Water Supply Study

Present and Planned Water Supply

• Operational (2001) spring water bottling plant, with groundwater extraction rates approximating 125 gpm.

• Planned groundwater extraction of up to 400 gpm.

• Concerns about impacts to nearby water bodies.

Critical Prediction

Calculate changes in Surface-Water Flows, Wetland and Lake Levels from Constant Production of 400 gpm

0ft 10000ft 20000ft

Regional Model Design

Study Area

Selected CodeMODFLOW2000

Model Summary4 layersConductivity zones derived from

regional/local geologic studiesVariable recharge derived from

published regression analysis

Local Model Area

Impoundment

Stream

Pumping Center

Spring

Outfall

Groundwater Flow

Shortcomings in Problem Formulation

Modeling Tool – Use of River Package

• Inability to realistically represent changes in streams, wetlands, and lakes.

• Inability to explicitly represent the impoundment-overflow

Stream

Impoundment CulvertDischarge

Stream

Revised Problem Formulation

• Digitized stream intersections and topo maps to assign MODFLOW Drain/River - revised during calibration.

• Impoundment and nearby lakes represented with Lake Package (Merritt and Konikow, 2000); outflow from impoundment explicitly modeled.

• Four wetlands with standing water modeled with Lake Package to explicitly simulate wetland water levels.

• Stream simulated using MODFLOW Drain Package plus Impoundment outflow.

• Regional river comprises down gradient drainage center.

Model Calibration

Calibration Strategy

• Steady-state calibration to water levels in 48 wells, baseflow in five creeks, and lake levels in five lakes.

• Transient calibration to drawdowns from long-term (72 hour) pumping test - one dozen wells with time-series drawdown data

• Prior information used to establish total transmissivity as ‘soft’ information during steady-state calibration

• Approx. 40 parameters – step-wise reduction using tied/untied parameters as calibration progressed

• PEST used in parallel across four 1.8GHz processors

PEST Pre-Post Processing

Advantages over GUI or ‘prompt’ Execution

• Ability to assess progress with every run

• Ability to re-parameterize (tie, hold, transform, scale, prior, regularize) model without ‘rebuild’

• Ability to alter run type with one (or two) quick Control File modifications – Forward run, Estimation, Regularization, and Prediction

program fluxes

c Read output from MF2K Lak package modified by Mark Kuhl, to sum

c baseflows over target reaches and write to single file for use

c as PEST targets.

c General declarations

parameter(ncol=243,nrow=164,nlay=4)

implicit double precision (c,d,r,g,s,m, b)

dimension riv(:,:), drn(:,:), iriv_rch(:,:) , idrn_rch(:,:)

integer kper, kstp, jj, i, j, k, idrn_rch, iriv_rch, nriv, idum

c Files produced by MKUHL's MODFLOW Package

character*20 drnfile, rivfile

character*23 lakfile

c Output file from this program for PEST

character*12 pestout

c Specific Target Names

c 1: COLE_CREEK: Drain Reach 1

c 2: GILBERT_CREEK: Drain Reach 2, River Reach 2

c 3: DEAD_STREAM: Drain Reach 3

c 4: BURDON_CREEK: River Reach 3

c 5: MUSKEGON_RIVER: River Reach 4 + SUMMED COMPONENTS

allocatable riv, drn, idrn_rch, iriv_rch

allocate(riv(ncol,nrow),drn(ncol,nrow), idrn_rch(ncol,nrow),

+ iriv_rch(ncol,nrow))

drnfile='drain_cell_flows.dat'

rivfile='river_cell_flows.dat'

lakfile='lake_flow_and_level.dat'

pestout='pestout.dat'

idrn_rch=0

iriv_rch=0

c=======================================================================

c MAIN PROGRAM START

c=======================================================================

c Read drain flows: KPER, KSTP ,R, C, Q (L^3/T)

Open(1,file=drnfile)

Read(1,*)

