On the efficiency of Runge-Kutta-Nystrom methods with interpolants for solving equations of the form Y″ = F(T,Y, Y′) over short timespans

Runge-Kutta-Nystrom (RKN) codes for the solution of the initial value problem for the general second order differential system have been developed recently, although the methodology on which they are based was known many years ago. In this paper we try to examine the efficiency of several known general Runge-Kutta-Nystrom (GRKN) methods by posing some criteria of cost and accuracy. These methods supplied with the corresponding interpolants, have been applied to some problems of Celestial Dynamics. The results obtained show that these codes have a good response in the approximation of the solution of these problems.Department of Mechanics     

Environmental impact of drainage of Dianzi Iron Mine on the groundwater system of the Dawu Water Supply Base

Due to growing water extraction for industry and agriculture, the Dawu Water Supply Base, in the east of Zibo, China, has been in a state of serious over-extraction. It will also be affected by the deep drainage of the Dianzi Iron Mine, which will be exploited in 2005. As to the environmental impact on the groundwater system of the Dawu Water Supply Base is concerned, this paper makes a systematic study about the influence of the mine draining on the water-supply environment of the Dawu Water Supply Base by using the numerical model of groundwater system. The result shows that the groundwater level will have an additional drawdown of 1.2–1.8 m/yr by the mine draining alone. The numerical analysis results indicate that the optimal model for determining the best extraction plan is the solution for the contradiction between water supply and water drainage.     

A very large scale GIS-based groundwater flow model for the Nubian sandstone aquifer in Eastern Sahara (Egypt,northern Sudan and eastern Libya)

A three-dimensional GIS-based groundwater flow model for the Nubian Sandstone Aquifer in the eastern Sahara was developed and calibrated under steady-state and transient conditions. The model was used to simulate the response of the aquifer to climatic changes that occurred during the last 25,000 years. The simulation results indicated that the groundwater in this aquifer was formed by infiltration during the wet periods 20,000 and 5,000 years b.p. The recharge of groundwater due to regional groundwater flow from more humid areas in the south was excluded. It also indicates that the Nubian Aquifer System is a fossil aquifer, which had been in an unsteady state condition for the last 3,000 years.

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Resumen Fue desarrollado un modelo de flujo de agua subterránea en tres dimensiones, basado en un SIG, para el Acuífero Arenisca Nubian en el Sahara Oriental, el cual fue calibrado para condiciones de estado estacionario y transitorio. El modelo se usó para simular la respuesta del acuífero a los cambios climáticos que ocurrieron durante los últimos 25000 años. Los resultados de esta simulación indicaron que el agua subterránea en este acuífero, se formó por infiltración, durante los períodos húmedos que hubo hace 20000 y 5000 años, antes del presente. Fue excluida la recarga del acuífero debida a un flujo regional de agua subterránea proveniente de áreas con un clima más húmedo en el sur. El modelo también muestra, que el Sistema Acuífero Nubian es un acuífero fósil, el cual ha permanecido en una condición de estado no estacionario, durante los últimos tres mil años.

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Résumé Pour laquifère gréseux Nubien de Sahara -Est on a mis au points un modèle tridimensionnel, basé sur GIS. Le modèle a été calibré tant pour lécoulement stationnaire que pour lécoulement transitoire. On a simulé après la réponse de laquifère aux changements climatiques des derniers 25000 ans. Les résultats des simulations indiquent que la nappe a été rechargée par des infiltrations pendant une période humide qui sétend 5000 et 20000 ans, dès temps actuel. On na pas pris en compte la recharge de laquifère par la zone plus humide située dans sa partie sud. Le modèle indique aussi que leau de laquifère Nubien est une eau fossile qui a eu un écoulement transitoire pendant les derniers 3000 ans.

     

Instabilities of the tidally induced bottom boundary layer in the rotating frame and their mixing effect

To investigate the stability of the bottom boundary layer induced by tidal flow (oscillating flow) in a rotating frame, numerical experiments have been carried out with a two-dimensional non-hydrostatic model. Under homogeneous conditions three types of instability are found depending on the temporal Rossby number Ro_t, the ratio of the inertial and tidal periods. When Ro_t < 0.9 (subinertial range), the Ekman type I instability occurs because the effect of rotation is dominant though the flow becomes more stable than the steady Ekman flow with increasing Ro_t. When Ro_t > 1.1 (superinertial range), the Stokes layer instability is excited as in the absence of rotation. When 0.9 < Ro_t < 1.1 (near-inertial range), the Ekman type I or type II instability appears as in the steady Ekman layer. Being much thickened (100 m), the boundary layer becomes unstable even if tidal flow is weak (5 cm/s). The large vertical scale enhances the contribution of the Coriolis effect to destabilization, so that the type II instability tends to appear when Ro_t > 1.0. However, when Ro_t < 1.0, the type I instability rather than the type II instability appears because the downward phase change of tidal flow acts to suppress the latter. To evaluate the mixing effect of these instabilities, some experiments have been executed under a weak stratification peculiar to polar oceans (the buoyancy frequency N²  10⁻⁶ s⁻²). Strong mixing occurs in the subinertial and near-inertial ranges such that tracer is well mixed in the boundary layer and an apparent diffusivity there is evaluated at 150–300 cm²/s. This suggests that effective mixing due to these instabilities may play an important role in determining the properties of dense shelf water in the polar regions.     

