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segment.py
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segment.py
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import numpy as np
import netCDF4
import matplotlib
import matplotlib.pyplot as plt
from mpl_toolkits.basemap import Basemap
import helpers
#watershed has a few options for implementation:
#-for every cell, walk down steepest gradient to the basin
def find_basinBoundaries(cell2Site, cell0, mesh):
"""a basin boundary is a cell with a cell2Site pointing to another basin"""
isBoundary = np.zeros(mesh.nCells, dtype=int)
for cell in iter(cell0.copy()): #not that cell referring to cell0 changes cell0
if (not cell.isInRegion()):
continue
iCell = cell.ind
nbrs = cell.get_nbrInds()
val0 = cell2Site[iCell]; valNbrs = cell2Site[nbrs]
if ( np.any(val0 != valNbrs) ): #have nbr with different basin
isBoundary[iCell] = 1
return isBoundary
def find_minCells_region_flat(vals, cell0, mesh):
"""return array[nCells] with 1 if cell is min and cell in region"""
isMin = np.zeros(mesh.nCells,dtype=int)
for cell in iter(cell0.copy()): #not that cell referring to cell0 changes cell0
if (not cell.isInRegion()):
continue
iCell = cell.ind
nbrs = cell.get_nbrInds()
#assume that every cell inRegion has >1 neighbor inRegion
nbrsInRegion = nbrs[mesh.isIndsInRegion(nbrs)]
val0 = vals[iCell]; valNbrs = vals[nbrsInRegion]
#print val0, valNbrs
if (np.all(val0<=valNbrs)): #is site if can't descend from it
isMin[iCell] = 1
nMin = np.sum(isMin)
print "Number of local min: ", nMin
return isMin
def watershed_region(vals, cellIsMin, cell0, mesh):
"""
Map every cell to a basin following local steepest gradient. Regional minima map to self.
Follow steepest-descent gradient until reach a site that is a minimum. Filter basins so have to be a min within specified region (disk of radius dRegion).
Return map of cell to basin.
Arguments:
vals - values
cellIsMin - array >0 if cell is local minimum
cell0 - cell for iterating through mesh
mesh - Mesh instance
"""
'''
#to adapt global watershed to region, make values outside of region huge so
don't steepest descend that way. since we pass in minCells, do this before call:
bigVal = 1.e10
vals = np.copy(valsIn)
vals[inRegion<1] = bigVal
'''
cell2Site = -np.ones(mesh.nCells,dtype=int) #so no cell2Site[iCell]=iCell
#get local steepest path
dMin = min(1.e-6,mesh.r/mesh.nCells);
for cell in iter(cell0.copy()):
if (not cell.isInRegion()):
continue
iCell = cell.ind
if (cellIsMin[iCell]>0): #steepest path is to self
cell2Site[iCell]= iCell
else:
nbrs = cell.get_nbrInds()
nbrs = nbrs[mesh.isIndsInRegion(nbrs)]
val0 = vals[iCell]
valNbrs = vals[nbrs]
#correspondence is towards minimum gradient.
lat0, lon0 = mesh.get_latLon_inds(iCell)
latNbrs, lonNbrs = mesh.get_latLon_inds(nbrs)
dNbrs = helpers.calc_distSphere_multiple(mesh.r, lat0, lon0, latNbrs, lonNbrs)
dNbrs[dNbrs<dMin]=dMin #avoid divide by 0
#print valNbrs, dNbrs, val0
valNbrs = (valNbrs-val0)/dNbrs
iNbr = np.argmin(valNbrs)
if (True):
if (valNbrs[iNbr]>=0):
print "Uhoh. Steepest descent for cell {0}->{2} is {1}, which isn't negative!".format(iCell, valNbrs[iNbr], nbrs[iNbr])
cell2Site[iCell] = nbrs[iNbr]
#Filter local extrema by area to limit high (spatial) frequency "noise".
#An extremum must be an extremum within the filter region
nRedirect = 0
for cell in iter(cell0.copy()):
if (not cell.isInRegion()):
continue
iCell = cell.ind
if (cellIsMin[iCell]>0):
#see if cell is min in region, not just neighbors.
