**User\'s Guide to the Adaptive Environmental Assessment Models**

**Developed for the Upper Mississippi River**

**Prepared for the**

**March 3-4, 1998 Upper Mississippi River**

**Adaptive Environmental Assessment Workshop**

**President Casino's Blackhawk Hotel**

**Davenport, Iowa**

**1.0 Introduction**

At the heart of Adaptive Environmental Assessment (AEA) is the
development of science-based heuristic models to facilitate
communication and learning across discipline lines. The models are
considered tools for learning and focus on dynamic complexity rather
than on detail complexity and exacting predictions of future outcomes.
Development of such models helps river managers identify gaps in
knowledge and determine where additional research is needed. The models
run on personal computers and are designed to test understanding,
highlight uncertainty, and explore a range of management alternatives
surrounding resource issues. Because they are heuristic tools developed
to facilitate cooperative learning, AEA models may be discarded if they
outlive their usefulness for conveying ideas and concepts.

The Upper Mississippi River AEA computer model is rooted in the
fundamental river processes of water and sediment movement within the
floodplain. The current model actually consists of two models working at
different spatial scales but linked by hydrologic and sediment inputs.
One model operates at a river system level and the other is a pool
model. Both are hydrodynamic and sedimentation mass balance models that
track water and sediment movement over time.

Developers of the Upper Mississippi River AEA model have attempted to
balance mathematical computational time with the need to explore a
variety of management options in a timely manner and at an appropriate
level of detail. Efforts have been made to assure that the models are
calibrated to real life observations and measurements. More complex
computer models requiring main frame or super computers could increase
the level of detail, but uncertainties would always remain.

Simplification of the model allows researchers to focus on the big
picture without getting lost in a myriad of details. By simplifying some
of the complex physical processes and calculations, model run-times have
been kept reasonably short. The Upper Mississippi River AEA model is
easy to apply, and anyone with a Pentium computer using Windows 95 or NT
operating systems can run the model.

The two computer models were developed based on the input of
participants at the first of a series of workshops (December 1995)
focused on using the Adaptive Environmental Assessment (AEA) process to
explore policy alternatives for improving ecosystem health in the Upper
Mississippi River system (UMRS). Two models were developed because key
processes of the system are occurring at both a large basin-scale
extent, and at a much finer scale, such as the dynamics of small areas
within a pool. The River System Model tracks the flow of water and
sediment throughout the UMRS on a daily timestep and provides a basic
accounting framework which allows the implementation of stage height
policies at one or more pools, taking into account natural variation in
flows and the operating constraints of the lock and dam system. The
sediment transport component tracks the input and export of fine and
coarse sediment in each pool. The navigation/economic component
translates the effects of stage policies (influencing sediment
deposition/dredging and channel depth) into dredging volumes and
reductions in shipping potential. Discharge and water elevations
associated with a user-defined stage policy enacted in the River System
Model are translated into site-specific effects in the Pool Model. The
pool model predicts equilibrium hydrologic and sedimentation regimes on
a 100 x 100 m grid cell resolution at a monthly timestep within a single
pool. These predictions are used to compute mean water depth and the
wetted period of each cell in the grid, which in turn is used to drive
vegetation and fisheries submodels.

The River System and Pool Models were evaluated at a second AEA workshop
held January 15-17, 1997. The main objective of this workshop was to
provide a forum to discuss and improve the models so that they
eventually represent a consensus model, or a series of alternatives,
through which various policies can be screened. Following the second
workshop, a series of desired refinements to the River System and Pool
Models were identified. Members of the UMR AEA Steering Committee and
others agreed to pursue some of the key changes prior to beginning Phase
II of the AEA process, which will focus on using the models to explore
potential management scenarios. This document describes the current
version of the AEA River System and Pool Models, including substantial
revisions made to the River System Model based on the refinements
proposed after the January 1997 workshop. The models, as well as plans
for initiating Phase II of the UMR AEA, will be the subject of a March
3-4, 1998 workshop.

**2.0 Installation**

Both models can be run on a PC with a 32-bit operation system, such as
Windows 95 or Windows NT. Copies of the river system and pool models can
be obtained via the Internet, from the U.S. Geological Survey's
Environmental Management Technical Center (EMTC). The EMTC's home page
address is \<[http://www.emtc.usgs.gov](http://www.emtc.usgs.gov/)\>.
The AEA model can be accessed under "Related Study Efforts" through a
link called "UMRS - Adaptive Environmental Assessment." Download the
files pool.zip, basin.zip, and regocx.zip. These are PKZIP archive files
which contain a compressed version of the installation programs and all
files required to run each model. Unzip pool.zip (e.g. type 'pkunzip
pool') and basin.zip into their own temporary directories. Installation
instructions beyond this point are identical to installation using the
distribution diskettes.

1.  Insert the first installation diskette for the pool or basin into
    the 3.5" drive. Run setup.exe on the 3.5" drive using the Run menu
    choice in Windows 95. If you obtained the model by FTP you will find
    setup.exe in the temporary directory where you unzipped pool.zip or
    basin.zip. Follow instructions of the installation program which
    will prompt you for additional diskettes. Repeat the procedure for
    the other model not yet installed.

2.  To start the River System Model, move to the directory where it was
    installed (e.g. c:\\upmiss\\river) and double click on the file
    basin.exe from the Windows file explorer. If you encounter an error
    while loading the model, proceed to steps a-c below.

3.  To start the Pool Model, move to the directory where it was
    installed (e.g. c:\\upmiss\\pool) and double click on the file
    pool.exe from the Windows file explorer. If you encounter an error
    while loading the model, proceed to steps a-c below.

```{=html}
<!-- -->
```
a.  Copy the contents of the diskette labelled Register OCX to the
    windows\\system directory. If you obtained the model by FTP, unzip
    the contents of regocx.zip into the windows\\system directory. When
    prompted if you want to overwrite the files MFC40.DLL and
    JGRAPH.OCX, say yes (overwrite them).

b.  From the Run menu choice in Windows 95, type
    c:\\windows\\system\\regocx.exe and hit OK. This will start a
    program which will register JGRAPH.OCX.

c.  A window will appear with two buttons (Register OCX and Unregister
    OCX). Click on the Register OCX button. A dialogue box will appear
    with a list of .OCX files located in the Windows\\system directory.
    If you are not in that directory move to it. Select the file
    JGRAPH.OCX and click on the open button. Close the OCX registration
    program.

**3.0 River System Model**

The River System Model was developed to simulate processes occurring
over the large spatial extent of the Upper Mississippi River mainstem.
Its main purpose is to move water and sediment between navigation pools,
incorporating the operating constraints of the dams and natural seasonal
and interannual variability in discharge, and sediment loads delivered
from major tributaries. The model allows the user to set a stage height
policy on a monthly basis over the year for one or more pools and then
calculates the daily discharge at each lock and dam given the historical
discharge (1959-1995) required to meet the policy. The daily discharge
and stage predictions drive calculations in the sediment transport,
dredging, vegetation, fisheries impact, and navigation components of the
model. Currently, the model operates for Pools 2-22.

**3.1 Hydrology Submodel**

Discharge (Q) and stage data collected by the Corps' St. Paul and Rock
Island Districts for Lock & Dams 2 - 22 were compiled from 1959 -- 1995,
the period for which these data are consistently available for all locks
and dams in the two districts. (Note: The data necessary to extend the
River System Model to Pool 24 -- Open River were not available from the
Corps' St. Louis District in time to use in this version of the model.
It is not yet clear whether the St. Louis District will be able to
provide these data, or whether other approaches to modeling this portion
of the Upper Mississippi River may be available.) Tributary inflow to
each pool was computed by subtracting the annual difference in total
discharge at the upstream and downstream dams, and then dividing the
annual discharge into daily values based on the relative contribution of
each day's flow to the total annual flow. This method ensured that local
inflows for any day would always be positive values and minimized the
effects of lags and inaccurate discharge estimates at the dams.

Daily local discharge estimates for each pool drive the model
calculations. The model begins a simulation on January 1, 1959 at flat
project pool elevations and computes discharge and stage at each pool in
a downstream direction based on a user-defined stage policy. The total
flow entering a pool for the current model day (= discharge from
upstream pool computed by model + local inflow calculated from data) is
added to the volume in the pool from the day before. This total volume
is converted to a stage height based on a USACE storage curve (provided
for each pool) to predict the resulting volume from this inflow combined
with the volume already there at the beginning of the day. The stage is
then compared to the user-defined target stage for the current day. If
the stage is less than the target, all water is held back (discharge
from downstream dam = 0) and the stage is the value computed from the
storage curve. If the stage is greater than the target, enough water is
released from the dam so that the target is met. If the amount of water
which must be spilled exceeds the operating limits of the dam (i.e. the
maximum discharge which can be released between the gates), the target
stage will be exceeded. In this case, the total storage behind the dam
is computed based on the difference between upstream and tributary
inflows and the outflow from the dam. Stage is then predicted based on
the stage-storage volume relations. The model predicts stage heights at
the current USACE control points for each pool, which are either at
mid-pool or at the downstream dam.

Users can alter the sequence of discharge data driving the model by
opening the "Create Synthetic Multi-Year Hydrograph" dialogue box from
the "Hydrology" menu item under the "Parameters" main menu. The dialogue
box lists the rank order of each year based on the total discharge over
the specified period (default = entire year, month 1-12). Users can
change the month window and resort the data. The sequence of simulation
years can be adjusted by clicking on the desired year in the list box
and then clicking on the appropriate cell in the adjacent grid ("Order"
refers to the order of years in the simulation sequence). Holding the
mouse down while dragging across rows in the grid copies applies one
year across multiple simulation years.

The model can be run in a 'Natural-System-Model' (NSM) mode in which the
river is allowed to operate as if the dams were not there. Discharge at
each dam is simply the sum of all flows (coming from upstream dam and
local inflows) entering the pool. Stage is not set by policy but
predicted by the model using the stage-discharge rating curves for each
pool. These relationships provide a relatively accurate prediction of
stage when discharge is high (near and beyond the operating limits of
the dams), but unfortunately do not characterise the stage at flows
below the operating limit. This is because we do not have natural rating
curves for the pools since there are little stage-flow data available
prior to the construction of the dams. As it stands, therefore, this
option does not provide an accurate NSM.

**3.2 Sediment Transport and Dredging Submodels**

The sediment transport component of the river system model provides a
mass-balance budget of fine and coarse sediment input and export from
each pool on a daily timestep. Suspended sediment input from tributaries
is calculated from sediment transport curves (suspended sediment
discharge vs. water discharge from tributary) developed for each pool's
major tributary (Table 1). Tributary bedload inputs are calculated as a
fraction of the suspended tributary load (Table 1). A user-defined
fraction of the suspended load entering from tributaries is transferred
to the coarse sediment pool to reflect the reduced stream power of the
mainstem Mississippi River relative to its tributaries.

Of this total tributary fine and coarse load, the proportion making it
to the main channel is computed based on the current drawdown (i.e.
daily stage - project pool elevation) relative to an assumed maximum
drawdown of 10 ft.; as the drawdown approaches maximum drawdown, the
proportion of tributary sediment reaching the main channel approaches
one. At flat pool when drawdown = 0, the proportion is pool specific and
is generally quite low for most tributaries (e.g. 0.1). The tributary
sediment load which does not reach the channel is stored in tributary
delta fine and coarse sediment pools which are tracked over time. During
drawdown, a fraction of each delta sediment pool can be eroded to
simulate the effect of the tributary cutting through newly exposed
portions of the delta and delivering additional sediment to the main
channel. The amount of the delta component of sediment input is computed
by estimating the volume of delta cut each day, and converting this
volume to short tons. The daily volume of delta cut is computed by
assuming a rectangular cut shape, where length is the length of the
exposed portion of the delta (which is a function of drawdown), the cut
width (computed based on tributary discharge using at-a-station
hydraulic geometry), and an assumed daily depth of delta which is cut
(which is proportional to tributary discharge).

