Text—is a character variable (199 characters) that starts in column 2. Any characters can be included in Text. The “#” character must be in column 1. Except for the name file, lines beginning with # are restricted to these first lines of the file. Text is printed when the file is read.

LN is a one-dimensional array specifying the model layer assignments for each system of no-delay interbeds. The array has NNDB values.

LDN is a one-dimensional array specifying the model layer assignments for each system of delay interbeds. The array has NDB values.

RNB is an array specifying the factor nequiv (equation 20) at each cell for each system of delay interbeds. The array also is used to define the areal extent of each system of interbeds. For cells beyond the areal extent of the system of interbeds, enter a number less than 1.0 in the corresponding element of this array.

Equation 20 from Subsidence package report

See DZ for the definition of bequiv.

HC is an array specifying the preconsolidation head or preconsolidation stress in terms of head in the aquifer for systems of no-delay interbeds. For any model cells in which specified HC is greater than the corresponding value of starting head, the value of HC will be set to that of starting head.

Sfe is an array specifying the dimensionless elastic skeletal storage coefficient for systems of no-delay interbeds. Values may be estimated using equation 17.

Equation 17 from Subsidence package report

Sfv is an array specifying the dimensionless inelastic skeletal storage coefficient for systems of no-delay interbeds. Values may be estimated using equation 17.

Equation 17 from Subsidence package report

[ComE(NCOL,NROW)] U2DREL if NNDB > 0

ComE

COMV is an array specifying the starting inelastic compaction in each system of no-delay interbeds. Inelastic compaction values computed by the package are added to values in this array so that printed or stored values of inelastic compaction and land subsidence may include previous components. Values in this array do not affect calculations of storage changes or resulting inelastic compaction. For simulations in which output values are to reflect inelastic compaction and subsidence since the start of the simulation, enter zero values for all elements of this array.

DP is an array containing a table of material properties for systems of delay interbeds. For each of the NMZ zones of material properties, vertical hydraulic conductivity, elastic specific storage, and inelastic specific storage are read.

Dstart is an array specifying starting head in interbeds for systems of delay interbeds. For a particular location in a system of interbeds, the starting head is applied to every node in the string of nodes that approximates flow in half of a doubly draining interbed.

DHC is an array specifying the starting preconsolidation head in interbeds for systems of delay interbeds. For a particular location in a system of interbeds, the starting preconsolidation head is applied to every node in the string of nodes that approximates flow in half of a doubly draining interbed. For any location at which specified starting preconsolidation head is greater than the corresponding value of the starting head, Dstart, the value of the starting preconsolidation head will be set to that of the starting head.

[DCOME(NCOL,NROW)] U2DREL if NDB > 0

DCOME

DCOMV is an array specifying the starting inelastic compaction in each system of delay interbeds. Inelastic compaction values computed by the package are added to values in this array so that printed or stored values of inelastic compaction and land subsidence may include previous components. Values in this array do not affect calculations of storage changes or resulting inelastic compaction. For simulations in which output values are to reflect inelastic compaction and subsidence since the start of the simulation, enter zero values for all elements of this array.

DZ is an array specifying the equivalent thickness for a system of delay interbeds (bequiv in equation 19).

Equation 19 from Subsidence package report

NZ is an array specifying the material zone numbers for systems of delay interbeds. The zone number for each location in the model grid selects the hydraulic conductivity, elastic specific storage, and inelastic specific storage of the interbeds.

Flow quantities into and out of interbeds computed in the SUB Package are added to the overall volumetric budget printed by MODFLOW-2000. This printed budget includes flow rates and total volumes of water for all flow-component and stress packages used in a simulation. Two separate components are added for the SUB Package. The first added component is “INST. IB STORAGE” and describes the changes in storage in all systems of no-delay interbeds. This component is equivalent to the storage term calculated in the IBS1 Package. The second additional component is “DELAY IB STORAGE” and encompasses the changes in storage in all systems of delay interbeds. The sign convention for storage changes in both types of systems of interbeds is the same as that used in other MODFLOW packages, with positive numbers for flow into the aquifer system and negative numbers for flow out of the aquifer system. Dissipation of water from the interbeds is considered inflow to the system; uptake of water by the interbeds from the surrounding aquifers is considered outflow.

During the execution of MODFLOW-2000, the SUB Package generates information related to interbeds, including information on subsidence, compaction, vertical displacement, critical head, and volumetric budgets. The package allows complete control of printing and saving this information. The SUB Package Output Control should not be confused with the MODFLOW-2000 Output Control. These are two separate sets of instructions controlling different types of model output.