#if not regional min, update cell2Site so local min goes to another basin
cellsRegion = cell.get_regionInds()
valsRegion = vals[cellsRegion]
minInd = np.argmin(valsRegion)
minVal = valsRegion[minInd]; minCell = cellsRegion[minInd];
val0 = vals[iCell]; #print val0, minVal
if (minVal < val0):
#print "Redirecting cell {0} to {1}".format(iCell, minCell)
cellIsMin[iCell] = 0
cell2Site[iCell] = minCell
nRedirect = nRedirect+1
else:
#cell is min, but not necessarily distinct min (ie strictly less than all other values w/in disk).
#here, we deal with the case where multiple cells in region all have the exact same value.
#3 (or nLon) neigboring mins should be 1 tpv, not 3 (physically).
#we'll redirect to the maximum index within disk (so all cells redirect to accepted min).
#While unlikely for 2 general floats to be equal, this can arise from:
#-idealized initialization
#-compressed storage of variables (eg, ERA-I stores as shorts where val=short*scale+offset)
isDiskMin = valsRegion==minVal
if (np.sum(isDiskMin)>1):
indsOfMins = cellsRegion[isDiskMin>0]
minCell = np.max(indsOfMins)
if (iCell != minCell):
cellIsMin[iCell] = 0
cell2Site[iCell] = minCell
nRedirect = nRedirect+1
print "Number of min after redirect: ", np.sum(cellIsMin>0)
#follow local steepest path (and any redirections from, say, regional thresholds) to site
for cell in iter(cell0.copy()):
if (not cell.isInRegion()):
continue
iCell = cell.ind
nextCell = cell2Site[iCell]
nCount = 0
while (not cellIsMin[nextCell]>0):
nextCell = cell2Site[nextCell]
#print "Cell {0} going to {1}".format(iCell,nextCell); print vals[iCell], vals[nextCell]
nCount=nCount+1
if (nCount>mesh.nCells): #something is probably quite wrong
#seems to happen if values w/in a region have the exact same value. Storing values as shorts in files makes this more likely.
print "Uhoh, stuck in while loop for cell {0} with value {1}".format(iCell, vals[iCell])
nbrs = cell.get_nbrInds(); valNbrs = vals[nbrs]
print "Neighbor's values are: ", valNbrs
break
#end not cellIsMin
cell2Site[iCell] = nextCell
return (cell2Site, cellIsMin)
def segment_high_low_watershed_region(theta, vort, cell0, mesh, segRestrictPerc):
"""
Segment a continuous surface into high and low watershed basins
Steps: get high and low basin seeds, associate cells to both high and low basins if not extrema.
to decide whether "really" part of high or low basin, we have options:
-(anti-)cyclonic for (high) low...is local vorticity noisy?
-closer theta value to maxima a la color scale grouping...huge min or max value now matters
-whether steeper gradient is to high or low
-physical distance
-concavity of surface a la last closed contour
Arguments:
theta - potential temperature
vort - vertical vorticity
cell0 - cell for iterating through mesh
mesh - Mesh instance
segRestrictPerc - Percentile for restricting watershed basins (percentile of amplitudes of cells on boundary of watershed basin)
"""
#mins
print "Finding minima"
#to adapt global watershed to region, make values outside of region huge so don't steepest descend that way
bigVal = 1.e10
vals = np.copy(theta) #so don't affect variable passed in
vals[np.logical_not( mesh.get_inRegion1d() )] = bigVal
cellIsMin = find_minCells_region_flat(vals, cell0.copy(), mesh)
cell2SiteMin, cellIsMin = watershed_region(vals, cellIsMin, cell0.copy(), mesh)
#maxs: perform min on an inverted surface
print "Finding maxima"
#adapt global watershed to region
vals = -np.copy(theta)
vals[np.logical_not( mesh.get_inRegion1d() )] = bigVal
cellIsMax = find_minCells_region_flat(vals, cell0.copy(), mesh)
cell2SiteMax, cellIsMax = watershed_region(vals, cellIsMax, cell0.copy(), mesh)
#"voting" procedure for low/high classification ------
print "Associating to max or min by local vorticity"
cell2Site = -np.ones(mesh.nCells, dtype=int)
for cell in iter(cell0.copy()):
if (not cell.isInRegion()):
continue
iCell = cell.ind
if (cellIsMin[iCell]>0 or cellIsMax[iCell]>0): #allows for cyclonic max. is that right?
