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What’s the Diel with this Signal?
Jason AlbrightNathaniel GustafsonMichaeline Nelson
Bianca Rodríguez-CardonaChris Shughrue
Funded by NSF and DODAward Number 1005175
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Diel Fluctuations in stream heightW
ater
Hei
ght (
m)
8 9 10 11 12 13
Days in July, 2010
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Which Areas Contribute?
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Evapotranspiration
Solar Radiation Air Temp VPD
Q Soil Moisture Sap Flow
![Page 5: What’s the Diel with this Signal? Jason Albright Nathaniel Gustafson Michaeline Nelson Bianca Rodríguez-Cardona Chris Shughrue Funded by NSF and DOD Award](https://reader035.vdocument.in/reader035/viewer/2022062423/56649e425503460f94b3587f/html5/thumbnails/5.jpg)
Volume from S.G.• Q = P – ET + ∆S
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Significance
• Use discharge to approximate ET• Interesting eco-informatics question because
looks at watershed as a complete system
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Eco-informatics conceptual model
Empirical Model
Observed Diel
Analytical Model
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Questions
• What factors are principally responsible for creating diel signals?
• How are ET induced signals affected by base-flow levels and watershed characteristics?
• Are diel fluctuations synchronized across a watershed?
• Does channel morphology influence diel fluctuations?
• What are the mechanisms for the influence of ET on diel fluctuations?
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Watershed 1
• 95.9ha area• Clear cut in the 60’s– Red Alder
• Most steam reaches are alluvial deposits
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Watershed 2
• 60.3ha area• Old Growth – Western Hemlock and
Douglas Fir
• Channel mostly bedrock
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What factors are principally responsible for creating diel signals?
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What we have to work with
• Abundant data available through HJ Andrews• Lots of collaboration, local knowledge
• Personally ‘familiar’ with 2-3 watersheds
WS Max signal amplitude
1 0.055 cfs
2 0.005 cfs
10 0.005 cfs
9 0.003 cfs
8 0.001 cfs
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Data
slope
Parameters
Process
soil type
Diel strength*
Solar Radia’n
Drainage parameters
Effective Riparian area** WS ground-
water content
*Diel Strength = amplitude of diel signal in cfs** (Riparian) area contributing to diel signal, m2
Stream network length
Snow-melt
(mm/day)
Evapo-Transpiration
(mm/day)
Estimated
WS Snow content
Measured
Temporal WS property
Air temp
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Diel signals
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Overview of a year
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Summertime
~.05cfs
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Temperature vs. Solar Radiation
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What we’re seeing
• Diel signal ≈ Solar Radiation– Conditional: WS has enough ground-water
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Another fun metric
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Another fun metric
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http://farm4.static.flickr.com/3407/4617034064_e46e675a86.jpg
WS1
Mack Creek
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Early summer signal?
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Discharge spike with that signal?
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Snowmelt!
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Temp helpful
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What we’re seeing
• Diel signal ≈ Sol.Rad. via ET in summer– Conditional: WS has enough ground-water
• Temperature -> Snowmelt signals in spring– IF snow is present and melting
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What we’re seeing
• Diel signal ≈ Sol.Rad. via ET in summer– Conditional: WS has enough ground-water
• Temperature -> Snowmelt signals in spring– IF snow is present and melting
• Watersheds may have neither, one, or both
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Data
slope
Parameters
Process
soil type
Diel strength*
Solar Radia’n
Drainage parameters
Effective Riparian area** WS ground-
water content
*Diel Strength = amplitude of diel signal in cfs** (Riparian) area contributing to diel signal, m2
Stream network length
Snow-melt
(mm/day)
Evapo-Transpiration
(mm/day)
Estimated
WS Snow content
Measured
Temporal WS property
Air temp
![Page 29: What’s the Diel with this Signal? Jason Albright Nathaniel Gustafson Michaeline Nelson Bianca Rodríguez-Cardona Chris Shughrue Funded by NSF and DOD Award](https://reader035.vdocument.in/reader035/viewer/2022062423/56649e425503460f94b3587f/html5/thumbnails/29.jpg)
How are ET induced signals affected by base-flow levels and watershed characteristics?
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Watershed 1: July 1 -July 7, 2000 - 2009
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Watershed 1: 2009
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Watershed 10: 2009 Watershed 9: 2009
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How are ET induced signals affected by base-flow levels and watershed characteristics?
1. WS1, WS9, and WS10 show signals that correlate with air temperature, while WS2, WS3, WS6, WS7 and WS8 signals don’t correlate
2. WS1 phase shifts are correlated to precipitation and height of base flow.
3. WS1 time lags behave different from WS9 and WS10.
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Are diel fluctuations synchronized across a watershed?
