Calculating the ocean's mean dynamic topography from a mean sea surface and a geoid

In principle the global mean geostrophic surface circulation of the ocean can be diagnosed by subtracting a geoid from a mean sea surface (MSS). However, because the resulting mean dynamic topography (MDT) is approximately two orders of magnitude smaller than either of the constituent surfaces, and because the geoid is most naturally expressed as a spectral model while the MSS is a gridded product, in practice complications arise. Two algorithms for combining MSS and satellite-derived geoid data to determine the ocean’s mean dynamic topography (MDT) are considered in this paper: a pointwise approach, whereby the gridded geoid height field is subtracted from the gridded MSS; and a spectral approach, whereby the spherical harmonic coefficients of the geoid are subtracted from an equivalent set of coefficients representing the MSS, from which the gridded MDT is then obtained. The essential difference is that with the latter approach the MSS is truncated, a form of filtering, just as with the geoid. This ensures that errors of omission resulting from the truncation of the geoid, which are small in comparison to the geoid but large in comparison to the MDT, are matched, and therefore negated, by similar errors of omission in the MSS. The MDTs produced by both methods require additional filtering. However, the spectral MDT requires less filtering to remove noise, and therefore it retains more oceanographic information than its pointwise equivalent. The spectral method also results in a more realistic MDT at coastlines. 1. Introduction An important challenge in oceanography is the accurate determination of the ocean’s time-mean dynamic topography (MDT). If this can be achieved with sufficient accuracy for combination with the timedependent component of the dynamic topography, obtainable from altimetric data, then the resulting sum (i.e., the absolute dynamic topography) will give an accurate picture of surface geostrophic currents and ocean transports.

Integrated marine gravity field in the Brazilian coast from altimeter-derived sea surface gradient and shipborne gravity

Sea surface gradients derived from the Geosat and ERS-1 satellite altimetry geodetic missions were integrated with marine gravity data from the National Geophysical Data Center and Brazilian national surveys. Using the least squares collocation method, models of free-air gravity anomaly and geoid height were calculated for the coast of Brazil with a resolution of 2` x 2`. The integration of satellite and shipborne data showed better statistical results in regions near the coast than using satellite data only, suggesting an improvement when compared to the state-of-the-art global gravity models. Furthermore, these results were obtained with considerably less input information than was used by those reference models. The least squares collocation presented a very low content of high-frequency noise in the predicted gravity anomalies. This may be considered essential to improve the high resolution representation of the gravity field in regions of ocean-continent transition. (C) 2010 Elsevier Ltd. All rights reserved.

Arcabouço geofísico, isostasia e causas do magmatismo cenozóico da província Borborema e de sua margem continental (Nordeste do Brasil)