cell2Site[iCell] = iCell
else:
#cyclonic ~ sign(vorticity) depends on hemisphere
signHem = 1 #sign function is problematic since sign(0)=0
lat0, lon0 = mesh.get_latLon_inds(iCell)
if (lat0<0): #lat=0 gets put in NH
signHem = -signHem
if (signHem*vort[iCell]<0): #anticyclonic
cell2Site[iCell] = cell2SiteMax[iCell]
else: #0 or cyclonic
cell2Site[iCell] = cell2SiteMin[iCell]
#restrict basins to closed contours -------
print "Restricting basins to last closed contour w/in watershed"
isBoundary = find_basinBoundaries(cell2Site, cell0.copy(), mesh)
for cell in iter(cell0.copy()):
iCell = cell.ind
if (cell2Site[iCell] == iCell): #loop by basin
theta0 = theta[iCell]
boundingBasin = (cell2Site==iCell)*(isBoundary)
thetaBoundary = theta[boundingBasin>0]
#defining the last closed contour as smallest amplitude on boundary covers min and max.
#cells outside of contour are set to -1 == background
#minAmp = np.min( np.absolute(thetaBoundary-theta0) )
minAmp = np.percentile(np.absolute(thetaBoundary-theta0), segRestrictPerc)
print 'theta0, thetaMinBound, thetaMaxBound, minAmp, site: ', theta0, np.min(thetaBoundary), np.max(thetaBoundary), minAmp, iCell
#[cell2Site[i]=-1 for i in xrange(mesh.nCells) if (cell2Site[i]==iCell and abs(theta[i]-theta0)>minAmp)] #i don't think we can set values in list comprehension
'''
for i in xrange(mesh.nCells):
if (cell2Site[i]==iCell and abs(theta[i]-theta0)>minAmp):
cell2Site[i]=-1
'''
toRemove = (cell2Site==iCell)*(np.absolute(theta-theta0)>minAmp); print 'Removed cells {0}/{1}'.format(np.sum(toRemove), np.sum(cell2Site==iCell))
cell2Site[toRemove>0] = -1
return (cell2Site, cellIsMin, cellIsMax)
def segment(theta, vort, cell0, mesh, segRestrictPerc):
"""Wrapper for segmenting surface into high and low watershed basins"""
cell2Site, cellIsMin, cellIsMax = segment_high_low_watershed_region(theta, vort, cell0, mesh, segRestrictPerc)
sitesMin = cell2Site[cellIsMin>0]
sitesMax = cell2Site[cellIsMax>0]
return (cell2Site, sitesMin, sitesMax)
def write_netcdf_header_seg(fName, info, nCells, nSitesMax):
"""Make and write header for segmentation tpvTrack netcdf file"""
#I don't know how to make ragged arrays, so we'll use
#array[nTimes,nMax] and nElts[nTimes]
data = netCDF4.Dataset(fName, 'w', format='NETCDF4')
data.description = info
# dimensions
data.createDimension('time', None)
data.createDimension('nCells', nCells)
data.createDimension('nMax', nSitesMax)
# variables
cell2Site_data = data.createVariable('cell2Site', 'i4', ('time','nCells',))
sitesMin_data = data.createVariable('sitesMin', 'i4', ('time','nMax',)) #could make unsigned...careful about any arithmetic later though
nSitesMin_data = data.createVariable('nSitesMin', 'i4', ('time',))
sitesMax_data = data.createVariable('sitesMax', 'i4', ('time','nMax',))
nSitesMax_data = data.createVariable('nSitesMax', 'i4', ('time',))
#units and descriptions
cell2Site_data.description = 'Map[cell]->basin'
sitesMin_data.description = 'Cell indices of minima'
sitesMax_data.description = 'Cell indices of maxima'
nSitesMin_data.description = '# minima = # cyclonic tpvs'
return data
def write_netcdf_iTime_seg(data, iTime, cell2Site, sitesMin, sitesMax, nSitesMax):
"""Write 1 time into segmentation tpvTrack netcdf file"""
# fill file. with time as unlimited, dimension will just keep growing
data.variables['cell2Site'][iTime,:] = cell2Site[:]
nSites = len(sitesMin)
if (nSites>nSitesMax):
print "Uhoh. Only storing {0}/{1} sites".format(nSitesMax,nSites)
nSites = nSitesMax
data.variables['sitesMin'][iTime,0:nSites] = sitesMin[0:nSites]
data.variables['nSitesMin'][iTime] = nSites
nSites = len(sitesMax)
if (nSites>nSitesMax):
print "Uhoh. Only storing {0}/{1} sites".format(nSitesMax,nSites)
nSites = nSitesMax
data.variables['sitesMax'][iTime,0:nSites] = sitesMax[0:nSites]
data.variables['nSitesMax'][iTime] = nSites
#
def run_segment(fSeg, info, dataMetr, cell0, mesh, nTimes, segRestrictPerc=5.):
"""Run segmentation over multiple times of input data"""
nSitesMax = (mesh.get_inRegion1d()).sum() #can't have more sites than cells...
