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8/12/2019 L2_Hydrographs
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1
Well Hydrographs
• Today
– Measuring Water
Levels
– Water Level
Fluctuations
– Examples
– Best reference:
Todd and Mays,
Groundwater Hydrology ,
Wiley, 2004
(Todd, 1980)
2
(Sanders, 1998)
One-time measurements: electrical circuit indicator
Measuring Water Levels
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Long-term monitoring
(Sanders, 1998)
Measuring Water Levels
Old method—Stevens chart recorders
(McGlashan, 1921, plate IV)
4
Modern method—electronic sensing and data logger
The submerged pressuretransducer contains asensitve element,
e.g., a piezometric crystal,
vibrating wire, or deflecting
membrane.
(Sanders, 1998)
Long-term monitoringMeasuring Water Levels
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 thesensitve element varies
in response to thepressure exerted upon it.
The liquid level or distance
transducer uses a variety ofmethods, 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
6
Measuring observation-well water levels for time-
drawdown analysis of a pumping test
(Figures from Schwartz & Zhang, 2005)
Various ways of
plotting for diagnosticsand 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) W
e e k l y P r e c i p ( c m )
A v e r a g e W a t e r L e v e l E l e v . ( 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 S s ( ! " 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?
8
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 fluctuationsare driven by ET.
Other diel fluctuations are
driven by stream stage, oceantides, 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
D e p t h t o w a t e r t a b l e ( m )
10
Confined aquifer head changes,
responding to atmospheric pressure.
(Todd, 1980; after Robinson)
Days of the month
W a
t e r l e v e l a b o v e d a t u m
( m )
0 . 7
5 x a t m o
s p h e r i c p r e s s u r e ( m H 2 0 )
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?
i n c r e a
s i n g d o w n w a r d
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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,
responding to atmospheric pressure.
Aquiclude
Aquiclude
Aquifer
uncapped well
12
patm
# patm
patm
h1
h2
# ptm
Confined aquifer head changes, open hole,
responding to atmospheric pressure.
Head drops with
increase in patms
(Todd, 1980)
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Confined aquifer head changes, open hole,
responding to atmospheric pressure.
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:
dV w = " (n# +$ ) V t dp
" dpaquifer =#dV w
n$ +% ( )V t
14
Confined aquifer head changes, open hole,
responding to atmospheric pressure.
In the open hole the only elastic response is compression
of the water:
dpV ndV t w ! "=
" dpwell =#dV w
n$ V t
" dpwell
dpaquifer
= #n$ V t dV w( )#dV w % + n$ ( )V t
= n$ % + n$
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15
Confined aquifer head changes, open hole,
responding to atmospheric pressure
Barometric efficiency is expressed in terms of the ratio
of the change in well head to change in atmosphericpressure. We therefore have to divide by ! to convert:
BE =" water#hwell
# patm
=
n$
% + n$ =
" n$
S s
! and " are constants and we can often estimate
n fairly well. If so, we can use BE to estimate Ss:
S s=
" n#
BE
16
(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
18
Confined aquifer near the oceanThe aquifer under the ocean has the usual compressive
response:
" dpaquifer =#dV w
n$ +% ( )V t
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 =#dV w
$ V t
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19
Confined aquifer near the ocean
TE ="h
well
"htide
=
#V w$ dV
w
# $ + n% ( )V wdV w=
$
$ + n% =
&$
S s
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)
20
(Todd, 1980; after Robinson)
Confined aquifer head changes, open hole,
responding to the moon: earth tides.
Days of the month
W a
t e r l e v e l a b o v e d a t u m
( m )
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21
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
Confined aquifer head changes, open hole,
responding to the moon: earth tides.
22
patm
# patm
pw# pw
#$ e
$ e
# pw (aquifer)< # patm
Because the packed off well bore is not directly connected to the atmosphere thewater 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 = % & r w2 bo,
where bo is height of the interval below the packing.
Confined aquifer head changes, packed-off interval,
responding to atmospheric pressure.
Aquiclude
Aquiclude
Aquifer
Packing
# pin well = ?# pin well ! # pw(aquifer)bo
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23
Groundwater
head fluctuations
Wells at various
distances from a
river
(Todd, 1980; after Werner and Noren)
Water table aquifer near a river Elbe River in Germany
Note:
Amplitude Reduction
Phase Lag
(not evident in this
example)
Both increase with
distance from the
river.
24
“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 s L2 /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 S s ( ! " 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.
26
What is it?
5 cm
1 day
Groundwater head fluctuationshead
time
Frog
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27
Well Hydrographs
• Review
– Measuring Water
Levels
– Water Level
Fluctuations
– Examples
• Fluctuations due to well
tests, ET, recharge,
atms. pressure, earth
tides, river stage, oceantides, surface loading,
etc.
• Next time
– Simulation Methods
– Computer Models
Visual Modflow