EFFECTS OF TIME STEP SIZE IN IMPLICIT DYNAMIC ROUTING1

ABSTRACT The effects of the size of the Δt time step used in the integration of the implicit difference equations of unsteady open-channel flow are determined for numerous typical hydrographs with durations in the order of days or even weeks. Truncation errors related to the size of the Δt time step cause a numerical distortion (dispersion and attenuation) of the computed transient. The magnitude of the distortion is related directly to the size of the time step, the length of channel reach, and the channel resistance and inversely to the time of rise of the hydrograph. The type of finite difference expression which replaces spatial derivatives and non-derivative terms in the partial differential equations of unsteady flow has an important influence on the magnitude of the numerical distortion, as well as the numerical stability of the implicit difference equations. Time step sizes in the range of 3 to 6 hrs generally tend to minimize the combination of required computation time and numerical distortion of transients having a time of rise of the order of several days.     

NONLINEAR DUPUIT EQUATIONS FOR THE PHREATIC SURFACE OF A SEMI-INFINITE AQUIFER1

ABSTRACT. We present a new approach to the nonlinear equations for the phreatic surface of groundwater flow from or into a reservoir. The differential equation is converted into an equivalent integral equation, which is then solved by a method of iteration. We obtain exact results for both drawdown and infiltration, including the special case of groundwater penetration into dry soil.     

Sedimentary radioactive tracers and diffusive models

This paper examines the underlying assumptions and consequences of applying a steady-state equation to sediment profiles of radioactive tracers in order to deconvolute sedimentation from bioturbation processes modelled as a diffusive type process.Several factors follow immediately from this investigation:

(i)

if the observed radioactive concentration increases with depth over any finite depth range then the proposed steady-state, constant flux equation is not applicable. Any increase in radioactive concentration with depth implies a negative mixing coefficient which is a physical impossibility;

(ii)

when the radioactive concentration systematically decreases with increasing sedimentary depth then solutions to the steady-state conservation equation exist only when either the constant solid state flux to the sediment surface is small enough so that a positive mixing coefficient results or when the mixing coefficient is small enough so that a positive flux results.

If the radioactive concentration, porosity and/or density of the solid phase are such that the proposed equation is inappropriate (because no physically acceptable solution exists) then one must abandon the proposed steady-state equation.Further: if the flux of solid sediment to the sediment surface varies with time then, of course, a steady-state conservation equation is also inappropriate.Simple examples illustrate that the assumption of steady-state restricts the applicability of this modelling approach to a relatively small sub-set of expected situations in the real world.     

Emergy algebra: Improving matrix methods for calculating transformities

Transformity is one of the core concepts in Energy Systems Theory and it is fundamental to the calculation of emergy. Accurate evaluation of transformities and other emergy per unit values is essential for the broad acceptance, application and further development of emergy methods. Since the rules for the calculation of emergy are different from those for energy, particular calculation methods and models have been developed for use in the emergy analysis of networks, but double counting errors still occur because of errors in applying these rules when estimating the emergies of feedbacks and co-products. In this paper, configurations of network energy flows were classified into seven types based on commonly occurring combinations of feedbacks, splits, and co-products. A method of structuring the network equations for each type using the rules of emergy algebra, which we called “preconditioning” prior to calculating transformities, was developed to avoid double counting errors in determining the emergy basis for energy flows in the network. The results obtained from previous approaches, the Track Summing Method, the Minimum Eigenvalue Model and the Linear Optimization Model, were reviewed in detail by evaluating a hypothetical system, which included several types of interactions and two inputs. A Matrix Model was introduced to simplify the calculation of transformities and it was also tested using the same hypothetical system. In addition, the Matrix Model was applied to two real case studies, which previously had been analyzed using the existing method and models. Comparison of the three case studies showed that if the preconditioning step to structure the equations was missing, double counting would lead to large errors in the transformity estimates, up to 275 percent for complex flows with feedback and co-product interactions. After preconditioning, the same results were obtained from all methods and models. The Matrix Model reduces the complexity of the Track Summing Method for the analysis of complex systems, and offers a more direct and understandable link between the network diagram and the matrix algebra, compared with the Minimum Eigenvalue Model or the Linear Optimization Model.     

