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.     

Hydrological trends and the evolution of catchment research in the Alptal valley,central Switzerland

When the observation of small headwater catchments in the pre-Alpine Alptal valley (central Switzerland) started in the late 1960s, the researchers were mainly interested in questions related to floods and forest management. Investigations of geomorphological processes in the steep torrent channels followed in the 1980s, along with detailed observations of biogeochemical and ecohydrological processes in individual forest stands. More recently, research in the Alptal has addressed the impacts of climate change on water supply and runoff generation. In this article, we describe, for the first time, the evolution of catchment research at Alptal, and present new analyses of long-term trends and short-term hydrologic behaviour. Hydrometeorological time series from the past 50 years show substantial interannual variability, but only minimal long-term trends, except for the ~2°C increase in mean annual air temperature over the 50-year period, and a corresponding shift towards earlier snowmelt. Similar to previous studies in larger Alpine catchments, the decadal variations in mean annual runoff in Alptal's small research catchments reflect the long-term variability in annual precipitation. In the Alptal valley, the most evident hydrological trends were observed in late spring and are related to the substantial change in the duration of the snow cover. Streamflow and water quality are highly variable within and between hydrological events, suggesting rapid shifts in flow pathways and mixing, as well as changing connectivity of runoff-generating areas. This overview illustrates how catchment research in the Alptal has evolved in response to changing societal concerns and emerging scientific questions.     

On the expansions of intermediate orbit for general planetary theory

Intermediate orbit for general planetary theory is constructed in the form of multivariate Fourier series with numerical coefficients. The structure and efficiency of the derived series are illustrated by giving various statistical properties of the coefficients.The ability of the recently proposed elliptic function approach to compress the Fourier series representing the intermediate orbit is investigated. Our results confirm that when mutual perturbations of a pair of planets are considered the elliptic function approach is quite efficient and allows one to compress the series substantially. However, when perturbations of three or more planets are under study the elliptic function approach does not give any advantages.     

The formation and stability of the configuration of the planetary system HD 126611

Recent Doppler velocity measurements have revealed the existence of two planets orbiting the star HD 12661 on medium-eccentricity orbits. The inner planet has a period of 263.6 d and a mass of 2.3 Jupiter masses, and the outer planet has a period of 1444.5d and a mass of 1.57 Jupiter masses. The stability of this system requires the two planets to be in a state of mean-motion orbit resonances. By numerical method we have studied the orbit migration and stability of the system in its early ages under the action of the proto-stellar disk, and calculated the probabilities of the planets being captured into the mean -motion resonances during their migrations. It is found that at present the two planets are probably situated at the edge of the 11:2 mean-motion resonance and are in chaotic motions. This result may be helpful to clarify the arguments on the present configuration. Besides, it is indicated that very probably, after the formation of the system, the gaseous disk has almost disappeared before the planets migrated to the present configuration.