Tetrahedral Plots of the Phase Relations for Basalts

The phase relations of quaternary systems are generally represented by projections onto ternary compositional planes. Such projections often obscure relationships that would only be evident in a three-dimensional tetrahedral plot. The tetrahedral plot requires that compositions of the minerals and melts be transformed into Cartesian coordinates. It is shown here how this transformation is carried out. The application is demonstrated by tetrahedral plots of experimental melt compositions of partially molten lherzolite. Furthermore, the plot can be used to evaluate whether or not a particular basaltic composition represents a primary melt. The methods are applicable to any four-component system.     

Evaluating soil moisture estimation from ground-penetrating radar hyperbola fitting with respect to a systematic time-domain reflectometry data collection in a boreal podzolic agricultural field

The upper 30 cm of the soil profile, which hosts the majority of the root biomass, can be considered as the shallow agricultural root zone of most temperate crops. The electromagnetic wave velocity in the soil obtained from reflection hyperbolas in ground-penetrating radar (GPR) data can be used to estimate soil moisture (SM). Finding shallow hyperbolas in a radargram and minimizing the subjective error associated with the hyperbola fitting are the main challenges in this approach. Nevertheless, we were motivated by the recent improvements of hyperbola fitting algorithms, which can reduce the subjective error and processing time. To overcome the difficulty of finding very shallow hyperbolas, we applied the hyperbola fitting method to reflections ranging from 27- to 50-cm depth using a 500-MHz centre-frequency GPR and compared the estimated moisture with vertically installed, 30-cm-long time-domain reflectometry (TDR) sensors. We also compared TDR and GPR sample areas in a 2-D plane using different GPR survey types and different hyperbola depths. SM measured with TDR and GPR were not significantly different according to Mann–Whitney's test. Our analyses showed that a root mean square error of 0.03 m³ m⁻³ was found between the two methods. In conclusion, the proposed method might be suitable to estimate SM with an acceptable accuracy within the root zone if the soil profile is fairly uniform within the application depth range.     

Implications of measurement metrics on soil freezing curves: A simulation of freeze–thaw hysteresis

Soil freeze–thaw events have important implications for water resources, flood risk, land productivity, and climate change. A property of these phenomena is the relationship between unfrozen water content and sub-freezing temperature, known as the soil freezing characteristic curve (SFC). It is documented that this relationship exhibits hysteretic behaviour when frozen soil thaws, leading to the definition of the soil thawing characteristic curve (STC). Although explanations have been given for SFC/STC hysteresis, the effect that ‘scale’ – particularly ‘measurement scale’ – may have on these curves has received little attention. The most commonly used measurement scale metric is the ‘support’, which is the spatial (or temporal) unit within which the measured variable is integrated or soil volume sampled. We show (a) measurement support can influence the range and shape of the SFC and (b) hysteresis can be attributed, in part, to the support and location of the measurements comprising the SFC/STC. We simulated lab measured temperature, volumetric water content (VWC), and permittivity from soil samples undergoing freeze–thaw transitions using Hydrus-1D and a modified Dobson permittivity model. To assess the effect of measurement support and location on SFC/STC, we masked the simulated temperature and VWC/permittivity extent to match the instrument's support and location. By creating a detailed simulation of the intra- and inter-support variability associated with the penetration of a freezing front, we demonstrate how measurement support and location can influence the temperature range over which water freezing events are captured. We show it is possible to simulate hysteresis in homogenous media with purely geometric considerations, suggesting that SFC/STC hysteresis may be more of an apparent phenomenon than mechanistically real. Lastly, we develop an understanding of how the location and support of soil temperature and VWC/permittivity measurements influence the temperature range over which water freezing events are captured.     

The synoptic‐ and planetary‐scale signatures of precipitating systems over the Mackenzie River Basin