Assessing selected natural and anthropogenic impacts on freshwater lens morphology on small barrier Islands: Dog Island and St. George Island, Florida, USA

Abstract The freshwater lens morphologies of the barrier islands Dog Island and St. George Island on the panhandle coast of Florida (FL), USA, are controlled to varying degrees by both natural and anthropogenic factors. Variable-density groundwater flow models confirm that spatial variability of recharge values can account for the observed lens asymmetry on these islands. The depth to the base of the lens does not vary significantly seasonally. Human development has altered recharge patterns in some areas, locally thinning the freshwater lens. Aqueduct water supply to St. George Island represents 7–25% of natural recharge; higher recharge rates are required to simulate the lens on St. George Island than on Dog Island. On both islands, coastal erosion rates are sufficiently rapid that the freshwater lens may not be in equilibrium with current boundary conditions.

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Resumen Las morfologías de los lentes de agua dulce en las islas de barrera: Islas Dog y St. George, en la costa alargada y estrecha de Florida, EUA, están controladas en diferentes grados por factores antropogénicos y naturales. Los modelos de flujo con densidad variable del agua subterránea, confirman que la variabilidad espacial de los valores de recarga, pueden ser la causa de la asimetría observada en los lentes de estas islas. La profundidad hasta la base de los lentes no varía significativamente con las estaciones climáticas. El desarrollo humano ha alterado las tendencias de recarga en algunas áreas, causando adelgazamiento local de los lentes de agua dulce. El abastecimiento de agua del acueducto en la Isla St. George, representa entre 7% y 25% de la recarga natural; por otro lado se necesitan cantidades mayores de recarga para simular los lentes en la Isla St. George que en la Isla Dog. En ambas islas, las tasas de erosión costera son tan rápidas, que las lentes de agua dulce podrían no estar en equilibrio con las condiciones actuales de frontera.

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Résumé La morphologie des lentilles deau douce des îles de Dog et de St. George, situés dans le district côtier de Florida-Etats Unis est contrôlé dans une mesure variable par des facteurs naturelles et humaines. Les modèles découlement à densité variable des eaux souterraines confirment que la variation spatiale de la recharge peut expliquer les asymétries observées des lentilles des cettes îles. La profondeur des lentilles ne présente pas des variations saisonnières importantes. Les activités humaines ont modifié la recharge dans certaines zones en amincissant localement les lentilles deau douce. Lalimentation en eaux de lîle de St. George représente 7–25% de la recharge naturelle; pour simuler les lentilles de lîle de Dog il a été nécessaire dintroduire des valeurs plus élevées de la recharge par rapport aux ceux utilisés pour lîle de St. George. Pour les deux îles lérosion côtière est assez rapide ainsi que les lentilles de eau douce ne sont pas en équilibre avec les conditions à la frontière.

     

Climate change impacts on groundwater recharge- uncertainty, shortcomings, and the way forward?

An integrated approach to assessing the regional impacts of climate and socio-economic change on groundwater recharge is described from East Anglia, UK. Many factors affect future groundwater recharge including changed precipitation and temperature regimes, coastal flooding, urbanization, woodland establishment, and changes in cropping and rotations.Important sources of uncertainty and shortcomings in recharge estimation are discussed in the light of the results. The uncertainty in, and importance of, socio-economic scenarios in exploring the consequences of unknown future changes are highlighted. Changes to soil properties are occurring over a range of time scales, such that the soils of the future may not have the same infiltration properties as existing soils. The potential implications involved in assuming unchanging soil properties are described.To focus on the direct impacts of climate change is to neglect the potentially important role of policy, societal values and economic processes in shaping the landscape above aquifers. If the likely consequences of future changes of groundwater recharge, resulting from both climate and socio-economic change, are to be assessed, hydrogeologists must increasingly work with researchers from other disciplines, such as socio-economists, agricultural modellers and soil scientists.