Do jj=1,20000

c Use drntemp to account for multiple reaches in one cell

drntemp=0.

read(1,1,end=991) kper, kstp, i, j, drntemp

drn(j,i) = drn(j,i)+drntemp

End do

991 Close(1)

c Read river flows: KPER, KSTP ,R, C, Q (L^3/T)

Open(1,file=rivfile)

Read(1,*)

Do jj=1,20000

c Use rivtemp to account for multiple reaches in one cell

rivtemp=0.

read(1,1,end=992) kper, kstp, i, j, rivtemp

riv(j,i) = riv(j,i) + rivtemp

End do

992 Close(1)

c Read Osprey Lake outflows, and stages for the five simulated lakes

Open(1,file=lakfile)

Read(1,*) sprey_out, sL1, sL2

Close(1)

c=======================================================================

c 1: COLE CREEK - Comprises drains ONLY: SG-103

c=======================================================================

c Drain flows within COL-ROW range

COLE_CREEK = 0.

do i=1,nrow

do j=1,ncol

if (i.ge.21.and.i.le.121) then

if (j.ge.16.and.j.le.144) then

COLE_CREEK = COLE_CREEK + drn(j,i)

idrn_rch(j,i) = 1

endif

endif

end do

end do

c Subtract flows which accumulate and go northwards at divide

COLE_NORTH = 0.

do i=1,nrow

do j=1,ncol

if (i.ge.32.and.i.le.47) then

if (j.ge.42.and.j.le.49) then

COLE_NORTH = COLE_NORTH + drn(j,i)

idrn_rch(j,i) = 0

endif

endif

end do

end do

COLE_CREEK = COLE_CREEK - COLE_NORTH

c=======================================================================

c 2: GILBERT_CREEK - Comprises drains and rivers: SG-101

c=======================================================================

c Drain flows within COL-ROW range

GILBERT_DRAIN = 0.

do i=1,nrow

do j=1,ncol

if (i.ge.16.and.i.le.96) then

if (j.ge.166.and.j.le.211) then

GILBERT_DRAIN = GILBERT_DRAIN + drn(j,i)

idrn_rch(j,i) = 2

endif

endif

end do

end do

c River flows upgradient of drain delineation

GILBERT_RIVER = 0.

do i=1,nrow

do j=1,ncol

if (i.ge.4.and.i.le.15) then

if (j.ge.16.and.j.le.210) then

GILBERT_RIVER = GILBERT_RIVER + riv(j,i)

iriv_rch(j,i) = 2

endif

endif

end do

end do

GILBERT_CREEK = GILBERT_DRAIN + GILBERT_RIVER

write(*,*) GILBERT_DRAIN, GILBERT_RIVER

c=======================================================================

c 3: DEAD_STREAM - Comprises drains and Osprey Lake Outflow: SG-102

c=======================================================================

c Drain flows within COL-ROW range

DEAD_STREAM = 0.

do i=1,nrow

do j=1,ncol

if (i.ge.97.and.i.le.113) then

if (j.ge.175.and.j.le.204) then

DEAD_STREAM = DEAD_STREAM + drn(j,i)

idrn_rch(j,i) = 3

endif

endif

end do

end do

c Osprey Lake outflows: use NEGATIVE of Sprey_out as this is +ve

DEAD_STREAM = DEAD_STREAM + (-SPREY_OUT)

c=======================================================================

c 4: BURDON_CREEK - Comprises rivers only: SG-104

c=======================================================================

c River flows within COL-ROW range

BURDON_CREEK = 0.

do i=1,nrow

do j=1,ncol

if (i.ge.92.and.i.le.126) then

if (j.ge.11.and.j.le.53) then

BURDON_CREEK = BURDON_CREEK + riv(j,i)

iriv_rch(j,i) = 3

endif

endif

end do

end do

c=======================================================================

c 5: MUSKEGON_RIVER - All drainage contributing to tri-lakes: SG-105

c=======================================================================

c Begin by summing all the components calculated above

MUSKEGON_RIVER = 0.

