Avoiding numerical stability problems of long duration DGPS/INS Kalman filters

A current pursuit of the geodetic community is the optimal integration of differential GPS (DGPS) and inertial navigation system (INS) data streams for precise and efficient position and gravity vector surveying. Therein a complete INS and multiple-antenna GPS receiver payload, mounted on a moving platform, is used in conjunction with a network of ground-fixed single antenna GPS receivers. This paper presents a complete, GPS-based, external updating measurement model for the applicable Kalman filter. The model utilizes four external observation types for every GPS satellite in-view: DGPS range differences, single phase differences, and single phase-rate differences; as well as the mobile, multipleantenna GPS receiver's measurement of theerrors in the INS's estimate of the phase difference between any two vehicle-borne GPS antennae. Although not widely conveyed in the geodetic world, the inertial navigation community has long known that traditional Kalman filter covariance propagation recurrences are inherently unstable when such highly accurate external updates are repeatedly applied (every 1 second) over long time durations. A hybrid square root covariance/U — D covariance factorization approach is a numerically stable alternative and is reviewed herein. The hybrid makeup of the algorithm is necessitated by the correlated nature of the fourth type of GPS external measurement listed above (each vehicle-borne GPS antenna formstwo baselines). Such measurement correlations require a functional transformation of the overall external updating model to permit the multiple updates (simultaneously available at each updating epoch) to be sequentially (and efficiently) processed. An appropriate transformation is given. Stable covariance propagation relationships are presented and the transformed Kalman gain is also furnished and its use in the determination of the externally updated error states is discussed. Specific DGPS/INS instabilities produced by the traditional recurrences are displayed. The stable alternative method requires about 25% more CPU time than the traditional Kalman recurrences. With the ever-increasing computational speeds of microprocessors, this added CPU time is of no real concern.     

Free cupric ion concentrations and Cu complexation in selected Swiss lakes and rivers

[Cu²⁺] and Cu complexation parameters in some selected freshwater systems in Switzerland were determined by the technique of ligand-exchange and DPCSV. Results from the water columns of some eutrophic and oligotrophic lakes are presented and compared to small acid lakes. Cu is strongly complexed by organic ligands which with very high stability constants at low concentrations are probably biologically produced, as indicated by the seasonal variations in the eutrophic lakes and by the relationship between Cu complexation and algal activity in the eutrophic (pCu=15–16), oligotrophic (pCu=13–14) and acidic (pCu=9–10) lakes. The extent of Cu complexation in river waters was generally lower than in the eutrophic lakes, at similar DOC levels. No obvious correlation between Cu complexation and DOC was observed, indicating that Cu complexing ligands are specific organic compounds.     

Petroleum Hydrocarbon Bioventing Kinetics Determined in Soil Core, Microcosm, and Tubing Cluster Studies

Aerobic biodegradation of vapor-phase petroleum hydrocarbons was evaluated in an intact soil core from the site of an aviation gasoline release. An unsaturated zone soil core was subjected to a flow of nitrogen gas, oxygen, water vapor, and vapor-phase hydrocarbons in a configuration analogous to a biofilter or an in situ bioventing or sparging situation. The vertical profiles of vapor-phase hydrocarbon concentration in the soil core were determined by gas chromatography of vapor samples. Biodegradation reduced low influent hydrocarbon concentrations by 45 to 92 percent over a 0.6-m interval of an intact soil core. The estimated total hydrocarbon concentration was reduced by 75 percent from 26 to 7 parts per million. Steady-state concentrations were input to a simple analytical model balancing advection and first-order biodegradation of hydrocarbons. First-order rate constants for the major hydrocarbon compounds were used to calibrate the model to the concentration profiles. Rate constants for the seven individual hydrocarbon compounds varied by a factor of 4. Compounds with lower molecular weights, fewer methyl groups, and no quaternary carbons tended to have higher rate constants. The first-order rate constants were consistent with kinetic parameters determined from both microcosm and tubing cluster studies at the field site.     

Micellar-Enhanced Ultrafiltration and Air Stripping for Surfactant-Contaminant Separation and Surfactant Reuse

Micellar-enhanced ultrafiltration (MELT) and air stripping were evaluated for surfactant-contaminant separation and surfactant recovery. Two linear alkyl diphenyloxide disulfonate (DPDS) surfactants were evaluated with the contaminants naphthalene and trichloroethylene. A separation model developed from micellar partitioning principles showed a good correlation to batch MEUF studies, whereas flux analysis highlighted concentration polarization effects in relation to hydrophobe length. MEUF effectively concentrated the surfactant-contaminant system (93 to 99 percent retention); however, this did not result in surfactant-contaminant separation. Batch and continuous flow air stripping models were developed based upon air/water ratio, surfactant concentration, and Micellar partitioning; model predictions were validated by experimental data. Sensitivity analyses illustrated the decline in contaminant-surfactant separation with increasing surfactant concentration (e.g., TCE removal efficiency declines from 83 percent to 37 percent as C-16 DPDS concentration increases from 0 to 55 mM). This effect is greater for more hydrophobic contaminants (naphthalene vs. TCE) and surfactants with greater solubilization potential (C16-DPDS vs. C-12 DPDS). The resulting design equations can account for this effect and thus properly size air strippers to achieve the desired removal efficiency in the presence of surfactant micelles. Proper selection and design of surfactant-contaminant separation and surfactant recovery systems are integral to optimizing surfactant-enhanced subsurface remediation.     

