"""MFD Height Above Nearest Drainage (HAND).
Uses MFD dominant-neighbor (highest fraction) for downstream tracing.
HAND = elevation - drain_elevation.
Algorithm
---------
CPU : Kahn's BFS topological sort with reverse propagation of drain_elev.
GPU : CuPy-via-CPU.
Dask: iterative tile sweep with BoundaryStore exit-label propagation.
"""
from __future__ import annotations
import numpy as np
import xarray as xr
try:
import dask.array as da
except ImportError:
da = None
from xrspatial.hydro._boundary_store import BoundaryStore
from xrspatial.hydro.watershed_mfd import (
_dominant_offset_mfd_py,
_preprocess_mfd_tiles,
_to_numpy_f64,
)
from xrspatial.utils import (
_validate_matching_shape,
_validate_mfd_fractions,
_validate_raster,
has_cuda_and_cupy,
is_cupy_array,
is_dask_cupy,
ngjit,
)
# =====================================================================
# Memory guards
# =====================================================================
#
# CPU peak working set per pixel for ``_hand_mfd_cpu``:
# in_degree : int32 -> 4
# valid : int8 -> 1
# is_stream : int8 -> 1
# drain_elev : float64 -> 8
# hand_out : float64 -> 8
# order_r : int64 -> 8
# order_c : int64 -> 8
# Total ~38 bytes/pixel. The caller-provided ``fractions`` (8, H, W),
# ``flow_accum``, and ``elevation`` arrays already live in RAM before the
# kernel runs and are not double-counted here.
_BYTES_PER_PIXEL = 38
# GPU peak working set per pixel for ``_hand_mfd_cupy``: that path copies
# fractions/fa/elev to host via ``.get()`` then runs ``_hand_mfd_cpu``.
# Host working set is dominated by the same 38 B/px as the numpy path; on
# the device we keep the fractions array (8 * float64 = 64 B/px), the two
# 2D inputs (2 * float64 = 16 B/px) and the output (float64 = 8 B/px),
# but the input copies already exist before dispatch. Use 32 B/px as a
# conservative budget mirroring the d8 sibling guard.
_GPU_BYTES_PER_PIXEL = 32
def _available_memory_bytes():
"""Best-effort estimate of available host memory in bytes."""
try:
with open('/proc/meminfo', 'r') as f:
for line in f:
if line.startswith('MemAvailable:'):
return int(line.split()[1]) * 1024 # kB -> bytes
except (OSError, ValueError, IndexError):
pass
try:
import psutil
return psutil.virtual_memory().available
except (ImportError, AttributeError):
pass
return 2 * 1024 ** 3
def _available_gpu_memory_bytes():
"""Best-effort estimate of free GPU memory in bytes.
Returns 0 if CuPy / CUDA is unavailable or the query fails -- callers
use that as a sentinel meaning "no GPU info, skip the guard".
"""
try:
import cupy as _cp
free, _total = _cp.cuda.runtime.memGetInfo()
return int(free)
except Exception:
return 0
def _check_memory(height, width):
"""Raise MemoryError if the HAND kernel would exceed 50% of RAM."""
required = int(height) * int(width) * _BYTES_PER_PIXEL
available = _available_memory_bytes()
if required > 0.5 * available:
raise MemoryError(
f"hand_mfd on a {height}x{width} grid requires "
f"~{required / 1e9:.1f} GB of working memory but only "
f"~{available / 1e9:.1f} GB is available. Use a "
f"dask-backed DataArray for out-of-core processing."
)
def _check_gpu_memory(height, width):
"""Raise MemoryError if the CuPy kernel would exceed 50% of free GPU RAM.
Skips the check (returns silently) when ``_available_gpu_memory_bytes``
cannot determine the free memory -- e.g. on hosts without CUDA, where
the kernel will fail at the cupy.asarray boundary anyway.
"""
available = _available_gpu_memory_bytes()
if available <= 0:
return
required = int(height) * int(width) * _GPU_BYTES_PER_PIXEL
if required > 0.5 * available:
raise MemoryError(
f"hand_mfd on a {height}x{width} grid requires "
f"~{required / 1e9:.1f} GB of GPU working memory but only "
f"~{available / 1e9:.1f} GB is free on the active device. "
f"Use a dask+cupy DataArray for out-of-core processing."
