def get_approximate_discharge_timeseries(sww_filename,
polylines,
desired_ds=0.5,
k_nearest_neighbours=1,
search_mesh=True,
verbose=True):
"""Given an sww_filename and a dictionary of 1D polylines, estimate the
discharge timeseries through each polyline by interpolating the centroid
uh/vh onto evenly spaced points on the polyline (with spacing ~ desired_ds),
computing the flux normal to the line, and using the trapezoidal rule to
integrate it.
The interpolation of centroid uh/vh onto the polyline points can be either
based on 'k-nearest-neighbours', or a direct-search of the mesh triangles.
The former can be fast and allow for smoothing, while the latter is often
still fast enough, and might be more accurate.
The positive/negative discharge direction is determined from the polyline.
Consider a river channel. If the polyline begins on the left-bank and ends
on the right bank (left/right defined when facing downstream) then
discharge in the downstream direction is positive.
WARNING: The result is approximate only because ANUGA's internal edge
fluxes are derived differently (with the reimann solver), and because the
interpolation does not follow ANUGA's, and because your transect might not
be exactly perpendicular to the flow. None of the methods give an exact
result at present.
Errors can be significant where the solution is changing rapidly. It may
be worth comparing multiple cross-sections in the vicinity of the site of
interest [covering different mesh triangles, with slightly different
orientations].
@param sww_filename name of sww file
@param polylines dictionary of polylines, e.g.
polylines = {
'Xsection1': [ [495., 1613.], [495., 1614.], [496., 1615.] ],
'Xsection2': [ [496., 1614.], [4968., 1615.] ]
}
@param desired_ds point spacing used for trapozoidal integration on
polylines
@param k_nearest_neighbours number of nearest neighbours used for
interpolation of uh/vh onto polylines
@param search_mesh If True AND k_nearest_neighbours=1, we search the
mesh vertices to find the triangle containing our point. Otherwise
do nearest-neighbours on the triangle centroids to estimate the
'nearest' triangle
@param verbose
@return a list of length 2 with the output_times as a numpy array, and a
dictionary with the flow timeseries
"""
if (search_mesh) & (k_nearest_neighbours > 1):
msg = 'k_nearest_neighbours must be 1 when search_mesh is true'
raise Exception(msg)
# 2 ways to associate transect points with triangle values
# 1) knn on centroids, or
# 2) directly search for mesh triangles containing transect points
# 1 can be faster + allows for smoothing, but 2 might be usually better
use_knn = (search_mesh == False) | (k_nearest_neighbours != 1)
if use_knn:
# Centroids are used for knn
p = util.get_centroids(sww_filename, timeSlices=0)
sww_xy = numpy.vstack([p.x + p.xllcorner,
p.y + p.yllcorner]).transpose()
point_index_kdtree = scipy.spatial.cKDTree(sww_xy)
else:
# Vertices are used for mesh search
p = util.get_output(sww_filename, timeSlices=0)
# To conserve memory read from netcdf directly
from anuga.file.netcdf import NetCDFFile
sww_nc = NetCDFFile(sww_filename)
ud = sww_nc.variables['xmomentum_c']
vd = sww_nc.variables['ymomentum_c']
output_times = sww_nc.variables['time'][:]
discharge_series = {}
for pk in polylines.keys():
if verbose: print pk
pl_full = polylines[pk]
for segment_num in range(len(pl_full) - 1):
pl = [pl_full[segment_num], pl_full[segment_num + 1]]
segment_length = ( (pl[0][0] - pl[1][0])**2 +\
(pl[0][1] - pl[1][1])**2 )**0.5
# Normal vector
n1 = (pl[0][1] - pl[1][1]) / segment_length
n2 = -(pl[0][0] - pl[1][0]) / segment_length
# Approximate segment as npts points
npts = int(numpy.ceil(segment_length / (desired_ds) + 1.0))
gridXY = numpy.vstack([
scipy.linspace(pl[0][0], pl[1][0], num=npts),
scipy.linspace(pl[0][1], pl[1][1], num=npts)
]).transpose()
# Actual distance between points
ds = (numpy.diff(gridXY[:, 0])**2 +
numpy.diff(gridXY[:, 1])**2)**0.5
ds_trapz = numpy.hstack([ds[0], (ds[0:-1] + ds[1:]), ds[-1]]) * 0.5
if verbose: print 'Finding triangles containing point'
if use_knn:
point_distance, point_indices = point_index_kdtree.query(
gridXY, k=k_nearest_neighbours)
else:
gridXY_offset = gridXY * 0.
