Botswana gravity reference net

Gravity reference stations for the National Gravity Survey of Botswana have been established at twenty-three sites throughout the country in a net linked to existing bases in South Africa, Kenya and Zambia with an internal accuracy of better than 0.5 gravity units (one gravity unit, gu, equals an acceleration of 10⁻⁶ m.s⁻²). The field procedure and reduction of data are explained and a list is given of the gravity values.     

Earth＇s Temporal Principal Moments of Inertia and Variable Rotation

Based on the gravity field models EGM96 and EIGEN-GL04C, the Earth＇s time-dependent principal moments of inertia A, B, C are obtained, and the variable rotation of the Earth is determined. Numerical results show that A, B, and C have increasing tendencies; the tilt of the rotation axis increases 2.1×10^ 8 mas/yr; the third component of the rotational angular velocity, ω3 , has a decrease of 1.0×10^ 22 rad/s^2, which is around 23% of the present observed value. Studies show in detail that both 0 and ω3 experience complex fluctuations at various time scales due to the variations of A, B and C.     

National height datum,the Gauss–Listing geoid level value w0 and its time variation 0 (Baltic Sea Level Project: epochs 1990.8, 1993.8, 1997.4)

 A methodology for precise determination of the fundamental geodetic parameter w ₀, the potential value of the Gauss–Listing geoid, as well as its time derivative ₀, is presented. The method is based on: (1) ellipsoidal harmonic expansion of the external gravitational field of the Earth to degree/order 360/360 (130 321 coefficients; http://www.uni-stuttgard.de/gi/research/ index.html projects) with respect to the International Reference Ellipsoid WGD2000, at the GPS positioned stations; and (2) ellipsoidal free-air gravity reduction of degree/order 360/360, based on orthometric heights of the GPS-positioned stations. The method has been numerically tested for the data of three GPS campaigns of the Baltic Sea Level project (epochs 1990.8,1993.4 and 1997.4). New w ₀ and ₀ values (w ₀=62 636 855.75 ± 0.21 m²/s², ₀=−0.0099±0.00079 m²/s² per year, w ₀/&γmacr;=6 379 781.502 m,₀/&γmacr;=1.0 mm/year, and &γmacr;= −9.81802523 m²/s²) for the test region (Baltic Sea) were obtained. As by-products of the main study, the following were also determined: (1) the high-resolution sea surface topography map for the Baltic Sea; (2) the most accurate regional geoid amongst four different regional Gauss–Listing geoids currently proposed for the Baltic Sea; and (3) the difference between the national height datums of countries around the Baltic Sea. Received: 14 August 2000 / Accepted: 19 June 2001     

The CARIB97 high-resolution geoid height model for the Caribbean Sea

A 2×2 arc-minute resolution geoid model, CARIB97, has been computed covering the Caribbean Sea. The geoid undulations refer to the GRS-80 ellipsoid, centered at the ITRF94 (1996.0) origin. The geoid level is defined by adopting the gravity potential on the geoid as W ₀=62 636 856.88 m²/s² and a gravity-mass constant of GM=3.986 004 418×10¹⁴ m³/s². The geoid model was computed by applying high-frequency corrections to the Earth Gravity Model 1996 global geopotential model in a remove-compute-restore procedure. The permanent tide system of CARIB97 is non-tidal. Comparison of CARIB97 geoid heights to 31 GPS/tidal (ITRF94/local) benchmarks shows an average offset (h–H–N) of 51 cm, with an Root Mean Square (RMS) of 62 cm about the average. This represents an improvement over the use of a global geoid model for the region. However, because the measured orthometric heights (H) refer to many differing tidal datums, these comparisons are biased by localized permanent ocean dynamic topography (PODT). Therefore, we interpret the 51 cm as partially an estimate of the average PODT in the vicinity of the 31 island benchmarks. On an island-by-island basis, CARIB97 now offers the ability to analyze local datum problems which were previously unrecognized due to a lack of high-resolution geoid information in the area. Received: 2 January 1998 / Accepted: 18 August 1998     

Results of the first North American comparison of absolute gravimeters, NACAG-2010

