Vertical vibration of a rigid strip footing on viscoelastic half-space

This paper presents an analytical method for modeling the dynamic response of a rigid strip footing subjected to vertical-only loads. The footing is assumed to rest on the surface of a viscoelastic half-space; therefore, effects of hysteretic soil damping on the impedance of the foundation and the generated ground vibrations are considered in the solution. To solve the mixed boundary value problem, we use the Fourier transform to cast a pair of dual integral equations providing contact stresses, which are solved by means of Jacobi orthogonal polynomials. The resulting soil and footing displacements and stresses are obtained by means of the Fourier inverse transform. The solution provides more realistic estimates of footing impedance, compared to existing solutions for elastic soil, as well as of the attenuation of ground vibrations with distance of the footing. The latter is important for the estimation of machine vibration effects on nearby structures and installations.     

Characterizing spatial and temporal variation in 18O and 2H content of New Zealand river water for better understanding of hydrologic processes

Time series of hydrogen and oxygen stable isotope ratios (δ²H and δ¹⁸O) in rivers can be used to quantify groundwater contributions to streamflow, and timescales of catchment storage. However, these isotope hydrology techniques rely on distinct spatial or temporal patterns of δ²H and δ¹⁸O within the hydrologic cycle. In New Zealand, lack of understanding of spatial and temporal patterns of δ²H and δ¹⁸O of river water hinders development of regional and national-scale hydrological models. We measured δ²H and δ¹⁸O monthly, together with river flow rates at 58 locations across New Zealand over a two-year period. Results show: (a) general patterns of decreasing δ²H and δ¹⁸O with increasing latitude were altered by New Zealand's major mountain ranges; δ²H and δ¹⁸O were distinctly lower in rivers fed from higher elevation catchments, and in eastern rain-shadow areas of both islands; (b) river water δ²H and δ¹⁸O values were partly controlled by local catchment characteristics (catchment slope, PET, catchment elevation, and upstream lake area) that influence evaporation processes; (c) regional differences in evaporation caused the slope of the river water line (i.e., the relationship between δ²H and δ¹⁸O in river water) for the (warmer) North Island to be lower than that of the (cooler, mountain-dominated) South Island; (d) δ²H seasonal offsets (i.e., the difference between seasonal peak and mean values) for individual sites ranged from 0.50‰ to 5.07‰. Peak values of δ¹⁸O and δ²H were in late summer, but values peaked 1 month later at the South Island sites, likely due to greater snow-melt contributions to streamflow. Strong spatial differences in river water δ²H and δ¹⁸O caused by orographic rainfall effects and evaporation may inform studies of water mixing across landscapes. Generally distinct seasonal isotope cycles, despite the large catchment sizes of rivers studied, are encouraging for transit time analysis applications.     

联合GPS和GRACE数据分析陕甘宁地区地表垂直形变

采用甘肃省CORS网和中国大陆构造环境监测网络中共48个台站的GPS观测数据，解算得到观测台站的垂直位移，并与GRACE时变重力场Mascon模型解CSR RL05M数据计算得到的垂直形变进行比较，分析区域地表垂直形变特征。结果表明，研究区内台站垂直形变存在局部特征，甘肃庆阳和平凉地区垂直形变与其他地区存在明显差异，相关系数、均方根减少量和周年信号减少量均高于其他地区；扣除趋势项后，观测台站GPS垂直位移与GRACE垂直形变时间序列相关系数均值为0.72，GPS和GRACE周年信号振幅均值分别为6.00 mm和3.70 mm，周年信号减少量和均方根误差减少量均值分别为0.51和0.29；研究区内GPS垂直位移和GRACE垂直形变时间序列一致性较强，GRACE垂直形变能有效解释50%以上的GPS垂直位移周年信号，GPS垂直位移时间序列包含的非构造形变中平均约29%来源于环境负载变化所引起的负荷形变。     

Modelling spatial variations in dissolved oxygen in fine‐grained streams under uncertainty

This paper presents a novel triple‐layer model, called VART DO‐3L, for simulation of spatial variations in dissolved oxygen (DO) in fine‐grained streams, characterized by a fluid mud (fluff or flocculent) layer (an advection‐dominated storage zone) as the interface between overlying stream water and relatively consolidated streambed sediment (a diffusion‐dominated storage zone). A global sensitivity analysis is conducted to investigate the sensitivity of VART DO‐3L model input parameters. Results of the sensitivity analysis indicate that the most sensitive parameter is the relative size of the advection‐dominated storage zones (A_s/A), followed by a lumped reaction term (R) for the flocculent layer, biological reaction rate (μ_o) in diffusive layer and biochemical oxygen demand concentration (L) in water column. In order to address uncertainty in model input parameters, Monte Carlo simulations are performed to sample parameter values and to produce various parameter combinations or cases. The VART DO‐3L model is applied to the Lower Amite River in Louisiana, USA, to simulate vertical and longitudinal variations in DO under the cases. In terms of longitudinal variation, the DO level decreases from 7.9 mg l at the Denham Springs station to about 2.89 mg l^?1 at the Port Vincent station. In terms of vertical variation, the DO level drops rapidly from the overlying water column to the advection‐dominated storage zone and further to the diffusive layer. The DO level (C_F) in the advective layer (flocculent layer) can reach as high as 40% of DO concentration (C) in the water column. The VART DO‐3L model may be applied to similar rivers for simulation of spatial variations in DO level. Copyright © 2014 John Wiley & Sons, Ltd.     