gridXY_offset[:, 0] = gridXY[:, 0] - p.xllcorner
gridXY_offset[:, 1] = gridXY[:, 1] - p.yllcorner
point_indices = numpy.zeros(gridXY.shape[0]).astype(int)
# Provide the order to search the points (might be faster?)
v1 = p.vols[:, 0]
search_order_update_freq = 1
for i in range(gridXY.shape[0]):
# For efficiency, we don't recompute the order to search points
# everytime
if i % search_order_update_freq == 0:
# Update the mesh triangle search order
first_vertex_d2 = (p.x[v1] - gridXY_offset[i,0])**2 +\
(p.y[v1] - gridXY_offset[i,1])**2
search_order = first_vertex_d2.argsort().tolist()
# Estimate how often we should update the triangle ordering
# Use "distance of point to vertex" / "point spacing"
# Crude
search_order_update_freq = \
int(numpy.ceil((first_vertex_d2[search_order[0]]**0.5)/ds[0]))
point_indices[i] =\
util.get_triangle_containing_point(p, gridXY_offset[i,:],
search_order = search_order)
if verbose: print 'Computing the flux'
if k_nearest_neighbours == 1:
point_uh = ud[:][:, point_indices]
point_vh = vd[:][:, point_indices]
else:
point_uh = numpy.zeros(
(len(output_times), len(point_indices[:, 0])))
point_vh = numpy.zeros(
(len(output_times), len(point_indices[:, 0])))
# Compute the inverse distance weighted uh/vh
numerator = point_uh * 0.
denominator = point_uh * 0.
inv_dist = 1.0 / (point_distance + 1.0e-12
) #Avoid zero division
# uh
for k in range(k_nearest_neighbours):
ud_data = ud[:][:, point_indices[:, k]]
for ti in range(len(output_times)):
numerator[ti, :] += ud_data[ti, :] * inv_dist[:, k]
denominator[ti, :] += inv_dist[:, k]
point_uh = numerator / denominator
#vh
numerator *= 0.
denominator *= 0.
for k in range(k_nearest_neighbours):
vd_data = vd[:][:, point_indices[:, k]]
for ti in range(len(output_times)):
numerator[ti, :] += vd_data[ti, :] * inv_dist[:, k]
denominator[ti, :] += inv_dist[:, k]
point_vh = numerator / denominator
Q = [ ((point_uh[i,:]*n1 + point_vh[i,:]*n2)*ds_trapz).sum() \
for i in range(len(output_times)) ]
if segment_num == 0:
discharge_series[pk] = numpy.array(Q)
else:
discharge_series[pk] += numpy.array(Q)
return [output_times, discharge_series]
p = util.get_output(sww_file, timeSlices=[0])
pc = util.get_centroids(p, timeSlices=[0])
# Get centroid information
xc = pc.x + pc.xllcorner
yc = pc.y + pc.yllcorner
elevation_c = pc.elev
# Make file connection
fid = NetCDFFile(sww_file)
#gauge_indices = [((xc - p[0]) ** 2 + (yc - p[1]) ** 2).argmin()
# for p in gauge_coordinates]
gauge_indices = []
for gc in gauge_coordinates:
new_gauge_point = [gc[0] - p.xllcorner, gc[1] - p.yllcorner]
gi = util.get_triangle_containing_point(p, new_gauge_point)
gauge_indices.append(gi)
time = fid.variables['time'][:]
nts = len(time)
# Export flow data for all gauges
for i, gi in enumerate(gauge_indices):
#stage = util._getCentVar(fid, 'stage_c', time_indices=range(nts), space_indices=gi)
try:
stage = fid.variables['stage_c'][:, gi]
except:
vols = fid.variables['volumes'][gi, :]
stage = (fid.variables['stage'][:, vols[0]] +
fid.variables['stage'][:, vols[1]] +
fid.variables['stage'][:, vols[2]]) / 3.