MUSKEGON_RIVER = COLE_CREEK + GILBERT_CREEK + DEAD_STREAM +

+ BURDON_CREEK

Write(*,*) 'MUSKEGON TRIBS :', MUSKEGON_RIVER

c Now account for river cells representing the main lakes, etc.

do i=1,nrow

do j=1,ncol

if (i.ge.89.and.i.le.125) then

if (j.ge.54.and.j.le.213) then

MUSKEGON_RIVER = MUSKEGON_RIVER + riv(j,i)

C if (riv(j,i).ne.0) then

C write(*,*) j,i,riv(j,i)

C end if

iriv_rch(j,i) = 4

endif

endif

end do

end do

Write(*,*) 'MUSKEGON TRIBS + WEST RIVERS:', MUSKEGON_RIVER

do i=1,nrow

do j=1,ncol

if (i.ge.126.and.i.le.128) then

if (j.ge.197.and.j.le.211) then

MUSKEGON_RIVER = MUSKEGON_RIVER + riv(j,i)

iriv_rch(j,i) = 4

endif

endif

end do

end do

Write(*,*) 'MUSKEGON TRIBS + MID RIVERS :', MUSKEGON_RIVER

do i=1,nrow

do j=1,ncol

if (i.ge.129.and.i.le.129) then

if (j.ge.209.and.j.le.211) then

MUSKEGON_RIVER = MUSKEGON_RIVER + riv(j,i)

iriv_rch(j,i) = 4

endif

endif

end do

end do

Write(*,*) 'MUSKEGON TRIBS + ALL BODIES :', MUSKEGON_RIVER

c=======================================================================

c Write target data to single file for PEST

c=======================================================================

COLE_CREEK = (LOG10(-COLE_CREEK))

GILBERT_CREEK = (LOG10(-GILBERT_CREEK))

DEAD_STREAM = (LOG10(-DEAD_STREAM))

BURDON_CREEK = (LOG10(-BURDON_CREEK))

MUSKEGON_RIVER= (LOG10(-MUSKEGON_RIVER))

if (sprey_out.gt.0.) then

Sprey_out = (LOG10(Sprey_out))

else

sprey_out = 0.

End if

Open(1,file=pestout)

Write(1,'(a30)') 'FLUX TARGET MODELED'

Write(1,'(a19,e15.7)') 'COLE_CREEK :', COLE_CREEK

Write(1,'(a19,e15.7)') 'GILBERT_CREEK :', GILBERT_CREEK

Write(1,'(a19,e15.7)') 'DEAD_STREAM :', DEAD_STREAM

Write(1,'(a19,e15.7)') 'BURDON_CREEK :', BURDON_CREEK

Write(1,'(a19,e15.7)') 'MUSKEGON_RIVER :', MUSKEGON_RIVER

Write(1,'(a19,e15.7)') 'OSPREY LAKE OUTFL :', Sprey_out

Write(1,'(a19,e15.7)') 'OSPREY LAKE LEVEL :', sL1

Write(1,'(a19,e15.7)') 'LAKE 2 LEVEL :', sL2

Write(1,'(a19,e15.7)') 'LAKE 3 LEVEL :', sL3

Write(1,'(a19,e15.7)') 'LAKE 4 LEVEL :', sL4

Write(1,'(a19,e15.7)') 'LAKE 5 LEVEL :', sL5

Close(1)

Write(*,*) 'GILBERT_CREEK :', GILBERT_CREEK

c=======================================================================

c Read original MODFLOW DRN and RIV packages, and assign REACHES

c=======================================================================

c Comment-out the GOTO to re-write packages with reach numbers

goto 20

Open(1,file='MICHIGAN_No_Reaches.riv')

Open(2,file='Michigan_reaches.riv')

c MODFLOW 2000 headers

Read(1,*)

Read(1,*)