Inference and uncertainty of snow depth spatial distribution at the kilometre scale in the Colorado Rocky Mountains: the effects of sample size,random sampling,predictor quality,and validation procedures

Historically, observing snow depth over large areas has been difficult. When snow depth observations are sparse, regression models can be used to infer the snow depth over a given area. Data sparsity has also left many important questions about such inference unexamined. Improved inference, or estimation, of snow depth and its spatial distribution from a given set of observations can benefit a wide range of applications from water resource management, to ecological studies, to validation of satellite estimates of snow pack. The development of Light Detection and Ranging (LiDAR) technology has provided non‐sparse snow depth measurements, which we use in this study, to address fundamental questions about snow depth inference using both sparse and non‐sparse observations. For example, when are more data needed and when are data redundant? Results apply to both traditional and manual snow depth measurements and to LiDAR observations. Through sampling experiments on high‐resolution LiDAR snow depth observations at six separate 1.17‐km² sites in the Colorado Rocky Mountains, we provide novel perspectives on a variety of issues affecting the regression estimation of snow depth from sparse observations. We measure the effects of observation count, random selection of observations, quality of predictor variables, and cross‐validation procedures using three skill metrics: percent error in total snow volume, root mean squared error (RMSE), and R². Extremes of predictor quality are used to understand the range of its effect; how do predictors downloaded from internet perform against more accurate predictors measured by LiDAR? Whereas cross validation remains the only option for validating inference from sparse observations, in our experiments, the full set of LiDAR‐measured snow depths can be considered the ‘true’ spatial distribution and used to understand cross‐validation bias at the spatial scale of inference. We model at the 30‐m resolution of readily available predictors, which is a popular spatial resolution in the literature. Three regression models are also compared, and we briefly examine how sampling design affects model skill. Results quantify the primary dependence of each skill metric on observation count that ranges over three orders of magnitude, doubling at each step from 25 up to 3200. Whereas uncertainty (resulting from random selection of observations) in percent error of true total snow volume is typically well constrained by 100–200 observations, there is considerable uncertainty in the inferred spatial distribution (R²) even at medium observation counts (200–800). We show that percent error in total snow volume is not sensitive to predictor quality, although RMSE and R² (measures of spatial distribution) often depend critically on it. Inaccuracies of downloaded predictors (most often the vegetation predictors) can easily require a quadrupling of observation count to match RMSE and R² scores obtained by LiDAR‐measured predictors. Under cross validation, the RMSE and R² skill measures are consistently biased towards poorer results than their true validations. This is primarily a result of greater variance at the spatial scales of point observations used for cross validation than at the 30‐m resolution of the model. The magnitude of this bias depends on individual site characteristics, observation count (for our experimental design), and sampling design. Sampling designs that maximize independent information maximize cross‐validation bias but also maximize true R². The bagging tree model is found to generally outperform the other regression models in the study on several criteria. Finally, we discuss and recommend use of LiDAR in conjunction with regression modelling to advance understanding of snow depth spatial distribution at spatial scales of thousands of square kilometres. Copyright © 2012 John Wiley & Sons, Ltd.     

A new standardized Palmer drought index for hydro‐meteorological use

Accepting the concept of standardization introduced by the standardized precipitation index, similar methodologies have been developed to construct some other standardized drought indices such as the standardized precipitation evapotranspiration index (SPEI). In this study, the authors provided deep insight into the SPEI and recognized potential deficiencies/limitations in relating to the climatic water balance it used. By coupling another well‐known Palmer drought severity index (PDSI), we proposed a new standardized Palmer drought index (SPDI) through a moisture departure probabilistic approach, which allows multi‐scalar calculation for accurate temporal and spatial comparison of the hydro‐meteorological conditions of different locations. Using datasets of monthly precipitation, temperature and soil available water capacity, the moisture deficit/surplus was calculated at multiple temporal scales, and a couple of techniques were adopted to adjust corresponding time series to a generalized extreme value distribution out of several candidates. Results of the historical records (1900–2012) for diverse climates by multiple indices showed that the SPDI was highly consistent and correlated with the SPEI and self‐calibrated PDSI at most analysed time scales. Furthermore, a simple experiment of hypothetical temperature and/or precipitation change scenarios also verified the effectiveness of this newly derived SPDI in response to climate change impacts. Being more robust and preferable in spatial consistency and comparability as well as combining the simplicity of calculation with sufficient accounting of the physical nature of water supply and demand relating to droughts, the SPDI is promising to serve as a competent reference and an alternative for drought assessment and monitoring. Copyright © 2013 John Wiley & Sons, Ltd.     

