Scattering of surface gravity waves over a pair of trenches

A numerical model based on boundary element method is developed to study the scattering of surface gravity waves over a pair of trenches of varied configurations under the assumption of small amplitude water wave theory. Both the cases of symmetric and asymmetric trenches are considered in the present study. The accuracy of the numerical results is validated by comparing the reflection and transmission coefficients with energy identity, and the known results associated with single trench available in the literature. The study reveals that wave reflection decreases in an oscillatory manner with an increase in trench width. Moreover, Bragg resonance in wave reflection is observed for wave number corresponding to waves in shallow and intermediate depths in the case of a pair of trenches. Further, Bragg reflection increases with an increase in the number of trenches. In the case of multiple trenches, subharmonic peaks in Bragg reflection are depicted and the number of subharmonic peaks between two harmonic peaks is found to be two less than the number of trenches. However, for triangular trenches, the occurrence of the subharmonic peak is invariant of the number of trenches and the same vanishes for larger trench depth. Irrespective of trench configurations, wave reflection follows certain uniform oscillatory pattern with an increase in the gap between the trenches in case of deep water.     

Regional economic impacts of fish resources utilization from the Barents Sea: Trade-offs between economic rent,employment and income

A multi-objective programming model has been developed to investigate the trade-offs among regional employment, regional income, and economic rent of the North Norwegian cod fisheries in the Barents Sea, where all vessels are regulated by an individual quota system. Fishery managers are confronted with the problem on how best to allocate the total allowable catch (TAC) among four vessel groups. It is apparent that depending on how fishery managers view the importance of each objective, the desirable allocation of TAC will differ. Therefore, the trade-offs information can be very useful to fishery managers indicating the relative “expensiveness” of trading one objective with another. Decision maps are generated depicting how the trade-offs between two objectives are affected by the third objective. Compromise solutions taking into account all three objectives will allocate the TAC to satisfy the maximum capacity of both the factory trawlers and the small-scale vessels with the remaining TAC distributed to the coastal fleet and fresh fish trawlers.     

Tactical planning of offshore petroleum production

This paper describes a model for tactical planning of Norwegian petroleum production. The problem involves regulation of production levels from wells, splitting of production flows into oil and gas products, further processing of gas and transportation in a pipeline network. Blending and processing of gas is necessary to satisfy quality requirements in the markets. The problem is formulated with multi-component flows, regulation alternatives in production, non-linear splitting for chemical processing and linear quality constraints on composite products. Production and splitting are modelled with integer requirements. The model is implemented in Xpress^MP with a Visual Basic supported user interface in Excel. It is constructed in cooperation with the major Norwegian oil company, Statoil and can identify optimal production patterns and assist in planning of possible shut-downs, demonstrate system robustness to customers and aid in contract negotiations.     

Productivity change and innovation in Norwegian electricity distribution companies

Regulators of electricity distribution networks have typically applied Data Envelopment Analysis (DEA) to cross-section data for benchmarking purposes. However, the use of panel data to analyse the impact of regulatory policies on productivity change over time is less frequent. The main purpose of this paper is to construct a Malmquist productivity index to examine the recent productivity change experienced by Norwegian distribution companies between 2004 and 2007. The Malmquist index is decomposed in order to explore the sources of productivity change, and to identify the innovator companies that pushed the frontier forward each year. The input and output variables considered are those used by the Norwegian regulator. In order to reflect appropriately the exogenous conditions where the companies operate, the efficiency model used in this paper incorporates geography variables as outputs of the DEA model. Unlike the model used by the regulator, we included virtual weight restrictions in the DEA formulation to correct the biases in the DEA results that may be associated to a judicious choice of weights by some of the companies.     

