1. SCOPE & EFFECT EQUATIONS Chapter 7

2. Chapter Objectives Explain Background Behind Drainage Systems
Describe Hydraulic Conductivity Relating to Drainage
Describe 4 Equations for Determining Affect of Water Management on Wetlands
Adjust Le for a Wetland at the Base of a Slope
Explain How State Drainage Guides Are a Tool for Understanding Water Management Systems

3. Typical application of observation wells, Scope and Effect equations, DRAINMOD
ENDOSATURATION

4. For Wetlands with a g. w. source
For Wetlands with a g.w. source. S&E does not apply directly, flow intercepted , back drainage systems off multiple times the lateral effect distance.

5. Hydraulic Conductivity
Where K and T Are the Hydraulic Conductivity and Thickness of Each Layer
(flow being evaluated is horizontal flow only, so flow is by layers)

6. Effective Radius of Tile

7. Equations for Determining the Affect of Water Management on Wetlands
Ellipse
Hooghoudt (used in DRAINMOD)
van Schilfgaarde
Kirkham - removal of surface water (used in DRAINMOD)

8. Permeability Classes
Permeability should not be used for Saturated Hydraulic Conductivity. Use Hydraulic Conductivity determined by: measurements, algorithms using texture (MUUF, ROSETTA, Soil Water Characteristic Triangle).

9. Values from ROSETTA Class Averages http://www. ussl. ars. usda
Texture Drained f Ksat
Class cm cm
(cm) (cm/cm) (cm/hr)
Clay
C Loam
Loam
L Sand
Sand
S Clay
S C L
S Loam
Silt
Si Clay
Si C L
Si Loam

10. Use of Ellipse Equation
- The equation has been used to design drainage and water supply systems across the United States.
- It is a steady state equation - basically removes the rain that falls at a constant rate.
- It is used to determine approximate economical spacings and depths of agricultural drain tubing and ditches for ag. crops assuming that the water table should be lowered below the root zone within 24 to 48 hours.
- It has also been used to determine the hydrology of a wetland that has been modified by drainage measures.

11. Ellipse Equation Assumptions
Soil is Homogeneous and Has a Hydraulic Conductivity, K
Drains are Evenly Spaced a Distance “S” Apart
Impermeable Layer Underlies Drain at Depth “a”
Rain Is Falling or Irrigation Water Applied at Rate, “v”

12. Limitations of Ellipse Equation
Does Not Apply When Vertical K Exceeds Horizontal K
Assumes Homogeneous Soils
No Direct Factor for Time
Assumes Surface Water is Removed
Tile in Good Repair with an adequate outlet

13. Ellipse Equation S = [(4K) (m2 + 2am) / q]1/2
K and q must be in same units, e.g. in/hr, ft/day
S will be in units of a and m
Le=1/2(S)

14. Ellipse Equation S = [(4K) (m2 + 2am) / q]1/2
For wetland hydrology determination,
q is evaluated as water that must be removed by drainge in lowering water table (drained volume) divided by the time to remove.
Example: lower water table from surface to 12”below in 14 days.
Drained volume is 0.01” (WT 0” to -12”)
q = 0.01 in/14 days = in/day

15. Ellipse Equation S = [(4K) (m2 + 2am) / q]1/2
For wetland hydrology determination,
Sometimes a term called drainable porosity (f) is used. “f” is drained volume divided by depth water table was lowered.
Drained volume is 0.01” (WT 0” to -12”)
f = 0.01 in/12 in = (dimensionless)
Therefore to get q from f
q=(f x depth drained)/time=( x 12 in)/14 days= in/day (same as on previous slide)

16. Figure 1: Example Using The Ellipse Equation
m=d-c
S = [(4K) (m2 + 2am) / q]1/2

17. Review Results
Here are 4 important points to consider in evaluating whether equation is being applied correctly:
Is the Time For the Saturation to be Removed an important point?
Is the assumption of Steady State Conditions valid?
Can a Reasonable Drainage Coefficient be calculated or assumed?
Was an Equivalent Hydraulic Conductivity Value, K, calculated if multiple soil layers are involved?

