M. Sadeghi; B. Ghahraman; A.N. Ziaei; K. Davary
Abstract
After introducing similar media theory, many scaling methods were developed and have been widely used to cope with soil variability problem as well as to achieve invariant solutions of Richards’ equation. Recently, a method was developed for scaling Richards’ equation (RE) for dissimilar soils such ...
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After introducing similar media theory, many scaling methods were developed and have been widely used to cope with soil variability problem as well as to achieve invariant solutions of Richards’ equation. Recently, a method was developed for scaling Richards’ equation (RE) for dissimilar soils such that the scaled RE is independent of soil hydraulic properties for a wide range of soils. This method uses exponential – power hydraulic functions which are restricted to a limited range of soil-water content and matric potential. Hence, this method does not apply to the phenomena in which soil-water content and matric potential exceeds this range. Therefore, this research was performed to extend the method for a wider range of soil-water content and matric potential. This objective was achieved by modifying the exponential – power hydraulic functions and the scaling method was extended to the entire range of soil wetness (from saturated to dry). This study was followed to solve RE for soil-water infiltration using scaling. To do so, numerical solutions of the scaled RE was approximated by a scaled form of Philip three-term equation with soil-independent coefficients. The obtained approximate solution was tested using literature data of infiltration experiments on a sandy and two clayey soils. Results indicated that the solution can reasonably estimate (with the average relative error at most 9% for the cases studied here) measured infiltrated water. Also, it was shown that this solution can accurately approximate (with the average relative error at most 4% for the cases studied here) the numerical solutions of RE (for the same conditions and hydraulic functions). Hence, because of its simplicity, the solution is proposed as an alternative for numerical solutions of RE or other empirical equations for soil-water infiltration. Additionally, this solution can be easily applied to determine soil hydraulic functions by inverse solutions.
B. Ghahraman; M. Sadeghi; J. Mohammadi
Abstract
Abstract
Spatial variability of soils makes difficult analysis of soil water flow phenomena especially in a large area such as a watershed. Using scaling methods is a solution in variability problems. The objective of this study was to investigate the effect of the non-linear variability on performance ...
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Abstract
Spatial variability of soils makes difficult analysis of soil water flow phenomena especially in a large area such as a watershed. Using scaling methods is a solution in variability problems. The objective of this study was to investigate the effect of the non-linear variability on performance of the scaling methods of Richards’ equation for modeling infiltration in a watershed. The method of Warrick et al. by adopting van Genuchten hydraulic functions was used and variability of n values (power of van Genuchten hydraulic functions) was considered as the nonlinear variability. Marghmalek watershed, a sub watershed of Zayanderoud, with 97 Sq. kilometers was studied. In addition, ten virtual watersheds with various degrees of variability of n were evaluated which were generated by stochastic method of Monte Carlo. Using HYDRUS-1D model, original and scaled Richards’ equations were solved for infiltration condition with constant hydraulic head and uniform initial soil water content. The results indicated that coefficient of variations of n values in the Marghmalek watershed (equal to 2.57%) is small enough that the scaling method can be used efficiently in modeling infiltration. Therefore, in this watershed, generalized solutions of Richards’ equation can be adequately used instead of individual solutions for every points of the watershed. Evaluations in the virtual watersheds indicated that variability of n values considerably affect the error between the generalized and individual solutions. Based on the result of this study, it can be concluded that scaling methods of Richards’ equation can be adequately applied in the watersheds in which coefficient of variations of n values does not exceed 3%.
Keywords: Scaling, Richards’ equation, Infiltration, Nonlinear variability, Marghmalek watershed
M. Sadeghi; B. Ghahraman
Abstract
Abstract
Scaling methods, which are based on similar media theory, are used to simplify the statistic description of soil spatial variations. To simulate the water flow in heterogeneous soils, simultaneous scaling of soil hydraulic functions, including soil water retention and unsaturated hydraulic ...
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Abstract
Scaling methods, which are based on similar media theory, are used to simplify the statistic description of soil spatial variations. To simulate the water flow in heterogeneous soils, simultaneous scaling of soil hydraulic functions, including soil water retention and unsaturated hydraulic conductivity functions, is highly desirable. In the similar media theory, the simultaneous scaling is expected for geometrically similar soils. In this paper, it is indicated that although the geometric similarity is a necessity, it is not sufficient for validation of the similar media theory in the reality. It is shown that, in addition, the values of Kshm2 (β) must be identical in all similar soils (where Ks is the saturated hydraulic conductivity and hm is the median suction head in the water retention curve). To evaluate the theory, method of Tuli et al. (13) was used which applies the similar media theory to the similar soils of Kosugi and Hopmans (4) with identical σ (standard deviation in the log-normal hydraulic models). The method was also generalized such that it can well scale the soil hydraulic functions of the similar soils even where the β values are not identical. The theoretical descriptions were tested by data of 26 soils from UNSODA database. The soils were classified into six groups of similar soils based on the equality of their σ. As it was expected, the method of Tuli et al. did not perform well in the groups in which β values were significantly different. The results also showed that the proposed method can considerably improve the performance of the method of Tuli et al. It was indicated that the performance of the proposed method do not depend on β values and the geometric similarity is the only condition for that.
