This article was downloaded by: [University of Stellenbosch] On: 09 October 2013, At: 03:04 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Archives of Agronomy and Soil Science Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/gags20 Evaluation of different methods for the determination of saturated hydraulic conductivity for simulation of water table depth and drainage discharge using the DRAINMOD computer simulation model Nahid Nabi-Sichani a & Ali Reza Sepaskhah a a Irrigation Department , Shiraz University , Shiraz , Islamic Republic of Iran Published online: 05 Jul 2011. To cite this article: Nahid Nabi-Sichani & Ali Reza Sepaskhah (2012) Evaluation of different methods for the determination of saturated hydraulic conductivity for simulation of water table depth and drainage discharge using the DRAINMOD computer simulation model, Archives of Agronomy and Soil Science, 58:8, 887-901, DOI: 10.1080/03650340.2010.550282 To link to this article: http://dx.doi.org/10.1080/03650340.2010.550282 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &
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This article was downloaded by: [University of Stellenbosch]On: 09 October 2013, At: 03:04Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Archives of Agronomy and Soil SciencePublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/gags20
Evaluation of different methods for thedetermination of saturated hydraulicconductivity for simulation of watertable depth and drainage dischargeusing the DRAINMOD computersimulation modelNahid Nabi-Sichani a & Ali Reza Sepaskhah aa Irrigation Department , Shiraz University , Shiraz , IslamicRepublic of IranPublished online: 05 Jul 2011.
To cite this article: Nahid Nabi-Sichani & Ali Reza Sepaskhah (2012) Evaluation of differentmethods for the determination of saturated hydraulic conductivity for simulation of water tabledepth and drainage discharge using the DRAINMOD computer simulation model, Archives ofAgronomy and Soil Science, 58:8, 887-901, DOI: 10.1080/03650340.2010.550282
To link to this article: http://dx.doi.org/10.1080/03650340.2010.550282
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.
This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &
Evaluation of different methods for the determination of saturated
hydraulic conductivity for simulation of water table depth and drainage
discharge using the DRAINMOD computer simulation model
Nahid Nabi-Sichani and Ali Reza Sepaskhah*
Irrigation Department, Shiraz University, Shiraz, Islamic Republic of Iran
(Received 29 April 2010; final version received 8 December 2010)
The purpose of this study was to investigate application of the DRAINMODcomputer simulation model for estimation of water table depth (W) and drainagedischarge (q) by using different values of saturated hydraulic conductivity (Ks) ina subsurface drainage system in Kooshkak area in Fars province. These values ofKs were obtained from the drainage system, a direct measurement of Ks calculatedfrom drainage data (Ks1), Porchet method with saturated inverse hole (Ks2),ordinary Porchet method (Ks3) and saturated Porchet obtained using an empiricalequation presented by Sepaskhah and Rezaee (Ks4) (Sepaskhah AR, Rezaee A.1998. Hydraulic conductivity measurement for subsurface drainage system. IranAgr Res. 17:139–150). The results indicated that saturated Porchet and saturatedPorchet calculated using Equation (17) are reliable for determination of Ks
because their values are close to that obtained from the direct method.Furthermore, the results indicated that W fluctuations and q are estimatedproperly by the DRAINMODmodel, as shown by an index of agreement of 0.90–1.0 and 0.99 for W and q, respectively. However, q estimations were moreaccurate than W fluctuations, as shown by a mean absolute error of 0.045–0.243and 1.73–25.44 for q and W, respectively. Using different values of Ks in themodel caused tangible differences between the results, especially in W fluctua-tions, and showed that the model is sensitive to this parameter. Among theindirect methods of Ks determination, using the measured Ks obtained by thesaturated Porchet method (Ks2) resulted in more accurate W and q. It wasdetermined that the saturated Porchet method is more difficult and time-consuming than the ordinary Porchet method. Therefore, a relationship betweenthese two tests has been developed in the study area [similar to the equation thatwas presented by Sepaskhah and Rezaee (1998)] and estimation of Ks fromordinary Porchet method can then be converted to saturated Porchet method foruse in DRAINMOD model.