Read(1,*) nriv,idum

Write(2,'(2I10)') nriv,idum

Read(1,*) nriv

Write(2,*) nriv

c Lay, Row, Col

Do n=1,nriv

Read(1,*) k,i,j,stage,cond,rbot

Write(2,2) k,i,j,stage,cond*10,rbot,iriv_rch(j,i)

End do

Close(1)

Close(2)

Open(1,file='MICHIGAN_No_Reaches.drn')

Open(2,file='Michigan_reaches.drn')

c MODFLOW 2000 headers

Read(1,*)

Read(1,*)

Read(1,*) nriv,idum

Write(2,'(2I10)') nriv,idum

Read(1,*) nriv

Write(2,*) nriv

Do n=1,nriv

c Lay, Row, Col

Read(1,*) k,i,j,rbot,cond

Write(2,3) k,i,j,rbot,cond,idrn_rch(j,i)

End do

Close(1)

Close(2)

20 Continue

c=======================================================================

c FORMAT STATEMENTS

c=======================================================================

1 Format(4I11,F21.0)

2 Format(3I10,F10.3,E10.3,F10.3,I10)

3 Format(3I10,F10.3,E10.3,I10)

c=======================================================================

c END OF PROGRAM

c=======================================================================

STOP 'Normal Exit'

END

Batch File

Batch and Post-ProcessingPost-Processor

REM File Management

del headsave.hds

copy mich_fin.hds headsave.hds

del mich_fin.hds

del mich_fin.ddn

del calibration.hds

REM Run array multiplers

cond_mult

rech_mult

REM Run custom MF2K Lake Package

cust_lak3 <modflowq.in

REM get the water level target data

targpest

REM get the flux target data

flux_targets

copy mich_fin.hds calibration.hds

REM Check for water above land surface

wl_above_ls

Calibration Results – SSBaseflows Water Levels

0.E+00

1.E+06

2.E+06

3.E+06

4.E+06

0.E+00 1.E+06 2.E+06 3.E+06 4.E+06

940.0

960.0

980.0

1000.0

1020.0

1040.0

9.4E+02 9.6E+02 9.8E+02 1.0E+03 1.0E+03 1.0E+03

WL Sum of Squares (PHI) = ~ 115 ft2

Count = 48 wells

Mean Residual = - 0.2 ftMean Absolute Residual = 1.1 ftStDev of the residuals = 1.5 ftRange = 63 ftStDev/Range = ~

2.25%

Calibration Results – TransientDrawdowns

OW-4

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.1 1 10

Elapsed Time (Days)

MW-102

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00

0.00

0.1 1 10

Elapsed Time (Days)

MW-104S

-0.40

-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.0001 0.001 0.01 0.1 1 10

Elapsed Time (Days)

OW-7

-1.00

-0.75

-0.50

-0.25

0.00

0.1 1 10

Elapsed Time (Days)

Predictive Analysis

Problem Formulation and Execution

• Reformulate the PEST calibration control file to estimate the max and min baseflow depletions in stream, while maintaining calibration – i.e. establish the range of uncertainty

• Typically the increment added to the calibration objective function (min + is about 5% of min.

For our analysis, this was raised by 50%

Predictive Analysis

Present and Planned Water Supply• With total planned groundwater extraction of 400 gpm.

-Predicted stream depletion at regional river: 400 gpm

-Depletion of interest stream: small but measurable*

-Changes in wetland water levels: small but measurable*

The calculated upper- and lower-bound estimates of the change in flow at the stream are on the order of five percent (above or below) of the ‘most likely’ estimated change.

*This is consistent with the observation that wetland water levels, and the areal extent of wetlands based on aerial photographs were not significantly affected by the construction of the impoundment .

Salient Point(s)

• Problem formulation is key to the ‘integrity’ of the predictive analysis – the selected code must be designed to simulate the type of prediction of interest.

• The fairly tight bounds on the prediction may also arise from the ability of models to predict changes far better than absolute numbers.