from typing import Tuple
import dask
import dask.array
import numba
import numpy as np
import scipy.ndimage
import xarray as xr
DIM_Z = 0
DIM_Y = 1
DIM_X = 2
LOWER = 3
UPPER = 4
FRONT = 5
BACK = 6
RIGHT = 7
LEFT = 8
def _outer_edge(da):
faces = np.full(da.shape, np.nan)
unique_ids = np.unique(da.values)
unique_ids = unique_ids[~np.isnan(unique_ids)]
# Number the faces by their id
for unique_id in unique_ids:
data = (da == unique_id).values
from_edge = ~scipy.ndimage.binary_dilation(~data)
is_edge = (data == 1) & (from_edge == 0)
faces[is_edge] = unique_id
return xr.DataArray(faces, da.coords, da.dims)
@numba.njit
def _face_indices(face, budgetzone):
nface = int(np.isfinite(face).sum())
shape = (nface, 9)
indices = np.zeros(shape, dtype=np.int32)
if nface == 0:
return indices
# Loop over cells
nlay, nrow, ncol = budgetzone.shape
count = 0
for k in range(nlay):
for i in range(nrow):
for j in range(ncol):
face_value = face[k, i, j]
if ~np.isnan(face_value):
# Store indices
indices[count, DIM_Z] = k
indices[count, DIM_Y] = i
indices[count, DIM_X] = j
# Default value: part of domain for edges
lower = front = right = upper = back = left = face_value
if k > 0:
upper = budgetzone[k - 1, i, j]
if k < (nlay - 1):
lower = budgetzone[k + 1, i, j]
if i > 0:
back = budgetzone[k, i - 1, j]
if i < (nrow - 1):
front = budgetzone[k, i + 1, j]
if j > 0:
left = budgetzone[k, i, j - 1]
if j < (ncol - 1):
right = budgetzone[k, i, j + 1]
# Test if cell is a control surface cell for the direction
if lower != face_value:
indices[count, LOWER] = 1
if upper != face_value:
indices[count, UPPER] = 1
if front != face_value:
indices[count, FRONT] = 1
if back != face_value:
indices[count, BACK] = 1
if right != face_value:
indices[count, RIGHT] = 1
if left != face_value:
indices[count, LEFT] = 1
# Incrementer counter
count += 1
return indices
@numba.njit
def _collect_flowfront(indices, flow):
result = np.zeros(flow.shape)
nface = indices.shape[0]
for count in range(nface):
k = indices[count, DIM_Z]
i = indices[count, DIM_Y]
j = indices[count, DIM_X]
if indices[count, FRONT]:
result[k, i, j] += flow[k, i, j]
if indices[count, BACK]:
result[k, i, j] -= flow[k, i - 1, j]
return result
@numba.njit
def _collect_flowlower(indices, flow):
result = np.zeros(flow.shape)
nface = indices.shape[0]
for count in range(nface):
k = indices[count, DIM_Z]
i = indices[count, DIM_Y]
j = indices[count, DIM_X]
if indices[count, LOWER]:
result[k, i, j] += flow[k, i, j]
if indices[count, UPPER]:
result[k, i, j] -= flow[k - 1, i, j]
return result
@numba.njit
def _collect_flowright(indices, flow):
result = np.zeros(flow.shape)
nface = indices.shape[0]
for count in range(nface):
k = indices[count, DIM_Z]
i = indices[count, DIM_Y]
j = indices[count, DIM_X]
if indices[count, RIGHT]:
result[k, i, j] += flow[k, i, j]
if indices[count, LEFT]:
result[k, i, j] -= flow[k, i, j - 1]
return result
def delayed_collect(indices, front, lower, right):
indices = indices.compute()
result_front = dask.delayed(_collect_flowfront, nout=1)(indices, front.values)
result_lower = dask.delayed(_collect_flowlower, nout=1)(indices, lower.values)
result_right = dask.delayed(_collect_flowright, nout=1)(indices, right.values)
dask_front = dask.array.from_delayed(result_front, front.shape, dtype=np.float64)
dask_lower = dask.array.from_delayed(result_lower, lower.shape, dtype=np.float64)
dask_right = dask.array.from_delayed(result_right, right.shape, dtype=np.float64)
return dask_front, dask_lower, dask_right
