def gridcell_areas(lat,
lon,
mask=None,
radius=6372000.,
lat_edges_in=False,
lon_edges_in=False):
### assume uniform longitude spacing
lat_edges, lon_edges = get_gridcell_edges(lat, lon)
if lon_edges_in:
IM = lon.shape[0] - 1
lon_edges = lon[:]
res_lon = lon_edges[1] - lon_edges[0]
else:
IM = lon.shape[0]
res_lon = lon[1] - lon[0]
#
if lat_edges_in:
JM = lat.shape[0] - 1
lat_edges = lat[:]
else:
JM = lat.shape[0]
southern_edge = np.fmax(lat_edges[0:JM], np.ones(JM) * -89.99)
northern_edge = np.fmin(lat_edges[1:], np.ones(JM) * 89.99)
#
area = Ngl.gc_qarea(southern_edge,np.zeros(JM)-res_lon/2.,\
northern_edge,np.zeros(JM)-res_lon/2.,\
northern_edge,np.zeros(JM)+res_lon/2.,\
southern_edge,np.zeros(JM)+res_lon/2.,\
radius=radius) ### 1-D array in meters sq.
area_array = np.array(np.reshape(np.repeat(area, IM), [JM, IM]))
if not mask == None:
area_array = np.ma.array(area_array, mask=mask)
return area_array
def gridcell_areas(lat, lon, mask=None, radius=6372000., lat_edges_in=False, lon_edges_in=False):
### assume uniform longitude spacing
lat_edges, lon_edges = get_gridcell_edges(lat, lon)
if lon_edges_in:
IM = lon.shape[0] - 1
lon_edges = lon[:]
res_lon = lon_edges[1] - lon_edges[0]
else:
IM = lon.shape[0]
res_lon = lon[1]-lon[0]
#
if lat_edges_in:
JM = lat.shape[0] - 1
lat_edges = lat[:]
else:
JM = lat.shape[0]
southern_edge = np.fmax(lat_edges[0:JM], np.ones(JM)*-89.99)
northern_edge = np.fmin(lat_edges[1:], np.ones(JM)*89.99)
#
area = Ngl.gc_qarea(southern_edge,np.zeros(JM)-res_lon/2.,\
northern_edge,np.zeros(JM)-res_lon/2.,\
northern_edge,np.zeros(JM)+res_lon/2.,\
southern_edge,np.zeros(JM)+res_lon/2.,\
radius=radius) ### 1-D array in meters sq.
area_array = np.array(np.reshape(np.repeat(area,IM), [JM,IM]))
if not mask==None:
area_array = np.ma.array(area_array, mask=mask)
return area_array
def conservative_regrid(data_in, lats_in, lons_in, lats_out, lons_out, centers_out=True, weights_in=None, spherical=True, radius=6372000., dilute_w_masked_data=True, return_frac_input_masked=False):
#
""" do a conservative remapping from one 2-d grid to another. assumes that input coordinate arrays are monotonic increasing (but handles lon jump across meridian) and that lat and lon are second-to last and last dimensions
possible to mask the input data either by using a masked array or by setting weights array to zero for masked gridcells
option dilute_w_masked_data means that where the input data is masked, a value of zero is averaged into the output grid, so that global integrals equal.
setting this false will mean that global integrals do not equal, hoe=wever this could be back-calculated out using the fraction masked if return_frac_input_masked is set to true
using the weights_in argument will also lead to non-equal global integrals """
#
shape = data_in.shape
ndims = len(shape)
JM_i = shape[ndims-2]
IM_i = shape[ndims-1]
maxlat = 89.9
if weights_in == None:
weights_in = np.ones([JM_i,IM_i])
weights_mask = np.zeros([JM_i,IM_i], dtype=np.bool)
else:
weights_mask = weights_in[:] == 0.
