On the practice of estimating fractal dimension

Coastlines epitomize deterministic fractals and fractal (Hausdorff-Besicovitch) dimensions; a divider [compass] method can be used to calculate fractal dimensions for these features. Noise models are used to develop another notion of fractals, a stochastic one. Spectral and variogram methods are used to estimate fractal dimensions for stochastic fractals. When estimating fractal dimension, the objective of the analysis must be consistent with the method chosen for fractal dimension calculation. Spectal and variogram methods yield fractal dimensions which indicate the similarity of the feature under study to noise (e.g., Brownian noise). A divider measurement method yields a fractal dimension which is a measure of complexity of shape.     

Flare stars and solar bursts: High resolution in time and frequency

Coronal loops on the Sun and nearby stars are investigated using observations at 20 cm wavelength with high resolution in time and frequency. Observations of the dwarf M star AD Leonis with high time resolution using the Arecibo Observatory have resulted in the discovery of a quasi-periodic train of circularly polarized spikes with a mean periodicity of 32 ± 5 ms and a total duration of 150 ms. The individual spikes had rise times of 5 ms, leading to an upper limit to the linear size L 1.5 × 10⁸ cm for the spike emitter. This size is only 0.005 of the estimated radius of AD Leonis. Provided that the emitter is symmetric, it has a brightness temperature of T _B 10¹⁶ K, suggesting a coherent burst mechanism such as an electron-cyclotron maser. Coronal oscillations might modulate the maser output, producing the quasi-periodic spikes. Observations at closely spaced wavelengths, or high frequency resolution, using the Very Large Array have revealed narrow-band structure (v/v 0.01) in solar bursts and in the slowly-varying radiation of the dwarf M star YZ Canis Minoris. The narrow-band emission cannot be explained by continuum emission processes, but it might be attributed to electron-cyclotron maser radiation. Maser action at the second or first harmonic of the gyrofrequency implies magnetic field strengths of 250 and 500 G, respectively. Thus, observations with high resolution in time and frequency suggest coherent processes in the coronae of the Sun and dwarf M stars. The scientific potential of these discoveries may be best fulfilled by the construction of a solar-stellar synthesis radiotelescope.Proceedings of the Workshop on Radio Continua during Solar flares, held at Duino (Trieste), Italy, 27–31 May, 1985.     

Upwelling, species, and depth effects on coral skeletal cadmium-to-calcium ratios (Cd/Ca)

Skeletal cadmium-to-calcium (Cd/Ca) ratios in hermatypic stony corals have been used to reconstruct changes in upwelling over time, yet there has not been a systematic evaluation of this tracer’s natural variability within and among coral species, between depths and across environmental conditions. Here, coral skeletal Cd/Ca ratios were measured in multiple colonies of Pavona clavus, Pavona gigantea and Porites lobata reared at two depths (1 and 7 m) during both upwelling and nonupwelling intervals in the Gulf of Panama (Pacific). Overall, skeletal Cd/Ca ratios were significantly higher during upwelling than during nonupwelling, in shallow than in deep corals, and in both species of Pavona than in P. lobata. P. lobata skeletal Cd/Ca ratios were uniformly low compared to those in the other species, with no significant differences between upwelling and nonupwelling values. Among colonies of the same species, skeletal Cd/Ca ratios were always higher in all shallow P. gigantea colonies during upwelling compared to nonupwelling, though the magnitude of the increase varied among colonies. For P. lobata, P. clavus and deep P. gigantea, changes in skeletal Cd/Ca ratios were not consistent among all colonies, with some colonies having lower ratios during upwelling than during nonupwelling. No statistically significant relationships were found between skeletal Cd/Ca ratios and maximum linear skeletal extension, δ¹³C or δ¹⁸O, suggesting that at seasonal resolution the Cd/Ca signal was decoupled from growth rate, coral metabolism, and ocean temperature and salinity, respectively. These results led to the following conclusions, (1) coral skeletal Cd/Ca ratios are independent of skeletal extension, coral metabolism and ambient temperature/salinity, (2) shallow P. gigantea is the most reliable species for paleoupwelling reconstruction and (3) the average Cd/Ca record of several colonies, rather than of a single coral, is needed to reliably reconstruct paleoupwelling events.     

