Benettin ph.d. days presentation

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Catchment Transport and Travel Time Distributions:
Theoretical Developments and Applications
Paolo Benettin
PhD Days di In...

the Ph.D. dissertation
Cin
- Travel-time distributions
- Hydrologic and solute transport

University of Padua,
Padua, Italy
Gianluca Botter
EPFL,
Lausanne, CH
Andrea Rinaldo
PH.D. SUPERVISORS

Introduction

age = time since entrance
age T
𝒑 𝑸(𝑻, 𝒕)
Distribution of water parcels
time
𝐶 𝑡 =
0
∞
𝑐 𝑇 𝒑 𝑸 𝑻, 𝒕 𝑑𝑇
fundamental link
be...

source: ARPAV
Ecological
Status 2013
Sufficient
Poor
GoodVenice Lagoon drainage basin
Nitrate Loads
!
2001 2003 2005 2007 ...

Sanford and Pope, Env. Sci. and Technol., 2013
why studying water age

propagation of a pressure wave rather than actual water
‘new’ rainfall
discharge‘old’ stored water
CONCEPTUAL
EXPLANATION:...

Kirchner et al., 2000, Nature
WATER
CHLORIDE
why hydrologic transport isn’t so simple (1)

data from Plynlimon UHF catchment, UK
[mm/h][mg/l]
silica
chloride
[mg/l]
dry
period
wet
period
why hydrologic transport i...

why hydrologic transport isn’t so simple (3)
McDonnell et al., 2010, HP
realistic distributionsideal distributions

ages in storage
T
𝒑 𝑺(𝑻, 𝒕)
0
time
tt2t1
INJECTION TIMES
t3
S(t)
ages in the discharge
T
𝒑 𝑸(𝑻, 𝒕)
hydrologic transport pr...

What relationship exists between
particles in storage
and particles in the fluxes?
‘StorAge-Selection’
functions
𝑝 𝑄(𝑇, 𝑡)...

age-selection
ω 𝑇, 𝑡 =
𝑝 𝑄(𝑇, 𝑡)
𝑝 𝑆(𝑇, 𝑡)
preference for
younger ages
no preference
(random sampling)
preference for
olde...

My contribution

dissertation overview
• 1. Unified theory of water age
and life expectancy distributions
• 2. Kinematics of age mixing in
...

Ype van der Velde Sjoerd van der Zee
NL
outlet
Conservative solutes from an agricultural area (Chapter 3)
Can we use
time-...

SOIL
STORAGE
GROUNDWATER
STORAGE
a simple transport model
soil water mean [d] ≈ 90
st.dev. [d] ≈ 20
groundwater
mean [d] ≈...

Model results
shorter (30-100 d)
travel times
Q[mm/h]
longer (2-3 y)
travel times

how do ages mix
in advection-
dispersion processes?
Age mixing in advection-dispersion models (Chapter 2)
flux
𝑝 𝑆 𝑻, 𝑡 ST...

Age mixing in advection-dispersion models (Chapter 2)
STORAGE age
‘‘StorAge-Selection’’ function𝜔 𝑇, 𝑡 =
𝑝 𝑄(𝑇, 𝑡)
𝑝 𝑆(𝑇, ...

Pe = 1
relative age [%]
ω[-]
𝜔 𝑇, 𝑡 =
𝑝 𝑄(𝑇, 𝑡)
𝑝 𝑆(𝑇, 𝑡)

Experiences abroad
Kevin J. McGuire
James W. Kirchner
period abroad at
Virginia Tech University
and
AGU fall meeting 2013

High-frequency chloride at Plynlimon (UK) (Chapter 4)
Benettin et al., 2015, WRR
Upper Hafren Catchment (UK)
2 years of 7-...

CALIBRATED HYDROCHEMICAL MODEL
Parameters
posterior distributions

age dynamics
Tracer
response
input
variability+general affinity
for younger ages
younger ages older ages
StorAge Selection...

MOBILE
WATER
MINERAL
silica transport in a forested catchment (Chapter 5)
Benettin et al., in review
How can we use age
di...

Travel time distributions
NS= 0.62

Silicon (Si)
Nov-2006 Nov-2007 Nov-2008
Age-dependent transport
dry days:
many old particles
wet days:
many young particle...

Silica and sodium at
Hubbard Brook Watershed 3
data kindly provided by G. Likens and D. BusoNS= 0.42 - 0.76
Silicon (Si) S...

OUTLET
ti te
TT = te- ti
time
TRAVEL TIME
t
AGE LIFE EXPECTANCY
back to basics

Tracer injection experiment
Water samples
at a catchment outlet
Cin
Cout
time
Queloz et al., WRR, 2015a,b
PAST
entrance ti...

Q (t)
J (t)
S (t)
Definitions: distributions of particles

Governing equations
𝑑𝑆(𝑡)
𝑑𝑡
= 𝐼𝑁 𝑡 − 𝑂𝑈𝑇 𝑡• Hydrologic Balance:
• CONTINUITY for each age class T (either 𝑇𝑅 or 𝑇𝐸)
𝜕
𝜕𝑡
...

Life-expectancy
tracking
Age
tracking
modeling implications

0
1
2
3
4
5
0 10 20 30 40 50 60 70 80 90
Millions
age [years]
1940
source: CDC/NCHS, National Vital Statistics System, USA...

source: CDC/NCHS, National Vital Statistics System, USA
US age at death, 1940 - 2010
0.00
0.05
0.10
0 10 20 30 40 50 60 70...

0.00
0.01
0.02
0 20 40 60 80
pdf[1/y]
age [y]
pS(T,t)
1940
1950
1960
1970
1980
1990
2000
2010
0.00
0.02
0.04
0 20 40 60 80...

Theory Applications
• development of the master
equation generator
(introduction of the forward
formulation)
• definition ...

acknowledgments
Plynlimon data:
Ype van der Velde
Hupsel Brook data:
Hubbard Brook data:
S. Bailey, JP Gannon, M. Green, J...

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