沙尘暴对暴露儿童健康效应的研究

为了研究沙尘暴对儿童可能造成的急性危害,以沙尘暴源区——甘肃省武威市的某2所小学3～5年级的1040名学生(年龄8～14岁)为研究对象,在2004年和2005年的3～5月沙尘暴频发期间进行健康状况问卷调查,共调查4场沙尘暴事件,所调查的症状有咳嗽、咯痰、气短、肺部喘鸣、胸部憋闷、咽干口苦、眼睛干涩、流泪、流涕、打喷嚏、心情压抑等11种常见的症状.结果表明,沙尘暴发生当天(滞后0d)儿童各种所查症状发生的相对危险度(RR)均有不同程度地升高,沙尘暴过后(滞后1～5d),儿童各种症状的RR逐渐降低,沙尘暴过后4d(滞后4d),几乎所有症状均恢复正常.暴露儿童在沙尘暴发生当天,除肺部喘鸣和胸部憋闷发生的RR升高不显著外(p>0.05),其他所查症状发生的RR均有显著性升高(p<0.05,p<0.01,p<0.001).沙尘暴过后虽然各种症状RR均有所下降,但下降速度不同:在滞后1～2d,气短、眼睛干涩、流泪和心情压抑等4种症状RR仍显著高于沙尘暴前,直到滞后3d才恢复到正常水平;而咳嗽、咯痰、咽干口苦和打喷嚏等4种症状RR在滞后4d才恢复正常;流涕症状RR在滞后5d才基本恢复正常.不同年度和不同时期的沙尘暴事件对儿童健康症状的影响有所不同.从以上结果可以看出:沙尘暴对儿童的健康既有当日急性效应又有一定的短期滞后效应.     

新型高阶Boussinesq方程的一维数值模型及其实验验证

基于刘忠波等(2004)推导的新型高阶Boussinesq方程,建立了预报-校正差分格式的数值模型。为考察该数值模型的适用性,针对较大坡度的潜堤上的波浪传播变形进行了数值研究。将数值结果与实验结果进行比较,二者较为吻合,验证了本文的数值模型,同时也说明本方程可用于模拟较陡地形的波浪变形。     

Implications of network particle tracking (NPT) for ecological model interpretation

Network particle tracking (NPT), building on the foundation of network environ analysis (NEA), is a new development in the definition of coherence relations within and between connected systems. This paper evaluates three ecosystem models in a comparison of throughflow- and storage-based NEA and NPT. Compartments in models with high indirect effects and Finn cycling showed low correlation of NEA storage and throughflow with particle repeat visits and numbers of particles in compartments at steady state. Conversely, the correlation between NEA and NPT results was high with two models having lower indirect effects and Finn cycling. Analysis of ecological orientors associated with NEA showed NPT to fully support conventional NEA results when the common conditions of donor control and steady state are satisfied. Particle trajectories are recorded in the new concept of a particle “passport”. Ability to track and record particle in-system histories enables views of multiple scales and opens the possibility of making pathway-dependent modeling decisions. NPT may also enable modeling of time, allowing integration of Newtonian, organismal and stochastic modeling perspectives in a single comprehensive analysis.     

Robust benchmark dose determination based on profile score methods

We investigate several methods commonly used to obtain a benchmark dose and show that those based on full likelihood or profile likelihood methods might have severe shortcomings. We propose two new profile likelihood-based approaches which overcome these problems. Another contribution is the extension of the benchmark dose determination to non full likelihood models, such as quasi-likelihood, generalized estimating equations, which are widely used in settings such as developmental toxicity where clustered data are encountered. This widening of the scope of application is possible by the use of (robust) score statistics. Benchmark dose methods are applied to a data set from a developmental toxicity study.