Uranophane dissolution and growth in CaCl2-SiO2(aq) test solutions

The dissolution and growth of uranophane [Ca(UO₂)₂(SiO₃OH)₂·5H₂O] have been examined in Ca- and Si-rich test solutions at low temperatures (20.5 ± 2.0 °C) and near-neutral pH (∼6.0). Uranium-bearing experimental solutions undersaturated and supersaturated with uranophane were prepared in matrices of ∼10⁻² M CaCl₂ and ∼10⁻³ M SiO₂(aq). The experimental solutions were reacted with synthetic uranophane and analyzed periodically over 10 weeks. Interpretation of the aqueous solution data permitted extraction of a solubility constant for the uranophane dissolution reaction and standard state Gibbs free energy of formation for uranophane ( kJ mol⁻¹).     

Crystal-Melt Separation and the Development of Isotopic Heterogeneities in Hybrid Magmas

If a magma is a hybrid of two (or more) isotopically distinctend-members, at least one of which is partially crystalline,separation of melt and crystals after hybridization will leadto the development of isotopic heterogeneities in the magmaas long as some of the pre-existing crystalline material (antecrysts)retains any of its original isotopic composition. This holdstrue whether the hybridization event is magma mixing as traditionallyconstrued, bulk assimilation, or melt assimilation. Once a magma-scaleisotopic heterogeneity is formed by crystal–melt separation,it is essentially permanent, persisting regardless of subsequentcrystallization, mixing, or equilibration events. The magnitudeof the isotopic variability resulting from crystal–meltseparation can be as large as that resulting from differentialcontamination, multiple isotopically distinct sources, or insitu isotopic evolution. In one model, a redistribution of one-thirdof the antecryst cargo yielded a crystal-enriched sample with⁸⁷Sr/⁸⁶Sr of 0·7058, whereas the complementary crystal-poorsample has ⁸⁷Sr/⁸⁶Sr of 0·7068. In other models, crystal-richsamples are enriched in radiogenic Sr. Isotopic heterogeneitiescan be either continuous (controlled by the modal distributionof crystals and melt) or discontinuous (when there is completeseparation of crystals and liquid). The first case may be exemplifiedby some isotopically zoned large-volume rhyolites, formed bythe eruptive inversion of a modally zoned magma chamber. Inthe latter case, the isotopic composition of any (for example)interstitial liquid will be distinct from the isotopic compositionof the bulk crystal fraction. The separation of such an interstitialliquid may explain the presence of isotopically distinct late-stageaplites in plutons. Crystal–melt separation provides anadditional option for the interpretation of isotopically zonedor heterogeneous magmas. This option is particularly attractivefor systems whose chemical variation is otherwise explicableby fractionation-dominated processes. Non-isotopic chemicalheterogeneities can also develop in this fashion. KEY WORDS: isotopic heterogeneity; zoning; hybrid magma; crystal separation; Sr isotopes; aplite; rhyolite     

Acoustic-gravity wave propagation in an atmosphere with two sound channels

Summary In order to interpret the observed features of pressure records produced by waves from large explosions in the earth's atmosphere, the writers have obtained numerical solutions of the homogeneous equations governing acoustic-gravity wave propagation in a stratified compressible fluid. Theoretical dispersion curves and variations of perturbation kinetic energy with altitude are presented for 11 normal modes. It is shown that the step-like character of the phase velocity curves in the velocity-period plane can be interpreted as being the result of interference between two families of normal modes-«quasi-horizontal modes» representing energy propagation in the lower atmosphere (below the ozonosphere) and «quasi-vertical modes» representing energy propagation in the upper atmosphere (above the ozonosphere). The theoretical prediction that several normal modes contribute to the observed barogram traces is verified by Fourier analysis of a number of wave records.Lamont Geological Observatory Contribution No. 611. — This research was supported by National Science Foundation Grant NSF-G-11997, Office of Naval Research Contract Nonr 266 (70), and National Science Foundation Grant NSF-GP-550. — Part of this research was done at the NASA Institute for Space Studies, New York, N. Y.     

