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.     

A Global Vertical Reference Frame Based on Four Regional Vertical Datums

A Global Vertical Reference Frame (GVRF) has been realized by means of several regional and local vertical datums (LVD) distributed world-wide: the North American Vertical Datum 1988 (NAVD 88), Australian Height Datum 1971 (AHD 71), LVD France, Institute Géographique National 1969 (IGN 69) and Brazilian Height Datum 1957 (BHD 57). The vertical shifts of the above LVD origins have been related to the adopted reference geopotential value W ₀ = (62 636 856.0 ± 0.5) m²s^–2 and they were determined at the 5 cm level. However, the W ₀ reference value can be chosen arbitrarily, the methodology, which was developed here, does not require that the above value be adopted.     

On The Determination Of The Earth's Model – The Mean Equipotential Surface

The sea surface cannot be used as reference for Major Vertical Datum definition because its deviations from the ideal equipotential surface are very large compared to rms in the observed quantities. The quasigeoid is not quite suitable as the surface representing the most accurate Earth's model without some additional conditions, because it depends on the reference field. The normal Earth's model represented by the rotational level ellipsoid can be defined by the geocentric gravitational constant, the difference in the principal Earth's inertia moments, by the angular velocity of the Earth's rotation and by the semimajor axis or by the potential (U ₀ ) on the surface of the level ellipsoid. After determining the geopotential at the gauge stations defining Vertical Datums, gravity anomalies and heights should be transformed into the unique vertical system (Major Vertical Datum). This makes it possible to apply Brovar's (1995) idea of determining the reference ellipsoid by minimizing the integral, introduced by Riemann as the Dirichlet principle, to reach a minimum rms anomalous gravity field. Since the semimajor axis depends on tidal effects, potential U ₀ should be adopted as the fourth primary fundamental geodetic constant. The equipotential surface, the actual geopotential of which is equal to U ₀ , can be adopted as reference for realizing the Major Vertical Datum.     

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.     

Determining the impact of the Holocene highstand at the coastal‐fluvial interface,Shoalhaven River,south‐eastern Australia

With enhanced rates of sea‐level rise predicted for the next century, the upstream extent of sea‐level influence across coastal plains is a topic of public importance. Australian coastal rivers provide a testing ground for exploring this issue because the area is tectonically stable, was not glaciated, and experienced a Holocene highstand between 7.4 and 2 ka of up to 1.5 m above Australian Height Datum (AHD). In the Shoalhaven River of New South Wales, investigation of a confined bedrock reach at Wogamia, 32 km inland, has identified a unit of dark, cohesive silt and sand with marine diatoms, shell fragments, and enhanced pyrite content, interpreted as estuarine. The unit is up to 13 m thick, thickens downstream, and is overlain by fluvial channel and floodplain deposits. The estuarine unit on‐laps a remnant Pleistocene terrace and extends to approximately +2.2 m AHD. Optically stimulated luminescence (OSL) and radiocarbon ages suggest that estuarine deposition commenced prior to 7.8 ka cal bp , predating the highstand by ~ 500 years, and that marine influence in the area continued to 5.3 ± 0.7 ka. During this period, a delta probably persisted at Wogamia, where a narrow upstream reach opens out, and subsequently advanced to fill the broad Shoalhaven coastal embayment. Although the effect of sea‐level rise depends on many factors, the results suggest that, during a highstand at or above present sea level, a strong marine influence may extend for tens of kilometres inland and penetrate confined bedrock reaches landward of coastal embayments. Copyright © 2013 John Wiley & Sons, Ltd.     

Gravity potential at the Major Vertical Datum as primary geodetic constant

Summary On the basis of the fundamental relations of the Molodensky's Earth's figure theory (1945), admitting the inequality of the gravity potentials at the Major Vertical Datum W₀ and on the surface of the reference level ellipsoid U₀, and taken into account that potential W₀ enters into equations directly, it is recomended, W₀ should be adopted as a primary geodetic constant. Parameters of the best fitting ellipsoid are not needed for the solution of geodetic problems and for the investigation of the Earth's gravity field. The reason for requiring the reference and actual fields be close is only that the boundary-value problem can be solved in the linear approximation. Dedicated to the Memory of M.S. Molodensky Contribution to the I.A.G. Special Commission SC3 Fundamental Constants (SCFC).     

