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– See papers by
• Western and Grayson• McGlynn• McNamara• Stieglitz• Pringle• April James
– Talk by McNamara• http://a-c-s.confex.com/crops/2010am/webprogram/Paper61589.html
Physically Lumped Properties
• Thresholds– See papers by
• McNamara• McGuire• McDonnell• Many others
0
200
400
600
7/2 8/31 10/30 12/29 2/27 4/28 6/27
Dept
h (m
m)
Total PrecipitationWater InputEvapotranspiration
0
0.1
0.2
7/2 8/31 10/30 12/29 2/27 4/28 6/27
Soil
Moi
stur
e
0
10
20
30
Bedr
ock
Flow
(mm
)
15 cm30 cm65 cmBedrock Flow
0
20
40
60
7/2 8/31 10/30 12/29 2/27 4/28 6/27
Stre
amflo
w
(lite
rs/m
in)
5
8
(mg/
L)
Streamflow
dissolved solids
Threshold responses
0
1
0 10 20 30 40 50Moisture content (%)
Runo
ff ra
tioSatelliteTarrawarra
Courtesy of Roger GraysonRoger Grayson, pers. Com.
Physically Lumped Properties
• Residence Time– See papers by
• Tetzlaff, Soulsby• McGuire• McDonnell
Figure from Jim Kirchner
)(tCin
)(tCout
This approachsimplified
Model Theory: The Convolution Integral
Input Function:Derived from precipitation d18O signal Represents d18O in water that contributes to recharge
System Response Function:Time distribution of water flow paths
Predicted or simulated output d18O signature
t
in dtgt dd )()()(
Soil water residence time
2 4 1 0 5 5 0 2 4 1 0 6 0 0 2 4 1 0 6 5 0 2 4 1 0 7 0 0 2 4 1 0 7 5 0 2 4 1 0 8 0 0
5 9 0 1 8 5 0
5 9 0 1 9 0 0
5 9 0 1 9 5 0
5 9 0 2 0 0 0
5 9 0 2 0 5 0
5 9 0 2 1 0 0
2 .0
4 .0
6 .0
8 .0
1 0 .0
1 2 .0
1 4 .0
1 6 .0
N ea r S tre a m
P it 5
P it A
T e n s io m e te r N e tw o rk
ln (a /ta n)
R a in g au g e
Annual DataP 2250 mmQ 1350 mmE 850 mm
Average DataSlope 34o
Relief 100-150mKsat 5 m/hr
Soils DataDepth 1 mStrong catenary sequence
Soil water Residence
Time
-4
-8
-12
-16
d18O
‰ -4
-8
-12
-16
d18O
‰
Soil WaterPrecipitation
Average -9.4‰Amplitude 0.1‰Std Dev. 3.4 ‰
Average -9.4‰Amplitude 1.2‰Std Dev. 0.6 ‰
If bedrock quite impermeableMRT and distance from the divide
2 4 10 5 5 0 24 1 0 6 0 0 2 41 0 6 5 0 2 4 10 7 0 0 2 4 10 7 5 0 2 4 10 8 0 0
59 0 1 8 5 0
59 0 1 9 0 0
59 0 1 9 5 0
59 0 2 0 0 0
59 0 2 0 5 0
59 0 2 1 0 0
2.0
4.0
6.0
8.0
10 .0
12 .0
14 .0
16 .0
N ea r S tre am
P it 5
P it A
T en s io m e te r N e tw o rk
ln (a / ta n )
R a in g au g e
0
40
80
120
160
0 10 20 30 40 50 60 70 80
Distance from divide (m)
Mea
n R
esid
ence
tim
e (d
ays)
MRT = 1.9(Distance) + 19.0r 2̂ = 0.88
Vache and McD WRR 2005
Storage in Hydrologic Modeling
• Review – Classic linear and non-linear reservoir modeling– Semenova model– Kirchner model