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Full Equations (FEQ) Model for the Solution of the Full, Dynamic Equations of Motion for One-Dimensional Unsteady Flow in Open Channels and Through Control Structures

U.S. GEOLOGICAL SURVEY WATER-RESOURCES INVESTIGATIONS REPORT 96-4240

13.3 Tributary Area Block--Tributary Area Tables


Purpose:The areas for each land use that are tributary to each computational element are supplied with this block. This block only appears if DIFFUS=YES in the Run Control Block (section 13.1). The unit number of the Diffuse Time-Series File (DTSF) (appendix 2) containing the runoff intensity for each land use as a function of time also is given in this block. All branches must appear in the input even if they have no tributary area. The branch mode of input is used to assign a tributary area of zero to these branches. Lines 7, 8, and 9 or 9a are repeated as needed until all branches have been described.

Heading:One line of user-selected information. The suggested string is TRIBUTARY AREA.
LINE 1

Variable: TSFDSN, TSFNAM

Format: 7X, I5, A64

Example: TSFDSN=00012\SALT\TSFLONG

Explanation:

TSFDSN is the Fortran unit number (see appendix 3) for the DTSF containing the unit-area runoff intensities on the tributary areas.

TSFNAM is the name of the DTSF containing the unit-area runoff intensities on the tributary areas. If TSFNAM is entered, then a file will be opened with a name given by the contents of TSFNAM (most microcomputers) as the DTSF. On IBM mainframes, the name given in TSFNAM will be the ddname for the DD statement defining the data set. If the TSFNAM is blank, an implicit open will be done on IBM mainframes if the proper DD statement defining the unit number given in TSFDSN is listed. In some microcomputer systems, the user will be prompted for the file name in this case, whereas program execution will be terminated on other microcomputer systems.

For convenience in conceptualizing the stream system, the tributary area contributing runoff to the branches is divided into subareas on the basis of the source of the rainfall data used to estimate the unit-area runoff intensities stored in the DTSF. These data may come from a single rain gage, from multiple rain gages, or from some other source such as weather radar. The Tributary Area Block is primarily designed to read time series of unit-area runoff computed in the Hydrologic Simulation Program Fortran, HSPF, (Johanson and others, 1984) as tributary inflow to a stream system simulated with FEQ; however, the source of the unit-area runoff data in the DTSF is not important for FEQ application. Any rainfall-runoff simulation model or approximation can be used to compute the time series of unit-area runoff in the DTSF. In FEQ simulation, the tributary-area runoff data must be stored and retrieved with respect to (1) a rain gage, (2) some subarea of the total area, and (3) land uses or land covers within that subarea. At least one rain-gage subarea must be specified in the input to FEQ, and at least two land uses must be stored in the DTSF even if only one is used in FEQ simulation. This requirement is a result of the detailed format used to store the runoff events in the DTSF, as explained in appendix 2. The relations among rain gages, land uses, and time series of unit-area runoff are described in the following discussion.

The user assigns rain-gage numbers to each rain-gage subarea for later reference. These numbers are required to start at 1 and be consecutive. Land-cover types are used in the hydrologic analysis and are associated with the rain-gage number. For example, three rain gages might be used for a given watershed, and five different land-cover types (impervious, flat-slope grassland, medium-slope grassland, steep-slope grassland, and forest) might be present in the watershed. Then, 15 combinations of rain gages and land-cover types are possible. For each time in the hydrologic computations, 15 numbers of unit-area runoff intensities from the watershed are stored in the DTSF in an order defined in the input to the utility program applied to develop the DTSF. Additional details are given in appendix 2. The order of the diffuse time series is under the control of the user, but a logical ordering should be used because the order of input for tributary areas is related to the order of appearance of the runoff values in the DTSF. Giving the runoff values in land-cover-type order for each rain gage is suggested.

