# imod.evaluate – Evaluate model output¶

Function to calculate GxG groundwater characteristics from head time series.

GLG and GHG (average lowest and average highest groundwater level respectively) are calculated as the average of the three lowest (GLG) or highest (GHG) head values per hydrological year (april - april), for head values measured at a semi-monthly frequency (14th and 28th of every month). GVG (average spring groundwater level) is calculated as the average of groundwater level on 28th of March, 14th and 28th of April. Supplied head values are resampled (nearest) to the 14/28 frequency. Hydrological years without all 24 14/28 dates present are discarded.

Requires bottleneck.

Parameters
• head (xr.DataArray of floats) – Head relative to sea level, in m, or m below surface level if below_surfacelevel is set to True. Must be of dimensions ("time", "y", "x").

• below_surfacelevel (boolean, optional) – False (default) if heads are relative to sea level. If True, heads are taken as m below surface level.

Returns

gxg – Dataset containing glg: average lowest head, ghg: average highest head, and gvg: average spring head.

Return type

xr.Dataset

Examples

>>> import imod


Transform to meters below surface level by substracting from surface level:

>>> surflevel = imod.idf.open("surfacelevel.idf")
>>> gxg = surflevel - gxg


Or calculate from groundwater level relative to surface level directly:

>>> gwl = surflevel - heads
>>> gxg = imod.evaluate.calculate_gxg(gwl, below_surfacelevel=True)


Function to convert point water head (as outputted by seawat) into freshwater head, using Eq.3 from Guo, W., & Langevin, C. D. (2002):

$h_{f}=\frac{\rho}{\rho_{f}}h-\frac{\rho-\rho_{f}}{\rho_{f}}Z$

An edge case arises when the head is below the cell centre, or entirely below the cell. Strictly applying Eq.3 would result in freshwater heads that are lower than the original point water head, which is physically impossible. This function then outputs the freshwaterhead for the uppermost underlying cell where the original point water head exceeds the cell centre.

Requires bottleneck.

Parameters
• pointwaterhead (float or xr.DataArray of floats) – the point water head as outputted by SEAWAT, in m.

• density (float or xr.DataArray of floats) – the water density at the same locations as pointwaterhead.

• elevation (float or xr.DataArray of floats) – elevation at the same locations as pointwaterhead, in m.

• density_fresh (float, optional) – the density of freshwater (1000 kg/m3), or a different value if different units are used, or a different density reference is required.

Returns

Return type

float or xr.DataArray of floats

imod.evaluate.facebudget(budgetzone, front=None, lower=None, right=None, netflow=True)[source]

Computes net face flow into a control volume, as defined by budgetzone.

Returns a three dimensional DataArray with in- and outgoing flows for every cell that is located on the edge of the control volume, thereby calculating the flow through the control surface of the control volume.

Front, lower, and right arguments refer to iMOD face flow budgets, in cubic meters per day. In terms of flow direction these are defined as:

• front: positive with y (negative with row index)

• lower: positive with layer (positive with layer index)

• right: negative with x (negative with column index)

Only a single face flow has to be defined, for example, if only vertical fluxes (lower) are to be considered.

Note that you generally should not define a budgetzone that is only one cell wide. In that case, flow will both enter and leave the cell, resulting in a net flow of zero (given there are no boundary conditions present).

The output of this function defines ingoing flow as positive, and outgoing flow as negative. The output is a 3D array with net flows for every control surface cell. You can select specific parts of the control surface, for example only the east-facing side of the control volume. Please refer to the examples.

Parameters
• budgetzone (xr.DataAray of floats) – Array defining zones. Non-zones should be with a np.nan value. Dimensions must be exactly ("layer", "y", "x").

• front (xr.DataArray of floats, optional) – Dimensions must be exactly ("layer", "y", "x") or ("time", "layer", "y", "x").

• lower (xr.DataArray of floats, optional) – Dimensions must be exactly ("layer", "y", "x") or ("time", "layer", "y", "x").

• right (xr.DataArray of floats, optional) – Dimensions must be exactly ("layer", "y", "x") or ("time", "layer", "y", "x").

• netflow (bool, optional) – Whether to split flows by direction (front, lower, right). True: sum all flows. False: return individual directions.

Returns

• facebudget_front, facebudget_lower, face_budget_right (xr.DataArray of floats) – Only returned if netflow is False.

• facebudget_net (xr.DataArray of floats) – Only returned if netflow is True.