Keywords: DRAINMOD model; methods of determining hydraulic conductivity;subsurface drainage; water table fluctuations; drainage discharge
Introduction
Mathematical models are used in irrigation and drainage investigations.DRAINMOD is a computer simulation model that implements a mathematicalmodel in this investigation. This model simulates water movement and storage in
the soil, resulting in water table fluctuation and drainage discharge. TheDRAINMOD model was developed and then evaluated using a simulation ofwater table and drainage discharge by Skaggs (1978) in North Carolina,Skaggs (1982), Gayle et al. (1985) in Louisiana and Fouss et al. (1987). Changet al. (1983) used this model to evaluate the simulation of seepage losses onfarmland in California. Chang et al. demonstrated the validity of theDRAINMOD model for various soils, plants and climates by comparing theresults with measured data. Investigations on the DRAINMOD model show thatit is sensitive to variation in soil hydraulic properties such as hydraulicconductivity (Ks) (Anderson et al. 1987; Workman and Skaggs 1994; Haan &Skaggs 2003; Wang et al. 2006). Field measurement of Ks is complicatedbecause of the size of the required sample, spatial variability and themethods of measuring. There are laboratory and field methods for measuringKs in the soil. However, laboratory methods have some shortcomings. Forexample, the distribution of the samples and the inadequate size of samplesmeans that they cannot replicate the natural conditions of the field soil. For thisreason, in drainage study and design in Iran, field methods are usually used tomeasure Ks although there may be some uncertainties in these measurements. Thesuitability of methods for measuring Ks can be determined by applying theirvalues in models studying fluctuations in water table depth (W) and drainagedischarge (q).
The purpose of this study was to evaluate the suitability of different methods ofdetermining saturated hydraulic conductivity in a simulation of drainage dischargeand water table depth fluctuation using the DRAINMOD model in a subsurfacedrainage system in Kooshkak area of Fars province.
Model description
The DRAINMOD model was first presented by Skaggs (1978) and three years later,this model was promoted by Fortran programming and presented as DRAINMODversion 4. DRAINMOD is a software to model moisture migration through a soilprofile with shallow groundwater in drainage systems. This model is able to simulatefluctuations in the water table, drainage discharge, surface run-off, infiltration orleakage of water, estimation of evapotraspiration and decreasing crop productionunder water shortage conditions. The DRAINMOD model is based on waterbalance in the soil profile and its effective components are: water input (rainfall orirrigation), infiltration, surface and subsurface drainage, evapotranspiration anddistribution of water in the soil.
One of the basic equations in the model is water balance, which is considered fora segment of soil of unit surface area, in the mid point between two drainage pipes,from ground level to the impermeable layer. The water balance equation in themodel consists of two root zones: surface and subsurface.
Surface water balance
In this zone, it is assumed that the surface storage of water in a field is distributeduniformly. Water flow occurs when the level of the surface water is higher than thelevel in the surface storage, and flows quickly to the surface drainage as run-off (RO).This equation can be written as:
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Fþ DSþ RO� P ¼ 0 ð1Þ
where F is the amount of infiltrated water in the soil (cm), DS is the change in soilwater storage (cm), P is the rainfall (cm) and RO is the surface flow (cm).
Subsurface water balance
The subsurface water balance is written for a thin segment of soil that is locatedbetween two drains as follows:
DVa ¼ Dþ ETþDs � F ð2Þ
where DVa is the drained volume per unit area (cm), D is the depth of irrigationwater by subirrigation or drainage water (cm), ET is the evapotranspiration (cm), Ds
is the deep (vertical) seepage (cm) and F is the amount of water entering thesubsurface soil section by infiltration (cm).