Evaluation of the use of paleotsunami deposits to reconstruct inundation distance and runup heights associated with prehistoric inundation events,Crescent City,southern Cascadia margin

Historic‐ and prehistoric‐tsunami sand deposits are used to independently establish runup records for tsunami hazard mitigation and modeled runup verification in Crescent City, California, located in the southern Cascadia Subduction Zone. Inundation from historic (1964) farfield tsunami (~5–6 m runup height) left sand sheet deposits (100–200 m width) in wetlands located behind a low beach ridge [3–4 m elevation of the National Geodetic Vertical Datum of 1988 (NAVD88)]. The most landward flooding lines (4·5–5 m elevation) in high‐gradient alluvial wetlands exceed the 1964 sand sheet records of inundation by 1–2 m in elevation. The most landward flooding in low‐gradient alluvial wetlands exceed the corresponding sand sheet record of inundation distance by 1000 m. Nevertheless, the sand sheet record is an important proxy for high‐velocity inundation. Sand sheet deposition from the 1964 historic tsunami closely corresponds to the landward extent of large debris transport and structural damage in the Crescent City waterfront. The sand sheet deposits provide a proxy for maximum hazard or ‘kill zone’ in the study area. Six paleotsunami sand sheets (0·3–3 ka) are recorded in the back‐ridge marshes in Crescent City, yielding a ~450 year mean recurrence interval for nearfield Cascadia tsunami. Two paleotsunami sand deposit records, likely correlated to Cascadia ruptures between 1·0 and 1·5 ka, are traced to 1·2 km distance and 9–10 m elevation, as adjusted for paleo‐sea level. The paleotsunami sand deposits demonstrate at least twice the runup height, and four times the inundation distance of the farfield 1964 tsunami sand sheet in the same marsh system. The preserved paleotsunami deposits in Crescent City are compared to the most landward flooding, as modeled by other investigators from a predicted Cascadia (~ Mw 9) rupture. The short geologic record (~1·5 ka) yields slightly lower runup records than those predicted for the modeled Mw 9 rupture scenario in the same marsh, but it generally verifies predicted maximum tsunami runup for use in the planning of emergency response and rapid evacuation. Copyright © 2011 John Wiley & Sons, Ltd.     

Temporal Variations in Sea Surface Topography and Dynamics of the Earth's Inertia Ellipsoid

Temporal variations in the nine elements of the Earth's inertia ellipsoid due to sea surface topography dynamics were derived from TOPEX/POSEIDON altimeter data 1993 - 1996. The variations amount to about 10 mm in the position of the center of the Earth's inertia ellipsoid (E _i ), 0.15' in the polar axis direction of E _i and to about 0.0003 in the denominator of its polar flattening. The approach used is based on the temporal variations of distortions computed by means of the geopotential model EGM96 which is used as reference.     

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).     

Application of a New Vertical Profiling Tool (ESASS) for Sampling Groundwater Quality During Hollow‐Stem Auger Drilling

A new tool called ESASS (Enhanced Screen Auger Sampling System) was developed by the U.S. Geological Survey. The use of ESASS, because of its unique U.S. patent design (U.S. patent no. 7,631,705 B1), allows for the collection of representative, depth‐specific groundwater samples (vertical profiling) in a quick and efficient manner using a 0.305‐m long screen auger during hollow‐stem auger drilling. With ESASS, the water column in the flights above the screen auger is separated from the water in the screen auger by a specially designed removable plug and collar. The tool fits inside an auger of standard inner diameter (82.55 mm). The novel design of the system constituted by the plug, collar, and A‐rod allows the plug to be retrieved using conventional drilling A‐rods. After retrieval, standard‐diameter (50.8 mm) observation wells can be installed within the hollow‐stem augers. Testing of ESASS was conducted at one waste‐disposal site with tetrachloroethylene (PCE) contamination and at two reference sites with no known waste‐disposal history. All three sites have similar geology and are underlain by glacial, stratified‐drift deposits. For the applications tested, ESASS proved to be a useful tool in vertical profiling of groundwater quality. At the waste site, PCE concentrations measured with ESASS profiling at several depths were comparable (relative percent difference <25%) to PCE concentrations sampled from wells. Vertical profiling with ESASS at the reference sites illustrated the vertical resolution achievable in the profile system; shallow groundwater quality varied by a factor of five in concentration of some constituents (nitrate and nitrite) over short (0.61 m) distances.     

Coarse bed load transport in an alluvial gravel bed stream,Dupuyer Creek,Montana

Coarse bed load was sampled in a gravel/cobble bed stream during two major floods in the snowmelt runoff season. The channel is characterized by high rates of bank erosion and, therefore, high rates of sediment supply and bed load flux. Peak discharge reached four times bank‐full, and bed load was sampled at flows 0·7–1·7 times bank‐full. A large aperture bed load sampler (1 m by 0·45 m) captured the largest particles in motion, and specifically targeted the coarse bed load size distribution by using a relatively large mesh (32 mm or D₂₅ of streambed surface size distribution). Bed load flux was highly variable, with a peak value of 0·85 kg/s/m for the coarse fraction above 38 mm. Bed load size distribution and maximum particle size was related to flow strength. Entrainment was size selective for particles D₇₀ and larger (88–155 mm), while particles in the range D₃₀–D₇₀ (35–88 mm) ceased to move at essentially the same flow. Bed load flux was size selective in that coarse fractions of the streambed surface were under‐represented in or absent from the bed load. Painted tracer particles revealed that the streambed surface in the riffles could remain stable even during high rates of bed load transport. These observations suggest that a large proportion of bed load sediments was sourced from outside the riffles. Repeat surveys confirmed major scour and fill in pools (up to 0·75 m), and bank erosion (>2 m), which together contributed large volumes of sediment to the bed load. Copyright © 2007 John Wiley & Sons, Ltd.     

