imod.wq  Create Water Quality model¶
Create Water Quality model.
Create an imod.wq.SeawatModel
and add desired packages to the model
(e.g. imod.wq.Well
, imod.wq.Dispersion
). See Examples
and Model for workflow documentation.

class
imod.wq.
AdvectionFiniteDifference
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.Package
Solve the advection term using the explicit Finite Difference method (MIXELM = 0) with upstream weighting

courant
¶ Courant number (PERCEL) is the number of cells (or a fraction of a cell) advection will be allowed in any direction in one transport step. For implicit finitedifference or particle tracking based schemes, there is no limit on PERCEL, but for accuracy reasons, it is generally not set much greater than one. Note, however, that the PERCEL limit is checked over the entire model grid. Thus, even if PERCEL > 1, advection may not be more than one cell’s length at most model locations. For the explicit finitedifference, PERCEL is also a stability constraint, which must not exceed one and will be automatically reset to one if a value greater than one is specified.
 Type
real

weighting
¶ Indication of which weighting scheme should be used, set to default value “upstream” (NADVFD = 0 or 1) Default value: “upstream”
 Type
{“upstream”, “central”}, optional

courant
¶

weighting
¶


class
imod.wq.
AdvectionHybridMOC
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.Package
Hybrid Method of Characteristics and Modified Method of Characteristics with MOC or MMOC automatically and dynamically selected (MIXELM = 3)

courant
¶ Courant number (PERCEL) is the number of cells (or a fraction of a cell) advection will be allowed in any direction in one transport step. For implicit finitedifference or particle tracking based schemes, there is no limit on PERCEL, but for accuracy reasons, it is generally not set much greater than one. Note, however, that the PERCEL limit is checked over the entire model grid. Thus, even if PERCEL > 1, advection may not be more than one cell’s length at most model locations. For the explicit finitedifference, PERCEL is also a stability constraint, which must not exceed one and will be automatically reset to one if a value greater than one is specified.
 Type
float

max_particles
¶ is the maximum total number of moving particles allowed (MXPART).
 Type
int

tracking
¶ indicates which particle tracking algorithm is selected for the EulerianLagrangian methods. ITRACK = 1, the firstorder Euler algorithm is used; ITRACK = 2, the fourthorder RungeKutta algorithm is used; this option is computationally demanding and may be needed only when PERCEL is set greater than one. ITRACK = 3, the hybrid 1st and 4th order algorithm is used; the Runge Kutta algorithm is used in sink/source cells and the cells next to sinks/sources while the Euler algorithm is used elsewhere.
 Type
int

weighting_factor
¶ is a concentration weighting factor (WD) between 0.5 and 1. It is used for operator splitting in the particle tracking based methods. The value of 0.5 is generally adequate. The value may be adjusted to achieve better mass balance. Generally, it can be increased toward 1.0 as advection becomes more dominant.
 Type
real

dceps
¶ is a small Relative Cell Concentration Gradient below which advective transport is considered negligible. A value around 105 is generally adequate.
 Type
real

nplane
¶ is a flag indicating whether the random or fixed pattern is selected for initial placement of moving particles. NPLANE = 0, the random pattern is selected for initial placement. Particles are distributed randomly in both the horizontal and vertical directions by calling a random number generator. This option is usually preferred and leads to smaller mass balance discrepancy in nonuniform or diverging/converging flow fields. NPLANE > 0, the fixed pattern is selected for initial placement. The value of NPLANE serves as the number of vertical “planes” on which initial particles are placed within each cell block. The fixed pattern may work better than the random pattern only in relatively uniform flow fields. For twodimensional simulations in plan view, set NPLANE = 1. For cross sectional or threedimensional simulations, NPLANE = 2 is normally adequate. Increase NPLANE if more resolution in the vertical direction is desired.
 Type
int

npl
¶ is number of initial particles per cell to be placed at cells where the Relative Cell Concentration Gradient is less than or equal to DCEPS. Generally, NPL can be set to zero since advection is considered insignificant when the Relative Cell Concentration Gradient is less than or equal to DCEPS. Setting NPL equal to NPH causes a uniform number of particles to be placed in every cell over the entire grid (i.e., the uniform approach).
 Type
int

nph
¶ is number of initial particles per cell to be placed at cells where the Relative Cell Concentration Gradient is greater than DCEPS. The selection of NPH depends on the nature of the flow field and also the computer memory limitation. Generally, use a smaller number in relatively uniform flow fields and a larger number in relatively nonuniform flow fields. However, values exceeding 16 in twodimensional simulation or 32 in threedimensional simulation are rarely necessary. If the random pattern is chosen, NPH particles are randomly distributed within the cell block. If the fixed pattern is chosen, NPH is divided by NPLANE to yield the number of particles to be placed per vertical plane.
 Type
int

npmin
¶ is the minimum number of particles allowed per cell. If the number of particles in a cell at the end of a transport step is fewer than NPMIN, new particles are inserted into that cell to maintain a sufficient number of particles. NPMIN can be set to zero in relatively uniform flow fields, and a number greater than zero in diverging/converging flow fields. Generally, a value between zero and four is adequate.
 Type
int

npmax
¶ is the maximum number of particles allowed per cell. If the number of particles in a cell exceeds NPMAX, all particles are removed from that cell and replaced by a new set of particles equal to NPH to maintain mass balance. Generally, NPMAX can be set to approximately twice of NPH.
 Type
int

dchmoc
¶ is the critical Relative Concentration Gradient for controlling the selective use of either MOC or MMOC in the HMOC solution scheme. The MOC solution is selected at cells where the Relative Concentration Gradient is greater than DCHMOC; The MMOC solution is selected at cells where the Relative Concentration Gradient is less than or equal to DCHMOC
 Type
real

cell_max_nparticles
¶

cell_min_nparticles
¶

courant
¶

dconcentration_epsilon
¶

dconcentration_hybrid
¶

nparticles_advection
¶

nparticles_no_advection
¶

nplane
¶

sink_nparticles
¶

sink_particle_placement
¶

tracking
¶

weighting_factor
¶


class
imod.wq.
AdvectionMOC
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.Package
Solve the advection term using the Method of Characteristics (MIXELM = 1)
Nota bene: number of particles settings have not been tested. The defaults here are chosen conservatively, with many particles. This increases both memory usage and computational effort.