The Borborema Province (BP) is a geologic domain located in Northeastern Brazil. The BP is limited at the south by the São Francisco craton, at the west by the Parnaíba basin, and both at the north and east by coastal sedimentary basins. Nonetheless the BP surface geology is well known, several key aspects of its evolution are still open, notably: i)its tectonic compartmentalization established after the Brasiliano orogenesis, ii) the architecture of its cretaceous continental margin, iii) the elastic properties of its lithosphere, and iv) the causes of magmatism and uplifting which occurred in the Cenozoic. In this thesis, a regional coverage of geophysical data (elevation, gravity, magnetic, geoid height, and surface wave global tomography) were integrated with surface geologic information aiming to attain a better understanding of the above questions. In the Riacho do Pontal belt and in the western sector of the Sergipano belt, the neoproterozoic suture of the collision of the Sul domain of the BP with the Sanfranciscana plate (SFP) is correlated with an expressive dipolar gravity anomaly. The positive lobule of this anomaly is due to the BP lower continental crust uplifting whilst the negative lobule is due to the supracrustal nappes overthrusting the SFP. In the eastern sector of the Sergipano belt, this dipolar gravity anomaly does not exist. However the suture still can be identified at the southern sector of the Marancó complex arc, alongside of the Porto da Folha shear zone, where the SFP N-S geophysical alignments are truncated. The boundary associated to the collision of the Ceará domain of the BP with the West African craton is also correlated with a dipolar gravity anomaly. The positive lobule of this anomaly coincides with the Sobral-Pedro II shear zone whilst the negative lobule is associated with the Santa Quitéria magmatic arc. Judging by their geophysical signatures, the major BP internal boundaries are: i)the western sector of the Pernambuco shear zone and the eastern continuation of this shear zone as the Congo shear zone, ii) the Patos shear zone, and iii) the Jaguaribe shear zone and its southwestern continuation as the Tatajuba shear zone. These boundaries divide the BP in five tectonic domains in the geophysical criteria: Sul, Transversal, Rio Grande do Norte, Ceará, and Médio Coreaú. The Sul domain is characterized by geophysical signatures associated with the BP and SFP collision. The fact that Congo shear zone is now proposed as part of the Transversal domain boundary implies an important change in the original definition of this domain. The Rio Grande do Norte domain presents a highly magnetized crust resulted from the superposition of precambrian and phanerozoic events. The Ceará domain is divided by the Senador Pompeu shear zone in two subdomains: the eastern one corresponds to the Orós-Jaguaribe belt and the western one to the Ceará-Central subdomain. The latter subdomain exhibits a positive ENE-W SW gravity anomaly which was associated to a crustal discontinuity. This discontinuity would have acted as a rampart against to the N-S Brasiliano orogenic nappes. The Médio Coreaú domain also presents a dipolar gravity anomaly. Its positive lobule is due to granulitic rocks whereas the negative one is caused by supracrustal rocks. The boundary between Médio Coreaú and Ceará domains can be traced below the Parnaíba basin sediments by its geophysical signature. The joint analysis of free air anomalies, free air admittances, and effective elastic thickness estimates (Te) revealed that the Brazilian East and Equatorial continental margins have quite different elastic properties. In the first one 10 km < Te < 20 km whereas in the second one Te ≤ 10 km. The weakness of the Equatorial margin lithosphere was caused by the cenozoic magmatism. The BP continental margin presents segmentations; some of them have inheritance from precambrian structures and domains. The segmentations conform markedly with some sedimentary basin features which are below described from south to north. The limit between Sergipe and Alagoas subbasins coincides with the suture between BP and SFP. Te estimates indicates concordantly that in Sergipe subbasin Te is around 20 km while Alagoas subbasin has Te around 10 km, thus revealing that the lithosphere in the Sergipe subbasin has a greater rigidity than the lithosphere in the Alagoas subbasin. Additionally inside the crust beneath Sergipe subbasin occurs a very dense body (underplating or crustal heritage?) which is not present in the crust beneath Alagoas subbasin. The continental margin of the Pernambuco basin (15 < Te < 25 km) presents a very distinct free air edge effect displaying two anomalies. This fact indicates the existence in the Pernambuco plateau of a relatively thick crust. In the Paraíba basin the free air edge effect is quite uniform, Te ≈ 15 km, and the lower crust is abnormally dense probably due to its alteration by a magmatic underplating in the Cenozoic. The Potiguar basin segmentation in three parts was corroborated by the Te estimates: in the Potiguar rift Te ≅ 5 km, in the Aracati platform Te ≅ 25 km, and in the Touros platform Te ≅ 10 km. The observed weakness of the lithosphere in the Potiguar rift segment is due to the high heat flux while the relatively high strength of the lithosphere in the Touros platform may be due to the existence of an archaean crust. The Ceará basin, in the region of Mundaú and Icaraí subbasins, presents a quite uniform free air edge effect and Te ranges from 10 to 15 km. The analysis of the Bouguer admittance revealed that isostasy in BP can be explained with an isostatic model where combined surface and buried loadings are present. The estimated ratio of the buried loading relative to the surface loading is equal to 15. In addition, the lower crust in BP is abnormally dense. These affirmations are particularly adequate to the northern portion of BP where adherence of the observed data to the isostatic model is quite good. Using the same above described isostatic model to calculate the coherence function, it was obtained that a single Te estimate for the entire BP must be lower than 60 km; in addition, the BP north portion has Te around 20 km. Using the conventional elastic flexural model to isostasy, an inversion of crust thickness was performed. It was identified two regions in BP where the crust is thickened: one below the Borborema plateau (associated to an uplifting in the Cenozoic) and the other one in the Ceará domain beneath the Santa Quitéria magmatic arc (a residue associated to the Brasiliano orogenesis). On the other hand, along the Cariri-Potiguar trend, the crust is thinned due to an aborted rifting in the Cretaceous. Based on the interpretation of free air anomalies, it was inferred the existence of a large magmatism in the oceanic crust surrounding the BP, in contrast with the incipient magmatism in the continent as shown by surface geology. In BP a quite important positive geoid anomaly exists. This anomaly is spatially correlated with the Borborema plateau and the Macaú-Queimadas volcanic lineament. The integrated interpretation of geoid height anomaly data, global shear velocity model, and geologic data allow to propose that and Edge Driven Convection (EDC) may have caused the Cenozoic magmatism. The EDC is an instability that presumably occurs at the boundary between thick stable lithosphere and oceanic thin lithosphere. In the BP lithosphere, the EDC mechanism would have dragged the cold lithospheric mantle into the hot asthenospheric mantle thus causing a positive density contrast that would have generated the main component of the geoid height anomaly. In addition, the compatibility of the gravity data with the isostatic model, where combined surface and buried loadings are present, together with the temporal correlation between the Cenozoic magmatism and the Borborema plateau uplifting allow to propose that this uplifting would have been caused by the buoyancy effect of a crustal root generated by a magmatic underplating in the Cenozoic

