stream-aquifer package

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STREAM-AQUIFER PACKAGE

• The Stream-Aquifer Package is an accounting program that tracks the flow in one or more streams which interact with groundwater.

• The program limits the amount of groundwater recharge to available stream flow, allow the streams to go dry, and allows the streams to rewet.

• The Stream-Aquifer Package is a calculated-stage package as opposed to a specified stage package—the river stages can be calculated by the Package instead of input as data.

• The program permits two or more streams to merge into one, with the flow in the merged stream equal to the sum of the tributary flows.

• The program permits diversions from the stream.

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• Streams are divided into segments and reaches.• A reach corresponds to the individual cells in the finite-difference grid.• A segment consists of a group of reaches connected in a down

stream order.• Leakage is calculated for each reach on the basis of the head

difference between the stream and the aquifer and a conductance term, and then is added or subtracted to the amount of stream flow into the reach.

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STREAM-AQUIFER PACKAGENumbering and Ordering of Streams• A segment (e.g. ) is a stream or

diversion in which streamflow from surface sources are added at the beginning or subtracted (as with a diversion) at the end of a segment,

• A reach (e.g. 1) is the part of the segment that corresponds to an individual cell in the finite difference grid.

• A segment consists of one or more reaches.

• Segments are numbered sequentially from the farthest upstream segment to the last downstream segment as are the reaches within each segment.

1

cell

Note that more than one reach in different segments can be assigned to the same mode cell.

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STREAM-AQUIFER PACKAGE• Streamflow is specified for the first

reach in each segment that enters the modeled area (e.g. , , )

• The streamflow that is computed at as entering an adjacent downstream reach in a segment (Sd) is equal to the inflow from the upstream reach (Su) plus or minus the leakage from or to the aquifer in the upstream reach (Lu)

Sd = Su – Lu

• The streamflow entering the model layer is assumed to be instantly available to downstream reaches.

1

cell

1 4 6

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STREAM-AQUIFER PACKAGE• Streamflow into a segment that is

formed from tributary streams is computed by adding the outflows from the last reach in each of the specified tributary segments.

• If the segment is a diversion, then the specified flow into the first reach of the segment is subtracted from the flow in the main stream

• If the specified flow for the diversion is greater than the flow in the stream it was diverted from, then the diversion is set to zero. (Note: this has been changed in later modifications of the Stream-Aquifer package)

1

cell

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STREAM-AQUIFER PACKAGE• Leakage to or from the stream bed is

computed by Dary’s Law,QL = CSTR(hS – ha)

where,QL is the leakage to or from the streambed [L3/t],HS is the stream stage elevation [L]

Ha is the head in the aquifer side of the streambed [L],CSTR is the streambed conductance [L2/t]

• The stream stage elevation is for the center of the reach.

• The head in the aquifer cell beneath the stream depends on the saturation.

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• If the materials are saturated, the head of the aquifer side of the streambed is equal to the head in the model cell beneath the stream reach.

• If the materials are unsaturated, the head in the aquifer beneath the streambed is equal to the elevation of the bottom of the streambed.

• If leakage through the streambed to the aquifer in a stream reach is greater than the amount of streamflow that enters the reach, then the leakage is set equal to the stream flow that enters the reach, and flow out of the reach is set to zero.

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STREAM-AQUIFER PACKAGEComputing Stream Stage in Reaches• The Stream-Aquifer Package has an option to calculate the stream stage in every

reach.• The stream stage is computed assuming incompressible steady state flow in the

stream at constant depth and using Manning’s formula,

where,Q is the stream discharge [L3/t],n is Manning’s roughness coefficient,A is the cross-sectional area of the stream [L2],R is the hydraulic radius [L],S is the slope of the stream channel, andC is a constant [L1/3/t], which is 1.486 for units of cubic feet per second and

1.0 for cubic meters per second.

)( 21

32

SARn

CQ

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STREAM-AQUIFER PACKAGE• The cross-sectional area and the hydraulic radius for a rectangular channel are,

and,

whered is the depth of water in the stream [L], andw is the width of the channel [L],

gives,

which computes the stream depth.

wdA

dw

wd

perimeterwetted

areationalseccrossR

2

53

21

CwS

Qnd

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• The streamflow estimates from Manning’s formula are accurate for the intermediate range of roughness coefficients shown in the table on the right.

• Stream stage is calculated prior to calculating leakage to or from the aquifer.

• An iterative procedure is adopted that for a reach, flow into the reach→calculate stream stage→calulate leakage→subtract (add) leakage from (to) flow→re-calculate stream stage→…

Note that this iterative scheme can sometimes lead to instability.

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STREAM-AQUIFER PACKAGEAssumptions and Limitations• The stream-Aquifer Package is not a true routing model because the

streamflow that enters into the first reach of each segment is instantly available in downstream reaches.

• The stream stage calculations assume a rectangular channel where, if Manning’s equation is to hold, the width is much greater than the depth.

• The width of a channel will likely vary with flow and stage in a real stream, requiring an external change of conductance values over stress periods.

• The leakage into the stream is assumed to be instantaneous, which is a valid assumption if there is a hydraulic connection between the stream and aquifer, or if the break in connection is not to great.

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NPSTR—is the number of stream parameters.

