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

age T

𝒑𝑸(𝑻, 𝒕)

Distribution of water parcels

time

𝐶 𝑡 = 𝑐 𝑇 𝒑𝑸 𝑻, 𝒕 𝑑𝑇

∞

0

fundamental link between water age and water quality

spatially-integrated approach

2

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

• 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

integrated catchment response

from McDonnell et al., 2010, HP

realistic distributions ideal distributions

𝒑𝑸(𝑻, 𝒕)

smooth, easy to parameterize

irregular, time-variant

5

𝜕 [𝑆 𝑡 𝒑𝑺 𝑇, 𝑡 ]

𝜕𝑡+𝜕[𝑆 𝑡 𝒑𝑺 𝑇, 𝑡 ]

𝜕𝑇= −𝑄 𝑡 𝝎(𝑇, 𝑡) 𝒑𝑺(𝑇, 𝑡)

Age Master Equation (after Botter et al., GRL, 2011):

younger water

𝝎 (𝑇, 𝑡)

1

older water

𝒑𝑺(𝑇, 𝑡)

age tracking at catchment scale

age distribution of the water storage

StorAge Selection (SAS) functions

age T

RS

6

Random sampling: 𝑝𝑄(𝑇, 𝑡) = 𝑝𝑆(𝑇, 𝑡)

∞ S(t)

Q(t) Q(t)

𝐶𝑄 𝑡 = 𝐶𝑆 𝑇∞

0

𝑝𝑸 𝑇, 𝑡 𝑑𝑇

𝐶𝑄 𝑡 = 𝐶𝑆 𝑇∞

0

𝑝𝑺 𝑇, 𝑡 𝑑𝑇 = 𝐶 𝑆 𝑡

solute concentration at the catchment outlet

= 𝑀𝑆 𝑡 /𝑆(𝑡)

S(t)

more on the RS

7

many RS compartments one non-RS compartment

𝝎 (𝑇, 𝑡) 𝝎 (𝑇, 𝑡) 𝝎 (𝑇, 𝑡)

two practical approaches

need for a full hydrologic model (internal fluxes) incorporates catchment characteristics (easier)

based on data

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DRAWBACKS • dry deposition • concentration is often too low (noise) • effect of plants: output conc. higher

than input conc.

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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

NL

outlet

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chloride as a tracer

Hupsel Brook (NL)

Upper Hafren Plynlimon (UK)

fertilization fertilization

shorter (30-100 d) travel times

Q [

mm

/h]

longer (2-3 y) travel times

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Hupsel Brook

Benettin et al., 2013, WRR

12

Upper Hafren, Plynlimon

longer travel times

shorter travel times

Benettin et al., 2015, WRR

water stable isotopes

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MAIN SOURCES • atmosphere • (deutered water for small experiments)

liquid 2H, 18O

vapor

depleted enriched

2H, 18O

heavy

lighter lighter

Deuterium Hubbard Brook WS3 (USA)

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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)

MOBILE WATER

MINERAL

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dissolved Si and Na

Hubbard Brook WS3 NH, USA

hydrologic transport in a forested catchment

NS= 0.62

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deuterium transport

travel time distributions

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:

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age-dependent transport

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

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non-RS compartment

Queloz et al., 2015a,b, WRR

Injection of fluorobenzoate (FBA) tracers

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ET

Q

fractional AGE older younger

validation

con

cen

trat

ion

[m

g/l

]

measurements

simulations

Q [

mm

/h]

mean age ~ 60-80 d ‘direct SAS approach’

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• 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

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:

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