if type(data_in) == np.ma.core.MaskedArray:
if ndims == 2:
mask_in = np.logical_or(data_in[:].mask, weights_mask)
elif ndims == 3:
mask_in = np.logical_or(data_in[0,:].mask, weights_mask)
elif ndims == 4:
mask_in = np.logical_or(data_in[0,0,:].mask, weights_mask)
else:
mask_in = np.logical_or(np.zeros([JM_i,IM_i], dtype=np.bool), weights_mask)
## check to see if coordinates input are for gridcell centers or edges. assume that if edges, length of vector will be one longer than length of data
#
#
#
#
####### lats_in
if len(lats_in) == JM_i:
if spherical:
lat_edges_in = np.zeros(JM_i+1)
lat_edges_in[0] = max(-maxlat, lats_in[0] - 0.5*(lats_in[1] - lats_in[0]))
lat_edges_in[JM_i] = min(maxlat, lats_in[JM_i-1] + 0.5*(lats_in[JM_i-1] - lats_in[JM_i-2]))
lat_edges_in[1:JM_i] = (lats_in[0:JM_i-1] + lats_in[1:JM_i])/2.
else:
lat_edges_in = np.zeros(JM_i+1)
lat_edges_in[0] = lats_in[0] - 0.5*(lats_in[1] - lats_in[0])
lat_edges_in[JM_i] = lats_in[JM_i-1] + 0.5*(lats_in[JM_i-1] - lats_in[JM_i-2])
lat_edges_in[1:JM_i] = (lats_in[0:JM_i-1] + lats_in[1:JM_i])/2.
elif len(lats_in) == JM_i+1:
lat_edges_in = lats_in
else:
raise RuntimeError
#
####### lats_out
if centers_out:
JM_o = len(lats_out)
if spherical:
lat_edges_out = np.zeros(JM_o+1)
lat_edges_out[0] = max(-maxlat, lats_out[0] - 0.5*(lats_out[1] - lats_out[0]))
lat_edges_out[JM_o] = min(maxlat, lats_out[JM_o-1] + 0.5*(lats_out[JM_o-1] - lats_out[JM_o-2]))
lat_edges_out[1:JM_o] = (lats_out[0:JM_o-1] + lats_out[1:JM_o])/2.
else:
lat_edges_out = np.zeros(JM_o+1)
lat_edges_out[0] = lats_out[0] - 0.5*(lats_out[1] - lats_out[0])
lat_edges_out[JM_o] = lats_out[JM_o-1] + 0.5*(lats_out[JM_o-1] - lats_out[JM_o-2])
lat_edges_out[1:JM_o] = (lats_out[0:JM_o-1] + lats_out[1:JM_o])/2.
else:
JM_o = len(lats_out) -1
lat_edges_out = lats_out
#
####### lons_in
if len(lons_in) == IM_i:
lon_edges_in = np.zeros(IM_i+1)
lon_edges_in[0] = lons_in[0] - 0.5*(lons_in[1] - lons_in[0])
lon_edges_in[IM_i] = lons_in[IM_i-1] + 0.5*(lons_in[IM_i-1] - lons_in[IM_i-2])
lon_edges_in[1:IM_i] = (lons_in[0:IM_i-1] + lons_in[1:IM_i])/2.
elif len(lons_in) == IM_i+1:
lon_edges_in = lons_in
else:
raise RuntimeError
#
####### lons_out
if centers_out:
IM_o = len(lons_out)
lon_edges_out = np.zeros(IM_o+1)
lon_edges_out[0] = lons_out[0] - 0.5*(lons_out[1] - lons_out[0])
lon_edges_out[IM_o] = lons_out[IM_o-1] + 0.5*(lons_out[IM_o-1] - lons_out[IM_o-2])
lon_edges_out[1:IM_o] = (lons_out[0:IM_o-1] + lons_out[1:IM_o])/2.