The extension of the magnetic time scale in sediments of the Central Pacific Ocean

The extension of the magnetic reversal record back to the early Miocene is presented. This record is pieced together with the aid of microfloral analysis from three low sedimentation rate siliceous deep sea cores from the Equatorial Pacific.Nineteen Magnetic Epochs are now recognized from the earliest Miocene to the Present. By correlating the micropaleontological data in our cores with selected foraminiferal datums from DSDP Leg IX we correlate these datums with the following magnetic epochs: the Pulleniatina Datum occurs in the lower part of Epoch 5, the G. acostaensis Datum occurs in Epoch 11, the G. nepenthes Datum occurs in Epoch 12, the Orbulina Datum at the Epoch 15/16 boundary and the G. dissimilis Datum in the lower part of Epoch 16. The Early/Middle Miocene boundary (Orbulina Datum) is tentatively placed at the top of Epoch 16.     

Ocean cable measurements of the tsunami signal from the 1992 Cape Mendocino earthquake

The movement of the seawater across the earth's magnetic field produces a large-scale motional electric field. Using the Point Arena, California, to Hanauma Bay, Hawaii, unpowered HAW-1 cable, we have studied the geopotential across this distance to look for possible tsunami-induced fields that might have been produced following the April 1992 Cape Mendocino earthquake. We have used a ten-day interval prior to and including the earthquake as a reference for geopotential signals and for geomagnetic activity. We have also used geomagnetic data from Point Arena, Honolulu and Boulder as reference data. The results of the analyses show that there are tsunami-related effects in the cable geopotential data. These are (a) larger voltage prediction errors (residuals) for the interval following the main shock; (b) enhanced (compared to the 10d reference interval) geopotential spectral power following the main shock: two enhancements are larger than geomagnetically-induced spectral power enhancements in the same time interval; and (c) strong evidence for an 30 min echo in the cable geopotential signal following the main shock.     

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.     

Applying the bootstrap technique for studying soil redistribution by caesium-137 measurements at basin scale

Abstract

The use of the bootstrap technique to estimate the reference level of¹³⁷ Cs in an uneroded site is tested. The analysis is developed using ¹³⁷Cs measurements made in a small experimental Sicilian basin. In the reference area the ¹³⁷Cs activity is normally distributed with a known sample mean value, m equal to 94.4 mBq cm^?2. The influence of¹³⁷ Cs reference site sampling was determined generating samples having a fixed size, N and six different values of the sample coefficient of variation, CV, by a Monte Carlo technique. Then, for each size N, the probability distribution of the mean μ of the sequences generated by Monte Carlo technique is defined. The soil redistribution is determined, both at morphological unit and basin scale, using the proportional method of Martz & de Jong for calculating the net soil loss. The analysis showed that the spatial distribution of the net soil loss E _i, and the basin value E _b are independent of the sample size, N, and the coefficient of variation, CV, of the samples drawn from the reference area, if the bootstrap technique is applied for estimating the mean μ(μ) to use as reference value. The soil redistribution is also examined using as reference value the quantiles μ2.5, μ25, μ75, μ97.5 corresponding to a frequency F(μ) equal to 2.5, 25, 75 and 97.5%, respectively. In conclusion, the analysis established that a robust estimate of the reference value can be obtained even in fields where a small number of samples was drawn (high CV of the ¹³⁷Cs activity of the field samples), using the bootstrap technique for generating sequences of reference values having known mean value m (the mean value of the ¹³⁷Cs activity of the drawn field samples) and large sample size (N = 50).     

Parameters of the Earth's tri-axial level ellipsoid

Summary Four parameters defining the Earth's tri-axial ellipsoid (E) have been derived on the basis of the condition that the gravity potential on E be constant and equal to the actual geopotential value (W₀) on the geoid. The geocentric gravitational constant, the angular velocity of the Earth's rotation, the actual 2nd degree geopotential Stokes parameters and W₀ are taken to be the primary geodetic constants defining E and its (normal) gravity field.     

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.     

