relationship between the storage coefficient and the soil-water retention curve in subsurface...

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Relationship between the Storage Coefficient and the Soil-Water Retention Curve in Subsurface Agricultural Drainage Systems: Water Table Drawdown Carlos Fuentes 1 ; Manuel Zavala 2 ; and Heber Saucedo 3 Abstract: Water dynamics in subsurface agricultural drainage systems are described by the Boussinesq equation for an unconfined aquifer that results from the continuity equation, the Darcy law, as well as from a hydrostatic pressure distribution hypothesis. The storage coefficient that appears in the equation is conceptualized according to the unsaturated zone that results from water table drawdown during the drainage process. The difference between drained depth and drainable depth, as well as the hydrostatic pressure distribution hypoth- esis, allows us to infer a relationship between storage coefficient, drainable porosity, and the soil-water retention curve. This relationship is illustrated by using the van Genuchten and Fujita–Parlange soil-water retention curves. Both resulting storage coefficient expressions are validated in an experiment reported in the literature using a numeric solution of the one-dimensional Boussinesq equation. A good description of the experimental results leads to a conclusion in which the proposed relationship between storage coefficient and the soil-water retention curve can be used in the context of studies in water dynamics in subsurface agricultural drainage systems. DOI: 10.1061/ASCE0733-94372009135:3279 CE Database subject headings: Porosity; Drainage; Coefficients; Soil water; Agriculture; Water tables. Introduction The analysis of water dynamics in subsurface agricultural drain- age systems can be done using the Boussinesq equation for an unconfined aquifer. This equation is a result of the mass con- servation principle, Darcy’s law, and the Dupuit–Forcheimer hy- pothesis concerning the hydrostatic distribution of pressure Bear 1972 H H t = · K s H - H i H + R 1 where H and H i = elevations of the free surface or hydraulic head and of the impervious layer, measured from the same reference level; when the impervious layer is approximately horizontal, we assume H i =0; = / x , / y; K s = saturated hydraulic con- ductivity; R = recharge per unity of time per aquifer area unit; H - H i represents the aquifer thickness; and H = storage coef- ficient that can be a function of the free surface position H, mainly for a shallow unconfined aquifer. In Fig. 1 variables em- ployed are showed. In some studies of subsurface agricultural drainage, storage coefficient has normally been considered as being independent from H and it has been assimilated to a drainable porosity value Dumm 1954; Kumar et al. 1991; Sing et al. 1996; Upadhyaya and Chauhan 2000. In other studies it has been proven that a drainable porosity depending on the free surface position, H, provides a more accurate description of the soil-water drainage process in a shallow unconfined aquifer Taylor 1960; Bhattacharya and Broughton 1979; Pandey et al. 1992; Mathew and Vos 2003; Samani et al. 2007. However, in some of these recent works, the relationship between storage coefficient H and drainable porosity H is not clear. This is the case for the assumption of Pandey et al. 1992 which considers the storage coefficient as being equal to variable drainable porosity, H = H. Samani et al. 2007 use the Pandey et al. 1992 relationship for the variable drainable porosity in analytical solutions obtained from Boussinesq equation with constant coefficients. When drainable porosity is a function of the free surface po- sition it is not equal to storage coefficient. In effect, due to con- tinuity Gupta et al. 1994, the variation of stored water volume susceptible to drainage by aquifer unit area, or drainable depth, is indeed given by dW = dHH - H i , where H is precisely the drainable porosity. This can be represented by W t = H H t 2 where storage coefficient is defined by H = dW dH = H + H d dH 3 in which H i = 0 has been assumed. The relation between storage coefficient and drainable porosity Eq. 3 is that used by Gupta et al. 1994. From this equation it 1 Researcher Professor, Univ. Autónoma de Querétaro, Cerro de las Campanas, 76010 Santiago de Querétaro, Querétaro, México. E-mail: [email protected] 2 Researcher, Instituto Mexicano de Tecnología del Agua, Paseo Cuauhnáhuac No. 8532, 62550 Jiutepec, Morelos, México corresponding author. E-mail: [email protected] 3 Researcher, Instituto Mexicano de Tecnología del Agua, Paseo Cuauhnáhuac No. 8532, 62550 Jiutepec, Morelos, México. E-mail: [email protected] Note. This manuscript was submitted on July 9, 2007; approved on September 12, 2008; published online on May 15, 2009. Discussion pe- riod open until November 1, 2009; separate discussions must be submit- ted for individual papers. This paper is part of the Journal of Irrigation and Drainage Engineering, Vol. 135, No. 3, June 1, 2009. ©ASCE, ISSN 0733-9437/2009/3-279–285/$25.00. JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING © ASCE / MAY/JUNE 2009 / 279 J. Irrig. Drain Eng. 2009.135:279-285. Downloaded from ascelibrary.org by Northeastern Univ Library on 01/20/14. Copyright ASCE. For personal use only; all rights reserved.