The user must specify the number of land-cover types to be associated with each rain gage. This number is often the same for each rain gage, but it could vary. Also, the land-cover types do not have to be the same for each rain gage, but the user must make sure that the order of storing the runoff values in the DTSF is the same as the order in which the tributary areas are given for the land-cover types in the input.

Each computational element is assigned the runoff from only one rain gage. The tributary area for a computational element should be kept small to prevent computational problems. Computational elements can be added if several rain gages are required for one or more reaches in the stream.

The tributary areas for a branch can be input in three modes. In the simplest and least flexible input mode, branch, the user must give the total area for each land-cover type for the entire branch. This area is distributed to each element in proportion to the ratio of the length of the element to the length of the branch. The tributary area is assumed to be uniformly distributed over the length of the branch in this mode of input.

In the second input mode, station interval, the user must specify a series of upstream and downstream stations along the branch and, for each station interval, the total area for each cover type. The area is distributed over that station interval in proportion to element length. In this mode, a nonuniform distribution of tributary area over the length of the branch can be specified. The upstream and downstream stations given must match computational-element boundaries.

In the final mode of input, the node mode, the user must give the tributary area for each element explicitly. This gives complete freedom of area assignment, but the user must input the tributary area for each element on the branch. Furthermore, if elements are added in the branch description table to solve computational problems, then the user must update the tributary area input accordingly.

On completion of tributary-area input, the areas are output as assigned to each branch and element so that the user can verify that the proper result has been obtained. Furthermore, a complete summary of tributary area is given for each branch and for the entire stream system. The total area for each land-cover type, rain gage, branch, and system is given to help in verifying the input.
LINE 2

Variable: FFFDSN, FFFNAM

Format: 7X, I5, A32

Example: FFFDSN=00011\SALT\UPMS\FFF

Explanation:

FFFDSN is the Fortran unit number (see appendix 3) for the file used to store the flows and stages required for a flood-frequency analysis.

FFFNAM is the name of the file used to store the flows and stages required for a flood-frequency analysis. If FFFNAM is not blank, then a file will be opened with a name given in FFFNAM (most microcomputers) to store the values needed for flood-frequency analysis. On IBM mainframes, the name given in FFFNAM will be the ddname for the DD statement defining the data set. If the FFFNAM is blank, an implicit open will be done on a IBM mainframe if the proper DD statement defining the unit number given by FFFDSN is present. In some microcomputer systems, the user will be prompted for the file name in this case, whereas execution will be aborted in other microcomputer systems.

LINE 3

Variable: NLUSE

Format: 6X, I5

Example: NLUSE=00006

Explanation: NLUSE is the number of land-cover type and rain-gage combinations represented by the tributary areas. For example, if three land covers are in each of two rain-gage segments in the hydrologic simulation then NLUSE=00006. The maximum number of diffuse, tributary areas allowed in FEQ is specified in the parameters MNDIFA and MXGLU in the INCLUDE file ARSIZE.PRM (appendix 3). The number may be increased and FEQ recompiled.
LINE 4

Variable: NGAGE

Format: 6X, I5

Example: NGAGE=00003

Explanation: NGAGE is the number of rain gages used to define the runoff intensities on the tributary area for the watershed. The maximum number of rain gages allowed in FEQ is specified in the parameter MXGAGE in the INCLUDE file ARSIZE.PRM (appendix 3). The number may be increased and FEQ recompiled.
LINE 5

Variable: HEAD

Format: A80

Example: GAGE NCOV

Explanation: This is the heading for the land-cover table for a given rain gage.
LINE 6 (one for each rain gage)

Variable: GAGE, NCOV

Format: 2I5

Example: 1 3

Explanation:

GAGE is the rain gage number (in ascending order).

NCOV is the number of land-cover types for the given rain gage. The sum of the number of land-cover types must be the same as the value of NLUSE given on Line 3.

