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terrain_utils.py
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terrain_utils.py
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import numpy as np
from scipy.stats import expon
from multiprocessing import Pool
from functools import partial
from rh_logging import info, warning, error, debug
"""
calc_network_length: calculate length of stream network
set_aspect_to_hillslope_mean_parallel: assign mean value to all points in a catchment
set_aspect_to_hillslope_mean_serial: assign mean value to all points in a catchment
TailIndex: return indices of tail of a distribution
SpecifyHandBounds: define bounds used to bin HAND distribution using aspect information
SpecifyHandBoundsNoAspect: define bounds used to bin HAND distribution
_calculate_hillslope_mean_aspect: calculate the vector-mean aspect value
_four_point_laplacian: calculate the laplacian of a binary mask
_inside_indices_buffer: return indices of a 2d array excluding those within buffer of edges
"""
# Parameters
# degrees to radians
dtr = np.pi / 180.0
# earth radius [m]
re = 6.371e6
# function definitions
def calc_network_length(
channel_ids,
channel_coords,
dem,
fdir,
lon,
lat,
latdir="south_to_north",
):
dirmap = (64, 128, 1, 2, 4, 8, 16, 32)
dir_to_index_dict = {dirmap[n]: n for n in range(len(dirmap))}
fjm, fim = dem.shape
dmask = np.zeros((fjm, fim))
# W -> E
addi = [0, 1, 1, 1, 0, -1, -1, -1]
# determine direction of latitude coordinates
if latdir == "south_to_north":
# S -> N
addj = [1, 1, 0, -1, -1, -1, 0, 1]
if latdir == "north_to_south":
# N -> S
addj = [-1, -1, 0, 1, 1, 1, 0, -1]
unique_ids = np.unique(channel_ids).astype(int)
reach_length = []
reach_elevation_difference = []
for n in range(unique_ids.size):
ind = np.where(unique_ids[n] == channel_ids)[0]
# record network elevation and indices
reach_elev = []
reach_j = []
reach_i = []
for k in range(ind.size):
ni = np.argmin(np.abs(channel_coords[ind[k], 0] - lon))
nj = np.argmin(np.abs(channel_coords[ind[k], 1] - lat))
reach_elev.append(dem[nj, ni])
reach_j.append(nj)
reach_i.append(ni)
# locate highest elevation point in reach
k1 = np.argmax(np.asarray(reach_elev))
j0, i0 = reach_j[k1], reach_i[k1]
# record index of each point in dmask and upstream neighbor
if fdir[j0, i0] < 1:
continue
else:
dmask_undx = [-1]
dmask_ndx = [[j0, i0]]
# follow gridded directions downstream
cnt = 0
while fdir[j0, i0] > 0 and cnt < fim * fjm:
if dmask[j0, i0] >= 1:
break
dmask_undx.append([j0, i0])
dmask[j0, i0] += 1
ddir = fdir[j0, i0]
m = dir_to_index_dict[ddir]
i0 += addi[m]
j0 += addj[m]
check_i = np.logical_or(i0 < 0, i0 >= fim)
check_j = np.logical_or(j0 < 0, j0 >= fjm)
if check_i or check_j or (fdir[j0, i0] < 1):
del dmask_undx[-1]
break
dmask_ndx.append([j0, i0])
cnt += 1
# sum elements of reach
length = 0
elevation_difference = 0
for k in range(1, len(dmask_ndx)):
j1, i1 = dmask_ndx[k]
j2, i2 = dmask_undx[k]
dlon = lon[i1] - lon[i2]
dlat = lat[j1] - lat[j2]
dist = np.power(np.sin(dtr * dlat / 2), 2) + np.cos(dtr * lat[j1]) * np.cos(
dtr * lat[j2]
