Project: NSF grant EAR-0724958 “CZO: Transformative Behavior of Water, Energy and Carbon in the Critical Zone: An Observatory to Quantify Linkages among Ecohydrology, Biogeochemistry, and Landscape Evolution” (PIs: J. Chorover and P.A. Troch). Many thanks to Ty Ferré for providing us with the Hydrus software. Please direct further questions about this poster to Ingo Heidbüchel at ingohei@hwr.arizona.edu or visit our website at www.hwr.arizona.edu/~surface.

Tracking of Varying Mean Transit Time Modeling Results

Application to Transit Time Modeling

Acknowledgements

Ingo Heidbüchel1, Peter A. Troch1

1Department of Hydrology and Water Resources, University of Arizona, Tucson, Arizona 85721, USA

What Controls the Shape of Transit Time Distributions?

• Hydrologic catchment response is difficult to capture because it can be extremely variable in space and time

Question / Problem Potential Controls

• Modeling transit times with a transfer function – convolution model relies on certain assumptions that are not always met

• The most common assumption is that transfer functions are time-invariant

• There have been attempts to let the scale parameter vary in time• This is an attempt to explore how shape parameters vary in time

Snowmelt: Storage increasing

Hydrologic response fast

Flowpaths slow / intermediate / fast

Spring: Storage

decreasing

Hydrologic responseintermediate

Flowpathsslow / intermediate

Fall: Storage

decreasing

Hydrologic responseslow

Flowpathsslow

Monsoon: Storage

constant / increasing

Hydrologic responseintermediate / fast

Flowpathsintermediate / fast

Interflow

Overland Flow

Base Flow

Modeling Approach

• We selected four potential controls on transit time distribution shapes:• Soil depth Dsoil

• Antecedent moisture content θant

• Soil saturated hydraulic conductivity Ks

• Subsequent precipitation intensity Psub (10 days after the event)

• In 24 model runs we varied:• Dsoil between 0.5 m and 1 m• θant between 9% and 18%• Ks between 20 mm/day and 2000 mm/day• Psub between 0.005 mm/day and 50 mm/day

• We compared the resulting modeled transit time distributions to three different types of distributions:• Exponential – Piston Flow Model EPF• Gamma Model GAM• Advection – Dispersion Model ADM

Potential Transit Time Distributions

• Drier conditions = sharper peaks for high and medium intensity Psub

• Wet conditions = sharper peaks for low intensity Psub

• GAM functions are most common

• ADM functions occur when high intensity Psub meets high Ks

Conclusion• The SFTN helps to pursue a more realistic modeling approach

• removes some of the uncertainty connected to shape-scale equifinality in transfer function-convolution modeling

• More modeling and testing to follow!

• To identify the thresholds that cause the switch between transfer function types we propose a

• Dimensionless number that combines information on the potential response controls storage, forcing and transport (SFT-Number):

Soil Layer

Bedrock Layer

Seepage Face

Free Drainage

200 m

40 m

Recharge

45 m

HYDRUS3-D Hillslope

High Intensity

Psub

0.12

0.1

0.08

0.06

0.04

0.02

0

0 20 40 60 80 100

Pro

bab

ility

Den

sity

ADM 4.0

ADM 1.4

ADM 1.2

GAM 1.0

GAM 2.2

Shallow Dry HighKs

Deep Dry HighKs

Shallow Wet HighKs

Deep Wet HighKs

Deep Wet LowKs

MEAN

0.06

0.05

0.04

0.03

0.02

0.01

0

0 20 40 60 80 100Time

Pro

bab

ility

Den

sity

EPF 1.1

GAM 0.5

ADM 0.5

EPF 1.25

GAM 1

ADM 1

EPF 1.5

GAM 2

ADM 2

Medium Intensity

Psub

0.06

0.05

0.04

0.03

0.02

0.01

0

0 20 40 60 80 100

Pro

bab

ility

Den

sity

ADM 1.4

GAM 0.95

GAM 1.0

GAM 2.3

GAM 2.4

Shallow Dry HighKs

Deep Dry HighKs

Shallow/Deep Wet HighKs

Shallow Wet LowKs

Deep Wet LowKs

Transit Time

• Higher Psub intensities = sharper peaks• Shallower soils = sharper peaks• Low Ks = flatter distributions (gamma shape parameter > 2)

Dsoil θant Ks Psub

𝑆𝐹𝑇𝑁=𝐷𝑠𝑜𝑖𝑙∗(𝑛−𝜃𝑎𝑛𝑡)𝑃𝑠𝑢𝑏−(𝐾 𝑠/100)

• SFTN < 1: ADM distributions 1 < shape parameter < 4• SFTN > 10: GAM distributions 1 < shape parameter < 2• SFTN > 100: GAM distributions 2 < shape parameter

• The SFTN can be determined for every time step before the transfer function-convolution model is run

• The resulting transfer functions can then be used as transit time distributions that change shapes in time

δout(t) = ∫δin (t-τ) * Vin (t-τ) * TTDv(τ)dτ

∫Vout (t-τ) * HRFv(τ)dτ

Low Intensity

Psub

0 20 40 60 80 100

GAM 0.8

GAM 0.95

ADM 6500

GAM 1.9

GAM 2.2

GAM 2.4

Shallow Wet HighKs

Shallow Wet LowKs

Deep Dry/Wet LowKs

Shallow Dry LowKs

Shallow/Deep Dry HighKs

Transit Time

Deep Wet HighKs