Benettin ph.d. days presentation
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Transcript of Benettin ph.d. days presentation
Catchment Transport and Travel Time Distributions:Theoretical Developments and ApplicationsPaolo Benettin
PhD Days di Ingegneria delle Acque – Trento, 6-8 Luglio 2015
the Ph.D. dissertation
Cin
Cout
- 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
𝒑𝑸(𝑻 ,𝒕)
Distribution of water parcels
time
𝐶 (𝑡 )=∫0
∞
𝑐 (𝑇 )𝒑𝑸 (𝑻 ,𝒕 )𝑑𝑇fundamental link
between water ageand water quality
source: ARPAV
EcologicalStatus 2013
Sufficient
Poor
GoodVenice Lagoon drainage basin
Nitrate Loads
!
2001 2003 2005 2007 2009 2011
why studying water age
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:
why hydrologic transport isn’t so simple (1)
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]
dryperiod
wetperiod
why hydrologic transport isn’t so simple (2)
why hydrologic transport isn’t so simple (3)
McDonnell et al., 2010, HP
realistic distributionsideal distributions
ages in storage
T
𝒑𝑺(𝑻 ,𝒕 )
0time
tt2t1
INJECTION TIMESt3
S(t)
ages in the discharge
T
𝒑𝑸(𝑻 ,𝒕)
hydrologic transport processes
What relationship exists between particles in storage
and particles in the fluxes?
‘StorAge-Selection’ functions
𝑝𝑄 (𝑇 , 𝑡)𝑝𝑆(𝑇 ,𝑡)
=𝜔(𝑇 , 𝑡)
flux
Storage
age-selection
ω (𝑇 , 𝑡 )=𝑝𝑄(𝑇 , 𝑡)𝑝𝑆(𝑇 , 𝑡)
preference for younger ages
no preference(random sampling)
preference for older ages
age
𝜔<1
𝜔>1𝜔[−
]
1
My contribution
dissertation overview
• 1. Unified theory of water age and life expectancy distributions
• 2. Kinematics of age mixing in advection-dispersion systems
• 3. Application to conservative fertilizer transport in a dutch catchment
• 4. Application to chloride transport in a highly monitored UK catchment
• 5. Application to non-conservative solutes in a forested US catchment
Logical orderChronological order
32415
Ype van der Velde Sjoerd van der Zee
NL
outlet
Conservative solutes from an agricultural area (Chapter 3)
Can we use time-variant age
distributionsto model chloride
transport?
SOILSTORAGE
GROUNDWATERSTORAGE
a simple transport model
soil water mean [d] 90 st.dev. [d] 20
groundwater
mean [d] 1100 st.dev. [d] 120
Model results
shorter (30-100 d)travel times
Q [
mm
/h]
longer (2-3 y) travel times
how do ages mixin advection-
dispersion processes?
Age mixing in advection-dispersion models (Chapter 2)
flux
Storage
𝑝𝑆 (𝑻 , 𝑡 ) STORAGE age
𝑝𝑄 (𝑻 , 𝑡 ) DISCHARGE age
𝜌 (𝒙 ,𝑻 ,𝑡 ) ‘age mass density’Ginn, 1999, WRR
Benettin et al., WRR, 2013b
Age mixing in advection-dispersion models (Chapter 2)
STORAGE age
‘‘StorAge-Selection’’ function𝜔 (𝑇 , 𝑡 )=𝑝𝑄(𝑇 , 𝑡)𝑝𝑆(𝑇 ,𝑡)
=𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑙𝑣 𝑜𝑙𝑢𝑚𝑒𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑙
𝑝𝑆 (𝑇 , 𝑡 )= 1𝑀 (𝑡)∫𝑉
❑
𝜌 (𝒙 ,𝑇 , 𝑡 )𝑑 𝒙
𝑝𝑄 (𝑇 , 𝑡 )= 1𝜑𝑜𝑢𝑡 (𝑡 )∫𝑆
❑
[𝑢 (𝒙 ,𝑡 )𝜌 (𝒙 ,𝑇 , 𝑡 )−𝑫 (𝒙 , 𝑡 )𝛻𝜌 (𝒙 ,𝑇 ,𝑡 ) ]𝒏𝑑𝜎 DISCHARGE age
𝜕𝜌 (𝒙 ,𝑇 , 𝑡 )𝜕𝑡
+𝜕 𝜌 (𝒙 ,𝑇 ,𝑡 )
𝜕𝑇+𝛻 ∙ [𝑢 (𝒙 , 𝑡 ) 𝜌 (𝒙 ,𝑇 , 𝑡 ) ]=−𝛻 ∙ [𝑫 (𝒙 ,𝑡 )𝛻𝜌 (𝒙 ,𝑇 ,𝑡 ) ]
discharge ageVS
storage age
Ginn, 1999, WRR
Pe = 1
relative age [%]
ω [-
]
𝜔 (𝑇 , 𝑡 )=𝑝𝑄(𝑇 , 𝑡)𝑝𝑆(𝑇 ,𝑡)
Experiences abroad
Kevin J. McGuire
James W. Kirchner
period abroad atVirginia Tech University
andAGU fall meeting 2013
High-frequency chloride at Plynlimon (UK) (Chapter 4)
Benettin et al., 2015, WRR
Upper Hafren Catchment (UK)2 years of 7-hour measurements
chloride
How can we explain the observed
high-frequency solute dynamics?
