A water management model for shallow water table soils

200  Download (1)

Full text

(1)

A WATER MANAGEMENT MODEL FOR SHALLOW WATER TABLE SOILS

R . N. Skaggs

Department of Biological and Agricultural Engineering North Carolina Agricultural Research Service

School of Agriculture and Life Sciences North Carolina S t a t e University

The work on which t h i s publication i s based was supported in part by funds provided by the Office of Uater Research and Technology, U . S . Department of the I n t e r i o r , through The University of,North Carolina .Water Resources Research I n s t i t u t e , as authorized under the Water

Resources Research Act of 1964, as amended. Additional support was provided by the North Carolina Agricultural Research Service.

Project No. A-086- NC Agreement No. 14-34-0001-7070

(2)

i i

ABSTRACT

A WATER MANAGEMENT MODEL

FOR SHALLOW

WATER

TABLE SOILS

by R . W. Skaggs

A study was conducted t o develop and t e s t

a

water management model, Q!?AINMOD, f o r shallow water t a b l e s o i l s , The o b j e c t i v e was t o develop a model f o r s o i l s t h a t norn~ally require a r t j f i e i a l drainage, e i t h e r surface or subsurface, f o r e f f i c i e n t crop production. The model has the capabi I 'Ity of simul atiny on a day- to-day, hour-by-hour bds i s

the water t a b l e position, soil water content, d r a ~ n a g e , ET and surface runoff in terms of climatological data, spi 1 properties, c r o p parameters, and the water managenlent system design. By simulating the performance of a l t e r n a t i v e system designs over several years of record, an optimum water management system ca'n be designed.

The basis of the rr~odel i s a s o i l water balance i n t h t t s u f l p r o f i l e . I t i s composed of a number of separate components, incorporated a s sub- routines t o evaluate various ,

.

mechanisms of water movement and storage

in the s o i i p r o f i l e . These components include methods

- .

t o evdluate i n - f i l t r a t i o n , subsurface drainige, surface drainage, po tentidl evapotrans- piration (ETY, actual ET, subi rrigation and s o i l - w a t e r d.i scr'bution. Approximate methods were used f o r each component so t h a t t h e required

inputs would be simplified and consistant w"ith-available data. The model was constructed so t h a t improved methods can e a s i l y be substituted f o r existing companents as they become available.

The model i s given i n fu1 l in an Appendix t o the iroepor*te Documen- tation includes a program 1 is t i n g with d e f i n i t i o n o f terms, a descri p- tion of each subroutine and examples of input data and computer output. Suggestions,for Smproving various components of the model ape given in the Recommendations section.

(3)

iii

water t a b l e depths were recorded c o n t i n u o u s l y on each s i t e and t h e observed water t a b l e e l e v a t i o n s were compared t o p r e d i c t e d day end values f o r t h e d u r a t i o n o f t h e experiments. Soi 1 p r o p e r t y i n p u t data were measured f o r each s i t e u s i n g f i e l d and l a b o r a t o r y procedures.

S o i l p r o p e r t y data f o r f i v e a d d i t i o n a l s o i l s were a l s o o b t a i n e d and a r e p r e d i c t e d i n t h e r e p o r t .

Comparison o f p r e d i c t e d and measured w a t e r tab1 e e l e v a t i o n s were i n e x c e l l e n t agreement w i t h standard e r r o r s o f e s t i m a t e o f t h e d a i l y water t a b l e depths r a n g i n g from 7.5 t o 19.6,cm. The average d e v i a t i o n s between p r e d i c t e d and observed water t a b l e depths f o r 21 p l o t years o f data ( a p p r o x i m a t e l y 7400 p a i r s o f d a i l y p r e d i c t e d and measured values were compared) was 8.1 cm.

(4)

TABLE OF CONTENTS

Page ABSThC

-:

...

i i TABLE OF COrlTEPITS

...

i v LIST OF FIGURES

...

v i i

f l "

...

LIST OF TrruLES ' x i i

...

SUMMARY AND CONCLUSIONS x i

v

RECOMMENDATIONS

...*...

xvi ACKNOWLEDGEMENTS

...

xxi

...

.

CHAPTER 1 INTRODUCTION 1

...

.

CHAPTER 2 THE MODEL 3

...

Background 3

...

Model Development 4

Model Components

...

6 P r e c i p i t a t i o n

...

6 I n f i l t r a t i o n

...

8

S u r f a c e Drainage

...

1 4

...

S u b s u r f a c e Drainage

...

,. 1 5 S u b f r r i g a t i o n

...

21

...

E v a p o t r a n s p i r a t i o n 21

...

S o i l Nater D i s t r i b u t i o n 29

...

Rooting Depth 36

...

CHAPTER 3

.

WATER MANAGEMENT SYSTEM OBJECTIVES 41

Working Days

...

42

...

SEW 43

Dry Days

...

44

...

Wastewater I r r i g a t i o n Volume 45

CHAPTER 4

.

SIMULATION OF WATER MANAGEMENT SYSTEfllS

.

PROCEDURES

..

46 Example

.

A Combination'Surface

.

S u b s u r f a c e Drainage System

..

46

...

I n p u t Data 46

...

S o i l P r o p e r t y Data 46

Crop I n p u t Data

...

47 Drainage System I n p u t Parameters

...

47

...

C l i m a t o l o g i c a l I n p u t Data 47

...

Other I n p u t Data 49

...

(5)

Page

.

CHAPTER 5 FIELD TESTING OF THE MODEL

...

53

<

Experimental Procedure

...

Field S i t e s

...

Aurora

...

Plymouth

...

...

...

Laurinburg ,...

...

Kinston

...

Field Measurements

...

Soil Property Measurements

...

Results

-

Soil Properties

...

Hydraulic Conductivity

...

Soil Water Characteristics and Drainage Volume

-

Water

Table Depth Relationships

...

I n f i l t r a t i o n Parameters

..

...*...

Upward Water Movement..

...

T r a f f i c a b i l i t y Parameters

...

Root Depths

. . . o . . . e . .

Cl imatological Data

...

..,.

...

Water Level in Drainage Outlet

...

Measured Versus Predicted Water Table Elevations

...

.

Plymouth

Aurora

...

Laurinburg

...

.

.

...

CHAPTER 6 APPLICATZON OF DRAINMOD EXAMPLES 88

Example 1

.

Combination Surface

.

Subsurface Drainage Systems

.

...

Drainage System Design

Soil Properties, Crop and Other Input Data

...

Results

-

Alternative Drainage System Designs

...

Example 2

-

Subirrigation and Controlled Drainage

...

...

Results

-

Subirrigation and Controlled Drainage

Example 3

-

I r r i g a t i o n of Wastewater on Drained Lands

...

...

Results

-

I r r i g a t i o n of Wastewater

Example 4

-

Effect of Root Depth an the Number and Frequency

...

of Dry Days

...

REFERENCES 109

APPENDIXES

...

116

..

...

....

APPENDIX IJRAIMMOD

-

COMPUTER PROGRAPI ROCUCIENTATIO!1

.'

111

...

Program Segments and Their .Functions 113

....

(6)

Page

S u b r o u t i n e ROOT

...

120

S u b r o u t i n e SURIRR

...

120

S u b r o u t i n e WET

...

120

S u b r o u t i n e EVAP

...

120

S u b r o u t i n e SOAK

...

120

S u b r o u t i n e DRAINS

...

121

S u b r o u t i n e ETFLUX

...

..

...

121

S u b r o u t i n e YDITCM . . . , . . . e . u a . . . 121

...

S u b r o u t i n e WORK 123 Su b r o u t i ne ORDER

...

124

...

S u b r o u t i n e RANK 124 Program L i s t i n g

...

125

I n p u t Data

...

155

S i m u l a t i o n R e s u l t s

-

Examples o f Program Output

...

155

APPENDIX B

.

SOIL PROFILE DESCRIPTIONS

...

165

APPENDIX C

.

ROOTING DEPTHS FOR EXPERIMENTAL SITES

...

168

(7)

LIST OF FIGURES

Page Figure 1 . Schematic of water management system with sub-

surface drains t h a t may be used f o r drainage o r

s u b i r r i g a t i o n . .

....

..

...

3 Figure 2. Schematic of water management system with drainage

t o d i t c h e s o r drain tubes. Components evaluated i n

t h e water balance a r e shown on t h e diagram

...

5 Figure 3. An abbreviated general flow c h a r t f o r DRAINMOD..

...

