Water table behaviour in drained lands: effect of evapotranspiration from the water table

Agricultural Water Management, 20 (1992) 313-328

313

Elsevier Science Publishers B.V., Amsterdam

Water table behaviour in drained lands: effect of evapotranspiration from the water table P.J. Nikam 1, H.S. Chauhan a, S.K. Gupta b and Sewa Ram a aGobind Ballabh Pant University of Agriculture and Technology, Pantnagar, India bCentral Soil Salinity Research Institute, Karnal, India (Accepted 11 November 1991 )

ABSTRACT Nikam, P.J., Chauhan, H.S., Gupta, S.K. and Sewa Ram, 1992. Water table behaviour in drained lands: effect of evapotranspiration from the water table. Agric. Water Manage., 20:313-328. Subsurface drain spacing is underestimated by the equations that do not account for evaporationevapotranspiration (ET) lowering the water table in drained lands. An analytical solution is proposed to evaluate water table behaviour in subsurface drained lands in the presence of ET. A piecewise linear model is proposed and used to describe any realistic functional relation between ET and depth to water table. Characteristics of the solution have been highlighted with the help of numerical examples for which drainage parameters have been chosen from two actually operating drainage systems installed in semi-arid regions. The accuracy of the proposed solution has been verified with the existing numerical scheme as well as by comparing the water table behaviour with the observed field data. Application of the solution in subsurface drainage design has been illustrated which suggests that drain spacing at this particular site could be increased by 9 to 18% if the contribution of ET in lowering the water table is taken into account.

INTRODUCTION

Development of objective methods and practical solutions for determining o p t i m u m spacing and depth of drains in terms of soil properties, site conditions, crop requirement and climatological conditions is the subject of present day drainage research in India. Although at present it is c o m m o n to use drainage design equations developed from experiences in h u m i d climates and apply them to irrigated areas in the arid and semi-arid regions, it is known to be the incorrect approach. It is understood that under such conditions, evaporation or evapotranspiration (ET) will play an important role in lowering the ground water table. Despite this knowledge, there is no satisfactory approach to account for the effect of ET on the rate of fall of the water table in drained lands as a closed form solution to such a physical problem has not yet been developed (Skaggs, 1975; Ribbens and Shaffer, 1976; Durnford et al., 1987; Gates and Grismer, 1987 ). Herein we propose a piecewise linear functional relation for describing the relation between ET and depth to water table. We proposed to use this rela0378-3774/92/$05.00

© 1992 Elsevier Science Publishers B.V. All rights reserved.

314

P.J. NIKAM ET AL.

tion for deriving an equation for assessing ground water table behaviour in the presence of ET in drained lands. Characteristics of the solutions are illustrated with the help of numerical examples which are relevant to the problem of drainage design. Field data are used to verify the proposed equations. It is expected that the solutions proposed in this paper will provide greater understanding of the problems related to drainage of agricultural lands commonly encountered in arid and semi-arid regions. FUNCTIONAL

RELATION

Skaggs (1975) solved the Boussinesq equation numerically, such that he accounted for the contribution of ET in lowering the water table. In this formulation, it was assumed that ET occurs at a constant rate. Such steady ET could occur in soils at a definite depth to water table and under specific climatic conditions. In the presence of subsurface drains, the water table is progressively lowered and therefore ET-evaporation will be a function of depth to water table. A number of empirical relations have been proposed to describe the variation of the ET-evaporation with depth to water table (Averianow, 1956; Gardner and Fireman, 1958; Singh et al., 1976; Sharma and Parihar, 1973; Hobbs, 1981 ). Grismer and Gates ( 1988 ) reported that the rate of upward flux from a water table in cropped lands could be estimated by a linear relation

ETd=a-bd

(1)

Here, ETd is the evapotranspiration, d is the depth to water table, a and b are the empirical constants having units of c m / d and d - ~ respectively. In order to avoid the constraint that a particular functional relation must be fitted to the relation between ET and depth to water table, a piecewise linear model is proposed to describe such a relationship. According to this proposal, any rectifiable curve could be approximated by piecewise linear segments (Fig. 1 ). Mathematically