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Page 1: Relationship between the Storage Coefficient and the Soil-Water Retention Curve in Subsurface Agricultural Drainage Systems: Water Table Drawdown

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Relationship between the Storage Coefficientand the Soil-Water Retention Curve in Subsurface

Agricultural Drainage Systems: Water Table DrawdownCarlos Fuentes1; Manuel Zavala2; and Heber Saucedo3

Abstract: Water dynamics in subsurface agricultural drainage systems are described by the Boussinesq equation for an unconfinedaquifer that results from the continuity equation, the Darcy law, as well as from a hydrostatic pressure distribution hypothesis. The storagecoefficient that appears in the equation is conceptualized according to the unsaturated zone that results from water table drawdown duringthe drainage process. The difference between drained depth and drainable depth, as well as the hydrostatic pressure distribution hypoth-esis, allows us to infer a relationship between storage coefficient, drainable porosity, and the soil-water retention curve. This relationshipis illustrated by using the van Genuchten and Fujita–Parlange soil-water retention curves. Both resulting storage coefficient expressionsare validated in an experiment reported in the literature using a numeric solution of the one-dimensional Boussinesq equation. A gooddescription of the experimental results leads to a conclusion in which the proposed relationship between storage coefficient and thesoil-water retention curve can be used in the context of studies in water dynamics in subsurface agricultural drainage systems.

DOI: 10.1061/�ASCE�0733-9437�2009�135:3�279�

CE Database subject headings: Porosity; Drainage; Coefficients; Soil water; Agriculture; Water tables.

Introduction

The analysis of water dynamics in subsurface agricultural drain-age systems can be done using the Boussinesq equation for anunconfined aquifer. This equation is a result of the mass con-servation principle, Darcy’s law, and the Dupuit–Forcheimer hy-pothesis concerning the hydrostatic distribution of pressure �Bear1972�

��H��H

�t= � · �Ks�H − Hi� � H� + R �1�

where H and Hi=elevations of the free surface or hydraulic headand of the impervious layer, measured from the same referencelevel; when the impervious layer is approximately horizontal,we assume Hi=0; �= �� /�x ,� /�y�; Ks=saturated hydraulic con-ductivity; R=recharge per unity of time per aquifer area unit;�H−Hi� represents the aquifer thickness; and ��H�=storage coef-ficient that can be a function of the free surface position �H�,mainly for a shallow unconfined aquifer. In Fig. 1 variables em-ployed are showed.

