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Plot scale
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What this section will address
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A
B
Plot scale
C
Hillslope scale
Catchment scale
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Outline
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 From core to plot
 Quick review of flow and transport in porous media
 Problems with the notion of linear upscaling of soil
core information
 Plot scale changes with depth
 Some experimental data
 Preferential flow changes with depth
 Some experimental data
 Summary
 Plot scale conceptualization and how this links to the
hillslope scale
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From core
to plot
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Our so-called subgrid parameterization
Jan Hopmans, UC Davis
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The steps
How does measurement uncertainty in these
steps affect estimation of K(h)?
Sherlock et al., 2000
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What’s important conceptually
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How we define this quantitatively
Source: Mike O’Kane
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Source: Mike O’Kane
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Just to be clear
So for unsaturated conductivity…
Hydraulic conductivity mm/hr
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1000
Water is the
conducting medium!
100
10
1
0
-100
-200
Water potential cmH2O
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Photo by Jim Kirchner
But wait, structure trumps texture!
Intact field soil very
different to
admixtures of
sand/silt/clay
Water content [-]
0.5
Sand
0.4
Loess
Clay
0.3
0.2
0.1
0
1
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10
100
 [cm]
1000
10000
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Preferential flow
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If Darcy were alive today…
Merde!
H
q  K 
z
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Two common strategies to deal with this
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Source: Brent Clothier, WISPAS Newsletter 2008
Darcy revisited
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 It’s not that Darcy does not apply (almost all of
the time)
 It’s just that a different physics kicks in during
brief windows in time
 Days or weeks of Darcian bordom, punctuated by
all (macropore) hell breaking loose!
 Think of it as a struggle between the Newtonian vs
Darwinian world views
 read John Harte’s 2002 paper in Physics Today (on
merging the Newtonian and Darwinian world views)
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The plot scale paradox
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surface,
topsoil
matrix
 While large pore space makes up only a small
percent of the total porosity, they control almost
all the flow at or near saturation
soil
soil pipes
soil base
permeable
layers
Almost all our theory is for the matrix
We‘ve learned about as much as we ever will for
pure textural mixtures and re-packed field soilshighly
Peter Kienzler, ETH Zurich
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Not a new idea
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The curse of
preferential
flow
1898 - Some 104 years ago
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Courtesy Brent Clothier
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Plot scale
changes with
depth
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At depth
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Evaporation
Transpiration
Infiltration
Lateral flow
Deep percolation
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Photo: Markus Weiler UBC
Hydrology’s most basic equation
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nZr ds/dt = I(s, t) - E(s, t) - L(s, t)
Where: n is porosity, Z is soil depth, s is the relative soil moisture
content, I is infiltration, E is evaporation and L is leakage
Rodriguez-Iturbe (2000, WRR) notes that “although
apparently simple, this presents serious challenges
when the terms in the RHS are considered
dependent on the state s.
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Changes with depth
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one of your benchmark papers
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Some data from the same site
Data from WS10, HJA, Kevin McGuire
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Ksat changes with depth!
Saturated hydraulic
conductivity with
exponential curve
fits. The dashed lines
indicate the envelope for
most data observations.
Data from WS10, HJA,
Kevin McGuire
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Drainable porosity
 Drainable porosity =
saturated water
content – water
content at field
capacity
 Change in drainable
porosity will directly
alter the depth
function of drainable
storage in the soil
 Relates to ground
water table
fluctuations
Data from WS10, HJA, Kevin McGuire
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Why such changes with depth?
Knocks / 5 cm
0
0
20
Soil depth (cm)
40
60
80
100
120
140
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5
10
15
20
.. and for many nutrients
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Also distinct depth
distributions
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Data from forest soils
(Hagedorn et al., 2001)
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The preferential flow – matrix link
Soil matrix changes
with depth conspire
with vertical
preferential flow:
Drainable porosity
Bulk density
z
Hydraulic conductivity
Pore size distribution
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?
Peter Kienzler, ETH Zurich
A now common mechanism
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Storm Rainfall Sd18O  10o/oo
dq/dZ
<0
<0
d18O  4.5o/oo
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 New water bypass flow
to depth
 Transient saturation at
soil-bedrock interface
 Lateral pipeflow of old
water due to limited
storage and head
 Bedrock surface
control of mobile water
 Rapid recession after
rainfall ends
 Important coupling of
unsaturated and
transient saturated
zones.
d18O  5o/oo
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Why this is important for runoff
generation?
Water cannot enter the pipe
drain when it is placed above the
level of the water table (i.e.
water will not flow from a
position of low potential in the
soil to a position of higher
potential). Water will only enter
the drain when it is placed within
