well hydrographs - new mexico tech earth and environmental ... · well hydrographs ¥review...

3/4/08

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Well Hydrographs

• Today

– Measuring Water

Levels

– Water Level

Fluctuations

– Examples

– Best reference:

Todd and Mays,

Groundwater Hydrology,

Wiley, 2004

(Todd, 1980)

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(Sanders, 1998)

One-time measurements: electrical circuit indicator

Measuring Water Levels

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Long-term monitoring

(Sanders, 1998)


Old method—Stevens chart recorders

(McGlashan, 1921, plate IV)

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Modern method—electronic sensing and data logger

The submerged pressure

transducer contains a

sensitve element, e.g., a piezometric crystal,

vibrating wire, or deflecting

membrane.

(Sanders, 1998)

Long-term monitoring


Two approaches:

- depth to water &

- height above submersible

transducer

What is a pressure transducer?

http://www.omega.com/prodinfo/pressuretransducers.html

Current or voltage in the

sensitve element varies

in response to the

pressure exerted upon it.

The liquid level or distance

transducer uses a variety of

methods, e.g., bubbler,

Ultrasonic distance, etc.

Ultrasonic

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Applications

• Well and other hydraulic tests

• Aquifer temporal response to natural & human

induced fluctuations

– Water supply or irrigation pumping

– Precipitation, ET, stream or lake stage, ocean levels

– Barometric pressures & earth tides

• Potentiometric, water level mapping

today

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Measuring observation-well water levels for time-

drawdown analysis of a pumping test

(Figures from Schwartz & Zhang, 2005)

Various ways of

plotting for diagnostics

and parameter

estimation, including

log-log and semilog

plots.

one application of water-level measurement devices).

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(Todd, 1980)

What do these

“”rises” represent?

Time (weeks)

We

ekly

Pre

cip

(cm

)

A

ve

rag

e W

ate

r L

eve

l E

lev.

(m

)

What do these “decays” represent?

Seasonal shallow-groundwater head

fluctuations & precipitation in Maryland

The groundwater response lags recharge. It is slow to respond to changes.

Response is characterized by a time constant, say !, that ranges from weeks to millennia,

depending on aquifer size L, conductivity K, and storage Ss ( ! " SL2/T or S s L2/KL2).

Related to stream base-flow recession

Why do seasonal

gw levels tend to

be low in the fall?

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Summer

After frost

(Todd, 1980; after White)

Notice these plots are depth to

the water level, a common way

of recording data;

head is elevation of the well

datum minus the depth.

These summer diel fluctuations

are driven by ET.

Other diel fluctuations are

driven by stream stage, ocean

tides, earth tides, etc.

Diel fluctuations of shallow-groundwater head

for two different seasons in Utah

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(Todd, 1980)

Long-term shallow-water level changes;

human impacts in Pakistan

What is happening?

Year

De

pth

to

wa

ter

tab

le

(m)

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Confined aquifer head changes,

responding to atmospheric pressure.

(Todd, 1980; after Robinson)

Days of the month

W

ate

r le

vel above d

atu

m (m

)

0.7

5 x

atm

ospheric p

ressure

(m

H20)

What is the

correspondence

between these

two time series?

Question? Why is there so little (almost unobservable)

time lag between atms. pressure and aquifer head?

incre

asin

g d

ow

nw

ard

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patm

#patm

patm

h1

h2

pw#pw

#$e

$e

#pw (aquifer)< #patm

#pin well = #patm

#patm

Confined aquifer head changes, open hole,


Aquiclude

Aquiclude

Aquifer

uncapped well

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patm

#patm

patm

h1

h2

#ptm



Head drops with

increase in patms

(Todd, 1980)

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Since z does not change, dhwell/dhatm = dpwell/dpatm

Atmospheric loading on the top of the aquifer is just

like any other loading (e.g., pumping). From basic

storage mechanics we remember:

!

dVw = " (n# +$) Vt dp

!

