Meixner functions for derivation of the unit hydrograph

The Meixner functions are utilized to relate the effective rainfall, the direct runoff and the unit hydrograph through linkage equations. The linkage equations are then employed to derive the unit hydrograph for given rainfall-runoff data on a small agricultural watershed. These functions are tested with regard to their ability to reproduce and predict the direct runoff hydrograph. The Meixner functions are found to be an effective analytical tool for hydrograph synthesis. Further, they compare well with the least squares and linear programming methods of the unit hydrograph derivation.     

Subduction Influence on Oxygen Fugacity and Trace and Volatile Elements in Basalts Across the Cascade Volcanic Arc

Fluids or melts derived from a subducting plate are often citedas a mechanism for the oxidation of arc magmas. What remainsunclear is the link between the fluid, oxygen fugacity, andother major and trace components, as well as the spatial distributionof the impact of those fluids. To test the potential effectsof addition of a subduction-derived fluid or melt to the sub-arcmantle, olivine-hosted melt inclusions from primitive basalticlavas sampled from across the central Oregon Cascades (43°–45°N)have been analyzed for major, trace and volatile elements andfO₂. Oxygen fugacity was determined in melt inclusions fromsulfur speciation determined by electron microprobe and fromolivine–chromite oxygen geobarometry. The overall rangein fO₂ based on sulfur speciation measurements is from <–0·25log units to + 1·9 log units (FMQ, where FMQ is fayalite–magnetite–quartzbuffer). Oxygen fugacity is positively correlated with fluid-mobiletrace element and light rare earth element contents in basaltsgenerated by relatively low-degree partial melting. Establishinga further correlation between fO₂ and fluid-mobile trace elementabundances with position along the arc requires the basaltsto be subdivided into shoshonitic, calc-alkaline, low-K tholeiiteand enriched intraplate basalt groups. Melt inclusions fromenriched intraplate and shoshonitic lavas show increasing fO₂and trace element abundances closer to the trench, whereas calc-alkalinemelt inclusions exhibit no significant across-arc variations.Low-K tholeiitic melt inclusions record an increase in incompatibletrace elements closer to the trench; however, there is no correlatedincrease in fO₂. The correlation observed in enriched intraplateand shoshonitic melt inclusions is interpreted to reflect aprogressively greater proportion of a fluid-rich, oxidized subductioncomponent in magmas generated nearer the subduction zone. Significantly,calc-alkaline melt inclusions with high ratios of large ionlithophile elements to high field strength elements, characteristicof ‘typical’ arc magmas, have oxidation states indistinguishablefrom low-K tholeiite and enriched intraplate basalt melt inclusions.The lack of across-arc geochemical variation in calc-alkalinemelt inclusions may suggest that these basalts are not necessarilythe most appropriate magmas for examining recent addition ofa subduction component to the sub-arc mantle. Flux and batchmelt model results produce a wide range of predicted amountsof melting and subduction component added to the mantle source;however, general trends characterized by increased melting andproportion of the subduction component from enriched intraplate,to low-K tholeiite, to calc-alkaline are robust. The model resultsdo not require enriched intraplate, low-K tholeiite and calc-alkalinemagmas to be produced from the same more fertile mantle source.However, enriched intraplate magmas, in contrast to calc-alkalineand low-K tholeiite magmas, cannot be generated from a depletedmantle source. Flux or batch melting of either the more fertileor depleted mantle sources used to generate the low-K tholeiite,calc-alkaline, and enriched intraplate magmas cannot reproduceshoshonitic compositions, which require a significantly depletedmantle source strongly metasomatized by a subduction component.The potential mantle source for shoshonitic basalts has a predictedfO₂ (after oxidation) from + 0·3 to + 2·4 logunits (FMQ) whereas the mantle source for low-K tholeiite, calc-alkaline,and enriched intraplate magmas may range from –1·1to + 0·7 log units (FMQ). KEY WORDS: basalt; Cascades; melt inclusions; oxidation state; volatiles     

Observations on the crystal structures of lueshite

Laboratory powder XRD patterns of the perovskite-group mineral lueshite from the type locality (Lueshe, Kivu, DRC) and pure NaNbO₃ demonstrate that lueshite does not adopt the same space group (Pbma; #57) as the synthetic compound. The crystal structures of lueshite (2 samples) from Lueshe, Mont Saint-Hilaire (Quebec, Canada) and Sallanlatvi (Kola, Russia) have been determined by single-crystal CCD X-ray diffraction. These room temperature X-ray data for all single-crystal samples can be satisfactorily refined in the orthorhombic space group Pbnm (#62). Cell dimensions, atomic coordinates of the atoms, bond lengths and octahedron tilt angles are given for four crystals. Conventional neutron diffraction patterns for Lueshe lueshite recorded over the temperature range 11–1,000 K confirm that lueshite does not adopt space group Pbma within these temperatures. Neutron diffraction indicates no phase changes on cooling from room temperature to 11 K. None of these neutron diffraction data give satisfactorily refinements but suggest that this is the space group Pbnm. Time-of-flight neutron diffraction patterns for Lueshe lueshite recorded from room temperature to 700 °C demonstrate phase transitions above 550 °C from Cmcm through P4/mbm to \(Pm\overline{3} m\) above 650 °C. Cell dimensions and atomic coordinates of the atoms are given for the three high-temperature phases. The room temperature to 400 °C structures cannot be satisfactorily resolved, and it is suggested that the lueshite at room temperature consists of domains of pinned metastable phases with orthorhombic and/or monoclinic structures. However, the sequence of high-temperature phase transitions observed is similar to those determined for synthetic NaTaO₃, suggesting that the equilibrated room temperature structure of lueshite is orthorhombic Pbnm.     