courant
¶ Courant number (PERCEL) is the number of cells (or a fraction of a cell) advection will be allowed in any direction in one transport step. For implicit finitedifference or particle tracking based schemes, there is no limit on PERCEL, but for accuracy reasons, it is generally not set much greater than one. Note, however, that the PERCEL limit is checked over the entire model grid. Thus, even if PERCEL > 1, advection may not be more than one cell’s length at most model locations. For the explicit finitedifference, PERCEL is also a stability constraint, which must not exceed one and will be automatically reset to one if a value greater than one is specified.
 Type
real

max_nparticles
¶ is the maximum total number of moving particles allowed (MXPART).
 Type
int

tracking
¶ indicates which particle tracking algorithm is selected for the EulerianLagrangian methods. ITRACK = 1, the firstorder Euler algorithm is used; ITRACK = 2, the fourthorder RungeKutta algorithm is used; this option is computationally demanding and may be needed only when PERCEL is set greater than one. ITRACK = 3, the hybrid 1st and 4th order algorithm is used; the Runge Kutta algorithm is used in sink/source cells and the cells next to sinks/sources while the Euler algorithm is used elsewhere. Default value is “hybrid”.
 Type
{“euler”, “rungekutta”, “hybrid”}, optional

weighting_factor
¶ is a concentration weighting factor (WD) between 0.5 and 1. It is used for operator splitting in the particle tracking based methods. The value of 0.5 is generally adequate. The value may be adjusted to achieve better mass balance. Generally, it can be increased toward 1.0 as advection becomes more dominant. Default value: 0.5.
 Type
float, optional

dconcentration_epsilon
¶ is a small Relative Cell Concentration Gradient below which advective transport is considered negligible. A value around 105 is generally adequate. Default value: 1.0e5.
 Type
float, optional

nplane
¶ is a flag indicating whether the random or fixed pattern is selected for initial placement of moving particles. NPLANE = 0, the random pattern is selected for initial placement. Particles are distributed randomly in both the horizontal and vertical directions by calling a random number generator. This option is usually preferred and leads to smaller mass balance discrepancy in nonuniform or diverging/converging flow fields. NPLANE > 0, the fixed pattern is selected for initial placement. The value of NPLANE serves as the number of vertical “planes” on which initial particles are placed within each cell block. The fixed pattern may work better than the random pattern only in relatively uniform flow fields. For twodimensional simulations in plan view, set NPLANE = 1. For cross sectional or threedimensional simulations, NPLANE = 2 is normally adequate. Increase NPLANE if more resolution in the vertical direction is desired. Default value: 2.
 Type
int, optional

nparticles_no_advection
¶ is number of initial particles per cell to be placed at cells where the Relative Cell Concentration Gradient is less than or equal to DCEPS. Generally, NPL can be set to zero since advection is considered insignificant when the Relative Cell Concentration Gradient is less than or equal to DCEPS. Setting NPL equal to NPH causes a uniform number of particles to be placed in every cell over the entire grid (i.e., the uniform approach). Default value: 10.
 Type
int, optional

nparticles_advection
¶ is number of initial particles per cell to be placed at cells where the Relative Cell Concentration Gradient is greater than DCEPS. The selection of NPH depends on the nature of the flow field and also the computer memory limitation. Generally, use a smaller number in relatively uniform flow fields and a larger number in relatively nonuniform flow fields. However, values exceeding 16 in twodimensional simulation or 32 in threedimensional simulation are rarely necessary. If the random pattern is chosen, NPH particles are randomly distributed within the cell block. If the fixed pattern is chosen, NPH is divided by NPLANE to yield the number of particles to be placed per vertical plane. Default value: 40.
 Type
int, optional

cell_min_nparticles
¶ is the minimum number of particles allowed per cell. If the number of particles in a cell at the end of a transport step is fewer than NPMIN, new particles are inserted into that cell to maintain a sufficient number of particles. NPMIN can be set to zero in relatively uniform flow fields, and a number greater than zero in diverging/converging flow fields. Generally, a value between zero and four is adequate. Default value is 5.
 Type
int, optional

cell_max_nparticles
¶ is the maximum number of particles allowed per cell. If the number of particles in a cell exceeds NPMAX, all particles are removed from that cell and replaced by a new set of particles equal to NPH to maintain mass balance. Generally, NPMAX can be set to approximately twice of NPH. Default value: 80.
 Type
int, optional

cell_max_nparticles
¶

cell_min_nparticles
¶

courant
¶

dconcentration_epsilon
¶

nparticles_advection
¶

nparticles_no_advection
¶

nplane
¶

tracking
¶

weighting_factor
¶


class
imod.wq.
AdvectionModifiedMOC
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.Package
Solve the advention term using the Modified Method of Characteristics (MIXELM = 2) Courant number (PERCEL) is the number of cells (or a fraction of a cell) advection will be allowed in any direction in one transport step.

courant
¶ Courant number (PERCEL) is the number of cells (or a fraction of a cell) advection will be allowed in any direction in one transport step. For implicit finitedifference or particle tracking based schemes, there is no limit on PERCEL, but for accuracy reasons, it is generally not set much greater than one. Note, however, that the PERCEL limit is checked over the entire model grid. Thus, even if PERCEL > 1, advection may not be more than one cell’s length at most model locations. For the explicit finitedifference, PERCEL is also a stability constraint, which must not exceed one and will be automatically reset to one if a value greater than one is specified.
 Type
real

tracking
¶ indicates which particle tracking algorithm is selected for the EulerianLagrangian methods. ITRACK = 1, the firstorder Euler algorithm is used; ITRACK = 2, the fourthorder RungeKutta algorithm is used; this option is computationally demanding and may be needed only when PERCEL is set greater than one. ITRACK = 3, the hybrid 1st and 4th order algorithm is used; the Runge Kutta algorithm is used in sink/source cells and the cells next to sinks/sources while the Euler algorithm is used elsewhere.
 Type
str, {“euler”, “rungekutta”, “hybrid”}