" dpaquifer =#dVw

n$ +%( )Vt

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In the open hole the only elastic response is compression

of the water:

dp VndV tw !"=

!

" dpwell =#dVw

n$Vt

!

"dpwell

dpaquifer=

#n$Vt dVw( )#dVw % + n$( )Vt

=n$

% + n$

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responding to atmospheric pressure

Barometric efficiency is expressed in terms of the ratio

of the change in well head to change in atmospheric pressure. We therefore have to divide by ! to convert:

!

BE ="water#hwell#patm

=n$

% + n$="n$

Ss

! and " are constants and we can often estimate

n fairly well. If so, we can use BE to estimate Ss:

!

Ss

="n#

BE

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(Todd, 1980; afer Meinzer)

Confined aquifer near the ocean.Effect of ocean tides along Maryland coast.

Note:

Amplitude Reduction

Phase Lag (if well is some distance from shore)

Both increase with distance from the ocean.

well is 100 ft. from from shore:

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Confined aquifer near the ocean

!

"hwell

"htide

= TE

Tidal Efficiency

if well is very close to ocean

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The aquifer under the ocean has the usual compressive

response:

!

" dpaquifer =#dVw

n$ +%( )Vt

The water level in the well responds to compression

in the aquifer, but is always at atm pressure (assumed

constant) and thus does not compress:

!

" dpwell =#dVw

$Vt

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!

TE ="h

well

"htide

=#V

w$dV

w

# $ + n%( )VwdV

w

=$

$ + n%=&$

Ss

!

TE ="

" + n#

!

BE =n"

# + n"

!

TE + BE =" + n#

" + n#=1

TE is useful for parameter estimation mostly only in a relative

sense (if TE<<1, then Ss is quite small)

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(Todd, 1980; after Robinson)


responding to the moon: earth tides.

Days of the month

W

ate

r le

vel above d

atu

m (m

)

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When the moon is overhead, the

Earth bulges out, pores dilate,

and water level drops

This effect is usually only seen

in stiff aquifers, such as

fractured granite


responding to the moon: earth tides.

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patm

#patm

pw#pw

#$e

$e

#pw (aquifer)< #patm

Because the packed off well bore is not directly connected to the atmosphere the

water pressure in the well increases with that in the aquifer (due to the very small

volume, V, of water needed to increase pressure by compressibility; V = % & rw2 bo,

where bo is height of the interval below the packing.

Confined aquifer head changes, packed-off interval,


Aquiclude

Aquiclude

Aquifer

Packing

#pin well = ?#pin well ! #pw(aquifer)bo

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Groundwater

head fluctuations

Wells at various

distances from a

river

(Todd, 1980; after Werner and Noren)

Water table aquifer near a riverElbe River in Germany

Note:

Amplitude Reduction

Phase Lag

(not evident in this

example)

Both increase with

distance from the

river.

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“Attenuation of a periodic signal”

Amplitude

reduction

in well 1

Phase lag well 1

Stream stage

Amplitude reduction & phase lag

increase with time constant,

SL2/T or S sL2/K,

where L is the appropriate

length scale.

Well 1 hydrograph (water level) at L=50m

Well 2 hydrograph at L=100m

The groundwater response lags periodic forcings and BC. Slowr esponse is

characterized by a time constant, say !, that ranges from weeks to millennia, depending

on aquifer size L, conductivity K, and storage Ss ( ! " SL2/T or S s L2/KL2).

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(Todd, 1980; after Vorhis)

What is it?

Groundwater head fluctuations in Chile

due to an earthquake.

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What is it?

5 cm

1 day

Groundwater head fluctuationshead

time

Frog

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Well Hydrographs

• Review

– Measuring Water

Levels

– Water Level

Fluctuations

– Examples

• Fluctuations due to well

tests, ET, recharge,

atms. pressure, earth

tides, river stage, ocean

tides, surface loading,

etc.

• Next time

– Simulation Methods

– Computer Models

Visual Modflow

well hydrographs - new mexico tech earth and environmental ... · well hydrographs ¥review...

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