital cameras can be applied for an accurate photogrammetric survey and that only a little effort was sufficient to greatly improve the accuracy potential of digital cameras.     

Variation in tree mortality and regeneration affect forest carbon recovery following fuel treatments and wildfire in the Lake Tahoe Basin, California, USA

Background

Forest fuel treatments have been proposed as tools to stabilize carbon stocks in fire-prone forests in the Western U.S.A. Although fuel treatments such as thinning and burning are known to immediately reduce forest carbon stocks, there are suggestions that these losses may be paid back over the long-term if treatments sufficiently reduce future wildfire severity, or prevent deforestation. Although fire severity and post-fire tree regeneration have been indicated as important influences on long-term carbon dynamics, it remains unclear how natural variability in these processes might affect the ability of fuel treatments to protect forest carbon resources. We surveyed a wildfire where fuel treatments were put in place before fire and estimated the short-term impact of treatment and wildfire on aboveground carbon stocks at our study site. We then used a common vegetation growth simulator in conjunction with sensitivity analysis techniques to assess how predicted timescales of carbon recovery after fire are sensitive to variation in rates of fire-related tree mortality, and post-fire tree regeneration.

Results

We found that fuel reduction treatments were successful at ameliorating fire severity at our study site by removing an estimated 36% of aboveground biomass. Treated and untreated stands stored similar amounts of carbon three years after wildfire, but differences in fire severity were such that untreated stands maintained only 7% of aboveground carbon as live trees, versus 51% in treated stands. Over the long-term, our simulations suggest that treated stands in our study area will recover baseline carbon storage 10?C35?years more quickly than untreated stands. Our sensitivity analysis found that rates of fire-related tree mortality strongly influence estimates of post-fire carbon recovery. Rates of regeneration were less influential on recovery timing, except when fire severity was high.

Conclusions

Our ability to predict the response of forest carbon resources to anthropogenic and natural disturbances requires models that incorporate uncertainty in processes important to long-term forest carbon dynamics. To the extent that fuel treatments are able to ameliorate tree mortality rates or prevent deforestation resulting from wildfire, our results suggest that treatments may be a viable strategy to stabilize existing forest carbon stocks.     

A bilinear approximation of the surface relief in terrain correction computations

A new method is presented for the computation of the gravitational attraction of topographic masses when their height information is given on a regular grid. It is shown that the representation of the terrain relief by means of a bilinear surface not only offers a serious alternative to the polyhedra modeling, but also approaches even more smoothly the continuous reality. Inserting a bilinear approximation into the known scheme of deriving closed analytical expressions for the potential and its first-order derivatives for an arbitrarily shaped polyhedron leads to a one-dimensional integration with – apparently – no analytical solution. However, due to the high degree of smoothness of the integrand function, the numerical computation of this integral is very efficient. Numerical tests using synthetic data and a densely sampled digital terrain model in the Bavarian Alps prove that the new method is comparable to or even faster than a terrain modeling using polyhedra.     

Hedonic price models with omitted variables and measurement errors: a constrained autoregression–structural equation modeling approach with application to urban Indonesia

Omitted variables and measurement errors in explanatory variables frequently occur in hedonic price models. Ignoring these problems leads to biased estimators. In this paper, we develop a constrained autoregression–structural equation model (ASEM) to handle both types of problems. Standard panel data models to handle omitted variables bias are based on the assumption that the omitted variables are time-invariant. ASEM allows handling of both time-varying and time-invariant omitted variables by constrained autoregression. In the case of measurement error, standard approaches require additional external information which is usually difficult to obtain. ASEM exploits the fact that panel data are repeatedly measured which allows decomposing the variance of a variable into the true variance and the variance due to measurement error. We apply ASEM to estimate a hedonic housing model for urban Indonesia. To get insight into the consequences of measurement error and omitted variables, we compare the ASEM estimates with the outcomes of (1) a standard SEM, which does not account for omitted variables, (2) a constrained autoregression model, which does not account for measurement error, and (3) a fixed effects hedonic model, which ignores measurement error and time-varying omitted variables. The differences between the ASEM estimates and the outcomes of the three alternative approaches are substantial.     