Comparison of GOCE-GPS gravity fields derived by different approaches

Several techniques have been proposed to exploit GNSS-derived kinematic orbit information for the determination of long-wavelength gravity field features. These methods include the (i) celestial mechanics approach, (ii) short-arc approach, (iii) point-wise acceleration approach, (iv) averaged acceleration approach, and (v) energy balance approach. Although there is a general consensus that—except for energy balance—these methods theoretically provide equivalent results, real data gravity field solutions from kinematic orbit analysis have never been evaluated against each other within a consistent data processing environment. This contribution strives to close this gap. Target consistency criteria for our study are the input data sets, period of investigation, spherical harmonic resolution, a priori gravity field information, etc. We compare GOCE gravity field estimates based on the aforementioned approaches as computed at the Graz University of Technology, the University of Bern, the University of Stuttgart/Austrian Academy of Sciences, and by RHEA Systems for the European Space Agency. The involved research groups complied with most of the consistency criterions. Deviations only occur where technical unfeasibility exists. Performance measures include formal errors, differences with respect to a state-of-the-art GRACE gravity field, (cumulative) geoid height differences, and SLR residuals from precise orbit determination of geodetic satellites. We found that for the approaches (i) to (iv), the cumulative geoid height differences at spherical harmonic degree 100 differ by only ≈10 % ; in the absence of the polar data gap, SLR residuals agree by ≈96 % . From our investigations, we conclude that real data analysis results are in agreement with the theoretical considerations concerning the (relative) performance of the different approaches.

Lithosphere Thickness, Heat Flow and Moho Depth in the South of Portugal

ABSTRACT In the last years, several models were presented trying to obtain lithosphere and Moho thickness in the Iberian Peninsula, using data related to geoid elevation and topography, gravity, seismicity and thermal analysis. The results obtained show a decrease in the thickness of the crust and the lithosphere in the SW part of the Iberian Peninsula. Density anomalies in the crust are also referred. The work I intend to present is related with the south of the Ossa Morena Zone, the South Portuguese Zone and the Algarve, in the south of Portugal. Data obtained in the region was collected and deviations from average values used were detected. Models were made taking into account the specific characteristics of the region. Heat flow, thermal conductivity, heat production, topography, gravity, seismic and geological data available for the region, are used to adapt the models. A special attention will be given to the spatial variation of heat flow values and to Moho depth in the region. The results show that this region is different from other parts of the Iberian Peninsula and a special attention must be given to it. The different values obtained using seismic, gravity, and geoid height data, and the results obtained with models using thermal data shows the importance of trying to know and understand the thermal structure of the regions. Problems related with the use of average values will be focused.