ETd~ =ETo - b i d

O
(2)

ETd2=ETo-bld~-b2(d-d2)

d~
(3)

ETai=ETo-b~d~-b2(d2-d~) . . . . bi(d-di) ETa,=ETo-b~d~ . . . . .

b,,(d-d,,)

di_,
d,,_l
(4) (5)

In these equations, ETa, is the evaporation or ET for segment i, d, is the depth to water table, ET0 is the ET when the water table is at the soil surface, and b, are the regression constants. All values with negative or zero subscripts are treated as zero. The parameter n is the total number of segments into which a rectifiable curve should be divided to get a close approximation of

WATER TABLE BEHAVIOUR IN DRAINED LANDS

Eo

-•'•'•'••• --

~\\

o

..... ~

315

Original function

Approximationby egments

E

D

1 dl

I d2

1 d5

I I d4 d5

I d6

r di

dn

Depth(cm)

Fig. I. F u n c t i o n a l r e l a t i o n o f e v a p o r a t i o n w i t h a r b i t r a r y n u m b e r o f straight lines.

the exact relation. Earlier, Gupta and Singh (1980) used the principle of approximating a rectifiable curve with piecewise linear segments in problems related to solute transport. Equations ( 1 ) - (5) could be related to hydraulic head, once d is replaced by ( h o - h ) . Here ho is the initial hydraulic head and h is the hydraulic head at any time t. By adjusting the values of bi, di and n, any curve could be approximated with reasonable accuracy. In writing eqs. ( 2 ) - ( 5 ), d has been defined as the depth to water table such that ho will always start from ground level; in practice, however, by defining ETo as the ET rate at the initial maximum ground water elevation (not necessarily at the ground level) and d as the depth to water table starting from this level, such difficulties could be circumvented without any change in the formulation and the solution of the problem. THEORY

For the derivation of the proposed equation, the Bouwer and Van Schilfgaarde (1963 ) approach was considered appropriate. In fact, the approach has been extensively used for deriving non-steady state solutions utilizing steady state discharge-hydraulic head relations. The usefulness of this approach for this purpose is illustrated in Appendix A. According to this ap-

316

P.J. N I K A M ET AL.

proach, the rate of fall of water table midway between the drains can be given by

q+ETd= -Cf(h)

dh/dt

(6)

Here, q is the instantaneous drainage rate from the drains as a function of h, is the evapotranspiration from the water table as a function of h, f (h) is the drainable pore space in fraction and as a function of h; t is the time and C is the correction factor. The correction factor is introduced in order to use a steady state solution which assumes a flux that is independent of time and distance from the drains for prediction of the rate of fall of the water table. The values of C usually range from 0.8 to 1.0 (Bouwer and van Schilfgaarde, 1963). For the present investigation, the following assumptions have been made. • The drainable pore space is not a function of h and therefore, it remains constant as the water table is lowered. • Hooghoudt relation is appropriate for describing discharge-hydraulic head relation (see Appendix A ). For convenience, the Hooghoudt equation is reproduced as follows.

ETd

q= (8K2deh+4K~h 2 ) / S 2

(7)

1£2

Here, K1 is the hydraulic conductivity of the layer above the drain level, is the hydraulic conductivity of the layer below the drain level, de is the equivalent depth to impermeable layer, and S is the drain spacing. Incorporating eq. (7) in eq. (6), we have

dh -dt=S2Cf(4K 1h2+8K-~eh +S2ETa) Incorporating ET~ values from eqs. ( 2 ) - ( 5 ) and integrating, gives

(8)

hi

dh)h-t-S2(ETo - fdt=S2Cf f (~IK, h2+ ( 8K2~ --~-S2bl ho

h2

-I-bl

ho))

dh

+S2CT";(4Klh2+8(K2de+S2b2)h+S2(ETal_b2hl))

(9)

hI

h~

dh +S2Cf f (,K, h2+(ZK2de+S2bn)h+S2(ETan_,-bnhn_l)) hn- I

Denominators in terms on the right hand side under the integration sign are quadratic equations of the form Thus the final integration

(mh2+rh+p).