The first North American Comparison of absolute gravimeters (NACAG-2010) was hosted by the National Oceanic and Atmospheric Administration at its newly renovated Table Mountain Geophysical Observatory (TMGO) north of Boulder, Colorado, in October 2010. NACAG-2010 and the renovation of TMGO are part of NGS’s GRAV-D project (Gravity for the Redefinition of the American Vertical Datum). Nine absolute gravimeters from three countries participated in the comparison. Before the comparison, the gravimeter operators agreed to a protocol describing the strategy to measure, calculate, and present the results. Nine sites were used to measure the free-fall acceleration of g. Each gravimeter measured the value of g at a subset of three of the sites, for a total set of 27 g-values for the comparison. The absolute gravimeters agree with one another with a standard deviation of 1.6?μGal (1 Gal ≡ 1?cm s ^?2). The minimum and maximum offsets are ?2.8 and 2.7?μGal. This is an excellent agreement and can be attributed to multiple factors, including gravimeters that were in good working order, good operators, a quiet observatory, and a short duration time for the experiment. These results can be used to standardize gravity surveys internationally.     

Global height datum unification: a new approach in gravity potential space

The problem of “global height datum unification” is solved in the gravity potential space based on: (1) high-resolution local gravity field modeling, (2) geocentric coordinates of the reference benchmark, and (3) a known value of the geoid’s potential. The high-resolution local gravity field model is derived based on a solution of the fixed-free two-boundary-value problem of the Earth’s gravity field using (a) potential difference values (from precise leveling), (b) modulus of the gravity vector (from gravimetry), (c) astronomical longitude and latitude (from geodetic astronomy and/or combination of (GNSS) Global Navigation Satellite System observations with total station measurements), (d) and satellite altimetry. Knowing the height of the reference benchmark in the national height system and its geocentric GNSS coordinates, and using the derived high-resolution local gravity field model, the gravity potential value of the zero point of the height system is computed. The difference between the derived gravity potential value of the zero point of the height system and the geoid’s potential value is computed. This potential difference gives the offset of the zero point of the height system from geoid in the “potential space”, which is transferred into “geometry space” using the transformation formula derived in this paper. The method was applied to the computation of the offset of the zero point of the Iranian height datum from the geoid’s potential value W ₀=62636855.8 m²/s². According to the geometry space computations, the height datum of Iran is 0.09 m below the geoid.     

The geopotential to (14, 14) from a combination of satellite and gravimetric data

A set of2261 5°×5° mean anomalies were used alone and with satellite determined harmonic coefficients of the Smithsonian' Institution to determine the geopotential expansion to various degrees. The basic adjustment was carried out by comparing a terrestrial anomaly to an anomaly determined from an assumed set of coefficients. The (14, 14) solution was found to agree within ±3 m of a detailed geoid in the United States computed using1°×1° anomalies for an inner area and satellite determined anomalies in an outer area. Additional comparisons were made to the input anomaly field to consider the accuracy of various harmonic coefficient solutions. A by-product of this investigation was a new γ_E=978.0463 gals in the Potsdam system or978.0326 gals in an absolute system if −13.7 mgals is taken as the Potsdam correction. Combining this value of γ_E withf=1/298.25, KM=3.9860122·10 ²² cm ³ /sec ² , the consistent equatorial radius was found to be6378143 m.     

The determination of potential difference by the joint application of measured and synthetical gravity data: a case study in Hungary

In an elementary approach every geometrical height difference between the staff points of a levelling line should have a corresponding average g value for the determination of potential difference in the Earth’s gravity field. In practice this condition requires as many gravity data as the number of staff points if linear variation of g is assumed between them. Because of the expensive fieldwork, the necessary data should be supplied from different sources. This study proposes an alternative solution, which is proved at a test bed located in the Mecsek Mountains, Southwest Hungary, where a detailed gravity survey, as dense as the staff point density (~1 point/34 m), is available along a 4.3-km-long levelling line. In the first part of the paper the effect of point density of gravity data on the accuracy of potential difference is investigated. The average g value is simply derived from two neighbouring g measurements along the levelling line, which are incrementally decimated in the consecutive turns of processing. The results show that the error of the potential difference between the endpoints of the line exceeds 0.1 mm in terms of length unit if the sampling distance is greater than 2 km. Thereafter, a suitable method for the densification of the decimated g measurements is provided. It is based on forward gravity modelling utilising a high-resolution digital terrain model, the normal gravity and the complete Bouguer anomalies. The test shows that the error is only in the order of 10⁻³mm even if the sampling distance of g measurements is 4 km. As a component of the error sources of levelling, the ambiguity of the levelled height difference which is the Euclidean distance between the inclined equipotential surfaces is also investigated. Although its effect accumulated along the test line is almost zero, it reaches 0.15 mm in a 1-km-long intermediate section of the line.     