Numerical multi-block grids in coastal ocean circulation modeling

In coastal ocean modeling, one desires to capture the evolution and interaction of multi-scales of physical phenomena in a complicated physical domain. With limited computer resources, an appropriate choice of the numerical grid has a key role in determining the quality of the solution of a numerical coastal ocean model. Traditionally, single-block rectangular grids have been most commonly used in coastal ocean modeling for their simplicity. An effective coastal ocean model represents the dynamics of the coastal ocean flow on a numerical grid, including the effects of complicated features such as coastlines, bottom topography (submarine canyons, seamounts, narrow straits), and multi-scale physical phenomena. These problems require a model grid system more efficient than a traditional single-block rectangular grid. The model grids must give better resolution of coastlines and boundary conditions, multi-scale physical phenomenon, and save computer resources. These grids can also easily increase horizontal resolution in a subregion of the model domain without increasing computer expense with high resolution over the entire domain. The multi-block numerical generation grid technique is used in developing a coastal ocean system applied to the Mediterranean Sea (MED) with complicated coastlines, bottom topography and multi-scale physical features. The MED coastal ocean system consists of the MED model based on the Princeton Ocean Model, numerical grid generation routines, and a grid package which allows the model to be coupled with model grids. The traditional, nine-block orthogonal grid, and eight-block curvilinear nearly orthogonal coastline-following grid are used in the study. The numerical solutions with the three grids are compared in term of effectiveness. The numerical simulations show some MED basic physical features.     

二分选择模型在滨海旅游经济价值评价中的应用

本文以大连滨海旅游资源为例,采用二分选择模型条件评价法(CVM)评价海水和沙滩质量改善的经济价值,探索滨海旅游资源生态补偿的价值。研究发现采用Logit二分选择模型估算旅游者意愿支付(WTP)比采用Probit模型更适合滨海旅游资源经济价值评价;在计算WTP的均值解时,采用线性效用差函数更为简单实用。将该方法用于大连旅游景区海水和沙滩质量价值评价的研究,结果表明:采用Logit和Probit模型能够得到一致的WTP;文中采用单解释变量模型可以反应多个解释变量模型的计算结果;测算得到海水沙滩质量改善的非使用价值为215元/人,进而对旅游或环境资源的保护和可持续利用可以有更明确的定量认识。这种经济价值研究方法与过程对探索滨海旅游资源生态补偿的定性研究具有重要意义。     

Stochastic programming for optimizing bidding strategies of a Nordic hydropower producer

From the point of view of a price-taking hydropower producer participating in the day-ahead power market, market prices are highly uncertain. The present paper provides a model for determining optimal bidding strategies taking this uncertainty into account. In particular, market price scenarios are generated and a stochastic mixed-integer linear programming model that involves both hydropower production and physical trading aspects is developed. The idea is to explore the effects of including uncertainty explicitly into optimization by comparing the stochastic approach to a deterministic approach. The model is illustrated with data from a Norwegian hydropower producer and the Nordic power market at Nord Pool.     

Sophus lie

This paper is a translation by the author of the biography presented in Norwegian at The Royal Norwegian Academy of Sciences and Letters in Trondheim, Norway, on 26 February 1992.     

SHARING THE NORTHEAST ARCTIC COD: POSSIBLE EFFECTS OF CLIMATE CHANGE

ABSTRACT. The Northeast Arctic cod inhabits the exclusive economic zones of Norway and Russia and migrates extensively between these zones. The stock is shared evenly between the two countries, with a small allocation to third countries. Higher temperatures in the Barents Sea and the Norwegian Sea are expected to affect the stock, probably increasing its size and leading to a larger share inhabiting the Russian economic zone. It is also conceivable that some spawning will begin to take place off the coast of Russia in addition to the spawning that now occurs exclusively in Norwegian waters. This paper looks at the implication of this for the division of the stock between the two countries. It is found that a greater presence of the stock in the Russian zone would strengthen rather than weaken the Norwegian bargaining position if the unit cost of fish is not sensitive to the size of the stock. If, on the other hand, the fishing costs are proportional to fishing mortality, Norway's position would be weakened almost on par with the fall in its share of the stock. The paper uses a Beverton‐Holt year class model with a Ricker recruitment function. The recruitment function is hump‐shaped, implying that a too large spawning stock is harmful for recruitment. Strong density‐dependence in the survival of eggs and larvae is a possible reason for this. It is shown that, for a stock being limited by carrying capacity at the pre‐recruit stage rather than the post‐recruit stage, one may expect a strongly asymmetric curve for sustainable yield as a function of total biomass. The biomass of an exploited population might possibly exceed the biomass of a pristine population under those circumstances.     