7 Figure 4, I n f i l t r a t i o n r a t e versus time f o r a sandy loam s o i l

i n i t i a l l y drained t o equilibrium t o a water t a b l e 1.0

m

deep. Note t h a t t h e i n f i l t r a t i o n - t i m e r e l a t i o n - ships a r e dependent on t h e r a i n f a l l r a t e . .

...

12 Figure

5.

I n f i l t r a t i o n r a t e

-

cumulative i n f i l t r a t i o n r d l a t i o n -

ships a s a f f e c t e d by r a i n f a l l r a t e f o r t h e same con-

...

d i t i o n s a s Figure 4 . . , . ,

...

...

12 Figure 6. I n f i l t r a t i o n r e l a t i o n s h i p s f o r t h e sandy loam s o i l of

Figure 4 i n i t i a l l y drained t o equilibrium a t various

...

water t a b l e depths..

...

.

.

.

...

....

13 Figure 7. Schematic of water t a b l e drawdown t o and subirrigation

from p a r a l l e l d r a i n tubes..

...

.

.

...

16 Figure 8. Water t a b l e position and hydraulic head,

H,

d i s t r i b u -

t i o n i n a Panoche s o i l a f t e r 20 hours of drainage t o ( a ) conventional 114 mm (4-inch) d r a i n tubes; ( b ) wide open (no w a l l s ) 114 mm diameter drain tubes; ( c ) a drain tube in

a

square envelope 0.5

m

x 0.5

m;

and (d) an open d i t c h 0 . 5 m wide. The d r a i n spacings in a l l

cases were 20

m.

(After Skaggs and Tang, 1978).

...

18 Figure 9. Equivalent l a t e r a l hydraul i c conductivity i s d e t e r -

mined f o r s o i l p r o f i l e s with up t o 5 l a y e r s

...

20 Figure 10. Schematic f o r upward water movement from a water

t a b l e due t o evaporation,.

...

26 Figure 51. Relationship between maximum r a t e of upward water

movement versus water t a b l e depth below t h e r o o t zone

(8)

v i i i

Page Figure 1 2 . P r e s s u r e head d i s t r i b u t i o n w i t h depth a t midpoint,

q u a r t e r p o i n t and n e x t t o t h e d r a i n f o r v a r i o u s times a f t e r d r a i n a g e begins f o r a Panoche loam s o i l ( a f t e r

Skaggs and Panc, 1976).

...

30 Figure 13. S o i l w a t e r c o n t e n t d i s t r i b u t i o n f o r a 0.4 m w a t e r

t a b l e depth. The water t a b l e was i n i t i a l l y a t t h e s u r f a c e and was drawn down by d r a i n a g e and evapora- t i o n , S o l u t i o n s a r e shown f o r t h r e e e v a p o r a t i o n Figure 34. S o i l w a t e r d i s t r i b u t i o n f o r a w a t e r t a b l e depth o f

O , 7

m

f o r v a r i o u s d r a i n a g e and e v a p o r a t i o n r a t e s . .

....

32 Figure 1 5. 'Vol ume o f water 1 eavi ng prof i 1 e (cm3/cm2) by d r a i n a g e

' and e v a p o r a t i o n v e r s u s water t a b l e depth. S o l u t i o n s

...

f o r f i v e e v a p o r a t i o n r a t e s a r e given 34 Figure 16. Schematic of s o i l water d i s t r i b u t i o n when a d r y zone

...*..

...

i s c r e a t e d n e a r t h e s u r f a c e

..,...

35 Figure 17.5 R e l a t i o n s h i p s f o r depth above which 50, 60, 70, and .

".80 p e r c e n t o f the t o t a l r o o t l e n g t h e x i s t s v e r s u s

' time a f t e r p l a n t i n g f o r c o r n . From d a t a given by

...

Mengel and Barber (1974). 38

Figure 18. Root d e p t h s and t o t a l d r y r o o t weight v e r s u s times a f t e r p l a n t i n g f o r c o r n . From d a t a given by Foth

...

. (1 962). 39

Figure 19. Schematic o f experimental s e t u p on the H. C a r r o l l

...

Austin Farm, Aurora, N.C..

....

...

57

F i g u r e . 2 0 . A water l e v e l c o n t r o l s t r u c t u r e i n the o u t l e t d i t c h a t the Tidewater Research S t a t i o n p e r m i t t e d c o n t r o l -

l e d d r a i n a g e and s u b i r r i g a t i o n on t h e Cape F e a r s o i l . . 57

Figure 21

.'

A s t a n d a r d e v a p o r a t i o n pan was modified t o r e c o r d pan e v a p o r a t i o n d i r e c t l y . A r e s e r v o i r was s e t up t o supply w a t e r t o t h e pan through a f l o a t v a l v e a s e v a p o r a t i o n took p l a c e . By r e c o r d i n g t h e w a t e r l e v e l i n t h e r e s e r v o i r , e v a p o r a t i o n could be determined a s

a f u n c t i o n o f time

...

61 Figure 22. Runoff from 3 m X 4 m p l o t s was recorded w i t h a t i p -

...

(9)

Page Figure 23. Drainage volume o r a l r volume (cm3/cm2) as a func-

tion of water table depth f o r s o i l s considered in

t h i s study

...

67 Figure 24. Green-Ampt parameters A and B versus water t a b l e depth

f o r the Lumbee sandy loam s o i l on the Aurora s i t e

...

68 Figure 25. Effect of water t a b l e depth on steady upward flux from

the water table

...

69 Figure 26. Observed and predicted water tab1 e elevations midway

between drains spaced 85

m

apart on the Plymouth s i t e

...

...

during 1973,.

..

74

Figure 27. Observed and predicted water table elevations midway between drains spaced 85 m apart on the Plymouth s i t e during 1974..,

...

74 Figure 28, Observed and predicted water t a b l e el evations midway

between drains spaced 85 m a p a r t on the Plymouth s i t e during 1975,.

...

....

...

.

.

...

75 Figure 29. Observed and predicted water t a b l e eTevations midway

between drains spaced 85

m

apart on the Plymouth s i t e during 1976..

...

,.

..

,.

...

75

Figure 30. Observed and predicted water t a b l e elevations midway between drains spaced 85

m

apart on the Plymouth s i t e d u r i n g 9977

...

76 Figure 31. Observed and predicted water t a b l e elevations midway

between drains spaced 7.5

m

a p a r t on the Aurora s i t e

during 1973

...

77 Figure 32. Observed and predicted water t a b l e elevations midway

between drains kpaced 7,5 m a p a r t on the Aurora s i t e during 1974

...

77 Figure 33. Observed and predicted water t a b l e elevations midway

between drains spaced 7.5

m

apart on the Aurora s i t e

during 1975..

...

78 Figure 34. Observed and predicted water t a b l e elevations midway

between drains spaced 7.5

m

apart on the Aurora s i t e

(10)

X

Page Figure 35. Observed and predicted water tab1 e elevations midway

between drains spaced 7.5

m

a p a r t on the Aurora s i t e

. during 1 9 7 7 . . . , , ,

...

79

Figure 36, Observed and predicted water tab9 e elevations midway between drains spaced 9 5

m

apart on the Aurora s i t e

during 1973

...

79 Figure 37. Observed and predicted water table elevations midway

between d r a i n s spaced 15

m

apart on the Aurora s i t e

during 9974

...

80 Figure 38. Observed and predicted water table elevations midway

between drains spaced 15 m apart on the Aurora s i t e

during $975,

...

80 Figure 39,: Observed and predicted water t a b l e elevations rnfdway

between drains spaced 75

m

a p a r t on the Aurora s i t e

during 1976

...

81 Figure 40,. Observed and predicted water t a b l e elevations midway

between drains spaced 15 rn a p a r t on the Aurora s i t e

during 1977

...

81 Figure 49, Observed and predicted water table elevations midway

between drains spaced 30

m

apart on the Aurora s i t e ,

9973

. . , . . . ~ . . . s 0 2 . . . : . . .

82 Figure 42. Observed and predicted water table elevations midway

between drains spaced 30

m

a p a r t on the Aurora s i t e ,

...

1974.. 82

Figure 43. Observed and predicted water table elevations midway ; between drains spaced 30

rn

apart on the Aurora s i t e

during 7975

...

83 Figure 44. Observed and predicted water tab1 e elevations midway

between drains spaced 30

m

a p a r t on the Aurora s i t e ,

...

1976 83

Figure 45. Observed and predicted water t a b l e elevations midway between drains spaced 30 rn apart on the Aurora s i t e ,

...

