The Catchment Isoscape:

The Catchment Isoscape:

A Meta-Model for Stable Isotope Tracers at the Shale Hills Critical Zone

Observatory

Christopher Duffy

2007-2013 NSF CZO Program

2013-2016 NSF INSPIRE CREATIV

2013-2017 EPA, Center for Integrated Multi-scale Nutrient Pollution Solutions,

In this paper:

•  Present a theory for “age” and “residence time” of mobile-immobile water flow in

soils and regolith

•  Describe a 5 year experiment for water isotopes at Shale Hills CZO

•  Compare theory and experiment to test for the existence of macropore- matrix flow at Shale Hills

“The Catchment Isoscape”

Advancing interdisciplinary studies of earth surface processes

Chris Duffy, PI 07-12 Sue Brantley

Rudy Slingerland David Eissenstat Henry Lin

Ken Davis Kamini Singha Laura Toran Pat Reed Karen Salvage Eric Kirby Tim White Kevin Dressler Kelly Cherry Doug Miller Brian Bills Beth Boyer Colin Duffy Chris Graham

Jennifer Williams CZEN

The Susquehanna/Shale Hills Critical Zone Observatory

Mukesh Kumar George Holmes Evan Thomas Xuan Yu Yu Zhang Ryan Jones Beth Boyer Lixin Jin

Danielle Andrews

….

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Shale Hills Observations & Experiments to Support

Earth System Models & Prediction

100m

CZO Isotope Network

Predicting the Age of Water at the Watershed Scale

C. Duffy PSU H. Lin, PSU G. Bhatt PSU G. Holmes. PSU E. Thomas, PSU L. Jin, PSU

P. Sullivan PSU

Instrumentation for Iso.Net

Stable Isotope Experiment 2008-20012 δ ^{2 H} − δ ^{18 O}

Precipitation

Tree Xylem Water Stream

Groundwater Soil Moisture

> 6000 Samples

LMWL

Holmes, Thomas, Gaines, Jin, Andrews, Lin, Duffy

Shale Hills Isotope Network

-­‐180   -­‐160   -­‐140   -­‐120   -­‐100   -­‐80   -­‐60   -­‐40   -­‐20   0  

-­‐25   -­‐20   -­‐15   -­‐10   -­‐5   0  

δ 2 H    

δ   ¹⁸ O      

Soil   Moisture  

Soil Moisture – Xylem Water Experiment

δ ^{2 H} − δ ^{18 O}

Tree Xylem Water Tightly bound soil water

Soil Moisture

LMWL

Katie Gaines, Dave Eissenstat

Shale Hills Isotope Network

0

-20

-40

-60

-80

-100

-120

-140

-160

-180

Soil Moisture

Groundwater Streamflow

δ ² H

δ ² H

δ ² H

δ ^{2 H}

A Single Dominant Period: 360 < T < 370 days

Precipitation Streamflow

Soil Moisture Groundwater

Catchment Signature From Time Series

Precipitation

Seasonal Variability over the Soil Profile

Precipitation

Data is fitted to a Meta-Model that Approximates

Seasonal variability Over the profile

δ ^{2 H} δ ^{18 O}

Seasonal Cycle Attenuates over Profile

The Catchment Isoscape & The Age of Water

The term “isoscape ” was coined by ecologists to describe the spatial and temporal patterns of isotope ratios over a landscape (Bowen, 2010 )

The goal is to develop a meta-model for space- time isotopic patterns over the catchment as a step towards predicting:

In this paper we explore an “isoscape” for

water isotopes of in soil and regolith δ ^{2 H} − δ ^{18 O}

“The Distributed Age and Residence Time of

Water Isotopes at the Shale Hills CZO”

Properties of the Age Distribution

µ _o ^{( , ) x t} " ^{C x t ( , )} = ^{c x t ( , , )} ! ^d !