)
# =====================================================================
# CPU kernel
# =====================================================================
@ngjit
def _hand_mfd_cpu(fractions, flow_accum, elevation, H, W, threshold):
"""Compute HAND via Kahn's BFS with MFD dominant-neighbor tracing."""
dy = np.array([0, 1, 1, 1, 0, -1, -1, -1], dtype=np.int64)
dx = np.array([1, 1, 0, -1, -1, -1, 0, 1], dtype=np.int64)
in_degree = np.zeros((H, W), dtype=np.int32)
valid = np.zeros((H, W), dtype=np.int8)
is_stream = np.zeros((H, W), dtype=np.int8)
drain_elev = np.empty((H, W), dtype=np.float64)
hand_out = np.empty((H, W), dtype=np.float64)
for r in range(H):
for c in range(W):
v = fractions[0, r, c]
if v == v:
valid[r, c] = 1
fa = flow_accum[r, c]
if fa == fa and fa >= threshold:
is_stream[r, c] = 1
drain_elev[r, c] = elevation[r, c]
else:
drain_elev[r, c] = np.nan
else:
drain_elev[r, c] = np.nan
hand_out[r, c] = np.nan
# In-degrees: all MFD neighbors with frac > 0 contribute
for r in range(H):
for c in range(W):
if valid[r, c] == 0:
continue
for k in range(8):
if fractions[k, r, c] > 0.0:
nr = r + dy[k]
nc = c + dx[k]
if 0 <= nr < H and 0 <= nc < W and valid[nr, nc] == 1:
in_degree[nr, nc] += 1
# BFS topological order
order_r = np.empty(H * W, dtype=np.int64)
order_c = np.empty(H * W, dtype=np.int64)
head = np.int64(0)
tail = np.int64(0)
for r in range(H):
for c in range(W):
if valid[r, c] == 1 and in_degree[r, c] == 0:
order_r[tail] = r
order_c[tail] = c
tail += 1
while head < tail:
r = order_r[head]
c = order_c[head]
head += 1
for k in range(8):
if fractions[k, r, c] > 0.0:
nr = r + dy[k]
nc = c + dx[k]
if 0 <= nr < H and 0 <= nc < W and valid[nr, nc] == 1:
in_degree[nr, nc] -= 1
if in_degree[nr, nc] == 0:
order_r[tail] = nr
order_c[tail] = nc
tail += 1
# Reverse pass: propagate drain_elev via dominant neighbor
for i in range(tail - 1, -1, -1):
r = order_r[i]
c = order_c[i]
if is_stream[r, c] == 1:
continue
best_k = -1
best_frac = 0.0
for k in range(8):
f = fractions[k, r, c]
if f > best_frac:
best_frac = f
best_k = k
if best_k == -1:
drain_elev[r, c] = elevation[r, c]
continue
nr, nc = r + dy[best_k], c + dx[best_k]
if nr < 0 or nr >= H or nc < 0 or nc >= W:
drain_elev[r, c] = elevation[r, c]
continue
if valid[nr, nc] == 0:
drain_elev[r, c] = elevation[r, c]
continue
de = drain_elev[nr, nc]
if de == de:
drain_elev[r, c] = de
else:
drain_elev[r, c] = elevation[r, c]
for r in range(H):
for c in range(W):
if valid[r, c] == 1:
hand_out[r, c] = elevation[r, c] - drain_elev[r, c]
else:
hand_out[r, c] = np.nan
return hand_out
# =====================================================================
# CuPy backend
# =====================================================================
def _hand_mfd_cupy(fr_data, fa_data, elev_data, threshold):
import cupy as cp
fr_np = fr_data.get().astype(np.float64)
fa_np = fa_data.get().astype(np.float64)
el_np = elev_data.get().astype(np.float64)
_, H, W = fr_np.shape
out = _hand_mfd_cpu(fr_np, fa_np, el_np, H, W, threshold)
return cp.asarray(out)
# =====================================================================
# Dask tile kernel
# =====================================================================
@ngjit
def _hand_mfd_drain_elev_tile(fractions, flow_accum, elevation, h, w,
threshold,
exit_top, exit_bottom, exit_left, exit_right,
exit_tl, exit_tr, exit_bl, exit_br):
"""Compute drain_elev for an MFD tile (for boundary propagation)."""