Abstract

The synoptic‐ and planetary‐scale signatures of precipitating systems over the Mackenzie River Basin (MRB) are elucidated using composites based on a 28‐year sample of widespread precipitation events. These wet events are defined as days on which 5 or more of 12 surface stations in the MRB receive at least 2.5 mm of precipitation. Seasonal composites based on a total of 600 wet events reveal a sequence of statistically significant flow anomalies. Examination of individual wet events motivates stratification of the seasonal samples according to sea‐level pressure distribution. One evolution that is particularly common during fall, winter and spring involves lee cyclogenesis over the southern MRB in association with a strong cyclone over the Gulf of Alaska; such events are dubbed Gulf Redevelopment (GR) cases. A composite based on 59 wintertime GR events indicates upslope flow north of the lee cyclone and warm advection along an east‐west oriented warm front during the precipitation event. Composites of the Q‐vector and the divergence of this field confirm the presence of quasigeostrophic (QG) forcing for ascent over the MRB during this period. A thermally indirect “topographic tilting” mechanism, involving downs‐lope warming over the southern MRB and upslope cooling to the north, is hypothesized to increase warm‐frontal baroclinicity over the MRB. The GR composite 500 hPa geopotential height anomaly pattern is characterized by a series of anomalies extending from the Bering Sea to the Gulf of Mexico. The western (eastern) anomalies tend to decay (amplify) with time. The composite exhibits a positive anomaly over the Bering Sea, a negative anomaly over the Gulf of Alaska that moves eastward into the MRB during the precipitation event, and a positive anomaly that moves eastward over western and central North America. The presence of large, slow‐moving flow anomalies and an extended period of enhanced southwesterly geostrophic flow over the MRB in the composite suggests that a persistent influx of Pacific moisture is required to moisten the atmosphere over the MRB sufficiently for widespread precipitation. An independent composite of dry MRB cyclone events exhibits substantially weaker southwesterly geostrophic flow into the MRB relative to the wet GR composite.     

Spatially controlled Fe and Si isotope variations: an alternative view on the formation of the Torres del Paine pluton

We present new Fe and Si isotope ratio data for the Torres del Paine igneous complex in southern Chile. The multi-composition pluton consists of an approximately 1 km vertical exposure of homogenous granite overlying a contemporaneous 250-m-thick mafic gabbro suite. This first-of-its-kind spatially dependent Fe and Si isotope investigation of a convergent margin-related pluton aims to understand the nature of granite and silicic igneous rock formation. Results collected by MC-ICP-MS show a trend of increasing δ⁵⁶Fe and δ³⁰Si with increasing silica content as well as a systematic increase in δ⁵⁶Fe away from the mafic base of the pluton. The marginal Torres del Paine granites have heavier Fe isotope signatures (δ⁵⁶Fe = +0.25 ± 0.02 2se) compared to granites found in the interior pluton (δ⁵⁶Fe = +0.17 ± 0.02 2se). Cerro Toro country rock values are isotopically light in both Fe and Si isotopic systems (δ⁵⁶Fe = +0.05 ± 0.02 ‰; δ³⁰Si = ?0.38 ± 0.07 ‰). The variations in the Fe and Si isotopic data cannot be accounted for by local assimilation of the wall rocks, in situ fractional crystallization, late-stage fluid exsolution or some combination of these processes. Instead, we conclude that thermal diffusion or source magma variation is the most likely process producing Fe isotope ratio variations in the Torres del Paine pluton.     

Biogenic volatile compound emissions from a temperate forest,China: model simulation

Emissions of biogenic volatile organic compounds (BVOC) were measured using a relaxed eddy accumulation (REA) technique on an above-canopy tower in a temperate forest (Changbai Mountain, Jilin province, China) during the 2010 and 2011 summer seasons. Solar global radiation and photosynthetically active radiation (PAR) were also measured. Based on PAR energy dynamic balance, an empirical BVOC emission and PAR transfer model was developed that includes the processes of BVOC emissions and PAR transfer above the canopy level, including PAR absorption and consumption, and scattering by gases, liquids, and particles (GLPs). Simulated emissions of isoprene and monoterpenes were in agreement with observations. The averages of the relative estimator biases for the flux were 39.3 % for isoprene, and 27.1 % for monoterpenes in the 2010 and 2011 growing seasons, with NMSE (normalized mean square error) values of 0.133 and 0.101, respectively. The observed and simulated mean diurnal variations of isoprene and monoterpenes in the 2010 and 2011 growing seasons were evaluated for the validation of the empirical model. Under observed atmospheric conditions, the sensitivity analysis showed that emissions of isoprene and monoterpenes were more sensitive to changes in PAR than to water vapor content or to the magnitude of the scattering factor. The emissions of isoprene and monoterpenes in the 2010 and 2011 growing seasons (from June to September) were estimated using this empirical model along with hourly observational data, with mean hourly emissions of 1.71 and 1.55 mg m^?2 h^?1 for isoprene, and 0.48 and 0.47 mg m^?2 h^?1 for monoterpenes in 2010 and 2011, respectively. As formaldehyde (HCHO) is considered as the main oxidation product of isoprene and monoterpenes, it is necessary to investigate the link between HCHO and BVOC emissions. GOME-2 HCHO vertical column densities (VCDs) can be used to estimate BVOC emission fluxes in the Changbai Mountain temperate forest.     