The total sediment load reaching the main channel is the sum of the
amount discharged from the upstream pool and the tributary inputs
reaching the channel either directly and through delta cutting during
drawdown. The total amount of sediment which is discharged is computed
by determining fine and coarse export factors (PropExport) calculated
as:

PropExport = 1 - exp (-kExport \*Vel),

Where Vel is a standardized velocity rate in the main channel which
increases with increasing discharge or with reduced depth and kExport is
a pool-specific constant which represents the potential of the pool to
export sediment and captures the effects of factors such as depth
patterns and retention time. As Vel or kExport increase so does the
proportion of sediment in the main channel that can be exported. Vel is
computed as:

Vel = k' \* Q/d\^2,

where Q is daily discharge; d is daily average channel depth, which
varies with stage; and k' is a pool-specific scaling parameter. Note
that the proportion of sediment exported from the pool will increase
with increasing discharge or decreasing depth due to reduced stage. The
total amount of sediment which can be discharged (SedOut) is:

SedOut = (Emax + SedIn) \* PropExport,

where SedIn is the total fine or coarse sediment load reaching the main
channel, and Emax is the quantity of fine or coarse sediment stored in
the main channel which is vulnerable to export on a daily basis. Emax is
computed by multiplying the current main channel fine or coarse sediment
storage pools by a daily vulnerability factor, which is the number of
days it would take to completely erode it. The difference between SedOut
and SedIn is the net quantity of fine or coarse sediment added to the
pool each day (G):

G = Sedin - SedOut,

which is positive for net deposition (SedIn \> SedOut) or negative for
net erosion (SedIn \< SedOut). G is simply added to the main channel
fine or coarse sediment storage pool to be used in the next day's
calculations. The amount of coarse material deposited in the navigation
channel is a user-defined fraction of G~coarse~. The amount of fine and
coarse material deposited in off-channel and backwater habitats is
simply the remaining amount of G~coarse~ not deposited in the main
channel plus all of G~fine~. The amount of off-channel sediment
deposition is used in conjunction with a relative sediment
deposition-water depth relationship to compute the change in elevation
slices in upper, middle, and lower sections of the pool (see Section 3.3
on riparian habitats submodel).

Table 1. Summary of suspended sediment rating curves used to predict
tributary inputs to each pool and the percentage bedload used to
estimate tributary inputs of bed material.

<table style="width:100%;">
<colgroup>
<col style="width: 4%" />
<col style="width: 17%" />
<col style="width: 6%" />
<col style="width: 7%" />
<col style="width: 3%" />
<col style="width: 2%" />
<col style="width: 2%" />
<col style="width: 3%" />
<col style="width: 0%" />
<col style="width: 4%" />
<col style="width: 4%" />
<col style="width: 4%" />
<col style="width: 4%" />
<col style="width: 1%" />
<col style="width: 7%" />
<col style="width: 0%" />
<col style="width: 1%" />
<col style="width: 0%" />
<col style="width: 0%" />
<col style="width: 2%" />
<col style="width: 3%" />
<col style="width: 0%" />
<col style="width: 4%" />
<col style="width: 4%" />
<col style="width: 4%" />
</colgroup>
<tbody>
<tr class="odd">
<td></td>
<td></td>
<td></td>
<td colspan="2"><strong>Suspended Load</strong></td>
<td colspan="2"></td>
<td colspan="2"></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td colspan="3"></td>
<td></td>
<td colspan="2"></td>
<td colspan="6"></td>
</tr>
<tr class="even">
<td><strong>Pool</strong></td>
<td><strong>Tributary-Station</strong></td>
<td><strong>Source</strong></td>
<td><strong>Constant</strong></td>
<td colspan="2"><strong>Slope</strong></td>
<td colspan="2"><strong>% Bed /Total</strong></td>
<td colspan="7"><strong>Comments</strong></td>
<td colspan="3"></td>
<td colspan="2"></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>2</td>
<td>Minnesota at Mankato, MN</td>
<td>Tornes, 86</td>
<td>0.286</td>
<td colspan="2">1.12</td>
<td colspan="2">10</td>
<td colspan="6"></td>
<td></td>
<td colspan="3"></td>
<td colspan="2"></td>
<td rowspan="2"></td>
<td rowspan="2"></td>
<td rowspan="2"></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>3</td>
<td>N/A for St. Croix</td>
<td></td>
<td></td>
<td colspan="2"></td>
<td colspan="2">10</td>
<td colspan="12">Used Minnesota River rating curve</td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>4</td>
<td>Chippewa near Pepin</td>
<td>Rose, 92</td>
<td>1.907E-05</td>
<td colspan="2">1.98</td>
<td colspan="2">50</td>
<td colspan="7">p. 25 Rose</td>
<td colspan="3"></td>
<td colspan="2"></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>5</td>
<td>Zumbro at Kellogg</td>
<td>Tornes, 86</td>
<td>8.83</td>
<td colspan="2">0.875</td>
<td colspan="2">10</td>
<td colspan="6"></td>
<td></td>
<td colspan="3"></td>
<td colspan="2"></td>
<td rowspan="3"></td>
<td rowspan="3"></td>
<td rowspan="3"></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>5a</td>
<td>no major tributaries</td>
<td></td>
<td></td>
<td colspan="2"></td>
<td colspan="2">10</td>
<td colspan="12">Use Zumbro River rating curve</td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>6</td>
<td>N/A for Trempealeau</td>
<td></td>
<td></td>
<td colspan="2"></td>
<td colspan="2">10</td>
<td colspan="12">Use Zumbro River rating curve</td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>7</td>
<td>Black River near Galesville</td>
<td>Rose, 92</td>
<td>0.0002564</td>
<td colspan="2">1.79</td>
<td colspan="2">43</td>
<td colspan="7">p. 26 Rose</td>
<td colspan="3"></td>
<td colspan="2"></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>8</td>
<td>Root River near Houston</td>
<td>Tornes, 86</td>
<td>276</td>
<td colspan="2">0.558</td>
<td colspan="2">10</td>
<td colspan="6"></td>
<td></td>
<td colspan="3" rowspan="3"></td>
<td colspan="2"></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>9</td>
<td>N/A for Upper Iowa River</td>
<td></td>
<td></td>
<td colspan="2"></td>
<td colspan="2">10</td>
<td colspan="7">Used Root River</td>
<td colspan="3"></td>
<td colspan="2"></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>10</td>
<td>Wisconsin River at Muscoda</td>
<td>Rose, 92</td>
<td>2.2E-08</td>
<td colspan="2">2.56</td>
<td colspan="2">49</td>
<td colspan="7">p. 35 Rose</td>
<td colspan="3"></td>
<td colspan="2"></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>11</td>
<td>Turkey near Garber</td>
<td>Nakato, 81</td>
<td>9.07E-04</td>
<td colspan="2">2.1</td>
<td colspan="2">20</td>
<td colspan="17"><p>Used Turkey River rating curve where bedload was
also available.</p>
<p>Bedload ratio based on Turkey</p></td>
</tr>
<tr class="even">
<td>12</td>
<td>N/A for Galena</td>
<td></td>
<td></td>
<td colspan="2"></td>
<td colspan="2">10</td>
<td colspan="12">Used Turkey River rating curve.</td>
<td></td>
<td rowspan="2"></td>
<td rowspan="2"></td>
<td rowspan="2"></td>
<td rowspan="2"></td>
</tr>
<tr class="odd">
<td>13</td>
<td>Maquoketa near Maquoketa</td>
<td>Nakato, 81</td>
<td>9.00E-05</td>
<td colspan="2">2.29</td>
<td colspan="2">10.3</td>
<td colspan="13">Used Maquoketa River rating curve as bedload data were
available.</td>
</tr>
<tr class="even">
<td>14</td>
<td>Wapsipinicon near Dewitt</td>
<td>Nakato, 81</td>
<td>8.36E-03</td>
<td colspan="2">1.58</td>
<td colspan="2">11</td>
<td colspan="6"></td>
<td></td>
<td colspan="3"></td>
<td colspan="2"></td>
<td></td>
<td rowspan="2"></td>
<td rowspan="2"></td>
<td rowspan="2"></td>
<td rowspan="2"></td>
</tr>
<tr class="odd">
<td>15</td>
<td>no major tributaries</td>
<td></td>
<td></td>
<td colspan="2"></td>
<td colspan="2">10</td>
<td colspan="13">Used Maquoketa River rating curve.</td>
</tr>
<tr class="even">
<td>16</td>
<td>Rock River near Joslin</td>
<td>Nakato, 81</td>
<td>6.19E-03</td>
<td colspan="2">1.44</td>
<td colspan="2">6</td>
<td colspan="6"></td>
<td></td>
<td colspan="3"></td>
<td colspan="2"></td>
<td></td>
<td rowspan="2"></td>
<td rowspan="2"></td>
<td rowspan="2"></td>
<td rowspan="3"></td>
</tr>
<tr class="odd">
<td>17</td>
<td>no major tributaries</td>
<td></td>
<td></td>
<td colspan="2"></td>
<td colspan="2">10</td>
<td colspan="13">Used Maquoketa River rating curve.</td>
</tr>
<tr class="even">
<td>18</td>
<td>Iowa River near New Boston</td>
<td>Nakato, 81</td>
<td>1.18E-03</td>
<td colspan="2">2.26</td>
<td colspan="2">5.5</td>
<td colspan="16">Used Iowa River rating curve as bedload data were
available</td>
</tr>
<tr class="odd">
<td>19</td>
<td>Skunk River near Augusta</td>
<td>Nakato, 81</td>
<td>1.90E-03</td>
<td colspan="2">1.69</td>
<td colspan="2">5.8</td>
<td colspan="6"></td>
<td></td>
<td colspan="3"></td>
<td colspan="2"></td>
<td></td>
<td></td>
<td rowspan="4"></td>
<td rowspan="4"></td>
<td rowspan="4"></td>
</tr>
<tr class="even">
<td>20</td>
<td>Fox River near Wayland</td>
<td>Nakato, 81</td>
<td>1.18E-03</td>
<td colspan="2">2.26</td>
<td colspan="2">10</td>
<td colspan="14">Estimated using relationship from Henderson River</td>
</tr>
<tr class="odd">
<td>21</td>
<td>Bear Creek</td>
<td>Nakato, 81</td>
<td>1.18E-03</td>
<td colspan="2">2.26</td>
<td colspan="2">10</td>
<td colspan="14">Estimated using relationship from Henderson River</td>
</tr>
<tr class="even">
<td>22</td>
<td>Fabius River</td>
<td>Nakato, 81</td>
<td>1.18E-03</td>
<td colspan="2">2.26</td>
<td colspan="2">10</td>
<td colspan="14">Estimated using relationship from Henderson River</td>
</tr>
</tbody>
</table>

The amount of material dredged over each month is dependent on
user-defined policies and predictions from the sediment transport
submodel. The dredging sub-model tracks the bed elevation at the
critical dredge cut in each pool, which was estimated from the
historical dredging database as the location where dredging was most
frequent. An annual sequence of water depths at the critical dredge cut
is specified by the user. As sediment accumulates in the main channel
(based on predictions of the sediment sub-model), bed elevation will
increase based on a pool specific accretion rate. These accretion rates
are the average accretion rate per ton of sediment deposited in channel
at the critical dredge cut, computed by taking the ratio of average
accretion rate at the critical cut to the average amount of material
dredged from the entire pool over the year (which is used as an estimate
for the total coarse sediment deposition in the main channel). (See
Table 2.) As the bed rises (if coarse sediment is accumulating), water
depth at the critical cut will decrease (assuming constant water surface
elevation). Two dredging policies can be implemented. In the first case,
dredging will remove enough sediment to maintain the bed elevation at
the critical cut, but not enough material to compensate for reductions
in water surface elevation due to pool drawdowns. In drawdown situations
where sediment is accumulating, water depth at the critical cut will not
be maintained in drawdown months and navigation will be effected. In the
second case, dredging will remove sufficient material so that the
user-defined water depth at the critical dredge cut is maintained
regardless of whether a drawdown is in place or not. With this option
under a drawdown policy, dredging volumes will be higher but navigation
will not be effected.

