Lateral Effect: Calculation and Parameters

Lateral Effect:
Calculation and Parameters
Wetland Delineation Course
Joel Peterson, PhD, PE
Board of Water and Soil Resources
Adjunct Assistant Professor, Biosystems &
Biological Engineering, University of MN
Credits
Greg Larson, BWSR
Dr. Gary Sands, U of M
Outline
Historical Background
Definitions
Analytical tools (the equations)
Limitations of data and predictions
Improving the accuracy of predictions
Guidance
A complicated subject!
To better understand this topic, I suggest:
-A primer on drainage principles, including
1. Soil water movement (Darcy’s Law)
2. Design of drainage systems
3. Basic groundwater hydrology
Drainage starts with Darcy
French Sanitation Engineer performed experiments
on sand columns
Flow out depends on:
Conductivity
Length of Tube
Head Differential
Cross Section
Q = Ks A (H1 – H2) / L
Why doesn’t drainage end with
Darcy?
Flow lines converge near the drain/ditch
Loss of energy for flow
Must account for this energy loss
R. Cooke
Add a mass conservation term
Flow out of system is a constant, with constant
recharge
Results in the Hooghoudt Equation (1940)
Assumes horizontal flow lines
Hydraulic Gradient = water surface slope
Dupuit-Forchheimer
The equations
The early ones were steady-state; later ones were nonsteady state
Non-steady state preferred in this part of country as a
water table rises and falls due to rainfall and ET
In some cases, all equations provide similar results—
but usually not. Is the difference significant? It
depends.
Equations for determining
Scope and Effect
Ellipse
Hooghoudt
van Schilfgaarde
Kirkham
Programs such as Hydrocad are good for modeling ditch flow, but do
not address water flow through the adjacent soil profile. In short, they
are not a suitable surrogate for drainage equations!
Ellipse
equation
Steady state (assumes the drain steadily removes rain
or irrigation that falls at a constant rate)
Assumes:
Homogeneity of soils, parallel evenly spaced drains,
impermeable layer, constant rainfall rate, functioning
outlet
Limitations:
Not applicable where Kh > Kv , non-homogeneous soils,
lacks a time factor, cannot deal with surface water
Hooghoudt equation
Steady state, K calculated separately for layers, depth to
impermeable barrier modified to “effective depth” - de
de provides correct results to account for flow convergence
Assumes:
homogeneity, parallel evenly spaced drains, impermeable
layer, constant recharge rate
Limitations:
non-homogeneous, lacks a time factor, cannot deal with
surface water or water flow above water table
Hooghoudt Equation
m
2r
h
d
de
S
IMPERMEABLE LAYER
4Km(m + 2d e )
S =
q
2
q = rainfall rate
or drainage
coefficient
Hooghoudt Equation
4Km(m + 2de )
q=
2
S
de =
πS
∞
S
2 πnd 

8 ln (
) + 16 ∑ lncoth(
)
π r0
S 
n =1 
≈
πS
∞
S
8 ln (
)+8 ∑
π r0
n = 1,3,5,....
4e
−
4nπd
S
n (1 − e
−
4nπd
S
)
Kirkham’s equation
Based on Potential Theory
Deals with ponded water
Used in conjunction with Ellipse, Hooghoudt, or van
Schilfgaarde
Handles removal of ponded water through subsurface
tile system with no surface intakes
Sensitive to depth of ponded water and may need to
consider ET
Kirkham’s equation
4πK(t + b − r)
q=
gS
 tan(π (2d − r ) / 4h) 
g = 2 ln 

tan(
d
/
4
h
)
π


 cosh(πmS / 2h) + cos(πr / 2h) 
 cosh(πmS / 2h) + cos(π (2d − r ) / 2h) 
+ 2∑ ln 
•
ln

 cosh(πmS / 2h) − cos(π (2d − r ) / 2h) 
−
cosh(
π
mS
/
2
h
)
cos(
π
r
/
2
h
)
m =1