1977 84

ure 46, Observed and predicted water table elevations midway between drains spaced 48 m apart on the Laurinburg

...

(11)

Figure 47.

Figure 48.

Figure 49.

Figure 50.

Figure 51.

Figure 52.

Figure 53.

Figure 54.

Figure 55.

Figure 56. Figure A.1,

x i

Page Working days during t h e period March 15

-

April 15

a s a f u n c t i o n of d r a i n spacing f o r t h e Bladen and

Wagram s o i 1 s . .

...

91 SEW30 a s a f u n c t i o n of d r a i n spacing f o r t h r e e s u r f a c e drainage t r e a t m e n t s on Bladen and Wagram s o i 1 s . .

...

92 Dry days during t h e growing season a s a f u n c t i o n of

d r a i n spacing f o r t h r e e water management methods on

Wagram s o i l . .

...

94 SEWT0 a s a f u n c t i o n of d r a i n spacing f o r conventional d r a ~ n a g e , s u b i r r i g a t i o n and c o n t r o l l e d drainage on Wagram s o i l . Results a r e p l o t t e d f o r two l e v e l s of

...

s u r f a c e d r a i n a g e 96

Dry days during t h e growing season f o r t h r e e water

management methods on Bladen s o i l . .

...

98 SEW30 a s a f u n c t i o n of d r a i n spacing f o r conventional d r a i nage, s u b i r r i g a t i on and c o n t r o l 1 ed drainage on Bladen s o i l . Resul t s a r e p l o t t e d f o r two l e v e l s of

s u r f a c e drainage

...

99 E f f e c t s of d r a i n spacing and i r r i g a t i o n frequency on

annual i r r i g a t i o n f o r i r r i g a t i o n scheduled once per

...

week, 25 mm per i r r i g a t i o n 102

E f f e c t of d r a i n spacing and i r r i g a t i o n frequency on

t o t a l annual i r r i g a t i o n f o r a Wagram loamy s o i l . .

...

104 E f f e c t of d r a i n s p a c i n g , s u r f a c e drainage and i r r i -

g a t i o n frequency on s t o r a g e volume required f o r a p p l i c a t i o n o f an average of 25 mm/week on a Wagram

loamy sand

...

106 E f f e c t of maximum r o o t depth on number of d r y days,

2 and 5 y e a r recurrence i n t e r v a l s

...

108 Schematic of drainage d i t c h with water t a b l e control

(12)

LIST OF TABLES

Table 1 . Table 2. Table 3. Table 4.

Table 5.

Table 6.

Table 7 .

Table 8. Table 9.

Page

....

Summary of PET prediction methods f o r humid regions 23 Summary of s o i l property and crop r e l a t e d input data

...

f o r Wagram loamy sand 48

...

Summary of drainage system input parameters 49 Inputs f o r c a l l i n g cl imatological data from HISARS

...

and ET c a l c u l a t i o n s 49

An example of computer output f o r d a i l y summaries

-

Wagram s o i l , J u l y , 1959. A11 values given in cm..

...

51 An example of computer output f o r monthly summaries

-

Wagram s o i l , 1959....,.,...,.ee.eaBe... 52 Example of computer output of y e a r l y summaries and

ranking of o b j e c t i v e functions

-

work days, SEW30,

...

dry days and y e a r l y i r r i g a t i o n , . 52 Drainage system parameters f o r t h e experimental s i t e s

. .

54 Crops grown on research s i t e s ; planting and harvesting

d a t e ~ ~ . . . ~ ~ ~ ~ ~ ~ ~ . . . ~ ~ ~ ~ . . . 55 Tab1 e 1 0. Summary of average hydraul i c conduc t i vi t y val ues from

...

...

auger hole and drawdown measurements..

...

...

63 Table 11. Summary s f K values of p r o f i l e l a y e r s used a s i n p u t

...

t o DRAINMOD.. 64

Table 12. Drainage branch pf t h e s o i l water c h a r a c t e r i s t i c s f o r t h e s o i l s considered i n t h i s study. Values given in

t a b l e a r e volumetric water contents...,... 66

Tab1 e 13. Estimates of c o e f f i c i e n t s f o r t h e Green-Ampt i n f i l t r a - t i o n equation a s a function of i n i t i a l equivalent

water t a b l e depth ,.,...........ae.ea.m..s........... 70

Table 54. T r a f f i c a b i l i t y parameters f o r plowing and seedbed

...

preparation 71

Table 75. A summary of standard e r r o r s of estimate (cq) and average devi a t 1 ons (cm) f o r comparison of observed

....

(13)

Page Table 17. I r r i g a t i o n parameter values used i n Example 3..

...

101 Table Al. Example input data f o r DRAINMOD

...

157 Table A2. Example simulation output f o r a r e l a t i v e l y dry year.

Daily summaries, Wagram s o i l , no i r r i g a t i o n . All

values given i n cm

...

161 Table A3, Example of monthly summary output f o r a r e l a t i v e l y dry

y e a r , Wagram s o i l ,

no

i r r i g a t i o n , .

...

..

162 Tab1 e A4. An example of ~ u t p u t f o r d a i l y summaries when waste

water a p p l i c a t i o n i s scheduled a t 2.5 cm, once per week. Note t h e l a s t column i s amount of waste water applied. Under d r i e r conditions 2.5 cm of water would have been applied on days 1 and 8, b u t t h e s e a p p l i c a t i o n s were skipped because of i n s u f f i c i e n t drained vo1 ume (TVOL)

a t t h e scheduled time of a p p l i c a t i o n . .

...

163 Table A5. An example o f output f o r monthly summaries when waste

water a p p l i c a t i o n i s scheduled a t 2.5 cm, once per

week on a Wagram loamy s a n d , ,

...

164 Table.A6. An example of y e a r l y summaries and ranking f o r 20

years of simulation f o r waste water a p p l i c a t i o n of

2,5 cm, once per week on a Wagram loamy sand..

...

164 Table C1. Rooting depths f o r experimental s i t e s a t Aurora and

...

Plymouth, N . G . , . . a . a a . . .

....

168

Table Dl Daily r a i n f a l l in Table D2. Daily r a i n f a l l i n Table D3. Daily r a i n f a l l i n

Table 04. Drain o u t l e t water

nehes a t the Plymouth s i t e

...

170 nches a t t h e Aurora s i t e .

...

172 nches a t t h e Laurinburg s i t e . ,

...

175 level e l e v a t i o n s (above datum) a t

t h e Plymouth s i t e . , . . . e e . e . . 175

Table D5. Drain o u t l e t water level elevations (above datum) a t

...

(14)

SUMMARY AND CONCLUSIONS

This report describes the development and t e s t i n g of a computer simulation model t o characterize the operation of drainage and water table control systems on shallow water t a b l e s o i l s . The model, DRAINMOD, was developed f o r design and evaluation of multicornponent water manage- ment systems which may i n d u d e f a c i l i t i e s f o r subsurface drainage, sur- face drainage, subirrigation or control led drainage and i r r i g a t i o n of wastewaters onto land, The model i s based on a water balance in the so31 prof-ile, I t uses e~lma%o%ogica% data t o predict, on a day-to-day, houv-by-hour basls, the response o f the water t a b l e and the soil water regime above i t , t o various combinations s f surface and subsurface water

ment. By simulating the performance of a l t e r n a t i v e systems over several years of record an optimum water management system can be de- signed on a probabilistic basis, DRAINMOD i s composed of a number of separate components, lneorporated as subroutines, t o evaluate the var- ious mechanisms of water movement and storage i n the s o i l p r o f i l e .

se components i n i t ude methods t o evaluate i n f i l t r a t i o n , subsurface drainage, surface drainage, potential evapotranspiration

(ET)

,

actual

ET, subirrigatfon and the soil ~ a t e r d i s t r i b u t i o n . In order t o simplify

t h e required inputs and t o make them consistent with available data, approximate methods were used f o r each component. The model was con- structed so t h a t -improved methods can be e a s i l y substituted f o r e x i s t - ing components as they become available,

The v a l i d i t y of DRAENMOD was tested using data from three experi- mental s f t e s collected ovep a f i v e year duration, Each s i t e involved

f j e l d scale drainage systems with provisions f o r subirrigation and con- l l e d drainage, The experiments included f i v e d i f f e r e n t treatments and provided a t o t a l of 2 % p l o t years of data, Rainfal I and water t a b l e elevations were measured contsnuously on each s i t e and the observed water

I e elevations were compared t o predicted daily values f o r the dura- t i o n o f the experiments. Numerous other f i e l d and laboratory measure- ments were made on each s o i l t o determine input s o i l property data.