WATER TABLE BEHAVIOUR IN DRAINED LANDS

317

will depend upon the relative values o f r and 4mp. We will therefore, have two solutions. Case 1: r 2 > 4mp For this case, the final solution from eq. (9) can be written as

t=

(10)

such that A1 = [ ( 8K2 de + S2b~ ) 2 _ 16K~ (ETd~_I - b~hi_ 1) S 2 ]1/2

( 11 )

B / = 8K1 h~_ 1 + 8/(2 de + S2bi

( 12 )

C~ = 81£1h~ + 8K2de + S2b~

( 13 )

Case 2: r 2 < 4mp In several combinations o f ETo and drain spacing S, possibility o f r 2 < 4mp can not be ruled out. For such cases, the solution from eq. (9) could be written as

t= i=1 L 2S2CfFtan-I Pi L (M~/PD-tan-I(N~/P~)]

(14)

Here P~ = [16K1 ( ETdi_ I - b~ho) S 2 - (8K2de -I- S2 bi ) 2 ] 1/2

(15)

M, = 8K1 hi_ 1 + 8K2de +S2b~

(16)

N, = 8KI hi + 8K2de + S2bi

( 17 )

For n = 1, E T o = 0 , b l = 0 and kl=K2, eq. (10) as well as eq. (14) reduce to the Bouwer and van Schilfgaarde (1963) equation which is rewritten as follows

$2 _

8Kde t Cfln[ho(2de +ht)/ht(2d2 +ho) ]

( 18 )

Characterizing the new solution for Eo = constant To test the equation derived in this paper for a special case ofEo = constant, the new equation was compared with the numerical simulation model o f Skaggs (1975). For this check, n was taken as 1 while bl was taken as zero. With these values, the new equation simulates a situation where evapotranspiration occurs at a constant rate given by Eo. Comparison of new solution with experimental data Drain outflow-hydraulic head data from a field experiment at Sampla were used to test the new equation. The data set selected for this study was taken

318

P.J. NIKAMETAL.

TABLE 1 Parameters used to test the proposed equations Parameters

Mundlana

Sampla

Hydraulic conductivity K~ (m/day) /(2 (m/day) Drainable pore space* ho (cm) h, (cm) Depth to impermeable layer (cm) Drain spacing (m)

0.80 0.80 0.10 175 145 345.00 50,60,84

1.03 7.50 0.10 175 145 120.00 25,50,75

*Assessed on the basis of soil texture.

at a time when recharge to the drained area was minimal. Briefly, the data used in this study have been obtained from a drainage experiment located in a semi-arid region with an average annual rainfall of 700 mm. Nearly 80% of this rainfall occurs during the monsoon season (June-September) when the waterlogging problem is most acute. The average annual potential ET exceeds 2000 mm. The soil profile is layered and hydraulic conductivity is higher in the lower than in the upper layer. The parameter of interest for this study from the experiment at Sampla as well as from another experiment at Mundlana are presented in Table 1. These parameters were used in various calculations for illustrating the characteristics of the solution. As the data for these examples are taken from real field experiments at Sampla and Mundlana, results of these calculations are relevant to the areas represented by these sites. In addition to collection of data from these sites, a number of studies carried out by various investigators at these sites (Rao et al., 1986) led us to believe that ET was a contributing factor in affecting the ground water table behaviour of the study region. For example ground water table behavior in the region in undrained land was found to be very well correlated with the potential ET. The higher the potential ET, the higher was the recession of the ground water table. Observations from the piezometers installed at various depths (2, 3 and 4 m ) did not reveal any deep seepage. Water balance studies also did not point out any unaccounted losses which could be attributed to deep seepage. RESULTS A N D D I S C U S S I O N

Equations (10) and ( 14 ) have been proposed to account for the contribution of evapotranspiration in lowering the water table in drained lands. The number of terms in these solutions can be reduced by restricting the number of segments (n). Further simplification is possible by approximating the

WATER TABLE BEHAVIOURIN DRAINED LANDS

319

E T - d relation by a step function such that slopes of each line segment are zero (Fig. 2). As already pointed out, both the proposed equations can be used for cases where there is no ET provided appropriate parameters are used. However, an additional advantage is that these solutions could be applied even to cases where the soil profile is layered unlike eq. ( 18 ) which can be used only for homogeneous soil profiles. Before we approach rigorous testing of the equation, characteristics of the solutions are first illustrated by evaluating the effect of each parameter appearing in the functional relation used to describe the hydraulic head-ET curve.

