Evaluation of pre-CHAMP gravity models `GRIM5-S1' and `GRIM5-C1' with satellite crossover altimetry

 The new GFZ/GRGS gravity field models GRIM5-S1 and GRIM5-C1, currently used as initial models for the CHAMP mission, have been compared with other recent models (JGM 3, EGM 96) for radial orbit accuracy (by means of latitude lumped coefficients) in computations on altimetry satellite orbits. The bases for accuracy judgements are multi-year averages of crossover sea height differences from Geosat and ERS 1/2 missions. This radially sensitive data is fully independent of the data used to develop these gravity models. There is good agreement between the observed differences in all of the world's oceans and projections of the same errors from the scaled covariance matrix of their harmonic geopotential coefficients. It was found that the tentative scale factor of five for the formal standard deviations of the harmonic coefficients of the new GRIM fields is justified, i.e. the accuracy estimates, provided together with the GRIM geopotential coefficients, are realistic. Received: 20 February 2001 / Accepted: 24 October 2001     

Comment on the “Analysis of the State of Stress During the 1997 Earthquake Swarm in Western Bohemia” by A. Slancová and J. Horálek (Studia geoph. et geod. 44(2000), 272–291)

Studia Geophysica et Geodaetica -     

The relation between rigorous and Helmert’s definitions of orthometric heights

Following our earlier definition of the rigorous orthometric height [J Geod 79(1-3):82–92 (2005)] we present the derivation and calculation of the differences between this and the Helmert orthometric height, which is embedded in the vertical datums used in numerous countries. By way of comparison, we also consider Mader and Niethammer’s refinements to the Helmert orthometric height. For a profile across the Canadian Rocky Mountains (maximum height of ~2,800 m), the rigorous correction to Helmert’s height reaches ~13 cm, whereas the Mader and Niethammer corrections only reach ~3 cm. The discrepancy is due mostly to the rigorous correction’s consideration of the geoid-generated gravity disturbance. We also point out that several of the terms derived here are the same as those used in regional gravimetric geoid models, thus simplifying their implementation. This will enable those who currently use Helmert orthometric heights to upgrade them to a more rigorous height system based on the Earth’s gravity field and one that is more compatible with a regional geoid model.     

Effect of common point selection on coordinate transformation parameter determination

The use of satellite positioning techniques commonly requires a transformation from a Conventional Terrestrial coordinate system to a Geodetic coordinate system, or vice versa. For such a transformation, the main problem is the determination of transformation parameters between these coordinate systems. The transformation parameters are estimated by a least-squares process using “common” points, i.e., those points whose coordinates are known in both systems. Therefore, the precision of so estimated transformation parameters is closely related to certain characteristics of the common points. In this contribution, we have formulated some theoretical relations between the transformation parameters and the number and the distribution of common points, and corroborated the theoretical results numerically, using a simulated geodetic network.     

Explicit formula for the geoid-quasigeoid separation

The explicit formula for the geoid-to-quasigeoid correction is derived in this paper. On comparing the geoidal height and height anomaly, this correction is found to be a function of the mean value of gravity disturbance along the plumbline within the topography. To evaluate the mean gravity disturbance, the gravity field of the Earth is decomposed into components generated by masses within the geoid, topography and atmosphere. Newton’s integration is then used for the computation of topography-and atmosphere-generated components of the mean gravity, while the combined solution for the downward continuation of gravity anomalies and Stokes’ boundary-value problem is utilized in computing the component of mean gravity disturbance generated by mass irregularities within the geoid. On application of this explicit formulism a theoretical accuracy of a few millimetres can be achieved in evaluation of the geoid-to-quasigeoid correction. However, the real accuracy could be lower due to deficiencies within the numerical methods and to errors within the input data (digital terrain and density models and gravity observations).     

Seeding agent dispersion within convective cloud as simulated by a 3-D numerical model

Summary The three-dimensional mesoscale cloud-resolving model ARPS (Advanced Regional Prediction System) was used to investigate the dispersal of an inert seeding agent within a cumulonimbus (Cb) cloud developing from two different initial states. In this paper, we stress the influence vortices in the cloud have on seeding agent dispersion. If a strong directional ambient wind shear is present in the lowest layer, a vortex pair formed at the flanks of the simulated cloud. Following the velocity field, a considerable amount of the injected seeding agent would be thrown out to the rear of the cloud, where both updrafts associated with vortices and downdrafts occurred. After a short time the agent was present only in the cloud periphery. If the Cb cloud developed under conditions where directional ambient wind shear did not exist, seeding agent dispersion would be quite different. In this case, almost all the seeding agent was transported into the main updraft, while the residence time of the agent within the cloud was longer due to the weaker cloud dynamics. Therefore, we must pay attention to whether or not the cloud contains vortices when we make the decision where to seed. This is necessary in order to minimize the loss of seeding material.     