Hydrometeorologische Ergebnisse aus Abflußmessungen im Bereich des Hintereisferners (Ötztaler Alpen) in den Jahren 1957 bis 1959

Zusammenfassung Während der Internationalen Geophysikalischen Jahre 1957 bis 1959 wurde an einer Pegelmeßstelle bei 2287 m Höhe der Abfluß vom Hintereis- und Kesselwandferner registriert. Im vorliegenden Arbeitsbericht sollen spezifischen Merkmale des Abflusses aus dem zu 58% vergleitscherten Einzugsgebiet 26,6 km²) im Zusammenhang mit den meteorologischen Beidingungen dargestellt werden.Der Jahresabfluß betrug im Haushaltsjahr 1957/58 1848 mm und im Haushaltsjahr 1958/59 1770 mm; bedingt durch den stark negative massenhaushat der Gletscher was die Gletscherspende mit 24% bzw. 20% des Jahresabflusses außergewöhnlich hoch. Der winterabfluß (Oktober bis März) betrug nur 5% bzw. 10% des Jahresabflusses; die drei Sommermonate Juli bis September Lieferten dagegen 76% bzw. 72%. Der größte Monatsabfluß wurde im August 1958 mit 575 mm, im Juli 1959 mit 559 mm registriert.Die Häufigkeitsverteilung der Tagesabflußmengen für das Jahr 1957/58 ließ eine Andauer des Niedrigwassers mit Tages-Mittelwerten kleiner als 18,8 l/s km² (0,5 m³/s) von 217 Tagen (Oktober bis Mai, 59% des Jahres) erkennen. Größere Tagesabflüsse als 225 l/s km² (6,0 m³/s) kamen nur im Juli und August vor. Als Maximum wurden Abflußwerte bis zu 640 l/s km² Gletscherfläche im Tagesmittel erreicht, entsprechen 55m Abflußhöhe von den Schnee- und Eisflächen. Der exponentielle Abfall der Abflußganglinie vom Herbst zum Minimum im Frühjahr deutet an, daß es sich bei Winterwasser vorwiegend um das verzögerte Abfließen von in den Gletschern zurückgehaltenem Schmelzwasser aus der vorangegangenen Ablationsperiode handelt. Das Ansteigen der Wasserführung nach dem Beiginn der Schneeschmelze im Frühjahr erfolgt wegen des Wiedergefrierens von Schmelzwasser und wegen des Retentionsvermögens der Schneedecke mit einiger Verzörgerung.Die unperiodischen Schwankungen im Abflußgang stehen in engem Zusammenhang mit Wettervorgängen, wobei Schneeniederschlägen die Größte Bedeutung zukommt, weil die hohe Albedo einer Neuschneedecke die Ablation auf den Gletschern tagelang fast völlig unterbrechen kann. Aus zweistündigen Mittelwerten wurde für die Monate Juni bis September der mittlere Tagesgang der Wasserführung ermittelt. Die Ursache für das frühere Eintreten des taglichen Abflußmaximums im Spätsommer durfte verminderte Abflußverzögerung sein. Die Beziehung zwischen den Abflußwerten der Pegel Steg-Hospiz und Vent läßt einen Jahresgang erkennen.

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Summary During the International Geophysical Years 1957–1959 the run-off from Hintereisferner and Kesselwandferner was recorded by a stream gauge installed at an altitude of 2287 m. a. s. 1. The annual run-off in relation to mass budget and precipitation has already been reported in [10, 11]. In the present report characteristic features of run-off from a catchment area (26.6 km²) glaciated to 58 per cent shall be discussed with regard to the meteorological conditions.In the budget years 1957/58 and 1958/59 the yearly run-off was 1848 mm and 1770 mm, respectively. Owing to the strongly negative mass budget of the glaciers the glacier quota of 24 per cent and of 20 per cent, respectively, of the annual run-off was exceptionally high. Winter run-off (October to March) amounting to 5 per cent and to 10 per cent, respectively, of the yearly run-off was only small while July to September supplied 76 per cent and 72 per cent, respectively. The maximum monthly run-off was recorded in August 1958 with 575 mm, and in July 1959 with 559 mm.The frequency distribution of the daily run-off in 1957/58 showed a period of low run-off during 217 days (October to May, 59 per cent of the year) with daily means below 18.8 l/s km² (0.5 m³/s). Daily run-off exceeding 225 l/s km² (6.0 m³/s) occurred only in July and August. Daily means exceeding 338 l/s km² (9.0 m³/s) were recorded only three times in July. The maximum daily means of run-off were up to 640 l/s km² of glacier surface which corresponds to 55 mm of run-off from the snow and ice surfaces. The highest two hourly mean value was 950 l/s km² of the glacier surface. The exponential decrease of the run-off curve from fall to the minimum in spring indicates that winter water consists mainly of the delayed run-off of melt water stored in the glaciers during the preceding ablation period. Owing to the refreezing of the melt water and to the storage capacity of the snow cover run-off is somewhat delayed after the snow melt has set in.The aperiodic variations in the run-off are closely related to weather conditions. Snow falls are of primary importance as the high albedo of a fresh snow cover may interrupt ablation on glaciers almost completely for days. The mean daily variation of run-off was determined from two-hourly mean values for the period June to September. The early occurrence of the daily run-off. The relation between the run-off values recorded at the water gauges Steg-Hospiz and Vent indicates and annual variation.