Coupling of a one-dimensional river routing model and a three-dimensional ocean model to predict overbank flows in a complex river–ocean system

River–ocean coupled models were developed to calculate overbank flows in a complex river–coastal ocean system comprising the Wu River and the adjacent coastal ocean of central Taiwan. The hydrodynamic quantities were exchanged between one-dimensional and three-dimensional domains during runtime to resolve the real-time exchange and interaction between the coastal waters and the river system. The coupled model was calibrated and verified with the observed water levels using data from three typhoon events. The results indicate a reasonable agreement between the model simulations and the observed data. The model was then used to calculate hydrographs of the overbank flow caused by Typhoon Kalmaegi, which occurred in 2008. The simulated overbank flows quantitatively agreed with the reported information. We also demonstrated that most of the overbank flows occurred at the upper reaches of the tributaries of the Wu River system, except for the tributary in the Fazi River.     

Conservation laws with a random source

We study the scalar conservation law with a noisy nonlinear source, namely,u _l + f(u)_x = h(u, x, t) + g(u)W(t), whereW(t) is the white noise in the time variable, and we analyse the Cauchy problem for this equation where the initial data are assumed to be deterministic. A method is proposed to construct approximate weak solutions, and we then show that this yields a convergent sequence. This sequence converges to a (pathwise) solution of the Cauchy problem. The equation can be considered as a model of deterministic driven phase transitions with a random perturbation in a system of two constituents. Finally we show some numerical results motivated by two-phase flow in porous media. This research has been supported by VISTA (a research cooperation between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap, Statoil) and NAVF (the Norwegian Research Council for Science and the Humanities).     

Bankruptcy theory development and classification via genetic programming

Bankruptcy is a highly significant worldwide problem with high social costs. Traditional bankruptcy risk models have been criticized for falling short with respect to bankruptcy theory building due to either modeling assumptions or model complexity.Genetic programming minimizes the amount of a priori structure that is associated with traditional functional forms and statistical selection procedures, but still produces easily understandable and implementable models. Genetic programming was used to analyze 28 potential bankruptcy variables found to be significant in multiple prior research studies, including 10 fraud risk factors. Data was taken from a sample of 422 bankrupt and non-bankrupt Norwegian companies for the period 1993–1998. Six variables were determined to be significant.A genetic programming model was developed for the six variables from an expanded sample of 1136 bankrupt and non-bankrupt Norwegian companies. The model was 81% accurate on a validation sample, slightly better than prior genetic programming research on US public companies, and statistically significantly better than the 77% accuracy of a traditional logit model developed using the same variables and data. The most significant variable in the final model was the prior auditor opinion, thus validating the information value of the auditor’s report. The model provides insight into the complex interaction of bankruptcy related factors, especially the effect of company size. The results suggest that accounting information, including the auditor’s evaluation of it, is more important for larger than smaller firms. It also suggests that for small firms the most important information is liquidity and non-accounting information.The genetic programming model relationships developed in this study also support prior bankruptcy research, including the finding that company size decreases bankruptcy risk when profits are positive. It also confirms that very high profit levels are associated with increased bankruptcy risk even for large companies an association that may be reflecting the potential for management to be “Cooking the Books”.     

Numerical grids used in a coastal ocean model with breaking wave effects

In coastal ocean modeling, traditional single-block rectangular (Cartesian) grids have been most commonly used for their simplicity. In many cases, these grids may be not well suited (even at very high resolutions) for regions with complicated physical fields, open boundaries, coastlines, and bottom bathymetry. The numerical curvilinear nearly orthogonal/orthogonal, single/multi-block coastline-following grids for the Mediterranean Sea, Monterey Bay and the South China Sea (SCS) are presented. These grids can be used in coastal ocean modeling to enhance model numerical solutions and save computer resources by giving better treatment of regions with high gradients such as areas of complicated coastlines and steep slopes of shelf breaks, complicated bottom topography, open boundaries, and multi-scale physical phenomenon. Grid generation techniques are used to designed these grids. This kind of grids can also easily increase horizontal resolutions in the subregion of the model domain, without increasing the computational expense, with a higher resolution over the entire domain.A three dimensional coastal ocean model with breaking wave effects is also presented and applied. The ocean system is a primitive equation modeling system with grid generation routines and a turbulent closure which is capable of taking surface breaking wave effects into account. The system also includes a grid package which allows model numerical grids to be coupled with the ocean model. The model code is written for multi-block grids, but a single-block grid is used for the South China Sea (SCS). The model with breaking wave effects and a grid of 121 × 121 grid points are used to simulate the winter circulation of the SCS as an example. The model output of the 60-day run shows the observed upwelling locations in the sea surface salinity field.     