1Researcher Professor, Univ. Autónoma de Querétaro, Cerro delas Campanas, 76010 Santiago de Querétaro, Querétaro, México. E-mail:[email protected]

2Researcher, Instituto Mexicano de Tecnología del Agua, PaseoCuauhnáhuac No. 8532, 62550 Jiutepec, Morelos, México �correspondingauthor�. E-mail: [email protected]

3Researcher, Instituto Mexicano de Tecnología del Agua, PaseoCuauhnáhuac No. 8532, 62550 Jiutepec, Morelos, México. E-mail:[email protected]

Note. This manuscript was submitted on July 9, 2007; approved onSeptember 12, 2008; published online on May 15, 2009. Discussion pe-riod open until November 1, 2009; separate discussions must be submit-ted for individual papers. This paper is part of the Journal of Irrigationand Drainage Engineering, Vol. 135, No. 3, June 1, 2009. ©ASCE,

ISSN 0733-9437/2009/3-279–285/$25.00.

JOURNAL OF IRRIGATIO

J. Irrig. Drain Eng. 200

In some studies of subsurface agricultural drainage, storagecoefficient has normally been considered as being independentfrom H and it has been assimilated to a drainable porosity value��� �Dumm 1954; Kumar et al. 1991; Sing et al. 1996; Upadhyayaand Chauhan 2000�.

In other studies it has been proven that a drainable porositydepending on the free surface position, ��H�, provides a moreaccurate description of the soil-water drainage process in ashallow unconfined aquifer �Taylor 1960; Bhattacharya andBroughton 1979; Pandey et al. 1992; Mathew and Vos 2003;Samani et al. 2007�. However, in some of these recent works,the relationship between storage coefficient ��H� and drainableporosity ��H� is not clear. This is the case for the assumption ofPandey et al. �1992� which considers the storage coefficient asbeing equal to variable drainable porosity, ��H�=��H�. Samaniet al. �2007� use the Pandey et al. �1992� relationship for thevariable drainable porosity in analytical solutions obtained fromBoussinesq equation with constant coefficients.

When drainable porosity is a function of the free surface po-sition it is not equal to storage coefficient. In effect, due to con-tinuity �Gupta et al. 1994�, the variation of stored water volumesusceptible to drainage by aquifer unit area, or drainable depth, isindeed given by dW=d���H��H−Hi��, where ��H� is precisely thedrainable porosity. This can be represented by

�W

�t= ��H�

�H

�t�2�

where storage coefficient is defined by

��H� =dW

dH= ��H� + H

d�

dH�3�

in which Hi=0 has been assumed.The relation between storage coefficient and drainable porosity

�Eq. �3�� is that used by Gupta et al. �1994�. From this equation it

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is clear that if drainable porosity is considered independent fromthe hydraulic head, then storage coefficient can be assumed equalto drainable porosity, �=�. Also, if ��H� is a lineal function of thehydraulic head then ��H� is a lineal function of the hydraulichead �Gupta et al. 1994�.

The integral version of Eq. �3� is

W�H� =�0

H

��H̄�dH̄ = ��H�H �4�

since W�0�=0.Considering that the Boussinesq equation is established under

the assumption of a hydrostatic pressure distribution and takeninto account that the water table drawdown induces an unsatur-ated zone, the aim of this work is to establish relationships be-tween storage coefficient and the soil-water retention curve in ashallow unconfined homogeneous aquifer.

Theory

Consider a subsurface agricultural drainage system with null re-charge �R=0�. Initially the free surface is located in the z=Hs

position �vertical coordinate z, positive upward�, during the drain-age process this position is located in the z=H position at a giventime �Fig. 2�, it is clear that the drained depth ��H� is

��H� =�H

Hs

��s − �mp�z��dz �5�

where �mp�z�=soil moisture profile; and �s=saturated volumetricwater content.

When the distribution of water pressure head in the unsatur-ated zone is known ��z�, the soil moisture profile in Eq. �5� canbe replaced by the soil-water retention curve ����, which relatesthe volumetric water content ��� and the water pressure head inthe soil ���.