**Table 2. Summary of mean annual dredging volumes (for entire pool) and
accretion rates at most active (critical) dredge cut. Dredging volumes
and accretion rates for pools 2-10 were computed as averages from
1975-1995. Average dredging volumes for pools 11-22 were calculated over
the 1945-1978 period\
(Nakato, 1981).**

  ----------- ------------------- ------------------ ---------------------
  Pool        Mean Annual Volume  Accretion Rate     Feet Accumulated at
              (yd\^3 across       (ft/yr) @ highest  critical cut per Ton
              years) -\           frequency dredge   of Sediment Dredged
              all cuts            cut                in Pool

  2           93257               0.76               6.417E-06

  3           15640               0.58               2.920E-05

  4           250032              1.38               4.346E-06

  5           69079               1.20               1.368E-05

  5a          39409               1.62               3.237E-05

  6           8274                0.38               3.616E-05

  7           36101               1.14               2.486E-05

  8           44197               1.34               2.387E-05

  9           34915               1.04               2.345E-05

  10          25760               0.76               2.323E-05

  11          147320              1.18               6.288E-06

  12          31750               0.72               1.786E-05

  13          160020              0.79               3.885E-06

  14          132080              0.82               4.910E-06

  15          17907               0.40               1.759E-05

  16          43561               0.82               1.476E-05

  17          64770               0.70               8.555E-06

  18          234950              1.28               4.300E-06

  19          237490              0.79               2.605E-06

  20          222250              1.20               4.251E-06

  21          274320              1.33               3.827E-06

  22          196850              1.12               4.462E-06
  ----------- ------------------- ------------------ ---------------------

**3.2.1 Calibrating Sediment and Dredging Submodels**

1.  Obtain coarse and fine sediment budgets for the series of pools you
    wish to calibrate (e.g. Simons, 1979 - Table 2 and 3; Nakato,
    1981-Table 5). Budgets should contain annual estimates of upstream
    inflow, tributary inflow, outflow, and dredging (coarse only) for
    fine and coarse sediment.

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2.  Pick a representative water year from the 1959-1995 simulation
    sequence that represents the conditions that your calibration budget
    was developed from(e.g. 2 or 10 yr annual flood). Use this for every
    year of the simulation by specifying the water year to simulate in
    the "Create Multi-Year Synthetic Hydrograph" dialogue box. Load the
    appropriate graphs to calibrate the model from the "Select Time
    Series Graphs" dialogue box (e.g. fine and coarse export, fine and
    coarse sediment budgets, dredging volumes).

3.  Open the "Sediment Transport and Distribution" dialogue box to begin
    adjusting the parameters controlling the sediment submodel. Start
    with most upstream pool. For the first pool only, calibrate the fine
    sediment mainstem sediment inflow entering the pool by adjusting the
    mainstem multiplier (parameter name = "Mainstem Inflow SS
    Multiplier"). Calibrate the coarse sediment upstream inflow by
    adjusting the bedload % ("Mainstem Inflow Bedload").

4.  Calibrate tributary inputs by adjusting the proportion of tributary
    sediment delivered to the main channel from the tributary at flat
    pool for fine and coarse components ("Prop. Trib. Sed  Main Channel
    at FP").

5.  Use best estimate to compute the fraction of bedload from
    tributaries entering the suspended load component in the mainstem
    ("Prop. Trib. SSLoad  Bedload").

6.  Adjust export coefficient ("Sed. Export coeff.") to calibrate total
    fine and coarse sediment export. For coarse material, temporarily
    set the proportion of coarse sediment deposition in the main channel
    ("Prop. Sed. Net. Deposit. in Nav.") to 0 and make sure that the
    coarse export used to calibrate the model includes the amount of
    material removed by dredging in the budget. If the export
    coefficient = 1 and you cannot get sufficient export to calibrate
    the model, reduce the number of years to erode the sediment storage
    pool. ("Years to Erode Sed. Storage Pool").

7.  Increase the proportion of coarse sediment deposition in the main
    channel so that the predicted dredge volume reflects the volume of
    dredging in the sediment budget.

8.  Repeat for downstream pools.

**3.3 Riparian Habitats Submodel**

Changes in water levels and sediment management practices would
influence the distribution of riparian habitat types ranging from open
water areas to upland woody forests. Sedimentation is gradually shifting
aquatic habitat from deep water to shallow, to the point in some areas
where emergent aquatic vegetation can develop, and where even
terrestrial plant communities might be able to develop again if water
levels were varied seasonally. For the River System Model we need a
relatively simple "signature" of these habitat structure changes, to be
used in evaluating impacts on ability of the riparian zone to support
various types of recreational activity (hunting, fishing, boating, bird
watching, etc.) and to produce economic benefit from this activity.
Since the River System Model does not include explicit mapped
information on the riparian zone for each pool, and such information is
not likely to be available soon, we need to summarize habitat area
information in terms of acreage patterns that can be derived from
analysis of information on total riparian areas, vegetation types, and
other data that are readily available. We have elected to summarize
habitat structure in terms of stage-area relationships as described
below.

**3.3.1 The Stage-Area Curve as a Habitat Structure Signature**

The River System Model stores information on, and attempts to predict
sediment-related changes in, a stage-area curve for each pool. This
curve simply specifies the total area flooded as a function of stage at
an index or control point along the river reach, where stage is measured
relative to the bottom of the navigation channel at the index point. The
slope of this stage-area curve at any stage is the amount of area that
would be flooded if the stage were raised or lower by one foot, and the
curve is entered into the model by specifying the added flooded area for
each foot increase in stage (the navigation channel area and backwaters
of equal depth are assumed to be flooded at a stage of 1 ft., i.e., the
channel is assumed to have a flat bottom).

The shape of the stage-area curve is an informative signature about the
spatial structure and diversity of the riparian zone. A linear-stage
area curve would occur if the riparian zone increased linearly in
elevation with distance from the channel, so as to have an even amount
of habitat flooded for each unit increase in stage. A decelerating
stage-area curve (increasing rapidly for first few feet of stage, then
more slowly for high stages) would occur if the flood plain were
U-shaped. An accelerating stage-area curve (increasing slowly at first,
then rapidly above some critical stage) is indicative of a riparian zone
that has been degraded by accumulation of sediment in bench-like
formations alongside the navigation channel, so that most of the
riparian area is shallow or would be flooded by a small increase in
stage (some lower river pools that have nearly filled in with sediment
have developed this curve shape).

The initial stage-area curve for each pool can be estimated by obtaining
(1) the area of the main navigation channel and closely associated deep
backwaters; (2) the area flooded at a few known, common stages as seen
during normal navigation pool operation; (3) the area flooded during
recent high stage flood events; and (4) the total riparian zone area
that might ever be flooded. These areas define four points along the
stage-area curve, from which we can interpolate the rest of the
relationship without having detailed contour elevation and water surface
elevation information. In the River System Model, the stage-area curve
is then stored as a set of discrete area slices, each slice being the
flooded area added by increasing stage at the index point by 1 ft. In
the current version of the model, we used the bathymmetric GIS coverages
from EMTC for Pools 4, 7, 8 and 13 to compute the amount of area at one
foot slices starting at flat pool and working down to the lowest
elevation cell (100 m resolution) in the pool. Three stage-area curves
were developed for each of these pools representing the habitat
structure signatures for the upper (riverine-like), middle
(transitional), and lower (reservoir-like) portions of each pool.

As the River System Model simulation proceeds, dynamic changes in stage
are used at each model time step to calculate how much area is flooded
during that time step, and to provide an annual summary of hydroperiod
and mean flooding depth for each 1 ft. area slice of the stage-area
relationship. These mean flooding depth and hydroperiod calculations are
then available for habitat area calculations for fish and wildlife
populations, and for simulations of changes in vegetation type for each
of the area slices. In future model versions, we may want to improve the
side channel and backwater area aspect of this calculation by having a
series of area sub-slices for each stage slice, with these sub-slices
representing depths of flooding when flooding does occur (i.e., for a
backwater that floods at stage X, the subslices would include area
components representing how much of this backwater is 1 ft deep, 2 ft
deep, etc.).

**3.3.2 Representing Effects of Sedimentation on the Stage-Area Curve**

A critical concern in the basin is long-term deterioration in riparian
habitat due to filling of backwater, side-channel, and lower pool areas
with sediment. For each pool, the model now provides a sediment budget
that accounts for inputs, outputs, and storages of fine and coarse
sediment in the pool over time. Sediment storage is represented as
having three components: (1) S~T~-sediment stored as deltas at the
mouths of tributaries and hence vulnerable to erosion if stages were
lowered and tributaries allowed to re-cut channels; (2) S~c~-sediment
stored in the main navigation channel and hence subject to management
through dredging; and (3) S~p~-sediment stored in pool areas off the
main navigation channel. It is mainly increases in the S~p~ storage
component that will eventually alter stage-area relationships
substantially.

For each model time step, we need to predict how the change in S~p~
(positive for net sedimentation, negative for net erosion) during that
step will alter the stage-area profile. We do this by first converting
∆S~p~ for the step from tons to acre-ft. sediment volume ∆V~p~, so that
dividing this volume by the area over which it is distributed (or from
which it erodes) will produce a change in depth or elevation. Next, we
assume that the proportion of ∆V~p~ "captured" by each stage-area slice
is proportional to (1) water depth over the slice during that time step,
and (2) the area of the slice. Let W~ds~=P(d)A(s) be a weight assigned
to stage-area slice s, where A(s) is the area of the slice in acres and
P(d) is a depth-weighting factor (relative units) for depth d water,
provided by the user (generally P(d) will increase with depth d due to
proximity to channel sediment sources, lack of turbulent energy due to
wind mixing, and higher water velocity transporting more sediment to the
slice). We then assume that stage-area slice s will capture a share of
∆V~p~ proportional to this weight:

∆d~s~= $\frac{W_{\text{ds}}}{A(s)\sum_{}^{}W_{\text{ds}}}D\text{Vp}$ (2)

where ∆d~s~ is the simulated change in elevation of slice s during the
step, and the sum is over all slices for which depth d\>0 in that
simulated time step. By adjusting the depth weighting factors P(d) in
the "Sediment Transport and Distribution" dialogue box, we can vary how
much of the sediment is deposited or eroded from shallow versus deep
sites, and hence from sites that are near or far from the main
navigation channel. The main trick in making this submodel behave
realistically will be in setting good values for the P(d) factors by
examining depth-sedimentation rate relationships in lower river pools
that have already been heavily impacted.

The calculated elevation change ∆d~s~ for each step is then used to move
the same proportion of the area from stage slice s to slice s+1:
A(s)~t+1~=A(s)~t~(1-∆d~s~), A(s+1)~t+1~=A(s+1)~t~+A(s)~t~∆d~s~ (or s-1
for eroding case). This simple proportional movement assumption is valid
only for short time steps and for depth slices of 1 ft.; intuitively, it
is based on the idea that if 0.1 ft. of sediment is deposited on (or
eroded from) an area that has elevations uniformly distributed over a 1
ft. elevation interval, then a proportion 0.1 of the new elevations will
then exceed the top elevation defining the area.

**3.3.3 Linking Stage-Area Information to Vegetation and Animal
Population Predictions**

We have incorporated a simplified version of the pool model vegetation
type submodel into the River System Model. This vegetation model
predicts the dominant, persistent vegetation type in each stage-area
elevation slice as a function of the mean annual depth and hydroperiod
on the slice. Under persistent (applied for many years) water management
policies that increase or decrease stage, so that the slices flooded
change in mean depth or hydroperiod, we should be able to predict
general changes in area occupied by different vegetation types. In
particular, we will be able to represent how bands of vegetation of
particular types, like emergent aquatics, would move up or down in the
riparian zone with changes in average stage. If we can develop an
improved vegetation model that accounts for effects of catastrophic (or
chronic) changes and lag times in vegetation recovery/succession after
such changes, we will also be able to simulate how these changes and
lags affect vegetation type over time for each stage-area slice. See
Section 4.2 (Macrophyte Seasonal Production and Distribution Submodel)
for a description of this sub-model.

The main fisheries evaluation submodel predicts population changes in
indicator fish (and invertebrate and system-dependent mammal)
populations by relating recruitment rates to habitat availability during
key juvenile life history stages or stanzas. At present, in the River
System Model, this submodel uses depth only to define suitable habitat
area for juveniles. See Section 4.3 for a description of this sub-model
of the fisheries impact sub-model.