Drainage discharge
Whenever the surface of the soil is not saturated, subsurface drainage discharge canbe determined using the Hooghoudt (1940) equation under steady-state conditions asfollows:
q ¼ 8Ke � de �mþ 4Ke �m2
L2ð3Þ
where q is the drainage discharge (cm h71), Ke is the effective lateral hydraulicconductivity (cm h71), m is the midpoint water table height above the drain (cm), Lis the distance between drains (cm) and de is the equivalent depth of the impermeablelayer below the drain (cm). In Equation (3), equivalent depth is applied instead ofreal depth to account for the convergence effect of the flow in the falling head nearthe drains (Skaggs 1991). Equivalent depth is calculated as follows:
de ¼d
1þ dL� ð8� p� LnðdrÞ � aÞ
0 � d
L� 0:3 ð4Þ
de ¼Lp
8� ðLnðLrÞ � 1:15Þd
L� 0:3 ð5Þ
a ¼ 3:55� 1:6� ðdLÞ þ 2� ðd
LÞ2 ð6Þ
where d is the distance from the impermeable layer to the drains (cm), L is thesubsurface distance of the drains (cm) and r is the radius of drains (cm). Wheneverthe water table reaches the soil surface, subsurface drainage discharge is calculated asfollows (Kirkham 1957):
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q ¼ 4� p� Keðsþ b� reÞG� L
ð7Þ
G ¼ 2Lntan ðpð2b� rÞ=4hÞ
tan ðpr=4hÞ
� �
þ 2X
LncoshðpmL=4hÞ þ cos ðpr=2hÞ coshðpmL=4hÞ � cos ðpð2d� rÞ=2hÞcoshðpmL=4hÞ � cos ðpr=2hÞ coshðpmL=4hÞ þ cos ðpð2d� rÞ=2hÞ
� �
ð8Þ
where q is the drainage discharge (cm h71), Ke is the effective lateral hydraulicconductivity (cm h71), s is the depth of water on the soil surface (cm), b is the depthof drains (cm), re is the effective radius of drains (cm), G is an infinite series (Equation 8) that is a function of b, drain depth (cm), r, drain radius (cm), h, depth ofsoil profile (cm), d, thickness of soil layer from drains to impermeable layer (cm) andL, drains distance (cm).
Infiltraton equation
The amount of infiltration into the soil is determinated using the Green and Ampt(1911) equation. The form of this equation is different according to the boundaryconditions and type of assupmtions. The explicit form of this equation is as follows:
f ¼ A
Fþ B ð9Þ
where f is the infiltration rate (cm h71), F is the cumulative infiltration (cm), and Aand B are experimental coefficients that are determined as follows:
A ¼ Ks �M � Sav ð10Þ
B ¼ Ks ð11Þ
where Ks is the vertical saturated hydraulic conductivity (cm h71), M is the initialsoil water deficit (difference between final and initial volumetric soil water contents)(m3/m73), Sav is the suction at the wetting front (cm).
Model inputs
The inputs of model are as follows:
1. Weather data
Water infiltration, water flow and surface water detention are dependent on rainfalldata, which is one of the most important weather parameters. Furthermore, becausethe steady-state condition is used, a short time interval for rainfall measurements isrequired for this assumption to be approximated. Rainfall is recorded hourly in mostweather stations, so rainfall with one hour time interval was used in the model.
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2. Potential evapotranspiration
Potential evapotranspiration is required for use in the model. This can be performed intwo ways: (1) in the first method, maximum and minimum daily temperatures are used,and potential evapotranspiration is then estimated using the model by Thornthwaite(1948); (2) in the second method, potential evapotranspiration values are entereddirectly into the model. In this study, potential evapotranspiration at Kooshkak wascalculated using the Penman–Monteith method (Allen et al. 1989) and the results wereentered into the model directly.
3. Soil hydraulic parameter
Soil hydraulic parameters as inputs are horizontal saturated hydraulic conductivity andsoil water release curve. This information was obtained from Rezaee (1993).
