What’s the Diel with this Signal?

Jason AlbrightNathaniel GustafsonMichaeline Nelson

Bianca Rodríguez-CardonaChris Shughrue

Funded by NSF and DODAward Number 1005175

Diel Fluctuations in stream heightW

ater

Hei

ght (

m)

8 9 10 11 12 13

Days in July, 2010

Which Areas Contribute?

Evapotranspiration

Solar Radiation Air Temp VPD

Q Soil Moisture Sap Flow

Volume from S.G.• Q = P – ET + ∆S

Significance

• Use discharge to approximate ET• Interesting eco-informatics question because

looks at watershed as a complete system

Eco-informatics conceptual model

Empirical Model

Observed Diel

Analytical Model

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?

Watershed 1

• 95.9ha area• Clear cut in the 60’s– Red Alder

• Most steam reaches are alluvial deposits

Watershed 2

• 60.3ha area• Old Growth – Western Hemlock and

Douglas Fir

• Channel mostly bedrock

What factors are principally responsible for creating diel signals?

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

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

Diel signals

Overview of a year

Summertime

~.05cfs

Temperature vs. Solar Radiation

What we’re seeing

• Diel signal ≈ Solar Radiation– Conditional: WS has enough ground-water

Another fun metric

Another fun metric

http://farm4.static.flickr.com/3407/4617034064_e46e675a86.jpg

WS1

Mack Creek

Early summer signal?

Discharge spike with that signal?

Snowmelt!

Temp helpful

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

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

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

How are ET induced signals affected by base-flow levels and watershed characteristics?

Watershed 1: July 1 -July 7, 2000 - 2009

Watershed 1: 2009

Watershed 10: 2009 Watershed 9: 2009

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.

Are diel fluctuations synchronized across a watershed?

• Cap. Rod graph

Data provided by Tom Voltz

8 9 10 11 12 13

Days in July, 2010

Are diel fluctuations synchronized across a watershed?

Yes: staff gage, capacitance rod, wells and stream in phase

Does channel morphology influence diel fluctuations?

Staff Gages in WS2

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

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

Does channel morphology influence diel fluctuations?

Yes: signal in alluvial reaches is stronger than bedrock reaches

What are the mechanisms for the influence of ET on diel fluctuations?

A Mathematical Model for Stream Bank Outflow

Equations Modeling Saturated Flow:

€

∂2h

∂x 2+∂ 2h

∂z2=

−ζ

k

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:

Equations Modeling Saturated Flow:

kz

h

x

h

kz

h

x

h

min2

2

2

2

max2

2

2

2

h(0,zH) Hh(x,z) zh(x,Z) Zhx

(X,z) 0

hz

(x,0) 0

Boundary Conditions:

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

∫ ) ⎤

⎦ ⎥

Piezometric Distribution:

Applications:

QQmax Qmin

Q2ql

Model Outputs:

Physical Data:

QQmax Qmin

hkq )(

Water Table Geometry and Discharge:

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?

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

Methods: Channel Classification

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

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

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

Methods: Observed Water Loss

Results

Results

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

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.

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

Thank youJulia, Jorge, Desiree and Travis