smrf/utils/wind/model.py
from __future__ import print_function
import os
# import matplotlib.pyplot as plt
# import progressbar
from datetime import datetime
import netCDF4 as nc
import numpy as np
from smrf.utils.wind import wind_c
class wind_model():
"""
Estimating wind speed and direction is complex terrain can be difficult due
to the interaction of the local topography with the wind. The methods
described here follow the work developed by Winstral and Marks (2002) and
Winstral et al. (2009) :cite:`Winstral&Marks:2002` :cite:`Winstral&al:2009`
which parameterizes the terrain based on the upwind direction. The
underlying method calulates the maximum upwind slope (maxus) within a
search distance to determine if a cell is sheltered or exposed.
The azimuth **A** is the direction of the prevailing wind for which the
maxus value will be calculated within a maximum search distance **dmax**.
The maxus (**Sx**) parameter can then be estimated as the maximum value of
the slope from the cell of interest to all of the grid cells along the
search vector. The efficiency in selection of the maximum value can be
increased by using the techniques from the horizon functio which calculates
the horizon for each pixel. Therefore, less calculations can be performed.
Negative **Sx** values indicate an exposed pixel location (shelter pixel
was lower) and positive **Sx** values indicate a sheltered pixel (shelter
pixel was higher).
After all the upwind direction are calculated, the average **Sx** over a
window is calculated. The average **Sx** accounts for larger lanscape
obsticles that may be adjacent to the upwind direction and affect the flow.
A window size in degrees takes the average of all **Sx**.
Args:
x: array of x locations
y: array of y locations
dem: matrix of the dem elevation values
nthread: number of threads to use for maxus calculation
"""
def __init__(self, x, y, dem, nthreads=1):
self.x = x
self.y = y
self.dem = dem
self.nx = len(x)
self.ny = len(y)
self.ngrid = self.ny * self.nx
self.nthreads = nthreads
self.dx = np.abs(x[1] - x[0])
self.dy = np.abs(y[1] - y[0])
X, Y = np.meshgrid(np.arange(0, self.nx), np.arange(0, self.ny))
self.X = X
self.Y = Y
self.shape = X.shape
def maxus(self, dmax, inc=5, inst=2, out_file='smrf_maxus.nc'):
"""
Calculate the maxus values
Args:
dmax: length of outlying upwind search vector (meters)
inc: increment between direction calculations (degrees)
inst: Anemometer height (meters)
out_file: NetCDF file for output results
Returns:
None, outputs maxus array straight to file
"""
if (dmax % self.dx != 0):
raise ValueError('dmax must divide evenly into the DEM')
self.dmax = dmax
self.inc = inc
self.inst_hgt = inst
# All angles that model will consider.
swa = np.arange(0, 360, inc)
self.directions = swa
# initialize the output file
self.out_file = out_file
self.type = 'maxus'
ex_att = {}
ex_att['dmax'] = dmax
# initialize output
self.output_init(self.type, out_file, ex_att=ex_att)
# run model over range in wind directions
for i, angle in enumerate(swa):
self.maxus_val = self.maxus_angle(angle, self.dmax)
self.output(self.type, i)
def tbreak(self, dmax, sepdist, inc=5, inst=2, out_file='smrf_tbreak.nc'):
"""
Calculate the topobreak values
Args:
dmax: length of outlying upwind search vector (meters)
sepdist: length of local max upwind slope search vector (meters)
angle: middle upwind direction around which to run model (degrees)
inc: increment between direction calculations (degrees)
inst: Anemometer height (meters)
out_file: NetCDF file for output results
Returns:
None, outputs maxus array straight to file
"""
if (sepdist % self.dx != 0) | (dmax % self.dx != 0):
raise ValueError(
'sepdist and dmax must divide evenly into the DEM')
self.dmax = dmax
self.sepdist = sepdist
self.inc = inc
self.inst_hgt = inst
# All angles that model will consider.
swa = np.arange(0, 360, inc)
self.directions = swa
# initialize the output file
self.out_file = out_file
self.type = 'tbreak'
# extra attributes
ex_att = {}
ex_att['dmax'] = dmax
ex_att['sepdist'] = sepdist
# initialize output
self.output_init(self.type, out_file, ex_att=ex_att)
# run model over range in wind directions
for i, angle in enumerate(swa):
# calculate the maxus value
maxus_outlying = self.maxus_angle(angle, self.dmax)
# calculate the local maxus value
maxus_local = self.maxus_angle(angle, self.sepdist)
self.maxus_val = maxus_local - maxus_outlying
self.output(self.type, i)
def maxus_angle(self, angle, dmax):
"""
Calculate the maxus for a single direction for a search distance dmax
Note:
This will produce different results than the original maxus
program. The differences are due to:
1. Using dtype=double for the elevations
2. Using different type of search method to find the endpoints.
However, if the elevations are rounded to integers, the cardinal
directions will reproduce the original results.