Measurement and Scaling of Carbon Dioxide (CO<Subscript>2</Subscript>) Exchanges in Wheat Using Flux-Tower and Remote Sensing

The present study investigates the characteristics of CO₂ exchange (photosynthesis and respiration) over agricultural site dominated by wheat crop and their relationship with ecosystem parameters derived from MODIS. Eddy covariance measurement of CO₂ and H₂O exchanges was carried out at 10 Hz interval and fluxes of CO₂ were computed at half-hourly time steps. The net ecosystem exchange (NEE) was partitioned into gross primary productivity (GPP) and ecosystem respiration (R _e) by taking difference between day-time NEE and respiration. Time-series of daily reflectance and surface temperature products at varying resolution (250–1000 m) were used to derive ecosystem variables (EVI, NDVI, LST). Diurnal pattern in Net ecosystem exchange reveals negative NEE during day-time representing CO₂ uptake and positive during night as release of CO₂. The amplitude of the diurnal variation in NEE increased as LAI crop growth advances and reached its peak around the anthesis stage. The mid-day uptake during this stage was around 1.15 mg CO₂ m⁻² s⁻¹ and night-time release was around 0.15 mg CO₂ m⁻² s⁻¹. Linear and non-linear least square regression procedures were employed to develop phenomenological models and empirical fits between flux tower based GPP and NEE with satellite derived variables and environmental parameters. Enhanced vegetation index was found significantly related to both GPP and NEE. However, NDVI showed little less significant relationship with both GPP and NEE. Furthemore, temperature-greenness (TG) model combining scaled EVI and LST was parameterized to estimate daily GPP over dominantly wheat crop site. (R ² = 0.77). Multi-variate analysis shows that inclusion of LST or air temperature with EVI marginally improves variance explained in daily NEE and GPP.     

Determination of Geopotential of Local Vertical Datum Surface

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A new gravity map, a new marine geoid around Japan and the detection of the Kuroshio current

About half a million marine gravity measurements over a 30^∘×30^∘ area centered on Japan have been processed and adjusted to produce a new free-air gravity map from a 5′×5′ grid. This map seems to have a better resolution than those previously published as measured by its correlation with bathymetry. The grid was used together with a high-degree and -order spherical harmonics geopotential model to compute a detailed geoid with two methods: Stokes integral and collocation. Comparisons with other available geoidal surfaces derived either from gravity or from satellite altimetry were made especially to test the ability of this new geoid at showing the sea surface topography as mapped by the Topex/Poseidon satellite. Over 2 months (6 cycles) the dynamic topography at ascending passes in the region (23^∘47^∘N and 123^∘147^∘E) was mapped to study the variability of the Kuroshio current. Received: 15 July 1994 / Accepted: 17 February 1997     

多视线向InSAR形变场约束的改则地震滑动分布反演

利用3种不同视线向LOS(Line Of Sight)的ENVISAT ASAR数据进行干涉处理,提取多视线向(Multi-LOS)的同震形变场;结合同震形变场特征与震源机制解,构建了改则地震双断层破裂模型;利用四叉树采样后的多视线向同震形变场进行约束,通过梯度下降法(Steepest Descent Method,SDM)与Crust2.0地壳分层模型反演了改则地震的同震滑动分布特征。结果表明:反演的形变残差得到有效控制,基本介于0±10 cm之间;主震断层的滑动量主要位于断层面2—16 km深部,最大滑动量可达1.34 m,位于断层面6.4 km深处;余震断层滑动量主要位于断层面2—6 km深部,最大滑动量可达0.90 m,位于断层面3.52 km深处;主震断层与余震断层均以正断为主,但主震断层还具有一定的左旋走滑分量,而余震断层的左旋走滑不明显;当剪切模量μ取3.2×1010Pa时,反演获得的主震与余震地震矩M0分别为6.34×1018N·M与1.20×1018N·M,分别相当于矩震级MW6.47与MW5.98。     

