Development of a Cumulative Streamflow Depletion Map for the Wisconsin Central Sands based on
the Modeled Impact of Agricultural High Capacity Well Pumping
David Mechenich and George Kraft
Center for Watershed Science and Education, UWSP
January 11, 2016
In order to quickly access the potential impacts of high capacity well development in the Wisconsin
Central Sands, a map of cumulative streamflow depletion from existing well pumping can be used as a
scoping tool to identify at risk areas. Depletion is the difference between the pumping and reference
condition and the goal is to display the depletion by stream reaches cumulatively from headwaters to
the stream outlet at the bounding waters (Plover and Wisconsin Rivers on the west and the Wolf and
Fox rivers on the east). The “Extended” MODFLOW model of the Wisconsin Central Sands area was used
as the basis to calculate the impact of pumping wells on surface waters.
The main process steps are:
1. Define the flow network using the modeled surface water hydrography layer. That is, define how the
flow system is joined so that modeled groundwater fluxes to surface waters can be traced downstream.
2. Using the surface water hydrography layer, define the reaches for displaying the streamflow
depletion.
3. Apply the surface water flow network and reach definition to the modeled representation of the
surface water source/sinks (model constant head, river, and drain cells).
4. Run the model for reference and pumping scenarios, and export the fluxes for source/sink cells.
5. Calculate the cumulative streamflow depletion by reach and map this depletion at an appropriate
scale with useful symbolization and annotation.
Defining the flow network
The hydrography layer as used for the Central Sands Extended model developed over time with roots in
other models for various subareas of the Central Sands. It is a combination of the Wisconsin 1:24k and
100k hydrography, edited and generalized in some cases, to capture the key surface water features
needed to implement the conceptual flow model. The flow network was defined using the source
hydrography rather than model cells directly to allow for a complete description of the flow network;
the 200 meter model source/sink cells are often a further generalization of multiple hydrographic
features.
The hydrography layer (flowlines and associated waterbody shoreline arcs) was dissolved when two
lines have an end vertex in common. This resulted in a clean layer with continuous segments between
junctions. Arc direction is upstream to downstream. To make the networking process manageable for
the entire model area, the stream arcs were divided into 50 subsystems, 23 for the Wisconsin River, 16
for the Wolf River, and 11 for the Fox. The constant head water table boundary along the southern
edge of the model was also included as a subsystem to complete the flux balance for the model. Using a
python script, hydrography arcs were uniquely numbered within each subsystem upstream to
downstream, and the tributaries to and diversion from each arc noted. Stream diversions split the flow
evenly unless specifically noted otherwise. Waterbody arcs were treated slightly differently; one of the
arcs for a given waterbody was assigned in the network to accumulate all flow so that the cumulative
flow for a reservoir waterbody encompassing multiple shoreline arcs and tributaries could be easily
calculated. A total of 2894 unique segments were included in the network.
Defining stream reaches
Because no available watershed based stream reach network appears to consistently provide a workable
breakdown, the stream reaches were initially defined as the individual segments mapped in the flow
network step above. Large reaches were then further divided according to specified rules. Because
headwater reaches are the most sensitive to pumping depletion, the objective is to divide longer
headwater reaches to maintain as closely as possible a progression of reach lengths, starting with a
minimum length of one mile, and progressing in one mile additions until a maximum length of 5 miles is
obtained. In other words, the ideal segmentation is 1, 2, 3, 4, 5, 5, 5… miles. The one mile reach is
defined as beginning at the stream wetup point (as determined by the unstressed reference model).
Obviously, dividing irregular length reaches results in segments slightly more or less than the ideal
progression, although a minimum length of one mile is maintained for the first segment. The
breakpoints for dividing reaches are given in table 1, and are the values resulting in the least overall
difference between calculated and ideal lengths. A target reach length in any given case is calculated as
a fraction of the total available length relative to the proportion of the ideal length to ideal cumulative
length.
Long non-headwater reaches (below one or more junctions) are also divided based on the rules noted
above. The initial step in this case is to determine where the reach to be divided falls in the 1, 2, 3, 4, 5,
5… progression. The cumulative stream length above the reach to be divided is compared to the
breakpoints and the ideal reach length at this position in the flow system is the maximum reach length
associated with that breakpoint. The specific number of new segments are determined by the
breakpoints adjusted by the number and length of shorter segments not included. For a 7.1 mile nonheadwater example starting with the 3 mile length segment, the 8 mile breakpoint becomes 5 by
subtracting 3 (the 1 and 2 mile lengths) and the corresponding number of reaches 4 becomes 2 by
subtracting 2 (the number of segments in the standard progression not included, that is, the 1 and 2
mile segments).
A python script was used that applies these rules to the stream network, creating a new stream layer
with the appropriate reach lengths. This increased the unique reach segments in the network to a total
of 3583.
Table 1. Breakpoints for dividing reaches and the resultant minimum and maximum reach lengths.
