Accuracy of Normal Heights Determined Using Improved Geopotential Models

The accuracy of determining the Molodensky normal heights using geopotential models has been investigated. On the basis of geopotential model JGM-3/OSU91A the Molodensky normal heights can be computed with an accuracy of about ±35 cm at the GPS sites in the central part of Europe. On the basis of JGM-3/OSU91A improved the accuracy becomes higher, about ±14 cm.     

Determination of the Geopotential Scale Factor from TOPEX/POSEIDON Satellite Altimetry

The geopotential scale factor R _o = GM/W _o (the GM geocentric gravitational constant adopted) and/or geoidal potential Wo have been determined on the basis of the first year's (Oct 92 – Dec 93) ERS-1/TOPEX/POSEIDON altimeter data and of the POCM 4B sea surface topography model: R _o °=(6 363 672.58°±0.05) m, W _o °=(62 636 855.8°±0.05)m ² s ^–2 . The 2°–°3 cm uncertainty in the altimeter calibration limits the actual accuracy of the solution. Monitoring dW _o /dt has been projected.     

Geoidal Geopotential and World Height System

The geoidal geopotential value of W ₀ = 62 636 856.0 ± 0.5m ² s ^–2 , determined from the 1993 –1998 TOPEX/POSEIDON altimeter data, can be used to practically define and realize the World Height System. The W ₀ -value can also uniquely define the geoidal surface and is required for a number of applications, including General Relativity in precise time keeping and time definitions. Furthermore, the W ₀ -value provides a scale parameter for the Earth that is independent of the tidal reference system. All of the above qualities make the geoidal potential W ₀ ideally suited for official adoption as one of the fundamental constants, replacing the currently adopted semi-major axis a of the mean Earth ellipsoid. Vertical shifts of the Local Vertical Datum (LVD) origins can easily be determined with respect to the World Height System (defined by W ₀ ), in using the recent EGM96 gravity model and ellipsoidal height observations (e.g. GPS) at levelling points. Using this methodology the LVD vertical displacements for the NAVD88 (North American Vertical Datum 88), NAP (Normaal Amsterdams Peil), AMD (Australian Height Datum), KHD (Kronstadt Height Datum), and N60 (Finnish Height Datum) were determined with respect to the proposed World Height System as follows: –55.1 cm, –11.0 cm, +42.4 cm, –11.1 cm and +1.8 cm, respectively.     

Zero-frequency tidal distrotion due to the orbital elements of tide-forming bodies

Summary It has been proved that orbital elements of perturbing bodies should be taken into account when 10^–10 accuracy is required for zero-frequency tidal distortion in the second zonal Stokes parameter of the geopotential. A solution at the 10^–15 level of magnitude has been presented. The zero-frequency tidal distortion in the fourth zonal Stokes parameter has been derived as 1·3×10^–10 if the secular Love number is unity. It should be reflected in the geopotential models respecting the 10^–10 level of magnitude.     

Geopotential model testing sites in the central part of Europe

Summary Sixteen geopotential model testing sites in the central part of Europe, coinciding with the first-order leveling network points, have been established. The geopotential values for these sites were determined with an accuracy not limiting the testing procedure. Tests have been carried out for models GEM-Tl, GEM-T3, JGM-l, JGM-2, JGM-3 and OSU91A.     

Determination of Geopotential Differences between Local Vertical Datums and Realization of a World Height System

The methodology developed for connecting Local Vertical Datums (LVD) was applied to the Australian Height Datum (AHD) and the North American Vertical Datum (NAVD88). The geopotential values at AHD and NAVD88 were computed and the corresponding vertical offset of 974 mm with rms 51 mm was obtained between the zero reference surfaces defined by AHD and NAVD88. The solution is based on the four primary geodetic parameters, the GPS/levelling sites and the geopotential model EGM96. The Global Height System (or the Major Vertical Datum) can be defined by a geoidal geopotential value used in the solution as the reference value, or by the geopotential value of the LVD, e.g. NAVD88.     