Examples

Load the face flows, and select the last time using index selection:

>>> import imod
>>> lower = imod.idf.open("bdgflf*.idf").isel(time=-1)
>>> right = imod.idf.open("bdgfrf*.idf").isel(time=-1)
>>> front = imod.idf.open("bdgfff*.idf").isel(time=-1)


Define the zone of interest, e.g. via rasterizing a shapefile:

>>> import geopandas as gpd
>>> zone2D = imod.prepare.rasterize(gdf, like=lower.isel(layer=0))


>>> zone = xr.ones_like(flow) * zone2D


Compute net flow through the (control) surface of the budget zone:

>>> flow = imod.evaluate.facebudget(
>>>     budgetzone=zone, front=front, lower=lower, right=right
>>> )


Or evaluate only horizontal fluxes:

>>> flow = imod.evaluate.facebudget(
>>>     budgetzone=zone, front=front, right=right
>>> )


Extract the net flow, only on the right side of the zone, for example as defined by x > 10000:

>>> netflow_right = flow.where(flow["x"] > 10_000.0).sum()


Extract the net flow for only the first four layers:

>>> netflow_layers = netflow_right.sel(layer=slice(1, 4)).sum()


Extract the net flow to the right of an arbitrary diagonal in x and y is simple using the equation for a straight line:

>>> netflow_right_of_diagonal = flow.where(
>>>    flow["y"] < (line_slope * flow["x"] + line_intercept)
>>> )


There are many ways to extract flows for a certain part of the zone of interest. The most flexible one with regards to the x and y dimensions is by drawing a vector file, rasterizing it, and using it to select with xarray.where().

To get the flows per direction, pass netflow=False.

>>> flowfront, flowlower, flowright = imod.evaluate.facebudget(
>>>    budgetzone=zone, front=front, lower=lower, right=right, netflow=False
>>> )

imod.evaluate.flow_velocity(front: xarray.core.dataarray.DataArray, lower: xarray.core.dataarray.DataArray, right: xarray.core.dataarray.DataArray, top_bot: xarray.core.dataarray.DataArray, porosity: float = 0.3) Tuple[xarray.core.dataarray.DataArray, xarray.core.dataarray.DataArray, xarray.core.dataarray.DataArray][source]

Compute flow velocities (m/d) from budgets (m3/d).

Parameters
• front (xr.DataArray of floats, optional) – Dimensions must be exactly ("layer", "y", "x").

• lower (xr.DataArray of floats, optional) – Dimensions must be exactly ("layer", "y", "x").

• right (xr.DataArray of floats, optional) – Dimensions must be exactly ("layer", "y", "x").

• top_bot (xr.Dataset of floats, containing 'top', 'bot' and optionally) – ‘dz’ of layers. Dimensions must be exactly ("layer", "y", "x").

• porosity (float or xr.DataArray of floats, optional (default 0.3)) – If xr.DataArray, dimensions must be exactly ("layer", "y", "x").

Returns

vx, vy, vz – Velocity components in x, y, z direction.

Return type

xr.DataArray of floats

imod.evaluate.interpolate_value_boundaries(values, z, threshold)[source]

Function that returns all exceedance and non-exceedance boundaries for a given threshold in a 3D values DataArray. Returned z-coordinates are linearly interpolated between cell mids. As many boundaries are returned as are maximally present in the 3D values DataArray. Function returns xr.DataArray of exceedance boundaries and xr.DataArray of z-coordinates where values fall below the set treshold.

Parameters
• values (3D xr.DataArray) – The datarray containing the values to search for boundaries. Dimensions layer, y, x

• z (1D or 3D xr.DataArray) – Datarray containing z-coordinates of cell midpoints. Dimensions layer, y, x. Should contain a dz coordinate.

• threshold (float) – Value threshold

Returns

• xr.DataArray – Z locations of successive exceedances of threshold from the top down. Dimensions boundary, y, x

• xr.DataArray – Z locations of successive instances of falling below threshold from the top down. Dimensions boundary, y, x

imod.evaluate.intra_cell_boundary_conditions(top_bot, porosity=0.3, riv=None, ghb=None, drn=None, drop_allnan=True)[source]

Function to pre-check boundary-conditions against one another for large intra-cell fluxes. ghb and river can function as source and sink, drn only as sink.

