Selection of Momentum Variables for a Three-Dimensional Variational Analysis

Three choices of control variables for meteorological variational analysis (3DVAR or 4DVAR) are associated with horizontal wind: (1) streamfunction and velocity potential, (2) eastward and northward velocity, and (3) vorticity and divergence. This study shows theoretical and numerical differences of these variables in practical 3DVAR data assimilation through statistical analysis and numerical experiments. This paper demonstrates that (a) streamfunction and velocity potential could potentially introduce analysis errors; (b) A 3DVAR using velocity or vorticity and divergence provides a natural scale dependent influence radius in addition to the covariance; (c) for a regional analysis, streamfunction and velocity potential are retrieved from the background velocity field with Neumann boundary condition. Improper boundary conditions could result in further analysis errors; (d) a variational data assimilation or an inverse problem using derivatives as control variables yields smoother analyses, for example, a 3DVAR using vorticity and divergence as controls yields smoother wind analyses than those analyses obtained by a 3DVAR using either velocity or streamfunction/velocity potential as control variables; and (e) statistical errors of higher order derivatives of variables are more independent, e.g., the statistical correlation between U and V is smaller than the one between streamfunction and velocity potential, and thus the variables in higher derivatives are more appropriate for a variational system when a cross-correlation between variables is neglected for efficiency or other reasons. In summary, eastward and northward velocity, or vorticity and divergence are preferable control variables for variational systems and the former is more attractive because of its numerical efficiency. Numerical experiments are presented using analytic functions and real atmospheric observations.     

Lava penetrating water: the different behaviours of pāhoehoe and ‘a‘ā at the Nesjahraun, Tingvellir, Iceland

The Nesjahraun is a basaltic lava flow erupted from a subaerial fissure, extending NE along the Tingvellir graben from the Hengill central volcano that produced pāhoehoe lava followed by ‘a‘ā. The Nesjahraun entered Iceland’s largest lake, Tingvallavatn, along its southern shore during both phases of the eruption and exemplifies lava flowing into water in a lacustrine environment in the absence of powerful wave action. This study combines airborne light detection and ranging, sidescan sonar and Chirp seismic data with field observations to investigate the behaviour of the lava as it entered the water. Pāhoehoe sheet lava was formed during the early stages of the eruption. Along the shoreline, stacks of thin (5–20 cm thick), vesicular, flows rest upon and surround low (<5 m) piles of coarse, unconsolidated, variably oxidised spatter. Clefts within the lava run inland from the lake. These are 2–5 m wide, >2 m deep, ∼50 m long, spaced ∼50 m apart and have sub-horizontal striations on the walls. They likely represent channels or collapsed tubes along which lava was delivered into the water. A circular rootless cone, Eldborg, formed when water infiltrated a lava tube. Offshore from the pāhoehoe lavas, the gradient of the flow surface steepens, suggesting a change in flow regime and the development of a talus ramp. Later, the flow was focused into a channel of ‘a‘ā lava, ∼200–350 m wide. This split into individual flow lobes 20–50 m wide along the shore. ‘A‘ā clinker is exposed on the water’s edge, as well as glassy sand and gravel, which has been locally intruded by small (<1 m), irregularly shaped, lava bodies. The cores of the flow lobes contain coherent, but hackly fractured lava. Mounds consisting predominantly of scoria lapilli and the large paired half-cone of Grámelur were formed in phreatomagmatic explosions. The ‘a‘ā flow can be identified underwater over 1 km offshore, and the sidescan data suggest that the flow lobes remained coherent flowing down a gradient of <10°. The Nesjahraun demonstrates that, even in the absence of ocean waves, phreatomagmatic explosions are ubiquitous and that pāhoehoe flows are much more likely to break up on entering the water than ‘a‘ā flows, which, with a higher flux and shallow underlying surface gradient, can penetrate water and remain coherent over distances of at least 1 km.     