In particular, the following two distributions of the water pres-sure in the soil can be assumed:1. Hydrostatic pressure distribution in the drainage system

�=H−z �Dupuit hypothesis�, for this condition the drained

Fig. 1. Subsurface drainage system

depth is

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J. Irrig. Drain Eng. 200

��H� =�H

Hs

��s − ��H − z��dz �6a�

it must be noted that pressure head ��� is negative in theunsaturated zone and positive in the saturated zone; and

2. Pressure distribution proposed in Fig. 3 if the field capacityconcept is introduced ��fc�. In this distribution, a constantpressure is considered in the field capacity zone and outsideof this zone, hydrostatic pressure distribution is assumed.The drained depth is

��H� =��H

Hs

��s − ��H − z��dz; Hs � Hfc

�H

Hfc

��s − ��H − z��dz + ��s − ��Hfc���Hs − Hfc�; Hfc � Hs��6b�

where Hfc=H+ ��fc� and �fc=pressure head that correspondsto the field capacity �sandy soils ��fc�1.0 m and clay soils��fc�3.3 m�.

Fig. 2. Schematic representation of drainage process

Fig. 3. �a� Volumetric water content distribution; �b� pressure headdistribution, for Hfc�Hs condition

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Since in Eq. �4� the drained depth is given by

��H� = Wmax − W�H� �7�

where Wmax represents the drainable depth maximum, beingWmax=W�Hs�=Ws when Eq. �6a� is considered or alsofor Hs�Hfc when Eq. �6b� is used, while for Hfc�Hs is Wmax

=W���c��+W�Hs− ��c��; W�H�=drainable depth that correspondsto position H.

The combination of Eqs. �3� and �7� results in the followingexpression for storage coefficient:

��H� = −d�

dH�8�

The Leibniz rule applied to Eqs. �6a� and �6b� and consideringEq. �8�, allows obtaining the relationship between the storagecoefficient and the soil-water retention curve

��H� = �s − ��H − Hs� �9a�

��H� = �s − ��H − Hs�; Hs � Hfc

�s − ��H − Hfc� + ��s − �fc�; Hfc � Hs� �9b�

According to Eqs. �9a� and �9b� for Hs�Hfc, storage coefficientis equal to the difference between volumetric water content in thefree surface �saturated water content� and the evolution of volu-metric water content in the initial position of the free surface.While if Hfc�Hs in Eq. �9b�, storage coefficient is equal to thedifference between volumetric water content in the free surface�saturated water content� and the evolution of volumetric watercontent in the position z=Hfc, plus the drained porosity related tothe capacity field zone.

In agreement with Eqs. �9a� and �9b� the storage coefficientcorresponds to a variable drained porosity.

Due to continuity, when a constant storage coefficient in agiven drainage system is assumed, it must be calculated as themean value

�̄ =1

Hs − Hd�

Hd

Hs

��H�dH �10�

where Hd=drain position.In practice, drains are buried at depths of between 1.2 and

2.5 m and are also installed on clay soils or clay-loamy soils. Inthis case, Eq. �6a� or Eq. �6b� for Hs�Hfc are more appropriate tostudy the water table drawdown in a subsurface drainage system.However if condition Hfc�Hs is observed in any subsurfacedrainage system, relation �9b� may be used.

Analytic Representation of Storage Coefficientfor Subsurface Drainage System

It is possible to obtain an analytic representation of storage coef-ficient based on the result of Eq. �9a� if the soil-water retentioncurve of the soil is known. Models of the retention curve used inthis work are the ones suggested by van Genuchten �1980� andFujita–Parlange. The first model has been widely accepted in fieldand laboratory studies, and the second model is used in analyticaldevelopments �Fuentes et al. 1992�.

The following is the van Genuchten �1980� model:

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J. Irrig. Drain Eng. 200

Se��� =1

�1 + ��/�d�n�m �11�

where Se= ��−�r� / ��s−�r�=effective saturation; �r=residualvolumetric water content; �d�0=pressure scale parameter;and m and n=form parameters related through m=1−2 /n �vanGenuchten 1980; Fuentes et al. 1992�.

