Comparison between cell-centered and nodal-based discretization schemes for linear elasticity

In this paper, we study newly developed methods for linear elasticity on polyhedral meshes. Our emphasis is on applications of the methods to geological models. Models of subsurface, and in particular sedimentary rocks, naturally lead to general polyhedral meshes. Numerical methods which can directly handle such representation are highly desirable. Many of the numerical challenges in simulation of subsurface applications come from the lack of robustness and accuracy of numerical methods in the case of highly distorted grids. In this paper, we investigate and compare the Multi-Point Stress Approximation (MPSA) and the Virtual Element Method (VEM) with regard to grid features that are frequently seen in geological models and likely to lead to a lack of accuracy of the methods. In particular, we look at how the methods perform near the incompressible limit. This work shows that both methods are promising for flexible modeling of subsurface mechanics.     

Spurious diapycnal mixing in terrain-following coordinate models: The problem and a solution

In this paper, we identify a crucial numerical problem in sigma coordinate models, leading to unacceptable spurious diapycnal mixing. This error is a by-product of recent advances in numerical methods, namely the implementation of high-order diffusive advection schemes. In the case of ROMS, spurious mixing is produced by its third-order upwind advection scheme, but our analysis suggests that all diffusive advection schemes would behave similarly in all sigma models. We show that the common idea that spurious mixing decreases with resolution is generally false. In a coarse-resolution regime, spurious mixing increases as resolution is refined, and may reach its peak value when eddy-driven lateral mixing becomes explicitly resolved. At finer resolution, diffusivities are expected to decrease but with values that only become acceptable at resolutions finer than the kilometer. The solution to this problem requires a specifically designed advection scheme. We propose and validate the RSUP3 scheme, where diffusion is split from advection and is represented by a rotated biharmonic diffusion scheme with flow-dependent hyperdiffusivity satisfying the Peclet constraint. The rotated diffusion operator is designed for numerical stability, which includes improvements of linear stability limits and a clipping method adapted to the sigma-coordinate. Realistic model experiments in a southwest Pacific configuration show that RSUP3 is able to preserve low dispersion and diffusion capabilities of the original third-order upwind scheme, while preserving water mass characteristics. There are residual errors from the rotated diffusion operator, but they remain acceptable. The use of a constant diffusivity rather than the Peclet hyperdiffusivity tends to increase these residual errors which become unacceptable with Laplacian diffusion. Finally, we have left some options open concerning the use of time filters as an alternative to spatial diffusion. A temporal discretization approach to the present problem (including implicit discretization) will be reported in a following paper.     

Distribution patterns of interstitial polychaetes in sandy beaches of southern Brazil

This study describes the distribution patterns of interstitial polychaetes along morphodynamic gradients on six exposed sandy beaches in Santa Catarina and Paraná (South Brazil). Three random transects were sampled at two points on each beach, one at the swash and another at the surf zone, in winter and summer conditions. Six sediment replicates were collected at each sampling point using a corer of 4.6 cm internal diameter that removed 10 cm into the sediment. Abundance and composition of interstitial polychaete were correlated to wave height, slope, grain size, CaCO₃, chlorophyll a , omega indexes, temperature and relative tide range using a canonical correspondence analysis (CCA). A factorial ANOVA showed that taxa richness, mean density and Shannon's diversity were significantly higher at the reflective beaches, but average values differ significantly between transects and these differences change according to the beach zones on both sampling dates. PERMANOVA showed that polychaete associations differ among transects according to the beach zones. The composition of interstitial polychaete associations was significantly correlated to beach morphodynamics and features (P < 0.01). Polychaete associations of reflective beaches were more diverse than in other morphodynamic states. Intermediate beaches may also sustain diverse associations due to temporal variability of the morphodynamic patterns. Beaches presenting extreme dissipative morphodynamics and compacted sediments appear to be unfavourable for the occurrence of interstitial polychaetes.     

Surface Synoptic Circulation and Daily Precipitation in Catalonia

Summary Catalonian daily precipitation patterns were obtained by means of S-mode Principal Component Analysis (PCA) applied to subsets built up according to synoptic surface airflow. Daily data from November to April 1990–1994 from 45 raingauge sites in Catalonia without missing data were used. Eight circulation classes for days in this period were considered. A Precipitation Activity Index (PAI) was calculated for each station and class, leading to the determination of the highest activity regions for each subset. In addition, we determined which circulation type produced most precipitation at each station of the network. Separate PCAs were performed for each of the eight classes considered and the first four Varimax rotated solutions were interpreted for each circulation type. The physical meaning of the rest of the factors were omitted as they were associated with local behaviour. Finally, some concluding remarks on the cyclogenic properties of the Western Mediterranean Basin and the diversity of the extracted patterns are presented and supported by the authors experience in forecasting in Catalonia. Received February, 11, 1997 Revised May 23, 1997     

