Shoaling waves: A discussion

Surface gravity waves are commonly observed to slow down and to stop at a beach without any noticeable reflection taking place. We assume that as a consequence the waves are continuously giving up their linear and angular momenta, which they carry with them, along with energy, as they propagate into gradually decreasing mean depths of water. It takes a force to cause a time rate of decrease in the linear momentum and a torque to produce a time rate of decrease in the angular momentum. Both a force and a torque operate on the shoaling waves, due to the presence of the sloping bottom, to cause the diminution of their linear and angular momenta. By Newton’s third law, action equals reaction, an equal but opposite force and torque are exerted on the bottom. No other mechanisms for transferring linear and angular momenta are included in the model. Since the force on the waves acts over a horizontal distance during shoaling, work is done on the waves and energy flux is not conserved. Bottom friction, wave interaction with a mean flow, scattering from small-scale bottom irregularities and set-up are neglected. Mass flux is conserved, which leads to a shoreward monotonic decrease in amplitude consistent with available swell data. The formula for the time-independent force on the bottom agrees qualitatively with observations in seven different ways: four for swell attenuation and three for sediment transport on beaches. Ardhuin (2006) argues against a mean force on the bottom that is not hydrostatic, mainly by using conservation of energy flux. He also applies the action balance equation to shoaling waves. Action is a difficult concept to grasp for motion in a continuum; it cannot be easily visualized, and it is not really necessary for solving the shoaling wave problem. We prefer angular momentum because it is clearly related to the observed orbital motion of the fluid particles in progressive surface waves. The physical significance of wave action for surface waves has been described recently by showing that in deep water action is equivalent to the magnitude of the wave’s orbital angular momentum (Kenyon and Sheres, 1996). Finally, Ardhuin requires that there be a significant exchange of linear momentum between shoaling waves and an unspecified mean flow, although the magnitude and direction of the exchange are not predicted. No mention is made of what happens to the orbital angular momentum during shoaling. Mass flux conservation is not stated.     

Calcite texture development in experimentally induced ductile shear zones

Specimens of fine grained micritic limestone were deformed in plane strain geometry in pure shear, a combination of simple and pure shear, and in simple shear. Temperatures were 400° C and 500° C, confining pressure was 100 MPa. In the experiments with a simple shear component strain is concentrated and approximately homogeneous in a 2–3 mm wide shear zone. Shear displacement is documented by marker lines and circles. Shear strain γ varies between 0.84 and 1.56. Strain is recorded by flattening of individual grains, defining a foliation normal to the axis of principal finite shortening ε ₁. No twinning is observed on a macroscopic scale. X-ray and neutron diffraction techniques were used to characterize texture before and after deformation. All specimens display strong preferred orientation as documented by 0006, 10¯14 and 11¯220 pole-figures, c axes pole-figures display three maxima in the ε₁–ε₃ plane. If the axes of the strain ellipsoids are used as a coordinate system textures in pure and simple shear are similar but there is considerable monoclinic distortion in simple shear which is attributed to the noncoaxial strain path.     

Über die Synthese von Albiten bei Temperaturen von 250 bis 700° C

A glass of composition NaAlSi₃O₈ with small contents of Fe has been crystallized in the presence of water vapor under 1000 bars, at temperatures in the range of 250 to 700° C for varying periods of time. The synthetic crystals were investigated microscopically and by x-ray powder diffraction methods. Most of the crystals are twinned according to the albite law, but other twins are found too. Size and form of the crystals seem to depend on the temperature of crystallization. The optic axial angles (2V _x ) of the albites being measurable on the universal stage are in the range of 50 to 100 degrees. There seems to exist a linear relation between the 2₁₃₁–2_1¯31 values (used as an indicator for the degree of ordering) and the 2V _x values. The change of the lattice parameters from albite (D) to albite (O) is suggested to deviate slightly from linearity.In contrast to previous investigations the steady value of 2₁₃₁–2_1¯31 which is characteristic of the temperature of crystallization was reached more rapidly. These results suggest that small content of Fe in the glass had a catalytic effect on the Al/Si ordering.

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Herrn Dr. F. Seifert (Ruhruniversität Bochum) danken wir herzlich für die Einweisung in die experimentellen Untersuchungsmethoden sowie für manchen kritischen Hinweis. Danken möchten wir auch Herrn Dr. P. K. Hörmann für die Kontrolle der chemischen Zusammensetzung des Albitglases sowie Herrn Dr. C. W. Burnham (Harvard University) für die Bereitstellung des Rechenprogramms. Nicht zuletzt danken wir Herrn Prof. Dr. F. Karl für die kritische Durchsicht des Manuskriptes.     

Machine Learning Based Predictive Modeling of Debris Flow Probability Following Wildfire in the Intermountain Western United States

It has been recognized that wildfire, followed by large precipitation events, triggers both flooding and debris flows in mountainous regions. The ability to predict and mitigate these hazards is crucial in protecting public safety and infrastructure. A need for advanced modeling techniques was highlighted by re-evaluating existing prediction models from the literature. Data from 15 individual burn basins in the intermountain western United States, which contained 388 instances and 26 variables, were obtained from the United States Geological Survey (USGS). After randomly selecting a subset of the data to serve as a validation set, advanced predictive modeling techniques, using machine learning, were implemented using the remaining training data. Tenfold cross-validation was applied to the training data to ensure nearly unbiased error estimation and also to avoid model over-fitting. Linear, nonlinear, and rule-based predictive models including naïve Bayes, mixture discriminant analysis, classification trees, and logistic regression models were developed and tested on the validation dataset. Results for the new non-linear approaches were nearly twice as successful as those for the linear models, previously published in debris flow prediction literature. The new prediction models advance the current state-of-the-art of debris flow prediction and improve the ability to accurately predict debris flow events in wildfire-prone intermountain western United States.     

