Modelling ocean wave climate with a Bayesian hierarchical space–time model and a log-transform of the data

Long-term trends in the ocean wave climate because of global warming are of major concern to many stakeholders within the maritime industries, and there is a need to take severe sea state conditions into account in design of marine structures and in marine operations. Various stochastic models of significant wave height are reported in the literature, but most are based on point measurements without exploiting the flexible framework of Bayesian hierarchical space–time models. This framework allows modelling of complex dependence structures in space and time and incorporation of physical features and prior knowledge, yet remains intuitive and easily interpreted. This paper presents a Bayesian hierarchical space–time model with a log-transform for significant wave height data for an area in the North Atlantic ocean. The different components of the model will be outlined, and the results from applying the model to data of different temporal resolutions will be discussed. Different model alternatives have been tried and long-term trends in the data have been identified for all model alternatives. Overall, these trends are in reasonable agreement and also agree fairly well with previous studies. The log-transform was included in order to account for observed heteroscedasticity in the data, and results are compared to previous results where a similar model was employed without a log-transform. Furthermore, a discussion of possible extensions to the model, e.g. incorporating regression terms with relevant meteorological data, will be presented.     

Multivariate statistical analysis of deformation tensors: independent vs. correlated tensor observations

In the presence of errors in measuring a random displacement field (under the normal distribution assumption of displacement field), stochastic behaviors of principal components of deformation tensors (strain tensor and tensor of change of curvature (TCC)), based on the intrinsic assumption of geometrical modeling of surface deformation analysis, are discussed. We divided the contents into two parts: In the first, we considered independent random vectors of repeated tensor measurements. In the second step, we considered correlations among repeated measurements. Then, covariance components between tensor elements by Helmert estimator, based on prior information of variance components, are estimated. As a case study, both assumptions are applied to the estimation of principal components of deformation rate tensor observations in Zagros region (Western Iran). The results of numerical analysis showed that greatest shortening is accommodated in oblique orientation (NS) with respect to the Main Recent Fault (MRF), northwest part of North Zagros, Central Iran block and MRF, respectively. Most of the extensions occurred in the east part of the belt. The pattern of eigenspace components of TCC shows highest positive values across the NW region, nearly in orthogonal direction to the MRF and Main Zagros Fault (MZF). The pattern has insignificant values in the Central Zagros. It takes the significant negative values across the SW part, especially along the SPF and Persian Gulf shore. The effect of non-independent observations on the estimation of eigenspace components of deformation tensors (strain tensor and TCC) shows that the estimation of covariance components has influence on the confidence intervals of eigenspace components, especially in seismically active regions of the belt (along the Persian Gulf shore, NW of the belt and region between the Central Iran block and MRF). The results demonstrate the importance of considering the correlation structure among the observations on statistical behavior of principal components of deformation tensors in seismically active regions.     

The Transition from Three-Dimensional Embedding to Two-Dimensional Euler-Lagrange Deformation Tensor of the Second Kind: Variation of Curvature Measures

Based on the Stein formulation of changes of curvature parameters, we describe the changes of Riemann two-dimensional manifolds of surface geometries. The three-dimensional left and right Euclidean manifolds with the curvature parameters “geodetic curvature, normal curvature, geodetic torsion” characterize the embedding “Riemann to Euclid” or 2d into 3d. The variation in time of the Euler-Lagrange deformation tensor of the second kind, in short “curvature variation” is studied.     

Upstream and downstream controls of recent avulsions on the Taquari megafan,Pantanal, south‐western Brazil

Avulsion, the natural relocation of a river, is a key process in the evolution of subaerial fans, river floodplains and deltas. The causes of avulsion are poorly understood, which is partly due to the scarcity of field studies of present avulsions. At present, two avulsions are occurring on the middle and lower Taquari megafan, Pantanal basin, south‐western Brazil. Here we present an analysis of the causes of these avulsions based on field and remote sensing data and show that avulsions on megafans can be controlled by both upstream and downstream processes. The middle fan avulsion (started in 1997–1998) is a result of upstream control: overbank aggradation was caused by the (variable) input of sandy sediment into the system, which caused channel‐belt superelevation and also created an easily erodible subsurface favouring bank retreat, crevassing, and scour of deep floodplain channels. The sandy subsurface in this area is inferred to have been a major factor in the causation of this avulsion under conditions of little gradient advantage. The lower fan avulsion (started c. 1990) results from interplay of upstream and downstream controls, the latter being related to the local base level (the Paraguay River floodplain) at the toe of the fan. Channel and overbank aggradation on the lower fan was influenced by fan sub‐lobe progradation and channel backfilling. Fan sub‐lobe progradation caused a significant gradient advantage of the avulsion channel over the parent channel. Avulsions are commonly supposed to be preferentially triggered by high‐magnitude floods, when there is considerable channel‐belt superelevation. However, both avulsions studied by us were triggered by small to average floods, with modest channel‐belt superelevation. We conclude that flood magnitude and channel‐belt superelevation have been overrated as causes of avulsion, and demonstrate additional causes that influence the growth of crevasses into avulsions. Copyright © 2012 John Wiley & Sons, Ltd.     

