Improved algorithms for generalized finite element simulations of three-dimensional hydraulic fracture propagation

This paper reports improvements to algorithms for the simulation of 3-D hydraulic fracturing with the Generalized Finite Element Method (GFEM). Three optimizations are presented and analyzed. First, an improved initial guess based on solving a 3-D elastic problem with the pressure from the previous step is shown to decrease the number of Newton iterations and increase robustness. Second, an improved methodology to find the time step that leads to fracture propagation is proposed and shown to decrease significantly the number of iterations. Third, reduced computational cost is observed by properly recycling the linear part of the coupled stiffness matrix. Two representative examples are used to analyze these improvements. Additionally, a methodology to include the leak-off term is presented and verified against asymptotic analytical solutions. Conservation of mass is shown to be well satisfied in all examples.     

Spatial and temporal variability of stable isotopes (δ18O and δ2H) in surface waters of arid,mountainous Central Asia

Characterization of spatial and temporal variability of stable isotopes (δ¹⁸O and δ²H) of surface waters is essential to interpret hydrological processes and establish modern isotope–elevation gradients across mountainous terrains. Here, we present stable isotope data for river waters across Kyrgyzstan. River water isotopes exhibit substantial spatial heterogeneity among different watersheds in Kyrgyzstan. Higher river water isotope values were found mainly in the Issyk‐Kul Lake watershed, whereas waters in the Son‐Kul Lake watershed display lower values. Results show a close δ¹⁸O–δ²H relation between river water and the local meteoric water line, implying that river water experiences little evaporative enrichment. River water from the high‐elevation regions (e.g., Naryn and Son‐Kul Lake watershed) had the most negative isotope values, implying that river water is dominated by snowmelt. Higher deuterium excess (average d = 13.9‰) in river water probably represents the isotopic signature of combined contributions from direct precipitation and glacier melt in stream discharge across Kyrgyzstan. A significant relationship between river water δ¹⁸O and elevation was observed with a vertical lapse rate of 0.13‰/100 m. These findings provide crucial information about hydrological processes across Kyrgyzstan and contribute to a better understanding of the paleoclimate/elevation reconstruction of this region.     

Quantitative estimation of submarine groundwater discharge using airborne thermal infrared data acquired at two different tidal heights

Submarine groundwater discharge (SGD) plays an important role in coastal biogeochemical processes and hydrological cycles, particularly off volcanic islands in oligotrophic oceans. However, the spatial and temporal variations of SGD are still poorly understood owing to difficulty in taking rapid SGD measurements over a large scale. In this study, we used four airborne thermal infrared surveys (twice each during high and low tides) to quantify the spatiotemporal variations of SGD over the entire coast of Jeju Island, Korea. On the basis of an analytical model, we found a linear positive correlation between the thermal anomaly and squares of the groundwater discharge velocity and a negative exponential correlation between the anomaly and water depth (including tide height and bathymetry). We then derived a new equation for quantitatively estimating the SGD flow rates from thermal anomalies acquired at two different tide heights. The proposed method was validated with the measured SGD flow rates using a current meter at Gongcheonpo Beach. We believe that the method can be effectively applied for rapid estimation of SGD over coastal areas, where fresh groundwater discharge is significant, using airborne thermal infrared surveys.     

Suspended sediment and total dissolved solid yield patterns at the headwaters of Urumqi River,northwestern China: a comparison between glacial and non‐glacial catchments

In order to understand the differences in the suspended sediment and total dissolved solid (TDS) yield patterns between the glacial and non‐glacial catchments at the headwaters of Urumqi River, northwestern China, water samples were collected from a glacier catchment and an empty cirque catchment within the region, during three melting seasons from 2006 to 2008. These samples were analyzed to estimate suspended sediment and TDS concentrations, fluxes and erosion rates in the two adjoining catchments. There were remarked differences in suspended sediment and TDS yield patterns between the two catchments. Suspended sediment concentrations were controlled mainly by the sediment source, whereas TDS concentrations were primarily related to the hydrologic interaction with soil minerals. Generally, the glacial catchment had much higher suspended sediment and TDS yields, together with higher denudation rates, than the non‐glacial catchment. Overall, glacial catchment was mainly dominated by physical denudation process, whereas the non‐glacial catchment was jointly influenced by physical and chemical denudation processes. The observed differences in material delivery patterns were mainly controlled by the runoff source and the glacial processes. The melting periods of glacier and snow were typically the most important time for the suspended sediment and TDS yields. Meanwhile, episodic precipitation events could generate disproportionately large yields. Subglacial hydrology dynamics, glaciers pluck and grind processes could affect erodibility, and the large quantities of dust stored on the glacier surface provided additional sources for suspended sediment transport in the glacial catchment. These mechanisms imply that, in response to climate change, the catchment behaviour will be modified significantly in this region, in terms of material flux. Copyright © 2013 John Wiley & Sons, Ltd.     

