Water Cycle Physical Processes – Emerging Science: Land Surface Hydrology and Watershed Dynamics

Jim McNamara Boise State University

Idaho, USA

Context: Predictive models tasked with representing processes “need preceded science” (Rafael Bras)

time

Prec

ipita

tion

time

flux

What knowledge is essential to incorporate into models?

Problems •  Problem: Calibrated models criticized for not representing processes

–  Black Box can be “Right for the Wrong Reasons” –  Flux right, internal states wrong –  Next generation models should get fluxes AND states right

•  Problem: Field experiments criticized for not asking the right questions

–  Irrelevant answers –  Site specific

time

Prec

ipita

tion

time

flux

?

Problems •  Problem: Calibrated models criticized for not representing processes

–  Black Box can be “Right for the Wrong Reasons” –  Flux right, internal states wrong –  Next generation models should get fluxes AND states right

•  Problem: Field experiments criticized for not asking the right questions

–  Irrelevant answers –  Site specific

•  Solution: –  Identify significant processes and properties on the ground at

watershed scale –  Develop new models informed by discovery

time

Prec

ipita

tion

time

flux

?

Problems

•  Solution: –  Processes are known –  Incorporate BEHAVIOR into model evaluation strategies

•  More than outputs, but INTERNAL DYNAMICS

?

“Emerging” Science significant processes and properties

•  “Old water” dominates storm hydrographs

1969

The old “Old Water” problem Hundreds of case studies since 1969

Scores of local explanations -watershed behavior highly heterogeneous

Continued recent discoveries -See work by Jeff McDonnell et al…and Jim Kirchner et al. -not old vs new, but stormflow is composed of a continuum of ages

Challenges to remain -Still at odds with concepts embedded in many commonly used models (Hortonian Overland Flow)

Stre

amflo

w

Emerging since 1969

Until models get this right, they are “Right for the Wrong Reasons” and cannot handle change (paraphrased from Kirchner)

The Heterogeneity Problem •  Two solutions

–  Measure everything everywhere, unknowns are simply a matter of poor characterization

•  Unrealistic (Newtonian, me, persevering science)

–  Recognize patterns and emergent

properties •  Watershed behavior is more the

accumulation of arrows (Darwinian, emerging science)

Emergent Behavior

-Watershed “lump” processes producing emergent properties -A physical basis for lumped parameter modeling

The Heterogeneity Issue Local controls vs General Concepts

Lumped Model Distributed Model,

Physics based Semi-Distributed Model,

Conceptual ),),(()( CAtPftQ =p

q

REW 1

REW 2 REW 3

REW 4

REW 5

REW 6 REW 7

Data Requirement:

Computational Requirement: Small Large

Process Representation: Parametric Physics-Based

Predicted States Resolution: Coarser Fine

ssQUt

+∇Γ∇+∇=∂∂ ).().( φφφ

Perceived Intellectual Value: Small Large

q q

Modified from Mukesh Kumar Model Structures

Lumped Model Distributed Model,

Physics based Semi-Distributed Model,

Conceptual ),),(()( CAtPftQ =p

q

REW 1

REW 2 REW 3

REW 4

REW 5

REW 6 REW 7

Outcome: Right for

Wrong Reasons Wrong for Right

Reasons

ssQUt

+∇Γ∇+∇=∂∂ ).().( φφφ

q q

History: Mathematical

Lumping Process

Understanding

Future: ? Process

Understanding

Modified from Mukesh Kumar

Physically Lumped Model Distributed Model,

Physics based ),),(()( CAtPftQ =

q

ssQUt

+∇Γ∇+∇=∂∂ ).().( φφφ

History: Mathematical Lumping

Process Understanding

Future: Process

Understanding Emergent properties

guide “lumping”

Physically lumped properties

Modified from Mukesh Kumar

Lumped Watershed Properties (emergent behavior)

•  Hydrologic Connectivity

– Timing of hillslope-stream connectivity dictates response

•  Thresholds – Non-linear response depending on hydrologic

state •  Water residence time

– Disrtribution key to watershed dynamics

Emergent Behavior: Hydrologic Connectivity

•  Facilitates lateral redistribution

Figure courtesy of Jeff McDonnell

LegendCalculation Value

High : 11.000000

Low : 4.000000

ln[UAA(m2)]