MXL—is the maximum number of stream reaches that will be defined using parameters.

MXACTS—is the maximum number of stream reaches in use during any stress period, including those that are defined with parameters.

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NSS—is the number of stream segments.

NTRIB—is the number of stream tributaries that can connect to one segment. Must be less than or equal to ten.

NDIV—is a flag, which when positive, specifies that diversions from segments are simulated

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ICALC—is a flag, which when positive, specifies that stream stages in reaches are calculated

CONST—is constant value used in calculating stream stages in reaches, and is specified whenever ICALC≥0. The value is dependent on units.Cubic-feet/sec→CONST = 1.486Cubic-meters/sec→CONST = 1.0

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STREAM-AQUIFER PACKAGEISTCB1—is a flag and unit number for the

option to write seepage between the stream reaches and model cells into the list file or binary file.ISTCB1 > 0, it is the unit number to which seepage between each stream reach and the corresponding model cell will be saved when a non-zero value for ICBCFL is specified in output control.ISTCB1 = 0, seepage between each stream reach and the corresponding model cell will not be written to any file.ISTCB1 < 0, stream flow for each reach and seepage between each stream reach and the corresponding model cell will be written to the List File when a non-zero value for ICBCFL is specified in output control.

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ISTCB2—is a flag and unit number for the option to store stream flow out of reach into the list file or binary file.ISTCB2 > 0, it is the unit number to which streamflow in each reach will be saved when a non-zero value for ICBCFL is specified in output control.ISTCB2 ≤ 0, streamflow in each reach will not be written to any file.

PARNAM—is the name of a parameter. This name can consist of 1 to 10 characters, and is not case specific.

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PARTYP—is parameter type. There is only one parameter type for the STR Package—the streambed conductance, STR.

Parval—is the parameter value.

NLST—is the number of stream reaches that are included in the parameter.

.

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STREAM-AQUIFER PACKAGEITMP—is a flag and a counter whose

meaning depends on whether or not stream parameters are being usedIf NPSTR>0, ITMP is the number of stream parameters being used in the current stress period (similar to NP of other packages).

If NPSTR=0,ITMP<0, non-parameter

stream data from last stress period will be reused.

ITMP≥0, ITMP will be the number of non-parameter stream reaches read for

current stress period.

.

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IRDFLG—is a flag, which when positive, suppresses printing of the stream input data for a stress period.If IRDFLG=0 and ICBCFL in output control is set, the input data are printed.

IPTFLG—is a flag, which when positive, suppresses printing of the stream results for a stress period.If IPTFLG=0, ICBCFL in output control is set, and ISTCB1<0, the results are printed.

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Layer—is the layer number of the stream reach.

Row—is the row number of the stream reach.

Column—is the column number of the stream reach.

Seg—is a number assigned to a group of reaches.Segments must be numbered in downstream order and are read into the program in sequential order.

.

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Reach—is a sequential number in a segment that begins with 1 for the furthest upstream reach and continues in downstream order to the last reach in the segment.Reaches must be read in sequentially because the order in which reaches are read determines the order of connection.

.

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STREAM-AQUIFER PACKAGEFlow—is the streamflow entering the

segment.This value is used for the first reach of each segment.The value should be specified as either a 0 or a blank when the reach number is not 1.When the inflow to the first reach of a segment is the sum of the outflows from upstream tributary segments, Flow should be specified as -1.When the segment is a diversion, the Flow for each reach is the amount to divert, however, there will be no diversion if the segment from which the diversion is obtained contains less than the value of Flow.

.

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Stage—is the stream stage.The value of stage is not used if ICALC>0

Condfact—is the factor used to calculate the streambed hydraulic conductance from the parameter value. The conductance is the product of Condfact and the parameter value.

Cond—is the streambed hydraulic conductance.

Sbot—is the elevation of the bottom of the streambed.

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STREAM-AQUIFER PACKAGEStop—is the elevation of the top of

the streambed.The value of Stop is used if the option to calculate stream stage is active (ICALC>0) or when the streambed has zero flow.

Pname—is the name of the parameter that is being used in the current stress period.ITMP parameter names will be read.They must be specified in an order that meets downstream ordering requirements for Seg and Reach.

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Width—is the width of the stream channel. It is only read when stream stage is calculated (ICALC>0)

Slope—is the slope of the stream channel.It is only read when stream stage is calculated (ICALC>0)

Rough—is Manning’s roughness coefficient.It is only read when stream stage is calculated (ICALC>0)

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STREAM-AQUIFER PACKAGEItrib—contains the segment number for

each tributary that flows into a segment.NTRIB values are read for each segment.Unused values of Itrib should be set to zero.Itrib records are read only if NTRIB>0

Example: There are 4 segment and NTRIB=3, the Format is 10I5

0 0 0

0 0 0

0 0 0

1 2 3

1

2

3

4

Tributaries

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STREAM-AQUIFER PACKAGEIupseg—is the number of upstream

segments from which water is diverted.If the segment is not a diversion, Iupseg should be set to zero.Iupseg records are read only if NDIV>0

Example: There are 5 segment and NTRIB=2, the Format is I10

01030

1

23

4

5

Diversions

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STREAM-AQUIFER PACKAGENo Parameters

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No ParametersNo Parameters, cont.

stream-aquifer package

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