4. Plant root characteristics
To predict water table depth and soil water content, it is necessary to determineroot growth as a function of time. In this model, the effective rooting depth wasestimated based on 60% of maximum root length. In this study, effective rootdepths are considered to be 0.27 m for wheat and 0.84 m for alfalfa, as presentedby Rezaee (1993).
5. Drainage system parameters
These parameters are depth of drains, distance between drains, distance of drainsfrom impermeable layer, drainage management, drains radius, gradient of draininstallation, primary water table depth, maximum amount of surface waterdetention and equivalent drain depth.
Model outputs
The model outputs are: (1) soil water regime, water infiltration, surface flow,drainage and capillary rise flux; (2) water table fluctuations; (3) amount of excess soilwetness; (4) number of working days during the growing season; (5) dry days duringthe growth season; and (6) relative yields.
Materials and methods
Site description and measurements
This study was conducted at Kooshkak Agricultural Experiment Station, ShirazUniversity, located 60 km north of Shiraz, Iran, in latitude 308400 and longitude358520, with a height of 1609 m from mean sea level. A summary of the weather datais presented in Table 1. The soil in this region is classified as clay loam, and itsphysical and chemical properties are given in Table 2. The soil water retention isshown by the following equation:
y ¼ 0:21þ 0:23ð1þ 0:015� hj j1:153Þ�0:133 ð12Þ
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where y is the soil volumetric water content in cm3/cm73, and h is the soil watermatric head in cm.
The size of the research station is *100 ha. The majority of this land dedicatedto wheat and alfalfa cultivation. Owing to groundwater seepage from upper landsand water storage by the Doroodzan dam, the water table depth is shallow.Furthermore, the low infiltration rate of the soil causes ponding in this area,especially during the rainy seasons. A subsurface drainage system was installed usingconcrete pipes and the diameter of drains is 0.3 m, the distance between two drains is88.7 m, drain depth is 2.05 m, drain radius is 0.15 m, drain length is 1116 m, draininstallation gradient is 0.0022 m m71 , primary water table depth is 0.37 m, there is amaximum amount of surface water detention of 0.002 m, the depth of theimpermeable layer from ground surface is 6.7 m, and the equivalent drain depth is4.0 m (Figures 1 and 2) (Rezaee 1993).
Data were collected from 5 ha field blocks where drains were installed. In eachsection, auger holes were excavated in the mid point between drains to maintain thewater table for a period of 90 days from 21 January 1991 to 20 April 1991. Tocompare drainage discharge with the results of the model, discharge of one of thesedrainpipes was measured for 14 days from 21 January 1991 to 5 February 1991.These measurements started when the water table head in the middle of the twodrains reached a maximum value as a result of rain, it then fell in the subsequentdays and reached the level of drains.
Rainfall and other weather parameters were measured and recorded in theKooshkak weather station. Three soil profiles of 3 m depth were drilled in each fieldblock and soil samples from the layers of 30 cm thickness were taken. These sampleswere used to determine the soil water retention curve. Moreover, coefficients of theGreen–Ampt infiltration equation were obtained by measuring infiltration in adouble ring infiltrometer with three replications while the water table was at differentdistances from the soil surface. The results are shown in Table 3.
Table 1. Summary of weather data for the experimental site.
Weather parameter Quantity
Annual precipitation 346 mmAnnual potential evapotranspiration 2280 mmMonthly mean minimum air temperature 73.28CMonthly mean maximum air temperature 36.18C
Table 2. Physical and chemical properties of Kooshkak soil (Malekzadeh, 1997).
Note: aParticles 50.002 mm. OM, organic matter; EC, electrical conductivity; CL, clay loam.
