1. science
2. weather
3. meteorological disaster
4. flood

How to Apply Process Information to Improve Prediction
Jim McNamara
Boise State University
Idaho, USA
Precipitation
• Improved prediction and improved process
understanding are mutually reliant
flow
time
time
Modified from Mukesh Kumar
Lumped Model
Q(t )  f ( P(t ), A, C )
Distributed Model,
Semi-Distributed Model,
Conceptual
REW 2
p
Physics based

 .(U )  .( )  Qss
t
REW 3
REW 4
REW 1
REW 5
REW 7
REW 6
q
q
q
Process Representation:
Parametric
Physics-Based
Predicted States Resolution:
Coarser
Fine
Data Requirement:
Small
Large
Computational Requirement:
Perceived
Intellectual Value:
Small
Large
Modified from Mukesh Kumar
Lumped Model
Q(t )  f ( P(t ), A, C )
Distributed Model,
Semi-Distributed Model,
Conceptual
REW 2
p
Physics based

 .(U )  .( )  Qss
t
REW 3
REW 4
REW 1
REW 5
REW 7
REW 6
q
q
q
Outcome:
Right for
Wrong Reasons
Wrong for Right
Reasons
History:
Mathematical
Lumping
Process
Understanding
?
Process
Understanding
Future:
In Defense of Hydrologic Reductionism
… an approach to understand the nature of complex things by reducing
them to the interactions of their parts…
…a philosophical position that a complex system is nothing but the sum of
its parts, and that an account of it can be reduced to accounts of individual
constituents …
My Past
Berkely Catchment Science
Symposium 2009
My Past:
In Defense of Reductionism
• Newton was right
• Model failures result from poor characterization of
heterogeneous landscapes leads to
– No emergent properties
• Our community struggles to identify grand, overarching
questions because…there are no grand unknowns
• Hydrology is a local science
The Response
Ciaran Harman, Catchment Science Symposium, EGU 2011
The Response
Ciaran Harman, Catchment Science Symposium, EGU 2011
Catchments Lump Processes
Emergent Behavior
Decades of case studies
have documented the
many ways that water
moves downhill
Recent work has identified many
Physically Lumped Properties
that are manifestations of the
system of states and fluxes
-A physical basis for lumped
parameter modeling
Physically Lumped Properties
(emergent behavior)
• Connectivity
• Thresholds
• Residence Time
600
Total Precipitation
Water Input
400
Evapotranspiration
0.2 7/2
15 cm
8/31 10/30
30 cm
65 cm
Bedrock Flow
12/29 2/27
4/28
6/27 30
20
0.1
10
0
60 7/2
0
Streamflow
8/31
10/30 12/29 2/27
4/28
6/27
8
dissolved solids
40
20
0
5
7/2
8/31
10/30 12/29
2/27
4/28
6/27
(mg/L)
Soil Moisture
0
Bedrock Flow (mm)
200
Streamflow
(liters/min)
• Connectivity
• Thresholds
• Residence Time
Depth (mm)
Physically Lumped Properties
Physically Lumped Properties
• Connectivity
• Thresholds
• Residence Time
Modified from Mukesh Kumar
Lumped Model
Q(t )  f ( P(t ), A, C )
Distributed Model,
Semi-Distributed Model,
Conceptual
REW 2
p
Physics based

 .(U )  .( )  Qss
t
REW 3
REW 4
REW 1
REW 5
REW 7
REW 6
q
History:
Future:
q
q
Mathematical
Lumping
Process
Understanding
?
Process
Understanding
Modified from Mukesh Kumar
Distributed Model,
Physics based
Physically Lumped Model

 .(U )  .( )  Qss
t
Q(t )  f ( P(t ), A, C )
Physically lumped
properties
q
History:
Future:
Mathematical
Lumping
Process
Understanding
Process
Understanding
Physically lumped
properties
How to Apply Process Information to
Improve Prediction
• Retain the computationally efficiency and lumped philosophy of
systems models
• Observe how catchments create physically lumped properties
• Replace mathematical lumping approaches with physically lumped
properties
– Use as validation targets
– Build into new model structures
What do we do with this
awareness?