dy = np.array([0, 1, 1, 1, 0, -1, -1, -1], dtype=np.int64)
dx = np.array([1, 1, 0, -1, -1, -1, 0, 1], dtype=np.int64)
in_degree = np.zeros((h, w), dtype=np.int32)
valid = np.zeros((h, w), dtype=np.int8)
is_stream = np.zeros((h, w), dtype=np.int8)
drain_elev = np.empty((h, w), dtype=np.float64)
known = np.zeros((h, w), dtype=np.int8)
for r in range(h):
for c in range(w):
v = fractions[0, r, c]
if v == v:
valid[r, c] = 1
fa = flow_accum[r, c]
if fa == fa and fa >= threshold:
is_stream[r, c] = 1
drain_elev[r, c] = elevation[r, c]
known[r, c] = 1
else:
drain_elev[r, c] = np.nan
else:
drain_elev[r, c] = np.nan
# Apply exit labels at boundaries where dominant neighbor exits tile
# Top row
for c in range(w):
if valid[0, c] == 1 and known[0, c] == 0:
best_k = -1
best_frac = 0.0
for k in range(8):
f = fractions[k, 0, c]
if f > best_frac:
best_frac = f
best_k = k
if best_k >= 0 and 0 + dy[best_k] < 0:
el = exit_top[c]
if el == el:
drain_elev[0, c] = el
known[0, c] = 1
else:
drain_elev[0, c] = elevation[0, c]
known[0, c] = 1
# Bottom row
for c in range(w):
if valid[h - 1, c] == 1 and known[h - 1, c] == 0:
best_k = -1
best_frac = 0.0
for k in range(8):
f = fractions[k, h - 1, c]
if f > best_frac:
best_frac = f
best_k = k
if best_k >= 0 and h - 1 + dy[best_k] >= h:
el = exit_bottom[c]
if el == el:
drain_elev[h - 1, c] = el
known[h - 1, c] = 1
else:
drain_elev[h - 1, c] = elevation[h - 1, c]
known[h - 1, c] = 1
# Left column
for r in range(h):
if valid[r, 0] == 1 and known[r, 0] == 0:
best_k = -1
best_frac = 0.0
for k in range(8):
f = fractions[k, r, 0]
if f > best_frac:
best_frac = f
best_k = k
if best_k >= 0 and 0 + dx[best_k] < 0:
el = exit_left[r]
if el == el:
drain_elev[r, 0] = el
known[r, 0] = 1
else:
drain_elev[r, 0] = elevation[r, 0]
known[r, 0] = 1
# Right column
for r in range(h):
if valid[r, w - 1] == 1 and known[r, w - 1] == 0:
best_k = -1
best_frac = 0.0
for k in range(8):
f = fractions[k, r, w - 1]
if f > best_frac:
best_frac = f
best_k = k
if best_k >= 0 and w - 1 + dx[best_k] >= w:
el = exit_right[r]
if el == el:
drain_elev[r, w - 1] = el
known[r, w - 1] = 1
else:
drain_elev[r, w - 1] = elevation[r, w - 1]
known[r, w - 1] = 1
# Corners
if valid[0, 0] == 1 and known[0, 0] == 0:
best_k = -1
best_frac = 0.0
for k in range(8):
f = fractions[k, 0, 0]
if f > best_frac:
best_frac = f
best_k = k
if best_k >= 0 and 0 + dy[best_k] < 0 and 0 + dx[best_k] < 0:
if exit_tl == exit_tl:
drain_elev[0, 0] = exit_tl
known[0, 0] = 1
if valid[0, w - 1] == 1 and known[0, w - 1] == 0:
best_k = -1
best_frac = 0.0
for k in range(8):
f = fractions[k, 0, w - 1]
if f > best_frac:
best_frac = f
best_k = k
if best_k >= 0 and 0 + dy[best_k] < 0 and w - 1 + dx[best_k] >= w:
if exit_tr == exit_tr:
drain_elev[0, w - 1] = exit_tr
known[0, w - 1] = 1
if valid[h - 1, 0] == 1 and known[h - 1, 0] == 0:
best_k = -1
best_frac = 0.0
for k in range(8):
f = fractions[k, h - 1, 0]
if f > best_frac:
best_frac = f
best_k = k
if best_k >= 0 and h - 1 + dy[best_k] >= h and 0 + dx[best_k] < 0:
if exit_bl == exit_bl:
drain_elev[h - 1, 0] = exit_bl
known[h - 1, 0] = 1
if valid[h - 1, w - 1] == 1 and known[h - 1, w - 1] == 0:
best_k = -1
best_frac = 0.0
for k in range(8):
f = fractions[k, h - 1, w - 1]
if f > best_frac:
best_frac = f
best_k = k
if best_k >= 0 and h - 1 + dy[best_k] >= h and w - 1 + dx[best_k] >= w:
if exit_br == exit_br:
drain_elev[h - 1, w - 1] = exit_br
known[h - 1, w - 1] = 1
# In-degrees
for r in range(h):
for c in range(w):
if valid[r, c] == 0 or known[r, c] == 1:
continue
for k in range(8):
if fractions[k, r, c] > 0.0:
nr = r + dy[k]
nc = c + dx[k]
if 0 <= nr < h and 0 <= nc < w:
if valid[nr, nc] == 1 and known[nr, nc] == 0:
in_degree[nr, nc] += 1
# BFS
order_r = np.empty(h * w, dtype=np.int64)
order_c = np.empty(h * w, dtype=np.int64)
head = np.int64(0)
tail = np.int64(0)
for r in range(h):
for c in range(w):
if valid[r, c] == 1 and known[r, c] == 0 and in_degree[r, c] == 0:
order_r[tail] = r
order_c[tail] = c
tail += 1
while head < tail:
r = order_r[head]
c = order_c[head]
head += 1
for k in range(8):
if fractions[k, r, c] > 0.0:
nr = r + dy[k]
nc = c + dx[k]
if 0 <= nr < h and 0 <= nc < w and valid[nr, nc] == 1 and known[nr, nc] == 0:
in_degree[nr, nc] -= 1
if in_degree[nr, nc] == 0:
order_r[tail] = nr
order_c[tail] = nc
tail += 1
# Reverse pass
for i in range(tail - 1, -1, -1):
r = order_r[i]
c = order_c[i]
best_k = -1
best_frac = 0.0
for k in range(8):
f = fractions[k, r, c]
if f > best_frac:
best_frac = f
best_k = k
if best_k == -1:
drain_elev[r, c] = elevation[r, c]
continue
nr, nc = r + dy[best_k], c + dx[best_k]
if nr < 0 or nr >= h or nc < 0 or nc >= w:
drain_elev[r, c] = elevation[r, c]
continue
if valid[nr, nc] == 0:
drain_elev[r, c] = elevation[r, c]
continue
de = drain_elev[nr, nc]
if de == de:
drain_elev[r, c] = de
else:
drain_elev[r, c] = elevation[r, c]
return drain_elev
@ngjit
def _hand_mfd_tile_kernel(fractions, flow_accum, elevation, h, w, threshold,
exit_top, exit_bottom, exit_left, exit_right,
exit_tl, exit_tr, exit_bl, exit_br):
"""HAND tile kernel: returns HAND values."""
drain_elev = _hand_mfd_drain_elev_tile(
fractions, flow_accum, elevation, h, w, threshold,
exit_top, exit_bottom, exit_left, exit_right,
exit_tl, exit_tr, exit_bl, exit_br)
out = np.empty((h, w), dtype=np.float64)
for r in range(h):
for c in range(w):
v = fractions[0, r, c]
if v == v:
out[r, c] = elevation[r, c] - drain_elev[r, c]
else:
out[r, c] = np.nan
return out