Intra‐event intermittency of rainfall: an analysis of the metrics of rain and no‐rain periods

The metric or ‘observable’ properties of intra‐event rainfall intermittency (IERI) are quantified using a 10‐year record from arid Fowlers Gap, Australia. Rainfall events were delineated using the minimum inter‐event time (MIT) criterion, using eight values in the range of 1 h – 24 h. Within events, no‐rain periods were defined as corresponding to rainfall rates R < 0.1 mm/h or R < 0.2 mm/h (both less than typical wet‐canopy evaporation rates during rainfall). In this way, rainfall events were subdivided into rain and no‐rain periods. Intermittency was characterised using two measures: the fraction of rainless time within an event, and the duration of the longest rainless period. Events identified using a minimum inter‐event time (MIT) of 24 h included on average 9.4 h of contiguous no‐rain time (47.5% of the mean event duration), and only 6.8 h of contiguous rain. Total IERI averaged 51.1% for these events. Events defined with MIT = 6 h (a value commonly adopted in the literature) exhibited a mean of 1.53 h of no‐rain and 9.04 h of contiguous rain. Total IERI averaged 13.9% for these events for R < 0.1 mm/h, but reached 39.2% if no‐rain periods were taken as those of <0.2 mm/h. The maximum contiguous no‐rain period for events defined using MIT = 6 h was 10.9 h from an event of 12.6 h duration, and this represents 86.5% of the event duration. Results demonstrate that smaller, shorter, and less intense rainfall events tend to exhibit higher IERI than larger, longer, and more intense events. IERI is relevant to the understanding of land surface processes. Information on the metric properties of IERI in different rainfall types (convective and stratiform) and rainfall climates (arid, maritime, and wet tropical) may prove to have significance for diverse studies in land surface hydrology. Copyright © 2015 John Wiley & Sons, Ltd.     

On conversion between potential and kinetic energy in the atmosphere

Summary The basic concept of synoptic statistical methods for construction of prognostic charts was outlined by the author in a previous paper. As a result of these investigations it was found that a high correlation exists between time and space means of contourheights of an isobaric surface (850 mb surface). As it has been shown later byPichler this result may be interpreted by assuming that the geopotential fields obeys a numerical solution of the second order homogenous differential equation for wave propagation (hyperbolic equation) provided the phase velocity is given by . SinceReuter has used for s=666 km and for t=24 hours the conclusion may be drawn that the phase velocity of the wave propagation has an order of magnitude of 5 m/sec. Actually for long waves in the westerlies such a value can be found on an average. The same method can be used for extended forecast procedures if the wave equation is set down for 5 days mean values. Theoretical considerations lead then to a prognostic formula for a 5 days mean chart (8a). This formula can be applied for a sufficient number of grid points in order to construct prognostic charts. The underlying assumption, namely that the mean geopotential field satisfies also a solution of the wave equation turns out to be quite accurate even if only average values of the phase velocity were used for the computation. The usefullness of the method is illustrated for two cases.

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Vortrag gehalten am 7. April 1961 auf der 9. Allgemeinversammlung der «Società Italiana di Geofisica e Meteorologia» (Genova, 6.8. April 1961).     

Geodetic Measurements of Crustal Deformation in the Western Mediterranean and Europe

—Geodetic measurements of crustal deformation over large areas deforming at slow rates (<5 mm/yr over more than 1000 km), such as the Western Mediterranean and Western Europe, are still a challenge because (1) these rates are close to the current resolution of the geodetic techniques, (2) inaccuracies in the reference frame implementation may be on the same order as the tectonic velocities. We present a new velocity field for Western Europe and the Western Mediterranean derived from a rigorous combination of (1) a selection of sites from the ITRF2000 solution, (2) a subset of sites from the European Permanent GPS Network solution, (3) a solution of the French national geodetic permanent GPS network (RGP), and (4) a solution of a permanent GPS network in the western Alps (REGAL). The resulting velocity field describes horizontal crustal motion at 64 sites in Western Europe with an accuracy on the order of 1 mm/yr or better. Its analysis shows that Central Europe behaves rigidly at a 0.4 mm/yr level and can therefore be used to define a stable Europe reference frame. In that reference frame, we find that most of Europe, including areas west of the Rhine graben, the Iberian peninsula, the Ligurian basin and the Corsica-Sardinian block behaves rigidly at a 0.5 mm/yr level. In a second step, we map recently published geodetic results in the reference frame previously defined. Geodetic data confirm a counterclockwise rotation of the Adriatic microplate with respect to stable Europe, that appears to control the strain pattern along its boundaries. Active deformation in the Alps, Apennines, and Dinarides is probably driven by the independent motion of the Adriatic plate rather than by the Africa-Eurasia convergence. The analysis of a global GPS solution and recently published new estimates for the African plate kinematics indicate that the Africa-Eurasia plate motion may be significantly different from the NUVEL1A values. In particular, geodetic solutions show that the convergence rate between Africa and stable Europe may be 30–60% slower than the NUVEL1A prediction and rotated 10–30° counterclockwise in the Mediterranean.