Submarine groundwater discharge revealed by aerial thermal infrared imagery: a case study on Jeju Island,Korea

Submarine groundwater discharge (SGD) is a global phenomenon that carries large volumes of groundwater and dissolved chemical species such as nutrient, metals, and organic compounds to coastal zones. We report the influence of SGD on the coastal waters of Jeju Island, Korea, using high‐resolution aerial thermal infrared (TIR) mapping techniques and field investigations. An aircraft‐based system was implemented using a cost‐effective TIR camera for aerial TIR mapping. Ground‐based calibrations and system integration with GPS/IMU (global positioning system/inertial measurement unit) were performed for the aerial systems. The aerial surveys showed distinct low‐temperature signatures of SGD along the coasts of Jeju Island, revealing large groundwater inputs from the coastal aquifers to the ocean. Multiple aerial surveys over a range of seasons and tidal stages revealed that SGD rates dynamically affect the sea surface temperature (SST) of the coastal zone. The in‐situ measurements supported that SGD has a substantial influence on the coastal water chemistry as well as SST. Our observations highlight the extent to which aerial‐based TIR mapping can serve as a powerful tool for studying SGD and other coastal processes. Copyright © 2016 John Wiley & Sons, Ltd.     

Interpreting zirconium‐in‐rutile thermometric results

At first sight, experimental results and observations on rocks suggest that the Zr content in rutile, where equilibrated with quartz and zircon, should be a useful thermometer for metamorphic rocks. However, diffusion data for Zr in rutile imply that thermometry should not, for plausible rates of cooling, give the high temperatures commonly observed in high‐grade metamorphic rocks. It is suggested here that such observations can be accounted for by high‐T diffusive closure of Si in rutile, causing the interior of rutile grains to become insensitive to the thermometer equilibrium well above the temperature of Zr diffusive closure. Paired with comparatively slow grain boundary diffusion and problematic zircon nucleation, this allows for cases of Zr retention in rutile through temperatures where Zr is still diffusively mobile within rutile grains. Other observations that may be accounted for in this context are large inter‐grain ranges of rutile Zr contents uncorrelated with rutile grain size, and flat Zr profiles across individual rutile grains, counter to what would be expected from diffusive closure. A consequence is that it is unlikely that Zr‐in‐rutile thermometry will be useful for estimating rock cooling rates.     

Dissolved inorganic carbon evolution in neutral discharge from mine tailings piles

We measured the concentrations of dissolved inorganic carbon (DIC) and major ions and the stable carbon isotope ratios of DIC (δ¹³C_DIC) in two creeks discharging from carbonate‐rich sulphide‐containing mine tailings piles. Our aim was to assess downstream carbon evolution of the tailings discharge as it interacted with the atmosphere. The discharge had pH of 6.5–8.1 and was saturated with respect to carbonates. Over the reach of one creek, the DIC concentrations decreased by 1.1 mmol C/l and δ¹³C_DIC increased by ~4.0‰ 200 m from the seep source. The decrease in the DIC concentrations was concomitant with decreases in the partial pressure of CO_2(aq) because of the loss of excess CO_2(aq) from the discharge. The corresponding enrichment in the δ¹³C_DIC is because of kinetic isotope fractionation accompanying the loss of CO_2(g). Over the reach of the other creek, there was no significant decrease in the DIC concentrations or notable changes in the δ¹³C_DIC. The insignificant change in the DIC concentrations and the δ¹³C_DIC is because the first water sample was collected 160 m away from the discharge seep, not accessible during this research. In this case, most of the excess CO_2(aq) was lost before our first sampling station. Our results indicate that neutral discharges from tailings piles quickly lose excess CO_2(aq) to the atmosphere and the DIC becomes enrich in ¹³C. We suggest that a significant amount of carbon cycling in neutral discharges from tailings piles occur close to the locations where the discharge seeps to the surface. Copyright © 2015 John Wiley & Sons, Ltd.     