Effect of parameter ETo The parameter ETo appearing in eq. (10) represents the rate of evaporation or ET when the water table is at the soil surface. This rate will mainly be governed by the potential ET. Although, in practice, the value of ETo will be only a fraction of the potential ET, it could have large variation in different seasons and even within a season. In order to study the effect of this parameter, time to lower the water table from soil surface to 30 cm below the ground surface was evaluated taking different values of ETo (Fig. 3 ). In all these calculations, parameter bl was taken as 0.00667. The results of these calculations, reported in Table 2 for the field site at Mundlana, show that time to lower the water table decreases with increasing ETo for all the three drain spacings. When effect of evaporation is neglected, time to lower the water table by 30 cm is larger even when compared with the lowest value of ETo. Although the general trend is maintained even for the case of Sampla, the differences are much smaller.

0

•8

b ;0"00667 ~ ' - ; : ~ 7,~ 1 - ~ - .

~o, _ ..,

- ..... --'--~

Realistic functional relation (assumed) Approximations to the relation

----i

0-4 . . . . . . . . . . ~ ' s r-' ~Ig ~~',,,~- (3 A)

L-

.' .

0

I0

20

30

.

.

.

40

.

.

o,5(2A

.

50

60

depth(cm) Fig. 2. A r e a l i s t i c f u n c t i o n a l r e l a t i o n b e t w e e n e v a p o r a t i o n a n d d e p t h t o w a t e n a b l e and its app r o x i m a t i o n s u s e d in calculations.

320

P.J. NIKAM ET AL.

d "''" \ ~ 06

\

N. 0 " 4 1 K o

"Ed = E T o - bl

"x

l\\\

\\ "

02t-

--. %

IL.

0

""

" ~ ".

hi"

"~ ~

6

N . uo,~.

"5.... a.. "- ° o f " - ~ >

....

"<.%~ ;, N"<.'%~"."e . . . ".... ..... N u6,~ ..ue~ \..

20

40

60

80

100

120

Depth(crn)

Fig. 3. Assumed functional relations between evaporation and depth to watertable for studying the effect o f E T 0 b~ on watertable behaviour. TABLE 2 Effect of E T o n time to lower water table by 30 cm (b~ =0.0066)

Drain spacing

C

t (d)

(m) Eq. (19)

ETo (cm/day) 0.4

0.6

0.8

Mundlana 50.0 67.0 84.0 Sampla 25.0 50.0 75.0

0.8 0.8 0.8

1.79 3.03 4.60

1.47 2.21 2.95

1.31 1.87 2.36

t.18 1.61 1.97

0.8 0.8 0.8

0.13 0.5l 1.10

0.13 0.48 0.99

0.13 0.46 0.91

0.13 0.44 0.85

Ej]ect of parameter b The parameter b in eq. ( 10 ) signifies the decrease in evaporation rate with increasing depth to water table. For the same depth to water table, the value of b would depend upon soil type. In order to study its effect on time to lower the water table by 30 cm, ETo was kept constant at 0.8 c m / d while b was varied from 0.0055 to 0.0078 (Fig. 3 ). As shown in Table 3, the time to lower the water table increases with increasing values of b~, For these typical examples, there are less noticeable differences probably because of the following reasons.

321

WATERTABLE BEHAVIOURIN DRAINED LANDS TABLE 3 Effect of b, on time to lower water table by 30 cm (Eo=0.8 c m / d a y ) Drain spacing ( m )

C

t(d) b,

Mundlana 50.0 67.0 84.0 Sampla 25.0 50.0 75.0

0.0055

0.00667

0.00778

0.8 0.8 0.8

1.17 1.59 1.94

1.18 1.61 1.97

1.19 1.64 2.00

0.8 0.8 0.8

0.13 0.44 0.84

0.13 0.44 0.85

0.12 0.44 0.92

• The parameter ETo is quite high in relation to bl times the depth to water table. • The time to lower water table by only 30 cm has been calculated which is a small fraction of the total depth to drains. The calculations show that if the water table is to be lowered by 150 cm below the soil surface, the time to lower the water table is 1.124 times that, when bi is equal to 0.00667 compared to when it is 0.0055.