the saturated zone (below the
water table) and if there is
sufficient hydraulic head.
(McLaren and Cameron, 1994)
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Remember this when we
move to the hillslope
scale…
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Kitihara-san’s Lab at FFPRI in Japan
R
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More detail on
preferential flow
changes with
depth
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It’s network-like and it’s
ubiquitous
A network of connected
macropores and fissures
that rapidly transmits
water & solutes through
the rootzone
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Courtesy Brent Clothier
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A quick case study to illustrate this
Sprinkling experiments on undisturbed soils: the work of Weiler and Naef
electric linear
actuator
nozzles
covered dry plot
wind protection
gutter
tensiometer and
TDR probes
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overland flow
measurement
pump and control
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Sprinkling and dye tracing
experiments
Markus Weiler, Freiburg University
Mapping
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0
High rainfall intensity
Dry soil
8 cm
50 cm
Horizontal dye
pattern
Depth
15 cm
Legend
unstained
stones
macropores
57 cm
Stained areas with
low concentration
medium concentration
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Markus Weiler, Freiburg University
high concentration
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Soil water content and preferential
flow
Soil water content measurement
Vertical dye pattern
Depth (m)
Flow process
1.0
Legend
High rainfall intensity
Dry soil
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Markus Weiler, Freiburg University
Surface initiation
Stained areas with
(water repellency)
unstained
low concentration
stones
medium concentration
high concentration
High interaction
(permeable matrix)
macropores
An animation
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High rainfall intensity
Depth (m)
Dry soil
Dye pattern
Water content change
1.0
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Markus Weiler, Freiburg University
Matric potential and preferential flow
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Recall Weyman, Burt and others from your reader….
Matric potential measurement
Vertical dye pattern
Depth (m)
Duration of sprinkling experiment
82 cm
5
Matric potential (kPa)
0
-5
98 cm
30 cm
-10
-15
-20
0
Flow process
18 cm
10 20
30 40 50 60 70 80 90 100
Time (min)
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1.0
Subsurface initiation
Legend
(saturated
matrix)
Stained areas with
unstained
low concentration
Low stones
interaction medium concentration
high concentration
macropores
(saturated matrix)
Markus Weiler, Freiburg University
Other sites
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High rainfall intensity
Depth (m)
Dry soil
Dye pattern
Water content change
1.0
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Markus Weiler, Freiburg University
Other sites
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Low rainfall intensity
Depth (m)
Dry soil
Dye pattern
Water content change
1.0
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Markus Weiler, Freiburg University
Other sites
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Low rainfall intensity
Depth (m)
Wet soil
Dye pattern
Water content change
1.0
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Markus Weiler, Freiburg University
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Infiltration in macroporous soils
Macropore Flow
Initiation
Water supply to the
macropores
Interaction
Water transfer between
macropores and the
surrounding soil matrix
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Markus Weiler, Freiburg University
How do macropores influence
runoff processes?
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Activated macropore
rapid infiltration
Runoff reaction
Storage
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Fast
Subsurface Flow
Overland Flow
Markus Weiler, Freiburg University
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The preferential flow – matrix link revisited
Soil matrix changes
with depth conspire
with vertical
preferential flow:
Drainable porosity
Bulk density
z
Hydraulic conductivity
Pore size distribution
Oregon State University
?
Peter Kienzler, ETH Zurich
A now common mechanism
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Storm Rainfall Sd18O  10o/oo
dq/dZ
<0
<0
d18O  4.5o/oo
Oregon State University
 New water bypass flow
to depth
 Transient saturation at
soil-bedrock interface
 Lateral pipeflow of old
water due to limited
storage and head
 Bedrock surface
control of mobile water
 Rapid recession after
rainfall ends
 Important coupling of
unsaturated and
transient saturated
zones.
d18O  5o/oo
Implications for modeling
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Traditional conceptual
runoff models
Unsaturated
storage
Saturated storage
What undergraduate textbooks will state
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Implications for modeling
A process
prerequisite
Unsaturated
storage
Saturated storage
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The use of qualitative, conceptual models
can overcome the shortcomings of
quantitative models. Conceptual models
consider the sum interaction of all
processes, even if not known, that result in
a particular phenomenon
(Pilkey and Pilkey-Jarvis, 2007).
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One example
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 z
nd ( z )  n0 exp   
 b
Weiler
and
McD, 2004 JoH
Oregon
State
University
z 

K ( z )  K o 1 

D

m 1
qSSF (t )  T (t )  w
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Conclusions
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Peter Kienzler, ETH Zurich
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This section
 From core to plot
 Quick review of flow and transport in porous
media
 Problems with the notion of linear upscaling
of soil core information
 Plot scale changes with depth
 Some experimental data
 Preferential flow changes with depth
 Some experimental data
 Summary
 Plot scale conceptualization and how this
links to the hillslope scale
Next section
From vertical to lateral flow
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Q
Q
Qs
Often an impeding horizon or soil-bedrock contact
z
Saturated vertical
hydraulic
conductivity
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% Saturation
Downward
percolation
Lateral
subsurface flow