#

$

0

µ ₁ ! " " "

0

( , ) x t # ( , ) x t = c x t ( , , ) d

$

%

A( x, t ) = µ ₁ ^{( x , t )}

µ _o ^{( x , t ) = Mean Age of water}

A Model for Age Distribution

Rotenberg 1972, J, of Theoretical Biology, 37, 291-305

L c D c

x u c

( ) ! " x

" # "

"

2 2

L (c) ⇒ Q _i

V (c _i − c)

DM (t, τ ) 1 or

V = ∂M

∂t + ∂M

∂ τ

⎛ ⎝⎜ ⎞

⎠⎟

1 V

V

+

Transport Model in Terms of Moments +

+

Source terms for the nth moment

Transport operator for the nth moment

Coupling Moment

A Theory for Concentration-Age For Mobile-Immobile Transport

Over the Soil Profile

∂C _m

∂t = D _m ∂ ² C _m

∂z ² − u _m ∂ C _m

∂z − k

θ _m (C _m − C _im )

∂C _im

∂t = k

θ _m (C _m − C _im ) dα _m

dt = C _m + D _m ∂ ² α _m

∂z ² − u _m ∂ α _m

∂z − k

θ _im (α _m − α _im ) dα _im

dt = C _im + k

θ _im (α _m − α _im )

A _m (t ) = α _m (t ) / C _m (t ); A _im (t ) = α _im (t ) / C _im (t )

C _m (0, t ) = C _i (t ); C ' _m (d, t ) = 0; α _m (0, t ) = α _im (0, t ) = α ' _m (d, t ) = 0 C _m (z, 0) = C _im ( z, 0) = 0; α _m ( z , 0) = α _im (z, 0) = 0

z

Simulated Seasonal Input C _i

(scaled)

Simulated Profile C _i

mobile immobile

phase lag

Simulated Isotope Ratio

Simulated Age of

Age Separation ~ k ^-1

100m

Modeling the Catchment Isoscape for Shale Hills

G. Bhatt 2012

Penn State Integrated Hydrologic Model (PIHM)

M. Kumar, G. Bhatt, Duffy 2009, Y. Shi

Land

Surface

Model

Semi-Discrete Approach: PIHM

Distributed IsotopeTransport ( Bhatt, 2012)

Transport Equation

Semi-Discrete Form

Horizontal Advection Vertical Flux Dispersive Flux

CZO Data ->lidar, Soil, Regolith,Veg

Simulated Average Age of Groundwater + Soil Water At Shale Hills CZO

G. Bhatt, PhD 2012

Random Input C _i and Q _i

Simulated Age PDF for Mobile and Immobile Water

Mean Age

Relative Frequency Groundwater Age

& Runoff Residence Time

Evan Thomas

G. Bhatt, PhD 2012

1979-2010 Reanalysis Forcing &

Dynamic Residence Time of Runoff

G. Bhatt, PhD 2012

Kei Yoshimura, University of Tokyo, Japan (Yoshimura et al., 2010)

Atmospheric Modeling of Stable Isotopes in Precipitation

A new research product

IsoRSM experiment over northeast US

10km Simulation covering 85.5W-71.3W/35.5N-46.2N Boundary Conditions: IsoGSM simulation based on

NOAA Climate Reanalysis

32

δ ^{18 O}

10 km res. δ ^{18 O} in precipitation

33

Validation of IsoRSM Stable Isotopes in Precipitation with Shale Hills CZO Data

Evan Thomas, MS Penn State

Conclusions:

The “Mean Age” of waters can be simulated directly using transport theory and stable isotopes

The particular form of the age- or transit-time distribution function is not necessary in this theory.

Mobile-Immobile storage attenuates the seasonal amplitude through lateral diffusive exchange, increasing the relative age of infiltrating waters

Vegetation using immobile water is not detached from the mobile phase but rather exchange occurs by capillary

diffusion

The isoscape is a powerful concept for assessing space-time patterns of age and residence time at the catchment scale

Thank You