Approximating the Bayesian estimate of the standard deviation in a linear model

The Bayesian estimates _b of the standard deviation σ in a linear model—as needed for the evaluation of reliability—is well known to be proportional to the square root of the Bayesian estimate (s ²) _b of the variance component σ² by a proportionality factor involving the ratio of Gamma functions. However, in analogy to the case of the respective unbiased estimates, the troublesome exact computation ofa _b may be avoided by a simple approximation which turns out to be good enough for most applications even if the degree of freedom ν is rather small. Paper presented to the Int. Conf. on “Practical Bayesian Statistics”, Cambridge (U.K.), 8.–11. July 1986.     

Controlling CO2 emissions for each area in a region: the case of Japan

Background

Unlike in the developed countries, Ethiopia does not have carbon inventories and databank to monitor and enhance carbon sequestration potential of different forests. Only small efforts have been made so far to assess the biomass and soil carbon sequestration at micro-level. This study was carried out to obtain sufficient information about the carbon stock potential of Gerba-Dima forest in south-western Ethiopia. A total of 90 sample plots were laid by employing stratified random sampling. Nested plots were used to collect data of the four carbon pools. For trees with a diameter range of 5 cm < diameter < 20 cm, the carbon stock was assessed from a plot size of 49 m² (7 m * 7 m). For trees with a diameter range of 20 cm < diameter < 50 cm, the carbon stock was assessed from a plot size of 625 m² (25 m * 25 m). For trees > 50 cm diameter, an additional larger sample of 35 * 35 m² was used. Litter, herb and soil data were collected from 1 m² subplot established at the center of each nested plot. To compute the above ground biomass carbon stock of trees and shrubs with DBH > 5 cm, their DBH and height were measured. The biomass carbon assessment of woody species having DBH < 5 cm, litter and herb were conducted by measuring their fresh weight in the field and dry weight in the laboratory.

Results

The mean total carbon stock density of Gerba-Dima forest was found to be 508.9 tons carbon ha⁻¹, out of which 243.8, 45.97, 0.03 and 219.1 tons carbon ha⁻¹ were stored in the above ground biomass, below ground biomass, litter biomass and soil organic carbon, respectively.

Conclusions

The existence of high carbon stock in the study forest shows the potential of the area for climate change mitigation. Thus, all stakeholders at the local and national level should work together to implement effective conservation measures and get benefit from the biocarbon fund.

     

DETERMINATION OF TAPE TEMPERATURES ON THE MEASUREMENT OF THE WANKIE AND SABI GEODETIC BASES,SOUTHERN RHODESIA (1953)

Abstract

The Wankie Geodetic Base was measured in May 1953 and the re-measurement of the Sabi Geodetic Base was also completed during the month following. For these measurements the standard “Macca” equipment was used, the gear being lent to the Southern Rhodesia Government by the Directorate of Colonial Surveys. As it was anticipated that both measurements would be made under hotter and more sunny conditions than normally prevail in England, the Directorate of Colonial Surveys suggested that the opportunity be taken of carrying out further tests in the determination of temperatures by the “resistance thermometer” as described by Messrs. Clark and Johnson of the National Physical Laboratory in their paper on the “Measurement of Temperature of Geodetic Surveying Tapes. Accordingly, through the good officesof the Director of the National Physical Laboratory, the apparatus comprising the resistance theremometer was made available for use on these two base measurements.     

Accurate formula expressing the difference between the normal gravity and its radial component

A simple formula is presented giving the value of γ−γ _r to better than 0.001 mgal associated with an arbitrary reference ellipsoid, where γ is the normal gravity and γ _r is its radial component. Further simplifications of this formula are possible, depending on the desired accuracy. Since in the actual field g−g_r equals γ−γ _r to a good approximation, this formula makes it possible to work in terms of g_r rather than in terms of the measured quantity g. Such a choice is attractive mainly because the spherical harmonic expansion of g_r is very simple.     

