Research papersImproving the Horton infiltration equation by considering soil moisture variation
Introduction
Infiltration is one of the critical hydrological processes. It determines the vertical redistribution of rainfall among surface water and soil moisture in different soil layers, and significantly affects interchanges between surface water and groundwater (Ferguson, 2017). Total infiltration is estimated to be 27.0% of total precipitation at the global scale (Oki and Kanae, 2006), and the proportion could even be over 75.0% in some karst regions (Jemcov and Petric, 2009). Infiltration is strongly related to water conservation, maintenance of ecosystem functions and health, flood control, etc. For example, infiltration clearly decreases as the amount of impermeable pavement in metropolitan regions increases, resulting in greater frequencies of urban flooding and waterlogging that have been observed in recent decades (Ebrahimian et al., 2016, Locatelli et al., 2017). Therefore, investigation of the mechanisms of infiltration is one of the foundational and important subjects receiving great interest in the hydrology community. These studies provide scientific support for a large number of hydrological- or ecological-related projects in the world, such as sponge city construction, artificial recharge of groundwater, and ecological restoration (Bonneau et al., 2018, Kidmose et al., 2015, Xia et al., 2017, Xu et al., 2018, Zhang et al., 2016).
The infiltration mechanism is complicated because it is highly affected by numerous factors including rainfall intensity and duration, soil characteristics, soil moisture, watershed topography, and land cover (Dunkerley, 2012, Schoener and Stone, 2019, Sihag et al., 2019, Wang et al., 2015, Yu and Coulthard, 2015). Many infiltration models have been proposed and can be divided into three categories, i.e., physically based models, empirical models, and semi-empirical models (Mishra and Singh, 1999, Sihag et al., 2017, Vand et al., 2018). The physically based models are directly deduced from the law of mass-conservation (i.e., Darcy’s laws) with a variety of simplifications and assumptions. The models are able to reflect the influence of different soil physical parameters and boundary conditions on infiltration, and provide results with high temporal and spatial resolutions (Ali et al., 2016, Ma et al., 2010). However, they require more input data as well as proper calibration before they can be successfully applied. The physically based models have been developed by Green and Ampt, 1911, Philip, 1957, Philip, 1969, Mein and Larson, 1971, Mein and Larson, 1973, Smith (1972), and Smith et al. (2002). The empirical models were developed based on a series of experimental observations, have simplified structures, and are easily applied to fields with little information. Typical models have been proposed by Kostiakov, 1932, Collis-George, 1977. The semi-empirical models employ simplified forms of the continuity equations and the relationships hypothesized between infiltration rate and cumulative infiltration. These models were usually developed using a systems approach which is popularly employed in surface hydrology, and are a compromise between empirical and physically based models (Mishra et al., 2003). The Horton equation (Horton, 1933, Horton, 1938) is one of the most widely used semi-empirical models. The classical exhaustion process in nature is used in the Horton equation to derive the infiltration capacity variation with time during rain. All of the processes affecting the rate of change of infiltration capacity are linearly proportional to the infiltration capacity remaining to be performed (Horton, 1941). Although the Horton equation is semi-empirical, it reveals the similar pattern of infiltration rate decline from the initial infiltration rate to the stable infiltration rate as other physically based models such as the Green-Ampt model and the Philip model (Beven, 2004).
However, some shortcomings still exist in the Horton equation. For example, the reduction law of infiltration capacity is accurate only when rainfall intensity exceeds infiltration capacity (Dunkerley, 2018). Additionally, the initial infiltration capacity is usually fixed without considering variations of the antecedent soil moisture conditions, and thus the equation is deficient for simulating the variable infiltration occurring under varying antecedent soil moisture conditions (Davidsen et al., 2017, Hayek, 2018). In practice, the infiltration capacity only depends on the cumulative infiltration volume, rather than the previous rainfall history (Assouline, 2013). Some improvements to the Horton equation have been made. Bauer (1974) proposed a modified Horton equation that used a simple linear relationship between soil moisture and accumulated infiltration. Esen and Almedeij (2013) modified the Horton equation by considering the rainfall intensity as an independent variable in addition to the other parameters used in the original model, and this is similar to the improvement proposed by Verma (1982). Assouline (2013) adopted the Time Compression Approximation method to deal with the restrictions of intermittent rainfall events, and the “equivalent time” was calculated based on the post cumulative infiltration from the Horton integrated curve. However, all of these improvements are still based on the relationships between infiltration capacity and rainfall duration, and do not reflect the cumulative infiltration variation that occurs with the increase of soil moisture, which is one of the critical driving forces (closely related to capillary potential gradients) for water infiltration into the soil (Liu et al., 2011). Therefore, incorporating the relationship between infiltration capacity and soil moisture may be an effective way to improve the Horton equation.
