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geospatial_utils.py
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geospatial_utils.py
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import numpy as np
from rh_logging import info, warning, error, debug
"""
routines for modifying geospatial data
smooth_2d_array: smooth a 2d array
fit_planar_surface: fit a planar surface to a 2d array
blend_edges: blend the edges of a 2d array
arg_closest_point: return the index of an array that is closest to a given value
calc_gradient: calculate gradient
std_dev: standard deviation
quadratic: return a solution of a quadratic equation
_four_point_laplacian: calculate laplacian using four neighboring points
_inside_indices_buffer: return indices excluding those in a buffer around array edges
_expand_mask_buffer: expand a mask spatially
"""
# Parameters
# degrees to radians
dtr = np.pi / 180.0
# earth radius [m]
re = 6.371e6
# function definitions
def smooth_2d_array(elev, land_frac=1, scalar=1):
hw = scalar / (land_frac**2 * np.min(elev.shape))
elev_fft = np.fft.rfft2(elev, norm="ortho")
ny, nx = elev_fft.shape
rowfreq = np.fft.fftfreq(elev.shape[0])
colfreq = np.fft.rfftfreq(elev.shape[1])
radialfreq = np.sqrt(
np.tile(colfreq * colfreq, (ny, 1)) + np.tile(rowfreq * rowfreq, (nx, 1)).T
)
# smaller hw -> more smooth
wl = np.exp(-radialfreq / hw)
return np.fft.irfft2(wl * elev_fft, norm="ortho", s=elev.shape)
def fit_planar_surface(elev, elon, elat):
elon2d = np.tile(elon, (elat.size, 1))
elat2d = np.tile(elat, (elon.size, 1)).T
ncoef = 3
g = np.zeros((elon2d.size, ncoef))
g[:, 0] = elat2d.flat
g[:, 1] = elon2d.flat
g[:, 2] = 1
gtd = np.dot(np.transpose(g), elev.flat)
gtg = np.dot(np.transpose(g), g)
# covm is the model covariance matrix
covm = np.linalg.inv(gtg)
# coefs is the model parameter vector
coefs = np.dot(covm, gtd)
elev_planar = elat2d * coefs[0] + elon2d * coefs[1] + coefs[2]
return elev_planar
def blend_edges(ifld, n=10):
fld = np.copy(ifld)
jm, im = fld.shape
# j axis
tmp = np.zeros((jm, 2 * n))
# begin at edges and work away
for i in range(n):
w = n - i
ind = np.arange(-w, (w + 1), 1, dtype=int)
# positive edge
tmp[:, n + i] = np.sum(fld[:, ind + i], axis=1) / ind.size
# negative edge
tmp[:, n - (i + 1)] = np.sum(fld[:, ind - (i + 1)], axis=1) / ind.size
# update fld values
ind = np.arange(-n, n, 1, dtype=int)
fld[:, ind] = tmp
# i axis
tmp = np.zeros((2 * n, im))
# begin at edges and work away
for j in range(n):
w = n - j
ind = np.arange(-w, (w + 1), 1, dtype=int)
# positive edge
tmp[n + j, :] = np.sum(fld[ind + j, :], axis=0) / ind.size
# negative edge
tmp[n - (j + 1), :] = np.sum(fld[ind - (j + 1), :], axis=0) / ind.size
# update fld values
ind = np.arange(-n, n, 1, dtype=int)
fld[ind, :] = tmp
return fld
def arg_closest_point(point, array, angular=False):
# find closest value in an array using 32 bit precision
if angular:
# unit are degrees
d = np.power(
np.cos(dtr * np.float32(point)) - np.cos(dtr * np.float32(array)), 2
) + np.power(
np.sin(dtr * np.float32(point)) - np.sin(dtr * np.float32(array)), 2
)
return np.argmin(np.abs(d))
else:
return np.argmin(np.abs(np.float32(point) - np.float32(array)))
def calc_gradient(z, lon, lat, method="Horn1981"):
if method not in ["Horn1981", "O1"]:
raise RuntimeError("method must be either Horn1981 or O1")
if method == "O1":
dzdy2, dzdx2 = np.gradient(z)
if method == "Horn1981":
dzdy, dzdx = np.gradient(z)
dzdy2, dzdx2 = np.zeros(dzdy.shape), np.zeros(dzdx.shape)
# average [-1,0,0,1] gradient values at each point, in each direction
# at edges, use 3 points instead of 4
eind = np.asarray([0, 0, 1])
dzdx2[0, :] = np.mean(dzdx[eind, :], axis=0)
