Reinvestigation on mixing length in an open channel turbulent flow

The present study proposes a model on vertical distribution of streamwise velocity in an open channel turbulent flow through a newly proposed mixing length, which is derived for both clear water and sediment-laden turbulent flows. The analysis is based on a theoretical consideration which explores the effect of density stratification on the streamwise velocity profile. The derivation of mixing length makes use of the diffusion equation where both the sediment diffusivity and momentum diffusivity are taken as a function of height from the channel bed. The damping factor present in the mixing length of sediment-fluid mixture contains velocity and concentration gradients. This factor is capable of describing the dip-phenomenon of velocity distribution. From the existing experimental data of velocity, the mixing length data are calculated. The pattern shows that mixing length increases from bed to the dip-position, having a larger value at dip-position and then decreases up to the water surface with a zero value thereat. The present model agrees well with these data sets and this behavior cannot be described by any other existing model. Finally, the proposed mixing length model is applied to find the velocity distribution in wide and narrow open channels. The derived velocity distribution is compared with laboratory channel data of velocity, and the comparison shows good agreement.     

最大熵时域逆散射层析成像的研究

用最大熵求解二维时域逆散射问题的层析成像算法反演井间、ＶＳＰ和ＳＲＰ中的二维介质波速分布。首先给出时域散射场与介质扰动的关系式，然后，应用最大熵剑桥算法从所有满足时域散射数据的模型中挑选图像熵最大的模型作为反演结果，并给出了该算法的实现步骤。数值试验的结果表明，本文算法用于反演含噪声，不完全的时域波场数据时，十分有效。     

MORPHOLOGIC EQUATIONS BASED ON THE PRINCIPLE OF MAXIMUM ENTROPY

ＭＯＲＰＨＯＬＯＧＩＣＥＱＵＡＴＩＯＮＳＢＡＳＥＤＯＮＴＨＥＰＲＩＮＣＩＰＬＥＯＦＭＡＸＩＭＵＭＥＮＴＲＯＰＹＤＥＮＧＺｈｉｑｉａｎｇ；ＺＨＡＮＧＫａｉｑｕａｎＡｂｓｔｒａｃｔ：Ｔｈｅｐｒｉｎｃｉｐｌｅｏｆｍａｘｉｍｕｍｅｎｔｒｏｐｙｉｓｕｓｅｄｔｏ...     

Entropy-based parameter estimation for extended Burr XII distribution

Two entropy-based methods, called ordinary entropy (ENT) method and parameter space expansion method (PSEM), both based on the principle of maximum entropy, are applied for estimating parameters of the extended Burr XII distribution. With the parameters so estimated, the Burr XII distribution is applied to six peak flow datasets and quantiles (discharges) corresponding to different return periods are computed. These two entropy methods are compared with the methods of moments (MOM), probability weighted moments (PWM) and maximum likelihood estimation (MLE). It is shown that PSEM yields the same quantiles as does MLE for discrete cases, while ENT is found comparable to the MOM and PWM. For shorter return periods (<10–30 years), quantiles (discharges) estimated by these four methods are in close agreement, but the differences amongst them grow as the return period increases. The error in quantiles computed using the four methods becomes larger for return periods greater than 10–30 years.     

An analysis of shear stress distribution in circular channels with sediment deposition based on Gene Expression Programming

Knowledge of the boundary shear stress distribution in channels is important because it is a key factor affecting on erosion and sedimentation rates. The presence of sediment deposits in sewers is often reported during operation, and circular channels are frequently used in sewer networks. Gene expression programming(GEP) is applied in this study to determine an equation for evaluating the shear stress distribution along the wetted perimeter of a circular channel with a flat bed, because of the presence of sediment on the bed. In view of the parameters affecting the shear stress distribution, five dimensionless parameters are applied to develop six GEP models to be used with 905 experimental data. The impact of the shear stress parameters is studied using the six GEP models and by dividing the wetted perimeter into wall and bed sections. Two equations are extracted from the GEP models' output to estimate wall and bed shear stresses. The best model results are compared with a well-known equation based on the entropy concept. The GEP model predictions of wall and bed shear stresses are very similar to the experimental outcomes, whereas the entropy-based model overestimates the shear stress distribution.The proposed GEP models demonstrate superior performance in estimating the shear stress distribution with a mean absolute percentage error(MAPE) of 3.79% compared to an existing equation with MAPE of 9.52%.     