Single-layer density as function of Stokes' constants

Summary A relation between Stokes' constants (harmonic coefficients) J _n ^(k) , S _n ^(k) has been derived in the development for the external geopotential and the coefficients in the development for the single-layer density distributed over the surface of the external ellipsoid, the external equipotential surface, as well as the smoothed physical surface of the actual Earth. Terms of the 2nd order, (J ₂ ⁽⁰⁾ ) ² , were taken into account, terms of the 3rd and lower orders were neglected.     

Methodology of Testing Geopotential Models Specified in Different Tide Systems

It is proved that the Testing Geopotential Model (TGM) results in identical model distortions when TGM is performed in the mean, zero, and tide- free systems. The Molodensky quasigeoid height is invariant in relation to different tide systems, however, the Molodensky normal height, the ellipsoidal height, as well as, the actual geopotential, expressed in the above different tide systems, differ.     

On the Spectral Decomposition of Geopotential and Temperature Fields in the Stratosphere

The spectral structure of stratospheric fields (temperature and geopotential) is analyzed in terms of spherical harmonics in an effort to study the long-term behaviour of large-scale circulation patterns, as well as their connections to some extra-terrestrial effects. The daily meteorological data from the Free University Berlin (FUB) cover more or less the period 1976–1996 and are available for stratospheric levels of 50, 30 and 10 hPa. The analysis of the annual cycle of spherical harmonics is introduced, and changes of the principal wave components are compared with the changes in different sets of solar, geomagnetic and global circulation indices. This paper also deals with interannual variability with special emphasis on quasibiennial oscillations (QBO) and El Nino and Southern Oscillations (ENSO). Although this is a rather preliminary study, the decomposition of the stratospheric field into complex spherical harmonics seems to be a powerful technique in investigating and qualifying the response of the global atmospheric system to the changes in solar and geomagnetic activity, and in qualifying the relationships between large-scale circulation patterns and various oscillations such as QBO or ENSO, Using this technique, reasonable strong connections were found between wave numbers and interannual factors, and these connections were tentatively interpreted in terms of statistics. A very high degree of correlation was found for the four-trough shape of the polar vortex.     

Spheroidal Integral Equations for Geodetic Inversion of Geopotential Gradients

The static Earth’s gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth’s surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet’s boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green’s kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth.     

ZERO—PHASE FORWARD FILTERS FOR RESISTIVITY SOUNDING*

Forward filters to transform the apparent resistivity function over a layered half-space into the resistivity transform have been derived for a number of sample intervals. The filters have no apparent Gibbs' oscillations and hence require no phase shift. In addition, the end points of the filter were modified to compensate for truncation. The filters were tested on simulated ascending and descending two-layer cases. As expected, “dense” filters with sample spacing of In (10)/6 or smaller performed very well. However, even “sparse” filters with spacing of In (10)/2 and a total of nine coefficients have peak errors of less than 5% for p₁:p₂ ratios of 10^–6 to 10⁶. If a peak error of 5.5% is acceptable, then an even sparser filter with only seven coefficients at a spacing of 3 In (10)/5 may be used.     

Geopotential Reconstruction,Decomposition, Fast Computation,and Noise Cancellation by Harmonic Wavelets

Harmonic wavelets are introduced within the framework of the Sobolev-like Hilbert space H of potentials with square-integrable restrictions to the Earth's (mean) sphere _R . Basic tool is the construction of H-product kernels in terms of an (outer harmonics) orthonormal basis in H. Scaling function and wavelet are defined by means of so-called H-product kernels. Harmonic wavelets are shown to be building blocks that decorrelate geopotential data. A pyramid scheme enables fast computations. Multiscale signal-to-noise thresholding provides suitable denoising. Multiscale modelling of the Earth's anomalous potential from EGM96-model data is illustrated by use of bandlimited harmonic wavelets, i.e. Shannon and CP-wavelets.     

