ABE 527
Computer Models in Environmental and Natural Resources Engineering
Rabi H. Mohtar
Drainage Principles
Surface ↔ subsurface drainage flow interaction.
The figures above are schematic of water movement for flat field system with
impermeable layer. If surface drainage is poor, subsurface drainage must be designed to
handle the extra infiltration.
Factors affecting subsurface drainage flow include:
1.
2.
3.
4.
5.
Hydraulic conductivity (K)
Drain depth
Spacing (L)
Profile depth (b)
Depth of water in the drains
Water Balance (in the soil matrix)
∆Va = D + ET + DS – F
where ∆Va = change in the air volume
D = lateral drainage
DS = deep seepage
F = infiltration
All variables are in (cm) in Δt time unit
Water Balance (on surface)
P = F + ∆S + RO
P = precipitation
F = infiltration,
∆S = change in water volume
RO = runoff
All in (cm) in ΔT time unit
DRAINMOD
Model components
1.
Precipitation: 1 hr increment data input
2.
Infiltration:
Factors affecting it:
 Soil: hydraulic conductivity
Initial water content
surface compaction
depth of profile
water table depth
 Plant: extent of cover
depth of rootzone
(1)
(2)

Climate:
intensity
rainfall
duration
time distribution
temperature and whether soil is frozen or not
Governing equation: Richard’s equation (h-based equation)
h 
h K (h)
C(h)
 (K(h)
)
t z
z
z
Where h = soil water pressure head
z = distance below soil surface
K(h) = hydraulic conductivity function
C(h) = water capacity function
Equation is non-linear and can only be solved numerically.
Green-Ampt equation
(for ponded infiltration, slug flow)
H 2  H1
Lf
f = infiltration rate cm/hr downward flux
Lf = length of wetted zone
Ks = hydraulic conductivity
H1 and H2 = hydraulic head at soil surface and wetting front.
If soil surface is taken as datum:
H1 = H0
H2 = hf – Lf
hf = soil water pressure head at wetting front
Then:
f = -Ks (hf – Lf – H0)/Lf
h f = -ve , if Sav = - hf = effective suction, then
f=-K s
(3)
(4)
(5)
f=Ks Sav  Ho  Lf  / Lf
(6)
F= s  i  Lf  MLf where s  wet zone moisture and i  initial water content
and if Ho is negligible compared to Sav + Lf
 f=Ks  Ks MSav / F
(7)
or
(8)
f=A/F + B
A, B are given parameters for a certain soil type.
F is not a function of application rate. A and B changes during simulation time steps
based on moisture content.
The figures below are numerical solutions of Richards equation.
*Note that the infiltration rate is dependent on the rainfall rate.
*Note that if you plot infiltration rate – cumulative infiltration relationship is independent
of the rainfall rate.
 for modeling purposes, the only input are parameters pertaining to initial conditions.
The figure above compares Richard’s and Green-Ampt solutions
3.
4.
Surface Drainage
Depression storage:
Micro – 0.1 cm for weathered soil, few cms for rough soil
Macro – 0 for smoothed (land formed soil)
> 3 cm for inadequate surface outlet or non-smoothed soil.
Surface detention or “film” storage depends on hydraulic roughness, slope,
runoff rate
Subsurface Drainage
Subsurface water movement into drains and ditches. Here we assume
saturated flow only.
Hooghoudt’s flow equation (steady state)
R = steady rain
dh
Q=-K h
(9)
dx
where Kh = lateral hydraulic saturated conductivity; h = water table height above
restricted layer
Q = flux per unit width
flux at (x) = total rain between x and the midpoint
dh
L

 R   x 
 -K h
(10)
dx
2

at x = 0, h = d
L
at x= , h = d + m
2
integrating and solving for R
4K(2 md + m2 )
 R=
(11)
L2
 taking flux = rainfall
if substituting q for R i.e., same flux gives same profile (m) value then
8Kd e m  4km 2
q
CL2
q = flux
m = midpoint water table height above drain
K = effective lateral hydraulic conductivity
average drain flux
C=
flux midway between drains
The above equation can be used to determine spacing.
de = equivalent depth to correct for convergence near the drains.
d
0  0.3
L
d
de 
d  8 d

1+  1n     
L  r 

1.6
2
  3.55  d  2  
L
L
d 0.3
2
L
 L

8  ln    1.15 
 r

where r = drain tube radius.
de 
(12)
(13)
(14)
(15)
For design purposes,  can be approximated by 3.4, effective radius re can be used to
account for limited (finite) openings in the tube. This induces additional head loss.
re = 0.51 cm for 11.4 cm O.D. tubing
K1d1  K 2 D 2  K 3D3  K 4 D 4
d1  D 2  D3  D 4
m in Figure 2-8 can be looked at as
m = hv + hh + hr
Ernst equation
hv = vertical flow loss
hr = radial flow loss (near drains)
hh = horizontal flow loss
Ke 
Hooghoudt – Ernst equation was used to generate the following results.
(16)
The above simulations assume curved (elliptical) water table where water table is below
soil surface. If water is logging on the surface the assumptions do not hold as stream lines
concentrate near drains (95% of flow). In this case Kirkham derived the following
equation:
q=
4 K (t+b-4)
where
gL
(17)

 cos h  m L/2h   cos  r/2h  cos h  m L/2h   cos  (2d-r)/2h  
 tan (  2d-r  / 4h 
g=2ln 


  2  ln 
m 1
tan

r/4h
cos( m L/2h)  cos( (2d-r)/2h) 


 cos  m L/2h   cos  r/2h 
(18)
where h = depth of profile not equivalent depth
Drain size
Drainage coefficient (D.C.) based (1-2 cm/day) depending on geography location, crops.
If q D.C., q=D.C.
5.
Subirrigation
If h=ho at x=0 is set equation equivalent to Hooghoudt’s flow steady state equation:
4k
q  2 (2 h o m m 2 )
(19)
L
M=hm – ho
To correct for convergence
ho = yo + de is used
ho > hm m and q are –ve
modifications of subirrigation flow equation


h
4km  2ho  o m 
Do 

q
(20)
2
L
where Do = Yo + d
ho = Yo + de
The above equation is used.
Controlled Drainage
A weir is set at a given elevation, when drain water exceeds the weir depth spillover
occurs. If water table in field is lower than drain water will move into field.
Effective or equivalent conductivity
6.
Evapotranspiration
Thornwaite method for estimating PET:
_
ej  c Tj a
where e j  monthly PET
_
and T j  monthly mean temp erature
c and a = constants depending on location and temperature
1.514
_

ij   T j / 5 


12
I   ij
i 1
i = monthly heat index
I = sum of monthly heat index
The upward flux in soil is:
d 
dh

(21)
 K h  K h   0
dz 
dz

h = soil water pressure head
z = distance from surface
The rate of upward movement increases with soil water suction (-h) at the surface. 
max evaporation rate for a given water table is approximated by solving the evaporation
flux equation presented earlier subject to a large h (-ve value) – 1000 cm at the surface
z=0, h=0, z=d water table depth.
If PET is less than y-axis value for that water table depth then table/graph value is taken
at ET or the difference has to be extracted from root zone storage
7.
Water distribution (soil water)
Water distribution profiles can be solved for where water was initially at the surface of
the soil column and solutions obtained at various evaporation rates for various spacing
and drain depth. The moisture content distribution is independent of the evaporation rate..
DRAINMOD has 2 soil layers:
1.
Water table to root zone or even through root zone where water content
profile is “drained to equilibrium” profile
2.
Dry zone of constant water content
8.
Rooting depth