Connectivity
Thresholds
Residence Time
Lump the lumps
It’s about Storage
P-ET-Q =dS/dt
Storage
Connectivity
Thresholds
Residence Time
A Tale of Two Catchments
Runoff Ratio
% Old Water
Flow (cms) Thaw Depth (cm)
A Natural Storage Experiment
60
Storage Capacity
40
20
0
6
4
2
0
85
13-Jun
3-Jul
23-Jul
12-Aug
75
65
0.4
13-Jun
13-Jul
12-Aug
0.2
0.0
13-Jun
13-Jul
12-Aug
• Storage regulates fluxes
(ET, Recharge,
Streamflow)
• Storage is responsible for
emergent behavior such
as connectivity,
thresholds, and
residence time
% Old Water
• The mechanisms by
which catchments
STORE water ultimately
characterize the
hydrologic SYSTEM
Runoff Ratio
P-ET-Q =dS/dt
Flow (cms) Thaw Depth (cm)
The Case for Storage
60
Storage Capacity
40
20
0
6
4
2
0
85
13-Jun
3-Jul
23-Jul
12-Aug
75
65
0.4
13-Jun
13-Jul
12-Aug
0.2
0.0
13-Jun
13-Jul
12-Aug
• We should concern
ourselves with how
catchments Retain
Water in addition to
how they release
water
% Old Water
• We should focus on
Runoff Prevention
mechanisms in
addition to runoff
generation
mechanisms
Runoff Ratio
P-ET-Q =dS/dt
Flow (cms) Thaw Depth (cm)
A Natural Storage Experiment
60
Storage Capacity
40
20
0
6
4
2
0
85
13-Jun
3-Jul
23-Jul
12-Aug
75
65
0.4
13-Jun
13-Jul
12-Aug
0.2
0.0
13-Jun
13-Jul
12-Aug
The Storage Problem
• Storage is not commonly measured
• Storage is often estimated as the residual
of a water balance
• Storage is treated as a secondary model
calibration target
CUAHSI Catchment Comparison
Exercise
Girnock, Scotland, Rain, humid
Dry Creek, Idaho, USA
Snowy, semi-arid,
ephemeral
Panola, Georgia, USA
Rain, humid, perennial
Reynolds Creek, Idaho, USA
Snowy, semi-arid, perennial
Gårdsjön, Sweden,
Snow, ephemeral
Storage Zones
Snow
Vegetation
Surface
Soils
Bedrock
S
t
Storage Time Series by Direct
Measurement
Main and Seep Channels
Soil Moisture Sample Locations
Weir
Weather Station
Precipitation Gage
52 51 50
North
55 45
46
47
44 43 42
54
1654
56
30
1646
29
1638
31
32
28 27 26
48
250
41 40 39 38
33 34
25
35
36
37
Treeline Study Site
24
22a
23
1630
16 17
18
11 10 9
1606
20
8
12 13
1590
snow
21
7
6
1598
Meters
200
22b
19
1614
15 5
3
4
2
1
14
Boise
0
50
100
150
soil moisture
Dry Creek Experimental Watershed
200
Meters
Stored Water (mm)
58 57
1622
Total
150
100
50
0
10/1
11/30
1/29
3/29
2003-2004
5/28
7/27
9/25
Storage-Discharge
Signature of geology?
Storage (mm)
10000
Dry Creek
Gårdsjön
Girnock
Reynolds
Panola
1000
S = 786.Q0.32
S = 253Q0.11
S = 251Q0.05
S = 219Q0.06
100
S = 87Q0.05
10
0.0
0.1
1.0
10.0
100.0
Streamflow (mm)
McNamara et al., 2011
Storage-Discharge
Storage (mm)
10000
Similar dynamic range?
