Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

On the accuracy of location of local shocks on the territory of Czechoslovakia and adjacent areas

Summary The calculation procedures for determining epicentre parameters of weak near shocks with foci in Poland are discussed and tested for explosions with known epicentres.

---

m m¶rt; ¶rt; n¶rt;u num a uu m num nmua n auauu, u mu a mumuu u, n muu ¶rt;au uu mau. au mam nam (a. 4) nu nuuu na 71 u m ¶rt;u n¶rt; ¶rt; a auu ¶rt;a [11].

     

Suspension and calibration of a sediment trap

The aim of this technical note is to introduce a new, simple construction of a buoy-carried, suspended sediment trap that meets given demands concerning design (geometry of vessels) and stability during the registration period. The device is based on a ball-and-socket joint in the center and two Plexiglas cylinders (D=5cm, H=30cm) on PVC plastic arms. The suspension consists of only three parts. To determine the optimal construction, the apparatus has been calibrated in a circulating flume at various water velocities.     

Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

Ocean eddy momentum fluxes at the latitudes of the Gulf Stream and the Kuroshio extensions as revealed by satellite data

Eddy momentum fluxes, i.e. Reynold stresses, are computed for the latitude bands of the Gulf Stream and Kuroshio extensions using 13 years of data from the merged satellite altimeter product of Le Traon et al. The spatial pattern and amplitude of the fluxes is remarkably similar to that found by Ducet and Le Traon using the 5 years of data that were available to them. In addition to updating the work of Ducet and Le Traon, we provide new insight into the role played by the underlying variable bottom topography, both for determining the structure of the eddy momentum fluxes seen in the satellite data and for influencing the way these fluxes feedback on the mean flow. While there is no clear evidence that eddies locally flux momentum into the eastward jets of the Gulf Stream and Kuroshio extensions, a clearer picture emerges after zonally integrating across each of the North Atlantic and North Pacific basins. We argue that the eddy momentum fluxes do indeed drive significant transport, a conclusion supported by preliminary results from a 3-D model calculation. We also present evidence that in the North Pacific, the Reynolds stresses are important for driving the recirculation gyres associated with the Kuroshio extension, taking advantage of new data from both observations and high-resolution model simulations.     

Impedance of flexible suction caissons

The dynamic response of offshore wind turbines is affected by the properties of the foundation and the subsoil. The aim of this paper is to evaluate the dynamic soil–structure interaction of suction caissons for offshore wind turbines. The investigations include evaluation of the vertical and coupled sliding–rocking vibrations, influence of the foundation geometry and examination on the properties of the surrounding soil. The soil is simplified as a homogenous linear viscoelastic material and the dynamic stiffness of the suction caisson is expressed in terms of dimensionless frequency‐dependent coefficients corresponding to different degrees of freedom. The dynamic stiffness coefficients for the skirted foundation are evaluated using a three‐dimensional coupled boundary element/finite element model. Comparisons with known analytical and numerical solutions indicate that the static and dynamic behaviours of the foundation are predicted accurately using the applied model. The analysis has been carried out for different combinations of the skirt length, Poisson's ratio of the subsoil and the ratio of the soil stiffness to the skirt stiffness. Copyright © 2007 John Wiley & Sons, Ltd.     

Shallow gas in the muddy sediments of Eckernförde Bay, Germany

The seafloor of central Eckernförde Bay is characterised by soft muddy sediments that contain free methane gas. Bubbles of free gas cause acoustic turbidity which is observed with acoustic remote sensing systems. Repeated surveys with subbottom profiler and side scan sonar revealed an annual period both of depth of the acoustic turbidity and backscatter strength. The effects are delayed by 3–4 months relative to the atmospheric temperature cycle. In addition, prominent pockmarks, partly related to gas seepage, were detected with the acoustic systems. In a direct approach gas concentrations were measured from cores using the gas chromatography technique. From different tests it is concluded that subsampling of a core should start at its base and should be completed as soon as possible, at least within 35 min after core recovery. Comparison of methane concentrations of summer and winter cores revealed no significant seasonal variation. Thus, it is concluded that the temperature and pressure influences upon solubility control the depth variability of acoustic turbidity which is observed with acoustic remote sensing systems. The delay relative to the atmospheric temperature cycle is caused by slow heat transfer through the water column. The atmospheric temperature cycle as ‘exiting function’ for variable gas solubility offers an opportunity for modelling and predicting the depth of the acoustic turbidity. In practice, however, small-scale variations of, e.g., salinity, or gas concentration profile in the sediment impose limits to predictions. In addition, oceanographic influences as mixing in the water column, variable water inflow, etc. are further complications that reduce the reliability of predictions.     

Talus slope geomorphology investigated at multiple time scales from high-resolution topographic surveys and historical aerial photographs (Sanetsch Pass,Switzerland)

Talus slopes are common places for debris storage in high-mountain environments and form an important step in the alpine sediment cascade. To understand slope instabilities and sediment transfers, detailed investigations of talus slope geomorphology are needed. Therefore, this study presents a detailed analysis of a talus slope on Col du Sanetsch (Swiss Alps), which is investigated at multiple time scales using high-resolution topographic (HRT) surveys and historical aerial photographs. HRT surveys were collected during three consecutive summers (2017–2019), using uncrewed aerial vehicle (UAV) and terrestrial laser scanning (TLS) measurements. To date, very few studies exist that use HRT methods on talus slopes, especially to the extent of our study area (2 km²). Data acquisition from ground control and in situ field observations is challenging on a talus slope due to the steep terrain (30–37°) and high surface roughness. This results in a poor spatial distribution of ground control points (GCPs), causing unwanted deformation of up to 2 m in the gathered UAV-derived HRT data. The co-alignment of UAV imagery from different survey dates improved this deformation significantly, as validated by the TLS data. Sediment transfer is dominated by small-scale but widespread snow push processes. Pre-existing debris flow channels are prone to erosion and redeposition of material within the channel. A debris flow event of high magnitude occurred in the summer of 2019, as a result of several convective thunderstorms. While low-magnitude (<5,000 m³) debris flow events are frequent throughout the historical record with a return period of 10–20 years, this 2019 event exceeded all historical debris flow events since 1946 in both extent and volume. Future climate predictions show an increase of such intense precipitation events in the region, potentially altering the frequency of debris flows in the study area and changing the dominant geomorphic process which are active on such talus slopes. © 2020 John Wiley & Sons, Ltd.