weighting_factor
¶ is a concentration weighting factor (WD) between 0.5 and 1. It is used for operator splitting in the particle tracking based methods. The value of 0.5 is generally adequate. The value may be adjusted to achieve better mass balance. Generally, it can be increased toward 1.0 as advection becomes more dominant.
 Type
real

dconcentration_epsilon
¶ is a small Relative Cell Concentration Gradient (DCEPS) below which advective transport is considered negligible. A value around 1.0e5 is generally adequate. Default value: 1.0e5.
 Type
float, optional

sink_particle_placement
¶ indicates whether the random or fixed pattern is selected for initial placement of particles to approximate sink cells in the MMOC scheme. (NLSINK)
 Type
int

sink_nparticles
¶ is the number of particles used to approximate sink cells in the MMOC scheme. (NPSINK)
 Type
int

courant
¶

dconcentration_epsilon
¶

sink_nparticles
¶

sink_particle_placement
¶

tracking
¶

weighting_factor
¶


class
imod.wq.
AdvectionTVD
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.Package
Total Variation Diminishing (TVD) formulation (ULTIMATE, MIXELM = 1).

courant
¶ Courant number (PERCEL) is the number of cells (or a fraction of a cell) advection will be allowed in any direction in one transport step. For implicit finitedifference or particle tracking based schemes, there is no limit on PERCEL, but for accuracy reasons, it is generally not set much greater than one. Note, however, that the PERCEL limit is checked over the entire model grid. Thus, even if PERCEL > 1, advection may not be more than one cell’s length at most model locations. For the explicit finitedifference, PERCEL is also a stability constraint, which must not exceed one and will be automatically reset to one if a value greater than one is specified.
 Type
float

courant
¶


class
imod.wq.
BasicFlow
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.Package
The Basic package is used to specify certain data used in all models. These include: 1. the locations of acitve, inactive, and specified head in cells, 2. the head stored in inactive cells, 3. the initial head in all cells, and 4. the top and bottom of the aquifer The number of layers (NLAY) is automatically calculated using the IBOUND. Thickness is calculated using the specified tops en bottoms. The Basic package input file is required in all models.
 Parameters
ibound (array of int (xr.DataArray)) – is the boundary variable. One value is read for every model cell. Values are read a layer at the time. If IBOUND(J,I,K) < 0, cell J,I,K has a constant head. If IBOUND(J,I,K) = 0, cell J,I,K is inactive. If IBOUND(J,I,K) > 0, cell J,I,K is active.
top (float or array of floats (xr.DataArray)) – is the top elevation of layer 1. For the common situation in which the top layer represents a watertable aquifer, it may be reasonable to set Top equal to landsurface elevation.
bottom (float or array of floats (xr.DataArray)) – is the bottom elevation of a model layer or a Quasi3d confining bed.
starting_head (float or array of floats (xr.DataArray)) – is initial (starting) head—that is, head at the beginning of the simulation (STRT). starting_head must be specified for all simulations, including steadystate simulations. One value is read for every model cell. Usually, these values are read a layer at a time.
inactive_head (float, optional) – is the value of head to be assigned to all inactive (no flow) cells (IBOUND = 0) throughout the simulation (HNOFLO). Because head at inactive cells is unused in model calculations, this does not affect model results but serves to identify inactive cells when head is printed. This value is also used as drawdown at inactive cells if the drawdown option is used. Even if the user does not anticipate having inactive cells, a value for inactive_head must be entered. Default value is 1.0e30.

bottom
¶

ibound
¶

inactive_head
¶

starting_head
¶

thickness
()[source]¶ Computes layer thickness from top and bottom data.
 Returns
thickness
 Return type
xr.DataArray

top
¶

class
imod.wq.
BasicTransport
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.Package
Handles basic tasks that are required by the entire transport model. Among these tasks are definition of the problem, specification of the boundary and initial conditions, determination of the stepsize, preparation of mass balance information, and printout of the simulation results.
 Parameters
icbund (xr.DataArray) – is an integer array specifying the boundary condition type (inactive, constantconcentration, or active) for every model cell. For multispecies simulation, ICBUND defines the boundary condition type shared by all species. Note that different species are allowed to have different constantconcentration conditions through an option in the Source and Sink Mixing Package. ICBUND=0, the cell is an inactive concentration cell for all species. Note that noflow or “dry” cells are automatically converted into inactive concentration cells. Furthermore, active cells in terms of flow can be treated as inactive concentration cells to minimize the area needed for transport simulation, as long as the solute transport is insignificant near those cells. ICBUND<0, the cell is a constantconcentration cell for all species. The starting concentration of each species remains the same at the cell throughout the simulation. (To define different constantconcentration conditions for different species at the same cell location, refer to the Sink/Source Mixing Package.) Also note that unless explicitly defined as a constantconcentration cell, a constanthead cell in the flow model is not treated as a constantconcentration cell. If ICBUND>0, the cell is an active (variable) concentration cell where the concentration value will be calculated.
starting_concentration (float or array of floats (xr.DataArray)) – is the starting concentration (initial condition) at the beginning of the simulation (unit: ML3) (SCONC). For multispecies simulation, the starting concentration must be specified for all species, one species at a time.
porosity (float, optional) – is the “effective” porosity of the porous medium in a single porosity system (PRSITY). Default value is 0.35.
n_species (int, optional) – is the total number of chemical species included in the current simulation (NCOMP). For singlespecies simulation, set n_species = 1. Default value is 1.
inactive_concentration (float, optional) – is the value for indicating an inactive concentration cell (ICBUND=0) (CINACT). Even if it is not anticipated to have inactive cells in the model, a value for inactive_concentration still must be submitted. Default value is 1.0e30
minimum_active_thickness (float, optional) – is the minimum saturated thickness in a cell (THKMIN), expressed as the decimal fraction of the model layer thickness, below which the cell is considered inactive. Default value is 0.01 (i.e., 1% of the model layer thickness).

icbund
¶

inactive_concentration
¶

minimum_active_thickness
¶

n_species
¶

porosity
¶

starting_concentration
¶

thickness
¶

class
imod.wq.
ConstantHead
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.BoundaryCondition
The Constant Head package. The TimeVariant SpecifiedHead package is used to simulate specified head boundaries that can change within or between stress periods.
 Parameters
head_start (array of floats (xr.DataArray)) – is the head at the boundary at the start of the stress period.
head_end (array of floats (xr.DataArray)) – is the head at the boundary at the end of the stress period.
concentration (array of floats (xr.DataArray)) – concentrations for the constant heads. It gets automatically written to the SSM package.
save_budget ({True, False}, optional) – is a flag indicating if the budget should be saved (ICHDCB). Default is False.