Effect of approximations of thefunctional relation of ET The functional relation proposed in this study could be simplified either by reducing the number of segments or by taking one of the regression constants (bi in this case) as zero. Effect of some approximations on time to lower the water table were studied (Fig. 2). Results of three approximations are presented in Table 4. Additional results for lowering the water table by 60 cm are given in Table 5 with few new approximations. There appears to be little difference in the time to lower water table with different approximations except for approximation 4 in Table 5. It appears from Fig. 2 that this approximation depicts the real function with m i n i m u m accuracy. These results would mean that if approximations of the function are made judiciously, it would be possible to reduce the number of segments for approximating a real function without affecting the accuracy of the results. There could be more than one way by which a single function could be approximated and yet similar results would be obtained. It may also be noted that each approximation will be valid only for the depth for which these have been initially made. In other words, approximations for each depth have to be made separately and judiciously. For example, if approximation 3 (Table 4) is used to calculate time to lower the water table by 15 era, it works out to be 0.552 d compared to

322

P.J. NIKAMETAL.

TABLE 4 Comparison of the time to lower water table by 30 cm obtained by various approximations of assumed function of evaporation Approxi- Drop in mation water table (cm)

1 2 3

ETo

b~

(cm/d)

(d - j )

Time (d) for drain spacings (m) 50

175-145 0.8 175-145 0.65 175-160 0.8 160-145

0.00857 0.0 0.00667 0.02

67

84

t

Total time

t

Total time

t

Total time

1.20 1.20 0.55 0.67

1.20 1.20 1.22

1.65 1.66 0.76 0.93

1.65 1.66 1.69

2.03 2.05 0.92 1.26

2.03 2.05 2.18

t f

/ (

TABLE 5 Comparison of time to lower water table by 60 cm obtained by various approximations of assumed function of evaporation Approxi- Dropin mation water

ETo

b~

(cm/d)

(cm/d)

Time (d) for drain spacings (m) 50

table

67

84

(cm)

IA 2A 3A

4A

175-115 175-145 145-115 175-160 160-145 145-125 125-115 175-115

0.8 0.65 0.15 0.8 0.4

0.0133 0.0 0.0 0.00667 0.02 0.0185 0.003 0.0

3.17 1.20 2.02 0.55 0.67 1.24 0.83 3.04

t ~ }

Total time

t

3.17

4.80 1.66 3.14 0.76 0.93 1.91 1.39 4.374

3.21 3.29 3.04

~ f }

Total time

t

4.80 4.80

6.37 2.05 4.31 0.92 1.26 2.60 2.08 5.57

4.98 4.37

Total time

~ f }

6.37 6.36

6.86 5.57

0.665 d with approximation 2 resulting in a difference of around 20%. On the other hand when these approximations were used to calculate the time to lower the water table by 30 cm, the time was more or less similar (Table 4 ).

Comparison with numerical scheme To compare the proposed eq. ( 1 ) or eq. ( 1 4 ) with the numerical scheme of Skaggs ( 1 9 7 5 ) , n was taken as 1 and bl was assumed to be zero. This was necessary because the numerical scheme is valid only for the case when ET occurs at a constant rate. Calculations were m a d e for the drains installed at Sampla and drain spacing was taken as 50 m. Initially eq. ( 18 ) was compared with the Skaggs model for the case when there is no ET (Fig. 4a). The trend

