### A FULL-NEWTON ALGORITHM FOR PARAMETER ESTIMATION IN

#### Abstract

An iterative algorithm based on a full-Newton method for the estimation of the saturated hydraulic

conductivity k in the unsaturated zone from drainage experiments is presented. The groundwater

ow is assumed to be described by Richards equation and the well-known van Genuchten constitutive

model. The cost functional used for the parameter optimization is dened as the L2-error between the

calculated pressure head values and the observed data at discrete points in the soil prole during the

drainage process. The derivative of pressure head with respect to the parameter k is obtained as the

solution of a differential equation with appropriate boundary and initial conditions. A Galerkin nite

element procedure is used to obtain approximated solutions of the two differential problems involved in

each iteration: the direct problem and the derivative of the functional. The algorithm was implemented

in one-dimensional domains and used to estimate k in layered soil using synthetically generated data.

Numerical examples show that the proposed algorithm yields very good estimations of the saturated

hydraulic conductivity and becomes a promising method for in situ estimation of this parameter.

conductivity k in the unsaturated zone from drainage experiments is presented. The groundwater

ow is assumed to be described by Richards equation and the well-known van Genuchten constitutive

model. The cost functional used for the parameter optimization is dened as the L2-error between the

calculated pressure head values and the observed data at discrete points in the soil prole during the

drainage process. The derivative of pressure head with respect to the parameter k is obtained as the

solution of a differential equation with appropriate boundary and initial conditions. A Galerkin nite

element procedure is used to obtain approximated solutions of the two differential problems involved in

each iteration: the direct problem and the derivative of the functional. The algorithm was implemented

in one-dimensional domains and used to estimate k in layered soil using synthetically generated data.

Numerical examples show that the proposed algorithm yields very good estimations of the saturated

hydraulic conductivity and becomes a promising method for in situ estimation of this parameter.

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**