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 . import wind_c [docs]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 [docs] 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) [docs] 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) [docs] 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 [docs] 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() [docs] 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] [docs] 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]) # # determine the distrance along the path # xpath = self.x[p[:,1]] # ypath = self.y[p[:,0]] # # xstart = self.x[start_point[1]] # ystart = self.y[start_point[0]] # # dpath = np.sqrt(np.power(xpath - xstart, 2) + np.power(ypath - ystart, 2)) # # # calculate the slope to each cell # rise = h - (h[0] + self.inst_hgt) # # slope = rise/dpath # # np.max(np.abs(slope[1:])) # 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 [docs] 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) [docs] 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)) [docs] 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 [docs] 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()