The Discontinuous Nature of Kriging Interpolation for Digital Terrain Modeling

Kriging is a widely employed method for interpolating and estimating elevations from digital elevation data. Its place of prominence is due to its elegant theoretical foundation and its convenient practical implementation. From an interpolation point of view, kriging is equivalent to a thin-plate spline and is one species among the many in the genus of weighted inverse distance methods, albeit with attractive properties. However, from a statistical point of view, kriging is a best linear unbiased estimator and, consequently, has a place of distinction among all spatial estimators because any other linear estimator that performs as well as kriging (in the least squares sense) must be equivalent to kriging, assuming that the parameters of the semivariogram are known. Therefore, kriging is often held to be the gold standard of digital terrain model elevation estimation. However, I prove that, when used with local support, kriging creates discontinuous digital terrain models, which is to say, surfaces with “rips” and “tears” throughout them. This result is general; it is true for ordinary kriging, kriging with a trend, and other forms. A U.S. Geological Survey (USGS) digital elevation model was analyzed to characterize the distribution of the discontinuities. I show that the magnitude of the discontinuity does not depend on surface gradient but is strongly dependent on the size of the kriging neighborhood.

A cross-sectional analysis of the association between polycyclic aromatic hydrocarbons and diesel particulate matter exposures and hypertension among individuals of Mexican origin residing in Houston, TX

Background. Research has shown that elevations of only 10 mmHg diastolic blood pressure (BP) and 5 mmHg systolic BP are associated with substantial (as large as 50%) increases in risks for cardiovascular disease, a leading cause of death, worldwide. Epidemiological studies have found that particulate matter (PM) increases blood pressure (BP) and many biological mechanisms which may suggest that the organic matter of PM contributes to the increase in BP. To understand components of PM which may contribute to the increase in BP, this study focuses on diesel particulate matter (DPM) and polycyclic aromatic hydrocarbons (PAHs). To our knowledge, there have been only four epidemiological studies on BP and DPM, and no epidemiological studies on BP and PAHs. ^ Objective. Our objective was to evaluate the association between prevalent hypertension and two ambient exposures: DPM and PAHs amongst the Mano a Mano cohort. ^ Methods. The Mano a Mano cohort which was established by the M.D. Anderson Cancer Center in 2001, is comprised of individuals of Mexican origin residing in Houston, TX. Using geographical information systems, we linked modeled annual estimates of PAHs and DPM at the census track level from the U.S. Environmental Protection Agency's National-Scale Air Toxics Assessment to residential addresses of cohort members. Mixed-effects logistic regression models were applied to determine associations between DPM and PAHs and hypertension while adjusting for confounders. ^ Results. Ambient levels of DPM, categorized into quartiles, were not statistically associated with hypertension and did not indicate a dose response relationship. Ambient levels of PAHs, categorized into quartiles, were not associated with hypertension, but did indicate a dose response relationship in multiple models (for example: Q2: OR = 0.98; 95% CI, 0.73–1.31, Q3: OR = 1.08; 95% CI, 0.82–1.41, Q4: OR = 1.26; 95% CI, 0.94–1.70). ^ Conclusion. This is the first assessment to analyze the relationship between ambient levels of PAHs and hypertension and it is amongst a few studies investigating the association between ambient levels of DPM and hypertension. Future analyses are warranted to explore the effects DPM and PAHs using different categorizations in order to clarify their relationships with hypertension.^

Lipids and polycyclic aromatic hydrocarbons in bottom sediments from the Atlantic sector of the Southern Ocean

Distribution and composition of lipids and contents of alkanes and polycyclic aromatic hydrocarbons(PAHs) in bottom sediments of the Scotia and Weddell seas are discussed. Comparatively low concentrations of organic carbon (average 0.35%) and lipids (average 0.024%) result from rapid decomposition of organic matter in upper layers of the water column. Composition of alkanes indicates that lipids are of autochthonous origin, and stable concentrations of PAHs (average 25.8 ppb, sigma 15.3 ppb) indicate that they represent the background level for bottom sediments. Higher concentrations of PAHs in sediments near the King George Island (252.1 ppb) and different distributions of individual polyarenes are produced there by the heating systems of the Polish Antarctic Station.

Terrain model of the eastern slope of the Porcupine Seabight (50 m grid size)

The topography of the eastern margin of the Porcupine Seabight was surveyed in June 2000 utilizing swath bathymetry. The survey was carried out during RV Polarstern cruise ANT XVII/4 as part of the GEOMOUND project. The main objective was to map and investigate the seafloor topography of this region. The investigated area contains a variability of morphological features such as deep sea channels and giant mounds. The survey was planned and realized on the basis of existing data so as to guarantee the complete coverage of the margin. In order to achieve a resolution of the final digital terrain model (DTM) that meets the project demands, data processing was adjusted accordingly. The grid spacing of the DTM was set to 50 m and an accuracy better than 1% of the water depth was achieved for 96% of the soundings.

Distribution of polycyclic aromatic hydrocarbons in eolian and eolian-deluvial sediments from the North Iceland

This work considers results of a study of Holocene cover sediments in Iceland. They are largely composed of wind-transported palagonitized hyaloclastite particles and coeval horizons of acid and basic tephras. It is established that polyciclic aromatic hydrocarbons (PAH) are released from basaltic glass in natural environments only in case of intense physicochemical alteration and destruction of its structure. This process does not influence PAH composition and their quantitative proportions. No new PAH formed during several thousands of years in Holocene section. Hydrocarbons are transferred from fixed state in basaltic glass into free state in palagonites practically without any changes. PAH were mainly redeposited by winds, derived together with palagonite from weathered hyaloclastites, and precipitated from atmosphere with tephra during eruptions.

Digital terrain model (DTM) of the central Fram Strait

Based on data from R/V Polarstern multibeam sonar surveys between 1984 and 1997 a high resolution bathymetry has been generated for the central Fram Strait. The area ensonified covers approx. 36,500 sqkm between 78°N-80°N and 0°E-7.5°E. Basic outcome of the investigation is a Digital Terrain Model (DTM) with 100 m grid spacing which was utilized for contouring and generation of a new series of bathymetric charts (AWI BCFS).

Terrain model of the Håkon Mosby Mud Volcano (10 m grid size)

The Håkon Mosby Mud Volcano is a natural laboratory to study geological, geochemical, and ecological processes related to deep-water mud volcanism. High resolution bathymetry of the Håkon Mosby Mud Volcano was recorded during RV Polarstern expedition ARK-XIX/3 utilizing the multibeam system Hydrosweep DS-2. Dense spacing of the survey lines and slow ship speed (5 knots) provided necessary point density to generate a regular 10 m grid. Generalization was applied to preserve and represent morphological structures appropriately. Contour lines were derived showing detailed topography at the centre of the Håkon Mosby Mud Volcano and generalized contours in the vicinity. We provide a brief introduction to the Håkon Mosby Mud Volcano area and describe in detail data recording and processing methods, as well as the morphology of the area. Accuracy assessment was made to evaluate the reliability of a 10 m resolution terrain model. Multibeam sidescan data were recorded along with depth measurements and show reflectivity variations from light grey values at the centre of the Håkon Mosby Mud Volcano to dark grey values (less reflective) at the surrounding moat.