Dry Creek
Gårdsjön
Girnock
Reynolds
Panola
1000
S = 786.Q0.32
S = 253Q0.11
S = 251Q0.05
S = 219Q0.06
100
S = 87Q0.05
10
0.0
0.1
1.0
10.0
100.0
Streamflow (mm)
McNamara et al., 2011
Relative Storage-Discharge
1.2
Relative Storage S/Smax
1
0.8
0.6
0.4
Dry Creek
Gardsjon
Girnock
Reynolds
Panola
0.2
0
0.0
2.0
4.0
6.0
8.0
10.0
Streamflow (mm)
12.0
14.0
16.0
McNamara et al., 2011
Relative Storage-Discharge
1.2
Relative Storage S/Smax
1
Course soils drain rapidly
No deep groundwater
Active storage uses limited range
0.8
0.6
0.4
Dry Creek
0.2
0
0.0
2.0
4.0
6.0
8.0
10.0
Streamflow (mm)
12.0
14.0
16.0
McNamara et al., 2011
Relative Storage-Discharge
1.2
Swedish catchment uses larger range at a
wetter state
Relative Storage S/Smax
1
0.8
0.6
0.4
Dry Creek
Gardsjon
0.2
0
0.0
2.0
4.0
6.0
8.0
10.0
Streamflow (mm)
12.0
14.0
16.0
McNamara et al., 2011
Relative Storage-Discharge
1.2
Southeast US
Highly seasonal
Connected to deep groundwater
Uses large range of storage
Relative Storage S/Smax
1
0.8
0.6
0.4
Dry Creek
Gardsjon
Panola
0.2
0
0.0
2.0
4.0
6.0
8.0
10.0
Streamflow (mm)
12.0
14.0
16.0
McNamara et al., 2011
Relative Storage-Discharge
1.2
Relative Storage S/Smax
1
0.8
0.6
0.4
Dry Creek
Gardsjon
Girnock
Reynolds
Panola
0.2
0
0.0
2.0
4.0
6.0
8.0
10.0
Streamflow (mm)
12.0
14.0
16.0
McNamara et al., 2011
Improved storage characterization
will lead to improved prediction
Reynolds Creek
Dry Creek
Precipitation
Boise Front annual precipitation 1999-2009
1200
precipitation (mm)
1100
1000
900
2000
2002
2004
2006
2008
2001
2003
2005
2007
2009
800
700
600
500
400
300
200
100
800
1000
1200
1400
1600
elevation (m)
1800
2000
Precipitation
(mm)
precipitation
precipitation
(mm)(mm)
200
150
963 mm
77% Snow
100
50
0
october
january
april
200
july
335 mm
32% Snow
Rain
150
Snow
100
50
0
october
january
april
2008 Water Year
july
Distributed Soil Moisture
Measurements - Aspect
Moisture and Aspect
Volumetric Moisture Content
0.30
0.20
0.10
0.00
S O N D
J
F M A M J
J
A
S O
S O N D
J
F M A M J
J
A
S O
0.30 S O N D
0.20
0.10
0.00
J
F M A M J
J
A
S O
S O N D
J
F M A M J
J
A
S O
0.30
0.20
0.10
0.00
0.30
0.20
0.10
0.00
2008 Water Year
Smith et al., in review
Soils properties vary with aspect
140
South aspect
Soil Depth (cm)
North aspect
120
100
80
60
40
20
0
0
Smith, T., in progress, MS Thesis
1
2
3
Smith et al., in review
• North facing aspects retain more water
than south facing aspects
Both Aspects
1000
900
800
Tension (cm)
700
600
500
400
300
200
100
0
0
0.2
0.4
0.6
3
3
Volumetric Water Content (cm /cm )
Geroy et al., in review
Soil Moisture Storage (mm)
More Storage on North aspects
Except at high elevation
300
S=(soil depth)(moisture content)
200
-Higher moisture content
100
-Higher moisture retention
0
-Deeper soils
300 7/ 7/ 8/ 9/ 10 11 12 1/ 2/ 3/ 4/ 5/ 6/ 7/ 8/ 9/
-Finer grained soils
200 1 31 30 29 /2 /2 /2 27 26 28 27 27 26 26 25 24
-Lower insolation
100
9 8 8
0
7/ 7/ 8/ 9/ 10 11 12 1/ 2/ 3/ 4/ 5/ 6/ 7/ 8/ 9/
1 31 30 29 /2 /2 /2 27 26 28 27 27 26 26 25 24
9 8 8
300
200
100
0
July Sep
1-Jul
30-
Nov
29-
Jan
28- Mar
26-
May
27- Jul
26-
Sep
25-
Aspect-Insolation-Soil Carbon
• Soil organic carbon
content increases with
aspect and elevation
S
N
S
N
S
Up
Hill
S