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• Cap. Rod graph
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Data provided by Tom Voltz
8 9 10 11 12 13
Days in July, 2010
![Page 41: What’s the Diel with this Signal? Jason Albright Nathaniel Gustafson Michaeline Nelson Bianca Rodríguez-Cardona Chris Shughrue Funded by NSF and DOD Award](https://reader035.vdocument.in/reader035/viewer/2022062423/56649e425503460f94b3587f/html5/thumbnails/41.jpg)
Are diel fluctuations synchronized across a watershed?
Yes: staff gage, capacitance rod, wells and stream in phase
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Does channel morphology influence diel fluctuations?
![Page 43: What’s the Diel with this Signal? Jason Albright Nathaniel Gustafson Michaeline Nelson Bianca Rodríguez-Cardona Chris Shughrue Funded by NSF and DOD Award](https://reader035.vdocument.in/reader035/viewer/2022062423/56649e425503460f94b3587f/html5/thumbnails/43.jpg)
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Staff Gages in WS2
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Bedrock channel staff gage (July 7-8, 2010)
Change in Stage Height=
Bedrock channel staff gage (July 14-15, 2010)
0.2- 0.3 cm
![Page 46: What’s the Diel with this Signal? Jason Albright Nathaniel Gustafson Michaeline Nelson Bianca Rodríguez-Cardona Chris Shughrue Funded by NSF and DOD Award](https://reader035.vdocument.in/reader035/viewer/2022062423/56649e425503460f94b3587f/html5/thumbnails/46.jpg)
Change in Stage Height=
Alluvial channel staff gage (July 7-8, 2010) Alluvial channel staff gage (July 14-15, 2010)
0.6 - 3.5 cm
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Does channel morphology influence diel fluctuations?
Yes: signal in alluvial reaches is stronger than bedrock reaches
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What are the mechanisms for the influence of ET on diel fluctuations?
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A Mathematical Model for Stream Bank Outflow
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Equations Modeling Saturated Flow:
€
∂2h
∂x 2+∂ 2h
∂z2=
−ζ
k
![Page 53: What’s the Diel with this Signal? Jason Albright Nathaniel Gustafson Michaeline Nelson Bianca Rodríguez-Cardona Chris Shughrue Funded by NSF and DOD Award](https://reader035.vdocument.in/reader035/viewer/2022062423/56649e425503460f94b3587f/html5/thumbnails/53.jpg)
Darcy’s Law:
q k h
Conservation of Mass:
q
khhk 2
Combining Darcy’s Law and Conservation of mass:
h(x,z) z pw (x,z)
g
Piezometric Head:
![Page 54: What’s the Diel with this Signal? Jason Albright Nathaniel Gustafson Michaeline Nelson Bianca Rodríguez-Cardona Chris Shughrue Funded by NSF and DOD Award](https://reader035.vdocument.in/reader035/viewer/2022062423/56649e425503460f94b3587f/html5/thumbnails/54.jpg)
Equations Modeling Saturated Flow:
kz
h
x
h
kz
h
x
h
min2
2
2
2
max2
2
2
2
![Page 55: What’s the Diel with this Signal? Jason Albright Nathaniel Gustafson Michaeline Nelson Bianca Rodríguez-Cardona Chris Shughrue Funded by NSF and DOD Award](https://reader035.vdocument.in/reader035/viewer/2022062423/56649e425503460f94b3587f/html5/thumbnails/55.jpg)
h(0,zH) Hh(x,z) zh(x,Z) Zhx
(X,z) 0
hz
(x,0) 0
Boundary Conditions:
![Page 56: What’s the Diel with this Signal? Jason Albright Nathaniel Gustafson Michaeline Nelson Bianca Rodríguez-Cardona Chris Shughrue Funded by NSF and DOD Award](https://reader035.vdocument.in/reader035/viewer/2022062423/56649e425503460f94b3587f/html5/thumbnails/56.jpg)
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Solution to the Boundary Value Problem:
€
h(x,z) = Z −∂
∂xG(η ,θ )
0
Z
∫ (0,z − Z) ⋅h(0,z − Z)dz ⎡
⎣ ⎢
−ζ
k⋅G(η ,θ )(x,z − Z)dxdz
0
X
∫0
Z
∫ ) ⎤
⎦ ⎥
![Page 58: What’s the Diel with this Signal? Jason Albright Nathaniel Gustafson Michaeline Nelson Bianca Rodríguez-Cardona Chris Shughrue Funded by NSF and DOD Award](https://reader035.vdocument.in/reader035/viewer/2022062423/56649e425503460f94b3587f/html5/thumbnails/58.jpg)
Piezometric Distribution:
![Page 59: What’s the Diel with this Signal? Jason Albright Nathaniel Gustafson Michaeline Nelson Bianca Rodríguez-Cardona Chris Shughrue Funded by NSF and DOD Award](https://reader035.vdocument.in/reader035/viewer/2022062423/56649e425503460f94b3587f/html5/thumbnails/59.jpg)
Applications:
QQmax Qmin
Q2ql
Model Outputs:
Physical Data:
QQmax Qmin
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hkq )(
Water Table Geometry and Discharge:
![Page 61: What’s the Diel with this Signal? Jason Albright Nathaniel Gustafson Michaeline Nelson Bianca Rodríguez-Cardona Chris Shughrue Funded by NSF and DOD Award](https://reader035.vdocument.in/reader035/viewer/2022062423/56649e425503460f94b3587f/html5/thumbnails/61.jpg)
Assuming the diel signal is local and additive over channel length, does sap flow in the vegetated alluvial channel account for observed diel fluctuations at the stream gage?