Short‐term forecasting with a multi‐level spectral primitive equation model part I ‐ model formulation

A global baroclinic primitive equation model using the spectral technique has been constructed for short‐ and medium‐range numerical weather prediction. The spectral technique, which is a special case of the Galerkin method, employs spherical harmonic basis functions in the evaluation of all horizontal derivatives. The use of a transform technique allows all the horizontal operations to be performed efficiently and allows physical processes to be evaluated in real space. The model employs a semi‐implicit algorithm for time integration and finite differencing in the vertical. Physical processes include orography, moist convection, large scale precipitation and boundary layer processes.     

Flexure of the Indian plate and intraplate earthquakes

The flexural bulge in central India resulting from India's collision with Tibet has a wavelength of approximately 670 km. It is manifest topographically and in the free-air gravity anomaly and the geoid. Calculations of the stress distribution within a flexed Indian plate reveal spatial variations throughout the depth of the plate and also a function of distance from the Himalaya. The wavelength (and therefore local gradient) of stress variation is a function of the effective elastic thickness of the plate, estimates of which have been proposed to lie in the range 40–120 km. The imposition of this stress field on the northward moving Indian plate appears fundamental to explaining the current distribution of intraplate earthquakes and their mechanisms. The current study highlights an outer trough south of the flexural bulge in central India where surface stresses are double the contiguous compressional stresses to the north and south. The Bhuj, Latur and Koyna earthquakes and numerous other recent reverse faulting events occurred in this compressional setting. The N/S spatial gradient of stress exceeds 2 bars/km near the flexural bulge. The overall flexural stress distribution provides a physical basis for earthquake hazard mapping and suggests that areas of central India where no historic earthquakes are recorded may yet be the locus of future damaging events.     

Did Lake Manly overflow at Ash Hill?

Near Ash Hill in the Mojave Desert, California, there is an impressive channel that is cut in bedrock. The channel is in a pass through which Lake Manly, the pluvial lake that occupied Death Valley, could have overflowed. Indeed, the channel has been attributed to such overflow. The pass, however, is 500 m above the highest shorelines of Lake Manly in Death Valley, and evidence from cores from dry lakes on either side of the pass does not support the overflow hypothesis. Despite its size, new field observations suggest that the channel was actually eroded by local runoff. Water from several tributaries collects into a single channel at this point, and the resulting discharge is apparently sufficient to cause retreat of a knickpoint from the downstream edge of the basalt flow into which the channel is cut. © 1998 John Wiley & Sons, Ltd.     

Convective energy transport in stellar atmospheres

The motion of convective cells in an environment which changes rapidly with depth is examined. In such an environment a cell may move through regions with different levels of ionization and with associated differences in heat capacity. The energy equation is cast in a manner which is independent of the history of these cells. The convective flux at a given level of the atmosphere is written as an average over an ensemble of cells originating at a range of other levels. A procedure for correcting the temperature gradient for these non-local effects is described and results for a model solar atmosphere are given. The principal results are: (1) The rms velocity varies smoothly and is non-zero well into the photosphere (e.g.,v _rsm=1.4 km/sec at =0.2); (2) Convective overshoot reduces the radiative flux to 60% and 90% of the total at =2.5 and 0.2 respectively; and (3) The interior adiabat of the convective envelope is less sensitive to the assumed value of the average cell size than in the usual treatment of convection.Supported in part by the National Science Foundation [GP-9433, GP-9114], the Office of Naval Research [Nonr-220(47)], and Air Force Grant AG-AFOSR-171-67.     

Crystal chemistry of titanite-structured compounds: the CaTi1-x Zr x OSiO4 (x≤0.5) series

Inhomogeneous aggregates of late-stage titanite enriched in Zr have been described recently from post-magmatic parageneses in silica-undersaturated rocks. In the natural samples, simple isovalent substitution of the large Zr (^[vi]R⁴⁺=0.72 Å) for Ti (^[vi]R⁴⁺=0.605 Å) is limited to an empirical maximum of 0.25 afu (15.3 wt.% ZrO₂). As the natural material is not suitable for crystallographic study, a series of CaTi_1-xZr_xOSiO₄ titanite samples have been synthesized by standard ceramic methods at ambient pressure in air, and their crystal structure determined by Rietveld refinement of laboratory powder X-ray diffraction patterns. All of the synthetic Zr-doped titanite varieties adopt space group A2/a and consist of distorted CaO₇ polyhedra together with less distorted (Ti_1-xZr_x)O₆ octahedra and SiO₄ tetrahedra. Cell dimensions and atomic coordinates together with volumes and distortion indices are given for all polyhedra. The empirical limit for Zr substitution in synthetic (F,OH)-free titanite is 0.5 afu (29.6 wt.% ZrO₂). The existence of a Zr analogue of titanite in nature is considered to be unlikely.