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The Interaction between Groundwater Pumping, Surface Water and Evapotranspiration:

The Concept of Capture

Tom Maddock

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Talk Outline

• Groundwater/Surface Water Interactions

• What is Capture?

• Is Capture of Critical Interest?

• How do you calculate Capture?

• Capture calculation example

• What are the capture model basic parts?

• Modeling mischief

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• If the water level in the aquifer is above the above the stream stage elevation, the stream is a gaining stream (I).

• If the water level in the in the aquifer is below the stream stage elevation (Dw<3W), the stream is a losing stream (II).

• For these two systems, QRIV=CRIV(HRIV−hA)

That is, the flow is proportional to the head difference between the stream (HRIV) and the aquifer (hA).

DW is an indicator of the difference between aquifer water level and stream stage elevation .

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• As the water level in in the aquifer drops, the seepage becomes less dependent upon the head in the aquifer (III).

• Ultimately the hydraulic connection between the bottom of the stream bed and the water table will break (IV).

• The interval below the stream bed is unsaturated, but the stream bed is assumed to remain saturated.

DW is an indicator of the difference between aquifer water level and stream stage elevation .

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CONCEPT OF CAPTURE

“Under natural conditions…previous to the development of wells, aquifers are in a state of approximate dynamic equilibrium.”

PRE-DEVELOPMENT

R

D

Average recharge R = Average discharge D

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CONCEPT OF CAPTUREPre-development Recharge and Discharge

Recharge:

Losing stream (LS)Underflow in (UI)Mountain front recharge (MFR

Discharge:Gaining stream (GS)Underflow out (UO)Evapotranspiration (ET)

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CONCEPT OF CAPTURE“Discharge by wells is thus a new discharge superimposed upon a

previously stable system, and it must be balanced by an increase in recharge of the aquifer, or a decrease in the old natural discharge, or by a loss of storage in the aquifer, or by a combination of these.”

DEVELOPMENT

R+ΔR

D-ΔDQ

Stress Q is introduced

The system may respond in three different ways: increase in recharge R→R+ ΔR

decrease in discharge D→D ΔDchange in aquifer storage ΔS

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CONCEPT OF CAPTURE

There is a new equilibrium:

remembering

gives

the term ΔR+ΔD is called capture.

( ) ( ) SR R D D Q t

R D

SR D Q t

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Reduced water table

CONCEPT OF CAPTURE

Stream

Evapotranspiration

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CONCEPT OF CAPTURE

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CONCEPT OF CAPTURE

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CONCEPT OF CAPTURE

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Nearly all water US Supreme Court cases in the western United States directly or indirectly involve issues of Capture.

• Arkansas • Pecos• Rio Grande• Republican• Platte• Colorado

Federal

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State

Nearly all issues of interactions between ground and surface water involve Capture.

• Prior-Appropriation v Reasonable Use

• Conjunctive management

• Domestic wells

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Capture Is Calculated with Models

• There will be a surface water model and a groundwater model.

• There will be a historical model and a base case model.

• The models will consist of control variables, state variables and parameters.

• There is no capture data values to compare or calibrate with calculated values.

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MODEL CHARACTERISTICS

S Ariv

H HQ KWL

M

• Surface water model is usually an accounting model that matches stress periods of the groundwater model.

• Groundwater model is distributed parameter (Two or Three Dimensional). MODFLOW is an example.

• Interaction between surface and ground- waters if governed by Darcy’s law

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HISTORICAL MODEL

• Attempts to match historical processes

• Can be calibrated with temporal and spatial data

• Used to demonstrate the viability, accuracy and robustness of the model

• Does not calculate capture.

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BASE MODEL

• Based on little or no data

• May be fictional or artificial in nature

• May be the result of a negotiation process or imposed by the court

• Should be composed of the same physical based parameters as the historical model

Examples: Classical (Steady State), Seasonal (Steady Oscillatory), Complex (Constrained Process)

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ClassicalSTEADY STATE

• The natural recharge and discharge are equal for all time periods (R=D)

• Time steps are annual

• There is no loss of groundwater storage

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SeasonalSTEADY OSCILLATORY

• Like the steady state but recharge and discharge can vary from season-to-season but these variations are the same each year (Ri≠Di).

