S. Assouline(1) and Y. Mualem(2)

1. The Institute of Soil, Water and Environmental Sciences, A.R.O., Volcani Center, Bet-Dagan 50250, Israel.
2. The Seagram center for Soil and Water Sciences, Faculty of Agricultural, Food and Environmental Quality Sciences, Hebrew University of Jerusalem, Rehovot 76100, Israel.

Water scarcity is a major constraint to any development of drylands. Water harvesting of runoff and floodwater, can represent an additional water resource of a good quality at a relatively low cost. Improving water-harvesting techniques necessitates a better estimation of the rainfall-runoff relationships. Also, accurate prediction of runoff yields enables a reliable feasibility analysis and efficient implementation of the appropriate water harvesting system. A wide range of factors affects rainfall-runoff relationships, which therefore, take diversified forms. In the case of small, bare watersheds, the most important factor is infiltration. This can be seriously affected by (i) the formation of a sealing layer at the soil surface due to the raindrops impact and the soil and water chemical conditions, (ii) the spatial variability of the soil hydraulic properties within the watershed. The resulting effect on water ponding, runoff and routing is addressed mostly by means of empirical approaches that relate little importance to the physical processes involved. A different approach is proposed in this study. First, rainfall physical properties are characterized. Then, the effect of rainfall on soil hydraulic properties is modeled and presented in a rigorous solution of the flow equations to yield the infiltration curves. Also, the effect of spatial variability on infiltration is accounted for. Finally, a cell-model, that transforms rainfall input into runoff output, is applied to express the combined effect of soil sealing and spatial variability on runoff hydrogram.

Rainfall is characterized by the raindrop size distribution related to the particular rainfall hydrogram. A model for this distribution is proposed, which indicates that similarity exists between the raindrop size distributions at different rainfall intensities. Consequently, the model yields a relatively simple calibration and prediction procedure of the regional rainfall characteristics, for any given site. Combined with the relationship between raindrop size and final velocity, the model permits the evaluation of the rainfall kinetic energy hydrogram from its intensity hydrogram only.

The impact of raindrops on the soil surface disturbs the soil upper layer and causes changes in its properties. The result is the sealing of the soil to water infiltration. A dynamic model is developed, that describes soil sealing in terms of the increase of the soil bulk density, being maximum at the soil surface and decreasing exponentially with depth. The formulation of the relationships between the soil bulk density and its hydraulic parameters allows the determination of the hydraulic functions at every point within the disturbed layer and at every moment during seal formation. It is, thus, possible to solve the flow equations not only for the undisturbed soil but also within the seal domain. Once calibrated, the predictive ability of the dynamic model was found to be rather good on basis of verification with extensive experimental results. Therefore, it can be used now to evaluate the effects of various variables affecting flow processes, like soil and rainfall properties, initial conditions, or chemical conditions of the soil-water system, on infiltration and runoff generation.

The dynamic model is used to compare the effects of spatial variability of soil hydraulic properties on infiltration during soil sealing with the case of unsealed soil. The spatial variability is described in terms of a log-normally-distributed saturated hydraulic conductivity that determine the other soil hydraulic parameter distributions. The results indicate that accounting for spatial variability of soil hydraulic properties, when soil sealing is considered, reduces the ponding time and increases the final infiltration rate. The infiltration curves resulting from considering both soil sealing and spatial variability are approximated in the next stage by a step function, defined by two constants, that can be integrated in a cell-model for runoff hydrogram computation. The cell-model divides the watershed into a system of sub-units (cells) connected by channels simulating the natural drainage network of the basin, every cell being defined by its specific infiltration constants. Soil sealing increases significantly the cumulative runoff from a watershed and enhances its formation. The effect of spatial variability is more complex and depends upon the soil properties and their distribution within the watershed. It appears that the soil sealing phenomenon restraints the effect of spatial variability. However, the lower the rainfall intensity is, the more significant the effect of the soil spatial variability becomes. Since rainfall events are mostly of low intensity, it is important to account for the spatial variability of soil properties for better forecasting of rainfall-runoff relationships. Another significant aspect revealed in this study is that spatial variability is generally described by statistical means. But, in reality, the geographical position of the different cells within a given watershed is uniquely defined. Different spatial arrangements of the cells lead to different runoff hydrograms even if the hydraulic properties of the cells are statistically having identical distributions. The statistical definition of spatial variability permits to evaluate the expected cumulative runoff from a given rainfall event. It cannot predict accurately important engineering parameters such as the time of ponding, the peak discharge and its time of occurrence. A deterministic approach in the watershed characterization will lead to a better expression of its specific rainfall-runoff relationship.