(15)

Comparison of predicted and measured water t a b l e elevations were in excellent agreement with standard e r r o r of estimates of the daily water table depths ranging from 7 . 5 to 19.6 cm. The average deviations between predicted and observed water table depths f o r 21 plot years of data (approximately 7400 pairs of daily predicted and measured values) was 8.1 cm.

Appl ication of the model was demonstrated with four exampl es

.

The f i r s t example consisted of an evaluation of a1 ternative designs f o r combination surface-subsurface drainage systems f o r two s o i l s . The use of controlled drainage and subirrigation was considered in the second example. DRAINMOD can also be used t o determine hydraulic loading capa- c i t i e s f o r systems f o r land application of waste water, and an example was given t o demonstrate t h i s use of the model. Finally, an example was given t o show how DRAINMOD can be used t o determine the e f f e c t s of root- ing depth limitations on the number of days and the frequency t h a t a crop suffers from drought s t r e s s .

The computer program i s documented in Appendix A of the report. This Appendix includes a program l i s t i n g with definition of terms, a description of each subroutine and examples of input data and computer o u t p u t .

(16)

xvi RECOMMENDATIONS

Recommendations resulting fvom t h i s project f a l l i n t o two cate- gories: recommendations f o r the -implementation of the model

t o

the design and evaluation of water management systems; and recommendations f o r f u r t h e r research t o improve components of the model and t o t e s t i t s re1 iabi 4 i t y for d i f f e r e n t water management systems and under di f

-

f e r e n t cl imatological and sol 1 conditions

.

Implementatlon of the model f i r s t requires t h a t i t be transmitted t o the users complete with documentation and input data needed f o r i t s appl ication. The model has been described to potential users through professional meetings, work shops and journal a r t i c l e s . This report will provide the needed documentation. A major need in t h i s area i s in- tensive use of the model in practice. This would involve production scale use of DRAINMOD i n the design and evaluation of drainage and water table control systems. T h i s i s envisioned as a research-extension

a c t i v i t y i n which extension personnel would work with the land owner, and agenc%es such a s the Soil Conservation Service t o gather the needed i n p u t data, and make a l t e r n a t i v e designs f o r the water management system. The performance s f proposed designs would be simul a t & using DRAINMOD and modifications made t o obtain the optimum system f o r a given s e t of design requirements. Experience gained in t h i s application would allow rapfd improvement of the model and streamlining of the procedures f o r obtaining i n p u t data. I t would also provide a data base t h a t would be applicable f o r the same and similar s o i l types i n other locations,

Another need i n t h i s same general category i s f o r design charts such as those given i n Flgures 47-52 f o r a range of s o i l s and locations. While these charts cannot be used d i r e c t l y , except on the s o i l f o r which they were derived, they could provide a basis f o r a rough a r f i r s t - c u t design. En eases where s p e c i f i c input data a r e not available such appro- ximations may be b e t t e r than present a l t e r n a t i v e s .

A t the end of nearly every research project there a r e recommenda- tions f o r continued research in the subject matter t o f u r t h e r t e s t the r e s u l t s o r t o refine methods developed 9'n the research. This project i s

(17)

xvi i

accuracy of the model and efficiency of i t s use can be improved by f u r t h e r research and development, Perhaps the most obvious need i s f o r f u r t h e r t e s t i n g under d i f f e r e n t s o i l and climatological conditions. Tests a r e underway using more t h a n 10 years of data collected near Sandusky, Ohio

(Schwab, e t al

.

,

1973, 1975)- Preliminary r e s u l t s look good f o r the t i g h t s o i l s of t h i s location. Plans a r e now being made t o also t e s t the model using the data from other locations in the U.S.

I n f i l t r a t i o n i s predicted in the present version of DRAINMOD with the Greem-Ampt equation using input parameters t h a t are selected as a function of the i n i t i a l water t a b l e depth. While t h i s equation has been found t o be s u f f i c i e n t l y f l e x i b l e f o r most f i e l d conditions, there i s no doubt t h a t the equation parameters depend

on

the stage of surface cover and t i l l a g e , both of which a f f e c t the condition of the surface. The e f f e c t of crusting due t o r a i n f a l l impact an an unprotected or p a r t i a l l y protected surface as well as breaking u p of c r u s t s due t o cultivation could be con- sidered in the model and reflected in the Green-Ampt equation parameters. Here again the determination of input data t o characterize a l l of the d i f - f e r e n t combinations of i n i t i a l conditions will pose a problem i n practical application, b u t t h i s can possibly be overcome with some we11 directed research. Presently, i n f i l t r a t i o n i s calculated based on r a i n f a l l r a t e s assumed to be constant f o r one-hour i n t e r v a l s . Actually r a i n f a l l i s not usually constant b u t may occur in short bursts of high i n t e n s i t y followed by low i n t e n s i t i e s during the hour. I t may be desirable to assume d i f f e r - ent r a i n f a l l rate-time d i s t r i b u t i o n s within each hour in order t o more precisely determine when r a i n f a l l excesses will occur. Additional studies need to be conducted on t h i s subject.

(18)

xvi i i

van Beers (1976) f o r steady s t a t e drainage under r a i n f a l l conditions will accommodate layered s o i l s and correct f o r convergence near the drains d i r e c t l y , These methods need t o be worked into the model and tested t o determine i f t h e i r use will improve the overall performance of DRAINMOD,

Although the saturated hydraulic conductivity i s assumed t o be constant, we know t h a t i t changes with water temperature, primarily as a r e s u l t of viscosity changes. Thus the conductivity i s usually higher durlng the summer months than during the winter. The model could be programed t o cons%der the e f f e c t of s o i l water temperature changes on K and thus on drainage flux. A predictive method could be used to calculate s o ? % temperatures a t a given depth in terms of average a i r temperature and s o i l thermal properties. Maximum and minimum a i r temperatures, which a r e used t o predict ET, may also be used to estimate s o i l temperature changes.

Freezing conditions a r e not currently considered in the model

.

Errors caused by the omission are reflected f o r early spring conditions in t e s t s of DRAINMOD currently being conducted with data from NW Ohio. Frozen s o i l s will have a b i g e f f e c t on both i n f i l t r a t i o n and drainage; more work i s needed on t h i s subject.

In discussing the r e s u l t s from Aurora (Chapter 5) we noted e r r o r s i n the predicted water t a b l e t h a t were caused by a f a i l u r e of DRAINMOD t o conslder the time lag of water table response a t the beginning of the subirrigation process. Methods f o r determining time lag in terms of t h e soi 7 properties, drain spacing, e t c . have been worked out (Skaggs

,

1974)

.

Such methods have not been employed in the model because of the complex- i t y of programing and the r e l a t i v e l y infrequent occurrence of the s i t u a - tion. However, t h i s capability should be added t o the model t o improve f t s accuracy during t r a n s i t i o n periods between drainage and s u b i r r i g a t i o n .

(19)

pletely s a t i s f y ET demands, I t would be more reasonable t o assume ( a f t e r Lagace; 1973) t h a t the a v a i l a b i l i t y of water i s reduced as the s o i l water content decreases. This would involve reducing actual ET based on the s o i l water content a f t e r the water content in the root zone decreases be1 ow some thresh01 d val ue.

Trafficable conditions a r e now based on whether the drained volume ( a i r volume) in the s o i l p r o f i l e i s greater than a given l i m i t , which i s determined from r a t h e r subjective f i e l d measurements. Further work needs t o be done t o define t r a f f i c a b l e conditions in terms of more basic soil properties and t o determine how both the water content and d i s t r i b u t i o n a f f e c t s those properties. Methods developed by Wendt, e t a1

.

(1 976) may be used to strengthen t h i s part of the simulation procedure.

Presently, DRAINMOD determines the t o t a l number of t r a f f i c a b l e days in a given time period. In the actual farm operation, i t may be more important t o know the frequency of t r a f f i c a b l e conditions f o r several days a t a time, and the e f f e c t of the drainage system on t h a t frequency. In order t o consider the t o t a l system i n t h i s regard, i t may be desirable to couple DRAINMBD with a machinery management model t o determine the optimum combination of farm machinery and drainage systems f o r a given s i t u a t i o n .

(20)

A logical extension of the above would be t o couple DRAINMOD with a plant growth model which would also include the capability of predict- ing root growth and development. This would permit the d i r e c t evaluation of the e f f e c t of a water management system q~ crop production without re- sorting t o mechanisms such as SEWsB. With the present stage o f develap- ment of crop models such an extension seems f e a s i b l e and f u r t h e r research

in t h i s direction should be given high p r i o r i t y .