Kunkel et al., in review
Geomorphology and Aspect
North facing slopes are steeper
and shorter
N (ish)
Poulos et al., in review
Storage Capacity
• Rooted in the co-evolution of landscape form
and hydrologic processes
Both Aspects
1000
900
800
Tension (cm)
700
600
500
400
300
200
100
0
0
0.2
0.4
0.6
3
3
Volumetric Water Content (cm /cm )
• Responsible for catchment-scale emergent
behavior – Physical Lumped Properties
– Connectivity, Thresholds, Residence time
Our Modeling Experience
• Soil Water Assessment Tool (SWAT)
Hydrograph “Right”
Storage Wrong
3.5
250
SWAT Soil Moisture
Observed
Average Soil Moisture BFU and BFL
Date
Oct-07
Jul-07
Apr-07
Oct-06
Jul-06
0
Apr-06
Jan-05
Oct-04
Jul-04
Apr-04
Jan-04
Oct-03
Jul-03
Apr-03
Jan-03
Oct-02
Jul-02
Apr-02
0.0
50
Jan-06
0.5
100
Oct-05
1.0
Jul-05
1.5
150
Apr-05
2.0
Jan-02
Flow (m^3/s)
2.5
200
Jan-05
Soil Moisture of Soil Colmn (mm)
Predicted
Jan-07
3.0
Date
Stratton et al., 2009
VERY Physically-Based 1D
Kelleners et al., 2010
VERY Physically-Based 1D
• Simulates Snow accumulation, melt, infiltration, and Bedrock
infiltration with “NO” shortcuts
– Over 70 equations just for 1 dimension
• NOT PRACTICAL
• Allows us to determine the relative importance of physical controls
•
•
•
•
•
•
•
Wavelength-dependent solar radiation
Iterative canopy energy balance => Tleaf
Iterative surface energy balance => Tsurface
Snow water flow
Soil water flow
Snow-soil-bedrock heat transport
Snow-soil water phase change
Kelleners et al., 2010
0.4
50
measured
calculated
5 cm
0.2
0.1
0
Jun-03 Oct-03 Jan-04 Apr-04 Aug-04 Nov-04
soil temperature (Celsius)
0.3
measured
calculated
40
5 cm
30
20
10
0
-10
Jun-03 Oct-03 Jan-04 Apr-04 Aug-04 Nov-04
0.4
50
60 cm
0.3
0.2
0.1
0
Jun-03 Oct-03 Jan-04 Apr-04 Aug-04 Nov-04
Root Mean Square Error: 20-38 %
Modeling Efficiency: 0.65-0.86
soil temperature (Celsius)
volumetric soil water content
volumetric soil water content
VERY Physically-Based 1D
40
60 cm
30
20
10
0
-10
Jun-03 Oct-03 Jan-04 Apr-04 Aug-04 Nov-04
Root Mean Square Error: 11-28 %
Modeling Efficiency: 0.88-0.95
Very Physically Based – 3D
Kelleners et al., 2010
Very Physically Based – 3D
• Catchment is divided into
141 grid cells (1010 m)
s u r fa
ce ru
n of f
vertical soil water flow
perched watertable
soil depth
H
bedrock
lateral
subsurf
ace flo
w
qdp
*
   j  Qstreami
 Qstreami    j   *   i 
2
2
i*
q dp
Kelleners et al., 2010
H D
 k sr
D

Very Physically Based – 3D
• Decent simulation of soil moisture, unsatisfactory
simulation of streamflow
– Wrong for the right reasons
Distributed Hydrology Soil Vegetation Model
(DHSVM)
Evaluate the impact of “improved” soil depth
information on streamflow and soil moisture
simulations
SSURGO Soil Depth
Modeled Soil Depth
Soil Depth: Field Data
Soil depth measurement
- 2.2 m rod
- 1.27 cm diameter
- Pounded to refusal
- 2 or 3 repeats
819 points (calibration)
- 8 subwatersheds
- 130 random points (testing)
- During Spring when soil was moist
Fence Post Pounder
Copper Coated Steel Rod
52
Predictor Variables
Symbol
Description
sca
Specific catchment area from the D method. This is contributing area divided by the
grid cell size
modcurv
Curvature modeled based on field observed curvature.