WATER

TABLE

BEHAVIOUR

IN DRAINED

323

LANDS

of the recession curve is similar in both cases, althoughit takes a longer time to get similar drawdown with Skaggs' model compared to eq. ( 18 ). This resuits from the fact that in the case of solution based on the Hooghoudt equation, lowering of the water table midway between the drains starts as soon as the drains are opened. In the case of the numerical solutions, however, lowering of the water table midway between the drains starts only after some time has elapsed. Skaggs and Gilliam (1986) reported that both the analytical solution and the numerical solution would give similar results provided this lapse of time is accounted for. In order to do so, a notional time was calculated utilizing the Glover and D u m m equation (Durum, 1960 ). The notional time was calculated by incorporating ht=ho in the equation proposed by Durum (1960). For the other known parameter K, de, f a n d S, with this step, lag time between the opening of the drains and the initiation of lowering of the water table at mid point between the drains could be obtained. The lag time or the notional time thus calculated was added to the results obtained with the integrated Hooghoudt equation. The curve thus generated matched closely with the curve obtained with Skaggs' model (Fig. 4a). A similar test with eq. ( 1 ) was made assuming ETo=0.6 cm/d. Curves generated through these calculations are reported in Fig. 4b. A comparison of Fig. 4a and 4b reveals that the order of magnitude of the errors between the numerical scheme and the derived analytical solution remains unaltered. Therefore, it is reasonable to conclude that the effect of evaporation could be included in the

IO ~ 0"9

1.0 * Skaggs numericol model without 0-9 ~ 0

~ -~ "~ ~

~

evaporation

•

$koggs numerical model with

Eq. (18) q. (I0) with additional time

.06-

%

=.

o\

.

06

\ o \ 0"4-0'5

" ~ ~

"~

e

0.4

:

°

0'3

i 020

I

I 2

I

•

I 4

I

I 6

I

I 8

[

I 0.2~) I0

I

I 2

Time (doys) (o)

Fig. 4. Test of the proposed equation with numerical scheme.

I

I

I

4

I

6

Time(days) (b)

I

0 I 8

I

I

I0

P.j. NIKAM ET AL.

324

Hooghoudt equation through the use of eq. (7) without affecting the accuracy o f the final solution.

Testing with field data Experimental data from subsurface drainage systems in the semi-arid regions are hardly amenable to existing equations which do not account for the process of evaporation - ET. As described in a previous section, ample experimental evidence leads us to believe that the discrepancies between the observed and predicted results were mainly due to failure to account evaporation-ET. A data set from a drainage experiment (Sampla, India) was chosen to illustrate this observation and to test the theory. The depth to water table at midpoint between the drains as a function o f time is plotted in Fig. 5. The predicted curves with eq. ( I 0 ) as well as with eq. (18) are also presented along with the observed data. It may be seen that transient water table as shown by curves B and C are quite close to the observed field data for about 160

Observed Integrated Hooghoudf eq.(lO) n--I ~ Ed =0.gcm/doy eq.(lO) n = 3

-0A C B

140

120

I00

1.6

u .c

8C

--

o

~

~-~--~---d A

1.4

0 B

60

40

c

~ab

)6 )4 f

"---

c

[B

)2

[

20

I

0

I

I

AI

i

I

[

20 4-0 60 80 I00 120 140 Depth to water table (cm) I I

i 2

I 3

i 4

[

] 5

I 6

I 7

Time(days) Fig. 5. Observed and predicted hydraulic heads in a drained plot at Sampta. See inset for functional relation between evaporation and depth to watertable.