The objectives of this study were to explore the relationship between infiltration and soil moisture using controlled experiments, and to propose an improved Horton equation to simulate the rainfall infiltration process with consideration of soil moisture variation following the basic form of the original Horton equation. The specific objectives were to: (1) determine relationships between experimentally observed infiltration data and soil moisture; (2) derive the infiltration-soil moisture equation following the basic form of the Horton equation; (3) validate the applicability and enhancement of the infiltration-soil moisture equation by comparing its simulation performance and uncertainty intervals with those of the original Horton equation. This study is expected to provide new insights into soil infiltration processes under variable rainfall and antecedent soil moisture conditions, and to further promote the applicability and scope of the Horton equation in the complicated field of hydrological modelling.
Section snippets
Artificial rainfall-infiltration experiment
An artificial rainfall-infiltration experimental system was designed to analyze the relationship between soil moisture and infiltration capacity. The system consisted of three parts, including a test cube of soil, an artificial rainfall simulation apparatus, and monitoring devices (Fig. 1). The system was able to provide multiple artificial simulated rainfall intensities ranging from 30 to 200 mm/h, and could monitor the high-precision overflow and soil moisture changes at five different depths
Derivation of infiltration capacity-soil moisture equation
The assumption of the Horton equation is that the reduction of infiltration capacity obeys the nature of exhaustion process as an inverse exponential law as rainfall continues (Horton, 1941). This means that the infiltration capacity (f: mm/h) decreases gradually with rainfall duration (t: hour) and approaches a constant value (i.e. stable infiltration capacity: fc: mm/h) when the rainfall duration increases to infinity. The rate at which infiltration capacity (df/dt) declines is proportional
Experimental observations of variable infiltration
The variations in infiltration rate under different soil moisture conditions are shown in Fig. 3a. The infiltration rate was observed to decline nonlinearly as soil moisture increased. Considering the data from all 32 experiments, infiltration rate decreased from 120 mm/h to 30 mm/h, while soil moisture increased from 0.27 to 0.44 m3/m3. At the initial stage of each experiment, due to the low soil moisture condition, the infiltration rate rapidly declined from 100 to 40 mm/h as the soil
Discussion
Soil infiltration is one of many complicated hydrological processes, and is affected by rainfall intensity and duration, soil moisture, soil structure, human activities (e.g., irrigation, tillage), and so on (Mishra et al., 2003, Liu et al., 2011). Most previous studies have focused on the reduction of infiltration capacity with rainfall duration (Horton, 1938). However, the reduction of infiltration capacity is mainly the result of decreased capillary potential gradients and increased soil
Conclusions
Soil water infiltration is one of the critical hydrological processes, and its simulation is still difficult in hydrological cycle modelling due to soil spatial heterogeneity and complicated soil structure. In our study, both an artificial rainfall experiment and numerical simulation were used to investigate the relationship between infiltration capacity and soil moisture. The results showed that:
- (1)
Infiltration capacity decreases nonlinearly as soil moisture increased, and approached a stable
CRediT authorship contribution statement
Moyuan Yang: Methodology, Software, Formal analysis, Resources, Data curation. Yongyong Zhang: Conceptualization, Investigation, Validation, Writing - original draft, Writing - review & editing. Xingyao Pan: Writing - original draft, Visualization, Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This study was supported by Natural Science Foundation of China (Nos. 41730645 and 41671024), Beijing Municipal Natural Science Foundation (No. 8194061), the Major Science and Technology Program for Water Pollution Control and Treatment (No. 2017ZX07103-002). Thanks to Dr. David C. Nielsen for the professional English and content editing, which helped improve the quality and presentation of the manuscript. Thanks also to the editors, and two anonymous referees for their constructive comments.
References (50)
- et al.
Green-Ampt approximations: a comprehensive analysis
J. Hydrol.
(2016) - et al.