else:
IM_o = len(lons_out) -1
lon_edges_out = lons_out
#
#
#
### first define ranges to loop over that map overlapping lat and lons
lon_looplist = [[]]
for i in range(IM_o):
if i > 0:
lon_looplist.append([])
### figure out which lon quadrant to normalize the data to. if -90<lon<90 then normalize to option 1, otherwise to zero
if (Ngl.normalize_angle(lon_edges_out[i], 1) < 90.) and (Ngl.normalize_angle(lon_edges_out[i], 1) > -90.):
lon_sector = 1
else:
lon_sector = 0
min_cell_lon_o = Ngl.normalize_angle(lon_edges_out[i], lon_sector)
max_cell_lon_o = Ngl.normalize_angle(lon_edges_out[i+1], lon_sector)
for ii in range(IM_i):
min_cell_lon_i = Ngl.normalize_angle(lon_edges_in[ii], lon_sector)
max_cell_lon_i = Ngl.normalize_angle(lon_edges_in[ii+1], lon_sector)
overlap_interval_lon = min(max_cell_lon_i, max_cell_lon_o) - max(min_cell_lon_i,min_cell_lon_o)
if overlap_interval_lon > 0.:
lon_looplist[i].append(ii)
#
#
#
lat_looplist = [[]]
for j in range(JM_o):
if j > 0:
lat_looplist.append([])
min_cell_lat_o = lat_edges_out[j]
max_cell_lat_o = lat_edges_out[j+1]
for jj in range(JM_i):
min_cell_lat_i = lat_edges_in[jj]
max_cell_lat_i = lat_edges_in[jj+1]
overlap_interval_lat = min(max_cell_lat_i, max_cell_lat_o) - max(min_cell_lat_i,min_cell_lat_o)
if overlap_interval_lat > 0.:
lat_looplist[j].append(jj)
#
#
#
### now begin looping over output grid
total_weights = np.zeros([JM_o,IM_o])
total_weights_inputmasked = np.zeros([JM_o,IM_o])
if ndims == 2:
total_value = np.zeros([JM_o,IM_o])
elif ndims == 3:
total_value = np.zeros([shape[0],JM_o,IM_o])
elif ndims == 4:
total_value = np.zeros([shape[0],shape[1],JM_o,IM_o])
else:
raise RuntimeError
for i in range(IM_o):
### figure out which lon quadrant to normalize the data to. if -90<lon<90 then normalize to option 1, otherwise to zero
if (Ngl.normalize_angle(lon_edges_out[i], 1) < 90.) and (Ngl.normalize_angle(lon_edges_out[i], 1) > -90.):
lon_sector = 1
else:
lon_sector = 0
min_cell_lon_o = Ngl.normalize_angle(lon_edges_out[i], lon_sector)
max_cell_lon_o = Ngl.normalize_angle(lon_edges_out[i+1], lon_sector)
for j in range(JM_o):
min_cell_lat_o = lat_edges_out[j]
max_cell_lat_o = lat_edges_out[j+1]
for ii in lon_looplist[i]:
for jj in lat_looplist[j]:
if not(mask_in[jj,ii]) or dilute_w_masked_data:
min_cell_lat_i = lat_edges_in[jj]
max_cell_lat_i = lat_edges_in[jj+1]
min_cell_lon_i = Ngl.normalize_angle(lon_edges_in[ii], lon_sector)
max_cell_lon_i = Ngl.normalize_angle(lon_edges_in[ii+1], lon_sector)
overlap_interval_lat = min(max_cell_lat_i, max_cell_lat_o) - max(min_cell_lat_i,min_cell_lat_o)
overlap_interval_lon = min(max_cell_lon_i, max_cell_lon_o) - max(min_cell_lon_i,min_cell_lon_o)
if overlap_interval_lat > 0. and overlap_interval_lon > 0.:
fractional_overlap_lat = overlap_interval_lat / (max_cell_lat_i - min_cell_lat_i)
fractional_overlap_lon = overlap_interval_lon / (max_cell_lon_i - min_cell_lon_i)
fractional_overlap_total = fractional_overlap_lat * fractional_overlap_lon
if spherical:
weight = fractional_overlap_total * weights_in[jj,ii] * Ngl.gc_qarea(min_cell_lat_i,min_cell_lon_i,max_cell_lat_i,min_cell_lon_i,max_cell_lat_i,max_cell_lon_i,min_cell_lat_i,max_cell_lon_i,radius=radius)