) * np.power(np.sin(dtr * dlon / 2), 2)
length += re * 2 * np.arctan2(np.sqrt(dist), np.sqrt(1 - dist))
if k == 1:
elevation_difference += dem[j2, i2]
if k == (len(dmask_ndx) - 1):
elevation_difference -= dem[j1, i1]
reach_length.append(length)
reach_elevation_difference.append(elevation_difference)
reach_length = np.asarray(reach_length)
reach_elevation_difference = np.asarray(reach_elevation_difference)
total_reach_length = np.sum(reach_length)
reach_slopes = (
reach_elevation_difference[reach_length > 0] / reach_length[reach_length > 0]
)
# weight average slope by reach length
w = reach_length[reach_length > 0]
mean_reach_slope = np.sum(w * reach_slopes) / np.sum(w)
debug(
"mean reach length and elevation difference ",
np.mean(reach_length[reach_length > 0]),
np.mean(reach_elevation_difference[reach_length > 0]),
)
debug("mean reach slope ", mean_reach_slope)
return {"length": total_reach_length, "slope": mean_reach_slope}
def _calculate_hillslope_mean_aspect(
did, drainage_id=None, aspect=None, hillslope=None, hillslope_types=None
):
# input arrays should be flattened
out = []
dind = np.where(drainage_id == did)[0]
# type 4 (channels) will be combined with other types, so decrement number in n loop
for n in hillslope_types[: hillslope_types.size - 1]:
# combine channels with other aspects
l2 = np.logical_or(hillslope[dind] == 4, hillslope[dind] == n)
ind = dind[np.where(l2)[0]]
if ind.size > 0:
mean_aspect = (
np.arctan2(
np.mean(np.sin(dtr * aspect[ind])),
np.mean(np.cos(dtr * aspect[ind])),
)
/ dtr
)
if mean_aspect < 0:
mean_aspect += 360.0
out.append([did, n, mean_aspect, ind])
return out
def set_aspect_to_hillslope_mean_parallel(
drainage_id, aspect, hillslope, npools=4, chunksize=5e3
):
# input arrays are 2d
l1 = np.logical_and(np.isfinite(drainage_id), drainage_id > 0)
uid = np.unique(drainage_id[l1])
hillslope_types = np.unique(hillslope[hillslope > 0]).astype(int)
aspect2d_catchment_mean = np.zeros(aspect.shape)
if uid.size == 0:
return aspect2d_catchment_mean
# set up multiprocessing pool
if npools == 0:
pool1 = Pool()
else:
pool1 = Pool(npools)
try:
# chunk data to reduce cost of array searches (i.e. np.where)
nchunks = int(np.max([1, int(uid.size // chunksize)]))
chunksize = np.min([chunksize, uid.size - 1])
for n in range(nchunks):
n1, n2 = int(n * chunksize), int((n + 1) * chunksize)
if n == nchunks - 1:
n2 = uid.size - 1
if n1 == n2: # single drainage case
cind = np.where(drainage_id.flat == uid[n1])[0]
else:
cind = np.where(
np.logical_and(
drainage_id.flat >= uid[n1], drainage_id.flat < uid[n2]
)
)[0]
x = pool1.map(
partial(
_calculate_hillslope_mean_aspect,
drainage_id=drainage_id.flat[cind],
aspect=aspect.flat[cind],
hillslope=hillslope.flat[cind],
hillslope_types=hillslope_types,
),
uid[n1 : n2 + 1],
)
for x2 in x:
for tmp in x2:
if len(tmp) > 0:
_, mean_aspect, ind = tmp[1:]
aspect2d_catchment_mean.flat[cind[ind]] = mean_aspect
finally:
pool1.close()
pool1.join()
return aspect2d_catchment_mean
def set_aspect_to_hillslope_mean_serial(drainage_id, aspect, hillslope, chunksize=5e2):