Args:
angle: middle upwind direction around which to run model (degrees)
dmax: length of outlying upwind search vector (meters)
Returns:
maxus: array of maximum upwind slope values within dmax
"""
print("Calculating maxus for direction: {}".format(angle))
angle *= np.pi / 180
# calculate the endpoints
# accually use the distances to ensure that we are searching far enough
Xi = self.X*self.dx + dmax * np.cos(angle-np.pi/2)
Yi = self.Y*self.dy + dmax * np.sin(angle-np.pi/2)
self.Xi = np.floor(Xi/self.dx + 0.5)
self.Yi = np.floor(Yi/self.dy + 0.5)
# underlying C code similar to Adams
maxus = wind_c.call_maxus(self.x, self.y, self.dem, self.X, self.Y,
self.Xi, self.Yi, self.inst_hgt,
self.nthreads)
# # my interpretation of the calculations in Python form
# maxus = np.zeros((self.ngrid,))
# pbar = progressbar.ProgressBar(max_value=self.ngrid)
# j = 0
# for index in range(5000, self.ngrid):
# maxus[index] = self.find_maxus(index)
# j += 1
# pbar.update(j)
# if j > 4999:
# break
# pbar.finish()
# maxus = np.reshape(maxus, self.shape)
# correct for values that are their own horizon
maxus[maxus <= -89.0] = 0
return maxus
def windower(self, maxus_file, window_width, wtype):
"""
Take the maxus output and average over the window width
Args:
maxus_file: location of the previously calculated maxus values
window_width: window width about the wind direction
wtype: type of wind calculation 'maxus' or 'tbreak'
Return:
New file containing the windowed values
"""
# open the previous file and get the directions
n = nc.Dataset(maxus_file, 'r')
directions = n.variables['direction'][:]
self.directions = directions
# create a new file based on the old file
name = os.path.splitext(maxus_file)
out_file = "%s_%iwindow.nc" % (name[0], window_width)
self.output_init(wtype, out_file)
self.out_file = out_file
# determine which directions are required for each single direction
window_width /= 2
inc = np.mean(np.diff(directions), dtype=int)
for i, d in enumerate(directions):
print("Windowing direction {}".format(d))
# determine which directions to include
window_start = d - window_width
window_end = d + window_width
# to ensure that it contains the end points
sl = np.arange(window_start, window_end+1, inc)
# correct for edge effects
sl[sl < 0] = sl[sl < 0] + 360
sl[sl > 360] = sl[sl > 360] - 360
# determine the indicies to the input file
idx = self.ismember(directions, sl)
# grab all the data for all directions and average
self.maxus_val = np.mean(n.variables[wtype][idx, :], axis=0)
# put it into the output file
self.output(wtype, i)
n.close()
def ismember(self, a, b):
bind = {}
for i, elt in enumerate(b):
if elt not in bind:
bind[elt] = True
return [bind.get(itm, False) for itm in a]
def find_maxus(self, index):
"""
Calculate the maxus given the start and end point
Args:
index: index to a point in the array
Returns:
maxus value for the point
"""
start_point = np.unravel_index(index, self.shape)
# determine the points along the endpoint line
end_point = (self.Yi[start_point], self.Xi[start_point])
p = self.bresenham(start_point, end_point)
# ensure the cases where it's on the edge
p = np.delete(p, np.where(p[:, 0] < 0)[0], axis=0)
p = np.delete(p, np.where(p[:, 1] < 0)[0], axis=0)
p = np.delete(p, np.where(p[:, 0] > self.ny)[0], axis=0)
p = np.delete(p, np.where(p[:, 1] > self.nx)[0], axis=0)
# determine the relative heights along the path
h = self.dem[p[:, 0], p[:, 1]] # - (self.inst_hgt + self.dem[index])
# find the horizon for each pixel along the path
hord = self.hord(self.x[p[:, 1]], self.y[p[:, 0]], h)
# calculate the angle to that point
pt = p[hord[0], :] # point that was found for horizon
d = np.sqrt(np.power(self.x[pt[1]] - self.x[start_point[1]], 2) +
np.power(self.y[pt[0]] - self.y[start_point[0]], 2))
slope = (h[hord[0]] - (h[0] + self.inst_hgt)) / d
maxus = np.arctan(slope) * 180 / np.pi
return maxus
def bresenham(self, start, end):
"""