Computational aspects in use of entropy theory in predicting water quality levels at discontinued stations

The computational aspects of using a new, entropy-based, theory to predict water quality values at discontinued water quality monitoring stations are discussed. The main computational issues addressed are the level of discretization used in converting the continuous probability distribution of water quality values to the discrete levels required for the entropy function, and the choice of the interval of time for which to assign the value of the water quality (period of time averaging) through the entropy function. Unlike most cases of entropy applications involving discretization of continuous functions the results of using entropy theory to predict water quality values at discontinued monitoring stations in this application appear to be insensitive to the choice of the level of discretization even down to the very coarse level discretization associated with only eight intervals. However, depending on the length of record available the choice of the time interval for which the water quality values are assigned (period for time averaging) appear to have a significant impact on the accuracy of the results.     

THE USE OF ENTROPY IN HYDROLOGY AND WATER RESOURCES

Since the development of the entropy theory by Shannon in the late 1940s and of the principle of maximum entropy (POME) by Jaynes in the late 1950s there has been a proliferation of applications of entropy in a wide spectrum of areas, including hydrological and environmental sciences. The real impetus to entropy-based hydrological modelling was provided by Amorocho and Espildora in 1972. A great variety of entropy applications in hydrology and water resources have since been reported, and new applications continue to unfold. This paper reviews the recent contributions on entropy applications in hydrology and water resources, discusses the usefulness and versatility of the entropy concept, and reflects on the strengths and limitations of this concept. The paper concludes with comments on its implications in developing countries. © 1997 by John Wiley & Sons, Ltd.     

MAXIMUM INFORMATION ENTROPY THEORY OF EFFLUENT BAND IN OPEN CHANNEL UNIFORM FLOW

ＭＡＸＩＭＵＭＩＮＦＯＲＭＡＴＩＯＮＥＮＴＲＯＰＹＴＨＥＯＲＹＯＦＥＦＦＬＵＥＮＴＢＡＮＤＩＮＯＰＥＮＣＨＡＮＮＥＬＵＮＩＦＯＲＭＦＬＯＷＫｅＺｈｏｎｇＨＵＡＮＧ１ａｎｄＴａｏＪＩＡＮＧ２ＡＢＳＴＲＡＣＴＴｈｅｐｒｉｎｃｉｐｌｅｏｆｍａｘｉｍｕｍ...     

Comparison between Shannon and Tsallis entropies for prediction of shear stress distribution in open channels

The concept of Tsallis entropy was applied to model the probability distribution functions for the shear stress magnitudes in circular channels (with filling ratios of 0.506, 0.666, 0.826), circular with flat bed (filling ratios of 0.333, 0.666), rectangular channel (1.34, 2, 3.94, 7.37 aspect ratios) and compound channel (with relative depths of 0.324, 0.46). The equation for the shear stress distribution was obtained according to the entropy maximization principle, and is able to estimate the shear stress distribution as much on the walls as the channel bed. The approach is also compared with the predictions obtained based on the Shannon entropy concept. By comparing the two prediction models, this study highlights the application of Tsallis entropy to estimate the shear stress distribution of open channels. Although the results of the two models are similar in the circular cross-section, the differences between them are more significant in circular with flat bed and rectangular channels. For a wide range of filling ratio values, experimental data are used to illustrate the accuracy and reliability of the proposed model.     

基于时频稀疏性分析法的低信噪比微震事件识别与恢复

微震监测是直观评价压裂过程和压裂效果的有效手段.微震事件识别是微震监测的首要步骤.然而对于低信噪比微震监测数据,常规识别方法很难取得满意效果.基于微震事件在时频域中的稀疏性,本文提出利用Renyi熵值表示微震监测数据的时频稀疏程度,并以时频距离为约束条件,建立以低熵值的道数为判别阈值的目标函数.本文方法能在识别出微震事件的同时,恢复出较为清晰的微震事件.通过数值计算和对实际监测数据的测试,表明该方法对低信噪比的微震监测数据有较好的处理效果.     