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Diel Signal and Channel Lithology
Objective:• Compare diel signal at stream gage to water
lost to trees growing in the channel:– 1) approximating water loss from different
combinations of channel reaches using LiDAR tree data
– 2) comparing these estimates to observed water loss to transpiration
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Methods: Channel Classification
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Allometric Conversions
• Chapman-Richards function (Richards, 1959)
where:DBH = diameter at breast height (cm)H = tree height (m)b0, b1, b2 = species-specific coefficient (Garman, 1995)
DBH ln 1 H 1.37
b0 1b2
b1
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Allometric Conversions• Douglas Fir Sapwood Area (Turner, 2000)
Where:SW = sapwood widthDBHib = DBH(1- 0.11)
SBA = sapwood area (m2)c, d = species-specific coefficients
SBA DBH ib
2
2
DBH ib
2 SW
2
SW c 1 e dDBH
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Allometric Conversions
• Red Alder– Used liner relationship derived from data in
Moore, 2004
• For both species:– Volume of water per tree per day = SBA x Sap flux
density– Sum volumes for trees in combinations of reaches
SBA 0.302443DBH - 0.03433
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Methods: Observed Water Loss
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Results
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Results
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Interpretation
• Overestimation implies too many trees are being included– Low flow zones upstream?
• Best approximations exclude bedrock channels and include all alluvial channels
• Solely vegetation in channel is capable of producing the entire diel signal
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Novel Findings
• Solar radiation is correlated to the amplitude of the diel signal.
• Air temperature and discharge time lags depend on watershed and antecedent precipitation.
• Diel signals exist and are in phase up the stream network.
• Alluvial stage height fluctuations are greater than bedrock stage height fluctuations.
• Vegetated alluvial channel area can produce the measured diel fluctuations observed at stream gage.
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References• Barnard, H.R., Graham, C.B., Van Verseveld, W.J., Brooks, J.R., Bond, B.J., and McDonnell, J.J.
2010. Mechanistic assessment of hillslope transpiration controls of diel subsurface flow: a steady-state irrigation approach. Ecohydrology. 3: 133–142
• Bond, B.J., Jones, J.A., Phillips, N., Post, D., and McDonnell, J.J. 2002. The zone of vegetation influence on baseflow revealed by diel patterns of streamflow and vegetation water use in a headwater basin. Hydrol. Process. 16: 1671–1677
• Clark, J. 2007. Models for Ecological Data: An Introduction. Oxford University Press.• Garman, Steven L., Acker, Steven A., Ohmann, Juliet L., Spies, Thomas A. 1995. Asympytotic
Height-Diameter Equations for Twenty-Four Tree Species in Western Oregon. Forest Research Laboratory, Oregon State University. Research Contribution 10
• Moore, G.W., Bond, B.J., Jones, J.A., Phillips, N., and Meinzer, F.C. 2004. Structural and compositional controls on transpiration in 40- and 450-year-old riparian forests in western Oregon, USA. Tree Physiology 24:481–491
• Richards, F.J. 1959. A flexible growth function for empirical use. Journal of Experimental Biology 10:290-300.
• Turner, David P., Acker, Steven A., Means, Joseph E., Garman, Steven L. 1999. Assessing alternative allometric algorithms for estimating leaf area of Douglas-fir trees and stands. Forest Ecology and Management. 126:61-76
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Thank youJulia, Jorge, Desiree and Travis