Six types of arrays can be printed or saved and one volumetric budget can be printed for specified sets of time steps. Variable names for formats, unit numbers, and flags, and array identifiers for these seven output items are given in table 1. Specific definitions for these output items are as follows:

1. Subsidence: Subsidence is the sum of the compaction from all interbed systems, including no-delay and delay systems. In the printout or header record of the saved array, the layer number for subsidence is set to 1.

2. Compaction by model layer: The SUB Package computes compaction for each system of interbeds. The model layer numbers to which each system belongs are specified in arrays LN and LDN for no-delay and delay systems, respectively. Each model layer can include more than one system of interbeds of either type or combinations of both types. The output option of compaction by model layer is the sum of compaction of all systems within each model layer. Arrays for model layers that do not contain any compressible interbeds are not printed or saved. The model layer number is included in the printout or header records of the saved arrays.

3. Compaction by interbed system: This output option saves compaction for each interbed system, including nodelay and delay systems. For printed arrays, the standard MODFLOW header indicates the model layer number that includes the system and a line of text preceding that record that indicates the type of system (no-delay or delay) and the sequence number of the system within each type. For saved arrays, the header record includes the sequence number of the system in the field normally used for the layer number. The sequence number is derived from the order in which systems of no-delay and delay interbeds are specified in the input data set.

4. Vertical displacement by model layer: Vertical displacement for a model layer is defined as the sum of the compaction in the layer and in all underlying layers. This displacement corresponds to movement of the upper surface of the model layer. The vertical displacement for layer 1 is equal to the subsidence. Any layers below the lowest system of compressible interbeds will have zero vertical displacement. The model layer number is included in the printout or header records of the saved arrays.

5. Critical head for systems of no-delay interbeds: Critical head is defined as the head at which pore pressure will result in effective stress being equal to preconsolidation stress. The SUB Package maintains an array of critical head for each system of no-delay interbeds. Because critical head arrays are identical for multiple systems in a single model layer, only one array is printed or saved for each model layer that contains one or more these systems. For printed arrays, the standard MODFLOW header indicates the model layer number, and a line of text preceding that record indicates all of the system numbers to which the critical head array applies. For saved arrays, the header record includes model layer number.

6. Critical head for systems of delay interbeds: This item is the critical head at the center of the representative interbed that is used to simulate delayed compaction. For printed arrays, the standard MODFLOW header indicates the model layer number that includes the system, and a line of text preceding that record indicates the sequence number of the system within each the group of systems that consider delay. For saved arrays, the header record includes the sequence number of the system in the field normally used for layer number.

7. Volumetric budget for systems of delay interbeds: A volumetric budget for all active model cells is a fundamental part of the MODFLOW listing. The SUB Package, however, solves equations for systems of delay interbeds separately from the ground-water flow equations to which the MODFLOW volumetric budget applies. The package computes a separate volumetric budget for systems of delay interbeds (fig. 4). The volumetric interbed budget can be used to determine how well equations describing flow in interbeds are being solved. If possible, the discrepancy in the budget should be less than a few percent. The budget can be printed in the main MODFLOW listing file for selected time steps, but cannot be saved to a file.

Table 1.

The sign convention for subsidence and vertical displacement is positive for lowering and negative for uplift. The sign convention for compaction is positive for compression or shortening and negative for expansion. Numbers for critical head are referenced to the same datum used for head in the model. The sign convention for the volumetric budgets of delay interbeds is positive for release of water from storage and for boundary flow from aquifers into the interbeds, and negative for the opposite conditions.

By default, the first six output items will not be printed or saved to files, but item 7 will be printed in the main MODFLOW listing file for the final time step of all transient stress periods. If output different from the default is desired for any model time steps, records specifying alternative output must be included as repetitions of input data item 16 (see “Input Instructions”). The defaults plus ISUBOC (see “Explanation of Fields”) repetitions of item 16 define the SUB Package scheme using a series of flags stored in memory for every time step in every stress period in the simulation. Each repetition of item 16 sets flags that control output for a set of time steps, where the set is specified as a range of time steps in each stress period for a range of stress periods. The set of time steps is defined in each repetition of item 16 by four integers that specify (1) the starting stress period in the range of stress periods, (2) the ending stress period in the range of stress periods, (3) the starting time step in the range of time steps in each stress period to be included in the set, and (4) the ending time step in the range of time steps in each stress period to be included in the set. Following the integers that define the set of time steps, each record includes 12 integer flags that specify whether or not to print or save each of the first six output items and a thirteenth flag that specifies whether or not to print output item 7. If any time step is included in more than one repetition of item 16, the flags in later repetitions override those in earlier repetitions for that time step. If the number read for a flag to print or save a data item is negative, the default or previously set value of the flag for printing or saving the data item will remain unchanged. If the number read for a flag is zero, the flag for printing or saving will be set to not print or save. If the number read for a flag to print or save a data item is positive, the flag for printing or saving will be set to print or save.