concentration
¶

head_end
¶

head_start
¶

save_budget
¶

class
imod.wq.
Dispersion
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.Package
Solves the concentration change due to dispersion explicitly or formulates the coefficient matrix of the dispersion term for the matrix solver.
 Parameters
longitudinal (float) – is the longitudinal dispersivity (AL), for every cell of the model grid (unit: L). Default value is 1.0 m. Nota bene: this is for regional applications.
ratio_horizontal (float) – is a 1D real array defining the ratio of the horizontal transverse dispersivity (TRPT), to the longitudinal dispersivity. Each value in the array corresponds to one model layer. Some recent field studies suggest that ratio_horizontal is generally not greater than 0.1.
ratio_vertical (float) – (TRPV) is the ratio of the vertical transverse dispersivity to the longitudinal dispersivity. Each value in the array corresponds to one model layer. Some recent field studies suggest that ratio_vertical is generally not greater than 0.01. Set ratio_vertical equal to ratio_horizontal to use the standard isotropic dispersion model. Otherwise, the modified isotropic dispersion model is used.
diffusion_coefficient (float) –
is the effective molecular diffusion coefficient (unit: L2T1). Set diffusion_coefficient = 0 if the effect of molecular diffusion is considered unimportant. Each value in the array corresponds to one model layer.
iMODwq always uses meters and days.

diffusion_coefficient
¶

longitudinal
¶

ratio_horizontal
¶

ratio_vertical
¶

class
imod.wq.
Drainage
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.BoundaryCondition
The Drain package is used to simulate headdependent flux boundaries. In the Drain package if the head in the cell falls below a certain threshold, the flux from the drain to the model cell drops to zero.
 Parameters
elevation (array of floats (xr.DataArray)) – elevation of the drain.
conductance (array of floats (xr.DataArray)) – is the conductance of the drain.
save_budget ({True, False}, optional) – A flag that is used to determine if cellbycell budget data should be saved. If save_budget is True cellbycell budget data will be saved. Default is False.

conductance
¶

elevation
¶

save_budget
¶

class
imod.wq.
EvapotranspirationHighestActive
(*args, **kwds)[source]¶ Bases:
imod.wq.evt.Evapotranspiration

class
imod.wq.
EvapotranspirationLayers
(*args, **kwds)[source]¶ Bases:
imod.wq.evt.Evapotranspiration

class
imod.wq.
EvapotranspirationTopLayer
(*args, **kwds)[source]¶ Bases:
imod.wq.evt.Evapotranspiration

class
imod.wq.
GeneralHeadBoundary
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.BoundaryCondition
The GeneralHead Boundary package is used to simulate headdependent flux boundaries. In the GeneralHead Boundary package the flux is always proportional to the difference in head.
 Parameters
head (array of floats (xr.DataArray)) – head value for the GHB (BHEAD).
conductance (array of floats (xr.DataArray)) – the conductance of the GHB (COND).
density (array of floats (xr.DataArray)) – is the density used to convert the point head to the freshwater head (GHBSSMDENS).
concentration ("None" or array of floats (xr.DataArray), optional) – concentration of the GHB (CGHB), get automatically inserted into the SSM package. Default is “None”.
save_budget ({True, False}, optional) – is a flag indicating if the budget should be saved (IGHBCB). Default is False.

add_timemap
(head=None, conductance=None, density=None, concentration=None, use_cftime=False)[source]¶

concentration
¶

conductance
¶

density
¶

head
¶

save_budget
¶

class
imod.wq.
GeneralizedConjugateGradientSolver
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.Package
The Generalized Conjugate Gradient Solver solves the matrix equations resulting from the implicit solution of the transport equation.
 Parameters
max_iter (int) – is the maximum number of outer iterations (MXITER); it should be set to an integer greater than one (1) only when a nonlinear sorption isotherm is included in simulation.
iter1 (int) – is the maximum number of inner iterations (iter1); a value of 3050 should be adequate for most problems.
isolve (int) – is the type of preconditioners to be used with the Lanczos/ORTHOMIN acceleration scheme: isolve = 1: Jacobi isolve = 2: SSOR isolve = 3: Modified Incomplete Cholesky (MIC) (MIC usually converges faster, but it needs significantly more memory)
lump_dispersion (bool) – is an integer flag for treatment of dispersion tensor cross terms: ncrs = 0: lump all dispersion cross terms to the righthandside (approximate but highly efficient). ncrs = 1: include full dispersion tensor (memory intensive).
cclose (float) – is the convergence criterion in terms of relative concentration; a real value between 104 and 106 is generally adequate.

