Generalized Explicit Models for Estimation of Wetting Front Length and Potential Recharge

Ali, Shakir; Ghosh, N. C.; Singh, Rudra Pratap; Sethy, B. K.

doi:10.1007/s11269-013-0295-2

Cited by 21 publications

(11 citation statements)

References 29 publications

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“…However, the GA model is expressed by an implicit equation and is solved using an iterative method, which, to a certain extent, limits the application of the model [7,13,14]. In the Ali model, the logarithmic term of the GA model (Equation (4)) is replaced by a sequential segmental second-order polynomial; subsequently, a generalized algebraic equation-based model is developed to estimate the Z f value of 1D vertical infiltration [27]. According to comparisons of the estimated values with the measured and simulated values, the largest RMSE, MAPRE, and PB values were 2.07 cm, 10.96%, and −11.54%, respectively, for the Ali model (Tables 4 and 5).…”

Section: Comparison and Discussion Of The Four Modelsmentioning

confidence: 99%

“…This finding indicated the reliability of the Ali model for estimating the Z f value of 1D vertical infiltration. Nonetheless, the Ali model is complex to employ, as Z f is estimated in three steps [27]. First, the periods are determined for different infiltration segments.…”

Section: Comparison and Discussion Of The Four Modelsmentioning

confidence: 99%

“…Ali et al [27] developed a generalized explicit model for estimating the time-varying depth of the advancement of the wetting front, Z f , by replacing the logarithmic term in Equation (4) with sequential segmental second-order polynomials. The derived explicit model for the wetting front depth is as follows [27]:…”

Section: Ali Modelmentioning

confidence: 99%

“…The numerical parameters of Equation (10), F 1 , F 2 and F 3 , are taken from the study by Ali et al [27]; Z f is computed from Equation (10) by using the respective segmental values of the numerical factors, F 1 , F 2 and F 3 , satisfying the dimensionless L * conditions (Equation (6)). …”

Section: Ali Modelmentioning

confidence: 99%

“…In the Stone model, it is assumed that the steady infiltration rate is equal to the saturated conductivity, which is inconsistent with the actual conditions [23][24][25][26]; thus, this assumption may reduce the accuracy of the model for estimating the wetting front depth. Ali et al [27] replaced the logarithmic term of the GA model by a sequential segmental second-order polynomial, producing explicit equation-based models for estimating the wetting front depth of 1D vertical infiltration, and the maximum relative error obtained between the approximation and the GA model was 0.5%. However, model parameters must be selected according to different infiltration segments; thus, applying the Ali model is complex.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Approximate Explicit Solution to the Green-Ampt Infiltration Model for Estimating Wetting Front Depth

Nie

Fei

2017

Water

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Obtaining reliable information on the wetting front depth of soil is beneficial to the understanding of one-dimensional (1D) vertical infiltration under border irrigation. This paper presents an approximate explicit solution to the Green-Ampt (GA) infiltration model for estimating the wetting front depth. Moreover, the model proposed in this study, the GA model, the Ali model, and the Stone model were validated and evaluated using laboratory experimental data and HYDRUS-1D simulation. Statistical comparisons (root mean square error-RMSE, mean absolute percent relative error-MAPRE, and percent bias-PB) of the estimated data with the measured and simulated data were conducted. The models were ranked on the basis of their overall performance index (OPI). The results demonstrated that all four models can be used to estimate the wetting front depth of 1D vertical infiltration for a wide range of soil textures; the proposed model provided the most accurate result. According to comparisons of the estimated values with the measured and simulated values, the maximum RMSE, MAPRE, and PB were 1.74 cm, 6.92%, and −6.74%, respectively, for the proposed model. On the basis of the OPI, the optimal model was the proposed model, followed by the Ali, GA, and Stone models.

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Section: Comparison and Discussion Of The Four Modelsmentioning

confidence: 99%

Section: Comparison and Discussion Of The Four Modelsmentioning

confidence: 99%

Section: Ali Modelmentioning

confidence: 99%

Section: Ali Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Approximate Explicit Solution to the Green-Ampt Infiltration Model for Estimating Wetting Front Depth

Nie

Fei

2017

Water

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Modeling Water Dynamics for Assessing and Managing Ecosystem Services in India

Ali¹,

Ojasvi²

2022

Enhancing Agricultural Research and Precision Management for Subsistence Farming by Integrating System Models With Experiments

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A simple, accurate, and explicit form of the Green–Ampt model to estimate infiltration, sorptivity, and hydraulic conductivity

Sadeghi,

Loescher,

Jacoby

et al. 2024

Vadose Zone Journal

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Finding an explicit solution to the widely used Green–Ampt (G–A) one‐dimensional infiltration model has been subject of efforts for more than half a century. We derived an explicit semiempirical approach that combines accuracy with simplicity, a concept that has been generally neglected in previous studies. The equation is , with F (L), Ks (L/T), S (L/T0.5) and t (T) being cumulative infiltration, saturated hydraulic conductivity, sorptivity, and time, respectively. Relative errors (ɛ) by the application of this equation generally do not exceed ±0.3% in most applied infiltration problems faced by water resources engineering today. We show both numerically and mathematically that │ɛ│> 0.3% could only occur if Kst/F > 0.904, a criterion that could apply to sand and loamy sand soils (i.e., coarse texture) and if they experience infiltration rates for over 6 h and 19 h, respectively. Hence, we also derived a simple linear adjustment in the model as Fadj ≅ 0.9796 F + 0.335 S2/Ks to address these longer infiltration rates, and to assure that ɛ remains within the expected ±0.3% range of uncertainty. A linearized regression technique was also developed to accurately estimate S and Ks when the G–A model is used. We numerically demonstrated that our fitting method could be used even when the G–A approach is less valid (diffusive soils), provided that the actual value of the capillary length (λ) is initially known. An added benefit of our approach is that by setting λ equal to 1/3 and 2/3, it can significantly limit the range of initializing, unknown, a priori values of S and Ks, as these two parameters are estimated through the inverse solution of implicit infiltration models. Due to the model's simplicity and accuracy, our solution should find application among hydrologists, natural resource scientists, and engineers who wish to easily derive accurate estimations from the G–A infiltration approach and/or estimate sorptivity and hydraulic conductivity without encountering divergence problems.

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Generalized Explicit Models for Estimation of Wetting Front Length and Potential Recharge

Cited by 21 publications

References 29 publications

Approximate Explicit Solution to the Green-Ampt Infiltration Model for Estimating Wetting Front Depth

Approximate Explicit Solution to the Green-Ampt Infiltration Model for Estimating Wetting Front Depth

Modeling Water Dynamics for Assessing and Managing Ecosystem Services in India

A simple, accurate, and explicit form of the Green–Ampt model to estimate infiltration, sorptivity, and hydraulic conductivity

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