What Does Height Really Mean? Part III: Height Systems

This is the third paper in a four-part series considering the fundamental question, “what does the word “height” really mean?” The first paper reviewed reference ellipsoids and mean sea level datums. The second paper reviewed the physics of heights culminating in a simple development of the geoid and explained why mean sea level stations are not all at the same orthometric height. This third paper develops the principle notions of height, namely measured, differentially deduced changes in elevation, orthometric heights, Helmert orthometric heights, normal orthometric heights, dynamic heights, and geopotential numbers. We conclude with a more in-depth discussion of current thoughts regarding the geoid.

Improved geoid solution for the Weddell Sea region

We present a geoid solution for the Weddell Sea and adjacent continental Antarctic regions. There, a refined geoid is of interest, especially for oceanographic and glaciological applications. For example, to investigate the Weddell Gyre as a part of the Antarctic Circumpolar Current and, thus, of the global ocean circulation, the mean dynamic topography (MDT) is needed. These days, the marine gravity field can be inferred with high and homogeneous resolution from altimetric height profiles of the mean sea surface. However, in areas permanently covered by sea ice as well as in coastal regions, satellite altimetry features deficiencies. Focussing on the Weddell Sea, these aspects are investigated in detail. In these areas, ground-based data that have not been used for geoid computation so far provide additional information in comparison with the existing high-resolution global gravity field models such as EGM2008. The geoid computation is based on the remove-compute-restore approach making use of least-squares collocation. The residual geoid with respect to a release 4 GOCE model adds up to two meters and more in the near-coastal and continental areas of the Weddell Sea region, also in comparison with EGM2008. Consequently, the thus refined geoid serves to compute new estimates of the regional MDT and geostrophic currents.

Photoelastic Analysis Of Fixed Partial Prosthesis Crown Height And Implant Length On Distribution Of Stress In Two Dental Implant Systems.

The aim of this study was to evaluate by photoelastic analysis stress distribution on short and long implants of two dental implant systems with 2-unit implant-supported fixed partial prostheses of 8 mm and 13 mm heights. Sixteen photoelastic models were divided into 4 groups: I: long implant (5 × 11 mm) (Neodent), II: long implant (5 × 11 mm) (Bicon), III: short implant (5 × 6 mm) (Neodent), and IV: short implants (5 × 6 mm) (Bicon). The models were positioned in a circular polariscope associated with a cell load and static axial (0.5 Kgf) and nonaxial load (15°, 0.5 Kgf) were applied to each group for both prosthetic crown heights. Three-way ANOVA was used to compare the factors implant length, crown height, and implant system (α = 0.05). The results showed that implant length was a statistically significant factor for both axial and nonaxial loading. The 13 mm prosthetic crown did not result in statistically significant differences in stress distribution between the implant systems and implant lengths studied, regardless of load type (P > 0.05). It can be concluded that short implants showed higher stress levels than long implants. Implant system and length was not relevant factors when prosthetic crown height were increased.

Waist-to-height Ratio Percentiles And Cutoffs For Obesity: A Cross-sectional Study In Brazilian Adolescents.