Where does infiltrated stormwater go? Interactions with vegetation and subsurface anthropogenic features
J. Hydrol.
(2018) - et al.
Comparison of infiltration models to simulate flood events at the field scale
J. Hydrol.
(2005) - et al.
A unified model for infiltration and redistribution during complex rainfall patterns
J. Hydrol.
(1997) How is overland flow produced under intermittent rain? An analysis using plot-scale rainfall simulation on dryland soils
J. Hydrol.
(2018)- et al.
Improved methods to estimate the effective impervious area in urban catchments using rainfall-runoff data
J. Hydrol.
(2016) An efficient analytical model for horizontal infiltration in soils
J. Hydrol.
(2018)- et al.
Effects of rainfall intensity, underlying surface and slope gradient on soil infiltration under simulated rainfall experiments
Catena
(2013) - et al.
Measured precipitation vs. effective infiltration and their influence on the assessment of karst systems based on results of the time series analysis
J. Hydrol.
(2009) - et al.
Parameter and modeling uncertainty simulated by GLUE and a formal Bayesian method for a conceptual hydrological model
J. Hydrol.
(2010)
Coupling of a distributed hydrological model with an urban storm water model for impact analysis of forced infiltration
J. Hydrol.
Evaluation of the subjective factors of the GLUE method and comparison with the formal Bayesian method in uncertainty assessment of hydrological models
J. Hydrol.
Effects of rainfall intensity and antecedent soil water content on soil infiltrability under rainfall conditions using the run off-on-out method
J. Hydrol.
Hydrologic impact of urbanization with extensive stormwater infiltration
J. Hydrol.
Theory of infiltration
Impact of antecedent soil moisture on runoff from a semiarid catchment
J. Hydrol.
Estimation and inter-comparison of infiltration models
Water Sci.
Modified Horton's infiltration equation
J. Hydrol.
Relationship between soil erodibility and modeled infiltration rate in different soils
J. Hydrol.
A simple analytical infiltration model for short-duration rainfall
J. Hydrol.
Design of sponge city: lessons learnt from an ancient drainage system in Ganzhou, China
J. Hydrol.
Evaluating the importance of catchment hydrological parameters for urban surface water flood modelling using a simple hydro-inundation model
J. Hydrol.
Uncertainty and its propagation estimation for an integrated water system model: An experiment from water quantity to quality simulations
J. Hydrol.
The relationships between grasslands and soil moisture on the Loess Plateau of China: a review
Catena
Infiltration into soils – conceptual approaches and solutions
Water. Resour. Res.
Cited by (25)
A novel irrigation canal scheduling model adaptable to the spatial-temporal variability of water conveyance loss
2022, Agricultural Water ManagementCitation Excerpt :In addition, the water permeability of a canal bed highly depends on its soil moisture condition, which is the crucial driving force for water infiltration into the soil (Furman et al., 2006). The infiltration rate decreases nonlinearly as soil moisture increases and finally approaches a stable rate when the soil is saturated (Horton, 1941; Philip, 1957; Yang et al., 2020). During canal scheduling, the water content in the soil profile of the canal bed often changes due to periodic water filling and drying.
Review of distribution of nitrogen and phosphorus in riparian zones of Chinese inland water bodies
2022, Acta Ecologica SinicaCitation Excerpt :The soil infiltration rates had a negative relationship with soil moisture, but a positive relationship with the below-ground biomass [76]. Yang et al. [82] improved the original Horton Eq. [83] and indicated that the infiltration rate decreased nonlinearly with the increase of soil moisture and finally became stable when the soil was saturated. The relationship between soil aggregates and infiltration is very close.
Experimental analysis of soil moisture response to rainfall in a typical grassland hillslope under different vegetation treatments
2022, Environmental ResearchCitation Excerpt :Zhu et al. (2014) also showed that the increase of surface soil moisture under dry conditions was significantly negatively correlated with initial soil water content. Dry soil has the potential to store more rainwater (Ziadat and Taimeh, 2013) and shows a faster wetting rate in response to high intensity rainfall (Liu et al., 2011; Zhu et al., 2014; Yang et al., 2020). However, the rainfall infiltration rate will decline under wet soil conditions due to the small hydraulic gradient at the wetting front (Liu et al., 2011).