## Indian Journal of Agricultural Research

**Chief Editor**V. Geethalakshmi**Print ISSN**0367-8245**Online ISSN**0976-058X**NAAS Rating**5.60**SJR**0.293

**Chief Editor**V. Geethalakshmi**Print ISSN**0367-8245**Online ISSN**0976-058X**NAAS Rating**5.60**SJR**0.293

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BIOSIS Preview, ISI Citation Index, Biological Abstracts, Elsevier (Scopus and Embase), AGRICOLA, Google Scholar, CrossRef, CAB Abstracting Journals, Chemical Abstracts, Indian Science Abstracts, EBSCO Indexing Services, Index CopernicusIndian Journal of Agricultural Research, volume 54 issue 3 (june 2020) : 277-284

Field Evaluation of Unsteady Drain Spacing Equations for Optimal Design of Subsurface Drainage System under Waterlogged Vertisols of Maharashtra

S.D. Rathod^{1}, S.D. Dahiwalkar^{2}, S.D. Gorantiwar^{2}, M.G. Shinde^{2}

**Submitted**23-07-2019|**Accepted**20-01-2020|**First Online**15-04-2020|

The field experiment was conducted at Agricultural Research Station, Kasbe Digraj, Dist. Sangli during Adsali sugarcane season of 2012-13 to 2013-14. The experiment was conducted by installing subsurface drainage system with 10, 20, 30 and 40 m drain spacing and 1 m drain depth. In view of different costs and effectiveness of subsurface drainage associated with the varying depths and spacings, field evaluation of unsteady drain spacing equations was important for finding out the optimal drain spacing equation among various equations. The field evaluation of unsteady drain spacing equations revealed that the van Schilfgaarde, Hammad, Modified Glover, Guyon and Integrated Hooghoudt’s equation performed satisfactory for estimation of water table depths among seven unsteady drain spacing equations. The Glover-Dumm and Modified Glover-Dumm’s equations were not performed satisfactory for estimation of water table depths. Among unsteady drain spacing equations, van Schilfgaarde’s equation performed better and hence recommended for water table depth estimation and in turn for optimal design of subsurface drainage system under waterlogged Vertisols of Maharashtra.

Subsurface drainage system (SSDS) is a proven technology to combat the twin problems of salinization and waterlogging. However, the effectiveness of SSDS depends upon the optimal combination of drain spacing (DS) and drain depth (DD). In view to costs associated with the varying depths and spacings, it is necessary to evaluate the different unsteady state drain spacing equations for finding out the optimal combination of DS and DD as the inappropriate combinations may results in under or over drainage, less productivity and extra cost. The modifications in conventional SSDS design parameters indicated that there is need to optimize DS and DD to satisfy the drainage requirements under varying soil types, climates, crops, cropping intensities and water management practices. Before establishing guidelines for SSDS design for particular agro-hydrological condition, it is important to conduct field studies. Hence, this field set up on different combinations of DS and DD helps us to optimize the DS and DD. Further, the comparison of different unsteady state drain spacing equations with field evaluation allows SSDS designers to select the appropriate design formula for use under specific agro-hydrological conditions. Considering specific characteristics of the sugarcane and its water management practices in Vertisols, application of a suitable equation for planning of SSDS was of great importance.

Different researchers*viz*., Buckland*et al*.,* (*1987), Firake (1987), Lal *et al*., (1989), Singh *et al*., (1992), Singh *et al*., (1999), Nasralla (2007) Tripathi *et al*., (2008), Kumar *et al*., (2013), Pali (2013), Naftchally *et al*., (2014), Pali (2015) and Yousef *et al*., (2016) etc. evaluated different steady and unsteady drain spacing equations in different soils and hydrological situations and most of them recommended unsteady drain spacing equations over steady drain spacing equations. Hussein (2015) also used unsteady drain spacing equation for Egyptian Vertisols. Hence, decided to evaluate unsteady drain spacing equations under waterlogged Vertisols of Maharashtra. Most of the researcher evaluated Modified Glover-Dumm, Hammad, Integrated Hooghoudt, Glover-Dumm, Modified Glover, van Schilfgaarde, Guyon, Luthin and Worstell, Dee zeeuw Hellinga and Massland’s unsteady drain spacing equations under different soils and hydrological situations. Firake (1987), Lal *et al*., (1989), Singh *et al*., (1992), Kumar *et al*., (2013) and Pali (2013) reported the satisfactory field performance of Modified Glover, van Schilfgaarde and Integrated Hooghoudt’s equation for design of SSDS in semi-arid conditions of India. The limited studies reported by researchers on field evaluation of drain spacing equations in sandy loam saline-waterlogged soils of Haryana and clay loams of Maharashtra emphasized the need of field evaluation of unsteady drain spacing equations to our agro-hydrological conditions especially for waterlogged Vertisols of Maharashtra as its drainage is the most important challenge in agricultural water management because of 40 to 70% clay content having the peculiar property of swelling and shrinking; very low infiltration rate and permeability; poor saturated hydraulic conductivity and drainable porosity. In view to above, seven unsteady drain spacing equations *viz.*, Glover-Dumm, Modified Glover-Dumm, Modified Glover, van Schilfgaarde, Integrated Hooghoudt, Hammad and Guyon’s equations were selected for finding the most appropriate SSDS design equation through field evaluations at our soil, climate and agro-hydrological condition.