Spatial and temporal variability in the lower food web of the tidal freshwater Hudson River

The mid Hudson River is a heterotrophic system where allochthonous inputs apparently fuel the largest proportion of secondary production and ecosystem metabolism. We have analyzed a 6-yr dataset collected quarterly at six stations spanning a 150-km reach to assess variability at inter- and intra-annual time scales and regional spatial scales. The major components of the lower food web: bacterial biomass, detrital particulate organic carbon (POC), and dissolved organic carbon (DOC), show surprisingly discordant patterns in temporal and spatial variability. Bacterial abundance shows significant variability at all three scales, but the interannual variability is by far the greatest. DOC concentrations showed greatest variability among years, with intra-annual and spatial variability roughly equal. Freshwater flow is commonly considered a major driving force in river-estuarine variability but simple discharge was not a strong predictor of any component of suspended matter or DOC. For organisms in the Hudson River food web, these multiple scales of variability indicate highly unpredictable food resources in time and space, and these fluctuations may contribute to the variability in higher trophic levels.     

Eddy correlation measurements of methane flux in a northern peatland ecosystem

A pilot study to measure methane flux using eddy correlation sensors was conducted in a peatland ecosystem in north central Minnesota. A prototype tunable diode laser spectrometer system was employed to measure the fluctuations in methane concentration.The logarithmic cospectrum of methane concentration and vertical wind velocity fluctuations under moderately unstable conditions had a peak nearf = 0.10 (wheref is the nondimensional frequency) and was quite similar to the cospectra of water vapor and sensible heat. Daytime methane flux during the first two weeks of August ranged from 120 to 270 mg m^-2 day^-1. The temporal variation in methane fluxes was consistent with changes in peat temperature and water table elevation. Our results compared well with the range of values obtained in previous studies in Minnesota peatlands.These field observations demonstrate the utility of the micrometeorological eddy correlation technique for measuring surface fluxes of methane. The current state-of-the-art in tunable diode laser spectroscopy makes this approach practical for use in key ecosystems.Published as Paper No. 9556, Journal Series, Nebraska Agricultural Research Division.     

Helium isotope geochemistry of mid-ocean ridge basalts from the South Atlantic

We report new helium isotope results for 49 basalt glass samples from the Mid-Atlantic Ridge between 1°N and 47°S.³He/⁴He in South Atlantic mid-ocean ridge basalts (MORB) varies between 6.5 and 9.0 R_A (R_A is the atmospheric ratio of1.39 × 10⁻⁶), encompassing the range of previously reported values for MORB erupted away from high³He/⁴He hotspots such as Iceland. He, Sr and Pb isotopes show systematic relationships along the ridge axis. The ridge axis is segmented with respect to geochemical variations, and local spike-like anomalies in³He/⁴He, Pb and Sr isotopes, and trace element ratios such as(La/Sm)_N are prevalent at the latitudes of the islands of St. Helena, Tristan da Cunha and Gough to the east of the ridge. The isotope systematics are consistent with injection beneath the ridge of mantle “blobs” enriched in radiogenic He, Pb and Sr, derived from off-axis hotspot sources. The variability in³He/⁴He along the ridge can be used to refine the hotspot source-migrating-ridge sink model.

MORB from the 2–7°S segment are systematically the least radiogenic samples found along the mid-ocean ridge system to date. Here the depleted mantle source is characterized by⁸⁷Sr/⁸⁶Sr of 0.7022, Pb isotopes close to the geochron and with²⁰⁶Pb/²⁰⁴Pb of 17.7, and³He/⁴He of 8.6–8.9 R_A. The “background contamination” of the subridge mantle, by radiogenic helium derived from off-ridge hotspots, displays a maximum between 20 and 24°S. The HePb and HeSr isotope relations along the ridge indicate that the³He/⁴He ratios are lower for the hotspot sources of St. Helena, Tristan da Cunha and Gough than for the MORB source, consistent with direct measurements of³He/⁴He ratios in the island lavas. Details of the HeSrPb isotope systematics between 12 and 22°S are consistent with early, widespread dispersion of the St. Helena plume into the asthenosphere, probably during flattening of the plume head beneath the thick lithosphere prior to continental breakup. The geographical variation in theHe/Pbratio deduced from the isotope systematics suggests only minor degassing of the plume during this stage. Subsequently, it appears that the plume component reaching the mid-Atlantic ridge was partially outgassed of He during off-ridge hotspot volcanism and related melting activity.

Overall, the similar behavior of He and Pb isotopes along the ridge indicates that the respective mantle sources have evolved under conditions which produced related He and Pb isotope variations.     

Multispectral thermal infrared mapping of the 1 October 1988 Kupaianaha flow field,Kilauea volcano,Hawaii

Multispectral thermal infrared radiance measurements of the Kupaianaha flow field were acquired with the NASA airborne Thermal Infrared Multispectral Scanner (TIMS) on the morning of 1 October 1988. The TIMS data were used to map both the temperature and emissivity of the surface of the flow field. The temperature map depicted the underground storage and transport of lava. The presence of molten lava in a tube or tumulus resulted in surface temperatures that were at least 10° C above ambient. The temperature map also clearly defined the boundaries of hydrothermal plumes which resulted from the entry of lava into the ocean. The emissivity map revealed the boundaries between individual flow units within the Kupaianaha field. In general, the emissivity of the flows varied systematically with age but the relationship between age and emissivity was not unique. Distinct spectral anomalies, indicative of silica-rich surface materials, were mapped near fumaroles and ocean entry sites. This apparent enrichment in silica may have resulted from an acid-induced leaching of cations from the surfaces of glassy flows. Such incipient alteration may have been the cause for virtually all of the emissivity variations observed on the flow field, the spectral anomalies representing areas where the acid attack was most intense.