Preferential flow is significant for its contribution to rapid response to hydrologic inputs at the soil surface and unsaturated zone flow, which is critical for flow generation in rainfall–runoff (RR) models. In combination with the diffuse and source-responsive flow equations, a new model for water infiltration that incorporates preferential flow is proposed in this paper. Its performance in estimating soil moisture at the catchment scale was tested with observed water content data from the Elder sub-basin of the South Fork Eel River, located in northern California, USA. The case study shows that the new model can improve the accuracy of soil water content simulation even at the catchment scale. The impacts of preferential flow on RR simulation were tested by the Modello Idrologico Semi-Distributio in continuo lumped hydrological model for the Elder River basin. Eleven significant floods events, which were defined as having flood peak magnitudes greater than ten times average discharge during the study period, were employed to assess runoff simulation improvement. The accuracy of the runoff simulation incorporating the preferential flow at the catchment scale improved significantly according to the likelihood ratio test.
INTRODUCTION
Water infiltration plays a major role in rainfall–runoff (RR) generation. Thus, reliable infiltration equations are essential for RR modeling accuracy in both theoretical and practical hydrological applications (Swamee et al. 2014). Preferential flow, which refers to the phenomenon of faster than average water movement through only a fraction of the pore space in a soil column, occurs when water infiltrates through the vadose zone of soil. Preferential flow can influence the soil moisture distribution which has effects on runoff hydrographs, especially subsurface flow in highly heterogeneous slopes (Hendrickx & Flury 2001; Jarvis 2007). It is also an important component of flow generation, especially in many humid regions where overland flow is rarely observed.
Preferential flow occurs in many soils, and is related to worm holes, root channels, and inter-aggregate fissures (Bouma 1981; Beven & Germann 1982), and associated with textural differences (Cislerova et al. 2002; Snehota et al. 2008). Preferential flow has also been increasingly recognized as a process of great practical significance for the transport of water at different scales (Ogawa et al. 2002; Krzeminska et al. 2012). There has been a wide variety of approaches to characterizing preferential flow, including the analysis of the flow in macropores formed by shrinkage and biological processes, within or over structured textural heterogeneous porous formations, unstable flows due to gravity instabilities or viscous instabilities, flow in natural soil pipes or man-made drain tubes, and topographically controlled local soil and groundwater recharge (Gerke et al. 2010). Poiseuille's equation (Ahuja & Hebson 1992), the Green and Ampt or Philip infiltration models (Ahuja & Hebson 1992; Chen & Wagenet 1992), the kinematic wave equation (Germann & Beven 1985; Jarvis 1994), and the Richards equation (Gerke & van Genuchten 1993) are used to calculate water flow in macropores or inter-aggregate pores. These equations assume that the porous medium consists of two interacting regions, and are widely applied in hydrologic simulation (Šimůnek et al. 2003; Gerke 2006; Jarvis 2007; Köhne et al. 2009; Vogel et al. 2010).
These dual-permeability models neglect or simplify the processes and geometrics of preferential flow, which are significantly different from those of non-preferential flow (Nimmo 2010). For example, capillarity is a dominant influence in diffuse unsaturated flow. ‘Source-responsive’ model refers to the thesis that preferential flow may be triggered and modulated in response to the source of water to the unsaturated medium, with the model's dependence on local potential gradients much less than in traditional unsaturated flow models (Nimmo 2010). However, upscaling the preferential flow process in the pores at the micrometer-range scale to the profile scale or even hillslope scale is still limited. There is, as yet, no real consensus as to how to quantify the effects of preferential flow pathways at catchment scales (Beven 2010; Gerke et al. 2010). The widely used infiltration equations in hydrological models cannot effectively simulate preferential flow resulting in rapid infiltration (Nieber & Sidle 2010; Beven & Germann 2013; Shao et al. 2015).
The objectives of this study were to (1) upscale the preferential flow process to the catchment scale and (2) analyze the effect of preferential flow on simulating the runoff process. To achieve this, the source-responsive model was combined with the Green and Ampt model, leading to expressions for soil moisture simulation at a catchment scale. We also applied a lumped hydrological model (Modello Idrologico Semi-Distribuito in continuo (MISDc)) to include the preferential flow process into flow generation, with the expectation of improving predictive models compared to no accounting of preferential flow.
METHODOLOGY
Model for the flux of diffuse and preferential flow using the Green–Ampt model


Green & Ampt (1911) produced an elegant infiltration formula for predicting cumulative infiltration in dry or uniformly wet soil based on the Darcy–Buckingham law for fluxes. In the Green–Ampt model, if the following assumptions for the diffuse-flow domain are satisfied, the approximate infiltration model for fluxes of diffuse and preferential flow can be derived:
As rain continues to fall and water infiltrates, the wetting front advances at the same rate as depth, which produces a well-defined wetting front.
The volumetric water content remains constant above and below the wetting front as it advances.
The soil-water suction immediately below the wetting front remains constant with both time and location as the wetting front advances.
A modified MISDc lump hydrological model which accounts for the diffuse and preferential flow in soil water balance
The MISDc is a semi-distributed RR model developed by Brocca et al. (2011) at the Research Institute for Geo-Hydrological Protection of Perugia, Italy. The model, which has a simple structure with few parameters and low computational effort, couples a soil water balance (SWB) model with an event-based RR model to obtain a simple and robust structure (Anctil et al. 2004; Manfreda et al. 2005; Sheikh et al. 2009). MISDc consists of two main components as follows.
The SWB model to simulate the soil moisture temporal pattern
The output of the SWB model is the degree of saturation, W(t)/Wmax, that is used to determine the initial condition in the MISD model.
