A Note to the Variable Sorptivity Infiltration Equation

A simplification for the variable sorptivity infiltration equation of Poulovassilis et al. (1989) is proposed. The resulting equation has three parameters S _x, c and K ₀. From these, S _x and c are considered as fitting parameters and K ₀ as a physical one. The new empirical infiltration equation is tested for precision, parameter time-dependence and applicability for soil surveys. The test was carried out by comparison with reference solutions i.e. infiltration data obtainedexperimentally, analytically or numerically for two different head conditionsat the infiltration surface. A good agreement is observed for all examinedcases. The dependence of the fitting parameters S _x and c on the initialand boundary conditions, as well as the error that arises by taking intoaccount different values of them, are examined. In fine textured soilsparameter c seems to be very small, so that one can easily suppose that the proposed equation reduces to the well-known Philip's infiltration equation (Philip, 1957).     

Estimation of air temperature and reference evapotranspiration using MODIS land surface temperature over Greece

Moderate Resolution Imaging Spectroradiometer (MODIS), land surface temperature data, during daytime (LST_day) or night-time (LST_night), were employed for predicting maximum (T_max) or minimum (T_min) air temperature measured at ground stations, respectively, in order to be used as alternative inputs in minimum data-based reference evapotranspiration (ET) models in 28 stations in Greece during the growing season (May–October). The deviations between daily LST_night and T_min were found to be small, but they were greater between LST_day and T_max. Furthermore, the temperature vegetation index (TVX) method was employed for achieving more accurate T_max values from LST_day, after determining the normalized difference vegetation index of a full canopy (NDVI_max). The TVX method was validated on ‘temporal’ basis, but when the method was tested spatially, the improvement on the T_max estimates from LST_day was not encouraging, for being used operationally over Greece. Thus, LST_day or LST_night MODIS data were used as inputs in three ET models [Hargreaves–Samani, Droogers–Allen, and Reference Evapotranspiration Model for Complex Terrains (REMCT)] and their estimations, as compared with ground-based Penman–Monteith estimates, indicated that the REMCT model achieved the most accurate ET predictions (r = 0.93, mean bias error = 0.44 mm day^–1 and root mean square error = 0.74 mm day^–1), which can allow the spatial analysis of ET at higher spatial resolutions in areas with lack of ground temperature data.     

A variable sorptivity infiltration equation

Horizontal and vertical one-dimensional infiltration are compared when they both occur in a homogeneous isotropic porous body initially at a uniform low water content _n under constant concentration (₀) or constant pressure head (H ₀) conditions. From a consideration of the physics governing infiltration under such conditions, the conclusion is reached that the magnitude of the pressure head gradient atx=0, wherex=0 denotes the infiltration surface in the horizontal case, must be larger than the magnitude of the pressure head gradient atz=0, wherez=0 denotes the infiltration surface in the vertical case, for all finitet>0, so that for the hydraulic head gradient atz=0 to be greater than (1/2K ₀)S _x t ^–1/2 but smaller than [(1/2K ₀)S _x t ^–1/2+1],K ₀ being the hydraulic conductivity at ₀ andS _x the sorptivity during horizontal infiltration. On these grounds, it is further argued that if the sorptivityS _z is introduced for the case of vertical infiltration, then it must be equal toS _x fort=0 only and that it must decrease with time. Results obtained by solving soil-water flow equations for the infiltration conditions defined above, and from experiment, support the above conclusions. An equation for the relationship between cumulative infiltration and time during vertical infiltration is developed after assuming thatS _z decreases with time in an exponential manner. Cumulative infiltration versus time relationships given by this equation are compared with those obtained from the numerical solution of the soil-water flow equation and from experiment.     

A Contribution to the Study of the Phenomenon of Horizontal Infiltration

In this work an attempt is made to compare experimental soil moisture profiles for a horizontal infiltration experiment (Poulovassilis, Water Resour Res 13:369?C374, 1977) with calculated profiles. These calculated profiles are obtained variously through the use of the computation code of HYDRUS 1D and through the semi-analytical solution of the appropriate diffusion equation when the soil water diffusivity is obtained directly from the experimental data. The necessary input data for using HYDRUS 1D are obtained in three different ways: First, the experimental data of the main wetting branch of the moisture retention curve (MRC) coupled with Ks (the hydraulic conductivity at saturation) are used. Second the predicted, according to the Parlange model (Parlange, Water Resour Res 12:224?C228, 1976) main wetting branch of the MRC, when experimental data points of the main drying branch of the MRC are used. Third the predicted, according to the Mualem model (Mualem, Water Resour Res 13:773?C780, 1977) main wetting branch of the MRC, again when experimental data points of the main drying branch of the MRC, are used. In the previous three cases predicting appropriate hydraulic conductivity K(??) relationship is obtained through the model of Mualem (Water Resour Res 12:513?C522, 1976). The comparison of the above soil moisture profiles leads to the following: The numerically calculated profiles are moving faster than the experimental ones. Calculated profiles exhibit a Green?CAmpt-like shape. Differences among the experimental and calculated profiles are more pronounced in larger ??-values. Closer to the experimental profiles are those obtained semi-analytically. From the cumulative infiltration versus square-root of time curves, it is evident that the HYDRUS 1D results are compatible with the requirements imposed by the Boltzmann transformation.