cclose
¶

inner_iter
¶

lump_dispersion
¶

max_iter
¶

preconditioner
¶

class
imod.wq.
LayerPropertyFlow
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.Package
The LayerProperty Flow (LPF) package is used to specify properties controlling flow between cells.
 Parameters
k_horizontal (float or array of floats (xarray.DataArray)) – is the hydraulic conductivity along rows (HK). HK is multiplied by horizontal anisotropy (see horizontal_anisotropy) to obtain hydraulic conductivity along columns.
k_vertical (float or array of floats (xarray.DataArray)) – is the vertical hydraulic conductivity (VKA).
horizontal_anisotropy (float or array of floats (xarray.DataArray)) – contains a value for each layer that is the horizontal anisotropy (CHANI). Use as many records as needed to enter a value of CHANI for each layer. The horizontal anisotropy is the ratio of the hydraulic conductivity along columns (the Y direction) to the hydraulic conductivity along rows (the X direction).
interblock (int) – contains a flag for each layer that defines the method of calculating interblock transmissivity (LAYAVG). Use as many records needed to enter a value for each layer. 0 = harmonic mean (This is most appropriate for confined and unconfined aquifers with abrupt boundaries in transmissivity at the cell boundaries or for confined aquifers with uniform hydraulic conductivity). 1 = logarithmic mean (This is most appropriate for confined aquifers with gradually varying transmissivities). 2 = arithmetic mean of saturated thickness and logarithmicmean hydraulic conductivity. (This is most appropriate for unconfined aquifers with gradually varying transmissivities).
layer_type (int) – contains a flag for each layer that specifies the layer type (LAYTYP). Use as many records needed to enter a value for each layer. 0 = confined not 0 = convertible
specific_storage (float or array of floats (xarray.DataArray)) – is specific storage (SS). Read only for a transient simulation (at least one transient stress period). Include only if at least one stress period is transient. Specific storage is the amount of water released when the head in an aquifer drops by 1 m, in one meter of the aquifer (or model layer). The unit is: ((m3 / m2) / m head change) / m aquifer = m1
specific_yield (float or array of floats (xarray.DataArray)) – is specific yield (SY). Read only for a transient simulation (at least one transient stress period) and if the layer is convertible (layer_type is not 0). Include only if at least one stress period is transient. The specific yield is the volume of water released from (or added to) the pore matrix for one meter of head change. The unit is: (m3 / m2) / m head change = dimensionless
save_budget (int) – is a flag and a unit number (ILPFCB). If save_budget > 0, it is the unit number to which cellbycell flow terms will be written when “SAVE BUDGET” or a nonzero value for save_budget is specified in Output Control. The terms that are saved are storage, constanthead flow, and flow between adjacent cells. If save_budget = 0, cellbycell flow terms will not be written. If save_budget < 0, cellbycell flow for constanthead cells will be written in the listing file when “SAVE BUDGET” or a nonzero value for ICBCFL is specified in Output Control. Cellbycell flow to storage and between adjacent cells will not be written to any file. The flow terms that will be saved are the flows through the right, front, and lower cell face. Positive values represent flows toward higher column, row, or layer numbers.
layer_wet (int) – contains a flag for each layer that indicates if wetting is active. Use as many records as needed to enter a value for each layer. 0 = wetting is inactive not 0 = wetting is active
interval_wet (int) – is the iteration interval for attempting to wet cells. Wetting is attempted every interval_wet iteration (IWETIT). If using the PCG solver (Hill, 1990), this applies to outer iterations, not inner iterations. If interval_wet less than or equal to 0, it is changed to 1.
method_wet (int) – is a flag that determines which equation is used to define the initial head at cells that become wet (IHDWET). If method_wet = 0, this equation is used: h = BOT + WETFCT (hn  BOT). (hn is the head in the neighboring cell that is causing the dry cell to convert to an active cell.) If method_wet is not 0, this equation is used: h = BOT + WETFCT(THRESH). WETFCT is a factor that is included in the calculation of the head that is initially established at a cell when it is converted from dry to wet.
head_dry (float, optional) – is the head that is assigned to cells that are converted to dry during a simulation (HDRY). Although this value plays no role in the model calculations, it is useful as an indicator when looking at the resulting heads that are output from the model. HDRY is thus similar to HNOFLO in the Basic Package, which is the value assigned to cells that are noflow cells at the start of a model simulation. Default value: 1.0e20.

head_dry
¶

horizontal_anisotropy
¶

interblock
¶

interval_wet
¶

k_horizontal
¶

k_vertical
¶

layer_type
¶

layer_wet
¶

method_wet
¶

save_budget
¶

specific_storage
¶

specific_yield
¶

class
imod.wq.
MassLoading
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.BoundaryCondition
Mass loading package. Has no direct effect on groundwater flow, is only included via MT3DMS source and sinks. (SSM ITYPE 15)
 Parameters
concentration (array of floats (xr.DataArray)) –

concentration
¶

class
imod.wq.
OutputControl
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.Package
The Output Control Option is used to specify if head, drawdown, or budget data should be saved and in which format.
 Parameters
save_head_idf ({True, False}, optional) – Save calculated head values in IDF format. Default value is False.
save_concentration_idf ({True, False}, optional) – Save calculated concentration values in IDF format. Default value is False.
save_budget_idf ({True, False}, optional) – Save calculated budget in IDF format. Default value is False.
save_head_tec ({True, False}, optional) – Save calculated head values in a format compatible with Tecplot. Default value is False.
save_concentration_tec ({True, False}, optional) – Save calculated concentration values in a format compatible with Tecplot. Default value is False.
save_budget_tec ({True, False}, optional) – Save calculated budget in a format compatible with Tecplot. Default value is False.
save_head_vtk ({True, False}, optional) – Save calculated head values in a format compatible with ParaView (VTK). Default value is False.
save_concentration_vtk ({True, False}, optional) – Save calculated concentration values in a format compatible with ParaView (VTK). Default value is False.
save_budget_vtk ({True, False}, optional) – Save calculated budget in a format compatible with ParaView (VTK). Default value is False.