∞
Kirkham’s equation
t
b
2r
h
d
S
IMPERMEABLE LAYER
4πK(t + b − r)
q=
gS
van Schilfgaarde Equation
Non-steady-state
Requires drainable porosity
Includes a parameter for time
Drain cannot rest on an impermeable layer
Uses “equivalent depth” which is computed from (D)
and (d) – same as Hooghoudt
Surface water must be removed
Used where a drain or ditch passes through a wetland
Suggested for use in Minnesota
van Schilfgaarde Equation
Falling Water Table
m0
m
2r
h
d
de
S
IMPERMEABLE LAYER
dA = π(m-dm)S/2-π
πmS/2 = -π
πdmS/2
m-dm
m
2r
h
S
d
IMPERMEABLE LAYER
4Km(m + 2de )
q=
2
S
π dm
q=− f
2 dt
van Schilfgaarde Equation
9Kd e (t − t 0 )  m 0 (m + 2d e ) 
S =
ln

f
 m(m0 + 2d e ) 
2
S – drain spacing, or S/2 = lateral effect
K – Saturated hydraulic conductivity
t – time to drop water table from m0 to m
f – drainable porosity
m0 – initial water table height above drain
m – water table height after time t
de – effective depth from drain to impermeable layer
−1
Calculating Lateral Effect
Web site: www.wli.nrcs.usda.gov/technical/web_tool/tools_java.html
Ellipse, Hooghoudt, van Schilfgaarde, or Kirkham’s
equations
Need soils and ditch/drain details
NRCS in Minnesota and North Dakota use a proprietary
program called “ND Drain”
My remarks focus on the Web site version
Ditch Dimensions
(See EFH Chp 19, MN Supplement
http://www.mn.nrcs.usda.gov/technical/eng/MN-EFH-pdf/Chapter%2019/19EFH_Apr05.pdf)
m0 – initial water table height above
drain – assume saturation at the soil
surface at t = 0. Therefore, the
depth from the soil surface to the
bottom of the drain
m – water table height after time t
above drain
d – depth of drain below ground
surface (for ditch, to water surface)
D – depth from ground surface to
impermeable layer, use 10 ft if
unknown
de – effective depth from drain to
impermeable layer, program will
calculate based on above
Hydraulic Conductivity
The rate at which water moves through a porous
medium-soil.
It is abbreviated as “k”
Sometimes called Ksat to denote saturated flow
through a porous medium.
Permeability also is used interchangeably
Mathematically there is a difference; for our purposes,
use of one or the other is not an issue.
All other factors equal, a higher K = a greater le. NRCS uses mid-point of
the range of K values as a compromise. The COE has used the lower end
of the range. What is correct?
Saturated Conductivity (K)
Where to get values:
Web Soil Survey
Published values for texture
Pedotransfer function
It’s not that scary
Field Measurement
K
Soil Survey
Listed multiple
places
Use from map
unit description
for MN
What value to use?
Based on textural class
TextureClass
Ks
(cm
/da
y)
Ks
(in
/hr
)
Clay
14.757
0.242
C loam
8.185
0.134
Loam
12.050
0.198
L Sand
105.196
1.726
Sand
642.688
10.543
S Clay
11.350
0.186
SCL
13.183
0.216
S loam
38.282
0.628
Silt
43.752
0.718
Si Clay
9.616
0.158
Si C L
11.117
0.182
Si Loam
18.239
0.299
Based on Schaap, M.G., 2000
Soil Survey Results provide more sitespecific information, by layer
Pedotransfer Functions
Mainly statistical relationships based on thousands of data p0ints to
relate easy-to-measure variables to hard-to-measure variables
Download from : http://hydrolab.arsusda.gov/soilwater/Index.htm
Use %sand, %clay
2.00 in/hr
Modify w/ & org matter
and %gravel
Will also help with
drainable porosity
2.29 in/hr
2.00 in/hr
2.29 in/hr
Rosetta Pedotransfer function
http://www.ars.usda.gov/Services
/docs.htm?docid=8953
USDA-ARS Salinity Lab
Hierarchical Neural Network
Model
Based on 2,085 data points
Methodology that NRCS uses
How to use Rosetta
After download and install
Open a new database
Select Hierarchical ANN
How to use Rosetta, cont
For each soil layer, enter the sand, silt, clay, bd
Click the SSCBD option button
Sand Silt Clay Bulk Density
How to use Rosetta, cont
Now predict parameters for current record
Ksat calculated
Given in log units
Ksat = 10^(log10(Ks))
Ksat = 42.8 cm/day
Calculate for other layers
Sand Silt Clay Bulk Density
Enter the K values into the
Calculator
Layer thickness
from web soil
survey
That was easy
Basics of Drainable Porosity (f)
The volume of water drained per
volume of soil, FOR A GIVEN
MATRIC POTENTIAL
From Saturation to Field
Capacity (gravity drainage ~ 24
hrs)
f = depth drained water (hw) /