100

543,689 Stream

Riparian Boundary

Well

UAA 45,000 m2

UAA 9,000 m2

UAA 20,000 m2

Jencso et al., 2009 WRR

Hillslope-riparian-stream water table connection

Upslope Accumulated Area (m2)

1000 10000

% w

ater

year

0

20

40

60

80

100R2=0.91

Max bar height = 100% Of the year

Hydrologic  connec-vity  may  be  a  good  predictor  of  watershed  runoff  

Strong  correla-ons  between  watershed  form  (UAA)  and  func-on  (connec-vity)  

Jencso et al., 2009 WRR

Frequency of connections controls watershed discharge rather than the magnitude at the connections

Models incorporating connectivity may lead to improved prediction

Emergent Behavior:

Thresholds at storm scale

Storm total precipitation (mm)

0 10 20 30 40 50 60 70 80 90 100

Sto

rm to

tal f

low

(mm

)

0

10

20

30

40

50

60

70

Panola, Georgia, USA (Tromp-van Meerveld and McDonnell, Chapter 1)Maimai, New Zealand (Mosley, 1979)Tatsunokuchi-yama exp. forest, Honsyu Island, Japan (Tani, 1997)H.J. Andrews exp. forest, Oregon, USA (McGuire, unpublished data)

PanolaH.J. Andrews

Maimai

Tatsunokuchi-ya

ma

Figure courtesy of Jeff McDonnell

Emergent Behavior: Thresholds at seasonal scale

0

200

400

600

7/2 8/31 10/30 12/29 2/27 4/28 6/27

Dept

h (m

m) Total Precipitation

Water InputEvapotranspiration

0

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7/2 8/31 10/30 12/29 2/27 4/28 6/27

Soil

Moi

stur

e

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Bedr

ock

Flow

(mm

)

15 cm30 cm65 cmBedrock Flow

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Stre

amflo

w

(lite

rs/m

in)

5

8

(mg/

L)

Streamflow

dissolved solids

McNamara et al., 2005

Emergent Behavior: Residence time distribution

Figure courtesy Chris Soulsby

01/01/95 01/01/97 01/01/99 01/01/01 01/01/03 Con

cent

ratio

n pr

ecip

itatio

n (m

g l-1

)

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cent

ratio

n st

ream

wat

er (m

g l-1

)

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35PrecipitationStreamwaterModelled

01/01/88 01/01/90 01/01/92 01/01/94 01/01/96 Con

cent

ratio

n pr

ecip

itatio

n (m

g l-1

)

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Con

cent

ratio

n st

ream

wat

er (m

g l-1

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35PrecipitationStreamwaterModelled

Transit times and catchment characteristics

Integrating across flows: Short TT (ca months) / Longer TT (ca years)

Fast responding catchments Deep-subsurface flow dominated catchments

Tetzlaff D, et al (2007) Journal of Hydrol. 346, 93-111.

Hrachowitz M, et al. (2009) Journal of Hydrol. doi:10.1016/j.jhydrol.2009.01.001

Cum

. den

sitie

s fu

nctio

n

50% 50%

Figure courtesy Chris Soulsby

Residence Time Predicted by Watershed Properties

Figure courtesy Chris Soulsby

Recent Theoretical Advances

Travel time distributions are a product of integrated catchment processes Can serve as a target to determine if models are right for the right reasons

Emerging science: Emergent properties

Connectivity Thresholds

Residence Time

How do we quantify? How do we incorporate in models?

Emergent properties are a function of storage

P-ET-Q =dS/dt

Connectivity Thresholds

Residence Time

Storage

A Tale of Two Catchments

A Natural Storage Experiment

0

20

40

60

Thaw

Dep

th (c

m)

0

2

4

6

13-Jun 3-Jul 23-Jul 12-Aug

Flow

(cm

s)

65

75

85

13-Jun 13-Jul 12-Aug

% O

ld W

ater

0.0

0.2

0.4

13-Jun 13-Jul 12-Aug

Run

off R

atio

Storage Capacity

McNamara et al., 1998

Storage-Discharge •  In SOME watersheds, discharge can be

modeled as a single function of storage •  The shape of the S-D curve may contain

information about the watershed

Kirchner, 2009

Importance of Storage

0

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60

Thaw

Dep

th (c

m)