(21)

xxi

ACKNOWLEDGEMENTS

This report i s baseb on research supported in part by funds by the Office of Water Research and Technology, Department of the

I n t e r i o r , through the Water Resources Research I n s t i t u t e of the Univ- e r s j t y of North Carolina and by the North Carolina Agricultural

Research Service. Appreciation i s expressed t o ~ r o f e s i o r D.

H.

Howel 1 s and Drs, J a Stewart afld N, Grigg, Directors of the I n s t i t u t e during the

study, and to Mrs, Linda Kiger; Administrative Manager f o r t h e i r a s s i s - tance during the project.

Several peopl e were involved in both the theoretical devel opment of the model and in data collection and analysis t o t e s t the v a l i d i t y of the model. Drs. S, Ghate, Y , K. Tmg and

5.

G. Wardak, and Mr. H . Chen a s s i s t e d in various stages of the computer programing and data analysis, Mr. Frank dissey and Mr, Ben Lane were the research tech- nicians in charge of day-to-day operation, maintenance and data col- lection phases of the study, Mr. Richard Kohrman also assisted in t h i s a c t i v i t y , I t would have been impossible to successively complete t h i s study without t h e i r willing and able assistance and t h e i r contributions a r e grateful l y acknowledged,

A note of thanks i s a1 so expressed t o Mr. H. Carroll Austin, Aurora, N . C . , f o r his cooperation throughout the experiment and to the McNair Seed Company, Laurinburg, N.C. f o r allowing

us

to monitor water table 'and soil water conditions on t h e i r lands.' This project would n o t have been possible without.use of the land, water and other resources from these cooperators. Thanks are also due t o Mr. Daniel M . Windley,

I I I , SCS technician, Washington, N , C , , f o r his help in conducting the field.experiments, Mr.

'L.

D. Hunnings, engineer with theeSCS and Far,

(22)

x x i i

The a u t h o r i s i n d e b t e d t o h i s colleagues, Dr. J. W . G i l l i a m ,

S o i l Science, and D r . E. H. Wiser, B i o l o g i c a l and A g r i c u l t u r a l Engineer- i n g f o r t h e i r guidance and f r e q u e n t a s s i s t a n c e i n many phases o f t h e study.

Dr. C a r l q s Ravelo used t h e model i n h i s Ph,D. t h e s i s work a t Texas A & M U n i v e r s i t y . During h i s s t u d y he spent some t i m e here a t

NCSU m o d i f y i n g t h e model t o b e t t e r p r e d i c t t h e e f f e c t o f drainage sys- tem design on c r o p y i e l d . The c o n t r i b u t i o n s o f C a r l o s and h i s a d v i s o r s , Drs, E

.

A, H i 1 e r and D. L. Reddell

,

a r e acknowledged.

Thanks a r e a l s o due t o Mrs. Thelma U t l e y , s e c r e t a r y , f o r t y p i n g t h e many r e p o r t s and papers r e q u i r e d i n t h i s p r o j e c t . F i n a l l y , a p p r e c i a t i o n

i s expressed t o t h e f o l l o w i n g s t u d e n t a s s i s t a n t s who helped w i t h v a r i o u s phases o f t h e s t u d y from f i e l d i n s t a l l a t i o n s t o p r e p a r a t i o n o f t h e

(23)

A WATER MANAGEMENT MODEL FOR SHALLOW WATER TABLE SOILS CHAPTER 1

INTRODUCTION

The d e s i g n o f e f f i c i e n t a g r i c u l t u r a l w a t e r management systems i s becoming more and more c r i t i c a l as c o m p e t i t i v e uses f o r o u r w a t e r

r e s o u r c e s i n c r e a s e , and as i n s t a l l a t i o n and o p e r a t i o n a l c o s t s c l i m b . I n humid r e g i o n s , a r t i f i c i a l d r a i n a g e i s necessary t o p e r m i t f a r m i n g o f some o f t h e n a t i o n ' s most p r o d u c t i v e s o i l s . Drainage i s needed t o p r o v i d e t r a f f i c a b l e c o n d i t i o n s f o r seedbed p r e p a r a t i o n and p l a n t i n g i n t h e s p r i n g and t o i n s u r e a s u i t a b l e env.ironment f o r p l a n t g r o w t h d u r i n g t h e g r o w i n g season. A t t h e same t i m e e x c e s s i v e d r a i n a g e i s u n d e s i r a b l e as i t reduces s o i l w a t e r a v a i l a b l e t o growing p l a n t s and leaches f e r t i l i z e r n u t r i e n t s , c a r r y i n g them t o r e c e i v i n g streams where t h e y a c t as p o l l u t a n t s . I n some cases, w a t e r t a b l e c o n t r o l o r s u b i r r i g a t i o n can be used t o m a i n t a i n a r e l a t i v e l y h i g h w a t e r t a b l e d u r i n g t h e growing season t h e r e b y s u p p l y i n g i r r i g a t i o n w a t e r f o r c r o p g r o w t h as we1 1 as p r e v e n t i n g e x c e s s i v e d r a i n a g e .

The d e s i g n and o p e r a t i o n of each component o f a w a t e r manage- ment system s h o u l d be dependent on s o i l p r o p e r t i e s , topography, c l imate, c r o p s grown and t r a f f i c a b i 1 i t y r e q u i r e m e n t s

.

F u r t h e r , t h e d e s i g n of one component s h o u l d depend on t h e o t h e r components. For example, a f i e l d w i t h good s u r f a c e d r a i n a g e w i l l r e q u i r e l e s s i n t e n - s i v e s u b s u r f a c e d r a i n a g e t h a n i t would i f s u r f a c e d r a i n a g e i s p o o r . T h i s has been c l e a r l y demonstrated i n b o t h f i e l d s t u d i e s o f c r o p

response (Schwab,

--

e t a l . , 1974) and by t h e o r e t i c a l methods (Skaggs, 1974). The r e l a t i v e i m p o r t a n c e of w a t e r management components v a r i e s w i t h c l i m a t e , so, i n humid r e g i o n s , a w e l l designed d r a i n a g e system may be c r i t i c a l i n some y e a r s y e t p r o v i d e e s s e n t i a l l y no b e n e f i t s i n

o t h e r s . Thus, methods f o r d e s i g n i n g and e v a l u a t i n g multicomponent w a t e r management systems s h o u l d be c a p a b l e o f i d e n t i f y i n g sequences o f weather c o n d i t i o n s t h a t a r e c r i t i c a l t o c r o p p r o d u c t i o n and o f d e s c r i b i n g t h e performance o f t h e system d u r i n g t h o s e p e r i o d s .

(24)

2

simulation program t h a t characterizes the response of the s o i l water regime t o various combinations of surface and subsurface water manage- ment. I t can be used to predict the response of the water t a b l e and

the soi 1 water above the water tabl e t o r a i nfal I , evapotranspiration ( E T ) , given degrees of surface and subsurface drainage, and the use of water tabl e control o r subi r r i g a t i on practices. Surface i r r i g a t i o n can a l s o be considered and the model has been used t o analyze s i t e s f o r land disposal of waste water. Climatological data a r e used i n

tM

model t o simulate the performance of a given water management system ov&r several years of record. In t h i s way optimum water management can be designed on a p r o b a b i l i s t i c basis as i n i t i a l l y proposed f o r subsurface drainage by van Schi lfgaarde (1965) and subsequently used by Young and Ligon (1 972) and Wiser, e t a1

.

(1 974).

