Boundary curves for families of planar orbits

For monoparametric familiesf(x,y)=c of planar orbits, created by a planar potentialV(x,y), we introduce the notion of the family boundary curves (FBC). All members of the familyf(x,y)=c are traced in an allowable region of thexy plane, defined by the corresponding FBC, with total energyE=E(c) varying along the family. Family boundary curves are also found for two-parametric familiesf(x,y,b)=c. The relation of equilibrium points and asymptotic orbits, possibly possessed by the potentialV(x,y), to be FBC is studied.     

Inverse reconstructions of ecosystem flows in investigating regime shifts: impact of the choice of objective function

Inverse analysis is increasingly used in ecosystem modelling to objectively reconstruct a large number of unknown flows or interactions from a small number of observations. This type of analysis may be useful in relating observed regime shifts in ecosystem structure to underlying processes. Inversions of ecosystem flow networks currently use a constrained least-squares solution which at the same time minimizes the squared norm (the sum of squares) of the reconstructed flows. This minimum norm (MN) inversion is thought to be a parsimonious solution to the ecosystem flow inverse problem, but it may well not reflect how ecosystems are organised. It has been proposed instead that ecosystems evolve to maximize energy/mass flows or that they maximize the information content of the network weighted by ecosystem flows (ascendancy). We used simulated inverse experiments, where inverse analyses are applied to simulations of flow networks, to explore objective functions different than the MN generally used. We could not compute inverse solutions that maximize ascendancy because the objective function is unbounded. We could calculate inversions that maximize flows; however, these generally overestimated the simulated flows, even though the simulations were designed to maximize flows. It appears that the ecosystem flow inverse problem is too under-determined (too few data relative to the number of unknowns) to allow the use of these maximizing goal functions. We introduce a new minimization that simultaneously minimizes the squared flows and the squared differences between flows. This smoothing minimization makes the inverse flows as even as possible and it helps with some technical issues with MN inversions. The simulated inverse experiments indicated that this smoothed norm (SM) is the most robust in comparative analyses of contrasting ecosystem states, such as those that can be associated with regime shifts. Like the MN inversion, the SM inversion has no ecological basis. However, it is a conservative norm that is less likely to produce false differences between the dynamics of regimes.     

Uncertainty as the overlap of alternate conditional distributions

An important task in modern geostatistics is the assessment and quantification of resource and reserve uncertainty. This uncertainty is valuable support information for many management decisions. Uncertainty at specific locations and uncertainty in the global resource is of interest. There are many different methods to build models of uncertainty, including Kriging, Cokriging, and Inverse Distance. Each method leads to different results. A method is proposed to combine local uncertainties predicted by different models to obtain a combined measure of uncertainty that combines good features of each alternative. The new estimator is the overlap of alternate conditional distributions.     

Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.     

On Szebehely's problem for holonomic systems involving generalized potential functions

We consider the problem of finding the generalized potential function V = U _i(q ¹, q ²,..., q ⁿ)q ⁱ + U(q ¹, q ²,...;q ⁿ) compatible with prescribed dynamical trajectories of a holonomic system. We obtain conditions necessary for the existence of solutions to the problem: these can be cast into a system of n – 1 first order nonlinear partial differential equations in the unknown functions U ₁, U ₂,...;, U _n, U. In particular we study dynamical systems with two degrees of freedom. Using adapted coordinates on the configuration manifold M ₂ we obtain, for potential function U(q ¹, q ²), a classic first kind of Abel ordinary differential equation. Moreover, we show that, in special cases of dynamical interest, such an equation can be solved by quadrature. In particular we establish, for ordinary potential functions, a classical formula obtained in different way by Joukowsky for a particle moving on a surface.Work performed with the support of the Gruppo Nazionale di Fisica Matematica (G.N.F.M.) of the Italian National Research Council.     