A semi-distributed event-based RR model for flood simulation
A semi-distributed event-based RR model (MISD) developed by Corradini et al. (1995) employed the Soil Conservation Service-Curve Number method for abstraction (SCS-CN) for estimation of losses; the geomorphological instantaneous unit hydrograph (IUH) for routing of rainfall in excess of subcatchments (Gupta et al. 1980); and the linear reservoir IUH, a diffusive linear approach, for routing of areas draining directly into the main channel.
STUDY AREA AND DATA
The stream hosts a US Geological Survey hydrologic benchmark station near its mouth (latitude 39 ° 43′ 47″, longitude 123 ° 38′ 34″) with 15-min continuous discharge records from 1967 to 2013. Rainfall data (from six stations), air temperature data (from 12 gauge stations), and soil moisture data (from two stations) are from Berkeley Sensor Database: Angelo Reserve Data. We used data from October 28, 2012 to August 31, 2014, converted to half hour (30 min) intervals. The areal data were calculated from every gauge station by using Thiessen polygon method.
For assessing the impacts of infiltration and preferential flow on RR, flood events characterized by a continuous rainfall pattern with greater than ten times average discharge () were selected; there were 11 such flood events in the study period. A time-domain reflectometry device was used to measure the soil moisture.
RESULTS AND DISCUSSION
Results from the MISDc model whose infiltration is estimated by the Green–Ampt equation
Parameter values of the SWB model based on different formulations for infiltration
The Green–Ampt equation model . | The model combing the source-responsive model and the Green–Ampt model . | ||||||||
---|---|---|---|---|---|---|---|---|---|
ψf . | Ks (mm h−1) . | λ . | b . | ψf . | Ks (mm h−1) . | λ . | b . | τ . | |
−0.800 | 12.505 | 0.640 | 0.761 | −0.800 | 12.505 | 0.520 | 0.827 | 550 | 40,500 |
The Green–Ampt equation model . | The model combing the source-responsive model and the Green–Ampt model . | ||||||||
---|---|---|---|---|---|---|---|---|---|
ψf . | Ks (mm h−1) . | λ . | b . | ψf . | Ks (mm h−1) . | λ . | b . | τ . | |
−0.800 | 12.505 | 0.640 | 0.761 | −0.800 | 12.505 | 0.520 | 0.827 | 550 | 40,500 |
is the average facial area density.
Comparison between observed and simulated soil moisture without accounting for diffuse and preferential flow.
Comparison between observed and simulated soil moisture without accounting for diffuse and preferential flow.
Comparison between observed and simulated runoff without accounting for diffuse and preferential flow, less base flow (6.27 m3/s).
Comparison between observed and simulated runoff without accounting for diffuse and preferential flow, less base flow (6.27 m3/s).
The accuracy of the soil moisture and runoff simulated models is demonstrated with standard performance indicators. Nash–Sutcliffe efficiency (NSE) coefficients were found equal to 0.61, while the root mean squared error (RMSE) was less than 0.04 when the Green–Ampt equation was used to simulate the soil moisture. As can be seen in Figures 2 and 3, the variation of the simulated soil moisture reflects the response of the rainfall to soil. The relatively large differences between the observed and the simulated soil moisture in Figure 3 are probably related to the poor soil moisture data representation for the study catchment. Specifically, the water content from the Green–Ampt equation for high rainfall intensity is overestimating the infiltration. The poor soil moisture representation is because there are only two stations. Additionally, the soil characteristics might be quite variable at different depths and at the whole catchment scale. NSE is 0.71 for the selected flood events. This implies that the MISDc hydrological model can mediate the errors from the soil moisture model, especially for the peak flow simulation.
Results from the MISDc model whose infiltration simulation has accounted for the diffuse and preferential flow
Comparison between observed and simulated soil moisture with accounting for diffuse and preferential flow.
Comparison between observed and simulated soil moisture with accounting for diffuse and preferential flow.
Comparison between observed and simulated runoff with accounting for diffuse and preferential flow, less base flow (6.27 m3/s).
Comparison between observed and simulated runoff with accounting for diffuse and preferential flow, less base flow (6.27 m3/s).
As shown in Figure 5, the performance of the soil moisture balance model incorporating preferential flow is better, with RMSE decreasing from 0.04 to 0.037 and NSE increasing from 0.61 to 0.66. Figure 6 compares the observed and simulated runoff with preferential flow in the 11 selected flood events, and shows a consistent temporal variation of the soil moisture balance simulation. Including preferential flow increased the NSE value to 0.73. We note that the preferential flow rate will decrease with the time t according to Equation (8). Therefore, the effect of preferential flow on soil moisture simulation should be reduced during a rainfall event.
CONCLUSIONS
This study demonstrated that soil moisture simulation accuracy in SWB models can be improved by incorporating preferential flow in the infiltration process.
The sensitivity of soil moisture to preferential flow is reduced over time during a rainfall event. However, the runoff simulation during flood events are highly correlated with the soil moisture evaluated by the SWB model, with low sensitivity to preferential flow. Incorporating preferential flow also significantly improves the accuracy of runoff simulation at the catchment scale through the likelihood ratio test (according to Occam's Razor rule, the more parameters, the higher accuracy of the simulation).
Moreover, the spatial heterogeneity of the soil characteristics and the real areal observed soil moisture data at the catchment scale can influence the accuracy of the model simulation and should be taken into account in future studies.
ACKNOWLEDGEMENTS
The authors thank William E. Dietrich and his research team members for contributing both data and valuable insights to this study. This work was supported by the National Science Foundation CZP EAR-1331940 for the Eel River Critical Zone Observatory and National Natural Science Foundation of China (Grant No. 51379148 and 51579183). Dedi Liu was also supported by the China Scholarship Council (Grant No. 201308420310).