Spatial Variability of Irrigated Corn Yield in Relation to Field topography and Soil Chemical Characteristics

Corn yield, topography and soil characteristics were sampled on a 26 ha area of a centre pivot irrigated cropland. The aim of the study was to determine relationships between corn yield, field topography and soil characteristics. The study was carried out in the Alentejo region of Portugal. Corn yield was measured with a combine harvester fitted with a grain-flow sensor and positioned by means of the Global Positioning System (GPS). A grid-based digital elevation model (DEM) with 1-m resolution was constructed and several topographic attributes were calculated from the DEM: the local slope gradient (S), profile curvature (Curv), specific catchments area (SCa), and a steady-state wetness index (W). Yield and topographical attributes were computed for areas of radius 5, 10, 25 and 50 m, being considered its maximum, minimum, range and average values. The soil was systematically sampled with a mechanical probe for a total of 109 soil profiles used for analysis of the following soil superficial (<0.30 m) characteristics: extractable phosphorous (P2O5) and extractable potassium (K2O), soil pH, cation exchange capacity (CEC) and exchangeable bases. With centre pivot irrigation systems, the Wave50 index was shown to be useful for the identification of field areas in which low corn yields may be due to lack of water. At the same time, SCa was found to be useful for the identification of field areas in which low yields are due to excess water and drainage problems. Higher positive correlation between pH, Ca and Curv were observed; calcium concentration was found on the transition areas between flat surfaces to concave ones, while lower values were detected in convex and concave areas. Topographical indexes, namely Wave50, SCa and Curv, can be especially helpful in site-specific management for delineating areas where crop yields are more sensitive to extreme water conditions

Soil carbonation processes as evidence of tillage-induced erosion

Tillage-induced soil erosion or redistribution increases spatial variation of several soil properties and often reduces the productive capacity of soil resources. Our objectives were to identify the extent of this type of erosion by observing the changes in soil morphological properties in the field and analysing its possible effects on soil productivity. The study was initiated in 2001 and conducted at two irrigated sites located approximately at Terena, Alandrol, 80 km east of Évora, Portugal. They were planted to corn (Zea mays L.) during this study, but have a long history of agricultural use with a trend toward increasing intensity in recent years. Soils in the field studies are classified mainly as Calcaric Regosols, Calcaric Cambisols, Luvisols and small areas of Fluvisols. The amount of erosion was estimated by simulation and verified by describing the lithology and measuring soil carbonates. The presence of carbonates in the superficial Ap horizons of soils that were previously devoid of this compound, provide evidence of soil redistribution: (1) in soils derived from calcareous parent material, this is the result of a re-carbonation process; (2) in soils derived from non-calcareous parent material the presence of carbonates in the superficial Ap horizons results from a carbonation process. On both sites, A and B, approximately 17% of the soils sampled were either carbonated or re-carbonated. Carbonation and re-carbonation of soil profiles confirmed that tillage had redistributed the soil-ploughing layer over time. Decreased corn yield was also observed as slope increase. If current agricultural practices are continued in this area, a decrease in soil quality and maximum yield on higher slopes can be expected

Catenaries and minimal surfaces of revolution in hyperbolic space

We introduce the concept of extrinsic catenary in the hyperbolic plane. Working in the hyperboloid model, we define an extrinsic catenary as the shape of a curve hanging under its weight as seen from the ambient space. In other words, an extrinsic catenary is a critical point of the potential functional, where we calculate the potential with the extrinsic distance to a fixed reference plane in the ambient Lorentzian space. We then characterize extrinsic catenaries in terms of their curvature and as a solution to a prescribed curvature problem involving certain vector fields. In addition, we prove that the generating curve of any minimal surface of revolution in the hyperbolic space is an extrinsic catenary with respect to an appropriate reference plane. Finally, we prove that one of the families of extrinsic catenaries admits an intrinsic characterization if we replace the extrinsic distance with the intrinsic length of horocycles orthogonal to a reference geodesic