LINE 7 (one for each branch in combination with Lines 8 and 9)

Variable: BRA, FAC2

Format: 7X, I5, 5X, F10.0

Example: BRANCH=00001 FAC= 1.05

Explanation:

BRA is the branch number for the tributary-area table. The branch numbers in the tributary-area input must be in ascending order with no omissions. If the branch number is zero, then the table describes the areas tributary to reservoirs. If the branch number is negative, then the station-interval mode is applied to specify tributary areas. Otherwise, the branch mode of input is used. A branch number of zero may be repeated as many times as needed to apply a different factor to the tributary area for reservoirs. A warning will be issued to the user that more than one branch number of zero is in the input. If the adjustment factor for each tributary area of each reservoir is the same, then only one branch number of zero is needed. All assignments of a branch number of zero must precede nonzero branch numbers.

FAC2 is a multiplier on each of the tributary areas given in the branch. The value of FAC2 is user specified. FAC2 is typically used to check the sensitivity of FEQ output to tributary-area flows without having to repeatedly run the hydrologic model. If omitted, the default is FAC2=1.0.

LINE 8 (one for each branch in combination with Lines 7 and 9)

Variable: HEAD

Modes: Node and branch

Format: A80

Example: NODE GAGE AREA1 AREA2 AREA3 AREA4 AREA5

Mode: Station interval

Format: A80

Example: USTAT DSTAT GAGE AREA1 AREA2 AREA3

Explanation: These are user-supplied headings descriptive of the tributary areas.

LINE 9 (one for each branch in branch mode and one for each node on the branch except the upstream node in node mode in combination with Lines 7 and 8)

Modes: Node and branch

Variables: NODE, GAGE, TRIBA(*)

Format: I5, I5, 10F6.0

Explanation:

NODE delineates the downstream node for the computational element to which the specified tributary area and gage apply. The nodes on a branch in the tributary-area input must be in ascending order.

GAGE denotes the rain gage used to estimate lateral inflow from a tributary area entering a computational element in FEQ simulation. The lateral inflow is identified among the various DTSF's of runoff by the rain gage most representative of rainfall on the tributary area, denoted by GAGE, and the area consisting of a given land-cover type, denoted by TRIBA.

TRIBA specifies the area tributary to a computational element on the branch consisting of a given land-cover type. The values in the TRIBA array must be given in the order of the DTSF's. In node mode, all nodes except the upstream node must be explicitly input even if the tributary area for that branch is zero. If the branch number on Line 7 is zero, then the node input is the flow-path end node label of the simulated reservoir. In this latter case, the node list must be terminated by a - 1 because only the reservoirs with tributary area must be entered in the table. As a result, the number of reservoirs included in model simulation is not known in advance. If the value for NODE is zero, then the branch mode of input for tributary area is applied, and the tributary areas given will be the total for the branch in each land-cover type.

The current limit on land-cover types that may contribute to a computational element is 10. Line 9 is repeated as needed to complete the input for the branch. The same mode of input must be used to complete the input for any branch.

LINE 9a (more than one for each branch in station-interval mode in combination with Lines 7 and 8)
Modes: Station interval Variables: USTAT, DSTAT, GAGE, TRIBA(*) Format: F10.0, F10.0, I5, 10F6.0 Explanation:

USTAT is the upstream station for the stational interval. DSTAT is the downstream station for the station interval.

GAGE denotes the rainfall gage used to estimate the lateral inflow from a tributary area entering a computational element in FEQ simulation. The lateral inflow is identified among the various DTSF's of runoff by the rain gage most representative of rainfall on the tributary area, denoted by GAGE, and the area consisting of a given land-cover type, denoted by TRIBA.

TRIBA denotes the area tributary to all computational elements between the specified upstream and downstream stations in the station-interval mode consisting of a given land-cover type. The values in the TRIBA array must be given in the order of the DTSF's. The branch number given on Line 7 must be negative to select the station-interval mode.

The upstream and downstream stations both must be available in the branch-description table for the branch. Any station interval not used will have zero tributary area. Line 9a is repeated as required to describe the tributary area for the branch. The last line must be a null tributary area with the identical upstream and downstream stations. This designation indicates that input for the branch is complete.


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