Initiation of large-volume silicic centers in the Yellowstone hotspot track: insights from H<Subscript>2</Subscript>O- and F-rich quartz-hosted rhyolitic melt inclusions in the Arbon Valley Tuff of the Snake River Plain

During the onset of caldera cluster volcanism at a new location in the Snake River Plain (SRP), there is an increase in basalt fluxing into the crust and diverse silicic volcanic products are generated. The SRP contains abundant and compositionally diverse hot, dry, and often low-δ¹⁸O silicic volcanic rocks produced through time during the formation of individual caldera clusters, but more H₂O-rich eruptive products are rare. We report analyses of quartz-hosted melt inclusions from pumice clasts from the upper and lower Arbon Valley Tuff (AVT) to gain insight into the initiation of caldera cluster volcanism. The AVT, a voluminous, caldera-forming rhyolite, represents the commencement of volcanism (10.44 Ma) at the Picabo volcanic field of the Yellowstone hotspot track. This is a normal δ¹⁸O rhyolite consisting of early and late erupted members (lower and upper AVT, respectively) with extremely radiogenic Sr isotopes and unradiogenic Nd isotopes, requiring that ~50 % of the mass of these elements is derived from melts of Archean upper crust. Our data reveal distinctive features of the early erupted lower AVT melt including: variable F concentrations up to 1.4 wt%, homogenous and low Cl concentrations (~0.08 wt%), H₂O contents ranging from 2.3 to 6.4 wt%, CO₂ contents ranging from 79 to 410 ppm, and enrichment of incompatible elements compared to the late erupted AVT, subsequent Picabo rhyolites, SRP rhyolites, and melt inclusions from other metaluminous rhyolites (e.g., Bishop Tuff, Mesa Falls Tuff). We couple melt inclusion data with Ti measurements and cathodoluminescence (CL) imaging of the host quartz phenocrysts to elucidate the petrogenetic evolution of the AVT rhyolitic magma. We observe complex and multistage CL zoning patterns, the most critical being multiple truncations indicative of several dissolution–reprecipitation episodes with bright CL cores (higher Ti) and occasional bright CL rims (higher Ti). We interpret the high H₂O, F, F/Cl, and incompatible trace element concentrations in the context of a model involving melting of Archean crust and mixing of the crustal melt with basaltic differentiates, followed by multiple stages of fractional crystallization, remelting, and melt extraction. This multistage process, which we refer to as distillation, is further supported by the complex CL zoning patterns in quartz. We interpret new Δ¹⁸O(Qz-Mt) isotope measurements, demonstrating a 0.4 ‰ or ~180 °C temperature difference, and strong Sr isotopic and chemical differences between the upper and lower AVT to represent two separate eruptions. Similarities between the AVT and the first caldera-forming eruptions of other caldera clusters in the SRP (Yellowstone, Heise and Bruneau Jarbidge) suggest that the more evolved, lower-temperature, more H₂O-rich rhyolites of the SRP are important in the initiation of a caldera cluster during the onset of plume impingement.     

Recursive algorithm for fast GNSS orbit fitting

Gaussian elimination is an efficient and numerically stable algorithm for estimating parameters and their precision. However, before estimating the parameters, it is often prudent to perform statistical tests to achieve the best fitting model. We use Gaussian elimination to select the best fitting model among candidate models. A succinct relationship between the weighted sum of squared residuals and the previous one is revealed by a volume formula. For quick parameter estimation and determination of weighted sum of squared residuals, a recursive elimination algorithm is proposed in the context of Gaussian elimination. In order to improve the model selection efficiency, the parameter estimation and the determination of the weighted sum of squared residuals are carried out in parallel using the proposed recursive elimination algorithm in which the improvement at each recursive stage is judged by the Bayesian information criterion. Ultimately, the computational complexity and numerical stability of the recursive elimination proposed are briefly discussed, and a GNSS orbit interpolation example is used to verify the results. It shows that the proposed recursive elimination algorithm inherits the numerical stability of the Gaussian elimination, and this algorithm can be used to examine the gain from the newly introduced parameter, dynamically assess the fitting model, and fix the optimal model efficiently. The optimal fitting model with the lowest information is very close to the real situation verified by checkpoints.