Breakpoint
miles
2
4.5
8
12.5
17.5
22.5
Number
of Reaches
1
2
3
4
5
6
7
Ideal:
-1.000
1.000
1.000
1.000
1.000
1.000
1
1
2
3
4
5
6
7
1.999
1.500
1.333
1.250
1.167
1.125
1.100
Minimum Divided Reach Length - miles
1.000
1.400
2.100
1.556
2.333
3.111
1.643
2.464
3.286
4.107
1.737
2.605
3.474
4.342
4.342
1.792
2.688
3.583
4.479
4.479
2
3
4
5
5
Maximum Divided Reach Length - miles
2.999
2.666
2.500
2.333
2.250
2.200
4.000
3.750
3.500
3.375
3.300
5.000
4.666
4.500
4.400
5.833
5.625
5.500
5.625
5.500
4.479
5
5.500
Waterbody arcs have their own rules in this procedure. Headwater lakes, ponds, and reservoirs are
included if there is a flux, but since there is only one bounding arc of the often irregularly shaped
waterbodies, there is no flow length associated with the waterbody and therefore the feature is not
subdivided or included in the cumulative length factor used for calculating ideal segment lengths noted
above. In network waterbody features such as reservoirs do add a length to the cumulative flow but are
not subdivided. As previously noted, one arc of a given waterbody accumulates the total flow for the
waterbody in the network. For depletion analysis (and display), this total flow is mapped to all segments
of the waterbody; effectively reducing unique reaches to 3378 for the model extent.
Apply the flow network and reach definition to model river/drain cells
The MODFLOW model constant head, river, and drain cells need to be associated with the flow network
and reach definition so that the individual model cell fluxes can be assigned to the correct reach. As
noted above, the relatively coarse 200 meter model grid source/sink cells are a generalization of the
hydrography, which makes a precise match of the arc network to cells impossible, especially at
junctions. Generally the model cell was assigned to the dominant reach, although some cells were
subjectively assigned to maintain a smooth flow of reaches along the mainstem of the stream. The
stream network/model cell association is defined in a “key” model cell layer that can be directly joined
to model output from the various modeling scenarios. The arc network connectivity was maintained in
the model cell key by adding 132 cells not present in the model but with the network connections
needed to accumulate flow correctly. These cells, generally for very short connecting stream arcs, do
not add or remove flux but pass the tributary flux to the cells in the next downstream reach in the
network.
Modeling scenarios
The model was run steady state with no stresses for the reference condition and with 2,448 high
capacity wells within the model domain pumping at three different levels. The highest rates, referred to
as the WDNR scenario, were annualized rates supplied by the WDNR and based on reported
withdrawals. The pump rates were generally based on the average annual pumpage for 2011-1014,
with IR10 wells further averaged by section to smooth irregularities resulting from cropping rotations
and well cycling. These rates assume no return flow or recharge changes on irrigated fields and are
therefore a maximum steady-state impact scenario. The 1,996 IR10 wells within the model domain
were also pumped at lower rates representing 4 inches and 2 inches of net consumption across average
size irrigated fields. These rates represent 35.6% and 17.8% of the WDNR rates respectively for these
wells. The IR10 rates used in the model for these scenarios were calculated by multiplying the WDNR
rate by the percentages noted above (35.6% and 17.8% respectively) to maintain the spatial distribution
of pumping. Total pumping under the 4 inch and 2 inch scenarios (non IR10 wells pumped at the WDNR
rate) was approximately 47.1% and 32.5% respectively of the WDNR scenario. Groundwater fluxes were
exported from within Groundwater Vistas as constant head, river, and drain boundary types to
shapefiles. These shapefiles were combined and related to the key model cell layer noted above to
assign flow network and reach information to each cell. This quantitative approach to cumulative flux in
the model revealed some minor issues with cumulative river flows going negative as a result of losing
reaches near lower flow headwater areas, especially when the high WDNR pumping stress was added.
While some negative flow might be reasonable assuming a surficial runoff source, several reaches were
changed from river to drain type to prevent unreasonable cumulative flows under stressed conditions.
Calculating and mapping cumulative streamflow
The total flux or streamflow for each reach is calculated by summing the groundwater flux for model
cells by the reach attribute. This table is then used to calculate the cumulative flux by reach utilizing the
stream network information. A VBA app in Access was used for this process, looping through the reach
summary table and cumulating flow data from upstream to downstream. This table of cumulated flow
by reach is then joined to the key model cell layer for display and depletion analysis. Cumulative flow
from the subsystems were summed and compared to model mass balances in Vista to verify the
network and calculations. The cumulative flow by reach for the reference and pumping scenarios were
gathered in one shapefile where cfs flux and depletion as cfs or percent is easily calculated.
The model source/sink cell layer is convenient for display because the cell dimensions make it relatively
visible at useful scales and the use of the actual model cells is descriptive of modeling scale and
generalizations. Maps were developed to display percent flow depletion for the three pumping levels.