save_budget_idf
¶

save_budget_tec
¶

save_budget_vtk
¶

save_concentration_idf
¶

save_concentration_tec
¶

save_concentration_vtk
¶

save_head_idf
¶

save_head_tec
¶

save_head_vtk
¶

class
imod.wq.
ParallelKrylovFlowSolver
(*args, **kwds)[source]¶ Bases:
imod.wq.slv.ParallelSolver
The Parallel Krylov Flow Solver is used for parallel solving of the flow model.
 Parameters
max_iter (int) – is the maximum number of outer iterations (MXITER); it should be set to an integer greater than one (1) only when a nonlinear sorption isotherm is included in simulation.
inner_iter (int) – is the maximum number of inner iterations (INNERIT); a value of 3050 should be adequate for most problems.
hclose (float) – is the head change criterion for convergence (HCLOSEPKS), in units of length. When the maximum absolute value of head change from all nodes during an iteration is less than or equal to HCLOSE, and the criterion for RCLOSE is also satisfied (see below), iteration stops.
rclose (float) – is the residual criterion for convergence (RCLOSEPKS), in units of cubic length per time. The units for length and time are the same as established for all model data. When the maximum absolute value of the residual at all nodes during an iteration is less than or equal to RCLOSE, and the criterion for HCLOSE is also satisfied (see above), iteration stops.
relax (float) – is the relaxation parameter used. Usually, RELAX = 1.0, but for some problems a value of 0.99, 0.98, or 0.97 will reduce the number of iterations required for convergence.
h_fstrict (float, optional) – is a factor to apply to HCLOSE to set a stricter hclose for the linear inner iterations (H_FSTRICTPKS). HCLOSE_inner is calculated as follows: HCLOSEPKS * H_FSTRICTPKS.
r_fstrict (float, optional) – is a factor to apply to RCLOSE to set a stricter rclose for the linear inner iterations (R_FSTRICTPKS). RCLOSE_inner is calculated as follows: RCLOSEPKS * R_FSTRICTPKS.
partition ({"uniform", "rcb"}, optional) – Partitioning option (PARTOPT). “uniform” partitions the model domain into equally sized subdomains. “rcb” (Recursive Coordinate Bisection) uses a 2D pointer grid with weights to partition the model domain. Default value: “uniform”
solver ({"pcg"}, optional) – Flag indicating the linear solver to be used (ISOLVER). Default value: “pcg”
preconditioner ({"ilu"}, optional) – Flag inicating the preconditioner to be used (NPC). Devault value: “ilu”
deflate ({True, False}, optional) – Flag for deflation preconditioner. Default value: False
debug ({True, False}, optional) – Debug option. Default value: False
load_balance_weight (xarray.DataArray, optional) –
2D grid with load balance weights, used when partition = “rcb” (Recursive Coordinate Bisection). If None (default), then the module will create a load balance grid by summing active cells over layers: (ibound != 0).sum(“layer”)
Note that even though the iMODSEAWAT helpfile states .idf is accepted, it is not. This load balance grid should be a .asc file (without a header). Formatting is done as follows: pd.DataFrame(load_balance_weight.values).to_csv(path, sep=’t’, header=False, index=False, float_format = “%8.2f”)

class
imod.wq.
ParallelKrylovTransportSolver
(*args, **kwds)[source]¶ Bases:
imod.wq.slv.ParallelSolver
The Parallel Krylov Transport Solver is used for parallel solving of the transport model.
 Parameters
max_iter (int) – is the maximum number of outer iterations (MXITER); it should be set to an integer greater than one (1) only when a nonlinear sorption isotherm is included in simulation.
inner_iter (int) – is the maximum number of inner iterations (INNERIT); a value of 3050 should be adequate for most problems.
cclose (float, optional) – is the convergence criterion in terms of relative concentration; a real value between 104 and 106 is generally adequate. Default value: 1.0e6.
relax (float, optional) – is the relaxation parameter used. Usually, RELAX = 1.0, but for some problems a value of 0.99, 0.98, or 0.97 will reduce the number of iterations required for convergence. Default value: 0.98.
partition ({"uniform", "rcb"}, optional) – Partitioning option (PARTOPT). “uniform” partitions the model domain into equally sized subdomains. “rcb” (Recursive Coordinate Bisection) uses a 2D pointer grid with weights to partition the model domain. Default value: “uniform”.
solver ({"bicgstab", "gmres", "gcr"}, optional) – Flag indicating the linear solver to be used (ISOLVER). Default value: “bicgstab”
preconditioner ({"ilu"}, optional) – Flag inicating the preconditioner to be used (NPC). Devault value: “ilu”.
debug ({True, False}, optional) – Debug option. Default value: False
load_balance_weight (xarray.DataArray, optional) –
2D grid with load balance weights, used when partition = “rcb” (Recursive Coordinate Bisection). If None (default), then the module will create a load balance grid by summing active cells over layers: (ibound != 0).sum(“layer”)
Note that even though the iMODSEAWAT helpfile states .idf is accepted, it is not. This load balance grid should be a .asc file (without a header). Formatting is done as follows: pd.DataFrame(load_balance_weight.values).to_csv(path, sep=’t’, header=False, index=False, float_format = “%8.2f”)

class
imod.wq.
PreconditionedConjugateGradientSolver
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.Package
The Preconditioned Conjugate Gradient Solver is used to solve the finite difference equations in each step of a MODFLOW stress period.
 Parameters
max_iter (int) – is the maximum number of outer iterations  that is, calss to the solutions routine (MXITER). For a linear problem max_iter should be 1, unless more than 50 inner iterations are required, when max_iter could be as large as 10. A larger number (generally less than 100) is required for a nonlinear problem.
inner_iter (int) – is the number of inner iterations (iter1). For nonlinear problems, inner_iter usually ranges from 10 to 30; a value of 30 will be sufficient for most linear problems.
rclose (float) –
is the residual criterion for convergence, in units of cubic length per time. The units for length and time are the same as established for all model data. When the maximum absolute value of the residual at all nodes during an iteration is less than or equal to RCLOSE, and the criterion for HCLOSE is also satisfied (see below), iteration stops.
Default value: 100.0. Nota bene: this is aimed at regional modelling. For detailed studies (e.g. lab experiments) much smaller values can be required. Very general rule of thumb: should be less than 10% of smallest cell volume.
hclose (float) – is the head change criterion for convergence, in units of length. When the maximum absolute value of head change from all nodes during an iteration is less than or equal to HCLOSE, and the criterion for RCLOSE is also satisfied (see above), iteration stops. Default value: 1.0e4. Nota bene: This is aimed at regional modelling, ` for detailed studies (e.g. lab experiments) much smaller values can be required.
relax (float, optional) – is the relaxation parameter used. Usually, RELAX = 1.0, but for some problems a value of 0.99, 0.98, or 0.97 will reduce the number of iterations required for convergence. Default value: 0.98.
damp (float, optional) – is the damping factor. It is typically set equal to one, which indicates no damping. A value less than 1 and greater than 0 causes damping. DAMP does not affect inner iterations; instead, it affects outer iterations. Default value: 1.0.

damp
¶

hclose
¶

inner_iter
¶

max_iter
¶

rclose
¶

relax
¶

class
imod.wq.
RechargeHighestActive
(*args, **kwds)[source]¶ Bases:
imod.wq.rch.Recharge
The Recharge package is used to simulate a specified flux distributed over the top of the model and specified in units of length/time. Within MODFLOW, these rates are multiplied by the horizontal area of the cells to which they are applied to calculate the volumetric flux rates. In this class the Recharge gets applied to the highest active cell in each vertical column (NRCHOP=3).
 Parameters
rate (float or array of floats (xr.DataArray)) – is the amount of recharge.
concentration (float or array of floats (xr.DataArray)) – is the concentration of the recharge
save_budget ({True, False}, optional) – flag indicating if the budget needs to be saved. Default is False.