18. Hooghoudt Equation
K1 = weighted hydraulic conductivity above the drainage feature, in/hr K2= weighted hydraulic conductivity below the drainage feature, in/hr Note: K1 and K2 do not have to be different
(also uses an equivalent depth that will be discussed later)

19. van Schilfgaarde Equation
m = height of water table above the center of the drain at midplane after time t, ft m0= initial height of water table above the center of the drain at t=0, ft t = time for water table to drop from m0 to m, days a = depth from free water surface in drainage feature to impermeable layer, ft f = drainable porosity of the water conducting soil, dimensionless s = water trapped on the surface by soil roughness, ft s= ft (0.1 in) would be typical
Note: set s=0 if unsure of appropriate value

20. van Schilfgaarde Equation Data Requirements
This equation requires information on Hydraulic Conductivity
A Drainable Porosity Value (f) is needed, and can be determined most readily by an application of the MUUF soils program (which is used with the DRAINMOD computer program), ROSETTA, or SPAW Soil Water Characteristic routine. f is calculated for depth drained, not a set value (ex. 60 cm used for agricultural production).
The time to Remove the Saturation and the Height of the Water Table After Drainage are specified in the NFSAM and COE criteria

21. van Schilfgaarde Equation Limitations
This is a Non-Steady State Equation. Assumptions of equation are appropriate for many parts of US where the rainfall is sporadic rather than constant
Equation does not yield a reasonable solution when the Drain Rests on the Impermeable Layer; that is, when “a” = 0
Equation must use Equivalent Depth instead of Actual Depth to give the best results

22. van Schilfgaarde Equation Limitations (continued)
Surface water must be removed from a site in order to apply this equation correctly. The Surface Water my be removed by a Ditch, Natural Ground Slope, or the Surface Intake of a Tile

23. van Schilfgaarde Equation Limitations (continued)
Equations for “de” below allow one to convert Actual Depth to the Impermeable Layer to Equivalent Depth
de = a ;for a/S’<0.3
1 + a/S’ [(8/pi) ln(a/re) - 3.4]
de = S’ pi ;for a/S’<0.3
8[ln(S’/ re)

24. van Schilfgaarde Equation Factors Affecting Accuracy
van Schilfgaarde equation does include a Parameter for Time, so it can be used to Compare How Much Water is Removed in 7 days vs. Removal in 14 days
Time Period selected does affect the results noticeably
Drainable Porosity (f) affects the results of the equation, but “f” Values that are similar in magnitude result in Minor Differences in Spacing

25. van Schilfgaarde Equation Procedure
Use with the known depth, “a”, in place of “de” to determine Estimated spacing, S’
Use Estimated spacing, S’ in Appropriate Equation to determine Equivalent Depth “de” , which replaces “a” in the van Schilfgaarde Equation for final computations

26. van Schilfgaarde Equation Procedure (continued)
Use “de” to determine the Spacing, S, in the van Schilfgaarde Equation
Compare the Estimated S’ to S, if they are within 10% of each other, the Difference Can Be Assumed to be Negligible. If the Difference is More Than 10%, use the Calculated S Value as S’, Repeat Calculations until the S’ and S Values are Within 10%

28. Figure 2: Pothole With Tile Drainage System

29. Kirkham’s Equation
Kirkham’s Equation for Parallel Drains For removal of ponding only

30. Kirkham’s Equation

31. Definition of Terms for Kirkham’s Equation

32. Kirkham’s Equation Kirkham’s Equation for a Single Drain
Q = 2(pi)K (t + d - re)
ln(2d/re)

33. Kirkham’s Equation

34. Figure 3: Adjusting for a Wetland at the Base of a Slope

35. Figure 4- Locating a tile w/probe

36. Analyzing the correct problem

37. d Non-Typical application of Scope and Effect equations, DRAINMOD
Observation wells must be installed appropriately: EPISATURATION
Many wetlands are created by this type hydrology: a shallow depth of saturation to fragipan (may be <12”) and/or ponding on surface.

38. ??
Care must be taken in applying Scope and Effect equations, DRAINMOD to this situation. Which water table is being analyzed? How do you install observation wells and interpret data?
EPISATURATION

39. The factors affecting the accuracy
1. the value assumed for the drainage coefficient has a significant effect on the results of the equation
2. minor variability in K does not change the drain spacing much
3. the depth to the impermeable layer affects the resultant spacing most significantly when the K is high, such as with sandy soils
4. assumes no rainfall event with in the same time period (multiple events), can be incorporated in drainage rate.
5. assumes no Evapotranspiration (can be incorporated in drainage rate)

40. Differences between Wetland Hydrology Determination and No-Impact Evaluation
Wetland Determination No Impact
existing system new system
ex. 12 in., 14 days ex in., 90 days
Le = 95 ft Le = 295 ft
minimal wetland fully functional wetland

43. 93’

44. Note: with drain at 3’ (lowering WT 0
Note: with drain at 3’ (lowering WT 0.5’ from previous) Le is only 7’ more. Major impact is ET.

46. Ellipse Example Problem
1. Soil Water Properties
2. Problem

47. End