Analytical investigation of the exact groundwater divide between rivers beyond the Dupuit–Forchheimer approximation

The groundwater divide is a key feature of river basins and significantly influenced by subsurface hydrological processes. For an unconfined aquifer between two parallel rivers or ditches, it has long been defined as the top of the water table based on the Dupuit–Forchheimer approximation. However, the exact groundwater divide is subject to the interface between two local flow systems transporting groundwater to rivers from the infiltration recharge. This study contributes a new analytical model for two-dimensional groundwater flow between rivers of different water levels. The flownet is delineated in the model to identify groundwater flow systems and the exact groundwater divide. Formulas with two dimensionless parameters are derived to determine the distributed hydraulic head, the top of the water table and the groundwater divide. The locations of the groundwater divide and the top of the water table are not the same. The distance between them in horizontal can reach up to 8.9% of the distance between rivers. Numerical verifications indicate that simplifications in the analytical model do not significantly cause misestimates in the location of the groundwater divide. In contrast, the Dupuit–Forchheimer approximation yields an incorrect water table shape. The new analytical model is applied to investigate groundwater divides in the Loess Plateau, China, with a Monte Carlo simulation process taking into account the uncertainties in the parameters.     

Peaks of People: Using Topographic Prominence as a Method for Determining the Ranked Significance of Population Centers

This article borrows a statistical method from physical geography—topographical prominence—to suggest a new technique for measuring the relative significance or rank of population centers. Unlike raw population measures, prominence gives consideration to both the spatial intensity of concentrated population areas as well as the spatial dependence or independence of neighboring settlement clusters in relation to one another. We explain how to apply the topographic prominence calculation method to gridded population data and examine its practical utility through case studies of several U.S. states. We then discuss some ways in which parametric choices about point-to-surface transformations can result in considerably different outcomes and offer further suggestions for conceptualizing and measuring population center significance.     

城镇化与生态环境耦合的动态模拟——研究进展与展望

Urbanization and eco-environment coupling is a research hotspot.Dynamic simulation of urbanization and eco-environment coupling needs to be improved because the processes of coupling are complex and statistical methods are limited.Systems science and cross-scale coupling allow us to define the coupled urbanization and eco-environment system as an open complex giant system with multiple feedback loops.We review the current state of dynamic simulation of urbanization and eco-environment coupling and find that:(1)The use of dynamic simulation is an increasing trend,the relevant theory is being developed,and modeling processes are being improved;(2)Dynamic simulation technology has become diversified,refined,intelligent and integrated;(3)Simulation is mainly performed for three aspects of the coupling,multiple regions and multiple elements,local coupling and telecoupling,and regional synergy.However,we also found some shortcomings:(1)Basic theories are inadequately developed and insufficiently integrated;(2)The methods of unifying systems and sharing data are behind the times;(3)Coupling relations and the dynamic characteristics of the main driving elements are not fully understood or completely identified.Additionally,simulation of telecoupling does not quantify parameters and is not systemically unified,and therefore cannot be used to represent spatial synergy.In the future,we must promote communication between research networks,technology integration and data sharing to identify the processes governing change in coupled relations and in the main driving elements in urban agglomerations.Finally,we must build decision support systems to plan and ensure regional sustainable urbanization.     

Canonical theory of perturbations using eccentric anomaly as independent variable

It is shown in this paper how to build a canonical transformation of variables, so that the eccentric anomaly becomes the new independent variable. In the case of eccentric elliptical orbits it changes the equations of motion so, that they can be integrated analytically to any order of approximation comparatively easy.