This report begins with a description of each of the model com- ponents. Then r e s u l t s o f f i e l d evperiments to t e s t the v a l i d i t y of the model f o r multi-component water management systems a r e given. Finally,

(25)

3 CHAPTER 2 THE MODEL Background

A schematic o f t h e t y p e o f w a t e r management system c o n s i d e r e d i s g i v e n i n F i g u r e 1. The s o i l i s n e a r l y f l a t and has an impermeable l a y e r a t a r e l a t i v e l y s h a l l o w d e p t h . Subsurface d r a i n a g e i s p r o v i d e d b,y d r a i n tubes o r p a r a l l e l d i t c h e s a t a d i s t a n c e d, above t h e imperme- a b l e l a y e r and spaced a distance, L, a p a r t . When r a i n f a l l o c c u r s , w a t e r i n f i l t r a t e s a t t h e s u r f a c e and p e r c o l a t e s t h r o u g h t h e p r o f i l e r a i s i n g t h e w a t e r t a b l e and i n c r e a s i n g t h e s u b s u r f a c e d r a i n a g e r a t e . I f t h e r a i n f a l l r a t e i s g r e a t e r t h a n t h e c a p a c i t y o f t h e s o i 1 t o i n f i l - t r a t e , w a t e r b e g i n s t~ c o l l e c t on t h e s u r f a c e . When good s u r f a c e d r a i n a g e i s p r o v i d e d so t h a t t h e s u r f a c e i s smooth and on grade, most o f t h e s u r f a c e w a t e r w i l l be a v a i l a b l e f o r r u n o f f . However, i f s u r -

RAINFALL OR E T

I l l l l l l l l l l t t t t t t t t t t t t

DEPRESSION STORAGE ( S

-

-

/

I

(26)

face drainage i s poor, a certain amount of water must be stored in de- pressions before runoff can begin. After r a i n f a l l ceases, i n f i l t r a t i o n continues until the water stored in surface depressions i s i n f i l t r a t e d into the s o i l . Thus, poor surface drainage e f f e c t i v e l y lengthens the i n f i l t r a t i o n event f o r a given storm permitting more water t o i n f i l t r a t e and a larger r i s e in the water table than would occur i f depression storage did not e x i s t .

The r a t e water i s drai-.ed from the p r o f i l e depends on the hydraulic conductivity of the s o i l , the drain depth and spacing, the e f f e c t i v e pro- f i l e depth, and the depth of water in the drains. When the water level i s raised in the drainage ditches, f o r purposes of supplying water t o the root zone of the crop, the drainage r a t e will be reduced and water may move from the drains into the s o i l p r o f i l e giving the shape shown by the broken curve in Figure 1. I t was shown in a previous study

(Skaggs, 1974) t h a t a high water table reduces the amount of storage available f o r i n f i l t r a t i n g r a i n f a l l and may r e s u l t in frequent condi- tions of excessive s o i l water i f the system i s not properly designed and managed. Water may also be removed from the p r o f i l e by ET, and by deep seepage, bath of which must be considered in the calculations i f the soil water regime i s t o be modeled successfully.

Model Development

(27)

be modified when b e t t e r methods are developed.

The basis f o r the computer model i s a water balance f o r the s o i l p r o f i l e (Figure 2 ) . The r a t e s of i n f i l t r a t i o n , drainage, and evapotranspiration, and the d i s t r i b u t i o n of s o i l water in the p r o f i l e can be computed by obtaining numerical solutions to nonlinear d i f - f e r e n t i a l equations (e.g

.

,

Freeze, 1971 )

.

However these methods would require prohibitive amounts of computer time f o r long term simulations and thus could not be used in the model. Instead, approximate methods were used t o characterize the water movement processes. In order t o insure t h a t the approximate methods provided r e l i a b l e estimates, they were compared t o exact methods f o r a range of s o i l s and boundary con- d i t i o n s . Further, the r e l i a b i l i t y of the t o t a l model was tested using f i e l d experiments.

RAINFALL OR IRRIGATION~P)

I

I

DRAIN TUBE

DEEP SEEPAGE (Ds)

(28)

The b a s i c r e l a t i o n s h i p i n t h e model i s a water balance f o r a t h i n s e c t i ~ n o f s o i l o f u n i t s u r f a c e area which extends from t h e imperme- a b l e l a y e r t o t h e s u r f a c e and i s l o c a t e d midway between a d j a c e n t d r a i n s . The w t e r balance f o r a t i m e increment of ~t may be expressed as,

A V ~ = D

+

ET 4 OS

-

F

( 1 )

where AV, i s t h e change i n t h e a i r volume (cm), D i s drainage (cm) fmm ( o r s u b i r r i g a t i o n i n t o ) t h e s e c t i o n , ET i s e v a p o t r a n s p i r a t i o n (cm), DS

i s deep seepage (cm) and F i s i n f i l t r a t i o n (cm) e n t e r i n g t h e s e c t i o n i n

a t ,

The terms on t h e r i g h t - h a n d s i d e o f e q u a t i o n 1 a r e computed i n terms o f t h e water t a b l e e l e v a t i o n , s o i l water content, s o i l p r o p e r t i e s , s i t e and drainage system parameters, c r o p and stage o f growth, and atmospheric c o n d i t i o n s , The amount o f r u n o f f and s t o r a g e on t h e s u r f a c e i s computed from a water balance a t t h e s o i l s u r f a c e f o r each t i m e increment which may be w r i t t e n as,

P = F + A S + R O ( 2 )

where P i s t h e p r e c i p i t a t i o n (cm), F i s i n f i l t r a t i o n (cm), AS i s t h e change i n volume o f water s t o r e d on t h e s u r f a c e (cm), and RO i s r u n o f f (cm) d u r i n g t i m e ~ t , The b a s i c t i m e increment used i n equations 1 and 2 i s 1 hour. However when r a i n f a l l does n o t occur and drainage and ET

r a t e s a r e slaw such t h a t t h e water t a b l e p o s i t i o n moves slowly w l t h time, equation 1 i s based on A t o f 1 day. Conversely, t i m e increments of 0.05 hour o r ' l e s s a r e used t o compute F when r a i n f a l l r a t e s exceed t h e i n f i l - t r a t i o n c a p a c i t y . A general F l o w Chart f o r DRAINMOD i s g i v e n i n F i g u r e

3. Methods used t o e v a l u a t e t h e terms i n equations 1 and 2 and o t h e r model components a r e discussed i n t h e f o l l o w i n g s e c t i o n s .

P r e c i p i t a t i o n

Model Components

P r e c i p i t a t i o n records a r e one o f t h e major i n p u t s o f DRAINMOD.

(29)
(30)

b e t t e r estimates of these model components than will l e s s frequent data. A basic time increment of one hour was selected f o r use in the model because of the a v a i l a b i l i t y of hourly r a i n f a l l

d a t a .

l h l l e data f o r shorter time increments a r e available f o r a few locations, hourly rain- f a l l data a r e readily available f o r many locations in the U.S.

Hourly r a i n f a l l records a r e stored in the computer based HISARS (Wiser, 1972, 1975) f o r several locations in North Carolina and these records a r e automatically accessed as inputs t o the model. Hourly data f o r other locations in the U.S. can be obtained from the National

weather Service a t Ashevi 1 le , N . C . I n f i l t r a t i o n

I n f i l t r a t i o n of water a t the s o i l surface i s a complex process which has been studied extensively during the past two decades. A re- cent review of i nfi 1 t r a t i o n and methods f o r quantifying inf i 1 t r a t i o n rates was presented by Skaggs,

--

e t a l . (1979). Philip (1969), Hilel (1 971 )

,

Morel -Seytoux ( 1 973) and Hadas,

- -

e t a1

.

(1973) have a1 so pre- sented reviews of the i n f i l t r a t i o n processes. I n f i l t r a t i o n i s affected by s o i l f a c t o r s such as hydraulic conductivity, i n i t i a l water content, surface compaction, depth of p r o f i l e , and water table depth; plant factors such as extent of cover and depth of r o o t zone; and r a i n f a l l f a c t o r s such as i n t e n s i t y , duration, and time d i s t r i b u t i o n of r a i n f a l l .

Methods f o r characterizing the i n f i l t r a t i o n process have concentra- ted on the e f f e c t s of s o i l factors and have generally assumed t h e s o i l system t o be a fixed or undeformable matrix with well defined hydraulic conductivity and s o i l water c h a r a c t e r i s t i c functions. Under these assumptions and the additional assumption t h a t there i s negligible resistance t o the movement of displaced a i r , the Richards equation may be taken as the governing relationship f o r the process. For v e r t i c a l water movement, the Richards equation may be written a s ,

(31)

s o i l water c h a r a c t e r i s t i c . The e f f e c t s of r a i n f a l l r a t e and time d i s - t r i b u t i o n , i n i t i a l s o i l water conditions, and water t a b l e depth a r e incorporated as boundary and i n i t i a l conditions in the solution of equation 3.

A1 though the Richards equation provides a rather comprehensive method of determining the e f f e c t s of many i n t e r a c t i v e f a c t o r s on i n f i l - t r a t i o n , input and computational requirements prohibits i t s use in DRAINMOD. The hydraul i c conductivity function required in the Richards equation i s d i f f i c u l t t o measure and i s available in the l i t e r a t u r e f o r only a few s o i l s . Furthermore, equation 3 i s nonl inear and f o r the general case, must be solved by numerical methods requiring time incre- ments in the order of a few seconds. The computer time required by such solutions would c l e a r l y be prohibitive f o r long term simulations cover- ing several years of record. Nevertheless, these solutions can be used t o evaluate approximate methods and, in some cases, t o determine para- meter values required in these methods.