WATER TABLE BEHAVIOUR IN DRAINED LANDS

325

three days. Beyond this period there is increasing mismatch between the curves. The observed depth to water table is higher than the predicted values. Overall curve B describes the data better than curve C mainly because in the former variation in the evaporative demand has been accounted for. The integrated Hooghoudt equation without ET term always predicts much higher elevations than the observed ones. Therefore the lowering of the water table was much faster than was predicted by the Bouwer and van Schilfgaarde ( 1963 ) equation. The mismatch between the observed and predicted curves with the proposed equation could be due to many reasons. One of the reasons could be the inappropriate value of C which has been taken as a constant while in practice it increases as the depth to water table increases. In field situations and particularly in the isolated drainage systems as the one from which this data set has been collected, there is the possibility of increased recharge from the adjacent undrained land resulting in relatively slow decline in the water table in the drained land after the initial drawdown. Another reason for the discrepancy could be the fact that the water table never reached the drain level at the boundaries whereas in all calculations it has been assumed to have reached that level. Finally, in spite of our best estimates of the ETo used in these calculations, there may be some differences in actual field conditions. It is however, very clear that with the incorporation of the process of evaporation-ET, the accuracy of the predictions made by the integrated Hooghoudt equation has improved significantly. Equations (10) and (14) could also be used to study ground water table behaviour in the drained lands in the presence of recharge. An additional assumption that recharge is equally spread over the drainage area is made. As the recharge usually would increase with increasing depth to water table, sign of b~ values could be taken as positive such that it simulates this situation. The effect of such a change for a typical example is shown in Fig. 6. It shows that drain spacing would be reduced in the event of recharge to the area. For this specific example, the drain spacing is reduced by 20%. Asymptotic behaviour of the curve beyond drain spacing of 62 m indicates that recharge rate will be more than the drainage rate beyond this drain spacing even before the water table is lowered to 30 cm below the ground surface.

Practical application Recent investigations in India and elsewhere have conclusively established that drain spacing estimated with the existing equations would be inappropriate as long as the actual processes of evaporation and recharge are not accounted for in the design equations (Skaggs, 1975; Gupta, 1985; Rao et al., 1986 ). It has been seen that larger drain spacings would perform equally well in maintaining the salt and water balance as well as crop production. Therefore, in implementing subsurface drainage plans in developing countries where resources are often limited, realistic design equations would be quite useful.

326

P.J. N I K A M E T A L .

14-

/

12

/

I0

~, 8 o

I-

07

/

_,o~f/

G

9J

o,

i

~.~iI

~/ / /

/

D,,T/

,o"/

~o CO, ~ /

(,/ (~< z /~zl

i I

I 0

20

40

60

80

I00

120

140

16o

Drain spacing (m)

Fig. 6. Effect of drain spacing, evaporation, recharge or variability in drainable pore space on time to lower watertable by 30 cm.

The application of the proposed equation in the design of subsurface drainage system at the Mundlana site at low evaporative demand is illustrated in Fig. 6. The design spacing calculated to meet the drainage criterion that water table should be lowered by 30 cm within 2 d if water table reaches the soil surface, shows that drain spacing could be increased from 55 to 60 m. The spacing can be increased by about 9% over and above the design spacing with conventional drainage design equation. At high evaporative demand of 0.8 c m / d and with b= 0.005, calculated drain spacing for the same site is 65 m. Rao et al. (1986) reported that for this site, a drain spacing of 84 m performed equally well when performance of three drain spacings i.e. 50, 67 and 84 m were compared. These results suggest that although some other factors are possibly affecting drainage design, a significant improvement could be brought about allowing for the contribution of the evaporative demand during the most critical periods. In terms of money such an increase in drain spacing would reduce the cost of the drainage system by 16 percent. REFERENCES Averianov, S., 1956. Seepage from irrigation canals and its influence on regime of ground water table. In: Influence of Irrigation Systems on Regime of Ground Water. Academic Press USSR, 140-151.