The introduction of Eq. �11� in Eq. �9a� allows us to obtain thefollowing storage coefficient relationship:

��H� = ��s − �r��1 −1

1 + ��H − Hs�/�d�n�m� �12�

Eq. �12� does not allow a closed formula for drained depth�Eq. �6a�� and therefore it does not provide a closed formula fordrainable depth �W�, nor for drainable porosity ���.

The Fujita–Parlange model is obtained from the Fujita �1952�diffusivity equation and from the relationship between hydraulicconductivity and hydraulic diffusivity of Parlange et al. �1982�,�Fuentes et al. 1992�

D�Se� = � Ks�c

�s − �r� 1 −

�1 − Se�2 �13�

K�Se� = Ks

Se�1 − + � − �Se�1 − Se

�14�

where and =nondimensional form parameters that 0��1and 0��1. The Bouwer scale �Bouwer 1966� �c is defined by

�c =1

Ks�

−�

0

K���d� �15�

the retention curve is obtained from the hydraulic diffusivityD���=K���d� /d� thus

��Se� = �c

ln� 1 − Se

�1 − �Se� +

�1 − �ln�1 − + � − �Se

�1 − �Se��

�16�

where �c=−�c.The ���� function becomes explicit if the = hypothesis is

accepted. This means

Se��� =1

+ �1 − �exp��/�c��17�

the = hypothesis leads to the hydraulic conductivity modelproposed by Gardner �1958�: K���=Ks exp�� /�c�.

The introduction of the Eq. �17� in Eq. �6a� allows one todeduce the following closed form of the drained depth:

��H� = ��s − �r�

���Hs − H� −�c

ln� 1

1 − + exp�− �Hs − H�/�c���

�18�

The storage coefficient defined by Eq. �9a� with ��H−Hs� calcu-lated with Eq. �17� is as follows:

��H� = ��s − �r�1 −1

+ �1 − �exp��Hs − H�/�c�� �19�

Its development in a Taylor series around Hs, ��H�= ��s−�r���1−��Hs−H� /�c+O��Hs−H�2� can explain the lineal depen-

dencies used by Gupta et al. �1994�.

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Drainable depth W�H� is deducted from Eq. �7�: W�H�=��0�−��H�, since Ws=��0�. Considering Eq. �18�

W�H� = ��s − �r�H −�c

ln�1 − + exp�− �Hs − H�/�c�

1 − + exp�− Hs/�c����20�

Drainable porosity is obtained using Eq. �4�. It must be noted that��0�=��0�.

Application

The established theory is applied to the experiment carried out inthe laboratory by Pandey et al. �1992�. The physical characteris-tics of the drainage system considered here are the following:drains separation L=9.40 m; drain depth Pd=1.22 m; drains po-sition from the impervious layer Hd=0.38 m; and null recharge�R=0� during drainage time, since soil surface is previously cov-ered with plastic in order to avoid evaporation. Soil texture is clayloam �53.9% sand, 20.5% silt, and 25.6% clay�. The bulk densityof soil is t=1.50 g /cm3; and particle density is o=2.65 g /cm3.Total soil porosity is �=0.434 cm3 /cm3 estimated with the clas-sic relation �=1− t / o. The value of 0.0375 m /day was used forthe saturated hydraulic conductivity Ks.

Evaluation of the models for storage coefficient is carried outsimulating the Pandey et al. �1992� drainage test using a one-dimensional numerical solution of Eq. �1�, subjected to initial andboundary conditions

H�x,0� = Hs �21�

H�0,t� = H�L,t� = f�t� �22�

where Hs=1.60 m is the elevation of free surface at the start ofthe experiment; and f�t�=variable hydraulic head at drains, re-ported in Fig. 10 in the study of Pandey et al. �1992�. For theanalysis of this experiment, saturated volumetric water content isconsidered as the total porosity �s=�; it is also assumed that the

Fig. 4. Experimental drainable porosity of Pandey et al. �1992�,fitted using relation between drainable porosity and storage co-efficient �Eq. �4��, considering soil-water retention curves: �1� vanGenuchten �1980�, Eq. �11� with m=0.13, �d=−1.25 m and RMSE=0.0021 m3 /m3; �2� Fujita �1952� and Parlange et al. �1982�,Eq. �17� with =0.99, �c=−0.55 m, and RMSE=0.0019 m3 /m3

residual volumetric water content equals zero �r=0.