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Résumé Pendant les Années Géophysiques Internationales de 1957 à 1959 l'écoulement du Hintereisferner et du Kesselwandferner a été enregistré par un limnigraphe installé à une altitude 2287 m. Un rapport a déjà été présenté dans [10, 11] sur l'écoulement annuel en rapport avec le bilan hydrologique du bassin. Dans le présent rapoort il sera traité des caractères spécifiques de l'écoulement d'un bassin dont 58% sont recouverts par le glacier, les quels seront mis en rapport avec les conditions météorologiques.L'écoulement annuel au cours de l'année hydrologique 1957/58 a été de 1848 mm et dans l'année hydrologique 1958/59 de 1770 mm. L'eau libérée par la perte de substance glacière représente 24% pour 1957/58 et 20% pour 1958/59 de l'écoulement annuel. Les pourcentages extrêmement élevés doivent être attribués au bilan fortement négatif des glaciers. L'écoulement d'hiver (Octobre à Mars) représentant 5% pour l'année 1957/58 et 10% pour 1958/59 de l'écoulement annuel a été petit tandis que les trois mois d'été (Juillet–Septembre) fournissaient 76% (1957/58) et 72% (1958/59). L'écoulement mensuel le plus élevé a été enregistré en Aôut 1958 avec 575 mm, et, en Juillet 1959 avec 559 mm.La répartition des fréquences des écoulements journaliers pour l'année 1957/58 indique une période d'étiage de 217 jours (Octobre à Mai, 59% de l'année) avec valeurs journalières en dessous de 18.8 l/s km² (0.5 m³/s). Des écoulements dépassant 225 l/s km² (6.0 m³/s) n'ont été enregistrés qu'en Juillet et Aôut. Les moyennes journalières n'ont dépassé les 338 l/s km² (9.0 m³/s) que trois fois en Juillet. Les valeurs maximums des moyennes journalières d'écoulement se sont élevées à 640 l/s km² de la surface des glaciers, correspondant à 55 mm d'écoulement des surfaces de neige et de glace. La valeur maximum d'une moyenne de deux heures a été de 950 l/s km² de la surface des glaciers. La chute exponentielle de la courbe d'écoulement allant de l'automne au minimum enregistré au printemps indique que dans les cas d'étiage il s'agit de l'écoulement retardé des aux de fonte refenues dans les glaciers pendant la période d'ablation précédente. L'accroissement de l'écoulement après le comencement de la fonte de neige au printemps est retardé dans une certaine mesure par le regel des aux de fonte et la capacité de rétention de la couche de neige. Les variations apériodiques dans l'écoulement sont en relations étroites avec les conditions atmospheriques dont les chutes de neige sont de la plus grade importance car l'albédo élevé d'une couche de neige fraîche interrompt parfois et presque complétement l'ablation sur les glaciers pour des jours entiers.L'amplitude moyenne de la variation journalière de l'écoulement a été, pour les mois de Juin à Septembre, détérminée à la base des valeurs moyennes de deux heures. L'apparition précoce du maximum d'écoulement journalier en fin d'été est probablement due à la diminution du retardement de l'écoulement en cette période. La relation entre le valeurs d'écoulement des limnigraphes de Steg-Hospiz et de Vent met en évidence une variation annuelle.

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Die für diesen Bericht erforderliche weitere Bearbeitung der Abflußdaten und die Fertigstellung des Manuskriptes wurde dem Verfasser im Rahmen seiner Tätigkeit bei der Kommission für Glaziologie an der Bayerischen Akademie der Wissenschaften ermöglicht, wofür an dieser Stelle gedankt sei.