Approximate equations f o r predicting the inf i 1 t r a t i o n have been proposed by Green and Ampt (1 91 1 ), Horton (1 939), Phi 1 i p (1957) and Hol ton,

- -

e t a l . (19671, among others. Of these, the Green-Ampt equation appears t o be the most f l e x i b l e and i s used to characterize the i n f i l - t r a t i o n component in DRAINMOD. The Green-Ampt equation was o r i g i n a l l y derived f o r deep homogeneous prof i1 es with a uniform i n i t i a l water content. The equation may be written as,

f = KS

+

KS Md S f / F (4)

where f i s the i n f i l t r a t i o n r a t e , F i s accumulative i n f i l t r a t i o n , Kg i s the hydraulic conductivity of the transmission zone, Md i s the d i f f e r - ence between f i n a l and i n i t i a l volumetric water contents (Md =

eo

-

e i ) ,

and Sf i s the e f f e c t i v e suction a t the wetting f r o n t . For a given s o i l with a given i n i t i a l water content equation 4 may be written a s ,

f = A/F

+

B ( 5

(32)

In addition t o uniform p r o f i l e s f o r which i t was o r i g i n a l l y de- r i v e d , t h e Green-Ampt equation has been used ~ s t h good r e s u l t s f o r p r o f i l e s t h a t become denser with depth (Childs and Bybordi

,

1 X ? : 1:1d f o r s o i l s w i t h p a r t i a l l y sealed surfaces ( H i l l e l and Gardner, 1970). Bouwer (1969) showed t h a t i t may a l s o be used f o r nonuniform i n i t i a l water contents.

Hein and Larson (1973) used t h e Green-Ampt equation t o p r e d i c t i n f i l t r a t i o n from steady r a i n f a l l . Their r e s u l t s were in good agree- ment w i t h r a t e s obtained from s o l u t i o n s t o the Richards equation f o r a wide v a r i e t y of s o i l types and a p p l i c a t i o n r a t e s . Mein and Larson's r e s u l t s imply t h a t , f o r uniform deep s o i l s with constant i n i t i a l water contents, t h e i n f i l t r a t i o n r a t e may be expressed in terms of cumula- t i v e i n f i l t r a t i o n , F , alone, regarilless of t h e a p p l i c a t i o n r a t e . This i s i m p l i c i t y assumed i n t h e Green-Ampt equation and i n the parametric model proposed by Smith (1972). Reeves and Miller (1 975) extended

t h i s assumption t o t h e case of e r r a t i c r a i n f a l l where t h e unsteady a p p l i c a t i o n r a t e dropped below i n f i l t r a t i o n capacity f o r a period of time followed by a high i n t e n s i t y a p p l i c a t i o n . Their i n v e s t i g a t i o n s showed t h a t t h e i n f i l t r a t i o n capacity could be approximated a s a simple function of F regardless of t h e a p p l i c a t i o n r a t e versus time h i s t o r y . These r e s u l t s a r e extremely important f o r model ing e f f o r t s of t h e type discussed herein. I f t h e i n f i l t r a t i o n r e l a t i o n s h i p i s independent of a p p l i c a t i o n r a t e , the only input parameters required a r e those pertaining t o t h e necessary range of i n i t i a l conditions. On t h e o t h e r hand, a s e t of parameters covering the possible range i b applica- ~ tion r a t e s would be required f o r each i n i t i a l condition i f t h e i n f i l - t r a t i o n r e l a t i o n s h i p depends on appl i c a t i o n r a t e ,

A frequent i n i t i a l condition f o r shallow water t a b l e s o i l s i s an unsaturated p r o f i l e in equi 1 i b r i m w i t h t h e water t a b l e . Solutions f o r t h e i n f i l t r a t i o n r a t e

-

time r e l a t i o n s h i p f o r a p r o f i l e i n i t i a l l y

(33)

on both time and the application r a t e . However, when i n f i l t r a t i o n r a t e t

i s plotted versus cumulative i n f i l t r a t i o n , F =

lo

f d t , (Figure 5) the relationship i s nearly independent of the application r a t e . This i s consistant with Mein and Larson's (1973) r e s u l t s discussed above f o r deep s o i l s with uniform i n i t i a l water contents.

I t should be noted t h a t resistance t o a i r movement was neglected in predicting the i n f i l t r a t i o n relationships given in Figures 4 and 5. Such e f f e c t s can be quite s i g n i f i c a n t f o r shallow water tables where a i r may be entrapped between the water t a b l e and the advancing wetting f r o n t (McWhorter, 1971, 1976). Morel -Seytoux and Khanji (1974) showed t h a t the Green-Ampt equation retained i t s original form when the e f f e c t s of a i r movement were considered f o r deep s o i l s with uniform i n i t i a l water contents. The equation parameters were simply modified to incl ude the e f f e c t s of a i r movement.

I n f i l t r a t i o n relationships f o r a range of water t a b l e depths a r e plotted in Figure 6 f o r the sandy loam considered above. Although these curves were determined from solutions to the Richards equation, similar relationships could have been measured experimentally. The parameters A and B in equation 5 may be determined by using regression methods t o f i t the equation t o the observed i n f i l t r a t i o n data. The r e s u l t a n t parameter values w f 7 1 r e f l e c t the e f f e c t s of a i r movement as well as other f a c t o r s which would have otherwise been neglected. I n f i l -

t r a t i o n predictions based on such measurements will usually be more r e l i a b l e than i f the predictions a r e obtained from basic s o i l property measurements.

The model requires inputs f o r i n f i l t r a t i o n in the form of a t a b l e of A and B versus water t a b l e depth. When r a i n f a l l occurs, A and B

(34)

TIME (mivutes)

Figure

4. Infiltration rate versus time for a sandy loam soil initially

drained to equilibrium to

a

water table

1.0 rn

deep. Note that

the inf

i

1

tration-time re1 ationshi ps are dependent on the

rainfall rate.

I--

- PONDED

Y

R = 4 cmlhr

R 8 l c m l h r

01 I I

I I I I 1

I 2 3 4 5 6 7

CUMULATIVE INFILTRATION (cm)

(35)

INITIAL WATER

TABLE DEPTH

SANDY LOAM

CUMULATIVE INFILTRATION ( c m )

ure 6. I n f i l t r a t i o n relationships f o r the sandy loam s o i l of Figure 4 i n i t i a l l y drained to equilibrium a t various water table depths.

(36)

used f o r as long as the r a i n f a l l event continues. An exception i s when the water t a b l e r i s e s to the surface, a t which point A i s s e t t o A = 0 and B i s s e t equal to the sum of the drainage, ET and deep seep- age r a t e s . An i n f i l t r a t i o n event i s assumed to terminate and new A and

B values obtained f o r succeeding events when no r a i n f a l l or surface water has been available f o r i n f i l t r a t i o n f o r a period of a t l e a s t 2 hours. This time increment was selected a r b i t r a r i l y and can be e a s i l y changed in the program.

Although i t i s assumed in the present version of the model t h a t the A and B matrix i s constant, i t i s possible t o allow i t

t o

vary with time or t o be dependent on events t h a t a f f e c t surface cover, compaction, e t c . Surface Drainage

Surface drainage i s characterized by the average depth of depres- sion storage t h a t must be s a t i s f i e d before runoff can begin. In most cases i t i s assumed t h a t depression storage i s evenly distributed over the f i e l d . Depression storage may be f u r t h e r broken down into a micro component representing storage in small depressions due t o surface s t r u c t u r e and cover, and a macro component which i s due t o larger sur- face depressions and which m y be a1 tered by land forming, grading, e t c . A f i e l d study conducted by Gayle and Skaggs (1978) showed t h a t the micro-storage component varies from about 0.1 cm f o r s o i l surfaces t h a t have been smoothed by weathering (impacting r a i n f a l l and wind) t o several centimeters f o r rough plowed larid. Macro-storage values f o r eastern N . C . f i e l d s varied from nearly 0 f o r f i e l d s t h a t have been land formed and smoothed or t h a t a r e naturally on grade t o > 3 cm f o r f i e l d s with numerous pot holes and depressions or which have inadequate sW- face o u t l e t s . Surface storage could be considered as a time dependent function or t o be dependent on other events such as r a i n f a l l and the

time sequence of t i 1 7age operationsi' TherefoVe, the" va'riation in the micro- storage component during the year can be simulated. However, i t i s

assumed t o be constant in the present version of the model.