DEM-based numerical modelling of runoff and soil erosion processes in the hilly–gully loess regions

For sake of improving our current understanding on soil erosion processes in the hilly–gully loess regions of the middle Yellow River basin in China, a digital elevation model (DEM)-based runoff and sediment processes simulating model was developed. Infiltration excess runoff theory was used to describe the runoff generation process while a kinematic wave equation was solved using the finite-difference technique to simulate concentration processes on hillslopes. The soil erosion processes were modelled using the particular characteristics of loess slope, gully slope, and groove to characterize the unique features of steep hillslopes and a large variety of gullies based on a number of experiments. The constructed model was calibrated and verified in the Chabagou catchment, located in the middle Yellow River of China and dominated by an extreme soil-erosion rate. Moreover, spatio-temporal characterization of the soil erosion processes in small catchments and in-depth analysis between discharge and sediment concentration for the hyper-concentrated flows were addressed in detail. Thereafter, the calibrated model was applied to the Xingzihe catchment, which is dominated by similar soil erosion processes in the Yellow River basin. Results indicate that the model is capable of simulating runoff and soil erosion processes in such hilly–gully loess regions. The developed model are expected to contribute to further understanding of runoff generation and soil erosion processes in small catchments characterized by steep hillslopes, a large variety of gullies, and hyper-concentrated flow, and will be beneficial to water and soil conservation planning and management for catchments dealing with serious water and soil loss in the Loess Plateau.     

Stability of phlogopite in ultrapotassic kimberlite-like systems at 5.5–7.5 GPa

Hydrous K-rich kimberlite-like systems are studied experimentally at 5.5–7.5 GPa and 1200–1450?°C in terms of phase relations and conditions for formation and stability of phlogopite. The starting samples are phlogopite–carbonatite–phlogopite sandwiches and harzburgite–carbonatite mixtures consisting of Ol?+?Grt?+?Cpx?+?L (±Opx), according to the previous experimental results obtained at the same P–T parameters but in water-free systems. Carbonatite is represented by a K- and Ca-rich composition that may form at the top of a slab. In the presence of carbonatitic melt, phlogopite can partly melt in a peritectic reaction at 5.5 GPa and 1200–1350?°C, as well as at 6.3–7.0 GPa and 1200?°C: 2Phl?+?CaCO₃ (L)?Cpx?+?Ol?+?Grt?+?K₂CO₃ (L)?+?2H₂O (L). Synthesis of phlogopite at 5.5 GPa and 1200–1350?°C, with an initial mixture of H₂O-bearing harzburgite and carbonatite, demonstrates experimentally that equilibrium in this reaction can be shifted from right to left. Therefore, phlogopite can equilibrate with ultrapotassic carbonate–silicate melts in a?≥?150?°C region between 1200 and 1350?°C at 5.5 GPa. On the other hand, it can exist but cannot nucleate spontaneously and crystallize in the presence of such melts in quite a large pressure range in experiments at 6.3–7.0 GPa and 1200?°C. Thus, phlogopite can result from metasomatism of peridotite at the base of continental lithospheric mantle (CLM) by ultrapotassic carbonatite agents at depths shallower than 180–195 km, which creates a mechanism of water retaining in CLM. Kimberlite formation can begin at 5.5 GPa and 1350?°C in a phlogopite-bearing peridotite source generating a hydrous carbonate–silicate melt with 10–15 wt% SiO₂, Ca# from 45 to 60, and high K enrichment. Upon further heating to 1450?°C due to the effect of a mantle plume at the CLM base, phlogopite disappears and a kimberlite-like melt forms with SiO₂ to 20 wt% and Ca#?=?35–40.     

Chronology and Geochemistry of the Berezitovoe Polymetallic Gold Deposit in Eastern Siberia, Russia and its Geological Significance

The Berezitovoe deposit is a large-sized Au-Ag-Zn-Pb deposit in the east of the SelengaStanovoi superterrane, Russia. Au-Ag orebodies are hosted by tourmaline-garnet-quartz-muscovite metasomatic rocks; Zn-Pb orebodies are hosted by granodiorites, porphyritic granites and tourmalinegarnet-quartz-muscovite metasomatic rocks. These orebodies are surrounded by wall rocks dominated by the Tukuringra Complex granodiorites, porphyritic granites, and gneissic granodiorites. The alteration includes silicification and garnet, sericitization chloritization, carbonatization and kaollinization. LA-ICP-MS U-Pb zircon dating indicates that the gold mineralization can be divided into two stages in the Berezitovoe polymetallic gold deposit(at 363.5 ± 1.5 Ma, and133.4± 0.5).Hornblende-plagioclase gneisses of the Mogocha Group in the study area underwent Paleoproterozoic metamorphism(at 1870 ± 7.8 and 2400 ± 13 Ma), gneissic granodiorite of the Tukuringra Complex yields a late Paleozoic magmatic age(at 379.2 ± 1.1 Ma),and subalkaline porphyritic granitoid of the Amudzhikan Complex yield late Mesozoic magmatic ages(133-139 and 150-163 Ma). Granodiorites of the Tukuringra Complex in the study area have high concentrations of SiO_2(average of 60.9 wt%), are aluminum-oversaturated(average A/CNK of 1.49), are enriched in the large ion lithophile elements(e.g.,K, Rb, and Ba), U, Th, and Pb, are depleted in high field strength elements(e.g., Ta, Nb, and Ti), and have slightly negative Eu and no Ce anomalies in chondrite-normalized rare earth element diagrams.Fluid inclusions from quartz veins include three types: aqueous two-phase, CO_2-bearing three-phase,and pure CO_2. Aqueous two-phase inclusions homogenize at 167℃-249℃ and have salinities of 4.32%-9.47% NaCl equivalent, densities of 0.86-0.95 g/cm~3, and formed at depths of 0.52-0.94 km. In comparison, the C0_2-bearing three-phase inclusions have homogenization temperatures of 265℃-346℃,salinities of 7.14%-11.57% NaCl equivalent, and total densities of 0.62-0.67 g/cm~3. The geochemical and zircon U-Pb data and the regional tectonic evolution of the study area, show that the Berezitovoe polymetallic gold deposit formed in an island arc or active continental margin setting, most probably related to late Paleozoic subduction of Okhotsk Ocean crust beneath the Siberian Plate.     