Catenaries and minimal surfaces of revolution in hyperbolic space

We introduce the concept of extrinsic catenary in the hyperbolic plane. Working in the hyperboloid model, we define an extrinsic catenary as the shape of a curve hanging under its weight, where the weight is the distance with respect to a reference plane in the ambient Lorentzian space. We then characterize extrinsic catenaries in terms of their curvature and also as a solution to a prescribed curvature problem involving certain vector fields. Finally, we prove that the generating curve of any minimal surface of revolution in the hyperbolic space is an extrinsic catenary with respect to an appropriate reference plane.Comment: 17 pages. Keywords: Catenary, extrinsic catenary, hyperbolic space, minimal surface, surface of revolutio

Catenaries in Riemannian surfaces

The concept of catenary has been recently extended to the sphere and the hyperbolic plane by the second author (López, arXiv:2208.13694). In this work, we define catenaries on any Riemannian surface. A catenary on a surface is a critical point of the potential functional, where we calculate the potential with the intrinsic distance to a fixed reference geodesic. Adopting semi-geodesic coordinates around the reference geodesic, we characterize catenaries using their curvature. Finally, after revisiting the space-form catenaries, we consider surfaces of revolution (where a Clairaut relation is established), ruled surfaces, and the Grušin plane.</p

Catenaries and minimal surfaces of revolution in hyperbolic space

We introduce the concept of extrinsic catenary in the hyperbolic plane. Working in the hyperboloid model, we define an extrinsic catenary as the shape of a curve hanging under its weight as seen from the ambient space. In other words, an extrinsic catenary is a critical point of the potential functional, where we calculate the potential with the extrinsic distance to a fixed reference plane in the ambient Lorentzian space. We then characterize extrinsic catenaries in terms of their curvature and as a solution to a prescribed curvature problem involving certain vector fields. In addition, we prove that the generating curve of any minimal surface of revolution in the hyperbolic space is an extrinsic catenary with respect to an appropriate reference plane. Finally, we prove that one of the families of extrinsic catenaries admits an intrinsic characterization if we replace the extrinsic distance with the intrinsic length of horocycles orthogonal to a reference geodesic

Catenaries and singular minimal surfaces in the simply isotropic space

This paper investigates the hanging chain problem in the simply isotropic plane as well as its 2-dimensional analog in the simply isotropic space. The simply isotropic plane and space are two- and three-dimensional geometries equipped with a degenerate metric whose kernel has dimension 1. Although the metric is degenerate, the hanging chain and hanging surface problems are well-posed if we employ the relative arc length and relative area to measure the weight. Here, the concepts of relative arc length and relative area emerge by seeing the simply isotropic geometry as a relative geometry. In addition to characterizing the simply isotropic catenary, i.e., the solutions of the hanging chain problem, we also prove that it is the generating curve of a minimal surface of revolution in the simply isotropic space. Finally, we obtain the 2-dimensional analog of the catenary, the so-called singular minimal surfaces, and determine the shape of a hanging surface of revolution in the simply isotropic space.Comment: 21 pages, 2 figures; Keywords: Simply isotropic space, catenary, singular minimal surface, relative geometr

Catenaries in Riemannian Surfaces

The concept of catenary has been recently extended to the sphere and the hyperbolic plane by the second author [López, arXiv:2208.13694]. In this work, we define catenaries on any Riemannian surface. A catenary on a surface is a critical point of the potential functional, where we calculate the potential with the intrinsic distance to a fixed reference geodesic. Adopting semi-geodesic coordinates around the reference geodesic, we characterize catenaries using their curvature. Finally, after revisiting the space-form catenaries, we consider surfaces of revolution (where a Clairaut relation is established), ruled surfaces, and the Grušin plane

Catenaries in Riemannian surfaces

The concept of catenary has been recently extended to the sphere and the hyperbolic plane by the second author (López, arXiv:2208.13694). In this work, we define catenaries on any Riemannian surface. A catenary on a surface is a critical point of the potential functional, where we calculate the potential with the intrinsic distance to a fixed reference geodesic. Adopting semi-geodesic coordinates around the reference geodesic, we characterize catenaries using their curvature. Finally, after revisiting the space-form catenaries, we consider surfaces of revolution (where a Clairaut relation is established), ruled surfaces, and the Grušin plane.</p