COBEM2019-1110 COMPARISON OF VARIANTS OF THE LUUS-JAAKOLA METHOD IN THE ESTIMATION OF VAN GENUCHTEN RETENTION CURVE PARAMETERS Fábio Freitas Ferreira Wagner Rambaldi Telles Universidade Federal Fluminense fabiofreitasferreira@id.uff.br wr_telles@yahoo.com.br Gustavo Bastos Lyra Universidade Federal Rural do Rio de Janeiro bglyra@id.uff.br Antônio J. Silva Neto Universidade do Estado do Rio de Janeiro ajsneto@iprj.uerj.br Abstract. In order to predict volumetric water content, it is necessary to know the water retention curve in the soil, as well as the hydraulic conductivity function. These functions depend on parameters related to the soil physical characteristic such as texture. It is in this sense that the aim of this work is to compare the three versions of the Luus-Jaakola method. Keywords: Inverse Problem, Luus-Jaakola, Richards Equation, van Genuchten, Retention Curves 1. INTRODUCTION Inverse problems are of great importance in several relevant real world applications, and has attracted the attention of an increasing number of researchers. Many processes that usually require high financial costs, or time, can be improved with the application of optimization methods. Problems of infiltration of water into soil are of particular interest for enviromental modelling and food production, among many other applications. These problems depend on parameters that need to be obtained through specific equipment, which depends on the soil characteristic. To prescribe the infiltration of water into the soil, the Richards equation has been intensively used in Silva Neto and White (1994) and Kroes et al. (2017). This equation is a combination of the Darcy equation and the continuity equation, which depends on the water retention curve in the soil, as well as the hydraulic conductivity function. This problem has been treated over the decades, as can be seen in Silva Neto and White (1994) and Celia et al. (1990). In Temperini (2018) we find the solution of the Richards Equation by means of the Finite Volume Method (FVM). In Moura Neto and Silva Neto (2012), we find a description of inverse problems, and solution methods known as deterministic methods. Another class of inverse problems solution approach is related to stochastic methods. In Telles (2014) and in Silva Neto et al. (2016), we find the application of the Luus-Jaakola method, a probabilistic, easy-to- implement method that was developed to solve problems of maximization and minimization. Jez˙ owski et al. (2005) proposed two modifications in the Luus-Jaakola method. Both changes involves the strategy for the reduction of the search interval. It is in this sense that the aim of this work is to apply such modifications to the problem of infiltration of water in the soil, specifically the estimation of the van Genunchten retention curve parameters, and compare the solution with the original LJ. 2. MATHEMATICAL MODEL Let θ e be the soil volumetric water content (cm 3 /cm 3 ), obtained experimentally in a soil column, and θ c be the soil volumetric water content (cm 3 /cm 3 ) obtained by means of the algorithm developed by Temperini (2018), using the FVM. The residue between the experimental and the calculated values is given by R = θ c − θ e . We define the functional that