total depth (ht)
Example:
If f = 0.10 (10%) and we drain 2
feet (24 inches), what is depth
water?
= f * ht = 0.10 * 24” = 2.4 inches
SAT
FIELD CAP
Water States by Soil Texture
The most difficult to obtain input. Peat and muck soils have values such as
0.238 and 0.280. Clay/silt/loam soils have values of 0.02 to 0.07. MUUF files
are not supported by the NRCS and the website [NRCS National Climate Data
Center] for calculating them has been taken down. Drainable porosity data are
being developed.
Drainable Porosity
Where to get values:
Published values for texture
Pedo-transfer function
Field Measurement
Some Typical Values
Soil Texture
Field Capacity (%
by vol.)
Wilting Point (%
by vol.)
Drainable Porosity
(% by vol.)
clays, clay loams, silty clays
30-50%
15-24%
3-11%
well structured loams
20-30%
8-17%
10-15%
sandy
10-30%
3-10%
18-35%
From Sands (http://www.extension.umn.edu/distribution/cropsystems/DC7644.html)
(
http://age-web.age.uiuc.edu/classes/tsm352/lectures/Sub%20Irrigation%20requirements.pdf
)
(USBR, 1993)
Can we be more specific?
Yes! But….it’s complicated
Depends on site characteristics (head) in addition to
soil
Need to know the amount of water drained in the soil
column – how to estimate?
As we’ve seen, depends on the soil/water
characteristic curve
Estimates of Soil Moisture
The soil/water curve has been described by van
Genuchten (VG)
θ ( h) = θ r +
θs − θr
[1 + (αh) ]
n 1−1 / n
θ (h) = volumetric water content (cm/cm)
θ s = water content at saturation (cm/cm)
θ r = residual water content (cm/cm)
α = inverse of air entry suction (1/cm)
h
= suction head (cm)
n
= a measure of pore size distribution
How to use VG?
We’ve seen how to enter
data into Rosetta to get Ksat
Now use Rosetta output to
calculate ‘f’ in Excel
Prepare Inputs
θ (h) = θ r +
θs −θr
[1 + (α h ) ]
n 1− 1 / n
θ (h)
θs
θr
α
= volumetric water content (cm/cm)
h
n
= suction head (cm)
= water content at saturation (cm/cm)
= residual water content (cm/cm)
= inverse of air entry suction (1/cm)
= a measure of pore size distribution
Alpha =
10^(log10alpha)
n = 10^(log10n)
Calculate water drained
Breakdown soil into
depth increments
Head is total depth –
midpoint depth
Calculate water content
using VG
Water removed (D) is
(theta_s – water)*layer
thickness content in
layer
Paste down for entire
soil depth
Estimate Drainable Porosity (f)
Sum water drained
over entire soil
profile
Divide total water
drained by soil
profile depth
One wrinkle
We need to enter different VG parameters for water
drained by soil layer
HELP!
Spreadsheet tool that we just used available on BWSR
website:
Time (t)
The time for the water
table to drop from mo to
m in days
Engineering Field
Handbook, Part 650,
Chp 19, MN Supplement
provides additional
guidance
• Important note: 14 days
is policy from the
NFSAM (current
edition).
Regionalization of the
Manual will prescribe a
14 day hydrology
standard for sites that
have been
hydrologically modified.
Surface Roughness (s)
Use s = 0.1 in (EFH 19,
MN Supp)
Small amount of water on
surface, held by soil
particles, but not
depressional storage
Modifies drainable
porosity
Effective Radius (re)
Effective radius considers
actual open area for water to
enter tile
Smaller than actual
Computed internally
For ditch, re = 1 ft
Based on DRAINMOD
From EFH 19, Mn Supplement
S represents the midway point between two parallel drains, thus
describing the effects of two drains. Therefore, the equation will tend
to overestimate the lateral effect when one ditch or drain is being
considered.
Input Parameter Summary
Input Paramter
Where to get value – in
order of importance
S – drain spacing, or S/2 =
lateral effect
calculated
K – Saturated hydraulic
conductivity
From field measurement,
Rosetta program, soil survey
t – time to drop water table
from m0 to m
From NRCS EFH 19
Supplement
f – drainable porosity
From field measurement,
Rosetta/spreadsheet,
literature value
m0 – initial water table
height above drain
From NRCS EFH 19
Supplement (soil surface)
m – water table height after
time t
From NRCS EFH 19
Supplement (one ft below
soil surface)
de – effective depth from
drain to impermeable layer
Soil borings, soil survey, 10 ft
(max)
Essential References
NRCS Fact Sheet Eng-19 Lateral Effect
