Mapping variability of soil water content and flux across 1¿1000 m scales using the actively heated fiber optic method

The Actively Heated Fiber Optic (AHFO) method is shown to be capable of measuring soil water content several times per hour at 0.25 m spacing along cables of multiple kilometers in length. AHFO is based on distributed temperature sensing (DTS) observation of the heating and cooling of a buried fiber-optic cable resulting from an electrical impulse of energy delivered from the steel cable jacket. The results presented were collected from 750 m of cable buried in three 240 m colocated transects at 30, 60, and 90 cm depths in an agricultural field under center pivot irrigation. The calibration curve relating soil water content to the thermal response of the soil to a heat pulse of 10 W m−1 for 1 min duration was developed in the lab. This calibration was found applicable to the 30 and 60 cm depth cables, while the 90 cm depth cable illustrated the challenges presented by soil heterogeneity for this technique. This method was used to map with high resolution the variability of soil water content and fluxes induced by the nonuniformity of water application at the surface.

Two-dimensional isostatic meshes in the finite element method

In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's of the new mesh remain constant and equal to the initial FE mesh. In order to find the mesh producing the minimum of the selected objective function the steepest descent gradient technique has been applied as optimization algorithm. However this efficient technique has the drawback that demands a large computation power. Extensive application of this methodology to different 2-D elasticity problems leads to the conclusion that isometric isostatic meshes (ii-meshes) produce better results than the standard reasonably initial regular meshes used in practice. This conclusion seems to be independent on the objective function used for comparison. These ii-meshes are obtained by placing FE nodes along the isostatic lines, i.e. curves tangent at each point to the principal direction lines of the elastic problem to be solved and they should be regularly spaced in order to build regular elements. That means ii-meshes are usually obtained by iteration, i.e. with the initial FE mesh the elastic analysis is carried out. By using the obtained results of this analysis the net of isostatic lines can be drawn and in a first trial an ii-mesh can be built. This first ii-mesh can be improved, if it necessary, by analyzing again the problem and generate after the FE analysis the new and improved ii-mesh. Typically, after two first tentative ii-meshes it is sufficient to produce good FE results from the elastic analysis. Several example of this procedure are presented.