At‐a‐station hydraulic geometry relations, 1: theoretical development

This paper, the first of two, hypothesizes that: (1) the temporal variation of stream power of a river channel at a given station with varying discharge is accomplished by the temporal variation in channel form (flow depth and channel width) and hydraulic variables, including energy slope, flow velocity and friction; (2) the change in stream power is distributed among the changes in flow depth, channel width, flow velocity, slope, and friction, depending on the boundary conditions that the channels has to satisfy. The second hypothesis is a result of the principle of maximum entropy and the theory of minimum energy dissipation or its simplified minimum stream power. These two hypotheses lead to families of at‐a‐station hydraulic geometry relations. The conditions under which these families of relations can occur in the field are discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

The uncertainty of the Shannon entropy model for shear stress distribution in circular channels

The shear stress distribution at alluvial stream beds and banks is one of the essential parameters in channel stability analysis.In the current paper,a novel uncertainty analysis method based on the framework of a Bayesian Forecasting System(BFS) is presented to evaluate the Shannon entropy model for prediction of the shear stress distribution in both circular rigid-bed and alluvial-bed channels.The Johnson and Box-Cox transformation functions were applied to select the optimum sample size(SS) and corresponding transformation factor for determining a 95% confidence bound(CB) for the Shannon entropy model.The Shapiro-Wilk(SW) test is applied according to the SS used to evaluate the power of transformation functions in the data normalization.The results show that the error distribution between predicted and experimental shear stress values generated using the Box-Cox transformation is closer to a Gaussian distribution than the generated using the Johnson transformation.The indexes of the percentage of the experimental values within the CB(N_(in)) and Forecast Range Error Estimate(FREE) are applied for the uncertainty analyses.The lower values of FREE equal to 1.724 in the circular rigid-bed channel represent the low uncertainty of Shannon entropy in the prediction of shear stress values compared to the uncertainty for the circular alluvial-bed channel with a FREE value equal to 7.647.     

ON THE VERTICAL DISTRIBUTION OF SUSPENDED SEDIMENT CONCENTRATION

The problem of sediment concentration distribution in a vertical for channel and pipe flows is studied in this paper. Considering the variation of the vertical component of the fluctuation velocity v as an independent variable, two types of sediment concentration distribution can be derived. However, only one type of distribution is commonly quoted while the other one rarely reported. In this paper explanation for such phenomena is given and conditions for the occurrence of both types are also discussed.     

Analysis of frequency shifting in seismic signals using Gabor-Wigner transform

A hybrid time-frequency method known as Gabor-Wigner transform(GWT) is introduced in this paper for examining the time-frequency patterns of earthquake damaged buildings. GWT is developed by combining the Gabor transform(GT) and Wigner-Ville distribution(WVD). GT and WVD have been used separately on synthetic and recorded earthquake data to identify frequency shifting due to earthquake damages, but GT is prone to windowing effect and WVD involves ambiguity function. Hence to obtain better clarity and to remove the cross terms(frequency interference), GT and WVD are judiciously combined and the resultant GWT used to identify frequency shifting. Synthetic seismic response of an instrumented building and real-time earthquake data recorded on the building were investigated using GWT. It is found that GWT offers good accuracy for even slow variations in frequency, good time-frequency resolution, and localized response. Presented results confirm the efficacy of GWT when compared with GT and WVD used separately. Simulation results were quantified by the Renyi entropy measures and GWT shown to be an adequate technique in identifying localized response for structural damage detection.     