Approximate Stochastic Self-Similarity of Envelopes of High-Frequency Teleseismic P-Waves from Large Earthquakes

A wavetrain of high-frequency (HF) P waves from a large earthquake, when recorded at a distant station, looks like a segment of modulated noise, with its duration close to the duration of rupture. These wavetrains, with their bursts and fadings, look much more intermittent than a segment of common stationary random noise. We try to describe quantitatively this bursty behavior. To this end, variogram and spectral analyses are applied to time histories of P-wave envelopes (squared-amplitude or instant-power signals) in six HF bands of 1-Hz width. Nine M _w = 7.6–9.2 earthquakes were examined, using, in total, 232 records and 992 single-band traces. Variograms of integrated instant power are approximately linear on a log–log scale, indicating that the correlation structure of the instant-power signal is approximately self-similar. Also, estimates of the power spectrum of the instant-power signal look approximately linear on a log–log scale. Log–log slopes of the variograms and spectra deliver estimates of the Hurst exponent H that are mostly in the range 0.6–0.9, markedly above the value H = 0.5 of uncorrelated (white-noise) signals. The preferred estimate over the entire data set is H = 0.83, still, this estimate may include some bias, and must be treated as preliminary. The inter-event scatter of H estimates is about 0.04, reflecting individual event-to-event variations of H. Many of the average log–log spectral plots show slight concavity that perturbs the approximately linear slope; this is a secondary effect that seems to be mostly related to the limited bandwidth of the data. Evidence is given in support of the idea that the observed approximately self-similar correlation structure of the P-wave envelope originates in a similar structure of the body wave instant-power signal radiated by the source, so that the propagation-related distortions can be regarded as limited. The facts presented suggest that the space–time organization of the earthquake rupture process is multiscaled and bears significant fractal features; it deviates from the brittle-crack model with its two well-separated characteristic scales. Phenomenologically, the high-frequency body-wave radiation from an earthquake source can be thought of as a product of stationary noise and the square root of a positive random envelope function with a power-law spectrum. From the viewpoint of applications, the self-similarity of body wave envelopes provides a useful constraint for earthquake source models used to simulate strong ground motions.     

Transient Electric Field in the Mesosphere above a Γ-shape Lightning Stroke

We describe the space–time distribution of the pulsed electric field in the middle atmosphere above a positive Γ-shaped lightning stroke. The channel of such a discharge contains a vertical and a horizontal section. The current wave moves initially vertically and then turns horizontally so that radiation appears from the vertical electric dipole followed by that from the horizontal dipole. Combined with reflection from the perfectly conducting ground, the source provides three subsequent pulses in the atmosphere, with the lag being determined by the finite velocity of the current wave in the Γ-shaped stroke. The pulses are reproduced by reflections from the air-ground and the air-ionosphere interfaces and the waveform resembles the M-component, which is often noted in the negative strokes (e.g. Yashunin et al., J Geophys Res 112:D10109, 2007). The non-stationary fine structure appears in the spatial distribution of electric field, which persists for 2 ms or even more and exceeds the runaway electron threshold. Estimates support the idea of free electron bunching in the mesosphere by the pulsed electric field. Focusing may occur about 10 km away from the point of electron- field interaction; it is delayed by a few ms from the moment of interaction. The data presented might be helpful in realistic modeling of the red sprite formation.