[docs]
def facebudget(budgetzone, front=None, lower=None, right=None, netflow=True):
"""
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
>>> gdf = gpd.read_file("zone_of_interest.shp")
>>> zone2D = imod.prepare.rasterize(gdf, like=lower.isel(layer=0))
Broadcast it to three dimensions:
>>> 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
>>> )
"""
# Error handling
if front is None and lower is None and right is None:
raise ValueError("Atleast a single flow budget DataArray must be given")
if tuple(budgetzone.dims) != ("layer", "y", "x"):
raise ValueError('Dimensions of budgetzone must be exactly ("layer", "y", "x")')
shape = budgetzone.shape
for da, daname in zip((front, lower, right), ("front", "lower", "right")):
if da is not None:
dims = da.dims
coords = da.coords
if "time" in dims:
da_shape = da.shape[1:]
else:
da_shape = da.shape
if da_shape != shape:
raise ValueError(f"Shape of {daname} does not match budgetzone")
# Determine control surface
face = _outer_edge(budgetzone)
# Convert indices array to dask array, otherwise garbage collection gets
# rid of the array and we get a segfault.
indices = dask.array.from_array(_face_indices(face.values, budgetzone.values))
# Make sure it returns NaNs if no zones are defined.
if indices.size > 0:
# Create dummy arrays for skipped values, allocate just once
if front is None:
F = xr.full_like(budgetzone, 0.0, dtype=np.float64)
if lower is None:
L = xr.full_like(budgetzone, 0.0, dtype=np.float64)
if right is None:
R = xr.full_like(budgetzone, 0.0, dtype=np.float64)
results_front = []
results_lower = []
results_right = []
if "time" in dims:
for itime in range(front.coords["time"].size):
if front is not None:
F = front.isel(time=itime)
if lower is not None:
L = lower.isel(time=itime)
if right is not None:
R = right.isel(time=itime)
# collect dask arrays
dF, dL, dR = delayed_collect(indices, F, L, R)
# append
results_front.append(dF)
results_lower.append(dL)
results_right.append(dR)
# Concatenate over time dimension
dask_front = dask.array.stack(results_front, axis=0)
dask_lower = dask.array.stack(results_lower, axis=0)
dask_right = dask.array.stack(results_right, axis=0)
else:
if front is not None:
F = front
if lower is not None:
L = lower
if right is not None:
R = right
dask_front, dask_lower, dask_right = delayed_collect(indices, F, L, R)
else:
chunks = (1, *da_shape)
dask_front = dask.array.full(front.shape, np.nan, chunks=chunks)
dask_lower = dask.array.full(lower.shape, np.nan, chunks=chunks)
dask_right = dask.array.full(right.shape, np.nan, chunks=chunks)
if netflow:
return xr.DataArray(dask_front + dask_lower + dask_right, coords, dims)
else:
return (
xr.DataArray(dask_front, coords, dims),
xr.DataArray(dask_lower, coords, dims),
xr.DataArray(dask_right, coords, dims),
)
[docs]
def flow_velocity(
front: xr.DataArray,
lower: xr.DataArray,
right: xr.DataArray,
top_bot: xr.DataArray,
porosity: float = 0.3,
) -> Tuple[xr.DataArray, xr.DataArray, xr.DataArray]:
"""
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: xr.DataArray of floats
Velocity components in x, y, z direction.
"""
if "dz" not in top_bot:
top_bot["dz"] = top_bot["top"] - top_bot["bot"]
# cell side area (m2)
A_x = np.abs(top_bot.dz * right.dy)
A_y = np.abs(top_bot.dz * front.dx)
A_z = np.abs(lower.dx * lower.dy)
# Divide flux (m3/d) by area (m2) -> (m/d)
# Flip direction around for x (right)
return (
-right / (A_x * porosity),
front / (A_y * porosity),
lower / (A_z * porosity),
)