Propagation of surface gravitational waves over two parallel bottom inhomogeneities

On the basis of the method of power series we construct a solution of the two-dimensional problem of propagation of surface gravitational waves in water in the presence of two bottom trenches or projections. The problem is studied in the context of the shallow water model. We carry out an analysis of the effect of the trench parameters and their location on the amplitude of the reflected wave as functions of the wave number. Four figures. Bibliography: 6 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 27, 1997, pp. 126–132.     

Finite element modeling of a PE pipe heap leachate collection system

Results of finite element modeling for a series of corrugated polyethylene pipes under a typical 120 m high heap leach pad of copper bearing ore are presented. The modeling results for two different configurations illustrate the phenomena of soil structure interaction between the ore and the pipes. A trenchless configuration showed significantly smaller radial soil stresses at the springline of the pipes when compared to a shallow trench configuration with the pipes laid within a trench. Radial soil stresses at the crown and invert were of similar magnitude for both configurations. Circumferential stresses within the soil around the pipes were also similar. Pipe thrust and bending moment at the invert location were significantly reduced in the trench-less configuration.     

Supply chain design under uncertainty using sample average approximation and dual decomposition

We present a supply chain design problem modeled as a sequence of splitting and combining processes. We formulate the problem as a two-stage stochastic program. The first-stage decisions are strategic location decisions, whereas the second stage consists of operational decisions. The objective is to minimize the sum of investment costs and expected costs of operating the supply chain. In particular the model emphasizes the importance of operational flexibility when making strategic decisions. For that reason short-term uncertainty is considered as well as long-term uncertainty. The real-world case used to illustrate the model is from the Norwegian meat industry. We solve the problem by sample average approximation in combination with dual decomposition. Computational results are presented for different sample sizes and different levels of data aggregation in the second stage.     

THE USE OF TELESCOPING SPATIAL SCALES TO CAPTURE INSHORE TO SLOPE DYNAMICS IN MARINE ECOSYSTEM MODELING

Abstract Ecosystem processes function at many scales, and capturing these processes is a challenge for ecosystem models. Nevertheless, it is a necessary step for considering many management issues pertaining to shelf and coastal systems. In this paper, we explore one method of modeling large areas with a focus at a range of scales. We develop an ecosystem model that can be used for strategic management decision support by modeling the waters off southeastern Australia using a polygon telescoping approach, which incorporates fine‐scale detail at the coastal zone, increasing in scale to a very coarse scale in the offshore areas. This telescoping technique is a useful tool for incorporating a wide range of habitats at different scales into a single model.     

Pivoting rules and redundancy schemes in extreme point enumeration

We give an overview over how problems connected to degeneracy have been attacked in the literature in connection with extreme point enumeration in a convex polyhedron. We treat both the question of unique pivots and how to attach only one basis to each extreme point.Work supported by The Norwegian Fisheries Research Council and The Norwegian Research Council for Science and the Humanities.     

Stochastic Modelling of Temperature Variations with a View Towards Weather Derivatives

Daily average temperature variations are modelled with a mean‐reverting Ornstein–Uhlenbeck process driven by a generalized hyperbolic Lévy process and having seasonal mean and volatility. It is empirically demonstrated that the proposed dynamics fits Norwegian temperature data quite successfully, and in particular explains the seasonality, heavy tails and skewness observed in the data. The stability of mean‐reversion and the question of fractionality of the temperature data are discussed. The model is applied to derive explicit prices for some standardized futures contracts based on temperature indices and options on these traded on the Chicago Mercantile Exchange (CME).