Research papers
Improving the Horton infiltration equation by considering soil moisture variation

https://doi.org/10.1016/j.jhydrol.2020.124864Get rights and content

Highlights

  • Infiltration is directly affected by soil moisture, rather than rainfall duration.

  • Horton infiltration equation is improved by adopting soil moisture variation.

  • Improved equation is better in simulation performance and uncertainty intervals.

Abstract

Soil water infiltration simulation is a subject receiving great interest in hydrological cycle modelling. The traditional Horton equation is based on the curve of infiltration capacity-rainfall duration time. However, the infiltration process is directly affected by soil moisture content, rather than rainfall duration. The objective of this study was to determine a relationship between infiltration capacity and soil moisture content in order to improve the Horton infiltration equation. Artificial rainfall-infiltration experiments were used to determine a series of power functions. The improved equation was cross-validated with observations from 32 experiments of multiple rainfall intensities and antecedent soil moisture. The simulation performance and uncertainty of the improved equation were compared with those of the original Horton equation to verify its accuracy. The results showed that infiltration rate decreases nonlinearly as soil moisture increases, and finally approaches a stable infiltration rate when the soil is saturated. Overland flow simulations by the improved Horton equation closely matched the observations from all 32 experiments over a soil moisture range of 0.222–0.349 m3/m3. The simulation performance was rated as good for most of the experiments for both the calibration and validation data sets. Compared with the original Horton equation, the simulation performance of the improved equation clearly improved estimation of infiltration, particularly as quantified by the Nash-Sutcliffe efficiency coefficient (NSE) and the coefficient of determination (R2). The number of simulations with NSE values greater than 0.65 increased 11.59% and 2.50% for the calibration and validation data sets, respectively. The number of simulations with R2 values greater than 0.90 increased 31.14% and 22.50%, respectively. The uncertainty intervals of the improved Horton equation became a little greater than those of the original Horton equation. For all 32 experimental simulations, the average relative length of the uncertainty interval at the 95% confidence level increased from 40.52% with the original Horton equation to 49.17% with the improved Horton equation. The number of observations falling within the 95% confidence interval increased from 92.13% to 95.94% with the improved Horton equation. Most of the observations were accurately simulated using the improved Horton equation. The greatest improvements in simulating overland flow were seen for the experiments with low flow simulations. The study results provide insights into soil infiltration mechanisms, and also provide references to support improved infiltration simulation 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.

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