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