A heuristic model for potential geomorphic influences on trophic interactions in streams

Whereas certain linkages between stream channel morphology and stream ecology are fairly well-understood, how geomorphology influences trophic interactions remains largely unknown. As a first step, a simple, heuristic model is developed that couples reach-scale geomorphic morphology with trophic dynamics between vegetation, detritus, herbivores, and predators. Predation is assumed to increase with depth beyond a threshold depth, and herbivory is assumed to decrease with velocity beyond a threshold velocity. Results show that the modeled food chain is sensitive to channel geometry, particularly around the threshold conditions for predators and herbivores. Importantly, geomorphic influences are not isolated to a particular trophic level, but rather are transferred through the food chain via top-down and bottom-up effects. The modeled system is particularly sensitive to changes in the end-members of the food chain: vegetation and predators. Results illustrate that geomorphic disturbances, known to affect a single trophic level (e.g., fish), likely impact multiple trophic levels in the stream ecosystem via trophic interactions. Such impacts at the multiple trophic level are poorly understood. While limited by the lack of empirical long-term data for testing and calibration, this simple model provides a structure for generating hypotheses, collecting targeted data, and assessing the potential impacts of stream disturbance or restoration on entire stream ecosystems. Further, the model illustrates the potential for future coupled stream models to explore spatial and temporal linkages.     

华北地台北缘地球物理场特征与金属矿床预测

对华北地台北缘的地球物理场特征进行了探讨,根据重、磁异常数据反演计算了该地区的莫霍界面、居里界面、磁性界面的起伏.利用地球物理场资料和反演计算结果对该地区的构造格架和断裂进行了推断,同时预测了9个成矿远景区:(1)集宁一呼和浩特金成矿区;(2)张家口一赤城金、银多金属成矿区;(3)密云一高岭金、铜成矿区;(4)青龙一马兰庄金成矿区;(5)秦皇岛、金多金属成矿区;(6)郝家营多金属成矿区;(7)承德地区金、多金属成矿区;(8)赤峰一喀喇沁旗金成矿区;(9)宁城东金、多金属成矿区.     

Coupled inverse modelling of groundwater flow and mass transport and the worth of concentration data

This paper presents the extension of the self-calibrating method to the coupled inverse modelling of groundwater flow and mass transport. The method generates equally likely solutions to the inverse problem that display the variability as observed in the field and are not affected by a linearisation of the state equations. Conditioning to the state variables is measured by an objective function including, among others, the mismatch between the simulated and measured concentrations. Conditioning is achieved by minimising the objective function by gradient-based methods. The gradient contains the partial derivatives of the objective function with respect to: log conductivities, log storativities, prescribed heads at boundaries, retardation coefficients and mass sources. The derivatives of the objective function with respect to log conductivity are the most cumbersome and need the most CPU-time to be evaluated. For this reason, to compute this derivative only advective transport is considered. The gradient is calculated by the adjoint-state method. The method is demonstrated in a controlled, synthetic study, in which the worth of concentration data is analysed. It is shown that concentration data are essential to improve transport predictions and also help to improve aquifer characterisation and flow predictions, especially in the upstream part of the aquifer, even in the case that a considerable amount of other experimental data like conductivities and heads are available. Besides, conditioning to concentration data reduces the ensemble variances of estimated transmissivity, hydraulic head and concentration.     

SEDIMENT TRANSPORT MODEL OF A WATERSHED

ChinaisoneOfthecountrieswhichsufferfromthemostserioussoilerosionintheworld,andthehillyandgullyareasof~PlateauinthemiddlereachesOftheYellowRiverarethemostseriouserosionareainChina.Inthisarea,themainerosivefactorsarerainfallandrunoff.Sometimes,thesedimentyieldinasinglefloodeventcanbe40%oftheannualsedimentload.Therefore,itisveryimPOrtanttostudytheyieldandgraphOfSedimentOfsinglefindevent.Forthispn~,thispaperiswritten.AInongsedimentmodelsforsinglefloodevent,moreandmoreattentionwaspaidtOunitse…     

黄河上游梯级水电站施工洪水优化设计方法探讨--以黄河公伯峡水电站施工洪水优化设计为例

梯级水电站设计洪水方法一直是梯级水电站水文设计的难点．几十年来在黄河上游梯级电站设计中已总结出一套比较完整的设计洪水及施工洪水计算方法。通过黄河公伯峡水电站施工洪水优化设计过程，论述了该套方法．并就目前存在的一些观点及疑问给予了较为明确的回答。