The exponential decline in saturated hydraulic conductivity with depth: a novel method for exploring its effect on water flow paths and transit time distribution

The strong vertical gradient in soil and subsoil saturated hydraulic conductivity is characteristic feature of the hydrology of catchments. Despite the potential importance of these strong gradients, they have proven difficult to model using robust physically based schemes. This has hampered the testing of hypotheses about the implications of such vertical gradients for subsurface flow paths, residence times and transit time distribution. Here we present a general semi‐analytical solution for the simulation of 2D steady‐state saturated‐unsaturated flow in hillslopes with saturated hydraulic conductivity that declines exponentially with depth. The grid‐free solution satisfies mass balance exactly over the entire saturated and unsaturated zones. The new method provides continuous solutions for head, flow and velocity in both saturated and unsaturated zones without any interpolation process as is common in discrete numerical schemes. This solution efficiently generates flow pathlines and transit time distributions in hillslopes with the assumption of depth‐varying saturated hydraulic conductivity. The model outputs reveal the pronounced effect that changing the strength of the exponential decline in saturated hydraulic conductivity has on the flow pathlines, residence time and transit time distribution. This new steady‐state model may be useful to others for posing hypotheses about how different depth functions for hydraulic conductivity influence catchment hydrological response. Copyright © 2016 John Wiley & Sons, Ltd.     

Linking tracers,water age and conceptual models to identify dominant runoff processes in a sparsely monitored humid tropical catchment

Assessing catchment runoff response remains a key research frontier because of limitations in current observational techniques to fully characterize water source areas and transit times in diverse geographical environments. Here, we report a study that combines empirical data with modelling to identify dominant runoff processes in a sparsely monitored humid tropical catchment. The analysis integrated isotope tracers into conceptual rainfall–runoff models of varying complexity (from 5 to 11 calibrated parameters) that are able to simulate discharge and tracer concentrations and track the evolving age of stream water exiting the catchment. The model structures can be seen as competing hypotheses of catchment functioning and were simultaneously calibrated against uncertain streamflow gaugings and a 2‐year daily isotope rainfall–runoff record. Comparison of the models was facilitated using global parameter sensitivity analysis and the resulting effect on calibration. We show that a variety of tested model structures reproduced water and tracer dynamics in stream, but the simpler models failed to adequately reproduce both. The resulting water age distributions of the tested models varied significantly with little similarity between the stream water age and stored water age distributions. The sensitivity analysis revealed that only some of the more complex models (from eight parameters) could be better constrained to infer more plausible water age distributions and catchment storage estimates. These models indicated that the age of water stored in the catchment is generally older compared with the age of water fluxes, with evapotranspiration age being younger compared with streamflow. However, the water age distributions followed a similar temporal behaviour dominated by climatic seasonality. Stream water ages increased during the dry season (greater than 1 year) and decreased with increased streamflow (a few weeks old) during the wet season. We further show that the ratios of the streamwater age to stored water age distribution and the water age distribution of actual evapotranspiration to the stored water age distribution from constrained models could potentially serve as useful hydrological indicators of catchment functioning. Copyright © 2016 John Wiley & Sons, Ltd.     

Water mining from the deep critical zone by apple trees growing on loess

There have been significant recent advances in understanding the ecohydrology of deep soil. However, the links between root development and water usage in the deep critical zone remains poorly understood. To clarify the interaction between water use and root development in deep soil, we investigated soil water and root profiles beyond maximum rooting depth in five apple orchards planted on farmland with stand ages of 8, 11, 15, 18, and 22 years in a subhumid region on the Chinese Loess Plateau. Apple trees rooted progressively deeper for water with increasing stand age and reached 23.2 ± 0.8 m for the 22‐year‐old trees. Soil water deficit in deep soil increased with tree age and was 1,530 ± 43 mm for a stand age of 22 years. Measured root deepening rate was far great than the reported pore water velocity, which demonstrated that trees are mining resident old water. The deficits are not replenished during the life‐span of the orchard, showing a one‐way mining of the critical zone water. The one‐way root water mining may have changed the fine root profile from an exponential pattern in the 8‐year‐old orchard to a relative uniform distribution in older orchards. Our findings enhance our understanding of water‐root interaction in deep soil and reveal the unintended consequences of critical zone dewatering during the lifespan of apple trees.     

Size and spatial distribution of loess slides on the Chinese Loess Plateau

ABSTRACT

The size and spatial distribution of loess slides are important for estimating the yield of eroded materials and determining the landslide risk. While previous studies have investigated landslide size distributions, the spatial distribution pattern of landslides at different spatial scales is poorly understood. The results indicate that the loess slide distribution exhibits a power-law scaling across a range of the size distribution. The mean landslide size and size distribution in the different geomorphic types are different. The double Pareto and inverse gamma functions can coincide well with the empirical probability distribution of the loess slide areas and can quantitatively reveal the rollover location, maximum probability, and scaling exponents. The frequency of loess slides increases with mean monthly precipitation. Moreover, point distance analysis showed that > 80% of landslides are located < 3 km from other loess slides. We found that the loess slides at the two study sites (Zhidan and Luochuan County) in northern Shaanxi Province, China show a significant clustered distribution. Furthermore, analysis results of the correlated fractal dimension show that the landslides exhibit a dispersed distribution at smaller spatial scales and a clustered distribution at larger spatial scales.