Different researchers

In order to fulfill the objective of the study, the field experiment with four DS of 10, 20, 30 and 40 m and DD of 1.0 m. was installed on farmer’s field at Village Mouje Digraj located 3 km away from Agricultural Research Station, Kasbe Digraj, Dist. Sangli (Maharashtra) during

The saturated hydraulic conductivity of soil (K

The drainable porosity of soil (

Where, Q is average drain outflow for drainage period during which the water table dropped from h

The drainage coefficient q (mm day

Where, Q is average drain outflow for the certain drain out period in m

The depth to an impervious layer below soil surface (D) was recorded from the visible rock formation strata in irrigation well nearby the experimental area. Accordingly, the D was calculated. The D was assumed to be the same level at all points. The de was calculated by Moody’s empirical equation (Moody, 1966) for each DS and DD combination,

a) When 0<d/L ≤ 0.3,

Where,

L= drain spacing (m), r is radius of drain pipe (m) and

b) When d/L > 0.3,

The WTD under different combinations of DS and DD was measured from piezometers, which were manually augured at L/2 (location of piezometers at distance of half of drain spacing from lateral drain), L/4 (location of piezometers at distance of a quarter of drain spacing from lateral drain) and L/0 (location of piezometers at a zero distance from lateral drain i.e., not exactly on drain but very close to lateral drain) at both the sides of lateral drain by using a 120 mm outside diameter auger to a depth of 1.7 m from the soil surface for periodically measurement of WTD after rainfall or irrigation. An 80 mm internal diameter PVC pipe with perforations was then lowered in each piezometer to a depth of 1.7 m, while ensuring that a 30 cm length was above the ground level to prevent runoff water from flowing in. End caps were fitted to both ends of the pipe to prevent the intrusion of materials into the piezometers. Coarse sand was backfilled throughout the whole perforated section of pipe. This was to prevent clogging of the perforations by clay and silt particles. WTD at each piezometer was measured by gradually lowering the locally made measuring meter with float in the piezometers until metered hollow pipe floats on water. On the other hand, drainage outflows (Q) in ml min

The following unsteady drain spacing equations were evaluated,

Glover (Dumm, 1954 and Skaggs

Where, K

Skaggs (1973) observed that the initial WT shape encountered in the field was more often parabolic than flat. They modified the initial condition accordingly and found a solution for spacing between drains that different from Glover-Dumm’s equation only in that numerical constant 4/p was replaced by approximately 1.16. Thus, this results in the calculation of somewhat wider spacing between drains for the same rate of water table drop. The Modified Glover-Dumm’s equation is as follows,

Bouwer and van Schilfgaarde (1963) assumed that the instantaneous drainage rate midway between drains may be taken equal to the steady state drainage rate corresponding to the same water table elevation. Using Hooghoudt’s steady state relationship, they obtained a transient drain spacing equation, which may be written as,

Where, C is flux constant or correction factor defined as the ratio of the average flux between drains to the flux midway between drains. Typically C lies between 0.8 to 1. Hooghoudt’s equivalent depth, de, must be used in Bouwer-van Schilfgaarde’s equation as it is based on Dupuit-Forchheimer (D-F) assumptions.

van Schilfgaarde (1963) proposed an unsteady subsurface drainage equation, which corrected for D-F assumptions and avoided the assumption of a constant thickness of the flow region. The following equation was proposed,

van Schilfgaarde (1964) derived following equation based on D-F assumptions for an initially parabolic water table,

Guyon’s analysis is not based on the D-F assumptions, but on a more exact treatment of potential theory (Guyon, 1964 and van Schilfgaarde, 1965). For deeper impervious layer, he obtained the following drain spacing equation,

