This paper presents several exact and approximate analytical solutions of the equations describing convective-dispersive solute transport through large cylindrical macropores with simultaneous radial diffusion from the larger pores into the surrounding soil matrix. Adsorption effects were included through the introduction of linear isotherms for both the macropore region and the soil bulk matrix. In one formulation the macropores are surrounded by cylindrical soil mantles of finite thickness. Another formulation considers diffusion from a single cylindrical macropore into a radially infinite soil system. A relatively simple but very accurate approximate solution that ignores dispersion in the macropore region is also derived. The various analytical solutions in this paper can be used to calculate temporal and spatial concentration distributions in the macropore system. In addition, approximate solutions are presented for the radial concentration distribution within the adjacent soil matrix. By means of an example, it is demonstrated that at early times, little accuracy is lost when the radially finite soil mantle is replaced by an infinite system.

Estimating the size of the ponded surface area is a major source of error in modeling water movement under trickle irrigation. After reviewing available approaches and models for simulating water flow under trickle irrigation, we present a new numerical solution of the governing partial differential equations that improves the prediction of the size of the ponded area at the soil surface. A common formulation could be used for both Cartesian and axicylindrical flow geometries. The spatial operator was approximated using finite differences, and time integration was performed with an implicit method. Nonlinearity was treated by means of a fixed point iterative algorithm. The proposed model is applicable to saturated-unsaturated flow in layered soils having anisotropic hydraulic properties. Accuracy and stability of the solution are checked and comparisons made with previous numerical solutions for several trickle irrigation and other unsaturated flow problems.

Résumé — On teste en laboratoire et in situ les performances d'un capteur capacitif destiné à la mesure de l'humidité du sol. En laboratoire, on montre que les dérives thermiques propres à l'appareillage sont négligeables, que la mesure de permittivité diélectrique relative est dépendante de la qualité du contact sol-électrodes, et que le volume de mesure a des dimensions de l'ordre de quelques cm 3 . Les relations linéaires permittivité relative-teneur en eau volumique sont dépendantes de la texture, de la structure (agrégats de 2-3 mm et 4 mm disposés autour des électrodes ou structure continue), de la température (la variation de la permittivité relative en fonction de la température peut atteindre 0,20 par °C dans la gamme de 0 à 45 °C), de la salinité (la mesure de permittivité diélectrique relative est peu sensible à la concentration saline jusqu'à des valeurs de conductance électrique de l'ordre de 2 à 3 mS). In permittivité diélectrique / humidité / texture / structure du sol / salinité / température Summary — Soil moisture measurement using a capacitive probe. The performance of a capacitive probe for soil moisture measurement was studied under laboratory and field conditions. The probe (21-mm ED cylinder) was composed of 2 electrodes connected to an electronic oscillator (38 MHz) located in the probe. Four soils were used to analyse the 'dielectric permittivity-volumetric water content' relationships under laboratory or field conditions. The sensitivity of the probe including its electronic components in relation to the variations of the temperature (0-45 °C) was very low (< 0.5 permittivity unit). Permittivity measurements were dependent on the quality of the soil-electrodes contact, and on the soil structure near the electrodes. The order of magnitude of the volume of influence was a few cubic centimeters, and the area of the soil most affected by the permissibility measurements was located in the vicinity of the electrodes. The 'dielectric permittivity-volumetric water content' relationships were linear (r > 0.99), and dependent on soil texture and structure. Moreover, soil temperature influenced the measurements since increases of the order of magnitude of 0.20 permittivity unit per °C could be observed. Permittivity measurements were not sensitive to the concentration of the solution when the electric conductance was < 2-3 mS. Two field experiments were performed using 2 different soil textures. The first soil (C = 10.5%, L = 50.6%, S = 38.8%) was a bare soil, and showed a quite homogeneous soil structure, the second (C = 27.2%, L = 61.7%, S = 11.1%) was cultivated with soybean, and showed a more heterogeneous soil structure. For each experiment field, simultaneous measurements (1 or

A numerical solution for predicting soil water content distributions during trickle irrigation on stratified and anisotropic soils was compared with data from a field experiment carried out on a loamy clay soil using 24 field plots irrigated at different rates and frequencies. The unsaturated hydraulic conductivity was estimated from measured soil water retention and saturated hydraulic conductivities. Observed volumetric soil water contents and saturated areas on the soil surface were compared with model predictions. The effects of anisotropy and soil surface crusting on experimental and calculated soil water distributions were also investigated. Relatively good agreement was obtained between predicted and measured soil water content distributions vs. depth. The shape of the observed wetted soil volume was also predicted reasonably well. The effects of possible errors in the hydraulic characteristics on calculated water content distributions are discussed.

A partir des mesures du coefficient de diffusion de l'ion nitrate dans des matériaux de textures différentes et dans des situations humidité-densité multiples, nous avons pu décrire les variations de ce coefficient dans la gamme d'humidité pondérale variant de 10 à 36 p. 100 et de densité allant de 0,8 à l,7 g. cm-3. !. Par la suite, une approche de modélisation a été menée. Nous obtenons une expression où le coefficient de diffusion D est donné en fonction du coefficient de diffusion moléculaire dans l'eau D o , de la tortuosité dans l'agrégat (D;ç/D!), de la teneur en eau massique W et de la porosité structurale n,. Ce coefficient de diffusion a le même sens de variation que W et décroît lorsque n s augmente. Par ailleurs, ces deux variables explicatives (W, n,) présentent des valeurs seuils (W. , n_) en deçà desquelles le phénomène de diffusion est négligeable ; le seuil d'humidité est dépendant de la nature du sol, celui de porosité structurale, de la taille des agrégats. Cette approche qui a été utile pour la compréhension du système, permet d'aboutir à une estimation du coefficient de diffusion en fonction de la teneur en eau et de la compacité. Mots clés additionnels : Sols non saturés, porosité structurale, densité, humidité pondérale, texture.