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J. Irrig. Drain Eng. 200

The system, Eqs. �1�, �21�, and �22�, is numerically solvedfollowing the process employed by Zavala et al. �2007�. Spatialdiscretization is carried out using the Galerkin finite-elementmethod; temporal discretization is performed using an implicitfinite difference method. The resulting system becomes linealusing the Picard iterative method; the algebraic equation system issolved using a preconditioned conjugated gradient method �Noorand Peter 1987�. These methods are well documented; for in-stance, by Pinder and Gray �1977�, Mori �1986�, and Zienkiewiczet al. �2005�.

The parameters m and �d of Eq. �12�, as well as those of and�c of Eq. �19�, are estimated with the relation between drainableporosity and storage coefficient �Eq. �4�� and applying the leastsquare method with drainable porosity data reported by Pandeyet al. �1992�.

With the least square method, the optimal combination of mand �d values, as well as of and �c, is determined. The root-mean-square error �RMSE� is calculated with

RMSE =� 1

N − 1�i=1

N

��i − ��Hi��2 �23�

where �i and ��Hi�=respectively, experimental and calculatedvalues of drainable porosity, and N=total number of experimentaldata.

The optimization results are m=0.13 and �d=−1.25 m withRMSE=0.0021 m3 /m3 and =0.99 and �c=0.55 m with RMSE=0.0019 m3 /m3 �Fig. 4�. According to data retrieved from theGRIZZLY database �Haverkamp et al. 1998�, the m value param-eter obtained during calibration is representative of soils withtexture similar to the soil texture used in the experiment.

The drainage experiment is modeled considering the constantand variable storage coefficient. The results obtained are com-

Fig. 5. Variation of free surface at 0.50 m from drain: constant stor-age coefficient �mean value� �̄=0.0126 m3 /m3 and RMSE=0.10 m;Eq. �12� with m=0.13, �d=−1.25 m, and RMSE=0.14 m; Eq. �19�with =0.99, �c=0.546 m, and RMSE=0.14 m

pared with the evolution of measured hydraulic head at 0.50,

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2.20, and 4.33 m from the drain. For modeling with a constantstorage coefficient, a mean value of �̄=0.0126, calculated withEqs. �10� and �12�, has been used.

The hydraulic head evolution is shown in Figs. 5–7. The geo-metric mean of root-mean-square error considering the three dis-tances from the drain, shows that fitting of the data with thevariable storage coefficient is lower than that obtained with the

Fig. 6. Variation of free surface at 2.20 m from drain: constant stor-age coefficient �mean value� �̄=0.0126 m3 /m3 and RMSE=0.13 m;Eq. �12� with m=0.13, �d=−1.25 m, and RMSE=0.18 m; Eq. �19�with =0.99, �c=0.55 m, and RMSE=0.19 m

Fig. 7. Variation of free surface at 4.33 m from drain: constant stor-age coefficient �mean value� �̄=0.0126 m3 /m3 and RMSE=0.11 m;Eq. �12� with m=0.13, �d=−1.25 m, and RMSE=0.16 m; Eq. �19�with =0.99, �c=0.55 m, and RMSE=0.17 m

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J. Irrig. Drain Eng. 200

constant storage coefficient �variable storage RMSE=0.16 m andconstant storage RMSE=0.12 m�; this is because two parametersof the variable storage coefficient �m and �d or and �c� werecalibrated from a punctual event �drainable porosity values mea-sured in a soil column by Pandey et al. �1992��.

