Multifractal analysis of the effects of rainfall and Ks on surface infiltration and runoff

Abstract

This research analyzes the effects of rainfall and saturated hydraulic conductivity (Ks) on surface infiltration and runoff using numerical experiments in the framework of universal multifractal (UM) model. A set of criteria is first defined based on radial power spectrum of a physical field for its scaling in general and for fitting the UM model in particular. Then a technique is developed to estimate the UM model parameters of non-conservative multifractal fields. The estimation approaches for both conservative and non-conservative fields are evaluated and demonstrated to produce estimates with good to excellent accuracy. A physically based, distributed rainfall-runoff model, named DIMBRR, was developed for the study on surface infiltration and runoff. The event-based DIMBRR model employs the Green-Ampt model for infiltration and the kinematic wave model for routing. The routing hierarchy of a watershed is defined based on the D-infinity flow direction model. DIMBRR model is calibrated using data collected from the sub-watershed 11 of the USDA-ARS Walnut Gulch experimental watershed. To analyze the effects of driving fields (rain and Ks) on surface infiltration and runoff, a series of rainfall and Ks fields are generated including both random, non-scaling fields and multifractal fields produced using the UM model. By varying the UM model parameters based on physical considerations, rain and Ks fields with various characteristics are obtained. These rain and Ks data are then fed into the DIMBRR model to produce space-time infiltration and runoff processes. The scaling properties of these watershed processes are then analyzed to find the impact from the rain and Ks fields mainly in terms of the connections among the UM model parameters from the input and the output fields. Some of the major findings from this research are: 1) Ks, rather than rain, determines if the resulting infiltration field is scaling after an adjusting period; 2) some model parameters from both rain and Ks fields have a strong impact on infiltration while only rain parameters have a significant influence on runoff; 3) infiltration fields are usually non-homogeneous while runoff fields are usually homogeneous; 4) if an infiltration field becomes more singular (localized large infiltration rates) in time, it usually also becomes more sparse on average and more homogeneous; 5) a runoff field always becomes more singular in time, yet it also becomes more space-filling on average.