0

2

4

6

13-Jun 3-Jul 23-Jul 12-Aug

Flow

(cm

s)

65

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85

13-Jun 13-Jul 12-Aug

% O

ld W

ater

0.0

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13-Jun 13-Jul 12-Aug

Run

off R

atio

•  The mechanisms by

which catchments STORE water ultimately characterize the hydrologic SYSTEM

•  Storage regulates fluxes (ET, Recharge, Streamflow)

•  Storage is responsible for emergent behavior such as connectivity, thresholds, and residence time

Storage Capacity P-ET-Q =dS/dt

Importance of Storage

0

20

40

60

Thaw

Dep

th (c

m)

0

2

4

6

13-Jun 3-Jul 23-Jul 12-Aug

Flow

(cm

s)

65

75

85

13-Jun 13-Jul 12-Aug

% O

ld W

ater

0.0

0.2

0.4

13-Jun 13-Jul 12-Aug

Run

off R

atio

•  We should focus on Runoff Prevention mechanisms in addition to runoff generation mechanisms

•  We should concern ourselves with how catchments Retain Water in addition to how they release water

Storage Capacity P-ET-Q =dS/dt

The Storage Problem •  Storage is not commonly measured

•  Storage is often estimated as the residual of a water balance

•  Storage is treated as a secondary model calibration target

Our Modeling Experience

•  Soil Water Assessment Tool (SWAT)

0.0

0.5

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Flo

w (

m^3

/s)

Observed

Predicted

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l Moi

stur

e of

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l Col

mn

(mm

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SWAT Soil MoistureAverage Soil Moisture BFU and BFL

Hydrograph “Right” Storage Wrong

Stratton et al., 2009

Improved storage characterization will lead to improved prediction  

Seyfried et al., 2009, Hydrological Processes

Throughflow  

SWI  

Snow Water Input (ISNOBAL)

Get the inputs right (accumulation, STORAGE,and ablation of snow) Get the 1D soil water storage right Ignore all lateral movement No calibration to streamflow See what happens

•  Throughflow occurs when soil column water holding capacity is exceeded

•  Soil water storage parameterized by field

capacity, plant extraction limit, soil depth

Soil  Capacitance  Model  (Reynolds  Creek)  

Seyfried et al., 2009, Hydrological Processes

Throughflow  

SWI  

0

0.1

0.2

7/2 8/31 10/30 12/29 2/27 4/28 6/27

Soil

Moi

stur

e

0

0.1

0.2

0.3

65 cm

15 cm

30 cm

Өfc  

Өpel  

i

numlayeri

iiTS ∑

=

=

=1θ i

numlayeri

ifcFC TSi∑

=

=

=1θ

Distributed Model

No lateral flow simulated

Distributed energy balance forcing

Distributed soil properties by similarity classes

Simulated  storage  excess  agrees  with  streamflow  

PELFC

PELN SS

SSS−−=

Connec-vity  Index  

CUAHSI Catchment Comparison Exercise

Dry Creek, Idaho, USA Snowy, semi-arid, ephemeral

Reynolds Creek, Idaho, USA Snowy, semi-arid, perennial

Panola, Georgia, USA Rain, humid, perennial

Girnock, Scotland, Rain, humid

Gårdsjön, Sweden, Snow, ephemeral

Storage-Discharge

S = 786.Q0.32

S = 253Q0.11

S = 251Q0.05

S = 219Q0.06

S = 87Q0.05

10

100

1000

10000

0.0 0.1 1.0 10.0 100.0Streamflow (mm)

Stor

age

(mm

)

Dry CreekGårdsjönGirnockReynoldsPanola

Signature of geology?

McNamara et al., 2011

Summary •  Use internal BEHAVIOR of watersheds, in

addition to states and fluxes

•  Discover metrics of internal behavior (emerging science of emergent properties)

•  Requires creative coupled field and modeling experiments

Summary •  Watersheds “lump” processes producing emergent

behavior manifested in –  Connectivity, Thresholds, Residence Time

Distributions (old water)

•  Incorporate into new model structures or serve as validation targets

•  Evaluate model performance on watershed behavior, or

internal dynamics, in addition to traditional states and fluxes time series.

•  Quantifying Storage ….quantify emergent properties •  Get the States right, and the Fluxes will follow