Root‐zone moisture replenishment in a native vegetated catchment under Mediterranean climate

The root‐zone moisture replenishment mechanisms are key unknowns required to understand soil hydrological processes and water sources used by plants. Temporal patterns of root‐zone moisture replenishment reflect wetting events that contribute to plant growth and survival and to catchment water yield. In this study, stable oxygen and hydrogen isotopes of twigs and throughfall were continuously monitored to characterize the seasonal variations of the root‐zone moisture replenishment in a native vegetated catchment under Mediterranean climate in South Australia. The two studied hillslopes (the north‐facing slope [NFS] and the south‐facing slope [SFS]) had different environmental conditions with opposite aspects. The twig and throughfall samples were collected every ~20 days over 1 year on both hillslopes. The root‐zone moisture replenishment, defined as percentage of newly replenished root‐zone moisture as a complement to antecedent moisture for plant use, calculated by an isotope balance model, was about zero (±25% for the NFS and ± 15% for the SFS) at the end of the wet season (October), increased to almost 100% (±26% for the NFS and ± 29% for the SFS) after the dry season (April and May), then decreased close to zero (±24% for the NFS and ± 28% for the SFS) in the middle of the following wet season (August). This seasonal pattern of root‐zone moisture replenishment suggests that the very first rainfall events of the wet season were significant for soil moisture replenishment and supported the plants over wet and subsequent dry seasons, and that NFS completed replenishment over a longer time than SFS in the wet season and depleted the root zone moisture quicker in the dry season. The stable oxygen isotope composition of the intraevent samples and twigs further confirms that rain water in the late wet season contributed little to root‐zone moisture. This study highlights the significant role of the very first rain events in the early wet season for ecosystem and provides insights to understanding ecohydrological separation, catchment water yield, and vegetation response to climate changes.     

Syn‐metamorphic folding in the Tauern Window,Austria dated by Th–Pb ages from individual allanite porphyroblasts

High‐precision ²³²Th–²⁰⁸Pb dates have been obtained from allanite porphyroblasts that show unambiguous microstructural relationships to fabrics in a major syn‐metamorphic fold in the SE Tauern Window, Austria. Three porphyroblasts were analysed from a single garnet mica schist from the Peripheral Schieferhülle in the core of the Ankogel Synform, one of a series of folds which developed shortly before the thermal peak of Alpine epidote–amphibolite facies metamorphism: allanite grain 1 provided two analyses with a combined age of 27.7 ± 0.7 Ma; grain 2, which was slightly bent and fractured during crenulation, provided two analyses with a combined age of 27.7 ± 0.4 Ma; a single analysis from grain 3, which overgrew an already crenulated fabric, gave an age of 28.0 ± 1.4 Ma. The five ²³²Th–²⁰⁸Pb ages agree within error and define an isochron with an age of 27.71 ± 0.36 Ma (95% confidence level; MSWD = 0.46). The results imply that the crenulation event was in progress in a short interval (<1 Ma) c. 28 Ma, and that the Ankogel Synform was forming at this time. The thermal peak of regional metamorphism in the SE Tauern Window was probably attained shortly after 28 Ma, only c. 5 Ma after eclogite facies metamorphism in the central Tauern Window. Metasediment may contain allanite porphyroblasts with clear‐cut microstructural relationships to fabric development and metamorphic crystallization; for such rocks, ²³²Th–²⁰⁸Pb dating on microsamples offers a powerful geochronological tool.     

Frequency analysis of nonstationary annual maximum flood series using the time‐varying two‐component mixture distributions

The most popular practice for analysing nonstationarity of flood series is to use a fixed single‐type probability distribution incorporated with the time‐varying moments. However, the type of probability distribution could be both complex because of distinct flood populations and time‐varying under changing environments. To allow the investigation of this complex nature, the time‐varying two‐component mixture distributions (TTMD) method is proposed in this study by considering the time variations of not only the moments of its component distributions but also the weighting coefficients. Having identified the existence of mixed flood populations based on circular statistics, the proposed TTMD was applied to model the annual maximum flood series of two stations in the Weihe River basin, with the model parameters calibrated by the meta‐heuristic maximum likelihood method. The performance of TTMD was evaluated by different diagnostic plots and indexes and compared with stationary single‐type distributions, stationary mixture distributions and time‐varying single‐type distributions. The results highlighted the advantages of TTMD with physically‐based covariates for both stations. Besides, the optimal TTMD models were considered to be capable of settling the issue of nonstationarity and capturing the mixed flood populations satisfactorily. Copyright © 2016 John Wiley & Sons, Ltd.