Because percentages can be misleading when calculated for changes in small values, reaches with less
than one reference cfs are identified with a hatch pattern. The dry reaches above the reference wetup
point were also identified, as well as boundary reaches at the edge of the model. Because of the large
extent of the model area and readable symbolization limitations, the maps were published separately as
high resolution pdf’s of the full model extent (view at 100%), and as map books of the model area tiled
to 14 extents (Figure 1) at a fixed scale of 1:150k. Examples of tile 7 for the three pumping levels are
shown in figures 2, 3, and 4. A shapefile of the cumulative fluxes and depletion is also provided, along
with layer files to provide examples of the symbolization and layer definition with various attributes.
The shapefile attributes are described in table2.
Conclusions
Pre-calculated streamflow depletion maps are a quick scoping tool to identify high capacity well
proposals in stressed areas. Quick reference maps and inclusion as a GIS layer facilitate use in the hicap
review process. Cumulative flow and depletion can be easily calculated for other pumping rates. Until
the ET/recharge dynamics can be quantified seasonally for irrigated fields, projecting the impact of the
currently reported hicap withdrawals is difficult. The 2 inch and WDNR scenarios bracket the long term
impacts and the spatial relationship between pumping wells and stressed surface waters is apparent.
The 2 inch steady state annualized rate generally provides a snapshot of current lake drawdowns as the
system continues to respond to the pumping history.
Table 2. Attributes for the Cumulative_Depletion_Central_Sands shapefile.
row
column
type
BC_ID
Cell_Rank
System
SysID
Seg
Seg_S
Trib1
Trib2
Trib3
Div
Trib_Sys1
cell row number in MODFLOW model
cell column number in MODFLOW model
MODFLOW source/sink cell type
unique source/sink cell ID; format XRRRCCC where:
X = 1 for CH, 2 for Riv, 3 for Drn, 4 for Network Link
RRR = row number, CCC = column number
Cell order code, useful for display priority, values:
1 = primary source/sink display
2 = drain cell at same location as river cell
4 = network link cell (added only to maintain network)
5 = water table CH cell at southern model boundary
Major river system network subdivisions (51)
Numeric ID for river System; 1 through 50, also 51 for water table CH cells
Reach numbering, upstream to downstream, within each System
Reach subdivisions based on splitting criteria; a to d
Network link; First tributary reach (Seg)
Network link; Second tributary reach (Seg)
Network link; Third tributary reach (Seg)
Percent of flow from tributary reaches, equals:
0 for headwater reaches
100 when only one channel
Percent split when multiple channels
Network link; First tributary System
Trib_Sys2
Disp_Link
Network link; Second tributary System
Unique reach identifier for displaying cumulative statistics
usually same as SysSeg_S except for waterbodies where
cumulative waterbody flow reach displayed for all segments
SysSeg_S
Unique reach identifier within network (SysID+Seg+Seg_S)
Disp_Stat
Cell info for configuring display and analysis, values:
above: reach above wetup point
above-boundary: model boundary reach above wetup point
flux: normal reach within model below wetup
flux-boundary: model boundary reach below wetup
flux-incomplete: reach within model below wetup but
some portion of system as boundary; applies to
Plover and Mid Br Embarrass Rivers
network: cell added only to maintain network connection
no modeled flux, only pass cumulative flux
water table: constant head water table cells along southern boundary
rch_dep_D reach depletion in cfs for WDNR pump rates
rch_dep_4 reach depletion in cfs for 4 inch net consumption
rch_dep_2 reach depletion in cfs for 2 inch net consumption
rch_pcd_D reach depletion as percent for WDNR pump rates
rch_pcd_4 reach depletion as percent for 4 inch net consumption
rch_pcd_2 reach depletion as percent for 2 inch net consumption
r_ref_cfs
reach flow in cfs for non-stressed reference condition
r_DNR_cfs reach flow in cfs with WDNR pump rates
r_4in_cfs
reach flow in cfs with 4 inch net consumption
r_2in_cfs
reach flow in cfs with 2 inch net consumption
S_order
can be used to order cells by system and reach
WB_Type
Waterbody types, values:
NA: watertable CH cells
flowline: not a waterbody boundary
boundary: waterbody or stream bank used for model boundary
head: headwater waterbody within the model, one arc
intermediate: reservoir waterbodies, multiple arcs
WB_Name Waterbody name within the model
Figure 1. Tiling scheme for displaying 1:150k depletion maps covering the modeled extent. Each tile
includes some overlap with adjacent tiles.
Figure 2. Cumulative percent streamflow depletion with WDNR pumping rates for Tenmile, Fourteenmile, and upper Big Roche A Cri.
Figure 3. Cumulative percent streamflow depletion with 4 inch net consumption rates for Tenmile, Fourteenmile, and upper Big Roche A Cri.
Figure 3. Cumulative percent streamflow depletion with 2 inch net consumption rates for Tenmile, Fourteenmile, and upper Big Roche A Cri.