This study aimed to describe the distribution of waist-to-height ratio (WHtR) percentiles and cutoffs for obesity in Brazilian adolescents. A cross-sectional study including adolescents aged 10 to 15 years was conducted in the city of São Paulo, Brazil; anthropometric measurements (weight, height, and waist-circumference) were taken, and WHtRs were calculated and then divided into percentiles derived by using Least Median of Squares (LMS) regression. The receiver operating characteristic (ROC) curve was used in determining cutoffs for obesity (BMI ≥ 97th percentile) and Mann-Whitney and Kruskal-Wallis tests were used for comparing variables. The study included 8,019 adolescents from 43 schools, of whom 54.5% were female, and 74.8% attended public schools. Boys had higher mean WHtR than girls (0.45 ± 0.06 vs 0.44 ± 0.05; p=0.002) and higher WHtR at the 95th percentile (0.56 vs 0.54; p<0.05). The WHtR cutoffs according to the WHO criteria ranged from 0.467 to 0.506 and 0.463 to 0.496 among girls and boys respectively, with high sensitivity (82.8-95%) and specificity (84-95.5%). The WHtR was significantly associated with body adiposity measured by BMI. Its age-specific percentiles and cutoffs may be used as additional surrogate markers of central obesity and its co-morbidities.

Validity and reliability of self-reported weight and height measures for the diagnoses of adolescent's nutritional status

OBJETIVO: Avaliar a validade do peso, estatura e Índice de Massa Corporal (IMC) referidos e sua confiabilidade para o diagnóstico do estado nutricional de adolescentes de Piracicaba. MÉTODOS: Participaram do estudo 360 adolescentes de ambos os sexos, de escolas públicas de Piracicaba, com idade entre 10 e 15 anos. Os adolescentes auto-relataram seu peso e estatura, sendo esses valores obtidos por medidas diretas, logo em seguida, pelos entrevistadores. A validade do IMC referido foi calculada segundo índices de sensibilidade, especificidade e valor preditivo positivo (VPP). Avaliou-se a concordância entre as categorias de IMC obtido por meio das medidas referidas e aferidas a partir do coeficiente kappa ponderado, coeficiente de correlação de Lin. e gráficos de Bland e Altman e Lin. RESULTADOS: Verificou-se que tanto os meninos quanto as meninas subestimaram o peso (-1,0 meninas e meninos) e a estatura (meninas -1,2 e meninos -0,8) (p < 0,001). Os valores de IMC aferidos e referidos apresentaram uma concordância moderada. A sensibilidade do IMC referido para classificar os indivíduos obesos foi maior para os meninos (87,5%), enquanto a especificidade foi maior para as meninas (92,7%). O VPP foi elevado somente para a classificação da eutrofia. CONCLUSÕES: As medidas referidas de peso e estatura de adolescentes não representam medidas válidas e, portanto, não devem ser usadas em substituição aos valores mensurados. Além disso, verificou-se que 10% dos meninos obesos e 40% das meninas obesas poderiam permanecer não identificados utilizando-se as medidas auto-referidas, confirmando a baixa validade das medidas auto-referidas.

Ratio of weight to height gain: a useful tool for identifying children at risk of becoming overweight or obese at preschool age

PURPOSE: To analyze the usefulness of the weight gain/height gain ratio from birth to two and three years of age as a predictive risk indicator of excess weight at preschool age. METHODS: The weight and height/length of 409 preschool children at daycare centers were measured according to internationally recommended rules. The weight values and body mass indices of the children were transformed into a z-score per the standard method described by the World Health Organization. The Pearson correlation coefficients (rP) and the linear regressions between the anthropometric parameters and the body mass index z-scores of preschool children were statistically analyzed (alpha = 0.05). RESULTS: The mean age of the study population was 3.2 years (± 0.3 years). The prevalence of excess weight was 28.8%, and the prevalence of overweight and obesity was 8.8%. The correlation coefficients between the body mass index z-scores of the preschool children and the birth weights or body mass indices at birth were low (0.09 and 0.10, respectively). There was a high correlation coefficient (rP = 0.79) between the mean monthly gain of weight and the body mass index z-score of preschool children. A higher coefficient (rP = 0.93) was observed between the ratio of the mean weight gain per height gain (g/cm) and the preschool children body mass index z-score. The coefficients and their differences were statistically significant. CONCLUSION: Regardless of weight or length at birth, the mean ratio between the weight gain per g/cm of height growth from birth presented a strong correlation with the body mass index of preschool children. These results suggest that this ratio may be a good indicator of the risk of excess weight and obesity in preschool-aged children.