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Hydraulic conductivity
Soil hydraulic conductivity was measured using four different methods: (1)calculated directly from the data from drainage systems (Ks1), (2) Porchet insaturated inverse hole (Ks2), (3) ordinary Porchet in inverse hole (Ks3), and (4)estimated Ks using an empirical model (Ks4) (Sepaskhah and Rezaee 1998). In theinverted auger hole method (ordinary Porchet method) soil hydraulic conductivitywas measured at 70 points on 50 6 50 m grids in 2 m auger holes without anywater infiltration before the initiation of measurement (Oosterbaan and Nijland1994). In this method, the readings were taken after sufficient water had seepedinto the surrounding soil to create a fairly thick almost saturated zone. Therefore,it is assumed that the rate of seepage from the hole into the surrounding soil is*Ks. This is valid for medium to heavy textured soils, as used in our study(Smedema and Rycroft 1983). In the saturated Porchet method (saturated inverseauger hole), which is similar to the ordinary Porchet method, soil hydraulicconductivity was measured in six of these auger holes after 7 h of waterinfiltration, which is much longer that used in the ordinary inverse auger holemethod. For this reason, this method is called saturated Porchet (Sepaskhah andRezaee 1998).
Figure 1. Schematic map of the experimental station and drain locations.
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Calculation of Ks from data obtained from the drainage system, using theBoussinesque equations reported by Dieleman (1974) are as follows:
where, q(t) is the discharge intensity (m d71), h(t) is the hydraulic head in the middleof the drains (m), R is the recharge intensity (m d71), tr is the duration of steadyrecharge (d), t is the time from beginning of recharge (d) and m is the drainableporosity. The value of j is calculated by:
j ¼ ð1=aÞ ¼ ðmL2Þ=ðp2KdÞ ð15Þ
where j is the storage coefficient, d is the equivalent depth (m) and L is the drainagespacing (m). Equations (13) and (14) are valid at t 4 tr þ 0.4j. Replacing t ¼ t1 andt ¼ t2 4 tr þ 0.4j in Equations (13) and (14) gives:
Then using Equation (15) and L, m and d, the systemic hydraulic conductivity wasobtained.
The fourth method of Ks determination was based on estimations from an empiricalmodel (a correlation between the saturated Porchet and ordinary Porchet methods). Arelationship between hydraulic conductivity measured using the saturated Porchet andordinary Porchet methods in Kooshkak area with a similar soil texture to that used inthis study is reported by Sepaskhah and Rezaee (1998) as follows:
Ks2 ¼ 0:46þ 0:39 Ks3 R2 ¼ 0:936; n ¼ 6; p < 0:001 ð18Þ
In which Ks2 is hydraulic conductivity from saturated Porchet method (m d71) andKs3 is hydraulic conductivity from ordinary Porchet method (m d71). Values of thehydraulic conductivity measured at 70 points in a field using ordinary Porchetmethod were converted to saturated Porchet values using Equation (18) and theaverage of these values was calculated as the fourth method for Ks determination(12.04 cm h71). The Ks values estimated using methods 1, 2, 3 and 4 equate with Ke
in Equation (3). Finally, these different values of hydraulic conductivities obtainedusing the four different methods were used in the DRAINMOD model to simulateW(t) and q(t).
Model evaluation
To evaluate the methods of determining the soil hydraulic conductivity forsimulating water table and drainage discharge, the DRAINMOD model was runfour times using different hydraulic conductivity values from systemic, saturated andordinary Porchet methods, and calculated from Equation (18).
To determine the goodness-of-fit of the simulation, statistical analysis was usedto compare the measured and predicted results with the following equations:
Mean bias error ¼ N�1XNi¼1ðPi �OiÞ ð19Þ
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Normalized root mean square error ¼N�1
PNi¼1ðPi �OiÞ2
� �0:5
Oð20Þ
Mean absolute error ¼ N�1XNi¼1
Pi �Oij j ð21Þ
Index of agreement ¼ 1�PN
i¼1 ðPi �OiÞPNi¼1 ð P0i
�� ��þ O0i�� ��Þ2 0 � d � 1 ð22Þ
where Pi is the estimated values, Oi is the observed values, and N is the number ofobservations, P0i ¼ Pi � �O, and O0i ¼ Oi � �O.
