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 [email protected] 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
Top Related