On the integrated solute response of catchments: benchmark applications using chloride and isotopic tracers

1. On the Integrated Response of Catchments:
benchmark applications using chloride and isotopic tracers
Paolo Benettin
Workshop on coupled hydrological modling Padova | 23 – 24 April 2015

2. age T
𝒑 𝑸(𝑻, 𝒕)
Distribution of water parcels
time
𝐶 𝑡 = 𝑐 𝑇 𝒑 𝑸 𝑻, 𝒕 𝑑𝑇
∞
0 fundamental link
between water age
and water quality
spatially-integrated approach
2

3. NO FERTILIZATION
Measurements from the Hupsel Brook Catchment, NL
1 – slow transport
response
TTDs and transport
NL
outlet
2 – fast ‘reactivity’
during storms
CHLORIDE
concentration measurements
3

4. • fast calibration
• easy exploration of the
parameter space
spatially-integrated approach
simplification of the
system, no physically-based
descriptions
‘soft’ models that capture
the emergent transport
processes
suitable for hydrologic TRANSPORT and TTDs
effective integration of
spatial complexity
4

5. integrated catchment response
from McDonnell et al., 2010, HP
realistic distributionsideal distributions
𝒑 𝑸(𝑻, 𝒕)
smooth,
easy to parameterize
irregular,
time-variant
5

6. 𝜕 [𝑆 𝑡 𝒑 𝑺 𝑇, 𝑡 ]
𝜕𝑡
+
𝜕[𝑆 𝑡 𝒑 𝑺 𝑇, 𝑡 ]
𝜕𝑇
= −𝑄 𝑡 𝝎(𝑇, 𝑡) 𝒑 𝑺(𝑇, 𝑡)
Age Master Equation (after Botter et al., GRL, 2011):
younger
water
𝝎 (𝑇, 𝑡)
1
older
water
𝒑 𝑺(𝑇, 𝑡)
age tracking at catchment scale
age distribution of
the water storage
StorAge Selection
(SAS) functions
age T
RS
6

7. Random sampling: 𝑝 𝑄(𝑇, 𝑡) = 𝑝 𝑆(𝑇, 𝑡)
∞
S(t)
Q(t)
Q(t)
𝐶 𝑄 𝑡 = 𝐶𝑆 𝑇
∞
0
𝑝 𝑸 𝑇, 𝑡 𝑑𝑇
𝐶 𝑄 𝑡 = 𝐶𝑆 𝑇
∞
0
𝑝 𝑺 𝑇, 𝑡 𝑑𝑇 = 𝐶𝑆 𝑡
solute concentration
at the catchment outlet
= 𝑀𝑆 𝑡 /𝑆(𝑡)
S(t)
more on the RS
7

8. many RS compartments one non-RS compartment
𝝎 (𝑇, 𝑡)
𝝎 (𝑇, 𝑡)𝝎 (𝑇, 𝑡)
two practical approaches
8

9. DRAWBACKS
• dry deposition
• concentration is often too low (noise)
• effect of plants: output conc. higher
than input conc.
9
chloride as a tracer
MAIN SOURCES
• atmosphere (coastal areas)
• agriculture (KCl is widely used)
• (road salting)
TRACER?
• mostly yes
• no degradation
• nutrient for plants, but in very low
concentrations

10. NL
outlet
10
chloride as a tracer
Hupsel Brook (NL)
Upper Hafren
Plynlimon (UK)
fertilization fertilization

11. shorter (30-100 d)
travel times
Q[mm/h]
longer (2-3 y)
travel times
11
Hupsel Brook
Benettin et al., 2013, WRR

12. 12
Upper Hafren, Plynlimon
longer
travel times
shorter
travel times
Benettin et al., 2015, WRR

13. water stable isotopes
13
MAIN SOURCES
• atmosphere
• (deutered water for small experiments)
liquid
2H, 18O
vapor
depleted enriched
2H, 18O
heavy
lighter
lighter
DeuteriumHubbard Brook WS3 (USA)

14. 14
water stable isotopes
TRACER?
• mostly yes
• from precipitation to discharge
• if snowmelt and evaporation have
minor impact
precipitation
EPFL lysimeter
(CH)
Hubbard Brook WS3
(USA)

15. MOBILE
WATER
MINERAL
15
dissolved Si and Na
Hubbard Brook WS3
NH, USA
hydrologic transport in a forested catchment

16. NS= 0.62
16
deuterium transport
travel time distributions

17. Silicon (Si)
Nov-2006 Nov-2007 Nov-2008
dry days:
many old particles
wet days:
many young particles
𝐶 𝑡 = 𝐶𝑒𝑞 1 − 𝑒−𝑘𝑻
𝑝 𝑄 𝑻, 𝑡 𝑑𝑻
∞
0
𝐶𝑒𝑞 𝑐(𝑇)
1° order chemical kinetics:
17
age-dependent transport

18. 14-year dataset
dissolved silicon and sodium
NS= 0.42 - 0.76
Silicon (Si) Sodium (Na)
NS= 0.34 - 0.66
1/𝑘 ~ 10 − 13 𝑑𝑎𝑦𝑠
Benettin et al., in review 18

19. 19
non-RS compartment
Queloz et al., 2015a,b, WRR
Injection of fluorobenzoate
(FBA) tracers

20. 20
ET
Q
fractional AGE olderyounger
validation
concentration[mg/l]
measurements
simulations
Q[mm/h]
mean age ~ 60-80 d
‘direct SAS approach’

21. 21
• simple hydrochemical models
generate complex age
dynamics
• use of age distributions to
model geogenic solutes
• multi-RS system can
efficiently reproduce
emergent transport dynamics
• deeper exploration of ‘direct
SAS’ approach
• characterization of the age of
evapotranspiration
• move on to complex transport
dynamics (e.g. nitrates)
Summary Future perspectives

22. acknowledgments
Plynlimon data:
Ype van der Velde
Hupsel Brook data:
Hubbard Brook data:
K.J. McGuire, S.W. Bailey, JP Gannon, M. Green, J. Campbell, G. Likens, D. Buso
ENAC/IIE/ECHO lab
Pierre Queloz
Lysimeter data:
22