Keywords: Similar media, Simultaneous scaling, Retention curve, Hydraulic conductivity function
M. Sadeghi; M.R. Gohardoust Monfared; B. Ghahraman
Abstract
Abstract
To estimate spatial variability of soil hydraulic functions, scaling methods were developed and have been widely used. Among these functions, physically based methods have been found more desirable because of possibility of estimating soil hydraulic functions from soil physical properties. ...
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Abstract
To estimate spatial variability of soil hydraulic functions, scaling methods were developed and have been widely used. Among these functions, physically based methods have been found more desirable because of possibility of estimating soil hydraulic functions from soil physical properties. In this paper, a new and physically based method has been described for scaling soil hydraulic conductivity function. In this method, use of effective capillary drive (hcM) has been proposed for scaling of soil water suction axis in the hydraulic conductivity function. Using this method, data of all natural soils, from sand to clay, can be presented by a unique exponential curve as reference curve. The approach was validated by 396 sets of hydraulic conductivity data, including all soil texture classes, taken from UNSODA database. To determine hcM, fitting Brooks-Corey and Gardner-Philip models and also a model-free method were used. The results indicated an acceptable performance of the proposed method. Brooks-Corey and Gardner-Philip models and the model-free method results showed the average absolute error of relative hydraulic conductivity between the scaled data and the reference curve as 0.019, 0.056, and 0.059, respectively. In the employed methods, fitting capability of the mentioned models can be taken into account as the only limitation. Thus scaling performance would be well if the mentioned models could fit well the hydraulic conductivity data and vice versa.
Keywords: Scaling, Soil unsaturated Hydraulic conductivity, Effective capillary drive, Unique exponential reference curve
M. Sadeghi; B. Ghahraman; K. Davary
Abstract
Abstract
In recent years, many researchers have attempted to estimate the soil hydraulic functions (e.g. soil moisture characteristics curve, and hydraulic conductivity function) using particle-size distribution (PSD) curve. In these studies, an accurate mathematical representation of PSD is required ...
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Abstract
In recent years, many researchers have attempted to estimate the soil hydraulic functions (e.g. soil moisture characteristics curve, and hydraulic conductivity function) using particle-size distribution (PSD) curve. In these studies, an accurate mathematical representation of PSD is required for fitting the observed data. So far, some mathematical models were developed with different limitations. The goodness of fit is directly related to the number of the model parameters. However, estimating the parameters for higher-parameter models which have no mathematical or physical significance is a problem. Among the current models, 2-parameter Log-normal distribution model with mathematical significant parameters has been considered as a basis for many studies. In this study, it is indicated that the 2-parameter Log-normal distribution model can not be very accurate for representation of the PSD for all of soil textural classes. As an alternative, 2-parameter Gamma distribution model is proposed for more accurate representation of the PSD that its two parameters also are mathematical significant and readily computable. These two models have been compared in fitting the observed PSD data of 461 soil samples from UNSODA soil database. Gamma distribution model indicated a pronounced improvement in representation of the PSD. Based on Coefficient of determination (R2), in 362 samples and based on RMSE, in 323 samples, Gamma distribution model showed a better representation of the PSD than Log-normal. To evaluate the significance of the difference between two models, a t-test was performed. The results showed that, at confidence level of 1%, the R2-values of the Gamma model are significantly greater than those of Log-normal model. Also, at confidence level of 5%, a significant difference between the RMSE-values of two models was shown. Therefore, 2-parameter Gamma distribution model is judged to be better than 2-parameter Log-normal model for representation of PSD.
Key words: Particle-size distribution (PSD), Log-normal distribution, Gamma distribution, UNSODA
M. Sadeghi; B. Ghahraman; K. Davary
Abstract
Abstract
The rate and duration of downward flow during redistribution process determines the effective soil water storage at any time. This property is vitally important, particularly in arid and semi-arid regions where plants must rely for long periods of time on the remained soil water of the root ...
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Abstract
The rate and duration of downward flow during redistribution process determines the effective soil water storage at any time. This property is vitally important, particularly in arid and semi-arid regions where plants must rely for long periods of time on the remained soil water of the root zone. In this study a new approach for scaling of soil moisture redistribution process based on the Green-Ampt redistribution theory was developed. Using the scaled results of numerical solution of the general flow (Richards’ equation), an empirical equation for predicting the soil moisture profile during redistribution process was derived. An important advantage of the empirical equation is adopting the effect of hysteresis in soil retention curve on redistribution process. To validate the proposed empirical equation, its outputs were compared with those of Richards’ solution for 11 soil textural classes (from sand to clay). The comparison showed negligible amount of error for all of the 11 soil textural classes and for a wide range of initial conditions. However, some deviations from results of Richards’ solution were observed under high initial infiltrated water depth and/or high initial soil water content. Therefore, a model which can estimate the soil moisture content at any depth and time during redistribution phase with accuracy of numerical models and simplicity in application of analytical models was obtained.
Key words: Scaling, Soil moisture profile, Redistribution phase, Green and Ampt equation, Richards’ equation