Python implementation of the Bresenham algorthim to find
all the pixels that a line between start and end interscet
Args:
start: list of start point
end: list of end point
Returns:
Array path of all points between start and end
"""
# start = list(start)
# end = list(end)
path = []
x0 = start[0]
y0 = start[1]
x1 = end[0]
y1 = end[1]
steep = abs(y1 - y0) > abs(x1 - x0)
backward = x0 > x1
if steep:
x0, y0 = y0, x0
x1, y1 = y1, x1
if backward:
x0, x1 = x1, x0
y0, y1 = y1, y0
dx = x1 - x0
dy = abs(y1 - y0)
error = dx / 2
y = y0
if y0 < y1:
ystep = 1
else:
ystep = -1
for x in range(x0, x1+1):
if steep:
path.append((y, x))
else:
path.append((x, y))
error -= dy
if error <= 0:
y += ystep
error += dx
if backward:
path.reverse()
return np.array(path)
def hord(self, x, y, z):
'''
Calculate the horizon pixel for all z
This mimics the simple algorthim from Dozier 1981 but
was adapated for use in finding the maximum upwind slope
Works backwards from the end but looks forwards for
the horizon
Args:
x: x locations for the points
y: y locations for the points
z: elevations for the points
Returns:
array of the horizon index for each point
'''
N = len(z) # number of points to look at
# offset = 1 # offset from current point to start looking
# preallocate the h array
h = np.zeros(N, dtype=int)
h[N-1] = N-1
i = N - 2
# work backwarks from the end for the pixels
while i >= 0:
h[i] = i
j = i + 1 # looking forward
found = False
while not found:
d_i = np.sqrt(np.power(x[i] - x[j], 2) +
np.power(y[i] - y[j], 2))
d_h = np.sqrt(np.power(x[i] - x[h[j]], 2) +
np.power(y[i] - y[h[j]], 2))
pt_i = self._slope(0, z[i]+self.inst_hgt, d_i, z[j])
pt_h = self._slope(0, z[i]+self.inst_hgt, d_h, z[h[j]])
if (pt_i < pt_h):
if (j == N-1):
found = True
h[i] = j
else:
j = h[j]
else:
found = True
if (pt_i > pt_h):
h[i] = j
else:
h[i] = h[j]
i -= 1
return h
def _slope(self, xi, zi, xj, zj):
'''
Slope between the two points
'''
return (zj - zi) / (xj - float(xi))
def output_init(self, ptype, filename, ex_att=None):
"""
Initialize a NetCDF file for outputing the maxus values or tbreak
Args:
ptype: type of calculation that will be saved, either 'maxus' or
'tbreak'
filename: filename to save the output into
ex_att: extra attributes to add
"""
if ptype == 'maxus':
var = 'maxus'
desc = 'Maximum upwind slope'
elif ptype == 'tbreak':
var = 'tbreak'
desc = 'tbreak'
else:
raise ValueError('''Could not determine what to output, check type
value (maxus or tbreak)''')
dimensions = ('Direction', 'y', 'x')
s = nc.Dataset(filename, 'w', 'NETCDF4')
s.createDimension(dimensions[0], len(self.directions))
s.createDimension(dimensions[1], self.ny)
s.createDimension(dimensions[2], self.nx)
# create the variables
s.createVariable('direction', 'i', dimensions[0])
s.createVariable('y', 'f', dimensions[1])
s.createVariable('x', 'f', dimensions[2])
s.createVariable(var, 'f', dimensions)
# define some attributes
setattr(s.variables['y'], 'units', 'meters')
setattr(s.variables['y'], 'description', 'UTM, north south')
setattr(s.variables['x'], 'units', 'meters')
setattr(s.variables['x'], 'description', 'UTM, east west')
setattr(s.variables['direction'], 'units', 'bearing')
setattr(s.variables['direction'], 'description',
'Wind direction from North')
setattr(s.variables[var], 'units', 'angle')
setattr(s.variables[var], 'description', desc)
setattr(s, 'dateCreated', datetime.now().isoformat())
# set attributes
if ex_att is not None:
for key, value in ex_att.items():
setattr(s, key, value)
s.variables['y'][:] = self.y
s.variables['x'][:] = self.x
def output(self, ptype, index):
"""
Output the data into the out file that has previously been initialized.
Args:
ptype: type of calculation that will be saved, either 'maxus'
or 'tbreak'
index: index into the file for where to place the output
"""
s = nc.Dataset(self.out_file, 'r+')
s.variables['direction'][:] = self.directions
s.variables[ptype][index, :] = self.maxus_val
s.close()