l1 = np.logical_and(np.isfinite(drainage_id), drainage_id > 0)
uid = np.unique(drainage_id[l1])
hillslope_types = np.unique(hillslope[hillslope > 0]).astype(int)
aspect2d_catchment_mean = np.zeros(aspect.shape)
# chunk data to reduce cost of array searches (i.e. np.where)
nchunks = int(np.max([1, int(uid.size // chunksize)]))
chunksize = np.min([chunksize, uid.size - 1])
for n in range(nchunks):
n1, n2 = int(n * chunksize), int((n + 1) * chunksize)
if n == nchunks - 1:
n2 = uid.size - 1
if n1 == n2: # single drainage case
cind = np.where(drainage_id.flat == uid[n1])[0]
else:
cind = np.where(
np.logical_and(drainage_id.flat >= uid[n1], drainage_id.flat < uid[n2])
)[0]
# search a subset of array in each chunk
for did in uid[n1 : n2 + 1]:
dind = cind[np.where(drainage_id.flat[cind] == did)[0]]
# type 4 (channels) will be combined with other types, so decrement number in n loop
for n in hillslope_types[: hillslope_types.size - 1]:
# combine channels with other aspects
l2 = np.logical_or(hillslope.flat[dind] == 4, hillslope.flat[dind] == n)
ind = dind[np.where(l2)[0]]
if ind.size > 0:
mean_aspect = (
np.arctan2(
np.mean(np.sin(dtr * aspect.flat[ind])),
np.mean(np.cos(dtr * aspect.flat[ind])),
)
/ dtr
)
if mean_aspect < 0:
mean_aspect += 360.0
aspect2d_catchment_mean.flat[ind] = mean_aspect
return aspect2d_catchment_mean
def std_dev(x):
return np.power(np.mean(np.power((x - np.mean(x)), 2)), 0.5)
def TailIndex(fdtnd, fhand, npdf_bins=5000, hval=0.05):
# return indices of input arrays with tails removed
std_dtnd = std_dev((fdtnd[fhand > 0]))
fit_loc, fit_beta = expon.fit(fdtnd[fhand > 0] / std_dtnd)
rv = expon(loc=fit_loc, scale=fit_beta)
pbins = np.linspace(0, np.max(fdtnd), npdf_bins)
rvpdf = rv.pdf(pbins / std_dtnd)
r1 = np.argmin(np.abs(rvpdf - hval * np.max(rvpdf)))
ind = np.where(fdtnd < pbins[r1])[0]
return ind
def SpecifyHandBounds(fhand, faspect, aspect_bins, bin1_max=2, BinMethod="fastsort"):
"""
Determine hand bounds from a (flattened) hand array such
that approximately equal areas are obtained, subject to the
constraint that the first bin is less than 2 meters. In that
case, the area in the first bin may be smaller than the others.
Currently, 4 hand bins are created.
"""
std_hand = std_dev(fhand[fhand > 0])
# available methods: fit hand, explicit sum, fast sort
if BinMethod == "fithand":
_, fit_beta = expon.fit(fhand[fhand > 0].flat / std_hand)
xbin1 = np.min([-fit_beta * np.log(1 / 4), bin1_max / std_hand])
x33 = -fit_beta * np.log(2 / 3) + xbin1
x66 = -fit_beta * np.log(1 / 3) + xbin1
hand_bin_bounds = [0, xbin1 * std_hand, x33 * std_hand, x66 * std_hand, 1e6]
elif BinMethod == "explicitsum":
nhist = np.round(np.max(fhand)).astype(int)
nhist = np.max([int(200), nhist])
hbins = np.linspace(0, np.max(fhand), nhist + 1)
hind = np.where(np.logical_and(fhand >= hbins[0], fhand < hbins[1]))[0]
# replace bins with smaller range if histogram skewed towards small values
if (hind.size / fhand.size) > 0.5:
hbin1 = hbins[1]
hbins[:-1] = np.linspace(0, hbin1, nhist)
histo_hand = np.zeros((nhist))
for h in range(nhist):