**3.3.4 Policy Options Not Included in Stage-Area Curve Dynamics**

There was much interest at the January 1997 AEA workshop in evaluating
policies for re-engineering the system to provide managed hydropatterns
in diked or leveed areas for vegetation and animal management. Scenarios
for such engineering ranged from dividing each pool into a managed
navigation run and a free-flowing natural run (side-by-side), to simply
diking off particular restricted areas then varying water levels and
flows through these areas to achieve favorable conditions for particular
communities such as emergent aquatics. To model such policies, we would
have to partition the stage-area relationship into two vectors: areas by
stage in the free-flowing, managed river system, and areas by stage in
the controlled habitat management areas. We could then move area between
these vectors to represent development (and destruction) of dike and
levee systems. However, we would also have to provide this extended
model with a set of rules for managing (and failing to manage under
extreme flow conditions) flow and stage in the regulated areas; we have
not found a practical computational procedure yet for doing the
extensive water budget and area bookkeeping that this change would
require.

There was also much interest in finding better ways to manage sediment
transport processes so as to reduce sedimentation and remove accumulated
sediments, especially in the lower pools. The depth weightings P(d) for
sediment deposition do not account directly for management actions
involving structural modification of levees and training walls to reduce
sediment trapping in backwater areas that are created by such
structures. We could roughly mimic the effect of removing or adding
structures by changing the P(d) values, but we would also have to link
such changes to the parameters used in the sedimentation rate submodel
for overall sediment budgets in each pool. It is not yet clear how to
make such linkages realistically without using a spatially explicit
hydrodynamic calculation as in the Pool Model.

To test alternative assumptions about relative sedimentation rates as a
function of depth P(d), select the parameters menu item "Sediment
distribution". The P(d) function will appear as a graph (X axis depth d,
y axis P(d)). Pointing the mouse at this function then dragging (move
mouse with either button down) allows reshaping of this function. Do not
be concerned about absolute values of P; these are rescaled during
calculations anyway by the ratio operation (P divided by sum of P) in
equation 1. Note that the P(d) function only changes the depth
distribution of sedimentation, not total amounts. To change assumptions
about these totals, change parameters in the "sediment transport" menu
choice in the parameters menu.

A basic output indicator frame, showing cumulative stage-area curves for
the upper, middle, and lower sections of the currently selected pool
(for graphics display) and vegetation area information, appears below
the model time series graphs. This curve can be displayed for any pool
(where the data exist, currently Pools 4, 7, 8, and 13) at any
simulation time by selecting that pool as the indicator pool for graphic
display. For the selected pool, vegetation type for each depth slice is
shown by color coding the stage-area curve to the vegetation type. The
total amount of area for each vegetation type can also be displayed in
the time series graphs.

**3.4 Navigation Submodel**

The River System Model navigation submodel predicts shipping potential
in each pool on a monthly timestep based on the average channel depth
over the month and operating constraints of the barges and the lock and
dam system. Annual demand for shipping is based on a starting value
84,400,00 tons (tons shipped in 1995) and assumes an annual increase of
1.25%. The module then calculates, on a monthly timestep, the maximum
tons that could be shipped in each pool under optimum conditions, and
the potential tons shipped under actual conditions, for comparison to
the estimated demand.

The model assumes that shipping occurs between March 20 and December 5
for every year of the simulation. Optimum conditions for determining
maximum tonnage shipped include 15 barges per tow, 2 hour lock times
(for 600 ft locks) with no recreational lockages, and a 9 ft draft.
Reductions from maximum tonnage occur if channel depth is less than 9 ft
or if discharge exceeds the amount above which the locks can no longer
operate. At a channel depth of 8 ft or less, shipping stops for the
month. If depth is between 8 ft and 9 ft, barge capacity is reduced by
13% per foot of draft. Channel depth is calculated in the dredging
sub-model (section 3.2) and is affected in the model by water surface
and bed elevation predictions, the latter being controlled by the net
deposition of coarse sediment in the main channel.

There are two indicators for shipping. First, a bar graph compares
demand for shipping with maximum tons shipped under optimum conditions
and potential tons shipped under actual conditions in each year for the
whole system. Second, on the map, each pool can be color coded to
indicate the percentage of maximum tons capable of being shipped through
that pool given actual conditions for each year.

**3.5 Operating Instructions for River System Model**

To start the River System Model, double click on the file basin.exe from
the Windows Explorer. After some initial files are loaded, a graphical
user interface will appear with a menu on top of the main window or
form, a series of time series graphs on the left side showing indicators
(e.g. discharge, suspended sediment concentration) for a particular
pool, a map of the UMRB on the right, and a series of model controls and
map legend in the lower-right corner.

***3.5.1 Running the Model***

The main controls for the model are located in the frame at the bottom
mid-right section of the window. The model can be run for Pools 2-22
sequentially, or any set of continuous pools can be simulated by
specifying them in the "Select Pools for Simulation" dialogue box.
Results from only a single pool can be displayed in the time series
graphs at any time. To change the pool to view time series results for,
select the lock and dam (representing the downstream boundary of the
pool) in the dropdown list box below the "Start" button. Click on the
"Start" button to begin a simulation using discharge data beginning in
1959. When you first run the model, discharge data must be read-in which
will take a 20 seconds or so, but this occurs only once per modeling
session. Change the value in the text box entitled "Start Yr." if you
want to begin a simulation at a later start year. To temporarily suspend
model execution click on the "Pause" button. To resume execution, click
on the "Pause" button again. This feature works like the "Pause" button
on a tape recorder. To stop a simulation completely in order to restart
from the start year, click on the "Stop" button. The "Auto-Pause" option
automatically pauses the model after each simulation year is complete.
The "Wrap" option repeats the model simulation for 'x' cycles ('x' is
defined in the text box adjacent to the "Wrap" check box) without
reinitialization after the first cycle. It can be used to examine
long-term consequences of specific policies.

***3.5.2 Setting Stage Height and Dredging Policies***

To implement monthly stage height policies for one or more pools, select
the "Set Stage Height Policy" main menu item which brings up the Stage
Height Policy dialogue box. The dialogue box contains a graph showing
the current target stage heights at the control point for the pool shown
in the dropdown list box in the upper-left section of the dialogue box.
Stage height is represented as +/- x ft. relative to flat pool
elevation. To change target stage heights, hold the left mouse button
down on any part of the graph and drag the cursor to draw in the desired
policy. A table on the right hand side of the dialogue box allows the
user to view or edit monthly target stage heights so that a more precise
policy can be implemented than one developed from drawing on the graph.
Any changes made to the table are reflected in the graph after making
the change and hitting the "Enter". The same target stage policy can be
applied to all pools in the system by clicking on "Apply stage setting
all pools." Flat pool elevation relative to mean sea level and the
out-of-control discharge at the downstream dam are shown for the current
pool at the top of the dialogue box. The "Run of the River (NSM)" check
box allows the stage to vary with discharge to simulate a natural
systems model; however, the stage-discharge relationship used to run
this scenario will not accurately predict stage at discharges below the
out-of-control discharge of each dam (see Section 3.1). Stage height
policies can be implemented in specific years by toggling the values in
the "Set Yearly Interval to Apply Policy" dialogue box. By default, the
model will implement the specified stage height policy every year of the
simulation.

Dredging policies are specified in the "Set Dredging Policy" dialogue
box. The user can specify the minimum water depth at the critical dredge
cut when dredging will be initiated in the model. Dredging policies are
described in Section 3.2

***3.5.3 Viewing/Editing Model Parameters***

The parameters main menu choice has two submenus to access dialogue
boxes showing the parameters controlling the hydrology, sediment
transport, vegetation, fisheries impact, and navigation submodels. The
parameters are described in Sections 3.2 to 3.4. Model parameters can be
saved or retrieved from files by using the Save/Restore Parameter
dialogue boxes accessed from the "Files" main menu. Parameters
controlling the Fisheries Impact submodel are saved to a separate set of
files accessed from the "Files" main menu.

***3.5.4 Reviewing Historical Stage-Discharge Data***

Historical stage and discharge data for each pool can be reviewed by
selecting the "Stage-Discharge Data" main menu choice. It may take a
while for the dialogue box showing this information to appear, as the
entire 1959 - 1995 daily record must be read into memory before the data
for any pool can be displayed. However, once the data have been loaded
for the pool shown in the dropdown list box at the bottom of the main
window, the data do not have to be reloaded the next time the Historical
Stage-Discharge Data dialogue box needs to be accessed for this pool. In
the dialogue box, annual time series of daily records for up to four
stage locations and discharge at the lower dam are displayed in time
series graphs. Pool, stage location, and year can be changed using the
dropdown list boxes at the top of the dialogue box.

***3.5.5 Controlling Time Series Graphs***

When the model is running, pool-specific predictions will be displayed
in the time series graphs. The map is useful for looking at annual
indicators across pools, and gives an idea of the pool-to-pool
variability in selected indicators, while the time series data gives
more detailed results on a daily, monthly, or annual basis for an
individual pool. You can look at the results for any pool by pausing the
model (if in the middle of a simulation) and selecting another lock and
dam from the dropdown list box at the bottom of the main form. To change
the time series indicators you want to examine, click on the "Graphics -
Select Time Series Graphs" menu choice. Four graphs are represented on
the screen, and the indicators for each one can be selected from the
total group of indicators shown in each dropdown list box (Table 3).

**Table 3. List of Output Indicators Used in River System Model.**

+---+------------------------------------------------------------------+
| * | #  Indicator                                                     |
| * |                                                                  |
| G |                                                                  |
| r |                                                                  |
| a |                                                                  |
| p |                                                                  |
| h |                                                                  |
| \ |                                                                  |
| # |                                                                  |
| * |                                                                  |
| * |                                                                  |
+---+------------------------------------------------------------------+
|   | **Stage and Discharge**                                          |
+---+------------------------------------------------------------------+
| 1 | \"Daily Stage Height (ft above msl)\"                            |
+---+------------------------------------------------------------------+
| 2 | \"Daily Discharge (1000 \* cfs)\"                                |
+---+------------------------------------------------------------------+
| 3 | "Target and Average Monthly Stages (ft above msl)"               |
+---+------------------------------------------------------------------+
| 4 | "Days/Yr Stage Target not Met over Year\"                        |
+---+------------------------------------------------------------------+
|   |                                                                  |
+---+------------------------------------------------------------------+
|   | **Fine Sediment**                                                |
+---+------------------------------------------------------------------+
| 5 | \"Fine Sediment Exported from Pool (1000 tons) over Year\"       |
+---+------------------------------------------------------------------+
| 6 | \"Annual % Fine Sediment Export (outflow)/Input (trib + u/s      |
|   | inflow)\"                                                        |
+---+------------------------------------------------------------------+
| 7 | \"Fine Sediment Budget: (u/s inflow, tributary inflow,           |
|   | outflow) - 1000 tons\"                                           |
+---+------------------------------------------------------------------+
| 8 | "Ratio of Fine Sediment Stored relative to Storage at Start of   |
|   | Simulation"                                                      |
+---+------------------------------------------------------------------+
| 9 | \"Average Monthly Suspended Sediment Concentration (mg/l)\"      |
+---+------------------------------------------------------------------+
|   |                                                                  |
+---+------------------------------------------------------------------+
|   | **Coarse Sediment**                                              |
+---+------------------------------------------------------------------+
| 1 | \"Coarse Sediment Exported from Pool (1000 tons) over Year\"     |
| 0 |                                                                  |
+---+------------------------------------------------------------------+
| 1 | "Annual % Coarse Sediment Export (dredging + outflow)/Input      |
| 1 | (trib + u/s inflow)\"                                            |
+---+------------------------------------------------------------------+
| 1 | \"Coarse Sediment Budget: (u/s inflow, tributary inflow,         |
| 2 | dredging, outflow) - 1000 tons\"                                 |
+---+------------------------------------------------------------------+
| 1 | "Ratio of Coarse Sediment Stored relative to Storage at Start of |
| 3 | Simulation"                                                      |
+---+------------------------------------------------------------------+
| 1 | Annual Dredge Volume (1000 yds\^3)\"                             |
| 4 |                                                                  |
+---+------------------------------------------------------------------+
| 1 | "Monthly Bed and Water Surface Elevation at Critical Dredge Cut  |
| 5 | (ft above msl)\"                                                 |
+---+------------------------------------------------------------------+
|   |                                                                  |
+---+------------------------------------------------------------------+
|   | **Habitat**                                                      |
+---+------------------------------------------------------------------+
| 1 | Annual Off Channel Sediment Deposition (1000 tons)\"             |
| 6 |                                                                  |
+---+------------------------------------------------------------------+
| 1 | Habitat Area (open water, submerged veg., emergent veg.,         |
| 7 | riparian grass) 1000 acres"                                      |
+---+------------------------------------------------------------------+
|   |                                                                  |
+---+------------------------------------------------------------------+
|   | **Navigation**                                                   |
+---+------------------------------------------------------------------+
| 1 | "% of Max. Potential Tons Shipped for Pool (@ 9 ft draft) over   |
| 8 | Year\"                                                           |
+---+------------------------------------------------------------------+
| 1 | "Shipping Demand, Potential Shipping given Channel Depth, Max.   |
| 9 | Potential Shipping (@ 9 ft draft) \* 10\^6 tons\"                |
+---+------------------------------------------------------------------+
|   |                                                                  |
+---+------------------------------------------------------------------+
|   | **Fish**                                                         |
+---+------------------------------------------------------------------+
| 2 | "Biomass\"                                                       |
| 0 |                                                                  |
+---+------------------------------------------------------------------+
| 2 | "Mean Size\"                                                     |
| 1 |                                                                  |
+---+------------------------------------------------------------------+
| 2 | "Summer Rearing Capacity\"                                       |
| 2 |                                                                  |
+---+------------------------------------------------------------------+
| 2 | "Winter Rearing Capacity\"                                       |
| 3 |                                                                  |
+---+------------------------------------------------------------------+