Variable resolution on quasi-uniform grids: linear advection experiments

Summary A couple of different techniques for implementing the variable resolution within numerical models of the atmosphere that use quasi-uniform grids are estimated and compared based on their merit in the simple linear advection experiments. These techniques are: grid stretching, Schmidt transforming and grid overlapping. The quasi-uniform grids are: a conformal cubic and an octagonal grid. The techniques for the variable resolution are evaluated from the perspective of their effects on numerical solution and the practicality of their application. Our analysis suggests that the grid stretching is for now the most optimal choice. However, a special form of grid overlapping is presented that has potential to become a viable alternative in the future.     

U-Series Chronology of Lacustrine Deposits in Death Valley, California

Uranium-series dating on a 186-m core (DV93-1) drilled from Badwater Basin in Death Valley, California, and on calcareous tufas from nearby strandlines shows that Lake Manly, the lake that periodically flooded Death Valley during the late Pleistocene, experienced large fluctuations in depth and chemistry over the last 200,000 yr. Death Valley has been occupied by a long-standing deep lake, perennial shallow saline lakes, and a desiccated salt pan similar to the modern valley floor. The average sedimentation rate of about 1 mm/yr for core DV93-1 was punctuated by episodes of more-rapid accumulation of halite. Arid conditions similar to the modern conditions prevailed during the entire Holocene and between 120,000 and 60,000 yr B.P. From 35,000 yr B.P. to the beginning of the Holocene, a perennial saline lake existed, over 70 m at its deepest. A much deeper and longer lasting perennial Lake Manly existed from about 185,000 to 128,000 yr B.P., with water depths reaching about 175 m, if not 330 m. This lake had two significant “dry” excursions of 10²–10³yr duration about 166,000 and 146,000 yr B.P., and it began to shrink to the point of halite precipitation between 128,000 and 120,000 yr B.P. The two perennial lake periods correspond to marine oxygen isotopic stages (OIS) 2 and 6. Based on the shoreline tufa ages, we do not rule out the possible existence 200,000 yr ago of yet a third perennial lake comparable in size to the OIS 6 lake. The²³⁴U/²³⁸U data suggest that U in tufa owes its origin mainly to Ca-rich springs fed by groundwater that emanated along lake shorelines in southern Death Valley, and that an increase of this spring-water input relative to the river-water input apparently occurred during OIS 6.     

Applications of interannual-resolution stable isotope records of speleothem: Climatic changes in Beijing and Tianjin, China during the past 500 years—the δ 18O record

δ¹⁸O of a stalagmite collected from Shihua Cave, 50 km southwest of Beijing is analyzed. The uppermost 2 cm was sampled at about 3-year intervals by a computer-controlled microsampling device. A total of 133 samples were analyzed, covering the last 480 years. A comparison of the δ¹⁸O record with the instrumentally recorded precipitation in Beijing and Tianjin back to 1840 AD shows that high precipitation correlates with negative δ¹⁸O peaks. The long-term δ¹⁸O trend records temperature changes. Between 1620 and 1900 AD, the temperature was cooler than the average value for the 480-year record, corresponding to the Little Ice Age. Temperatures warmer than the average prevailed during 1520–1620 and 1900—present. Superimposed on the long-term trend are about 14 δ¹⁸O cycles of 30–40-year periodicity, with wet periods centered around 1985, 1955, 1910, 1880, 1840, 1800, 1760, 1730, 1690, 1660, 1630, 1600, 1560 and 1530 AD. Project supported by the National Natural Science Foundation of China (Grant No. 9615875).     

Speleothems as high-resolution paleoenvironment archives: Records from northeastern China

The isotopic compositions of oxygen and carbon and trace concentrations of magnesium and strontium in speleothems formed in limestone caves respond to climate changes outside the caves. Measurements of these properties on a stalagmite from Shihua Cave near Beijing, China, allowed reconstruction of the regional changes in precipitation, temperature and nature of vegetation. Over the last ∼ 500 years, there were fourteen precipitation cycles with a periodicity of 30–40 years, which may well reflect fluctuations in the strength of the East Asian summer monsoons reaching northeastern China. Relative to the mean temperature of this time interval, the period 1620–1900 AD was cold and periods 1520–1620 and 1900–1994 were warm. Over the last ∼ 3000-years, about eight wet/cool-dry/warm climatic cycles of 300–400 years duration occurred, the latest wet/cool half cycle corresponding to the Little Ice Age. The δ¹³C record registers the anthropogenic activities of fossil fuel CO₂ combustion in recent decades and regional deforestation between 13 and 16 centuries when Beijing was bustling with palatial constructions and being developed into the world’s most populated city.