A new method to detect transitory signatures and local time/space variability structures in the climate system: the scale-dependent correlation analysis

The study of transitory signals and local variability structures in both/either time and space and their role as sources of climatic memory, is an important but often neglected topic in climate research despite its obvious importance and extensive coverage in the literature. Transitory signals arise either from non-linearities, in the climate system, transitory atmosphere–ocean couplings, and other processes in the climate system evolving after a critical threshold is crossed. These temporary interactions that, though intense, may not last long, can be responsible for a large amount of unexplained variability but are normally considered of limited relevance and often, discarded. With most of the current techniques at hand these typology of signatures are difficult to isolate because the low signal-to-noise ratio in midlatitudes, the limited recurrence of the transitory signals during a customary interval of data considered. Also, there is often a serious problem arising from the smoothing of local or transitory processes if statistical techniques are applied, that consider all the length of data available, rather than taking into account the size of the specific variability structure under investigation. Scale-dependent correlation (SDC) analysis is a new statistical method capable of highlighting the presence of transitory processes, these former being understood as temporary significant lag-dependent autocovariance in a single series, or covariance structures between two series. This approach, therefore, complements other approaches such as those resulting from the families of wavelet analysis, singular-spectrum analysis and recurrence plots. A main feature of SDC is its high-performance for short time series, its ability to characterize phase-relationships and thresholds in the bivariate domain. Ultimately, SDC helps tracking short-lagged relationships among processes that locally or temporarily couple and uncouple. The use of SDC is illustrated in the present paper by means of some synthetic time-series examples of increasing complexity, and it is compared with wavelet analysis in order to provide a well-known reference of its capabilities. A comparison between SDC and companion techniques is also addressed and results are exemplified for the specific case of some relevant El Niño-Southern Oscillation teleconnections.     

Quality assessment of GPS reprocessed terrestrial reference frame

The International GNSS Service (IGS) contributes to the construction of the International Terrestrial Reference Frame (ITRF) by submitting time series of station positions and Earth Rotation Parameters (ERP). For the first time, its submission to the ITRF2008 construction is based on a combination of entirely reprocessed GPS solutions delivered by 11 Analysis Centers (ACs). We analyze the IGS submission and four of the individual AC contributions in terms of the GNSS frame origin and scale, station position repeatability and time series seasonal variations. We show here that the GPS Terrestrial Reference Frame (TRF) origin is consistent with Satellite laser Ranging (SLR) at the centimeter level with a drift lower than 1 mm/year. Although the scale drift compared to Very Long baseline Interferometry (VLBI) and SLR mean scale is smaller than 0.4 mm/year, we think that it would be premature to use that information in the ITRF scale definition due to its strong dependence on the GPS satellite and ground antenna phase center variations. The new position time series also show a better repeatability compared to past IGS combined products and their annual variations are shown to be more consistent with loading models. The comparison of GPS station positions and velocities to those of VLBI via local ties in co-located sites demonstrates that the IGS reprocessed solution submitted to the ITRF2008 is more reliable and precise than any of the past submissions. However, we show that some of the remaining inconsistencies between GPS and VLBI positioning may be caused by uncalibrated GNSS radomes.     

Geophysical exploration on the subsurface geology of La Garrotxa monogenetic volcanic field (NE Iberian Peninsula)

We applied self-potential (SP) and electrical resistivity tomography (ERT) to the exploration of the uppermost part of the substrate geology and shallow structure of La Garrotxa monogenetic volcanic field, part of the European Neogene–Quaternary volcanic province. The aim of the study was to improve knowledge of the shallowest part of the feeding system of these monogenetic volcanoes and of its relationship with the subsurface geology. This study complements previous geophysical studies carried out at a less detailed scale and aimed at identifying deeper structures, and together will constitute the basis to establish volcanic susceptibility in La Garrotxa. SP study complemented previous smaller-scale studies and targeted key areas where ERT could be conducted. The main new results include the generation of resistivity models identifying dykes and faults associated with several monogenetic cones. The combined results confirm that shallow tectonics controlling the distribution of the foci of eruptive activity in this volcanic zone mainly correspond to NNW–SSE and accessorily by NNE–SSW Neogene extensional fissures and faults and concretely show the associated magmatic intrusions. These structures coincide with the deeper ones identified in previous studies, and show that previous Alpine tectonic structures played no apparent role in controlling the loci of this volcanism. Moreover, the results obtained show that the changes in eruption dynamics occurring at different vents located at relatively short distances in this volcanic area are controlled by shallow stratigraphical, structural and hydrogeological differences underneath these monogenetic volcanoes.