Results and discussion
Hydraulic conductivity
The mean values of Ks obtained from different methods are presented in Table 4. It isindicated that the values of Ks for Ks1, Ks2 and Ks4 are similar and lower than that forKs3 (ordinary Porchet). Therefore, it is concluded that saturated Porchet andsaturated Porchet calculated by Equation (18) are reliable for determination of Ks
because their values are close to that obtained from direct method.Using the input data of model including rainfall, evapotranspiration, soil water
release curve, plant root depth, the DRAINMOD model was run four times withhydraulic conductivity values obtained from direct, saturated Porchet, ordinaryPorchet methods and calculated from Equation (18). Variations in measured andestimated water table depth for 90 days, are shown in Figure 3. The values ofmeasured and model-estimated water table depth are compared in Figure 4. Tocompare model-estimated results of water table depth by using different values ofhydraulic conductivity, some statistical parameters were calculated as shown inTable 5. Measured and estimated drainage discharge values for 14 days are shown inFigure 5. The values of measured and model estimated drainage discharge arecompared in Figure 6. To compare model-estimated results of drainage dischargeusing different values of hydraulic conductivity, some statistical parameters werecalculated as shown in Table 6. In this study, simulation of water table fluctuationsand drainage discharge was performed for 90 days. However, drainage dischargecomparisons were carried out for 14 days during which time the discharge wasmeasured. Figure 4 indicates that, using Ks from a direct calculation of drainage data
Table 4. Mean values of Ks obtained from different methods used in the DRAINMOD model.
Method of Ks determination Saturated hydraulic conductivity (m d71)
Direct 2.72Saturated Porchet 2.20Ordinary Porchet 4.48Saturated Porchet calculated from Equation (18) 2.89
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Figure 3. Variation in rainfall (mm), measured and DRAINMOD-estimated water tabledepth (cm) over time.
Figure 4. Relationship between measured and model-estimated water table depth (cm) usingKs from various methods: (a) direct, (b) saturated Porchet, (c) ordinary Porchet, and (d)calculated using Equation (18).
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(Ks1), the DRAINMOD model predicted the water table depth with an index ofagreement of 1.0 and the accuracy of the predicion was in the order Ks1 4 Ks2 4Ks4 4 Ks3. This is also shown in Table 5 by the order of different statisticalparameters. Figure 6 indicates that, using Ks from a direct calculation of drainagedata (Ks1), the DRAINMOD model predicted the drainage discharge with a differentaccuracy and the order of accuracy was Ks1 4 Ks2 4 Ks4 4 Ks3, which is similar tovalues obtained for the water table depth prediction. However, the model results forwater table and drainage discharge obtained by applying different values of Ks fromdifferent methods have considerable differences. In general, the accuracy of theDRAINMOD prediction for drainage discharge was higher than that for water tabledepth. Furthermore, according to the values of mean bias error (MBE), theDRAINMOD model underpredicted drainage discharge and overpredicted watertable depth. As expected, the model results for water table depth and drainagedischarge have correspond best with the observed values when direct Ks (Ks1) wasapplied in the model because in this method the drainage system data was used
Table 5. Statistical parameters for comparing measured and model-estimated values of watertable depth in four different methods of Ks determination.
Methods of Ks determination MBE NRMSE MAE Index of agreement
Note: MBE, mean bias error; NRMSE, normalised root mean square error; MAE, mean absolute error.
Figure 5. Variation in rainfall (mm), measured and DRAINMOD-estimated drainagedischarge (mm d71) over time.
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directly to determine Ks. The high values of R2 for water table depth (0.998) anddrainage discharge (0.994) demonstrate a high accuracy of simulation (Figures 4 and6). It is well known that drainage equations based on the Dupuit–Forchheimerassumptions, such as Hooghoudt’s equation, give good estimates of flow but notwater table height because of these assumptions (Knight 2005). The same resultswere obtained in our study.
