Overview of modeling methods
to estimate stream depletions
due to pumping
Gordon McCurry, PhD, PG
Senior Hydrogeologist, Geomega, Inc.
Colorado Aquifer Management Conference
November 28, 2012
Outline
• Background on Aquifer Response to Pumping
– Sources of water to a well
– Pumping Effects
– Lagged Depletions
• Analytical Models
– Simplifying Assumptions
– Models in Use
• Numerical Models
– Modeling Approaches
– URFs and Response Functions
Aquifer Response To Pumping
• Pumping initially takes
water from aquifer
storage
• Next stage is capturing
water that would
discharge to a stream
• Later stage is inducing
flow from the stream
Effect of Pumping on Streamflow
• Pumping reduces streamflow, but short-term
changes in flow still exist
Effect of Well Proximity on Depletions
• Wells closer to a stream have more immediate
effects and are more likely to induce stream flow
Effect of Well Proximity on Depletions
• Wells closer to a stream affect a smaller
reach than wells farther away
Effect of Multiple Wells
• Effects of multiple
pumping wells are
additive
• Incremental effects
of individual wells
can result in large
stream depletions
Effect of Streambed Sediment
Lagged Effect on Depletions
• Depletions occur
after pumping
ends, until the
cone of depression
is replenished.
• Lagged effects can
last months, with
peak depletions in
winter months
Analytical Modeling Approaches
• Require simplified aquifer settings and assumptions
• Are quick to implement, easy to explain
Qs = Qw erfc(a2S/4Tt)
Qs = stream depletion
Qw = well pumping rate
a = distance from well to stream
S = aquifer storage coefficient
T = aquifer transmissivity
t = duration of pumping
• Long history of use in Colorado; well accepted
Key Analytical Stream Depletion Models
• Glover and Balmer, 1954
• Hantush, 1965 (streambed sediment layer)
• Jenkins, 1968 (SDF concept)
Qs = 0.28* Qw ( = time to depletion)
• Colorado DWR, 1978 (SDF model)
• CSU IDS, 2004 (AWAS model)
• USGS, 2008 (STRMDEPL08 model)
Example SDF Map (AK River Valley)
Analytical Model Assumptions
• Alluvial aquifer settings are greatly simplified
(homogenous, uniform properties)
• Do not allow for meandering rivers, tributaries,
complex aquifer boundaries
• Can lead to over-prediction of stream depletions
Real Aquifer
Modeled Aquifer
Recent Analytical Approaches
• Include partially
penetrating streams,
streambed layers
(Hunt, Butler, Fox, Chen)
• and leaky aquifer
confining layers, lateral
boundary effects
(Zlotnik, Miller, Hunt)
Numerical Modeling Approaches
• Includes
heterogeneous
aquifers and
multiple stream
tributaries
• Aquifer settings
represented in
numerical grids
• Computationally
• Yields more accurate results
intensive; large
for complex settings
input & output files
Numerical Modeling Approaches -2
• Depletion effects estimated by:
– Running the model without the pumping well
and recording river flows over time
– Running the model with a pumping well at a
unit rate for a unit duration (1cfs for 1 month,
etc) and recording river flows over time
– Determine pumping-based depletions from
the difference in the model results ( = Unit
Response Functions, URFs)
– Tabulating depletions by river reach
Pumping Response Functions
• Developed using
analytical or numerical
models
• Describes the amount
of pumping that comes
from one or more
nearby streams
Response Function Examples
• Developed for San Luis
Valley, Colorado, for the
RGDSS
• 93 zones represent unit
response to pumping
• Zones oriented parallel
to rivers, with increasing
width away from rivers
• One well placed in each
zone, pumped at 1 cfs
for 20 years
Response Function Examples
• Platte River Basin, NE
• 28% depletion after 40 years of pumping
Response Function Examples
• Loup River, NE
• Map is percent of
pumping from stream
depletions after 50
years of pumping of 1
cfs in a given cell
• Developed using
numerical model with
unit response placed
in each of 22,000
model cells
Response Function Examples
• San Pedro River, AZ
• Depletions after 10
years of pumping
• Developed using
numerical model
(Modflow), with unit
response input per
model cell (~ 10,000
cells)
Summary and Conclusions
• Pumping depletes stream flow by capturing discharge
and inducing flow from the steam
• Analytical methods are commonly used due to
precedence and ease of use; can over-predict effects
• Numerical methods include complex aquifer settings
& tributary streams; yield more accurate results
• More accurate methods are appropriate as water use
efficiency becomes more critical
• Unit response functions developed from numerical
methods may be the most effective approach
Thank You