CALIBRATED HYDROCHEMICAL MODEL
Parameters posterior distributions
age dynamics
Tracer response
input variability+general affinity
for younger ages
younger ages older ages
StorAge Selection functionsCumulative age distributions
MOBILEWATER
MINERAL
silica transport in a forested catchment (Chapter 5)
Benettin et al., in review
How can we use age distributions
to model age-dependent
transport?
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 particles
𝐶 (𝑡 )=∫0
∞
𝐶𝑒𝑞 (1−𝑒−𝑘𝑻 ) �́�𝑄 (𝑻 ,𝑡 )𝑑𝑻
𝐶𝑒𝑞 𝑐 (𝑇 ) 1° order chemical kinetics:
Silica and sodium at Hubbard Brook Watershed 3
data kindly provided by G. Likens and D. BusoNS= 0.42 - 0.76
Silicon (Si) Sodium (Na)
NS= 0.34 - 0.66
1/𝑘 10−13𝑑𝑎𝑦𝑠
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 times
FUTUREexit times
time
mg/
L
Kirchner and Neal, PNAS, 2013
What is the link between
‘forward’ and ‘backward’ age
tracking?
Backward and forward age tracking (Chapter 1)
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 or )
𝜕𝜕𝑡
𝑁𝑺(𝑇 ,𝑡 )+𝑐𝜕𝜕𝑇
𝑁𝑺(𝑇 , 𝑡)=∑𝑖
𝐹 𝑖 (𝑡 )𝑝𝑭 𝒊(𝑇 , 𝑡)
• forward , , BC
• backward ,
Master Equation generator:
(define: volumetric quantity)
Benettin et al., 2015, Hydrol. Process.
Life-expectancytracking
Age tracking
modeling implications
0 10 20 30 40 50 60 70 80 900
1000000
2000000
3000000
4000000
5000000
age [years]
1940
source: CDC/NCHS, National Vital Statistics System, USA
US population by age class
1950196019701980199020002010
h𝑢𝑚𝑎𝑛𝑟𝑒𝑠𝑖𝑑𝑒𝑛𝑡 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛=�́�𝑆(𝑇 , 𝑡)
water particles as a dynamic population
source: CDC/NCHS, National Vital Statistics System, USA
US age at death, 1940 - 2010
0 10 20 30 40 50 60 70 80 900.00
50000.00
100000.00
19401950196019701980199020002010
age [years]
h𝑢𝑚𝑎𝑛𝑜𝑢𝑡𝑓𝑙𝑜𝑤 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛=�́�𝑄(𝑇 ,𝑡)
water particles as a dynamic population
0 10 20 30 40 50 60 70 80 900.00
0.01
0.02
pS(T,t)19401950196019701980199020002010
age [y]
pdf [
1/y]
0 10 20 30 40 50 60 70 80 900.00
0.02
0.04
pQ(T,t)19401950196019701980199020002010
age [y]
pdf [
1/y]
0.0 0.2 0.4 0.6 0.8 1.00
5
10
15
age selection𝜔(PS, )𝑡19401950196019701980199020002010
transformed age [-]
pdf [
-]
Progress
water particles as a dynamic population
Theory Applications
• development of the master equation generator (introduction of the forward formulation)
• definition of age concepts in general advection-dispersion systems
• generation of time-variant age dynamics through simple hydrochemical models
Summary of the results
• modeling of 3 diverse real-world catchments
• exploration of catchment functioning
• use of age distributions for reactive transport
acknowledgments
Plynlimon data:
Ype van der Velde
Hupsel Brook data:
Hubbard Brook data:
S. Bailey, JP Gannon, M. Green, J. Campbell, G. Likens, D. Buso