• There may be a storage loss or a storage gain each season but the total season storage loss plus the total seasonal storage gain is zero and .

i i

i i

R D

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ComplexCONSTRAINED PROCESS

• Recharge and discharge may vary from time step to time step but are the same for both the base and historical models.

• Some process such as pumping or diversions is constrained and is different from the historical model.

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Surface Water Model

Subtracting the historical streamflows from the base streamflows provides an estimate of surface water capture by groundwater pumping.

Groundwater ModelA capture is the increase to a previous [base-case] recharge and/or the decrease to a previous [base-case] discharge due to groundwater withdrawal from wells

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Classical

Predevelopment Stream

Gaining Stream (GS)

inSF

preoutSF

Losing Stream (LS)

Pr eout inSF SF LSGS

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Stream with Groundwater Development

Gaining Stream (GS-ΔGS)

inSF

deloutSF

Losing Stream (LS+ ΔLS)

delout inSF SF GS LSLGS S

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Pr eout inSF SF LSGS

delout inSF SF GS LSLGS S

Thus the Capture Calculation is:

From

Subtract

Giving

Capture GS LS

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Classical

Predevelopment Aquifer

Gaining Stream (GS)

Losing Stream (LS)

DischargRecharg e

UI LS

e

U GSMFR O

Underflow Out (UO)

Mountain Front Recharge (MFR)

Underflow In (UI)

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Aquifer with Groundwater Development

Gaining Stream (GS-ΔGS)

Losing Stream (LS+ΔLS)

UOUI LS MFRLS GSS Q

S

t

G

Underflow Out (UO)

Mountain Front Recharge (MFR)

Underflow In (UI)

Well (Q)

Capture

Gt

QS

LS S

which becomes

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CONCEPT OF CAPTURE

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CONCEPT OF CAPTURE

R D R+ΔR DΔD ΔR ΔD

Losing Stream Reaches 2.64 4.52 1.88

Mountain Front Recharge 17.33 17.33 0.00

Basin Inflow (from Mexico) 5.54 5.85 0.31

Gaining Stream Reaches 13.70 9.25 4.45

Evapotranspiration 10.91 7.97 2.94

Basin Outflow (to Benson Sub-Watershed) 0.90 0.90 0.00

Totals 25.51 25.51 27.70 18.12 2.19 7.39

Classical global capture (1980 values, Vionnet & Maddock)

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CONCEPT OF CAPTUREFlow between stream and aquifer at selected locations

-1

-0.5

0

0.5

1

1.5

1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990

Years

cfs

Near Palaminas Near Hereford Near lewis Springs Near Charl. Bridge

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CONCEPT OF CAPTURE

Classical Capture From Stream Reaches (1980, Vionnet & Maddock)Steady State Transient States

Reach Losing Reach Gaining Reach Losing Reach Gaining Reach ΔR ΔD

1 0.621 0.016 0.605

2 0.106 0.462 0.356

3 0.076 0.719 0.643

4 0.162 0.680 0.680 0.162

5 0.635 0.540 0.540 0.635

6 0.924 0.351 0.351 0.924

7 0.677 0.210 0.467

8 0.548 0.277 0.271

9 0.164 0.068 0.096

10 0.027 0.430

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STATE VARIABLES• Is a variable that describes the state of the

system (e.g. water levels, stream discharge, precipitation)

• Water managers have no direct control over state variables

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CONTROL VARIABLES

• Is a variable that describes something that can be controlled (e.g. Well pumping, streamflow diversions)

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PARAMETERS• Variable specified by the modeler and are

determine by the calibration process• Physically or scientifically based parameters –

Actual measurements• Calibration Factors – No measurements (or

bounds)• Calibration of the models’ physically based

parameters provides a measure of the natural error of the model.

• Calibration factors mask the natural error of the model and may improperly influence the Base Model

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KANSAS v COLORADO

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Crops

Riv

er

CanalEntity A

Entity B

Wells

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Crops

Riv

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Canal

Entity A

Entity B

Wells

Div

ersi

on

Red

uct

ion

Fac

tor

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Crops

Riv

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Canal

Entity A

Entity B

Wells

Div

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Mag

nif

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Fac

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