nSitesMax = 3000
dataSeg = write_netcdf_header_seg(fSeg, info, mesh.nCells, nSitesMax)
for iTime in xrange(nTimes):
print "Segmenting time index: ", iTime
theta = dataMetr.variables['theta'][iTime,:]
vort = dataMetr.variables['vort'][iTime,:]
cell2Site, sitesMin, sitesMax = segment(theta, vort, cell0.copy(), mesh, segRestrictPerc)
write_netcdf_iTime_seg(dataSeg, iTime, cell2Site, sitesMin, sitesMax, nSitesMax)
dataSeg.close()
def plot_basins_save(fNameSave, lat, lon, vals, sitesMin, sitesMax):
"""
Example of plotting segmentation with basins colored by site.
Input all as 1d arrays. lat/lon in radians
"""
plt.figure()
#m = Basemap(projection='ortho',lon_0=100,lat_0=60, resolution='l')
r2d = 180./np.pi
m = Basemap(projection='ortho',lon_0=0,lat_0=89.95, resolution='l')
x,y = m(lon*r2d, lat*r2d)
#print x.shape, y.shape
m.drawcoastlines(linewidth=.5)
#m.drawmapboundary()
#plot nan's with different color
maskedVals = np.ma.array(vals, mask=np.isnan(vals))
cmap = matplotlib.cm.RdBu_r #matplotlib.cm.jet
cmap.set_bad('w',1.)
pPlot = m.pcolor(x,y,maskedVals,tri=True, shading='flat',edgecolors='none',cmap=cmap, vmin=280, vmax=360)
xMin = x[sitesMin]; yMin = y[sitesMin]; m.scatter(xMin, yMin, c='k', marker="v")
xMax = x[sitesMax]; yMax = y[sitesMax]; m.scatter(xMax, yMax, c='w', marker="^")
plt.colorbar(pPlot)
plt.savefig(fNameSave, bbox_inches='tight'); plt.close()
def run_plotBasins(fDirSave, dataMetr, fSeg, mesh):
"""Plot segmentation"""
lat, lon = mesh.get_latLon_inds(np.arange(mesh.nCells))
if (True):
#latLon cells will have duplicate points, which mucks up the triangulation
#this is a quick hack but a more robust option may be needed...
sizeDelta = .05*np.pi/180.
dll = sizeDelta*np.random.uniform(-1.,1,mesh.nCells)
lat += dll
lon += dll
dataSeg = netCDF4.Dataset(fSeg,'r')
info = dataSeg.description
nTimes = len(dataSeg.dimensions['time'])
for iTime in xrange(nTimes):
fName = 'seg_{0}_{1}.png'.format(iTime, info)
fSave = fDirSave+fName
cell2Site = dataSeg.variables['cell2Site'][iTime,:]
sitesMin = dataSeg.variables['sitesMin'][iTime,:];
nMin = dataSeg.variables['nSitesMin'][iTime]; sitesMin = sitesMin[0:nMin]
sitesMax = dataSeg.variables['sitesMax'][iTime,:];
nMax = dataSeg.variables['nSitesMax'][iTime]; sitesMax = sitesMax[0:nMax]
theta = dataMetr.variables['theta'][iTime,:]
vals = theta[cell2Site]; vals[cell2Site<0] = np.nan; #print vals
print "Saving file: "+fSave
plot_basins_save(fSave, lat, lon, vals, sitesMin, sitesMax)
dataSeg.close()