ang
The D flow direction: the direction of the steepest outwards slope reported as the angle
in radians counter-clockwise from east
avr
Average D vertical rise to ridge
lspv
Longest vertical slope position
lvs
Longest D vertical drop to stream
slpg
Magnitude of topographic slope computed using finite differences on a 3x3 grid cell
window
sd8a
Slope averaged over a 100 m path traced downslope along D8 flow directions
elv
Elevation above sea level
plncurv
Plan curvature: the curvature of the surface perpendicular to the direction of the
maximum slope
pc1
First principal component from ERDAS IMAGINE
Newly derived variables
Land cover variable
53
Measured vs Modeled Soil Depth
Testing
Training and Testing
NSE = 0.58
95% Confidence interval
NSE = 0.47
1:1
Tesfa et al., 2009
54
Predicted Soil Depth Map
Soil Depth Map of Dry Creek Experimental Watershed
Soil Depth (cm)
Value
High : 374.366
Contour
Low : 16.7556
DHSVM
4
Recorded and Simulated stream flow (2002-2003)
Recorded
MODSD Simulated
SUSD Simulated
1
2
Calibration to streamflow
obliterates effect of soil
information
0
Stream flow (m3/s)
3
Insignificant difference with
improved soil depth
information
Oct
Dec
Feb
Apr
Jun
Aug
Oct
Months
Dec
Feb
Apr
Jun
Aug
Oct
Soil Capacitance Model (Reynolds Creek)
Snow Water Input (ISNOBAL)
SWI
Get the inputs right (accumulation, STORAGE,and
ablation of snow)
Get the 1D soil water storage right
Ignore all lateral movement
No calibration to streamflow
See what happens
Throughflow
Seyfried et al., 2009, Hydrological Processes
Soil Capacitance Model (Reynolds Creek)
SWI
• Throughflow occurs when soil column water
holding capacity is exceeded
• Soil water storage parameterized by field
capacity, plant extraction limit, soil depth
S
i  numlayer
 T
i 1
i i
S FC 
i  numlayer

i 1
T
fci i
0.3
Throughflow
Soil Moisture
Ө0.2
fc
0.2
65 cm
0.1
Өpel
15 cm
0.1
30 cm
0
0
7/2
Seyfried et al., 2009, Hydrological Processes
8/31 10/30 12/29 2/27 4/28 6/27
Good 1D Performance
Distributed Model
Distributed energy balance forcing
Distributed soil properties by similarity classes
No lateral flow simulated
Simulated storage excess agrees with
streamflow
Connectivity Index
SN 
S  S PEL
S FC  S PEL
How do we Apply Process
Understanding to Improve Prediction?
• Revisit the lumped philosophy of systems models
• Recognize catchments create physically lumped properties
• Replace mathematical lumping approaches with physically lumped
properties
– Use as validation targets
– Build into new model structures
• The mechanisms by which catchments STORE water characterize
the catchment system
• We should concern ourselves with how catchments Retain Water in
addition to how they release water
– Get storage right, and everything else will work out
How do we Apply Process
Understanding to Improve Prediction?
• …ecohydrology should synthesize Newtonian and
Darwinian approaches to science…combining
Newtonian principles of simplification, ideal systems, and
predictive understanding (often, but not solely embraced
by hydrologists) with Darwinian principles of complexity,
contingency, and interdependence (often, but not solely
embraced by ecologists)…offers the potential for
profound and more rapid advances in our understanding
of environmental process…
Brent Newmann
However…
• …ecohydrology should synthesize Newtonian and
Darwinian approaches to science…combining
Newtonian principles of simplification, ideal systems, and
predictive understanding (often, but not solely embraced
by hydrologists) with Darwinian principles of complexity,
contingency, and interdependence (often, but not solely
embraced by ecologists)…offers the potential for
profound and more rapid advances in our understanding
of environmental process…
Brent Newmann
How do we compare catchments?
• M. Robinson (1992)
– 20 papers from
western and central
Europe
– Key Conclusion:
Intercomparison is
difficult
How do we compare basins?
• Jones and Swanson (2001)
– A basin’s streamflow may be predicted by
characterizing basin storage capacities in
vegetation, soil, and snow…
How do we compare basins?
• McDonnell and Woods (2004)
– Governing principles are known
• Heterogeneity rules the day
– Possible classification metrics include
• Response time of dominant storage
How do we compare basins?
• Wagener et al. (2007)
• Classification is a rigorous scientific
inquiry into the causes of similarities and
relationships between catchments.
How do we compare basins?
• Wagener et al. (2007)
Runoff generation
commonly studied
How do we compare basins?
• Wagener et al. (2007)
Storage
uncommonly
studied
How do we compare basins?
• Landscape structure moderates transit
times
How to Apply Process Information to
Improve Prediction
• Recognize that the existence of true physically-based models is a myth
• Identify physically lumped properties
• Build conceptual models based on the ways catchments lump
properties, not mathematical
– Systems approaches using “essential” parameters
How to Apply Process Information to
Improve Prediction?
• Recognize that the existence of true physically-based models is a myth
• Identify hydrologically relevant processes or properties for
hydrogeographic regions
– Classification
• Build models that target relevant hydrologic processes or properties
– Systems approaches using “essential” parameters