Start‐Up Study on Biohydrogen from Palm Oil Mill Effluent in a Pilot‐Scale Reactor

A start‐up study for biohydrogen production from palm oil mill effluent (POME) is carried out in a pilot‐scale up‐flow anaerobic sludge blanket fixed‐film reactor (UASFF). A substrate with a chemical oxygen demand (COD) of 30 g L^?1 is used, starting with molasses solution for 30 days and followed by a 10% v/v increment of POME/molasses ratio. At 100% POME, a hydrogen content of 80%, hydrogen production rate of 36 L H₂ per day, and maximum COD removal of 48.7% are achieved. Bio‐kinetic coefficients of Monod, first‐order, Grau second‐order, and Stover‐Kincannon kinetic models are calculated to describe the performance of the system. The steady‐state data with 100% POME shows that Monod and Stover‐Kincannon models with bio‐kinetic coefficients of half‐velocity constant (K_s) of 6000 mg COD L^?1, microbial decay rate (K_d) of 0.0015 per day, growth yield constant (Y) of 0.786 mg volatile suspended solids (VSS)/mg COD, specific biomass growth rate (μ_max) of 0.568 per day, and substrate consumption rate of (U_max) 3.98 g/L day could be considered as superior models with correlation coefficients (R²) of 0.918 and 0.989, respectively, compared to first‐order and Grau's second‐order models with coefficients of K₁ 1.08 per day, R² 0.739, and K_2s 1.69 per day, a = 7.0 per day, b = 0.847.     

Lateral density anomaly distribution in the lower mantle obtained from satellite low order geopotential coefficients

In this paper, we attempt to use satellite gravity data and a new inversion method to study the lateral density anomaly distribution in the mantle. First, density difference Δρ(τ,θ,φ) is expanded in terms of a three—dimensional orthogonal function system, the coefficients of the expansion are to be determined. Then, a set of observation equations is established from the relationship between density anomaly and disturbing geopotential. In the equations the unknown vector contains the coefficients of density anomaly expansion, the observational vector is obtained by computing geopotential perturbations using the potential coefficients of GEM10B, and a filtering process is done for the observational values by properly selecting the harmonic degrees of geopotentical. Finally, the lateral density variations in the lower mantle (670 km toCM boundary) are investigated. In this case, the degrees of disturbing geopotential are selected as 2–11, the truncated degrees of density anomaly expansion are taken asL=6 andK=4, and the damping least squares method is used to solve the observation equations. The resulting model shows the high level of density perturbations at 670 km discontinuity and core — mantle boundary, a high — density zone circumscribing the Pacific and a lower—density region under the center of Pacific. These features are in agreement with the three—dimensional seismic velocity variation features by Dziewonski (1984). In the Antarctic region and some parts of Atlantic and Indian Ocean, however, the resulting density anomalies are negatively correlated with the seismic velocity anomalies, the cause resulting in these phenomena is preliminarily analysed in this paper. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 53–65, 1991. The principle and method represented in this paper can also be suitable to study the lateral density anomaly distribution in the earth’s crust and the upper mantle.     

Mean Earth'S Equipotential Surface From Topex/Poseidon Altimetry

The geopotential value of W ₀ = (62 636 855.611 ± 0.008) m ² s ^–2 which specifies the equipotential surface fitting the mean ocean surface best, was obtained from four years (1993 - 1996) of TOPEX/POSEIDON altimeter data (AVISO, 1995). The altimeter calibration error limits the actual accuracy of W ₀ to about (0.2 - 0.5) m ² s ^–2 (2 - 5) cm. The same accuracy limits also apply to the corresponding semimajor axis of the mean Earth's level ellipsoid a = 6 378 136.72 m (mean tide system), a = 6 378 136.62 m (zero tide system), a = 6 378 136.59 m (tide-free). The variations in the yearly mean values of the geopotential did not exceed ±0.025 m ² s ^–2 (±2.5 mm).     

Sorption of ortho‐Phenylphenol to Soils

Conflicting sorption coefficients for ortho‐phenylphenol (OPP) have been reported in the literatures, which resulted in the conflicting assessments on OPP mobility in soil. To ascertain the sorption coefficient of OPP, batch experiments were performed based on OECD guideline 106, using three types of soils. Headspace solid‐phase microextraction (HS‐SPME) and GC‐MS were applied to the determination of OPP concentration in the liquid phase. The sorption isotherms obtained for all three soils under equilibrium conditions were described well, assuming linear sorption. The organic carbon normalized distribution coefficients (K_oc) ranged from 894 to 1703 L kg^?1, which suggested that OPP is moderately mobile in soil. The results also showed that the K_oc value of OPP can be predicted precisely from K_ow, whereas it was underestimated by one order of magnitude when water solubility is used.     