WATER TABLE BEHAVIOUR IN DRAINED LANDS

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Bouwer, H. and van Schilfgaarde, J., 1963. Simplified method of predicting fall of water table in drained lands. Trans. ASAE, 6: 288-296. Dumm, L.D., 1960. Validity of use of transient flow concept in subsurface drainage. Trans. ASAE, 3: 142-146. Durnford, D.S., Gutwein, B.J. and Podmore, T.H., 1987. Computerized drainage design for arid, irrigated areas. In: Drainage Design and Management. Proc. 5th Nat. Drainage Symp. ASAE, Chicago, 45-52. Gardner, W.R. and Fireman, M., 1958. Laboratory studies of evaporation from soil columns in the presence of water table. Soil Sci., 85: 244-249. Gates, T.K. and Grismer, M.E., 1987. Optimal management of perched saline aquifers in irrigated regions. Calif. Agric., 41 (3-4) 20-21 ). Grismer, M.E. and Gates, T.K., 1988. Estimating saline water table contribution to crop water use. Calif. Agric., 42: 23-24. Gupta, S.K. and Singh, S.R., 1980. Analytical solution for predicting solute movement and their interpretation in recamation. J. Hyd., 45:341-349. Gupta, S.K., 1985. Subsurface drainage for waterlogged saline soils. Irrig. Power J., 42: 335342. Hobbs, E.H., 1981. Improving farm irrigation management by incorporating water table effects into scheduling programs. 1 lth Congr. Irrig. and Drainage, Grenoble, Vol. II: 491-499. Pandey, R.S., 1989. Prediction of water table and salinization with variable drainable porosity and evaporation under subsurface drainage. Ph.D. Thesis. Indian Agric. Res. Institute, New Delhi, pp. 185. Rao, K.V.G.K., Singh, O.P., Gupta, R.K., Kamra, S.K., Pandey, R.S., Kumbhare, P.S. and Abrol, I.P., 1986. Drainage investigations for salinity control in Haryana. Central Soil Salinity Research Institute, Karnal. Bull. No. 10: 95. Ribbens, E.W. and Shaffer, M.J., 1976. Irrigation return flow modelling for the Souris Loop. In: Environmental Impact of Irrigation and Drainage. Spec. Conf. ASCE Irrig. Drain. Div., 545557. Sharma, D.R. and Prihar, S.S., 1973. Effect of depth and salinity of groundwater on evaporation and soil salinization. Ind. J. Agric. Sci., 43: 582-586. Singh, M., Shukla, K.N. and Chauhan, H.S., 1976. Wind tunnel studies on evaporation from soil surface at varying wind velocities and water table depths. J. Agric. Eng., 13:119-123. Skaggs, R.W., 1975. Drawdown solutions for simultaneous drainage and evapotranspiration. J. Irrig. Drain., ASCE, 101: 279-291. Skaggs, E.W., 1976. Determination of the hydraulic conductivity drainable porosity ratio from water table measurements. Trans. ASAE, 19: 73-80, 84. Skaggs, R.W. and Gilliam, J.W., 1986. Modelling subsurface drainage and water management systems to alleviate potential water quality problems. In: A. Glorgini and F. Zingales (Editors), Agricultural Non-point Source Pollution: Model Selection and Application. Elsevier, New York, 295-318. APPENDIX A

Bouwer and van Schilfgaarde approach: a powerful tool for developing drainage design equations The Bouwer and van Schilfgaarde approach is an approach for developing transient state drainage design equations with the help of steady state equations. Although any steady state design equation could be used in this ap-

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proach, the Hooghoudt equation is more commonly used as has been done in this paper as well. With Ea=O a n d f ( h ) = f i n eq. (6) and utilizing various approximations of the second term in the numerator of eq. (7), many alternative equations can be derived. For example Pandey ( 1989 ) suggested that an identical equation to Bouwer and van Schilfgaarde ( 1963 ) equation could be obtained provided h 2 in this term is replaced by the geometric mean of the initial and final hydraulic heads such that h 2= hoht. A few more approximations are given as follows. If the second term is omitted which would be possible if de >> ho, and K~ =K2 =K, then with the help ofeq. (6)

S ~__

8Kdet Cfln ( ho/ h, )

(A. 1 )

It may be noted that this equation is similar to that of Luthin and Worstell and differs only by a constant that can be adjusted with C. Moreover, in case the notional time as calculated for making Fig. 4 in this paper is added to eq. (A. I ) then it is also identical to the Glover and D u m m ( D u m m , 1960) equation. The value of C could be selected in a manner that the constant of the Glover and D u m m equation can be obtained in eq. (A. 1 ) as well. With the approximation h 2 = hoh in the second term of the Hooghoudt equation, another equation could be derived as follows $ 2 _ 8K(de + h o / 2 ) t Cfln(ho/h,

(A.2)

It is an improved version ofeq. (A. 1 ) as the correction for the flow from the layer above the drains has been added. With addition of notional time as before it is also the corrected version of the Glover and D u m m equation. These derivations strengthen the case for the use of this approach in deriving more general equations to account for ET, recharge or variability in the drainable pore space each as a function of the hydraulic head.