Testing bedload transport equations with consideration of time scales

Bedload transport is known to be a highly fluctuating temporal phenomenon, even under constant (mean) flow conditions, as a consequence of stochasticity, bedform migration, grain sorting, hysteresis, or sediment supply limitation. Because bedload transport formulas usually refer to a single mean transport value for a given flow condition, one can expect that prediction accuracy (when compared to measurements) will depend on the amplitude and duration of fluctuations, which in turn depend on the time scale used for observations. This paper aims to identify how the time scale considered can affect bedload prediction. This was done by testing 16 common bedload transport formulas with four data sets corresponding to different measurement period durations: (i) highly fluctuating (quasi‐)instantaneous field measurements; (ii) volumes accumulated at the event scale on two small alpine gravel‐bed rivers, potentially affected by seasonal fluctuations; (iii) volumes accumulated at the interannual scale in a meandering gravel bed river, thought to be weakly subject to fluctuations; (iv) time‐integrated flume measurements with nearly uniform sediments. The tests confirmed that the longer the measurement period, the better the precision of the formula's prediction interval. They also demonstrate several consequential limitations. Most threshold formulas are no longer valid when the flow condition is below two times the threshold condition for the largest elements' motion on the bed surface (considering D₈₄). In such conditions, equations either predict zero transport, or largely overestimate the real transport, especially when D₈₄ is high. There is a need for new sediment data collected with highly reliable techniques such as recording slot bedload samplers to further investigate this topic. Copyright © 2012 John Wiley & Sons, Ltd.     

Improved estimators of correlation and R2 for skewed hydrologic data

ABSTRACT

The coefficient of determination R² and Pearson correlation coefficient ρ = R are standard metrics in hydrology for the evaluation of the goodness of fit between model simulations and observations, and as measures of the degree of dependence of one variable upon another. We show that the standard product moment estimator of ρ, termed r, while well-behaved for bivariate normal data, is upward biased and highly variable for bivariate non-normal data. We introduce three alternative estimators of ρ which are nearly unbiased and exhibit much less variability than r for non-normal data. We also document remarkable upward bias and tremendous increases in variability associated with r using both synthetic data and daily streamflow simulations from 905 calibrated rainfall–runoff models. We show that estimators of ρ = R accounting for skewness are needed for daily streamflow series because they exhibit high variability and skewness compared to, for example, monthly/annual series, where r should perform well.     

Spatial scale effect on the upper soil effective parameters of a distributed hydrological model

Nonlinear dynamics and spatial variability in hydrological systems make the formulation of scaling theories difficult. Therefore, the development of knowledge related to scale effects, scaling techniques, parameterization and linkages of parameters across scales is highly relevant. The main purpose of this work is to analyse the spatial effect of the static storage capacity parameter H_u and the saturated hydraulic conductivity parameter k_s from microscale (sub‐grid level) to mesoscale (grid level) and its implication to the definition of an optimum cell size. These two parameters describe the upper soil water characteristics in the infiltration process conceptualization of the TETIS hydrological model. At microscale, the spatial heterogeneity of H_u and k_s was obtained generating random parameter fields through probability distribution functions and a spatial dependence model with pre‐established correlation lengths. The effective parameters at mesoscale were calculated by solving the inverse problem for each parameter field. Results indicate that the adopted inverse formulation allows transferring the nonlinearity of the system from microscale to the mesoscale via non‐stationary effective parameters. Their values at each cell and time step are in the range of zero to the mean value of the parameter at microscale. The stochastic simulations showed that the variance of the estimated effective parameters decreases when the ratio between mesoscale cell size and correlation length at microscale increases. For a ratio greater than 1, we found cell sizes having the characteristics of a representative elementary area (REA); in such case, the microscale variability pattern did not affect the system response at mesoscale. Copyright © 2011 John Wiley & Sons, Ltd.     