# =====================================================================
# Dask iterative tile sweep
# =====================================================================
def _compute_exit_labels_mfd(iy, ix, boundaries, frac_bdry,
chunks_y, chunks_x, n_tile_y, n_tile_x):
from xrspatial.hydro.watershed_mfd import _compute_exit_labels_mfd as _ws_compute
return _ws_compute(iy, ix, boundaries, frac_bdry,
chunks_y, chunks_x, n_tile_y, n_tile_x)
def _process_tile_hand_mfd(iy, ix, fractions_da, flow_accum_da, elev_da,
boundaries, frac_bdry, threshold,
chunks_y, chunks_x, n_tile_y, n_tile_x):
y_start = sum(chunks_y[:iy])
y_end = y_start + chunks_y[iy]
x_start = sum(chunks_x[:ix])
x_end = x_start + chunks_x[ix]
fr_chunk = np.asarray(
fractions_da[:, y_start:y_end, x_start:x_end].compute(),
dtype=np.float64)
fa_chunk = np.asarray(
flow_accum_da.blocks[iy, ix].compute(), dtype=np.float64)
el_chunk = np.asarray(
elev_da.blocks[iy, ix].compute(), dtype=np.float64)
_, h, w = fr_chunk.shape
exits = _compute_exit_labels_mfd(
iy, ix, boundaries, frac_bdry,
chunks_y, chunks_x, n_tile_y, n_tile_x)
drain_elev = _hand_mfd_drain_elev_tile(
fr_chunk, fa_chunk, el_chunk, h, w, threshold, *exits)
new_top = drain_elev[0, :].copy()
new_bottom = drain_elev[-1, :].copy()
new_left = drain_elev[:, 0].copy()
new_right = drain_elev[:, -1].copy()
changed = False
for side, new in (('top', new_top), ('bottom', new_bottom),
('left', new_left), ('right', new_right)):
old = boundaries.get(side, iy, ix).copy()
with np.errstate(invalid='ignore'):
mask = ~(np.isnan(old) & np.isnan(new))
if mask.any():
diff = old[mask] != new[mask]
if np.any(diff):
changed = True
break
boundaries.set('top', iy, ix, new_top)
boundaries.set('bottom', iy, ix, new_bottom)
boundaries.set('left', iy, ix, new_left)
boundaries.set('right', iy, ix, new_right)
return changed
def _hand_mfd_dask(fractions_da, flow_accum_da, elev_da, threshold,
chunks_y, chunks_x):
n_tile_y = len(chunks_y)
n_tile_x = len(chunks_x)
frac_bdry = _preprocess_mfd_tiles(fractions_da, chunks_y, chunks_x)
boundaries = BoundaryStore(chunks_y, chunks_x, fill_value=np.nan)
max_iterations = max(n_tile_y, n_tile_x) * 2 + 10
for _iteration in range(max_iterations):
any_changed = False
for iy in range(n_tile_y):
for ix in range(n_tile_x):
c = _process_tile_hand_mfd(
iy, ix, fractions_da, flow_accum_da, elev_da,
boundaries, frac_bdry, threshold,
chunks_y, chunks_x, n_tile_y, n_tile_x)
if c:
any_changed = True
for iy in reversed(range(n_tile_y)):
for ix in reversed(range(n_tile_x)):
c = _process_tile_hand_mfd(
iy, ix, fractions_da, flow_accum_da, elev_da,
boundaries, frac_bdry, threshold,
chunks_y, chunks_x, n_tile_y, n_tile_x)
if c:
any_changed = True
if not any_changed:
break
boundaries = boundaries.snapshot()