Truncation Error due to Geopotential Model EGM96

The truncation error for the harmonic EGM96 series has been investigated on the basis of 24 242 testing points covering about 70% of the Earth's surface. No degree n of harmonics retained was found at which the series becomes divergent. The EGM96 rms diminishes with increasing n. The truncation error due to EGM96 at the physical Earth's surface has no limiting consequences.     

Computation of Ray Amplitudes in Inhomogeneous Media with Curved

The TOPEX/POSEIDON (T/P) satellite altimeter data from January 1, 1993 to January 3, 2001 (cycles 11–305) was used for investigating the long-term variations of the geoidal geopotential W ₀ and the geopotential scale factor R ₀ = GM÷W ₀ (GM is the adopted geocentric gravitational constant). The mean values over the whole period covered are W ₀ = (62 636 856.161 ± 0.002) m²s^-2, R ₀ = (6 363 672.5448 ± 0.0002) m. The actual accuracy is limited by the altimeter calibration error (2–3 cm) and it is conservatively estimated to be about ± 0.5 m²s^-2 (± 5 cm). The differences between the yearly mean sea surface (MSS) levels came out as follows: 1993–1994: –(1.2 ± 0.7) mm, 1994–1995: (0.5 ± 0.7) mm, 1995–1996: (0.5 ± 0.7) mm, 1996–1997: (0.1 ± 0.7) mm, 1997–1998: –(0.5 ± 0.7) mm, 1998–1999: (0.0 ± 0.7) mm and 1999–2000: (0.6 ± 0.7) mm. The corresponding rate of change in the MSS level (or R ₀) during the whole period of 1993–2000 is (0.02 ± 0.07) mm÷y. The value W ₀ was found to be quite stable, it depends only on the adopted GM, and the volume enclosed by surface W = W ₀. W ₀ can also uniquely define the reference (geoidal) surface that is required for a number of applications, including World Height System and General Relativity in precise time keeping and time definitions, that is why W ₀ is considered to be suitable for adoption as a primary astrogeodetic parameter. Furthermore, W ₀ provides a scale parameter for the Earth that is independent of the tidal reference system. After adopting a value for W ₀, the semi-major axis a of the Earth's general ellipsoid can easily be derived. However, an a priori condition should be posed first. Two conditions have been examined, namely an ellipsoid with the corresponding geopotential which fits best W ₀ in the least squares sense and an ellipsoid which has the global geopotential average equal to W ₀. It is demonstrated that both a-values are practically equal to the value obtained by the Pizzetti's theory of the level ellipsoid: a = (6 378 136.7 ± 0.05) m.     

Evaluation methods of heat discharge and their applications to the major active volcanoes in Japan

The rates at which thermal energy is released by non-eruptive mechanisms associated with active volcanoes in Japan have been estimated from surface temperature distributions or from shapes of the fumarolic plume rise. Values of 5.3 x 10⁷ W and 1.2 x 10⁸ W have been calculated for non-eruptive release rates in 100-km segments of the Northeast and the Southwest Japan Arc, respectively. It appears that non-eruptive heat discharge is of the same order as that caused by eruptions.     

Modeling the Effects of Meteorological Factors on SO2 and PM10 Concentrations with Statistical Approaches

Air quality has been deteriorated seriously in urban areas as a result of increasing anthropogenic activities. Meteorological conditions affect air pollution levels in the urban atmosphere significantly due to their important role in transport and dilution of the pollutants. This paper aims to investigate usability of some promising statistical methods for examining the impacts of metrological factors on SO₂ and PM10 levels. Data were collected from city centre of Kocaeli in winter periods from 2007 to 2010 as pollutant concentrations increase in winters due to expanding combustion facilities. Results of bivariate correlation analysis showed that humidity and rainfall have remarkable negative correlations with the pollutants. Multiple linear regression models and artificial neural network (ANN) models were used to predict next day's PM10 and SO₂ levels. In regression models calculated R² values were 0.89 and 0.75 for PM10 and SO₂, respectively. Among the various architectures, single layer networks provided better performance in ANN applications. Highest R² values were obtained as 0.89 and 0.69 for PM10 and SO₂, respectively, by using appropriate networks.