The use of the Boltzmann transform function, λ(θ), to solve the Richards equation when the diffusivity, D, is a function of only soil water content, θ, is now commonplace in the literature. Nevertheless, a new analytic solution of the Boltzmann transform λ(h) as a function of matric potential for horizontal water infiltration into a sand was derived without invoking the concept or use of D(θ). The derivation assumes that a similarity exists between the soil water retention function and the Boltzmann transform λ(θ). The solution successfully described soil water content profiles experimentally measured for different infiltration times into a homogeneous sand and agrees with those presented by Philip in 1955 and 1957. The applicability of this solution for all soils remains open, but it is anticipated to hold for soils whose air‐filled pore‐size distribution before wetting is sufficiently narrow to yield a sharp increase of water content at the wetting front during infiltration. It also improves and provides a versatile alternative to the well‐known analysis pioneered by Green and Ampt in 1911.

Fig. 2. Normalized moisture content θ/θ s as a function of the normalized Boltzmann variable ϕ/ϕ a (solid line). Th e dashes show θ/θ s = 0.

Based on physical laws of similarity, an analytic solution of the soil water potential form of the Richards equation was derived for water infiltration into a homogeneous sand. The derivation assumes a similarity between the soil water retention function and that of the soil water content profiles taken at fixed times. The new solution successfully described soil water content profiles experimentally measured for water infiltrating downward, upward, and horizontally into a homogeneous sand and agrees with that presented by Philip in 1957. The utility of this analysis is still to be verified, but it is expected to hold for soils that have a narrow pore‐size distribution before wetting and that manifest a sharp increase of water content at the wetting front during infiltration. The effect of van Genuchten's parameters α and n on the application of the solution to other porous media was investigated. The solution also improves and provides a more realistic description of the infiltration process than that pioneered by Green and Ampt in 1911.

In this work, a comparative study of the behaviour of an in-fibre Mach-Zehnder interferometer for salinity measurement in a water solution is presented. The fibre transducer is composed of two nearly identical long period gratings forming an inseries 7.38 cm long device written in the same fibre optic. Two inorganic and one organic salts (NaCl, KCl, NaCOOH) were characterized within the concentration range from 0 to 150 g L −1. For the long period grating interferometer, the average obtained sensitivities were −6.61, −5.58 and −3.83 pm/(g L −1) for the above salts, respectively, or equivalently −40.8, −46.5 and −39.1 nm RIU −1. Salinity measured by means of fibre refractometry is compared with measurements obtained using an Abbe refractometer as well as via electrical conductivity. For the long period grating refractometer, the best resolutions attained were 1.30, 1.54 and 2.03 g of salt per litre for NaCl, KCl and NaCOOH, respectively, about two times better than the resolutions obtained by the Abbe refractometer. An average thermal sensitivity of 53 pm °C −1 was measured for the grating transducer immersed in water, indicating the need for the thermal correction of the sensor. Resolutions for the same ionic constituent in different salts are also analysed.

RESUMO(1) Trabalho enviado para publicação em agosto de 1999 e aprovado em março de 2000.(2) Professor Titular do

Core Ideas The Green–Ampt theory may be now generalized for the unsaturated zone. This theory is applicable in any homogeneous soil for θi ≠ 0. The centenary limitation of the Green–Ampt theory for horizontal infiltration has been solved. In past work, an analytic solution of the Boltzmann transform as a function of matric potential was proposed to estimate the soil water content profile for horizontal water infiltration into porous media. However, it could only be successfully described for sands, but with singularity at position x = 0. Later, others introduced the concept of air‐entry pressure to divide the soil water retention curve into saturated and unsaturated domains to provide an exact solution of the Bruce and Klute equation, with no restrictions, while assuming the initial soil water content to be zero before the infiltration process. The problem remained that the above‐mentioned analytical solution was limited to sands, while the Bruce‐ and Klute‐based approach was limited to zero water content at the beginning. This study was based on both previous studies, and the objective was to develop a solution that works for all soil types and does not depend on zero initial soil moisture content. As a result, an alternative solution is presented that generalizes the centenary theory of Green and Ampt for any homogeneous soil.

RESUMOA avaliação do processo da redistribuição da água no solo, em condições de campo, demanda considerável tempo e apreciável custo, porque as propriedades hidráulicas do solo sofrem extensa variabilidade espacial e estão sujeitas a freqüentes alterações no tempo. O presente trabalho propõe dois modelos analíticos para estimar a dinâmica desse processo, a partir da adoção do gradiente de potencial hidráulico unitário na equação de Richards. O primeiro modelo estima a umidade do solo e o segundo estima a densidade de fluxo, ambos de acordo com o tempo de drenagem interna para a profundidade de interesse. Os resultados gerados pelos modelos confrontam-se satisfatoriamente física e estatisticamente com os valores medidos da umidade e densidade de fluxo durante o período de drenagem em diferentes profundidades numa Areia Marinha submetida a esse processo em condições de campo. Os modelos propostos exigem somente o conhecimento prévio dos dados da curva de retenção e da condutividade hidráulica do solo na profundidade de interesse.Termos de indexação: redistribuição da água no solo, equação de Richards, modelos analíticos.

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