Halogen oxide measurements at Masaya Volcano,Nicaragua using active long path differential optical absorption spectroscopy

Active Long Path Differential Optical Absorption Spectroscopy (LP-DOAS) measurements of halogen oxides were conducted at Masaya Volcano, in Nicaragua from April 14 to 26, 2007. The active LP-DOAS system allowed night-time halogen measurements and reduced the ClO detection limit by an order of magnitude when compared to previous passive DOAS measurements, as wavelengths below 300 nm could be used for the DOAS retrievals. BrO was detected with an average BrO/SO₂ molecular ratio of approximately 3 × 10⁻⁵ during the day. However, BrO values were below the detection limit of the instrument for all night-time measurements, a strong indication that BrO is not directly emitted, but rather the result of photochemical formation in the plume itself according to the autocatalytic “bromine explosion” mechanism. Despite the increased sensitivity, both ClO and OClO could not be detected. The achieved upper limits for the X/SO₂ ratios were 5 × 10⁻³ and 7 × 10⁻⁶, respectively. A rough calculation suggests that ClO and OClO should be present at similar abundances in volcanic plumes. Since the DOAS technique is orders of magnitude more sensitive for OClO than for ClO, this indicates that OClO should always be detectable in plumes in which ClO is found. However, further LP-DOAS studies are needed to conclusively clarify the role of chlorine oxides in volcanic plumes.     

Radiative transfer corrections for accurate spectroscopic measurements of volcanic gas emissions

There is widespread use of passive remote sensing techniques to quantify trace gas column densities in volcanic plumes utilizing scattered sunlight as a light source. Examples include passive DOAS, COSPEC, and the SO₂ camera. In order to calculate trace gas concentrations or volcanic emission fluxes, knowledge about the optical path through the plume is necessary. In the past, a straight photon path through the plume has always been assumed although it was known that this is not always true. Here we present the results of model studies conducted specifically to quantify the effects of realistic radiative transfer in and around volcanic plumes on ground-based remote sensing measurements of SO₂. The results show that measurements conducted without additional information on average photon paths can be inaccurate under certain conditions, with possible errors spanning more than an order of magnitude. Both over and underestimation of the true column density can occur. Actual errors depend on parameters such as distance between instrument and plume, plume SO₂ concentration, plume aerosol load, as well as aerosol conditions in the ambient atmosphere. As an example, a measurement conducted with an SO₂ camera is discussed, the results of which can only be correctly interpreted if realistic radiative transfer is considered. Finally, a method is presented which for the first time allows the retrieval of actual average photon paths in spectroscopic (i.e. DOAS) measurements of adequate resolution. By allowing for a wavelength dependent column density during the evaluation of DOAS measurements, we show how radiative transfer effects can be corrected using information inherently available in the measured spectra, thus greatly enhancing the accuracy of DOAS measurements of volcanic emissions.     

The fluoride in the groundwater of Guarani Aquifer System: the origin associated with black shales of Paraná Basin

This work presents petrological and geochemical results of the black shales interval from Permian and Devonian strata of the Paraná Basin, Brazil and its relationships with fluoride of groundwater from Guarani Aquifer System. The Guarani Aquifer, located in South Brazil, Uruguay, Paraguay and Argentine, presents contents of fluoride higher than the Brazilian accepted potability limits. Several hypotheses have been presented for the origin of the fluoride in the groundwater of the Guarani Aquifer. Microcrystalline fluorite was registered in black shales of Ponta Grossa and Irati formations from Paraná Basin. The results shown in this work suggest that fluoride present in groundwater of Guarani Aquifer can be originated in deeper groundwater that circulates in Ponta Grossa and Irati formations. The interaction of the groundwater coming from deeper black shales with the groundwater-bearing Aquifer Guarani System occurs through regional fragile structures (faults and fractures) that constitute excellent hydraulic connectors between the two sedimentary packages. The microcrystalline fluorite registered in Ponta Grossa and Irati Formations can be dissolved promoting fluoride enrichment in groundwater of these black shales and Guarani Aquifer System.     

A form-factor method for determing the structure of distorted stars

The equilibrium equations of a uniformly rotating and tidally distorted star are reduced to the same form as for a spherical star except for the inclusion of two form factors. One factor, expressing the buoyancy effects of centrifugal force, is determined directly from the integrated structure variables. The other factor, expressing the deviation from spherical shape, is shown to be relatively insensitive to errors in the assumed shape, so that accurate solutions are obtained in spite of the use of ana priori shape. The method is employed by adding computations for the factors to an existing spherical model program. Upper Main Sequence models determined by this method compare closely with results from the double approximation method even for critical rotation and tidal distortion.