Catalogue of large alluvial fans in martian impact craters

We conducted a systematic, global survey using Thermal Emission Imaging System Infrared (THEMIS IR) coverage (∼100 m/pixel) to search for large alluvial fans in impact craters on Mars. Our survey has focused on large fans (apron areas greater than ∼40 km², usually located in craters greater than 20 km in diameter) due to the resolution of the THEMIS images and Mars Orbiter Laser Altimeter (MOLA) coverage. We find that the host craters are found to have a distinctive diameter range from 30-150 km. The fans generally cluster in three geographic areas—southern Margaritifer Terra, southwestern Terra Sabaea, and southwestern Tyrrhena Terra, however several outliers do exist. The alluvial fans do not form in a particular orientation along the crater rim nor are they associated with the location of current high rim topography. Fan area magnitude and variability increase with crater diameter while fan concavity magnitude and variability increase with decreasing crater diameter. Smaller fan aprons in general have higher, more variable concavity. The source of the water forming these fans is uncertain given the challenges of accommodating the global distribution pattern and formation patterns within the craters.     

Steady flow to a well near a stream with a leaky bed

We present an explicit analytic solution for steady, two-dimensional ground water flow to a well near a leaky streambed that penetrates the aquifer partially. Leakage from the stream is approximated as occurring along the centerline of the stream. The problem domain is infinite and pumping on one side of the stream induces flow on the other side. The solution includes the effects of uniform flow in the far field and a sloping hydraulic head in the stream. We use the solution to investigate the interaction between ground water and surface water in the stream, the effects of pumping on the opposite side of the stream, and the effects of the leaky streambed on the capture zone envelope of the well. We develop a relationship between parameters such that the pumping well will not capture water from the stream, or from the opposite side of the stream. When the discharge of the well is large enough to capture water from the stream, the shape of the capture zone envelope depends on flow conditions on the side of the stream opposite the well.     

Soil frost effects on soil water and runoff dynamics along a boreal forest transect: 1. Field investigations

To determine how soil frost changes flowpaths of runoff water along a hillslope, a transect consisting of four soil profiles directed towards a small stream in a mature forest stand was investigated at Svartberget, near Vindeln in northern Sweden. Soil temperature, unfrozen water content, groundwater level and snow depth were investigated along the transect, which started at the riparian peat, and extended 30 m upslope into mineral soils. The two, more organic‐rich profiles closest to the stream had higher water retention and wetter autumn conditions than the sandy mineral soils further upslope. The organic content of the soil influenced the variation in frost along the transect. The first winter (1995–96) had abnormally low snow precipitation, which gave a deep frost down to 40–80 cm, whereas the two following winters had frost depths of 5–20 cm. During winter 1995–96, the two organic profiles close to the stream had a shallower frost depth than the mineral soil profile higher upslope, but a considerably larger amount of frozen water. The fraction of water that did not freeze despite several minus degrees in the soil was 5–7 vol.% in the mineral soil and 10–15 vol.% in the organic soil. From the measurements there were no signs of perched water tables during any of the three snowmelt periods, which would have been strong evidence for changed water flowpaths due to soil frost. When shallow soil layers became saturated during snowmelt, especially in 1997 and 1998, it was because of rising groundwater levels. Several rain on frozen ground events during spring 1996 resulted in little runoff, since most of the rain either froze in the soil or filled up the soil water storage. Copyright © 2001 John Wiley & Sons, Ltd.     

Temporal behavior of manganese and iron in a sandy coastal sediment exposed to water column anoxia

The influence of bottom water anoxia on manganese (Mn), iron (Fe), and sulfur (S) biogeochemistry was examined in defaunated sandy sediment from Kærby Fed, Denmark, under controlled laboratory incubations. The initial narrow peaks and steep gradients in solid Mn(IV) and Fe(III) as well as porewater Mn²⁺ and Fe²⁺ observed in the upper 2–5 cm of the sediment indicate rapid metal reduction-oxidation cycles under oxic conditions in the overlying water. The fe zones were generally displaced about 0.5 cm downward compared with the Mn zones due to differences in reactivity. Mn(IV) was reduced and gradually disappeared first (within 10 d) when the sediment was exposed to anoxia followed by reduction and disappearance of Fe(III) (day 7 to 18). The associated loss of Mn²⁺ to the overlying water was most rapid during the first 15 d, whereas the Fe²⁺ efflux initiated around day 10, and after a few days with modest rates the efflux peaked around day 20. A considerable portion of the total Mn (26%) and Fe (23%) inventory initially present in the sediment was lost by efflux after about 1 mo of anoxia. The ability of the sediment to retain upward diffusion of H₂S gradually disappeared in a temporal pattern closely related to the changes in pool size of the reactive Mn and Fe present. The total metal pool in Kærby Fed sediment prevented H₂S release to the overlying water for at least a month of anoxia. It is speculated that external supplies from the overlying water allows a rapid refuelling of surface Mn and Fe oxides in the field when oxic conditions returns between periods of anoxia.