HTI煤层介质槽波波场与频散特征初步研究

煤层内裂隙较为发育,具有明显的各向异性.目前槽波理论研究以各向同性介质为主,对HTI介质中槽波及其频散性质研究很少.本文以弱各向异性、含垂直裂隙HTI煤层介质为研究对象,研究了HTI煤层介质中的三维槽波波场,采用交错网格高阶有限差分法模拟槽波,推导了三层水平层状HTI煤层介质的Love型槽波理论频散公式和振幅深度分布,分析了HTI各弹性参数对频散曲线的影响.HTI介质和各向同性介质基阶Love槽波频散曲线差异较小,高阶较大;煤厚主要影响Airy相频率,而Airy相速度不变;煤层vs对Airy相速度影响很大;煤层γ对基阶Love槽波影响很小,高阶稍大.各波偏振方向不再与波的传播方向平行或垂直,而是呈一定夹角.利用基阶Love槽波频散曲线推测裂隙发育较为困难,可利用高阶频散曲线.     

Entropy-based correlated shrinkage of spatial random processes

This paper proposes a two-stage correlated non-linear shrinkage estimation methodology for spatial random processes. A block hard thresholding design, based on Shannon’s entropy, is formulated in the first stage. The thresholding design is adaptive to each resolution level, because it depends on the empirical distribution function of the mutual information ratios between empirical wavelet blocks and the random variables of interest, at each scale. In the second stage, a global correlated (inter- and intra-scale) shrinkage is applied to approximate the values of interest of the underlying spatial process. Additionally, a simulation study is developed, in the Gaussian context, to analyze the sensitivity, measured by empirical stochastic ordering, of the entropy-based block hard thresholding stage in relation to the parameters characterizing local variability (fractality) and dependence range of the spatial process of interest, the noise level, and the design of the region of interest.     

共反射面道集偏移速度建模

共反射面（CRS）叠加是一种与宏观速度模型无关，仅依赖于近地表速度的地震成像方法．其通过地震三参数的优化实现地震成像．本文推导了基于CRS叠加得出的优化三参数与偏移速度之间的解析关系，提出了在CRS道集通过优化三参数实现速度估计的CRS道集偏移速度建模方法．模型试算表明，这种速度建模方法效率较高，速度分析精度取决于优化三参数的精度，适于较复杂地质体的速度建模．      

Numerical Modeling of Ice Fog in Interior Alaska Using the Weather Research and Forecasting Model

An ice microphysics parameterization scheme has been modified to better describe and understand ice fog formation. The modeling effort is based on observations in the Sub-Arctic Region of Interior Alaska, where ice fog occurs frequently during the cold season due to abundant water vapor sources and strong inversions existing near the surface at extremely low air temperatures. The microphysical characteristics of ice fog are different from those of other ice clouds, implying that the microphysical processes of ice should be changed in order to generate ice fog particles. Ice fog microphysical characteristics were derived with the NCAR Video Ice Particle Sampler during strong ice fog cases in the vicinity of Fairbanks, Alaska, in January and February 2012. To improve the prediction of ice fog in the Weather Research and Forecasting model, observational data were used to change particle size distribution properties and gravitational settling rates, as well as to implement a homogeneous freezing process. The newly implemented homogeneous freezing process compliments the existing heterogeneous freezing scheme and generates a higher number concentration of ice crystals than the original Thompson scheme. The size distribution of ice crystals is changed into a Gamma distribution with the shape factor of 2.0, using the observed size distribution. Furthermore, gravitational settling rates are reduced for the ice crystals since the crystals in ice fog do not precipitate in a similar manner when compared to the ice crystals of cirrus clouds. The slow terminal velocity plays a role in increasing the time scale for the ice crystals to settle to the surface. Sensitivity tests contribute to understanding the effects of water vapor emissions as an anthropogenic source on the formation of ice fog.     

Migration velocity modeling based on common reflection surface gather

The common-reflection-surface (CRS) stacking is a new seismic imaging method, which only depends on seismic three parameters and near-surface velocity instead of macro-velocity model. According to optimized three parameters obtained by CRS stacking, we derived an analytical relationship between three parameters and migration velocity field, and put forward CRS gather migration velocity modeling method, which realize velocity estimation by optimizing three parameters in CRS gather. The test of a sag model proved that this method is more effective and adaptable for velocity modeling of a complex geological body, and the accuracy of velocity analysis depends on the precision of optimized three parameters.