By default, time series results are displayed in a single 20 year
'window' from 1959 -- 1979; after 1979, the remaining sequence is
displayed (1980 - 1995). However, if you want to shorten the viewing
window so that seasonal variation can be seen, change the value in the
text box entitled "Show daily time series in increments of \_\_\_ years"
in the Time Series Graphs dialogue box. For example, if you select a
value of 10, the graphs will show results over a 10 year period,
(1959-1969), and at the end of the period, will show the next (1970 -
1980) 10 year sequence.

To compare historical stage and discharge data with model predictions
when running the model at project pool elevations, check the "Plot
observed stage and discharge data with simulated results" check box.
Model predictions are shown in red and observed data in blue during a
simulation.

***3.5.6 Saving Model Output to a File***

To save simulation results to an ASCII-comma delimited text file (which
can easily be imported into a graphics package for plotting), click on
the "Save Subsequent Simulation Results to File" menu item under the
"Files" main menu choice. You will be prompted for the filename to which
to save the results. Begin a simulation and when it is finished, return
to this menu choice and click on it again to turn the file saving option
off. The results file will contain a header row with a series of
variable names for each field in the file. The file "headers.txt"
contains a description of each field. Note that saving results will
substantially slow down the execution speed of the model.

***3.5.7 Controlling the Map***

On the unzoomed map, the locations of locks and dams are shown by green
lines, the currently modeled section of the river is shown by the black
line between the locks and dams, and the unmodeled section is
highlighted in red. Zoom in on the modeled section of the river by
clicking on the "Zoom Map" check box in the lower right section of the
main window. A map legend is displayed at the bottom-right of the screen
which shows the colors associated with different levels of the indicator
shown in the dropdown list box at the top of the legend. To change the
indicator displayed in the map, just select another from this list box.
When the model is running, the values for each pool will be updated
based on last year's results; and the pools will appear in different
colors to reflect this. To see the exact value for any pool (and the
average and sum across pools), simply click on the pool with the mouse
and hold the left button down.

The colors and category divisions for the maps can be adjusted and saved
by selecting the "Graphics - Legend Editor" choice, thereby bringing up
the "Legend Editor" dialogue box. Each indicator can have a different
legend and indicators can be changed using the dropdown list box in the
upper-left section of the dialogue box. The number of categories for
each legend can be changed by modifying the value in the text box in the
lower-left section of the dialogue box. Colors for each category can be
changed by clicking on a color in the color palette and then clicking
the color boxes in the legend on the right side of the dialogue box.
Division breakpoints and text to be displayed for each breakpoint can be
edited. Legends can be saved and restored to ASCII files using the
"Restore Map Legend to File..." and "Save Legend to File..." menu items
below the Graphics main menu item.

**3.6 References**

Simons, D. B. 1979. Sediment transport in the Upper Mississippi River
within the St. Paul District. Attachment B. Prepared by Engineering
Research Center, Colorado State University.

Nakato. T. 1981. Sediment-budget study for the Upper Mississippi River,
Great-II Reach. IIHR Report No. 227. Iowa Institute of Hydraulic
Research, University of Iowa, Iowa City, Iowa.

Rose, W.J. 1992. Sediment transport, particle sizes, and loads in the
lower reaches of the Chippewa, Black, and Wisconsin Rivers in Western
Wisconsin. U.S. Geological Survey, Water-Resources Investigations Report
90-4124).

Tornes, L.H. 1986. Suspended sediment in Minnesota streams. U.S.
Geological Survey, Water-Resources Investigations Report 85-4312).

**4.0 Pool Model**

**4.1 Basic Structure of Hydrology/Sediment Transport Components**

This submodel represents individual pools on a spatial grid. Basic data
input consists of (1) elevation (ft. msl) mapped at 100m pixel
resolution; (2) historical monthly average inflows (cfs) to the pool;
(3) historical stages (ft. msl) at the head, control point(s), and just
upstream of the dam; and (4) sediment input concentrations and rates of
loss. The aim of the model is to produce monthly average water depth
(ft.), flow pattern (spatial velocity field), and sediment concentration
for each pixel, based on the assumption that the montly average values
for these variables will be near the equilibrium values that would occur
if all input rates were held constant at the monthly average values for
long enough to allow water levels, flows, and sediment concentrations to
reach equilibrium. At the 100m grid resolution, it is not practical to
simulate the full hydrodynamic transient responses at time scales
shorter than a month; the stable time step for numerical hydrodynamic
modelling at this spatial resolution and given typical upper
Mississippii flows is on order 0.1 sec.

Even the equilibrium flow/concentration field for each month takes 5-20
min. to compute using a 133mh Pentium PC. To speed up thecalculation, we
have incorporated a grid aggregation routine to perform the hydrodynamic
and sediment concentration calculations on larger grid cells with
lengths that are multiples (2,3,4, etc.) of the basic elevation grid
cells. Computational speed is increased by a factor of 4 for the
length-2 grid, a factor of 9 for the length-3 grid, etc. When coarser
grids are used, there is a corresponding loss of information about
detailed spatial variation in flow fields and sediment concentrations,
but the coarser grids may still be useful for quick analysis of long
term changes in sediment transport rates and accumulation for relatively
large areas within each pool (e.g., for whole area near the dam, for
main channel areas, etc.). To further speed up the computations for long
term simulations of vegetation change and sediment accumulation, we
initialize the monthly hydrodynamic calculations using a very efficient
one-dimensional model of water levels and flow velocities along the main
downstream axis of the pool; this first approximation can be used
without solving the two-dimensional hydrodynamic equations at all, to at
least represent broad seasonal patterns in flooding.

By varying the hydrodynamic submodel grid resolution and number of
iterations used in the calculation of spatial fields, model users can
easily evaluate the time costs and benefits of increasing precision in
this submodel. Low resolution runs can be used in quick evaluations of
alternative hypotheses about vegetation and other dynamics, then more
costly runs can be made later to obtain better spatial resolution in
particular parts of the modeled pool that are of special management
concern.

To date we have restricted test calculations to Pool 8, for which the
100m grid would have about 30,000 cells. For this test area, we have
further restricted calculations to the roughly 8000 grid cells
representing the plan pool for the dam; this restriction means in effect
assuming that cells further to the side of the main channel contribute
little in most months to water and sediment transport (i.e., have low
flow velocities and similar sediment concentrations to the cells along
the edge of the restricted model grid).

The following symbols are used in subsequent subsections describing
details of the hydrodynamic and sediment transport calculations:

Q=water flow, cfs

v=water velocity, ft/sec.

w=cell length or width, ft.

e~ij~=elevation (ft) at bottom of spatial cell in north-south row i,
west-east column j of map grid.

h~ij~=water depth (ft) on grid cell at north-south position i, west-east
position j.

s~ij~=stage at cell ij (s~ij~=e~ij~+h~ij~).

c~ij~=sediment concentration (arbitrary units) in water column of grid
cell ij.

V~ij~=volume of water (ft^3^) carrying sediment in cell ij.

W~ij~=index of wind/wave driven force causing sediment resuspension in
each cell ij.

### ***4.1.1 Hydrodynamic Simulation***

Hydrodynamic equilibrium (depth-velocity field over the grid) is
calculated for each month in two steps: (1) a one-dimensional stage
profile is computed from the top to the bottom of the pool, and depths
are initially assigned to be equal across each row of the grid (assumes
water surface is flat across channel and backwaters, sloped from north
to south along main axis of flow); and (2) a two-dimensional hydrodyamic
model then iterates forward in time from this starting depth field to
provide more accurate steady state slope-flow patterns along channel
meanders and through various hydrologic structures (subpools, etc.)
implied by the topography.

The basic assumption in both these steps is that flow velocity is
proportional to water depth and slope -- i.e., that water accelerates
according to the relation (dv/dt)=g(dh/dx)-fv/h implying steady state
v=(g/f)h(dh/dx) where x is a direction of flow and g and f are gravity
and friction constants. This assumption implies that flow for any small
section of the river (across the boundary between any two cells) will be
given by Q=vwh=(wg/f)h^2^(dh/dx)=kh^2^S, where k=(wg/f) is an aggregated
flow parameter, h is depth, and S is water slope between the cells. We
have obtained estimates of k by fitting the model to historical stage
data for Pool 8; k is recalculated for each simulated month to insure
that simulated stages and water slopes along the pool will match
observed control point and dam stages. Using this approach, we can match
observed stages from upstream to downstream in Pool 8 to within 0.5 ft
for almost all months of historical data from 1955-95. We miss midpool
stages by order 0.5 ft for a few flood months, but still match stages at
the upper and lower ends of the pool---the minor lack of fit is likely
due to discretization errors in the elevation profiles along the pool.

The one-dimensional or "startup" stage profile for each month is
obtained by a numerical procedure similar to the HEC2 model used by the
Corps of Engineers. We first precalculate Σh^2^ values across the cells
of each "test" map row (usually with test rows being every 2-4 map rows)
for a series of stage levels at that row (0.1 ft. stage increments), and
store the resulting table of "squared cross-sectional area" values. Then
each month we work backward up the pool from the dam, calculating the
slope at each test map row needed to produce the observed total
crosssectional flow past that map row (value of stage at the row needed
to have Q~across\ row~=kSΣh^2^=observed flow rate for the month). Note
that as we vary stage, slope S at the row is implied, since it is
measured relative to known stage at the next test row downstream. This
procedure is repeated recursively upstream, beginning at the dam.

The two-dimensional hydrodynamic model then does a time integration of
the differential equation
dh~ij~/dt=ΣQ~inflows~/w^2^-ΣQ~outlfows~/w^2^+inflow/w^2^ using a
variable step-size euler integration algorithm, where the Qinflows and
Qoutflows are calculated across the ij cell boundaries using the above
Q=kSh^2^ flow relation with S=h~ij~-h~lm~+e~ij~-e~lm~ for each cell pair
lm sharing a cell boundary with ij. "inflow" is added at cells
representing where the river and tributaries enter the pool. The
effective flow depth h for each cell-cell interface is taken to be the
stage at the "source" cell (upstream direction) less the larger of the
two elevations e~ij~, e~lm~. The step length ∆t for each time
integration step is taken to be that value for which the most rapidly
changing cell in the grid (cell with largest dh/dt) will change by no
more than ½ the mean water slope in the pool (where mean slope is just
taken to be elevation at inflow minus elevation at dam divided by the
number of rows in the grid).