Load Ratio Estimation Through Striation Height and Spacing Analysis of an Aerospace Al Alloy 7475-T7351

It is well known that striation spacing may be related to the crack growth rate, da/dN, through Paris equation, as well as the maximum and minimum loads under service loading conditions. These loads define the load ratio, R, and are considered impossible to be evaluated from the inter-spacing striations analysis. In this way, this study discusses the methodology proposed by Furukawa to evaluate the maximum and minimum loads based on the experimental fact that the relative height of a striation, H, and the striation spacing, s, are strongly influenced by the load ratio, R. Fatigue tests in C(T) specimens were conducted on SAE 7475-T7351 Al alloy plates at room temperature and the results showed a straightforward correlation between the parameters H, s, and R. Measurements of striation height, H, were performed using scanning electron microscopy and field emission gun (FEG) after sectioning the specimen at a large inclined angle to amplify the height of the striations. The results showed that for increasing R the values of H/s tend to increase. Striation height, striation spacing, and load ratio correlations were obtained, which allows one to estimate service loadings from fatigue fracture surface survey.

The viscosity parameter's dependence on the profile of the disk scale height

It is shown that, for accretion disks, the height scale is a constant whenever hydrostatic equilibrium and the subsonic turbulence regime hold in the disk. In order to have a variable height scale, processes are needed that contribute an extra term to the continuity equation. This contribution makes the viscosity parameter much greater in the outer region and much smaller in the inner region. Under these circumstances, turbulence is the presumable source of viscosity in the disk.

Visual Display Height

We examined the influence of backrest inclination and vergence demand on the posture and gaze angle that-workers adopt to view visual targets placed in different vertical locations. In the study 12 participants viewed a small video monitor placed in 7 locations around a 0.65-m radius arc (from 650 below to 300 above horizontal eye height). Trunk posture was manipulated by changing the backrest inclination of an adjustable chair. Vergence demand was manipulated by using ophthalmic lenses and prisms to mimic the visual consequences of varying target distance. Changes in vertical target location caused large changes in atlantooccipital posture and gaze angle. Cervical posture was altered to a lesser extent by changes in vertical target location. Participants compensated for changes in backrest inclination by changing cervical posture, though they did not significantly alter atlanto-occipital posture and gaze angle. The posture adopted to view any target represents a compromise between visual and musculoskeletal demands. These results provide support for the argument that the optimal location of visual targets is at least 15 below horizontal eye level. Actual or potential applications of this work include the layout of computer workstations and the viewing of displays from a seated posture.

The effect of imposed and self-selected computer monitor height on posture and gaze angle

Objective: The objectives were to determine the postural consequences of varying computer monitor height and to describe self-selected monitor heights and postures. Design: The design involved experimental manipulation of computer monitor height, description of self-selected heights, and measurement of posture and gaze angles. Background. Disagreement exists with regard to the appropriate height of computer monitors. It is known that users alter both head orientation and gaze angle in response to changes in monitor height; however the relative contribution of atlanto-occipital and cervical flexion to the change in head rotation is unknown. No information is available with regard to self-selected monitor heights. Methods. Twelve students performed a tracking task with the monitor placed at three different heights. The subjects then completed eight trials in which monitor height was first self-selected. Sagittal postural and gaze angle data were determined by digitizing markers defining a two-dimensional three-link model of the trunk, cervical spine and head. Results. The 27 degrees change in monitor height imposed was, on average, accommodated by 18 degrees of head inclination and a 9 degrees change in gaze angle relative to the head. The change in head inclination was achieved by a 6 degrees change in trunk inclination, a 4 degrees change in cervical flexion, and a 7 degrees change in atlanto-occipital flexion. The self-selected height varied depending on the initial monitor height and inclination. Conclusions. Self-selected monitor heights were lower than current 'eye-level' recommendations. Lower monitor heights are likely to reduce both visual and musculoskeletal discomfort. Relevance Musculoskeletal and visual discomfort may be reduced by placing computer monitors lower than currently recommended. (C) 1998 Elsevier Science Ltd. All rights reserved.