Multi‐temporal Mapping of Burned Forest over Canada Using Satellite‐based Change Metrics

Abstract

A procedure for continental‐scale mapping of burned boreal forest at 10‐day intervals was developed for application to coarse resolution satellite imagery. The basis of the technique is a multiple logistic regression model parameterized using 1998 SPOT‐4 VEGETATION clear‐sky composites and training sites selected across Canada. Predictor features consisted of multi‐temporal change metrics based on reflectance and two vegetation indices, which were normalized to the trajectory of background vegetation to account for phenological variation. Spatial‐contextual tests applied to the logistic model output were developed to remove noise and increase the sensitivity of detection. The procedure was applied over Canada for the 1998‐2000 fire seasons and validated using fire surveys and burned area statistics from forest fire management agencies. The area of falsely mapped burns was found to be small (3.5% commission error over Canada), and most burns larger than 10 km2 were accurately detected and mapped (R² = 0.90, P<0.005, n = 91 for burns in two provinces). Canada‐wide satellite burned area was similar, but consistently smaller by comparison to statistics compiled by the Canadian Interagency Forest Fire Centre (by 17% in 1998, 16% in 1999, and 3% in 2000).     

Mapping spiny aster infestations with QuickBird imagery

QuickBird satellite imagery acquired in June 2003 and September 2004 was evaluated for detecting the noxious weed spiny aster [Leucosyris spinosa (Benth.) Greene] on a south Texas, USA rangeland area. A subset of each of the satellite images representing a diversity of cover types was extracted and used as a study site. The satellite imagery had a spatial resolution of 2.8 m and contained 11-bit data. Unsupervised and supervised classification techniques were used to classify false colour composite (green, red, and near-infrared bands) images of the study site. Imagery acquired in June was superior to that obtained in September for distinguishing spiny aster infestations. This was attributed to differences in spiny aster phenology between the two dates. An unsupervised classification of the June image showed that spiny aster had producer's and user's accuracies of 90% and 93.1%, respectively, whereas a supervised classification of the June image had producer's and user's accuracies of 90% and 81.8%, respectively. These results indicate that high resolution satellite imagery coupled with image analysis techniques can be used successfully for detecting spiny aster infestations on rangelands.     

Field Measurements of Plant Emissivity Spectra: An Experimental Study on Remote Sensing of Vegetation in the Thermal Infrared Region

Spectral features of plant species in the visible to SWIR (0.4–2.5 μm) region have been studied extensively, but scanty attention has been given to plant thermal infrared (TIR: 4–14 μm) properties. This paper presents preliminary results of a study that was conducted first time in India to measure radiance and emissivity properties of eight plant species in TIR spectral region in the field conditions using a FTIR (Fourier Transform Infrared) field spectroradiometer working in 4–14 μm at an agriculture experimental farm. Several spectral features in the emissivity spectra of plant species were observed that are probably related to the leaf chemical constituents, such as cellulose and xylan (hemicellulose) and structural aspects of leaf surface like abundance of trichomes and texture. Observations and results from the field measurements were supported by the laboratory measurements like biochemical analysis. These preliminary field emissivity measurements of leaves in TIR show that there is useful spectral information that may be detectable by field-based instrument. More detailed field and laboratory measurements are underway to explore this research theme.     

High Resolution Köppen‐Geiger Classifications of Paleoclimate Simulations

The development and application of an algorithm to compute Köppen‐Geiger climate classifications from the Coupled Model Intercomparison Project (CMIP) and Paleo Model Intercomparison Project (PMIP) climate model simulation data is described in this study. The classification algorithm was applied to data from the PMIP III paleoclimate experiments for the Last Glacial Maximum, 21k years before present (yBP), Mid‐Holocene (6k yBP) and the Pre‐Industrial (0k yBP, control run) time slices. To infer detailed classification maps, the simulation datasets were interpolated to a higher resolution. The classification method presented is based on the application of Open Source Software, and the implementation is described with attention to detail. The source code and the exact input data sets as well as the resulting data sets are provided to enable the application of the presented approach.     

Modeling errors in upward continuation for INS gravity compensation

Accurate upward continuation of gravity anomalies supports future precision, free-inertial navigation systems, since the latter cannot by themselves sense the gravitational field and thus require appropriate gravity compensation. This compensation is in the form of horizontal gravity components. An analysis of the model errors in upward continuation using derivatives of the standard Pizzetti integral solution (spherical approximation) shows that discretization of the data and truncation of the integral are the major sources of error in the predicted horizontal components of the gravity disturbance. The irregular shape of the data boundary, even the relatively rough topography of a simulated mountainous region, has only secondary effect, except when the data resolution is very high (small discretization error). Other errors due to spherical approximation are even less important. The analysis excluded all measurement errors in the gravity anomaly data in order to quantify just the model errors. Based on a consistent gravity field/topographic surface simulation, upward continuation errors in the derivatives of the Pizzetti integral to mean altitudes of about 3,000 and 1,500 m above the mean surface ranged from less than 1 mGal (standard deviation) to less than 2 mGal (standard deviation), respectively, in the case of 2 arcmin data resolution. Least-squares collocation performs better than this, but may require significantly greater computational resources.