We tried various schemes for solving the linearized, steady state flow
equations for h~ij~ directly (schemes for solving such large, sparse
linear equation systems), without resorting to the time-stepping the
differential equations. These schemes do not work, since there are large
shallow areas that can go dry completely in some months, implying a
threshhold nonlinearity in the equation system (simple schemes can
predict negative depths under rather common flow conditions). However,
relatively few iterations (20-50) of the time scheme appear sufficient
to nicely characterize the 2-dimensional flow field, given that the
one-dimensional profile method gives a good approximation of major stage
field variation along the downstream axis of the pool to start the
iterations.

### ***4.1.2 Sediment Concentration Fields*** 

We have surprisingly found it numerically more difficult to estimate
steady state sediment/turbidity concentration fields than flow fields.
The basic equation for sediment concentration dynamics in a grid cell is
just

dV~ij~c~ij~/dt=ΣQ~inflows~c~inflows~-c~ij~ΣQ~outflows~-v~sink~w^2^c~ij~+C~susp~w^2^
(1)

where the Q flows include "flows" due to turbulent mixing of water,
v~sink~ is sediment sinking velocity, and C~susp~ represents
resuspension of sediments (functionally related to relative velocity of
water flow as measured by ΣQ~outflows~ /V~ij~). The transport Qc and
sinking terms in the above equation are easy to represent, in the same
accounting system as used for the 2-dimensional hydrodynamic
calculations; the difficulty is in modeling the resuspension rate
C~susp~. Given an estimate of the Q's from the hydrodynamic calculation,
v~sink~, and C~susp~, a trial equilibrium (dVc/dt=0) value for c~ij~ is
given by

c~ij~ =\[ΣQ~inflows~c~inflows~+C~susp~w^2^\]/\[
ΣQ~outflows~+v~sink~w^2^\] (2).

We solve for this trial value at each time iteration of the hydrodynamic
equations. Note that the resulting values converge rather slowly to the
steady state value for each ij, since the c~inflows~ are changing with
each iteration (these c~inflows~ are the c~lm~ values for other cells lm
that flow into cell ij). We have tried unsuccessfully to accelerate this
equilibration process by using sparse linear equation system and
overrelaxation methods.

We can perhaps find ways to accelerate the concentration equilibration
process, but these will not solve the key problem of how to model
resuspension processes represented by the C~susp~ term above. This term
must be quite substantial; without it, we predict using reasonable
sinking rates v~sink~ that sediment concentrations should drop quite
rapidly for most months within pools such as Pool 8, and parts of such
pools should have quite clear water due to slow water movement rates
(long residence times relative to sinking rates). That is, without
substantial resuspension rates, the pools should act as quite efficient
sediment traps. But sediment concentration does not drop rapidly along
the course of the Mississippii, so either effective sinking rates must
be very low or else there is considerable resuspension and erosion to
add sediments to the water column.

Resuspension rates C~susp~ are assumed to be proportional to a water
energy or shear index E~ij~=ΣQ~outflows~/V~ij~+W~ij~. Here the Q/V term
measures velocity of water flow through the cell, and the wind energy
term W~ij~ is calculated (for ice-free months only) by evaluating the
wind fetch structure from south to north along each column of the
spatial grid (assuming predominantly southerly winds during summer).
Wind energy in the water column is assumed to increase with distance
(fetch) by a process involving constant energy addition per distance and
frictional loss (bottom friction) inversely proportional to depth. These
assumptions lead to an exponential relationship across each cell:

W~nb~=W~e~+(W~sb~-W~e~)exp\[-k~1~w/h~ij~\] (3)

where

W~nb~ is energy at the north boundary of the cell,

> W~sb~ is energy at the south boundary (equal to energy at north
> boundary of last cell\
> in cumulative calculation proceeding northward across map rows),
>
> We=h~ij~k~1~/k~2~ is the equilibrium energy that would occur over a
> very large fetch at\
> depth h~ij~,
>
> k1,k2 are constants to be determined empirically so as to give
> realistic\
> resuspension patterns in shallow areas subject to large wind fetch.

Equation (3) is used rather than a simpler distance measure of wind
fetch in order to represent damping effects of shallow shoals (high
exponential loss of energy due to small depth h~ij~) on transmission of
wave energy along the pool.

## 4.1.3 Missing Pieces in Hydrology Submodel

There are at least three things that we should consider adding to the
submodel:

### (1) Microtopography "roughness" dynamics

A key concern in the system is that erosional forces (wind, waves from
barges, water flow) are breaking down the topographic microstructure of
channels and high spots that developed under natural flow conditions and
led to a spatially diverse vegetation community in the riparian zone.
Under natural conditions, rivers cut channels that then make adjacent
bank areas drier than if water flowed uniformly over the floodplain;
vegetation development on these drier microsites tends to further dry
out and stabilize the sites, and still further development of relief can
also occur due to seasonal deposition of silt during normal flooding.
That is, natural erosion/deposition forces tend to exaggerate the
"roughness" (channel vs upland) of the floodplain landscape at small
scales; these patterns are essentially "multiple equilibria" at small
scales. Under continuous flooding, it is not surprising that roughness
is decreasing, leading to development of large, unproductive mudflat
areas.

We do not think it is wise to try to model the dynamics of microscale
roughness by brute force, using very small grid cells and modeling all
components of the erosion/deposition dynamics explicitly. The
computational effort required to do this would be astronomical at the
navigation pool scale, and parameterization practically impossible
because of the detailed information needed about factors like soil type
and vegetation physiological requirements. We need to find a simple way
to model the roughness dynamics directly, based on empirical experience
with topographic changes that have already occurred in the system.

### (2) Nutrient availability dynamics

The navigation pools were probably more productive as aquatic ecosystems
shortly after they were formed than they are today, due to two factors:
(1) greater habitat complexity (spatial refuges, etc.) due to the
natural topographic roughness mentioned above; and (2) the "hay
infusion" effect generally seen when reservoirs are first flooded,
involving high availability of both organic detritus and nutrients to
the aquatic system. It appears that continuous flooding leads to
relatively tight binding of nutrients in the sediments, and to loss of
accumulated organic carbon from the original soils. It is possible that
changes in water management policy, to allow occasional or regular
seasonal drying of some flooded areas, would reestablish a more
productive aquatic regime by promoting nutrient release from the
sediments and by allowing some accumulation of organic matter due to
growth of terrestrial "weeds" on the dried areas.

If water level management to restore productivity is contemplated as a
system policy, we will need to model the seasonal and interannual
dynamics of nutrient (both inorganic and organic) availability and
accumulation. We will need to make at least some broad predictions about
the time scales of response (how quickly nutrients are mobilized and/or
grow under dry conditions, how quickly they are locked up or used again
after reflooding), in order to suggest meaningful management experments
to test for appropriate scales and patterns of drying.

### (3) Sediment transport by grain size (bedload vs suspended sediment movement)

Changes in water level management to enhance aquatic productivity or
restore natural riparian vegetation/roughness patterns will cause
potentially expensive changes in bedload transport regimes. Reduced flow
velocities due to maintaining high water levels in the pools have
probably led to substantial accumulation of bedload materials in some
locations (mainly along original channels) where flow velocities would
increase substantially if water levels were seasonally varied.

To realistically assess the transient and long term costs of changing
bedload transport regimes under various seasonal water level policies,
we would need to do separate spatial accounting of fine versus coarse
sediment movements. Further, we would need to provide the model with
spatial maps of current bedload/sediment accumulation patterns, to
properly "initialize" any scenario aimed at predicting transient changes
in erosion rates during removal of sediment accumulations due to recent
pool management.

**4.2 Macrophyte Seasonal Production and Distribution Submodel**

Aquatic macrophytes are a key indicator of ecological health in the
transportation pools, because of their importance in primary production,
refuge cover for juvenile fishes, and effect on stability of bottom
sediments. Policy suggestions for macrophyte management have included
summer drawdowns, presumably to increase the depth at which macrophytes
can obtain sufficient light. But such policies may backfire, by drying
out and killing more macrophyte area than they add. The pool model can
be used to evaluate spatial impacts of various seasonal water policies
on local biomass production and net annual change in biomass integrated
over production and loss rates, if we can provide a macrophyte "site
model" for each pool model grid cell that represents the effect of
seasonal production and depth changes on relative biomass dynamics in
that grid cell. The following subsections describe a first attempt to
develop such a seasonal biomass dynamics model.

***4.2.1 Seasonal Biomass Dynamics Propagation***

For each grid cell in the pool model, we propagate the following biomass
production-survival relationship over the 12 months (m) of each
simulated year:

B~m+1~=B~m~(1+P~m~)S~m~ (1)

where

m=month

B~m~=relative biomass in the cell at start of month m

P~m~=Production/Biomass in month m

S~m~=survival rate of produced and extant biomass over month

The key to making this making this biomass accounting relationship
useful is to develop predictive relationships for the P/B ratio P~m~ and
the survival rate S~m~ as functions of depth and other factors.

As a starting point for further development, we have initially modeled
the P/B ratio as dependent on biomass (space/nutrient competition) and
depth, with the relationship:

P~m~=P\*~m~e^-λd^/(1+P\*~m~B~m~/K~m~) (2)

where

P\*~m~=maximum P/B ratio in shallow water (at "zero" depth)

d=water depth (ft)

λ=light extinction coefficient (dependent on turbidity)

K~m~=production scaling parameter (maximum monthly production/grid cell,

set to 1.0 since absolute biomass scaling is unnecessary for policy
analysis)

Note that we can set up a seasonal production schedule that reflects
various phenological and seasonal production limiting factors by setting
an appropriate schedule for the monthly maximum P/B ratios P\*~m~.

We have initially modeled the monthly biomass survival rates as a
function of water depth and wind energy, to reflect the negative impacts
of seasonal drying and turbulence:

S~m~=S\*~m~\[s~min~+(1-s~min~)(d/k)(1+d/k)\]/\[1+(W~m~/(dk')\] (3)

where

S\*~m~=maximum biomass survival rates under optimum depth conditions

s~min~=minimum relative survival rate at zero water depth

k=depth needed to achieve about 1/2 of maximum survival rate

k'=wind energy needed to reduce survival rate by about 1/2

W~m~=wind+current turbulent energy at surface of the grid cell in the
month

(see hydrology submodel)

The basic idea behind this relationship is to have survival rate fall
off to S\*s~min~ when a grid cell is dry, and to have survival decrease
in areas with high wind/current energy. Note how S\*~m~ is multiplied by
two factors: a depth effect \[s~min~+(1-s~min~)(d/k)/(1+d/k)\] that
increases from s~min~ to 1 as d increases, and a turbulence effect
1/\[1+(W~m~/(dk')\] that decreases from 1 to 0 as W~m~/d increases. This
formulation may be unnecessarily redundant; most very shallow areas have
high W~m~/d, and hence the single depth effect may be all that is needed
to capture negative effects of very shallow conditions and drying on
macrophyte survival. We have not yet attempted to estimate the k and k'
parameters; the simplest way to do this will be to run the model with k
set very small (e.g. 10^-6^) and k' very large, then examine whether the
model extends macrophyte distribution into inappropriate areas.

***4.2.2 Persistence Conditions and Average Biomass Predictions***

The seasonal biomass dynamics implied by substituting equations (2) and
(3) into (1) (see Section 4.2.1) can generate very complex space-time
patterns when d and W~m~ also vary over space and time. To assist in
understanding the general effects of parameters P\*~m~,S\*~m~, and λ on
these patterns, the user interface for setting and manipulating these
parameters is linked to subroutines for performing two special
calculations: the "critical depth" d~c~ greater than which macrophyte
persistence will not occur even without seasonal drying and turbulence
effects, and the average January (m=1) biomass that would occur under
constant d and in the absence of drying and turbulence effects.

The critical depth d~c~ is calculated by noting that continued biomass
decline will occur whenever the annual cycle of production and survival
implied by equation 1 results in B~m+12~\<B~m~ even when B~m~ is very
low. The break-even condition B~m+12~=B~m~ for very low Bm satisfies the
following relationship to d~c~:

$1 = \prod_{\text{m=1}}^{\text{12}}{(1 + \text{P*}_{m}e^{- {\lambda d}_{c}}})\text{S*}_{m}$
(4)

This equation has to be solved numerically for d~c~; the model user
interface performs this numerical solution whenever the user changes any
of the parameters in equation (4), which makes it easy to check that a
hypothesized seasonal production/survival/light penetration pattern will
in fact produce reasonable estimates of the maximum depth for macrophyte
persistence.