Drainage of soil columns do not represent the conditions in thedrainage system with precision, in other words it is more conve-

Fig. 8. Evolution of free surface at 0.5 m from drain: constant stor-age coefficient �mean value� �̄=0.0243 m3 /m3 and RMSE=0.05 m;Eq. �12� with m=0.13, �d=−0.85 m, and RMSE=0.08 m; Eq. �19�with =0.99, �c=0.36 m, and RMSE=0.08 m

Fig. 9. Evolution of free surface at 2.20 m from drain; constantstorage coefficient �mean value� �̄=0.0243 m3 /m3 and RMSE=0.14 m; Eq. �12� with m=0.13, �d=−0.85 m, and RMSE=0.08 m;Eq. �19� with =0.99, �c=0.36 m, and RMSE=0.09 m

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nient to estimate the parameters of the soil-water retention curvefrom measurements carried out in the drainage system studied. Itis well known that the parameters m and are related to the shapeof the soil-water retention curve and are more stable than pressurescale parameters ��d ,�c�; accordingly, scale parameters should bedetermined from the evolution of the hydraulic head.

In fact, if the calibration is made using the water tabledrawdown observed, it is possible to obtain a best concordancebetween the experimental data and calculated with variable stor-age coefficient, the root-mean-square error is minimized with�d=−0.85 m and �c=0.34 m �RMSE=0.08 m�. For modelingwith a constant storage coefficient, a mean value of �̄=0.0243,calculated with Eqs. �10� and �12�, has been used; in this case, themean error between hydraulic head observed and hydraulic headcalculated is RMSE=0.13 m.

The hydraulic head variation is shown in Figs. 8–10 the bestconcordance between the experimental data and calculated withthe variable storage coefficient at 2.20 m from the drain �RMSE=0.08 m� and 4.33 m from the drain �RMSE=0.08 m� is reached;while at 0.50 m from the drain, a better concordance with theconstant storage coefficient is done. The same situation is re-ported by Pandey et al. �1992� and Gupta et al. �1994�. The resultobtained at 0.50 m is not very important because the hydraulichead evolution in this position is affected by the wall of the ex-perimental model �drain was placed at 0.30 m from a one wall ofthe model�.

Evolution obtained considering the variable storage coefficientproduces a similar curvature to that of the experimental data. Thisis not the case of the evolution obtained using a constant storagecoefficient which shows a change in the curvature at 2.20 and4.33 m from the drain. This comparison shows that a variablestorage coefficient is a more accurate representation of the water

Fig. 10. Evolution of free surface at 4.33 m from drain; constantstorage coefficient �mean value� �̄=0.0243 m3 /m3, and RMSE=0.21 m; Eq. �12� with m=0.13, �d=−0.85 m, and RMSE=0.07 m;Eq. �19� with =0.99, �c=0.36 m, and RMSE=0.07 m

table drawdown tendencies in a shallow unconfined aquifer.

284 / JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING © ASCE

J. Irrig. Drain Eng. 200

Conclusions

The concepts of drained depth and drainable depth have encour-aged discussions in terms of defining storage coefficient, drainedporosity, and drainable porosity. The consideration of the unsat-urated zone generated during drainage process has lead to a rela-tionship between storage coefficient and hydraulic head in whichthe knowledge of the soil-water retention curve is crucial. Thisrelationship is illustrated with the soil-water retention curves ofvan Genuchten and Fujita–Parlange. The resulting two expres-sions for storage coefficient have been validated in an experimentreported in the available literature. A good description of experi-mental results shows that the proposed relationship between stor-age coefficient and the soil-water retention curve for shallowunconfined aquifer can be used in studies of water dynamics insubsurface agricultural drainage systems.

Acknowledgments

This work was partially supported by CONACYT �Consejo Na-cional de Ciencia y Tecnología� through Project No. SEP-2004-C01-47083/A1.

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