dzdy2[:, 0] = np.mean(dzdy[:, eind], axis=1)
eind = np.asarray([-2, -1, -1])
dzdx2[-1, :] = np.mean(dzdx[eind, :], axis=0)
dzdy2[:, -1] = np.mean(dzdy[:, eind], axis=1)
ind = np.asarray([-1, 0, 0, 1])
for n in range(1, dzdx.shape[0] - 1):
dzdx2[n, :] = np.mean(dzdx[n + ind, :], axis=0)
for n in range(1, dzdy.shape[1] - 1):
dzdy2[:, n] = np.mean(dzdy[:, n + ind], axis=1)
# calculate spacing
dx = re * dtr * np.abs(lon[0] - lon[1])
dy = re * dtr * np.abs(lat[0] - lat[1])
dx2d = dx * np.tile(np.cos(dtr * lat), (lon.size, 1)).T
dy2d = dy * np.ones((lat.size, lon.size))
return [dzdx2 / dx2d, dzdy2 / dy2d]
def std_dev(x):
return np.power(np.mean(np.power((x - np.mean(x)), 2)), 0.5)
def quadratic(coefs, root=0, eps=1e-6):
ak, bk, ck = coefs
if (bk**2 - 4 * ak * ck) < 0:
# if negative due to roundoff, adjust a coefficient get zero
if np.abs(bk**2 - 4 * ak * ck) < eps:
ck = bk**2 / (4 * ak) * (1 - eps)
else:
raise RuntimeError(
"cannot solve quadratic with these values \
{:.2f} {:.2f} {:.2f}".format(
ak, bk, ck
)
)
dm_roots = [
(-bk + np.sqrt(bk**2 - 4 * ak * ck)) / (2 * ak),
(-bk - np.sqrt(bk**2 - 4 * ak * ck)) / (2 * ak),
]
debug("quadratic roots ", dm_roots)
return dm_roots[root]
def _four_point_laplacian(mask):
# mask is assumed to be 0-1 (used to multiply results)
jm = mask.shape[0]
im = mask.shape[1]
laplacian = -4.0 * np.copy(mask)
laplacian += mask * np.roll(mask, 1, axis=1) + mask * np.roll(mask, -1, axis=1)
temp = np.roll(mask, 1, axis=0)
temp[0, :] = mask[1, :]
laplacian += mask * temp
temp = np.roll(mask, -1, axis=0)
temp[jm - 1, :] = mask[jm - 2, :]
laplacian += mask * temp
return np.abs(laplacian)
def _inside_indices_buffer(data, buf=1, mask=None):
# return indices of non-edge points (outside of buf)
if mask is None:
mask = np.array([]).astype(int)
a = np.arange(data.size)
offset = int(data.shape[1])
top = []
for i in range(buf):
top.extend((i * offset + np.arange(offset)[buf:-buf]).tolist())
top = np.array(top, dtype=int)
bottom = data.size - 1 - top
left = []
for i in range(buf):
left.extend(np.arange(i, data.size, offset))
left = np.array(left, dtype=int)
right = data.size - 1 - left
exclude = np.unique(np.concatenate([top, left, right, bottom, mask]))
inside = np.delete(a, exclude)
return inside
def _expand_mask_buffer(mask, buf=1):
omask = np.copy(mask)
# this will use less memory by not accumulating all indices
# prior to assigning mask points to 1
inside = _inside_indices_buffer(mask, buf=buf)
lmask = np.where(_four_point_laplacian(mask) > 0, 1, 0)
ind = inside[(lmask.flat[inside] > 0)]
offset = mask.shape[1]
for k in range(-buf, buf + 1):
if k != 0:
omask.flat[ind + k] = 1
for j in range(buf):
j1 = j + 1
# upper
omask.flat[ind + k + j1 * offset] = 1
# lower
omask.flat[ind + k - j1 * offset] = 1
return omask
def identify_basins(dem, basin_thresh=0.25, niter=10, buf=1):
# create basin mask, 1 in basin, 0 outside of basin
# flat areas often have large dtnd and small hand values
# due to flowpaths in flooded/inflated part of dem
imask = np.zeros(dem.shape)
# find most common elevation value
udem, ucnt = np.unique(dem, return_counts=True)
ufrac = ucnt / dem.size
ind = np.where(ufrac > basin_thresh)[0]
if ind.size > 0:
for i in ind:
# if elevation is zero, assume open water and tighten tolerance
eps = 1e-2
if np.abs(udem[i]) < eps:
eps = 1e-6
imask[np.abs(dem - udem[i]) < eps] = 1
# remove isolated points
for n in range(niter):
imask = _expand_mask_buffer(imask, buf=buf)
# remove points each iteration
eps = 1e-2
for i in ind:
# if elevation is zero, assume open water and tighten tolerance
if np.abs(udem[i]) < eps:
eps = 1e-6
imask[_four_point_laplacian(1 - imask) >= 3] = 0
return imask