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.     

Forest operations,tree species composition and decline in rainfall explain runoff changes in the Nacimiento experimental catchments,south central Chile

Few long-term studies have explored how intensively managed short rotation forest plantations interact with climate variability. We examine how prolonged severe drought and forest operations affect runoff in 11 experimental catchments on private corporate forest land near Nacimiento in south central Chile over the period 2008–2019. The catchments (7.7–414 ha) contain forest plantations of exotic fast-growing species (Pinus radiata, Eucalyptus spp.) at various stages of growth in a Mediterranean climate (mean long-term annual rainfall = 1381 mm). Since 2010, a drought, unprecedented in recent history, has reduced rainfall at Nacimiento by 20%, relative to the long-term mean. Pre-drought runoff ratios were <0.2 under 8-year-old Eucalyptus; >0.4 under 21-year-old Radiata pine and >0.8 where herbicide treatments had controlled vegetation for 2 years in 38% of the catchment area. Early in the study period, clearcutting of Radiata pine (85%–95% of catchment area) increased streamflow by 150 mm as compared with the year before harvest, while clearcutting and partial cuts of Eucalyptus did not increase streamflow. During 2008–2019, the combination of emerging drought and forestry treatments (replanting with Eucalyptus after clearcutting of Radiata pine and Eucalyptus) reduced streamflow by 400–500 mm, and regeneration of previously herbicide-treated vegetation combined with growth of Eucalyptus plantations reduced streamflow by 1125 mm (87% of mean annual precipitation 2010–2019). These results from one of the most comprehensive forest catchment studies in the world on private industrial forest land indicate that multiple decades of forest management have reduced deep soil moisture reservoirs. This effect has been exacerbated by drought and conversion from Radiata pine to Eucalyptus, apparently largely eliminating subsurface supply to streamflow. The findings reveal tradeoffs between wood production and water supply, provide lessons for adapting forest management to the projected future drier climate in Chile, and underscore the need for continued experimental work in managed forest plantations.     

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.     

Simulations of multimode bolometric interferometers

We describe a procedure for the numerical modelling of astronomical interferometers, with particular relevance to far-infrared and submillimetre wavelengths. The scheme is based on identifying a set of modes that carry power from the sky to the detector. The procedure is extremely general, and can be used to model scalar or vector fields, in any state of coherence and polarization, the only limitation being that the propagation of a coherent field through the system be described by an integral transform, a constraint that is in practise always met.
We present simulations of ideal, multimode two-dimensional interferometers, and show that the modal theory reproduces the correct behaviour of both Michelson and Fizeau interferometers. We calculate simulated visibility data for a multimode bolometric Michelson interferometer, with a synthesized source, and produce a dirty map, recovering the original source with the usual artefacts associated with interferometers.     

Transient‐state groundwater flow in various geometries with wells at arbitrary positions: analytical methods

We have developed a method for analytically solving the porous medium flow equation in many different geometries for horizontal (two‐dimensional), homogeneous and isotropic aquifers containing impermeable boundaries and any number of pumping or injection wells located at arbitrary positions within the system. Solutions and results are presented for rectangular and circular aquifers but the method presented here is easily extendible to many geometries. Results are also presented for systems where constant head boundary conditions can be emulated internal to the aquifer boundary. Recommendations for extensions of the present work are briefly discussed. Copyright © 2003 John Wiley & Sons, Ltd.