class
imod.wq.
RechargeLayers
(*args, **kwds)[source]¶ Bases:
imod.wq.rch.Recharge
The Recharge package is used to simulate a specified flux distributed over the top of the model and specified in units of length/time. Within MODFLOW, these rates are multiplied by the horizontal area of the cells to which they are applied to calculate the volumetric flux rates. In this class the Recharge gets applied to a specific, specified, layer (NRCHOP=2).
 Parameters
rate (float or array of floats (xr.DataArray)) – is the amount of recharge.
recharge_layer (float or array of integers (xr.DataArray)) – layer number variable that defines the layer in each vertical column where recharge is applied
concentration (float or array of floats (xr.DataArray)) – is the concentration of the recharge
save_budget ({True, False}, optional) – flag indicating if the budget needs to be saved. Default is False.

class
imod.wq.
RechargeTopLayer
(*args, **kwds)[source]¶ Bases:
imod.wq.rch.Recharge
The Recharge package is used to simulate a specified flux distributed over the top of the model and specified in units of length/time. Within MODFLOW, these rates are multiplied by the horizontal area of the cells to which they are applied to calculate the volumetric flux rates. In this class the Recharge gets applied to the top grid layer (NRCHOP=1).
 Parameters
rate (float or array of floats (xr.DataArray)) – is the amount of recharge.
concentration (float or array of floats (xr.DataArray)) – is the concentration of the recharge
save_budget ({True, False}, optional) – flag indicating if the budget needs to be saved. Default is False.

class
imod.wq.
River
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.BoundaryCondition
The River package is used to simulate headdependent flux boundaries. In the River package if the head in the cell falls below a certain threshold, the flux from the river to the model cell is set to a specified lower bound.
 Parameters
stage (array of floats (xr.DataArray)) – is the head in the river (STAGE).
bottom_elevation (array of floats (xr.DataArray)) – is the bottom of the riverbed (RBOT).
conductance (array of floats (xr.DataArray)) – is the conductance of the river.
density (array of floats (xr.DataArray)) – is the density used to convert the point head to the freshwater head (RIVSSMDENS).
concentration ("None", float or array of floats (xr.DataArray), optional) – is the concentration in the river. Default is None.
save_budget ({True, False}, optional) – is a flag indicating if the budget should be saved (IRIVCB). Default is False.

add_timemap
(stage=None, conductance=None, bottom_elevation=None, concentration=None, density=None, use_cftime=False)[source]¶

bottom_elevation
¶

concentration
¶

conductance
¶

density
¶

save_budget
¶

stage
¶

class
imod.wq.
SeawatModel
(modelname, check='defer')[source]¶ Bases:
imod.wq.model.Model

modelname
¶  Type
str

check
¶ When to perform model checks {None, “defer”, “eager”}. Defaults to “defer”.
 Type
str, optional
Examples
>>> m = SeawatModel("example") >>> m["riv"] = River(...) >>> # ...etc. >>> m.time_discretization(endtime) >>> m.write()

render
(directory, result_dir, writehelp)[source]¶ Render the runfile as a string, package by package.

time_discretization
(times)[source]¶ Collect all unique times
 Parameters
times (str, datetime; or iterable of str, datetimes.) – Times to add to the time discretization. At least one single time should be given, which will be used as the ending time of the simulation.
Examples
Add a single time:
>>> m.time_discretization("20010101")
Add a daterange:
>>> m.time_discretization(pd.daterange("20000101", "20010101"))
Add a list of times:
>>> m.time_discretization(["20000101", "20010101"])

write
(directory=PosixPath('.'), result_dir=None, resultdir_is_workdir=False)[source]¶ Writes model input files.
 Parameters
directory (str, pathlib.Path) – Directory into which the model input will be written. The model input will be written into a directory called modelname.
result_dir (str, pathlib.Path) –
Path to directory in which output will be written when running the model. Is written as the value of the
result_dir
key in the runfile.See the examples.
resultdir_is_workdir (boolean, optional) – Wether the set all input paths in the runfile relative to the output directory. Because iMODwq generates a number of files in its working directory, it may be advantageous to set the working directory to a different path than the runfile location.
 Returns
 Return type
None
Examples
Say we wish to write the model input to a file called input, and we desire that when running the model, the results end up in a directory called output. We may run:
>>> model.write(directory="input", result_dir="output")
And in the runfile, a value of
../../output
will be written for result_dir.


class
imod.wq.
TimeDiscretization
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.Package
Time discretisation package class.
 Parameters
timestep_duration (float) – is the length of the current stress period (PERLEN). If the flow solution is transient, timestep_duration specified here must be equal to that specified for the flow model. If the flow solution is steadystate, timestep_duration can be set to any desired length.
n_timesteps (int, optional) – is the number of time steps for the transient flow solution in the current stress period (NSTP). If the flow solution is steadystate, n_timestep=1. Default value is 1.
transient ({True, False}, optional) – Flag indicating wether the flow simulation is transient (True) or False (Steady State). Default is True.
timestep_multiplier (float, optional) – is the multiplier for the length of successive time steps used in the transient flow solution (TSMULT); it is used only if n_timesteps>1. timestep_multiplier>0, the length of each flow time step within the current stress period is calculated using the geometric progression as in MODFLOW. Note that both n_timesteps and timestep_multiplier specified here must be identical to those specified in the flow model if the flow model is transient. timestep_multiplier ≤ 0, the length of each flow time step within the current stress period is read from the record TSLNGH. This option is needed in case the length of time steps for the flow solution is not based on a geometric progression in a flow model, unlike MODFLOW. Default is 1.0.
max_n_transport_timestep (int, optional) – is the maximum number of transport steps allowed within one time step of the flow solution (mxstrn). If the number of transport steps within a flow time step exceeds max_n_transport_timestep, the simulation is terminated. Default is 50_000.
transport_timestep_multiplier (float of {"None"}, optional) – is the multiplier for successive transport steps within a flow time step (TTSMULT). If the Generalized Conjugate Gradient (GCG) solver is used and the solution option for the advection term is the standard finite difference method. A value between 1.0 and 2.0 is generally adequate. If the GCG package is not used, the transport solution is solved explicitly as in the original MT3D code, and transport_timestep_multiplier is always set to 1.0 regardless of the userspecified input. Note that for the particle tracking based solution options and the 3rdorder TVD scheme, transport_timestep_multiplier does not apply. Default is {“None”}.
transport_initial_timestep (int, optional) – is the userspecified transport stepsize within each time step of the flow solution (DT0). transport_initial_timestep is interpreted differently depending on whether the solution option chosen is explicit or implicit: For explicit solutions (i.e., the GCG solver is not used), the program will always calculate a maximum transport stepsize which meets the various stability criteria. Setting transport_initial_timestep to zero causes the model calculated transport stepsize to be used in the simulation. However, the modelcalculated transport_initial_timestep may not always be optimal. In this situation, transport_initial_timestep should be adjusted to find a value that leads to the best results. If transport_initial_timestep is given a value greater than the modelcalculated stepsize, the modelcalculated stepsize, instead of the userspecified value, will be used in the simulation. For implicit solutions (i.e., the GCG solver is used), transport_initial_timestep is the initial transport stepsize. If it is specified as zero, the modelcalculated value of transport_initial_timestep, based on the userspecified Courant number in the Advection Package, will be used. The subsequent transport stepsize may increase or remain constant depending on the userspecified transport stepsize multiplier transport_timestep_multiplier and the solution scheme for the advection term. Default is 0.