Hammad (1962) derived his equation by using the potential theory. He made the assumptions that the receding water table between the drain tubes is nearly flat to derive equations for water table drawdown in both shallow and deep soils.

a) For shallow soils (d/L < 0.25), the spacing between drains is given by,

b) For deep soils (d/L > 0.25), the spacing between drains is

The predicted and observed MWT heights were compared by the percent deviation (PD), percent error (PE), mean absolute error (MAE), root mean square error (RMSE) and correlation coefficient (R

Where,

n is number of observations, Oi is observed MWT height above drain at Julian day i, O is arithmetic mean of observed daily MWT height above drain, Pi is predicted MWT height above drain at Julian day i and P is arithmetic mean of predicted daily MWT height above drain.

It is observed from Table 1, 2, 3 and 4 that the average observed MWT heights under DS of 10, 20, 30 and 40 m with DD of 1.0 m were 0.4198, 0.6481, 0.7443 and 0.9130 m, respectively. The average predicted MWT heights by Glover-Dumm, Modified Glover-Dumm, Modified Glover, Integrated Hooghoudt, van Schilfgaarde, Guyon and Hammad’s equation under DS of 10, 20, 30 and 40 m with DD of 1.0 m were 0.5131, 0.4836, 0.4103, 0.4045, 0.4371, 0.4100, 0.4471 m; 0.7671, 0.7173, 0.6118, 0.6042, 0.6513, 0.6161, 0.6574 m; 0.9150, 0.8467, 0.7263, 0.7202, 0.7616, 0.7263, 0.7604; and 1.1161, 1.0308, 0.8850, 0.8785, 0.9250, 0.8850 and 0.9250, respectively. Further, among these seven unsteady drains spacing equations; Modified Glover, Integrated Hooghoudt, van Schilfgaarde, Guyon and Hammad’s equation predicted the average MWT heights nearer to average observed MWT heights under all four drain spacings as the average percent deviation for these five equations were within the allowable limit of ±10% variations (Table 1, 2, 3 and 4). Whereas, the MWT heights predicted by Glover-Dumm and Modified Glover-Dumm’s equations looking most of the time largely away from the observed MWT heights under all four drain spacings as these equations recorded the higher average percent deviation values beyond the allowable limit of ±10% variations (Table 1, 2, 3 and 4). This was due to the fact that Glover-Dumm considered flat water table at the start of each drainage cycle and these equations are derived for isotropic and homogeneous soil. However, the experimental soil was heterogeneous and multi-layered vertisols. Whereas, the satisfactory performed equations considered the parabolic WT and avoided the assumption of a constant thickness of the flow region.

It is observed from Table 5 and 6 that the statistical parameters

Firake (1987) reported the performance order of different unsteady drain spacing equation as Modified Glover-Dumm, Hammad, Integrated Hooghoudt, Glover-Dumm, van Schilfgaarde and Guyon’s equation for clay loam soils of Maharashtra. Pali (2013) also reported the satisfactory field performance of Modified Glover, Integrated Hooghoudt and van Schilfgaarde’s equation in saline soils of Haryana. Kumar

The experiment on field evaluation of seven unsteady drain spacing equations under subsurface drainage system with varying drain spacing and depth in waterlogged Vertisols conducted at Agricultural Research Station, Kasbe Digraj, Dist. Sangli (M.S.), India concluded that van Schilfgaarde, Hammad, Modified Glover, Guyon and Integrated Hooghoudt’s equation performed satisfactory. Hence, these five unsteady drain spacing equations are suggested for prediction of mid-span water table heights under waterlogged Vertisols. Whereas, Modified Glover-Dumm and Glover-Dumm’s equations indicated statistically poor field performance and can be out rightly discarded for design of subsurface drainage system under waterlogged, heterogeneous and deep impervious layered Vertisols of Maharashtra.

Among seven unsteady drain spacing equations, the following van Schilfgaarde’s unsteady state drain spacing equation is recommended for better estimation of mid-span water table heights and in turn for the design of subsurface drainage system in terms of drain spacing and depth under waterlogged, heterogeneous and deep impervious layered Vertisols of Maharashtra.

Among seven unsteady drain spacing equations, the following van Schilfgaarde’s unsteady state drain spacing equation is recommended for better estimation of mid-span water table heights and in turn for the design of subsurface drainage system in terms of drain spacing and depth under waterlogged, heterogeneous and deep impervious layered Vertisols of Maharashtra.

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