The average January 1 biomass is estimated by numerically solving an
equation similar to (4), but including density dependent effects on P~m~
so that the equation can be solved for B\*~1~:

$1 = \frac{\prod_{\text{m=1}}^{\text{12}}{\lbrack 1 + \text{P*}_{m}e^{- \lambda d}}}{(}1 + \text{P*}_{m}\text{B*}_{m})\rbrack\text{S*}_{m}$
(5)

where
$\text{B*}_{\text{m+1}} = \text{B*}_{m}\lbrack\text{1+P*}_{m}\frac{e^{- \lambda d}}{(}1 + \text{P*}_{m}\text{B*}_{m})\rbrack\text{S*}_{m}$,
m\>1

This is just the population model without drying and turbulence effects.
Solving for B\*~1~ just amounts to substituting different values of it
into the product and monthly recursion, until the product equals 1.0. A
Newton iteration is used to make this search efficient.

***4.2.3 Possible Improvements in Macrophyte Submodel***

The biggest uncertainty in the above submodel is likely to be about
effects of seasonal drying and turbulence in very shallow water on the
biomass survival rates S~m~. If we set s~min~ very low, the model will
quickly wipe out macrophytes from shallow areas that are dried out for
even short times during summer. Likewise, we may want to make the
sensitivity to drying depend on season; it is likely that most
macrophytes are much less sensitive to drying periods during winter than
during the summer growing season. We will need to look at this
uncertainty carefully in workshop sessions.

Another uncertainty is about effects of seasonal drying on the
production rates P\*~m~. It is possible for example that drying an area
over part of the year, such as late winter, may increase P\*~m~ for at
least the following year, by stimulating nutrient release and/or
structure changes in the sediment.

The model currently constrains B~m~ to a low minimum value for each grid
cell, representing "seeding" or colonization of the cell from sources
that are not made explicit. This convention insures that cells which
become suitable for macrophyte growth under depth policy manipulations
do in fact begin a biomass growth dynamics. It is possible that we
should explicitly model seed sources and seed movements in order to
realistically predict colonization rates.

**4.3 Fisheries Impact Submodel**

For policies that involve substantial change in the management of the
navigation pools, we will need to make predictions about the impact of
changing water levels and velocity patterns on abundances of a variety
of fish species that are prized for recreational use. In particular,
drawdown policies aimed at restoring seasonality of levels and flows for
riparian vegetation and channel management may create bottlenecks for
fish species that have thrived under continuous pool flooding
conditions. Fish species that will need to be included in the analysis
range from large-mouth bass and small centrarchids that use mainly
backwater areas, to small-mouth bass, white bass, and walleye that
frequent deeper main channel areas. We propose a five-part submodel for
relating overall abundances of any indicator suite of fish species to
water level and flow conditions. This submodel uses outputs from the
hydrology submodel to provide temporal predictions of changes in habitat
availability, and uses these outputs to predict impacts on recruitment
and biomass dynamics. It is currently available as a stand alone program
which is not described in this guide.

***4.3.1 Age Structured Biomass Dynamics Models for Indicator Species***

Since we need to deal with a potentially large number of indicator fish
species (10+), we need to use a relatively simple population dynamics
representation for each species. A common modeling method in fisheries
under such circumstances is to represent population age structure using
a delay-difference model that stores only population biomass and total
numbers for each species. This model is an exact representation of the
age-structure dynamics only if survival rates are independent of age
beyond a base age k, and if body growth after this age follows the
Ford-Brody relationship; in practice, these two assumptions are not
usually violated except for species that have complex size-vulnerability
relationships to fishing.

The delay-difference model structure for any indicator species f,
f=1,...,F, has the following temporal structure for interannual
(t=annual time step) predictions:

B~f,t+1~=s~f,t~(α~f~N~f,t~+ρ~f~B~f,t~)+w~f,k~R~f,t+1~ (1)

> N~f,t+1~=s~f,t~N~f,t~+R~f,t+1~ (2)

where:

B~f,t~ = biomass of age k and older fish of species f in the spring of
year t+1

N~f,t~ = number of age k and older fish of species f in the spring of
year t+1

α~f~,β~f~,w~f,k~ are Ford-Brody body growth model parameters for species
f

s~f,t~ = survival rate of age k and older fish of species f over a year
(includes

fishing and natural mortality losses

R~f,t+1~ = number of age k recruits in the spring of year t+1

In practice, it will probably be best to set k=1 for most species, since
the main habitat impacts on population dynamics are likely to be those
influencing fish less than one year old - i.e., impacts on the
recruitment rates R~f,t+1~. Note that for this model, we must provide a
minimum of three growth parameters and one annual survival parameter for
each species, and more survival parameters if we decide to have survival
rates vary from year to year with changes in fishing pressure or fish
harvest management policy. Note further that the model can be used to
predict useful measures of population health and quality for fishing,
such as the average body size w=B/N.

Usually in fisheries analysis we treat the growth and natural survival
rate parameters as constant (except for density-dependent growth effects
on α~f~ for some situations, see Walters and Post Am. Fish. Soc. 1993),
and focus population dynamics attention on prediction of the recruitment
rate R~f,t~. This prediction is usually done with a stock-recruitment
relationship of the Beverton-Holt form, which relates recruits to the
parental biomass (index of population fecundity since fecundity is
related to body weight) B~f,t-k~ that produces the recruits:

R~f,t~=a~k~B~f,t-k~/(1+aB~f,t-k~/K~f~) (3)

where the parameter a~k~ is maximum number of age k recruits produced
per biomass of parental spawners when spawning abundance is low, and
K~f~ is the environmental carrying capacity to produce recruits (maximum
recruitment rate, rate that is independent of B~f,t-k~ for high spawning
biomass levels). In many fish populations, we never "see" effects of the
a~k~ parameter, and effectively we only observe the average recruitment
rate K~f~ for most spawning biomasses that are observed naturally
(recruitment appears completely flat when plotted against spawning
biomass, and the average of this flat level is the best estimate of
K~f~). This recruitment function is derived by assuming natural
mortality rate of pre-recruits to be linearly proportional to the
density of competing juveniles at every moment during the time required
to reach age k. In traditional fisheries analysis, K~f~ is treated as a
constant measure of habitat capacity to produce juveniles.

***4.3.2 Recruitment-Habitat Capacity Linkage Function***

We propose to link the population dynamics model defined by equations
(1)-(3) to changes in habitat conditions by making the recruitment
carrying capacity parameter K~f~ depend on amount of suitable habitat
available during the first year of life. The concept here is that
first-year juveniles are likely to be the most sensitive component of
most populations to changes in habitat (least able to deal with changes
in velocities and depths by moving to other locations, or simply
"sitting out" bad periods in small refuge areas within the pool). When
juvenile densities are very low, there is likely to be adequate refuge
habitat for these few juveniles no matter how the pool is managed, so we
propose to treat the maximum fecundity x survival parameter a~k~ as
constant for each species.

Juvenile fish generally undergo a series of habitat-related life history
stages or "stanzas" where they use different micro-habitats (e.g.
shallow weedy areas followed later by more open areas). It is likely
that a Beverton-Holt recruitment limitation relationship applies to the
input-output (number entering, number surviving to leave) relationship
for each of these stanzas. Luckily, there is a simple mathematical way
to apply a sequence of Beverton-Holt limiting relationships over stanzas
that follow one another, such that each stanza s results in an output
number R~f,s~ recruits to the next stanza (R~f,t-k~ is output from the
last stanza s) and another Beverton-Holt relationship then applies over
that next stanza. The input is spawning biomass B~f,t-k~ for the first
stanza s=1, and is R~f,s-1~ for each stanza that follows. If there are a
total of n~s~ stanzas over the period k years, the overall recruitment
relationship is still of Beverton-Holt functional form like equation
(3), but the a~f~ and K~f~ parameters are replaced by products of a~f,s~
and K~f,s~ parameter components for the stanzas s:

$R_{\text{f,t+k}} = \frac{B_{\text{f,t}}\prod_{s = 1}^{n_{s}}a_{\text{f,s}}}{\text{1+B}_{\text{f,t}}\left\lbrack a_{\text{f,1}}C_{\text{f,1}} + a_{\text{f,1}}a_{\text{f,2}}C_{\text{f,2}} + \text{.}\text{.}\text{.} + a_{\text{f,1}}a_{\text{f,2}}\text{.}\text{.}\text{.}a_{\text{f,n}_{f}}C_{\text{f,n}_{f}} \right\rbrack}$
(4)

That is, a~f~ is replaced by the product of the by-stanza maximum
fecundity or maximum survival rates a~f,s~, and K~f,s~ is replaced by a
weighted sum of carrying capacities C~f,s~ for each of the stanzas s. In
this formulation, recruitment may be effectively limited (or caused to
fail entirely) if one or more of the carrying capacities by stanza
C~f,s~ are reduced through habitat changes.

An obvious and relatively simple option for the stanza structure in
equation (4) is to set k=1 (recruit to overall population at age 1), and
n~s~=2 with these two stanzas being the first summer and first winter of
juvenile life. Another option is to set n~s~=12, and treat each month of
the first year of life as a separate juvenile stanza; this option would
allow representation of particular "limiting periods" such as a very low
flow or level period lasting only one month or less at some time during
the winter. However, we doubt that it will be possible to provide
reasonable parameter estimates for multi-stanza models, and have
initially programmed the summer-winter period structure n~s~=2 for use
in policy comparisons.

We return to the calculation of the habitat capacity parameters C~f,s~
in subsection (4) below. Basically, we propose to have these capacities
vary over time with changes in the area of habitat available for each
species f during each seasonal stanza s, with changes in water levels
and velocities.

***4.3.3 Pool Habitat Conditions Summary Function***

The pool model produces a spatial grid prediction, with 100m x 100m
pixel size, of water depths, velocities, and turbidities by month for
each simulated year. However, the predicted turbidities do not change
greatly over the spatial grid within each pool, and change predictably
with seasons. Therefore, the main variables that are likely to influence
fish populations differently under policy changes such as drawdowns are
the depths and velocities.

We have included a summary function in the pool hydrology submodel to
calculate the spatial extent of various depth-velocity (d,v) situations.
The way this is done is to set up a grid of discrete depth-velocity bins
(e.g, one bin might be water depth 0 to1 ft. with velocity 0 to 0.2
ft/sec., another would be depth 1-2 ft. with velocity 0-0.2 ft/sec.,
etc.). For each simulated month, we examine each model grid cell and add
its area (1 ha.) to the total area for the corresponding depth-velocity
bin (if a cell has depth 0.7 ft. and velocity 0.15 ft/sec., the
0-1,0-0.2 bin would be incremented by one ha to include this cell). The
result of this scan is a matrix (the grid) of habitat areas A~d,v~
(A~d,v~ = surface area in depth category d, velocity category v) by
depth and velocity category, which can be used for non-spatial analysis
of habitat area available to various fish species.

Why should we "throw away" explicit spatial information on arrangement
of depth-velocity patterns for calculations involving fish? The answer
to this question is two-fold: (1) we could not use the explicit
arrangement information for fish calculations without an explicit model
for how fish move about over the spatial mosiac; the information
requirements for doing such a movement model would be prohibitive, as
would the computer time requirements for a multispecies fish assessment;
(2) fish movement takes place on very short time scales (hours, days),
and it is likely that most types of fish can move around within a pool
enough on monthly time scales to fully "explore" the pool's habitat
opportunities (if suitable habitat is there, they will most likely find
it on time scales important for population dynamics.).