Results obtained by using Ks of the saturated and ordinary Porchet methods werecompared. It is clear that the results of the saturated Porchet method were closer tothe observed values, because the saturated Porchet method is more accurate because
Table 6. Statistical parameters for comparing measured and model-estimated values ofdrainage discharge in four different methods of Ks determination.
Methods of Ks determination MBE NRMSE MAE Index of agreement
Direct 70.033 0.1582 0.045 0.99Saturated Porchet 70.054 0.4346 0.115 0.99Ordinary Porchet 70.128 0.8495 0.243 0.99Saturated Porchet,calculated from Equation (18)
70.09 0.6035 0.171 0.99
Note: MBE, mean bias error; NRMSE, normalised root mean square error; MAE, mean absolute error.
Figure 6. Relationship between measured and model-estimated drainage discharge (mmd71) using Ks from various methods: (a) direct, (b) saturated Porchet, (c) ordinary Porchet,and (d) calculated using Equation (18).
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Ks is measured after 7 h water infiltration and in this condition the soil water suctionhead is closer to saturation.
Tables 5 and 6 show that the DRAINMOD model estimated drainage dischargebetter than water table depth and the index of agreement for drainage dischargeresults is smaller than for water table depth in different methods of Ks estimation.Furthermore, by comparing the values of NRMSE for the methods of saturated andordinary and saturated Porchet calculated from Equation (18), it is obvious that thesaturated Porchet method calculated from Equation (18) is more accurate than theordinary Porchet method and less accurate than the saturated Porchet method.However, the differences are small and the accuracy of this method is acceptable.Fisher’s F-test for comparing the relationship between the estimated and measuredwater table depth to a 1:1 line showed that for the different methods of Ks estimation(direct Ks from drainage system, saturated Porchet, ordinary Porchet and saturatedPorchet method calculated from Equation 18) there is no significant differencebetween their slopes and 1.0. However, the intercepts were significantly differentfrom 0 because of an overestimation of Ks, which leads to a deeper water tableestimation. Fisher’s F-test for comparing the relationship between the estimated andmeasured drainage discharge to 1:1 line showed that for the different methods of Ks
estimation (direct Ks from the drainage system, saturated Porchet, ordinary Porchetand saturated Porchet method calculated from Equation 18) there is no significantdifference between their slopes and intercepts with 1.0 and 0, respectively.
Conclusions
In this study, the DRAINMOD model was used to estimate fluctuations in watertable depth (W) and drainage discharge (q) properly. Therefore, it is recommendedthat this model is accompanied by other methods of evaluating and designingdrainage systems. It is concluded that the DRAINMOD model is more accurate andreliable for estimating drainage discharge than water table depth.
Using different methods to determine hydraulic conductivity in the model led totangible differences in the results, especially fluctuations in water table depth.Therefore, it is shown that the model is sensitive to this parameter and should bedetermined more carefully. It is concluded that saturated Porchet and saturatedPorchet calculated by Equation (18) are reliable methods for the determination of Ks
because their values are close to that obtained from direct method.Applying measured hydraulic conductivity by the saturated Porchet method in the
model resulted in a more accurate estimation of q and W. However, this method ismore difficult and time-consuming than the ordinary Porchet method for determiningKs. Therefore, it is recommended a relationship between the saturated and ordinaryPorchet measuring methods in the study area (such as Equation 18) is developed, thenthe value of Ks obtained using the ordinary Porchet method can be converted tosaturated Porchet values of Ks for a more accurate estimation of q and W.
Acknowledgements
This research supported in part by a research project funded by Grant No. 88-GR-AGR 42 ofShiraz University Research Council, the Drought National Research Institute, and the Centerof Excellence for On-Farm Water Management.
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