基于多模型的西宁市人口规模预测

人口是反映国情、国力基本情况的重要指标,是区域研究所必须考虑的重要因素之一。合理、准确地预测城市人口规模,是城市与区域规划中首先要考虑的基本问题,也是保证规划科学性与可实施性的关键性前提。以西宁市2000-2011年历年总人口为样本数据,分别构建了一元线性回归模型、马尔萨斯模型、logistic模型及GM（1,1）模型,并进行模型检验。结果表明：（1）模型均通过模型精度检验且精度较高,GM（1,1）模型拟合度最高,均误差达到0.004%,马尔萨斯模型拟合度最低,为-1.440 8%;（2）分析模型预测精度差异产生原因及适用性,表明深入、准确地分析样本数据特征,恰当选择分析方法对于控制人口预测精度尤为重要。由于西宁市2000-2011年人口样本数据在2005及2009年数据存在波动性,破坏了其与一元线性回归模型及马尔萨斯模型的拟合度,导致在4种模型中,Logistic及GM（1,1）模型预测精度较高,而GM（1,1）模预测精度最高,所以采用GM（1,1）模型进行西宁市人口预测,得到西宁市人口预测的最终结果：2012年西宁市总人口将达到225.89×10⁴人,2015年将达到233.39×10⁴人,2020年将达到246.37×10⁴人。从结果看,未来9 a西宁市人口将呈现持续平稳增长的态势,但随着时间推进人口增长速度将逐渐下降。     

中国天山山区235 a气候变化及降水趋势预测

  利用4个降水重建序列与天山山区10个气象站降水变化的响应关系,重建了天山山区近235 a来气候变化的年降水序列,重建序列的方差解释量达到47.7%。对过去235 a天山山区气候变化中降水变化的特征分析发现：降水大致经历了7干7湿的变化阶段,其中偏湿年份为124 a,多于偏干年份;天山山区的降水量以2.1 a、3.0 a、5.8 a、6.0 a的高频变化和24~25 a的低频变化周期最为显著。研究表明,近百年天山山区气候变化中的降水变化分为两个阶段,20世纪初到80年代,降水量逐渐减少,导致冰川退缩、河流径流量减少、湖泊萎缩、沙漠面积增大、植被覆盖率减少;80年代后期至今,降水量迅速增加,导致河川径流量增加、湖泊面积增大和沙尘暴日数减少,生态环境趋于好转,但同时造成洪水和地质灾害频繁。采用基于方差分析的周期叠加方法对天山山区未来23 a气候变化中降水的演变趋势进行预测,结果表明：未来23 a气候变化中天山山区以湿润为主,期间有部分年份可能较常年干旱。     

云南近50 年来的气候变化

利用1961—2008 年云南省124 站及其相邻省市区的37 个地面站的逐日平均气温、降水量资料,客观分析了考虑气温垂直递减率的气温细网格数据。在此基础上,分析研究了云南近50 年来的气候变化。(1)云南近50 年来的气温变化,趋势上与北半球和全国一致,但气候变暖的速率相对缓慢;(2) 云南气候带面积有明显变化,北热带和南亚热带面积增加,而中亚热带、北亚热带和温带的面积减少;(3) 云南冬季是气温上升幅度最大的季节,然后依次是秋季、夏季和春季,虽然近50 年来云南大部分区域气温呈上升趋势,但少数区域气温却呈下降趋势,这些降温区主要集中在低海拔河谷地区;(4) 云南近50 年来降水量年平均变化不大,但季节和空间分布的变化却比较明显,雨季和主汛期降水量呈下降趋势,干季呈上升趋势;在空间分布上,滇东地区呈一致性下降趋势,滇中呈一致性上升趋势;滇西和滇南地区降水量的增减趋势呈交错分布。      