Numerical simulations of the influence of the seasonal snow cover on the occurrence of permafrost at high latitudes

It has repeatedly been reported that snow cover is a dominating factor in determining the presence or absence of permafrost in the discontinuous and sporadic permafrost regions. The temperature at the snow-soil interface by the end of winter, known as the bottom temperature of winter snow (BTS) method, has been used to detect the existence of permafrost in European alpine regions when the maximum snow depth is about 1.0 m or greater. A critical snow thickness of about 50 cm or greater can prevent the development of permafrost in eastern Hudson Bay, Canada. The objective of this study is to investigate the impact of snow cover on the presence or absence of permafrost in cold regions through numerical simulations. A one-dimensional heat transfer model with phase change and a snow cover regime is used to simulate energy exchange between deep soils and the atmosphere. The model has been validated against the in situ data in the Arctic. The simulation results indicate that both snow depth and the onset date of snow cover establishment are important parameters in relation to the presence or absence of permafrost. Early establishment of snow cover can make permafrost disappear, even with a relatively thin snow cover. Permafrost may survive when snow cover starts after the middle of December even with a snow thickness >1.0 m. This effect of snow cover on the ground thermal regime can be explained with reference to the pattern of seasonal temperature variation. Early establishment of snow cover enhances the insulating impact over the entire cold season, thus warming and eventually thawing the permafrost. The insulating effect is substantially reduced when snow cover starts relatively late and snowmelt in the spring creates a huge heat sink, resulting in a favorable combination for permafrost existence.     

沙尘暴过程中沙尘对流层-平流层输送的数值模拟初步分析

在初步明确东亚沙尘气溶胶对流层-平流层输送监测事实的基础上,利用观测资料、NCEP再分析资料以及基于中尺度天气模式MM5的数值模拟方法,对一次蒙古气旋沙尘暴过程中沙尘对流层-平流层输送问题进行了初步分析.结果表明:斜压不稳定是本次蒙古气旋发展的主要强迫要素,伴随气旋发展成熟,高空切断低涡的形成引导高空急流下落并诱发对流层顶折叠和高空位涡下传.对流层顶折叠区呈漏斗状,底部达500 hPa左右.高空急流产生近似垂直的下落,并在高空切断低涡的南侧和东侧达到最强.在对流层顶折叠区周边的300-500 hPa,上升气流与低涡区偏西、偏南、偏东气流叠加,或水平横穿折叠的对流层顶,或斜升并准垂直地穿过下落的对流层顶到达平流层,且随时间的推移,空气质点能够进一步抵达平流层中部(100 hPa).轨迹分析表明,沙尘天气区对流层低层的空气质点在气旋涡旋上升气流的驱动下呈气旋式盘旋上升,并在对流层高层形成分支,一支穿过对流层顶到达平流层,并在平流层向下游进行反气旋式螺旋运动,另一支则留在对流层高层并向下游进行准水平的气旋式螺旋运动.在高空位涡下传过程中,主要产生平流层到对流层的净输送;高空位涡停止下传之后则出现对流层到平流层的净输送,且强度随时间呈指数型增长.这一特征有利于形成更强的沙尘对流层平流层输送.     

地形对门头沟一次大暴雨动力作用的数值研究

2002年6月24—25日,北京门头沟附近发生了一次大暴雨过程。为探讨地形在本次过程中的动力作用,采用美国俄克拉荷马大学风暴分析预测中心开发的ARPS模式,对大暴雨过程进行了数值试验。控制试验采用27、9 km双重单向嵌套网格,网格覆盖范围约为3000 km×3000 km、900 km×900 km。两层网格均采用全物理过程,使用的都是全球30″的地形资料。在控制试验的基础上,进行了3组敏感性试验:第1组试验采用干过程模拟,即不考虑凝结潜热的作用;第2组试验将地形整体向东/西平移1°;第3组试验是将门头沟西部的局地地形抠除一部分。试验结果表明,在不考虑凝结潜热作用时,东南风气流仍然可以爬升到2 km以上,超过了大气的抬升凝结高度,证实了地形的动力作用是本次大暴雨的触发机制;将地形向东/西平移1°后,由于大气的对流稳定度发生了改变,模拟的降水强度和落区也发生了变化,表明山坡和山顶的对流不稳定大气是导致本次大暴雨的必要条件;抠除局地地形后,模拟的降水量也发生了不同程度的改变,再次证明大暴雨是在多尺度地形以及一定的天气系统配置下产生的。     

A study of charge structure sensitivity in simulated thunderstorms

Two different thunderstorms are simulated by two distinct one-dimensional cloud models using four different parameterisations of the non-inductive mechanism of electric charging, based on laboratory studies. The results demonstrate that during the early (pre-lightning) stage of thunderstorm electrification, simulated charge density depends not only on the model charging parameterisation employed, but also on the specific representations of the kinematics and microphysical characteristics of the model itself. Though no conclusions are drawn regarding the physical suitability of the charging parameterisations themselves, the analysis indicates that the most significant differences between the simulated charge structures of the clouds produced in each particular model are the result of different distributions of model cloud characteristics and of the type of parameterisation of the microphysical processes. The study reveals that it is too early to make any conclusion regarding which, if any, of the existing parameterisation schemes are better suited to the realistic simulation of electrical charging in real clouds.