p = util.get_output(sww_file, timeSlices=[0])
pc = util.get_centroids(p, timeSlices=[0])
# Get centroid information
xc = pc.x + pc.xllcorner
yc = pc.y + pc.yllcorner
elevation_c = pc.elev
# Make file connection
fid = NetCDFFile(sww_file)
#gauge_indices = [((xc - p[0]) ** 2 + (yc - p[1]) ** 2).argmin()
# for p in gauge_coordinates]
gauge_indices = []
for gc in gauge_coordinates:
new_gauge_point = [gc[0] - p.xllcorner, gc[1] - p.yllcorner]
gi = util.get_triangle_containing_point(p, new_gauge_point)
gauge_indices.append(gi)
time = fid.variables['time'][:]
nts = len(time)
# Export flow data for all gauges
for i, gi in enumerate(gauge_indices):
#stage = util._getCentVar(fid, 'stage_c', time_indices=range(nts), space_indices=gi)
try:
stage = fid.variables['stage_c'][:, gi]
except:
vols = fid.variables['volumes'][gi, :]
stage = (fid.variables['stage'][:, vols[0]] +
fid.variables['stage'][:, vols[1]] +
fid.variables['stage'][:, vols[2]]) / 3.
def get_approximate_discharge_timeseries(sww_filename,
polylines,
desired_ds=0.5,
k_nearest_neighbours=1,
search_mesh=True,
verbose=True):
"""Given an sww_filename and a dictionary of 1D polylines, estimate the
discharge timeseries through each polyline by interpolating the centroid
uh/vh onto evenly spaced points on the polyline (with spacing ~ desired_ds),
computing the flux normal to the line, and using the trapezoidal rule to
integrate it.
The interpolation of centroid uh/vh onto the polyline points can be either
based on 'k-nearest-neighbours', or a direct-search of the mesh triangles.
The former can be fast and allow for smoothing, while the latter is often
still fast enough, and might be more accurate.
The positive/negative discharge direction is determined from the polyline.
Consider a river channel. If the polyline begins on the left-bank and ends
on the right bank (left/right defined when facing downstream) then
discharge in the downstream direction is positive.
WARNING: The result is approximate only because ANUGA's internal edge
fluxes are derived differently (with the reimann solver), and because the
interpolation does not follow ANUGA's, and because your transect might not
be exactly perpendicular to the flow. None of the methods give an exact
result at present.
Errors can be significant where the solution is changing rapidly. It may
be worth comparing multiple cross-sections in the vicinity of the site of
interest [covering different mesh triangles, with slightly different
orientations].
@param sww_filename name of sww file
@param polylines dictionary of polylines, e.g.
polylines = {
'Xsection1': [ [495., 1613.], [495., 1614.], [496., 1615.] ],
'Xsection2': [ [496., 1614.], [4968., 1615.] ]
}
@param desired_ds point spacing used for trapozoidal integration on
polylines
@param k_nearest_neighbours number of nearest neighbours used for
interpolation of uh/vh onto polylines
@param search_mesh If True AND k_nearest_neighbours=1, we search the
mesh vertices to find the triangle containing our point. Otherwise
do nearest-neighbours on the triangle centroids to estimate the
'nearest' triangle
@param verbose
@return a list of length 2 with the output_times as a numpy array, and a
dictionary with the flow timeseries
"""
if (search_mesh) & (k_nearest_neighbours > 1):
msg = 'k_nearest_neighbours must be 1 when search_mesh is true'
raise Exception(msg)
# 2 ways to associate transect points with triangle values
# 1) knn on centroids, or
# 2) directly search for mesh triangles containing transect points
# 1 can be faster + allows for smoothing, but 2 might be usually better
use_knn = (search_mesh == False) | (k_nearest_neighbours != 1)