***4.3.4 Species-Specific Habitat Capacity Relationship***

Presumably the by-stanza carrying capacities C~f,s~ of equation (4) are
related to the area of habitat within each pool that is of suitable
depth, velocity, etc. for species f juveniles at the time of year when
stanza s occurs. We make the simple assumption that

> C~f,s~=k~f,s~A~f,s~ (5)

where k~f,s~ is an empirical fish-per-area capacity estimate for species
f during stanza s and A~f,s~ is the assessed habitat area suitable for
species f during stanza s. We provide a user interface to define A~f,s~
from the monthly depth-velocity area summary table A~d,v~. The model
user defines for each f,s a domain of depth d and velocity v values that
are suitable for use by f,s. The model then scans the A~d,v~ table for
each month (or for a month that is "typical" of conditions encountered
by fish during stanza s), and adds suitable A values to the A~f,s~ total
for that month, for every f and s. This approach makes it easy to define
species differences in habitat requirements and preferences, as
differences in the d,v "domain" used by the various species.

We could include other information in the area summary table A~d,v~,
such as area with and without rooted macrophytes, and area with mud,
sand, and rocky bottom. However, these additional habitat variables are
likely to be closely correlated with the basic physical measures d,v, so
such a more complex table would be quite redundant and is not likely
needed for assessments of overall habitat change.

***4.3.5 Use of Initial Equilibrium Assumption to Reduce Complexity of
Parameter\
Estimation***

The population/habitat model defined by equations (1),(2), (4), and (5)
generates a formidable problem for empirical assessment of the various
population dynamics and habitat linkage parameters, especially if the
assessment is to include many species. However, we can use two ideas to
considerably reduce the complexity of this estimation problem: (1)
current population sizes for most species are probably near an
equilibrium or balanced level with respect to current habitat status and
mortality rates due to fishing, so that the assumption B~f,t+1~≈B~f,t~
can be used to structure relations between the variables and parameters
so as to eliminate a few parameters from the estimation; (2) population
biomass and numbers can be measured in arbitrary units for comparison
between simulation scenarios, and in particular we can set B~f,0~=1 to
represent biomass dynamics *relative to* the biomass at year 0.

In particular, the initial balance assumptions
B~f,0~=s~f,0~(α~f~N~f,0~+ρ~f~B~f,0~)+w~f,k~R~f,0~ and
N~f,0~=s~f,0~N~f,0~+R~f,0~ allow us to compute an initial recruitment
rate R~f,0~ for each population, as

R~f,0~=B~f,0~(1-ρ~f~s~f,0~)/\[ α~f~s~f,0~/(1-s~f,0~)+w~f,k~\] (6)

and initial numbers

N~f,0~=R~f,0~/(1-s~f,0~) (7)

using only the scaled inital biomass B~f,0~ and the growth-survival
parameters {α~f~, ρ~f~, w~f,k~, s~f,0~} that are relatively easy to
estimate for most fish species f. These relationships allow us to
initialize numbers and recruitment rates to be consistent with the
scaled biomass units of B~f,0~. Note that they also allow a check on the
growth survival parameters; if B~f,0~/N~f,0~ is not close to the
observed average body size for age k and older fish, we know that there
is a problem either with the units of measurement of the growth
parameters or with the assumed initial survival rate s~f,0~.

We can go further to simplify the assessment of the recruitment/habitat
parameters, using the initial recruitment assessment R~f,0~. Suppose we
set a~f,1~ to a reasonable estimate of the first life stanza product of
fecundity per biomass times maximum survival rate, and assign reasonable
values to maximum survival rates a~f,s~ for remaining stanzas s\>1. Let
the total product of these productivity values be
G~f~=a~f,1~a~f,2~...a~f,ns~. Finally, suppose we set reasonable
*relative* values for the carrying capacity per unit habitat parameters
k~f,s~ (using information on maximum density of stanza s juveniles per
unit suitable habitat, in any convenient density unit that is comparable
among stanzas) and compute C~f,s~ for every f,s using the habitat area
A~f,s~ assessments for the first hydrology simulation year. For this
initial year's calculation, let the denominator sum in equation (4) be

H~f,0~=a~f,1~/C~f,1~+a~f,1~a~f,2~/C~f,2~+...+a~f,1~a~f,2~...a~f,ns~/C~f,ns~
(8)

We can then re-express the recruitment relationship equation (4) in
terms of G~f~,H~f,0~, B~f,0~ and one additional habitat size-biomass
scaling parameter S~f~, as

R~f,0~=G~f~B~f,0~/(1+B~f,0~S~f~H~f,0~) (9)

which we can solve for the scaling parameter to give

S~f~=(G~f~B~f,0~/R~f,0~-1)/(B~f,0~H~f,0~) (10)

When used in the simulation, this value of S~f~ will insure that the
population carrying capacity parameters C~f,s~ are rescaled to the units
of B~f,0~, and that each population f remains at "balance" (constant
recruitment and abundance over time) provided the habitat areas A~f,s~
and survival rates s~f,t~ remain constant.

**4.4 Operating Instructions for Pool Model**

The Pool Model, currently configured to run using Pool 8 data, consists
of a graphical user interface with a main menu allowing access to a
variety of dialogue boxes; a graphics display area where simulation
results, in the form of maps and time series graphs can be displayed;
and a model control form or window at the bottom of the interface where
model operations are controlled.

***4.4.1 Running the Model***

All controls for model operation are located on the grey-colored model
control form at the bottom of the main window. Click on the "Start"
button to begin a 20 yr. simulation using discharge and stage data
beginning in 1959. If you want to run a shorter or longer simulation,
change the value in the "Years to simulate" text box To temporarily
suspend model execution during a run click on the "Pause" button. To
resume execution, click on the "Pause" button again. This feature works
like the "Pause" button on a tape recorder. To stop a simulation
completely, click on the "Stop" button. A Natural Systems Model
simulation can be run to simulate hydrology and sediment patterns as if
no dams were present by clicking on the 'Simulate Natural Depths' check
box. Other model controls (hydrologic iterations/plot update, hydrologic
cell ratio, sediment and hydrologic iterations/month) control how
quickly the model will reach equilibrium results for each monthly time
step. Increases in precision come at the cost of increased computational
demands and a longer time to complete a simulation.

Since a 20 year run can take a considerable time to compute, model
results can be recorded to a file (using the "Record" check box) and
played back in a subsequent sessions using the controls on the "Playback
Results" tab of the model control form. The "Current Files" tab of the
model control form displays the currently loaded files which define
model parameters, base map data, and control graphics. Double clicking
on any yellow filename text box brings up a dialogue box to let you load
alternative files.

The "Overlay" check box allows you to overlay time series results from a
new model run on results from a previous run. After completing a run,
click the overlay feature to activate it, change a policy option or
parameter value, and start a new run. Previous and current results will
be displayed together on the same time series graphs facilitating
comparisons between runs.

When a simulation is in progress, you can bring up a map legend for any
map, or a line legend for a time series graph, by double clicking on the
map/graph you are interested in. If you clicked on a map, a legend will
appear, and if you click again on the map, the current predicted value
for the cell you clicked on will be displayed in the legend. If you
clicked on a time series graph, a table of predictions will be presented
as well as a line legend for the graph.

***4.4.2 Controlling the Graphic Output***

The 'Graphics' main menu item contains a number of submenus. The "Show
Status Form" item toggles the model control form at the bottom of the
screen on and off. When the model control form is toggled off, the maps
and graphs resize and fill the entire screen, while graphic size is
reduced if the model control form is visible. A typical sequence for
using this option is to start a model run and then toggle the model
control form off (by clicking on the "Show Status Form" menu item). To
interrupt the run, toggle the model control form on by clicking on this
same menu item and bring up the model control form, where you can click
on the "Pause" or "Stop" buttons.

The "Setup Graphics" choice brings up the "Setup Graphics" dialogue box
which allows you to modify the display of maps and time series graphs
summarising model predictions. There are three basic displays which can
be used: 1) monthly maps for the detailed spatial grid (100 by 100 m);
2) time series graphs showing results for indicators averaged over the
entire grid, which do not vary over the grid, or at specific cell
locations on the grid; and 3) iteration map results, which show
predictions as they come to equilibrium within the month, and over the
coarser spatial grid that they are computed. A maximum of two such
display panels can be shown at any one time and this is controlled in
the "Display Panes (pick 1 or 2 of 3)" frame. Display panes can be
resized by clicking on and dragging the edges of the panes with the
mouse after you have exited the "Setup Graphics" dialogue box.

Up to six monthly maps can be displayed at one time based on the value
of the "Visible" check box beside the dropdown list showing potential
indicators to be displayed for each map. Drawing results to a map can
take considerable computational time for the detailed grid, so you can
plot results for only selected months (even though the model computes
results for each month) by selecting/deselecting months in the "Update
Maps in..." frame. The number of time series graphs, and the indicators
to be displayed in each graph are controlled by selecting/deselecting
the "Visible" check box in the "Time Series Graphs" frame and picking
the desired indicator in the dropdown list for each graph that is
visible. The "Format Graphs" tab allows users to format the output of
the time series graphs. Users can click on a graph component (e.g.,
Line 1) and then pick a color from the color palette or a line
thickness. The row and column numbers on this tab refer to the cell
positions where time series results (represented by lines 1-3 are
displayed.

The colors and category divisions for the input map data and simulated
maps can be adjusted and saved by selecting the "Graphics - Legend
Editor" choice, bringing up the "Legend Editor" dialogue box. Each map
layer can have a different legend and you can switch between layers by
using the dropdown list box in the upper-left section of the dialogue
box. The number of categories for each legend can be changed by
modifying the value in the text box in the lower-left section of the
dialogue box. Colors for each category can be changed by clicking on a
color in the color palette and then clicking the color boxes in the
legend on the right side of the dialogue box. Division breakpoints and
text to be displayed for each breakpoint can be edited. Legend details
can be saved and restored to ASCII files using the "Restore Map Legend
to File..." and "Save Legend to File..." menu items on the Graphics main
menu item. Continuous color scales can also be used for any map layer if
this option is selected and the upper and lower bounds of the color
scale are defined.

***4.4.3 Editing Base Maps***

Base maps used as input data for the pool model can be viewed and edited
using the Base Map Editor accessed through the "Base Maps - Edit Base
Maps" main menu choice. The map editing dialogue box contains a dropdown
list box of map layers, a different map layer can be displayed by
clicking on a different layer in the list box. To zoom in on part of the
map, click on the "Zoom In" check box and draw the area you want to zoom
in on by dragging the cursor over the map while holding down the left
mouse button. Clicking on any cell in the main map or "zoomed map"
displays the row and column number of the cell you selected as well as
the value for that cell for the currently displayed layer. To edit the
map, click on the "Edit" check box, click the mouse on the map and hold
the left mouse button down while you draw over the part of the map you
want to edit, enter the new value for the cells highlighted in white
that you selected, and hit the "Enter" key.

Map data are stored in ASCII files which can be restored or saved to
disk using the "Restore Base Maps..." and "Save Base Maps..." choices
under the "Base Maps" main menu item. Changes to the base maps using the
editor are saved to memory and effect all subsequent simulations until
another map file is loaded, but if you close the pool model the results
cannot be retrieved unless you first save them to a base map file.

***4.4.4 Editing Hydrology, Sediment Transport, and Vegetation Model
Parameters***

Parameters controlling hydrology, sediment transport, and vegetative
succession can be viewed and edited using the dialogue boxes accessible
under the "Hydrology" and "Vegetation" main menu items. Any changes made
to parameter values will effect subsequent model runs; and, if you want
to save edits permanently so they can be retrieved during a later
modeling session, you must save the results to file using the "Save
Vegetation (or Hydrology) Parameters to File..." option. These edits can
be retrieved by using the "Restore Vegetation (or Hydrology) Parameters
to File..." option.

Descriptions of parameters effecting hydrology and sediment transport
processes in the model are available in the Pool Model description in
Section 4.1. The vegetation parameter dialogue box consists of a list of
different vegetation types, each with an integer code. The mean water
depth - hydroperiod (months submerged) for any cell in the matrix
defines the equilibrium vegetation type that will occur under these
conditions. To change the vegetation type associated with any cell in
the matrix, click on the cell with the right mouse button, and change
the vegetation code (e.g., 3 - submerged aquatics) to a new type (e.g.,
4 - wetland grass). Parameters to the right of the matrix show the
number of years (Years to Stress) it will take the current vegetation
type to change to a different type given wetter (i.e., increased mean
depth, longer hydroperiod) or dryer (i.e., decreased mean depth, shorter
hydroperiod) conditions.