# Lazy assembly: each tile is recomputed on demand from the converged
# boundary state. Driver memory holds only the captured ``boundaries``
# / ``frac_bdry`` snapshots (boundary strips, not full tiles), so peak
# memory scales with chunk size rather than the full grid.
#
# ``fractions_da`` is 3D (8, H, W); we cannot align its chunks with the
# 2D output via map_blocks directly. We pre-compute the (y_start,
# y_end, x_start, x_end) offsets per tile so each map_blocks closure
# call only triggers its own fractions slice.
cum_y = np.zeros(n_tile_y + 1, dtype=np.int64)
np.cumsum(chunks_y, out=cum_y[1:])
cum_x = np.zeros(n_tile_x + 1, dtype=np.int64)
np.cumsum(chunks_x, out=cum_x[1:])
def _tile_fn(fa_block, el_block, block_info=None):
if block_info is None or 0 not in block_info:
return np.full(fa_block.shape, np.nan, dtype=np.float64)
iy, ix = block_info[0]['chunk-location']
y_start = int(cum_y[iy])
y_end = int(cum_y[iy + 1])
x_start = int(cum_x[ix])
x_end = int(cum_x[ix + 1])
fr_chunk = np.asarray(
fractions_da[:, y_start:y_end, x_start:x_end].compute(),
dtype=np.float64)
fa_chunk = np.asarray(fa_block, dtype=np.float64)
el_chunk = np.asarray(el_block, dtype=np.float64)
_, h, w = fr_chunk.shape
exits = _compute_exit_labels_mfd(
iy, ix, boundaries, frac_bdry,
chunks_y, chunks_x, n_tile_y, n_tile_x)
return _hand_mfd_tile_kernel(
fr_chunk, fa_chunk, el_chunk, h, w, threshold, *exits)
return da.map_blocks(
_tile_fn,
flow_accum_da, elev_da,
dtype=np.float64,
meta=np.array((), dtype=np.float64),
)
def _hand_mfd_dask_cupy(fractions_da, flow_accum_da, elev_da, threshold,
chunks_y, chunks_x):
import cupy as cp
fr_np = fractions_da.map_blocks(
lambda b: b.get(), dtype=fractions_da.dtype,
meta=np.array((), dtype=fractions_da.dtype))
fa_np = flow_accum_da.map_blocks(
lambda b: b.get(), dtype=flow_accum_da.dtype,
meta=np.array((), dtype=flow_accum_da.dtype))
el_np = elev_da.map_blocks(
lambda b: b.get(), dtype=elev_da.dtype,
meta=np.array((), dtype=elev_da.dtype))
result = _hand_mfd_dask(fr_np, fa_np, el_np, threshold,
chunks_y, chunks_x)
return result.map_blocks(
cp.asarray, dtype=result.dtype,
meta=cp.array((), dtype=result.dtype))
# =====================================================================
# Public API
# =====================================================================
[docs]
def hand_mfd(flow_dir_mfd: xr.DataArray,
flow_accum: xr.DataArray,
elevation: xr.DataArray,
threshold: float = 100,
name: str = 'hand_mfd') -> xr.DataArray:
"""Compute HAND using MFD flow direction.
Parameters
----------
flow_dir_mfd : xarray.DataArray
3D MFD flow direction array of shape (8, H, W).
flow_accum : xarray.DataArray
2D flow accumulation grid.
elevation : xarray.DataArray
2D elevation grid.
threshold : float, default 100
Minimum flow accumulation to define a stream cell.
name : str, default 'hand_mfd'
Name of output DataArray.
Returns
-------
xarray.DataArray
2D float64 HAND grid. Stream cells have HAND = 0.
"""
_validate_raster(flow_dir_mfd, func_name='hand_mfd',
name='flow_dir_mfd', ndim=3)
_validate_raster(flow_accum, func_name='hand_mfd', name='flow_accum')
_validate_raster(elevation, func_name='hand_mfd', name='elevation')
if not np.isfinite(threshold):
raise ValueError(
"threshold must be a finite number, got %s" % threshold
)
data = flow_dir_mfd.data
fa_data = flow_accum.data
el_data = elevation.data
if data.ndim != 3 or data.shape[0] != 8:
raise ValueError(
f"flow_dir_mfd must have shape (8, H, W), got {data.shape}")
_validate_mfd_fractions(data, func_name='hand_mfd',
name='flow_dir_mfd')
_, H, W = data.shape
_validate_matching_shape(
flow_accum, (H, W), func_name='hand_mfd',
name='flow_accum', expected_name='flow_dir_mfd')
_validate_matching_shape(
elevation, (H, W), func_name='hand_mfd',
name='elevation', expected_name='flow_dir_mfd')
if isinstance(data, np.ndarray):
_check_memory(H, W)
fr = data.astype(np.float64)
fa = np.asarray(fa_data, dtype=np.float64)
el = np.asarray(el_data, dtype=np.float64)
out = _hand_mfd_cpu(fr, fa, el, H, W, float(threshold))
elif has_cuda_and_cupy() and is_cupy_array(data):
_check_gpu_memory(H, W)
_check_memory(H, W)
out = _hand_mfd_cupy(data, fa_data, el_data, float(threshold))
elif has_cuda_and_cupy() and is_dask_cupy(flow_dir_mfd):
chunks_y = data.chunks[1]
chunks_x = data.chunks[2]
out = _hand_mfd_dask_cupy(data, fa_data, el_data,
float(threshold), chunks_y, chunks_x)
elif da is not None and isinstance(data, da.Array):
chunks_y = data.chunks[1]
chunks_x = data.chunks[2]
out = _hand_mfd_dask(data, fa_data, el_data,
float(threshold), chunks_y, chunks_x)
else:
raise TypeError(f"Unsupported array type: {type(data)}")
spatial_dims = flow_dir_mfd.dims[1:]
coords = {}
for d in spatial_dims:
if d in flow_dir_mfd.coords:
coords[d] = flow_dir_mfd.coords[d]
return xr.DataArray(out,
name=name,
coords=coords,
dims=spatial_dims,
attrs=flow_dir_mfd.attrs)