if use_knn:
# Centroids are used for knn
p = util.get_centroids(sww_filename, timeSlices=0)
sww_xy = numpy.vstack([p.x+p.xllcorner, p.y+p.yllcorner]).transpose()
point_index_kdtree = scipy.spatial.cKDTree(sww_xy)
else:
# Vertices are used for mesh search
p = util.get_output(sww_filename, timeSlices=0)
# To conserve memory read from netcdf directly
from anuga.file.netcdf import NetCDFFile
sww_nc = NetCDFFile(sww_filename)
ud = sww_nc.variables['xmomentum_c']
vd = sww_nc.variables['ymomentum_c']
output_times = sww_nc.variables['time'][:]
discharge_series = {}
for pk in polylines.keys():
if verbose: print pk
pl_full = polylines[pk]
for segment_num in range(len(pl_full)-1):
pl = [ pl_full[segment_num], pl_full[segment_num + 1] ]
segment_length = ( (pl[0][0] - pl[1][0])**2 +\
(pl[0][1] - pl[1][1])**2 )**0.5
# Normal vector
n1 = (pl[0][1] - pl[1][1])/segment_length
n2 = -(pl[0][0] - pl[1][0])/segment_length
# Approximate segment as npts points
npts = int(numpy.ceil( segment_length / (desired_ds) + 1.0))
gridXY = numpy.vstack([scipy.linspace(pl[0][0], pl[1][0], num=npts),
scipy.linspace(pl[0][1], pl[1][1], num=npts)]
).transpose()
# Actual distance between points
ds = (numpy.diff(gridXY[:,0])**2 + numpy.diff(gridXY[:,1])**2)**0.5
ds_trapz = numpy.hstack([ ds[0], (ds[0:-1] + ds[1:]), ds[-1]])*0.5
if verbose: print 'Finding triangles containing point'
if use_knn:
point_distance, point_indices = point_index_kdtree.query(gridXY,
k = k_nearest_neighbours)
else:
gridXY_offset = gridXY*0.
gridXY_offset[:,0] = gridXY[:,0] - p.xllcorner
gridXY_offset[:,1] = gridXY[:,1] - p.yllcorner
point_indices = numpy.zeros( gridXY.shape[0]).astype(int)
# Provide the order to search the points (might be faster?)
v1 = p.vols[:,0]
search_order_update_freq = 1
for i in range(gridXY.shape[0]):
# For efficiency, we don't recompute the order to search points
# everytime
if i%search_order_update_freq==0:
# Update the mesh triangle search order
first_vertex_d2 = (p.x[v1] - gridXY_offset[i,0])**2 +\
(p.y[v1] - gridXY_offset[i,1])**2
search_order = first_vertex_d2.argsort().tolist()
# Estimate how often we should update the triangle ordering
# Use "distance of point to vertex" / "point spacing"
# Crude
search_order_update_freq = \
int(numpy.ceil((first_vertex_d2[search_order[0]]**0.5)/ds[0]))
point_indices[i] =\
util.get_triangle_containing_point(p, gridXY_offset[i,:],
search_order = search_order)
if verbose: print 'Computing the flux'
if k_nearest_neighbours == 1:
point_uh = ud[:][:, point_indices]
point_vh = vd[:][:, point_indices]
else:
point_uh = numpy.zeros( (len(output_times),
len(point_indices[:,0])))
point_vh = numpy.zeros( (len(output_times),
len(point_indices[:,0])))
# Compute the inverse distance weighted uh/vh
numerator = point_uh*0.
denominator = point_uh*0.
inv_dist = 1.0/(point_distance+1.0e-12) #Avoid zero division
# uh
for k in range(k_nearest_neighbours):
ud_data = ud[:][:,point_indices[:,k]]
for ti in range(len(output_times)):
numerator[ti,:] += ud_data[ti,:]*inv_dist[:,k]
denominator[ti,:] += inv_dist[:,k]
point_uh = numerator/denominator
#vh
numerator *= 0.
denominator *= 0.
for k in range(k_nearest_neighbours):
vd_data = vd[:][:,point_indices[:,k]]
for ti in range(len(output_times)):
numerator[ti,:] += vd_data[ti,:]*inv_dist[:,k]
denominator[ti,:] += inv_dist[:,k]
point_vh = numerator/denominator
Q = [ ((point_uh[i,:]*n1 + point_vh[i,:]*n2)*ds_trapz).sum() \
for i in range(len(output_times)) ]
if segment_num == 0:
discharge_series[pk] = numpy.array(Q)
else:
discharge_series[pk] += numpy.array(Q)
return [output_times, discharge_series]