max_n_transport_timestep
¶

n_timesteps
¶

timestep_duration
¶

timestep_multiplier
¶

transient
¶

transport_initial_timestep
¶

transport_timestep_multiplier
¶

class
imod.wq.
TimeVaryingConstantConcentration
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.BoundaryCondition
Time varying constant concentration package. Has no direct effect on groundwater flow, is only included via MT3DMS source and sinks. (SSM ITYPE 1)
 Parameters
concentration (array of floats (xr.DataArray)) –

concentration
¶

class
imod.wq.
VariableDensityFlow
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.Package
Variable Density Flow package.
 Parameters
density_species (int) – is the MT3DMS species number that will be used in the equation of state to compute fluid density (mtdnconc). If density_species = 0, fluid density is specified using items 6 and 7, and flow will be uncoupled with transport if the IMT Process is active. If density_species > 0, fluid density is calculated using the MT3DMS species number that corresponds with density_species. A value for density_species greater than zero indicates that flow will be coupled with transport. If density_species = 1, fluid density is calculated using one or more MT3DMS species. Items 4a, 4b, and 4c will be read instead of item 4.
density_min (float) – is the minimum fluid density (DENSEMIN). If the resulting density value calculated with the equation of state is less than density_min, the density value is set to density_min. If density_min = 0, the computed fluid density is not limited by density_min (this is the option to use for most simulations). If density_min > 0, a computed fluid density less than density_min is automatically reset to density_min.
density_max (float) – is the maximum fluid density (DENSEMAX). If the resulting density value calculated with the equation of state is greater than density_max, the density value is set to density_max. If density_max = 0, the computed fluid density is not limited by density_max (this is the option to use for most simulations). If density_max > 0, a computed fluid density larger than density_max is automatically reset to density_max.
density_ref (float) – is the fluid density at the reference concentration, temperature, and pressure (DENSEREF). For most simulations, density_ref is specified as the density of freshwater at 25 °C and at a reference pressure of zero. Value of 1000 is often used.
density_concentration_slope (float) – is the slope d(rho)/d(C) of the linear equation of state that relates fluid density to solute concentration (denseslp). Value of 0.7143 is often used.
density_criterion (float) – is the convergence parameter for the coupling between flow and transport and has units of fluid density (DNSCRIT). If the maximum density difference between two consecutive coupling iterations is not less than density_criterion, the program will continue to iterate on the flow and transport equations or will terminate if ‘coupling’ is exceeded.
coupling (int) – is a flag used to determine the flow and transport coupling procedure (nswtcpl). If coupling = 0 or 1, flow and transport will be explicitly coupled using a onetimestep lag. The explicit coupling option is normally much faster than the iterative option and is recommended for most applications. If coupling > 1, coupling is the maximum number of nonlinear coupling iterations for the flow and transport solutions. SEAWAT2000 will stop execution after coupling iterations if convergence between flow and transport has not occurred. If coupling = 1, the flow solution will be recalculated only for: The first transport step of the simulation, or The last transport step of the MODFLOW timestep, or The maximum density change at a cell is greater than density_criterion.
correct_water_table ({"True", "False"}) – is a flag used to activate the variabledensity watertable corrections (IWTABLE). If correct_water_table = False, the watertable correction will not be applied. If correct_water_table = True, the watertable correction will be applied.
internodal ({"upstream", "central"}) – is a flag that determines the method for calculating the internodal density values used to conserve fluid mass (MFNADVFD). If internodal = “central”, internodal conductance values used to conserve fluid mass are calculated using a centralinspace algorithm. If internodal = “upstream”, internodal conductance values used to conserve fluid mass are calculated using an upstreamweighted algorithm.

correct_water_table
¶

coupling
¶

density_concentration_slope
¶

density_criterion
¶

density_max
¶

density_min
¶

density_ref
¶

density_species
¶

internodal
¶

read_density
¶

class
imod.wq.
Well
(*args, **kwds)[source]¶ Bases:
imod.wq.pkgbase.BoundaryCondition
The Well package is used to simulate a specified flux to individual cells and specified in units of length3/time.
 Parameters
id_name (str or list of str) – name of the well(s).
x (float or list of floats) – x coordinate of the well(s).
y (float or list of floats) – y coordinate of the well(s).
rate (float or list of floats.) – pumping rate in the well(s).
Layer ("None" or int, optional) – layer from which the pumping takes place.
time ("None" or listlike of np.datetime64, datetime.datetime, pd.Timestamp,) –
cftime.datetime – time during which the pumping takes place. Only need to specify if model is transient.
save_budget ({True, False}, optional) – is a flag indicating if the budget should be saved (IRIVCB). Default is False.

save_budget
¶