Parameters
• top_bot (xr.Dataset of floats) – ‘top_bot’ should at least contain top and bot data_vars

• porosity (float or xr.DataArray of floats, optional) – Effective porosity of model cells

• riv ((dict or list of) imod.RiverPackage, optional) –

• ghb ((dict or list of) imod.GeneralHeadBoundaryPackage, optional) –

• drn ((dict or list of) imod.DrainagePackage, optional) –

• drop_allnan (boolean, optional) – Whether source-sink combinations without overlap should be dropped from result (default True)

Returns

• dt_min (xr.DataArray of floats) – dt_min is the minimum calculated timestep over all combinations of boundary conditions

• dt_all (xr.DataArray of floats) – dt_all is the calculated timestep for all combinations of boundary conditions

imod.evaluate.quiver_line(frf, fff, flf, start, end)[source]

Obtain the u and v components for quiver plots for a line cross section through a three-dimensional flux field. The u and v components are obtained by first projecting the threedimensional flux components onto the provided cross-section.

Parameters
• frf (xarray.DataArray) – Three- (or higher) dimensional dataarray of flow component along the rows (FLOW RIGHT FACE).

• fff (xarray.DataArray) – Three- (or higher) dimensional dataarray of flow component along the columns (FLOW FRONT FACE).

• flf (xarray.DataArray) – Three- (or higher) dimensional dataarray of flow component along the layers (FLOW LOWER FACE).

• start ((2, ) array_like) – A latitude-longitude pair designating the start point of the cross section.

• end ((2, ) array_like) – A latitude-longitude pair designating the end point of the cross section.

Returns

• u (xarray.DataArray) – The u component (x-component) of the flow projection on the cross-section between start and end coordinate, with new dimension “s” along the cross-section. The cellsizes along “s” are given in the “ds” coordinate.

• v (xarray.DataArray) – The v component (y-component) of the flow projection on the cross-section between start and end coordinate, with new dimension “s” along the cross-section. The cellsizes along “s” are given in the “ds” coordinate.

Notes

Use imod.evaluate.flow_velocity() first to obtain groundwater velocities as input for this function. Velocity in x direction is, however, inverted and must be re-inverted before using as input here.

imod.evaluate.quiver_linestring(frf, fff, flf, linestring)[source]

Obtain the u and v components for quiver plots for a linestring cross section through a three-dimensional flow field. The u and v components are obtained by first projecting the threedimensional flow components onto the provided cross-section.

Parameters
• frf (xarray.DataArray) – Three- (or higher) dimensional dataarray of flow component along the rows (FLOW RIGHT FACE).

• fff (xarray.DataArray) – Three- (or higher) dimensional dataarray of flow component along the columns (FLOW FRONT FACE).

• flf (xarray.DataArray) – Three- (or higher) dimensional dataarray of flow component along the layers (FLOW LOWER FACE).

• linestring (shapely.geometry.LineString) – Shapely geometry designating the linestring along which to sample the cross section.

Returns

• u (xarray.DataArray) – The u component (x-component) of the flow projection on the cross-section between start and end coordinate, with new dimension “s” along the cross-section. The cellsizes along “s” are given in the “ds” coordinate.

• v (xarray.DataArray) – The v component (y-component) of the flow projection on the cross-section between start and end coordinate, with new dimension “s” along the cross-section. The cellsizes along “s” are given in the “ds” coordinate.

Notes

Use imod.evaluate.flow_velocity() first to obtain groundwater velocities as input for this function. Velocity in x direction is, however, inverted and must be re-inverted before using as input here.

imod.evaluate.stability_constraint_advection(front, lower, right, top_bot, porosity=0.3, R=1.0)[source]

Computes advection stability constraint as applied in MT3D for adaptive timestepping (Zheng & Wang, 1999 p54):

$\Delta t \leq \frac{R}{\frac{\left | v_{x} \right |}{\Delta x}+\frac{\left | v_{y} \right |}{\Delta y}+\frac{\left | v_{z} \right |}{\Delta z}}$

This function can be used to select which cells necessitate a small timestap, thereby slowing down calculations.

Front, lower, and right arguments refer to iMOD face flow budgets, in cubic meters per day. In terms of flow direction these are defined as:

• front: positive with y (negative with row index)

• lower: positive with layer (positive with layer index)

• right: negative with x (negative with column index)

Returns the minimum timestep that is required to satisfy this constraint. The resulting dt xr.DataArray is the minimum timestep over all three directions, dt_xyz is an xr.Dataset containing minimum timesteps for the three directions separately.

Parameters
• front (xr.DataArray of floats, optional) – Dimensions must be exactly ("layer", "y", "x").

• lower (xr.DataArray of floats, optional) – Dimensions must be exactly ("layer", "y", "x").