Soil respiration mapped by exclusively use of MODIS data for forest landscapes of Saskatchewan,Canada

Soil respiration (R_s) is of great importance to the global carbon balance. Remote sensing of R_s is challenging because of (1) the lack of long-term R_s data for model development and (2) limited knowledge of using satellite-based products to estimate R_s. Using 8-years (2002–2009) of continuous R_s measurements with nonsteady-state automated chamber systems at a Canadian boreal black spruce stand (SK-OBS), we found that R_s was strongly correlated with the product of the normalized difference vegetation index (NDVI) and the nighttime land surface temperature (LSTn) derived from Moderate Resolution Imaging Spectroradiometer (MODIS) imagery. The coefficients of the linear regression equation of this correlation between R_s and NDVI × LSTn could be further calibrated using the MODIS leaf area index (LAI) product, resulting in an algorithm that is driven solely by remote sensing observations. Modeled R_s closely tracked the seasonal patterns of measured R_s and explained 74–92% of the variance in R_s with a root mean square error (RMSE) less than 1.0 g C/m²/d. Further validation of the model from SK-OBS site at another two independent sites (SK-OA and SK-OJP, old aspen and old jack pine, respectively) showed that the algorithm can produce good estimates of R_s with an overall R² of 0.78 (p < 0.001) for data of these two sites. Consequently, we mapped R_s of forest landscapes of Saskatchewan using entirely MODIS observations for 2003 and spatial and temporal patterns of R_s were well modeled. These results point to a strong relationship between the soil respiratory process and canopy photosynthesis as indicated from the greenness index (i.e., NDVI), thereby implying the potential of remote sensing data for detecting variations in R_s. A combination of both biological and environmental variables estimated from remote sensing in this analysis may be valuable in future investigations of spatial and temporal characteristics of R_s.     

Assessment of sedimentation in harakud reservoir using digital remote sensing technique

As per recommendations of Working Group for National Action for Reservoir Sedimentation Assessment, National Institute of Hydrology has taken up study on sedimentation for 25 reservoirs in India during X plan period using remote sensing technique. One such study for Hirakud reservoir in Mahanadi basin in Orissa for year 1999–2001 is described here. Reservoir’s original utilizable and gross volumes were 5818 and 8136 M m³, respectively. Minimum draw down level (MDDL) and full reservoir level (FRL) for reservoir are 179.83 and 192.02 m, respectively. Linear Imaging Self Scanning (LISS)- III data of Indian Remote Sensing Satellites (IRS) 1C and 1D, covering elevation range between 180.68 and 191.89 m, were used. Rule based classification was applied to ‘water index’ and radiances of near infrared band to determine water spread area. Revised live storage capacity was 4842 M m³. The silt index for the live storage area was 2.623 ha m (100 km² year)^-1 (0.376 % of live storage or 21.9 M m³ year^-1). Total live storage lost in sedimentation was 984 M m³ (16.90 % of live storage).     

Fehlertheoretische Maxwell-Boltzmann-Verteilung

Summary The probability to find an error vector in multiples of the Helmert-Maxwell-Boltzmann point error σ² δ_ij(δ_ij Kronecker symbol) is calculated. It is found that the probability is for σ39%, for2 σ86% and for3 σ99% in two dimensions, for σ20%, for2 σ74% and for3 σ97% in three dimensions. The fundamental Maxwell-Boltzmann-distribution is tabulated0,02 (0,02) 4,50.      

Downward continuation of the free-air gravity anomalies to the ellipsoid using the gradient solution and terrain correction—An attempt of global numerical computations

The formulas for the determination of the coefficients of the spherical harmonic expansion of the disturbing potential of the earth are defined for data given on a sphere. In order to determine the spherical harmonic coefficients, the gravity anomalies have to be analytically downward continued from the earth's surface to a sphere—at least to the ellipsoid. The goal of this paper is to continue the gravity anomalies from the earth's surface downward to the ellipsoid using recent elevation models. The basic method for the downward continuation is the gradient solution (theg ₁ term). The terrain correction has also been computed because of the role it can play as a correction term when calculating harmonic coefficients from surface gravity data. Theg ₁ term and the terrain correction were expanded into the spherical harmonics up to180 ^th order. The corrections (theg ₁ term and the terrain correction) have the order of about 2% of theRMS value of degree variance of the disturbing potential per degree. The influences of theg ₁ term and the terrain correction on the geoid take the order of 1 meter (RMS value of corrections of the geoid undulation) and on the deflections of the vertical is of the order 0.1″ (RMS value of correction of the deflections of the vertical).