http://www.mn.nrcs.usda.gov/technical/eng/pdf/weble12-05.pdf
MN 19-57 Supplement to the EFH (4/05)
http://www.mn.nrcs.usda.gov/technical/eng/MN-EFH-pdf/Chapter%2019/19EFH_Apr05.pdf
Part 516 NFSAM, 4th Edition, Amend 4 Subpart B
Hydrology Tools
http://www.wli.nrcs.usda.gov/technical/web_tool/tools_java.html
Proper Selection Is Important!
Other factors to consider when selecting an equation:
-single ditch or drain
-pattern tile
-is ponding present
-drain is adjacent to the wetland versus through it
(Skaggs equation should be used where drain is near
the wetland)
-geographic location (see MN EFH 19)
Equation Selection
Equation Name
When to Use
Ellipse
n/a
Hooghoudt
Drainage design
Kirkham
Estimate time to remove
ponding
van Schilfgaard
Drain through wetland (most
cases)
Skaggs
Drain NEAR wetland
(guidance forthcoming)
University of Wisconsin Soils SS325
An extremely variable soil
property!
Mineral versus Organic Soils
Scope and effect equations work best in mineral soils
Water retention characteristics of organic soils are different
The national office of NRCS has funded research to extend the
applicability of scope and effect equations to organic soils
Be particularly cautious when using traditional scope and effect
equations in organic soils
Sensitivity of inputs
Ksat: a 10% increase in Ksat
results in a 5% increase in LE
f: a 10% increase in f results
in a 5% decrease in LE
Ksat and f are co-variates
Time: A 10% increase in T
results in a 5% increase in LE
de (effective depth): a 10%
change in D results in a 4%
increase in LE
m (the difference in predrainage water table to post
drainage water table): a 10%
increase results in a 15%
increase in LE
The effects are cumulative
Current Guidance on Scope and
Effect (Regional Supplements)
The NRCS Web-based tool is suggested
Using the Web Soil Survey and Rosetta Program are
recommended to generate parameter values
Their output are approximations only and may not reflect field
conditions
Their results should be verified by comparison with other
techniques for evaluating drainage and should not overrule onsite evidence of wetland hydrology
Other techniques include mapping conventions and the review
of other aerial photography
Suggested Strategy for Calculating
the Effect of a Drain
Consider goal of determination
(restoration or regulation)
Consider the water budget and its
inputs and outputs
Consider effect of diversions or
adjacent drains-even those outside
of project area
Type, depth and size of drain
Determine location of drain with
respect to wetland (through or
beside)
Dominant soil type(s)
Is ponding evident
May need to break assessment into
phases if complex soils or drainage
scheme
Determine suitable equation(s)
Select input parameters
Compare results against on-site
findings and mapping conventions
Considering the original goal and
other data, determine the
appropriate answer among the
range of +/- feet of output
May need to incorporate functional
assessment
Strive for consistency of inputs: do
not mix and match
Try to reach agreement before
invoking the technical standard
Improving predictions
Refine the soil map; look at horizon- specific Ksat
data
Monitor the water table to assess drainage effect from
existing ditch—calibrate input parameters
Assess hydrology indicators
The challenges of sites
Dense glacial till (shallow impermeable layers)
Ponded water (must use Kirkham)
Varying ditch and tile depths (can alter several
variables)
Organic soil (water retention characteristics differ)
Soil complexes (difficult to determine a representative
soil)
Regionally high water tables complicate matters
Take home message
All drains have some hydrologic effect
S&E equations are a guide not an absolute
The challenge is to determine the minimum
acceptable effect
The strength of S&E equations are improved with
other tools such as mapping conventions
Soil is VARIABLE and soil maps are an estimate
A site should be viewed from a landscape perspective
and assessed accordingly
Do not argue over a few feet!
Guidance?
For many reasons, BWSR is now
assuming a leadership role in
refining this guidance for a
broader purpose and audience
The St. Paul District and BWSR
funded a white paper on
drainage scope and effect
WEB-based applications and
other tools are being planned