• right (xr.DataArray of floats, optional) – Dimensions must be exactly ("layer", "y", "x").

• top_bot (xr.Dataset of floats, containing 'top', 'bot' and optionally) – ‘dz’ of layers. Dimensions must be exactly ("layer", "y", "x").

• porosity (float or xr.DataArray of floats, optional (default 0.3)) – If xr.DataArray, dimensions must be exactly ("layer", "y", "x").

• R (Retardation factor, optional (default)) – Only when sorption is a factor.

Returns

• dt (xr.DataArray of floats)

• dt_xyz (xr.Dataset of floats)

imod.evaluate.stability_constraint_wel(wel, top_bot, porosity=0.3, R=1.0)[source]

Computes sink/source stability constraint as applied in MT3D for adaptive timestepping (Zheng & Wang, 1999 p54).

$\Delta t \leq \frac{R\theta }{\left | q_{s} \right |}$

For the WEL package, a flux is known beforehand, so we can evaluate beforehand if a flux assigned to a cell will necessitate a small timestap, thereby slowing down calculations.

Returns a ipf DataFrame that includes a column for the specific discharge and resulting minimum timestep.

Parameters
• wel (pd.DataFrame) – pd.DataFrame that defines a WEL package. Minimally includes x, y, layer and Q column.

• top_bot (xr.Dataset of floats, containing 'top', 'bot' and optionally) – ‘dz’ of layers. Dimensions must be exactly ("layer", "y", "x").

• porosity (float or xr.DataArray of floats, optional (default 0.3)) – If xr.DataArray, dimensions must be exactly ("layer", "y", "x").

• R (Retardation factor, optional (default)) – Only when sorption is a factor.

Returns

wel – dt (minimum timestep) columns

Return type

pd.DataFrame containing addition qs (specific discharge) and

imod.evaluate.streamfunction_line(frf, fff, start, end)[source]

Obtain the streamfunction for a line cross section through a three-dimensional flow field. The streamfunction is obtained by first projecting the horizontal flow components onto the provided cross-section. The streamfunction can be contoured to visualize stream lines. Stream lines are an efficient way to visualize groundwater flow.

Note, however, that the streamfunction is only defined in 2D, non-diverging, steady-state flow without sources and sinks. These assumption are violated even in a 2D model, but even more so in the approach followed here. Flow perpendicular to the cross-section will not be visualized. It is up to the user to choose cross-sections as perpendicular to the main flow direction as possible.

The 2D streamfunction and stream line visualization is based on work of Em. Prof. Olsthoorn.

Parameters
• frf (xarray.DataArray) – Three- (or higher) dimensional dataarray of flow component along the rows (FLOW RIGHT FACE).

• fff (xarray.DataArray) – Three- (or higher) dimensional dataarray of flow component along the columns (FLOW FRONT FACE).

• start ((2, ) array_like) – A latitude-longitude pair designating the start point of the cross section.

• end ((2, ) array_like) – A latitude-longitude pair designating the end point of the cross section.

Returns

The streamfunction projected on the cross-section between start and end coordinate, with new dimension “s” along the cross-section. The cellsizes along “s” are given in the “ds” coordinate.

Return type

xarray.DataArray

imod.evaluate.streamfunction_linestring(frf, fff, linestring)[source]

Obtain the streamfunction for a linestring cross section through a three-dimensional flow field. The streamfunction is obtained by first projecting the horizontal flow components onto the provided cross-section. The streamfunction can be contoured to visualize stream lines. Stream lines are an efficient way to visualize groundwater flow.

Note, however, that the streamfunction is only defined in 2D, non-diverging, steady-state flow without sources and sinks. These assumption are violated even in a 2D model, but even more so in the approach followed here. Flow perpendicular to the cross-section will not be visualized. It is up to the user to choose cross-sections as perpendicular to the main flow direction as possible.

The 2D streamfunction and stream line visualization is based on work of Em. Prof. Olsthoorn.

Parameters
• frf (xarray.DataArray) – Three- (or higher) dimensional dataarray of flow component along the rows (FLOW RIGHT FACE).

• fff (xarray.DataArray) – Three- (or higher) dimensional dataarray of flow component along the columns (FLOW FRONT FACE).

• linestring (shapely.geometry.LineString) – Shapely geometry designating the linestring along which to sample the cross section.

Returns

The streamfunction projected on the cross-section defined by provided linestring, with new dimension “s” along the cross-section. The cellsizes along “s” are given in the “ds” coordinate.

Return type

xarray.DataArray