The trend on runoff variations in the Lhasa River Basin

Taking the Lhasa River Basin above Lhasa hydrological station in Tibetan Plateau as a study area, the characteristics of the annual and monthly mean runoff during 1956?2003 were analyzed, based on the hydro-data of the two hydrological stations (Lhasa and Tanggya) and the meteorological data of the three meteorological stations (Damxung, Lhasa and Tanggya). The trends and the change points of runoff and climate from 1956 to 2003 were detected using the nonparametric Mann-Kendall test and Pettitt-Mann-Whitney change-point statistics. The correlations between runoff and climate change were analyzed using multiple linear regression. The major results could be summarized as follows: (1) The annual mean runoff during the last 50 years is characterized by a great fluctuation and a positive trend with two change points (around 1970 and the early 1980s), after which the runoff tended to in-crease and was increasing intensively in the last 20 years. Besides, the monthly mean runoff with a positive trend is centralized in winter half-year (November to April) and some other months (May, July and September). (2) The trends of the climate change in the study area are generally consistent with the trend of the runoff, but the leading climate factors which aroused the runoff variation are distinct. Precipitation is the dominant factor influencing the annual and monthly mean runoff in summer half year, while temperature is the primary factor in winter season.     

Numerical modelling of rise and fall of a dense layer in salt diapirs

Numerical models are used to study the entrainment of a dense anhydrite layer by a diapir. The anhydrite layer is initially horizontally embedded within a viscous salt layer. The diapir is down-built by aggradation of non-Newtonian sediments ( n = 4, constant temperature) placed on the top of the salt layer. Several parameters (sedimentation rate, salt viscosity, perturbation width and stratigraphic position of the anhydrite layer) are studied systematically to understand their role in governing the entrainment of the anhydrite layer. High sedimentation rates during the early stages of the diapir evolution bury the initial perturbation and, thus, no diapir forms. The anhydrite layer sinks within the buried salt layer. For the same sedimentation rate, increasing viscosity of the salt layer decreases the rise rate of the diapir and reduces the amount (volume) of the anhydrite layer transported into the diapir. Model results show that viscous salt is capable of carrying separate blocks of the anhydrite layer to relatively higher stratigraphic levels. Varying the width of the initial perturbation (in our calculations 400–800 m), from which a diapir triggers, shows that wider diapirs can more easily entrain an embedded anhydrite layer than the narrower diapirs. The anhydrite layer is entrained as long as rise rate of the diapir exceeds the descent rate of the denser anhydrite layer. We conclude that the four parameters mentioned above govern the ability of a salt diapir to entrain an embedded dense layer. However, the model results show that the entrained blocks inevitably sink back if the rise rate of the diapir is less than the rate of descent of the anhydrite layer or the diapir is permanently covered by a stiff overburden in case of high sedimentation rates.     

Thin elastic shells with variable thickness for lithospheric flexure of one-plate planets

Planetary topography can either be modelled as a load supported by the lithosphere, or as a dynamic effect due to lithospheric flexure caused by mantle convection. In both cases the response of the lithosphere to external forces can be calculated with the theory of thin elastic plates or shells. On one-plate planets the spherical geometry of the lithospheric shell plays an important role in the flexure mechanism. So far the equations governing the deformations and stresses of a spherical shell have only been derived under the assumption of a shell of constant thickness. However, local studies of gravity and topography data suggest large variations in the thickness of the lithosphere. In this paper, we obtain the scalar flexure equations governing the deformations of a thin spherical shell with variable thickness or variable Young's modulus. The resulting equations can be solved in succession, except for a system of two simultaneous equations, the solutions of which are the transverse deflection and an associated stress function. In order to include bottom loading generated by mantle convection, we extend the method of stress functions to include loads with a toroidal tangential component. We further show that toroidal tangential displacement always occurs if the shell thickness varies, even in the absence of toroidal loads. We finally prove that the degree-one harmonic components of the transverse deflection and of the toroidal tangential displacement are independent of the elastic properties of the shell and are associated with translational and rotational freedom. While being constrained by the static assumption, degree-one loads can deform the shell and generate stresses. The flexure equations for a shell of variable thickness are useful not only for the prediction of the gravity signal in local admittance studies, but also for the construction of stress maps in tectonic analysis.