(37)

the runoff process. This volume i s referred t o as surface detention storage and depends on the r a t e of runoff, slope, and hydraulic rough- ness of the surface. I t i s neglected in the present version of the model which assumes t h a t runoff moves immediately from the surface to

the o u t l e t . Actually wster t h a t eventually runs off from one section of the f i e l d i s temporarily stored as surface detention and may be i n f i l t r a t e d or stored a t a location downslope as i t moves from the f i e l d . However the flow paths a r e r e l a t i v e l y short and t h i s volume i s assumed t o be small f o r the f i e l d s i z e units normally considered in t h i s model.

Subusrface Drainage

The r a t e of subsurface water movement into drain tubes or ditches depends on the hydraulic conductivity of the soi 1, drain spacing and depth, prof i 1 e depth and water tab1 e el evation

.

Water moves toward drains in both the saturated and unsaturated zones and can best be quantified by solving the Richards equation f o r two-dimensional flow. Solutions have been obtained f o r drainage ditches (Skaggs and Tang, l976), drainage 'in layered s o i l s (Tang and Skaggs, l978), and f o r drain tubes of various s i z e s (Skaggs and Tang, 1978). Input and computation- al requirements prohibit the use of these ntmerical methods in DRAINMOD, as was the case f o r i n f i l t r a t i o n discussed previously. However, num- e r i c a l solutions provide a very useful means of eval uating approximate methods of computing drainage flux.

The method used in DRAINMOD t o c a l c u l a t e drainage r a t e s i s based on the assumption t h a t l a t e r a l water movement occurs mainly in the saturated reg5on. The e f f e c t i v e horizontal saturated hydraulic con- ductivity i s used and the flux i s evaluated in terms of the water table elevation midway between the drains and the water level o r hy- draulic head in the drains. Several methods a r e available f o r e s t i - mating the drain flux including the use of numerical solutions to the

Figure

table control systems, determining permissible hydraulic loading rates

table control

systems, determining permissible hydraulic loading rates p.24
Figure 1. Schematic o f  water management system w i t h  subsurface drains t h a t  may be used f o r  drainage o r  s u b i r r i g a t i o n

Figure 1.

Schematic o f water management system w i t h subsurface drains t h a t may be used f o r drainage o r s u b i r r i g a t i o n p.25
Figure 9. Equivalent 1 ateral hydrau: i c  conductivity i s  determined f o r  s o i l  p r o f i l e s  w i t h  up t o  5 layers

Figure 9.

Equivalent 1 ateral hydrau: i c conductivity i s determined f o r s o i l p r o f i l e s w i t h up t o 5 layers p.42
Figure 14. S o i l  water d i s t r i b u t i o n  f o r  a water table depth of 0.7 m for various drainage and evaporation rates

Figure 14.

S o i l water d i s t r i b u t i o n f o r a water table depth of 0.7 m for various drainage and evaporation rates p.54
Table 2 ,

Table 2

, p.70
Table 3. Summary of drainage system input parame ters.

Table 3.

Summary of drainage system input parame ters. p.71
Table 5. An example of computer output for daily summaries - Wagram soil, July, 1959. A1 1 values given i n  cm

Table 5.

An example of computer output for daily summaries - Wagram soil, July, 1959. A1 1 values given i n cm p.73
Table 9. Crops grown on research s i t e s ;  planting and harvesting dates.

Table 9.

Crops grown on research s i t e s ; planting and harvesting dates. p.77
Figure 19. Schematic of experimental setup on the H .  Carroll Austin Farm, Aurora, N.C

Figure 19.

Schematic of experimental setup on the H . Carroll Austin Farm, Aurora, N.C p.79
Figure 22, Runoff from 3 m X 4 m plots was recorded with a tipping bucket apparatus and an event recorder

Figure 22,

Runoff from 3 m X 4 m plots was recorded with a tipping bucket apparatus and an event recorder p.83
Figure 21. A standard evapcration pan was modified t o  record pan evaporation directly

Figure 21.

A standard evapcration pan was modified t o record pan evaporation directly p.83
Figure 25. Effect of water table depth the water tab1 e.

Figure 25.

Effect of water table depth the water tab1 e. p.91
Figure 28. Observed and pr-edicted water t a b l e  i l l e v a t i o n s  midway k t w e e n  d r a i n s  spat(-+ 85 m a p a r t  on t h e  Plymouth s i t e  during 1975

Figure 28.

Observed and pr-edicted water t a b l e i l l e v a t i o n s midway k t w e e n d r a i n s spat(-+ 85 m a p a r t on t h e Plymouth s i t e during 1975 p.97
Figure 30. Observed and predicted water table elevations midway between drains spaced 55 m apart on the Plymouth s i t e  during 1977

Figure 30.

Observed and predicted water table elevations midway between drains spaced 55 m apart on the Plymouth s i t e during 1977 p.98
Figure 31. Observed and p r e d i c t e d  water t a b l e  elevations midway between d r a i n s  spaced 7.5 m a p a r t  on the Aurora s i t e  d u r i n g  1973

Figure 31.

Observed and p r e d i c t e d water t a b l e elevations midway between d r a i n s spaced 7.5 m a p a r t on the Aurora s i t e d u r i n g 1973 p.99
Figure J U L I Q N  DQTE 33. Observed and predicted water tab1 e elevations illidway between drains spaced 7.5 m apart on the Aurora s i t e  during 1975

Figure J

U L I Q N DQTE 33. Observed and predicted water tab1 e elevations illidway between drains spaced 7.5 m apart on the Aurora s i t e during 1975 p.100
Figure 37. Observed and predicted water table elevations midway between drains spaced 15 m apart on the Aurora site during 1974

Figure 37.

Observed and predicted water table elevations midway between drains spaced 15 m apart on the Aurora site during 1974 p.102
Figure 39. Observed and predicted water table elevations midway between drains spaced 15 m apart on the Aurora s i t e  during 1976

Figure 39.

Observed and predicted water table elevations midway between drains spaced 15 m apart on the Aurora s i t e during 1976 p.103
Figure 42. Observed and predicted water t a b l e  elevations nli dway between drains snaced 30 m a ~ a r t  on the Aurora s i t e

Figure 42.

Observed and predicted water t a b l e elevations nli dway between drains snaced 30 m a ~ a r t on the Aurora s i t e p.104
Figure 43. Observed and predicted water table elevations midway between drains spaced 30 m apart on the Aurora site, 1975

Figure 43.

Observed and predicted water table elevations midway between drains spaced 30 m apart on the Aurora site, 1975 p.105
Figure 45. Observed and predicted water table elevations midway between drains spaced 30 m apart on the Aurora s i t e ,  1977

Figure 45.

Observed and predicted water table elevations midway between drains spaced 30 m apart on the Aurora s i t e , 1977 p.106
Table 16. Summary of input data for the Bladen and Wagram soils.

Table 16.

Summary of input data for the Bladen and Wagram soils. p.112
Figure 48. SEW30 as a function of drain spacing for three surface drainage treatments on Bladen and Wagram

Figure 48.

SEW30 as a function of drain spacing for three surface drainage treatments on Bladen and Wagram p.114
Figure 50. SEW,, as a function of drain spacing f o r  conven- tional drainage, subirrigation and controlled

Figure 50.

SEW,, as a function of drain spacing f o r conven- tional drainage, subirrigation and controlled p.118
Figure 51. Dry days during the growing season for three water management methods on Bladen soil

Figure 51.

Dry days during the growing season for three water management methods on Bladen soil p.120
Figure 52. SEW30 as a function of drain spacing for conven- tional drainage, subirrigation and control led

Figure 52.

SEW30 as a function of drain spacing for conven- tional drainage, subirrigation and control led p.121
Figure m 54. Effect of drain spacing and irrigation frequency on total annual irrigation for a

Figure m

54. Effect of drain spacing and irrigation frequency on total annual irrigation for a p.126
Figure 56. Effect of maxinium root depth on number of dry days, 2 and 5 year recurrence intervals

Figure 56.

Effect of maxinium root depth on number of dry days, 2 and 5 year recurrence intervals p.130
table depth, dry none depth etc, for the end of the day, and

table depth,

dry none depth etc, for the end of the day, and p.141
Figure A.1.

Figure A.1.

p.144

References