hind = np.where(np.logical_and(fhand >= hbins[h], fhand < hbins[h + 1]))[0]
histo_hand[h] = hind.size
cum_histo_hand = np.zeros((nhist))
for h in range(nhist):
cum_histo_hand[h] = np.sum(histo_hand[: h + 1])
cum_histo_hand = cum_histo_hand / np.sum(histo_hand)
b25 = hbins[np.argmin(np.abs(0.25 - cum_histo_hand)) + 1]
# first bin must be <= bin1_max
if b25 > bin1_max:
b33 = hbins[np.argmin(np.abs(0.33 - cum_histo_hand)) + 1]
b66 = hbins[np.argmin(np.abs(0.66 - cum_histo_hand)) + 1]
if b33 == b66:
# just shift b66 for now
b66 = 2 * b33 - bin1_max
hand_bin_bounds = [0, bin1_max, b33, b66, 1e6]
else:
b50 = hbins[np.argmin(np.abs(0.50 - cum_histo_hand)) + 1]
b75 = hbins[np.argmin(np.abs(0.75 - cum_histo_hand)) + 1]
hand_bin_bounds = [0, b25, b50, b75, 1e6]
elif BinMethod == "fastsort":
quartiles = np.asarray([0.25, 0.5, 0.75, 1.0])
# if many zeros exist, both bins 0 and 1 may be equal to zero
hand_sorted = np.sort(fhand[fhand > 0])
hand_bin_bounds = np.asarray(
[0]
+ [
hand_sorted[int(quartiles[qi] * hand_sorted.size - 1)]
for qi in range(quartiles.size)
]
)
# first bin must be <= bin1_max unless too few
# points present in bin1_max bin
if hand_bin_bounds[1] > bin1_max:
# ensure enough points exist in the lowland bin
# for each aspect bin
min_aspect_fraction = 0.01
for asp_ndx in range(len(aspect_bins)):
if asp_ndx == 0:
l1 = np.logical_or(
faspect >= aspect_bins[asp_ndx][0],
faspect < aspect_bins[asp_ndx][1],
)
else:
l1 = np.logical_and(
faspect >= aspect_bins[asp_ndx][0],
faspect < aspect_bins[asp_ndx][1],
)
hand_asp_sorted = np.sort(fhand[l1])
if hand_asp_sorted.size > 0:
bmin = hand_asp_sorted[
int(min_aspect_fraction * hand_asp_sorted.size - 1)
]
else:
bmin = bin1_max
if bmin > bin1_max:
warning(
"Too few hand values < "
+ str(bin1_max)
+ "; setting lowest bin to "
+ str(bmin)
)
bin1_max = bmin
tmp = hand_sorted[hand_sorted > bin1_max]
if int(0.33 * tmp.size - 1) == -1:
warning("bad tmp ")
warning(tmp.size, bin1_max, hand_asp_sorted.size)
b33 = tmp[int(0.33 * tmp.size - 1)]
b66 = tmp[int(0.66 * tmp.size - 1)]
if b33 == b66:
# just shift b66 for now
b66 = 2 * b33 - bin1_max
hand_bin_bounds = [0, bin1_max, b33, b66, 1e6]
if (len(hand_bin_bounds) - 1) != 4:
raise RuntimeError("bad hand bounds")
return hand_bin_bounds
def SpecifyHandBoundsNoAspect(fhand, nbins=4):
"""
Determine hand bounds from a (flattened) hand array such
that approximately equal areas are obtained, subject to the
constraint that the first bin is less than 2 meters. In that
case, the area in the first bin may be smaller than the others.
Currently, 4 hand bins are created.
"""
# if many zeros exist, both bins 0 and 1 may be equal to zero
hand_sorted = np.sort(fhand[fhand > 0])
if nbins == 2:
quartiles = np.asarray([0.5, 1.0])
if nbins == 3:
quartiles = np.asarray([0.33, 0.66, 1.0])
if nbins == 4:
quartiles = np.asarray([0.25, 0.5, 0.75, 1.0])
hand_bin_bounds = np.asarray(
[0]
+ [
hand_sorted[int(quartiles[qi] * hand_sorted.size - 1)]
for qi in range(quartiles.size)
]
)
if (len(hand_bin_bounds) - 1) != nbins:
raise RuntimeError("bad hand bounds")
return hand_bin_bounds