An approximate analytical solution to the Boussinesq equation is presented here. Uniform initial conditions and a step function increase of piezometric head on the boundary are assumed. The one‐dimensional problem is reduced to an ordinary differential equation through Boltzmann's transformation, and a technique exploiting some basic characteristics of the exact solution leads to an approximate polynomial solution of the problem. The technique presented here can also be applied to one‐dimensional nonlinear diffusion problems. A numerical procedure incorporating some of the analytical characteristics of the exact solution is presented. A discussion concludes the paper.
Rainfall erosivity concerns the ability of rainfall to cause erosion on the surface of the earth. The difficulty in modeling the distribution, the size, and the terminal velocity of raindrops in relation to the detachment of soil particles led to the use of more tractable rainfall indices. Thus, in the universal soil loss equation (USLE), the coefficient of rainfall erosivity, R, was introduced. This coefficient is based on the product of the rainfall kinetic energy of a storm and its maximum 30-minute intensity. An important problem in the application of USLE and its revisions in various parts of the world concerns the computation of R, which requires pluviograph records with a length of at least 20 years. For this reason, empirical equations have been developed that are based on coarser rainfall data, such as daily, monthly, or yearly, which are available on larger spatial and temporal extents. However, the lack of denser data is dealt more effectively by means of machine learning methods. Computational systems for this purpose were recently developed based on feed-forward neural networks, yielding significantly better results.
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