else:
weight = fractional_overlap_total * weights_in[jj,ii]
total_weights[j,i] = total_weights[j,i] + weight
if not(mask_in[jj,ii]):
total_weights_inputmasked[j,i] = total_weights_inputmasked[j,i] + weight
if ndims == 2:
total_value[j,i] = total_value[j,i] + weight * data_in[jj,ii]
elif ndims == 3:
total_value[:,j,i] = total_value[:,j,i] + weight * data_in[:,jj,ii]
elif ndims == 4:
total_value[:,:,j,i] = total_value[:,:,j,i] + weight * data_in[:,:,jj,ii]
#
if ndims > 2:
total_weights_bc, total_value_bc = np.broadcast_arrays(total_weights, total_value)
total_weights_inputmasked_bc, total_value_bc = np.broadcast_arrays(total_weights_inputmasked, total_value)
else:
total_weights_bc = total_weights
total_weights_inputmasked_bc = total_weights_inputmasked
#
if total_weights_inputmasked.min() > 0.:
mean_value = total_value[:] / total_weights_bc[:]
fraction_maskedinput = total_weights_inputmasked[:] / total_weights[:]
else:
mean_value = np.ma.masked_array(total_value[:] / total_weights_bc[:], mask=total_weights_inputmasked_bc[:] == 0.)
fraction_maskedinput = np.ma.masked_array(total_weights_inputmasked[:] / total_weights[:], mask=total_weights_inputmasked[:] == 0.)
#
#
if not return_frac_input_masked:
return mean_value
else:
return mean_value, fraction_maskedinput
def conservative_regrid(data_in,
lats_in,
lons_in,
lats_out,
lons_out,
centers_out=True,
weights_in=None,
spherical=True,
radius=6372000.,
dilute_w_masked_data=True,
return_frac_input_masked=False):
#
""" do a conservative remapping from one 2-d grid to another. assumes that input coordinate arrays are monotonic increasing (but handles lon jump across meridian) and that lat and lon are second-to last and last dimensions
possible to mask the input data either by using a masked array or by setting weights array to zero for masked gridcells
option dilute_w_masked_data means that where the input data is masked, a value of zero is averaged into the output grid, so that global integrals equal.
setting this false will mean that global integrals do not equal, hoe=wever this could be back-calculated out using the fraction masked if return_frac_input_masked is set to true
using the weights_in argument will also lead to non-equal global integrals """
#
shape = data_in.shape
ndims = len(shape)
JM_i = shape[ndims - 2]
IM_i = shape[ndims - 1]
maxlat = 89.9
if weights_in == None:
weights_in = np.ones([JM_i, IM_i])
weights_mask = np.zeros([JM_i, IM_i], dtype=np.bool)
else:
weights_mask = weights_in[:] == 0.
if type(data_in) == np.ma.core.MaskedArray:
if ndims == 2:
mask_in = np.logical_or(data_in[:].mask, weights_mask)
elif ndims == 3:
mask_in = np.logical_or(data_in[0, :].mask, weights_mask)
elif ndims == 4:
mask_in = np.logical_or(data_in[0, 0, :].mask, weights_mask)
else:
mask_in = np.logical_or(np.zeros([JM_i, IM_i], dtype=np.bool),
weights_mask)
## check to see if coordinates input are for gridcell centers or edges. assume that if edges, length of vector will be one longer than length of data
#
#
#
#
####### lats_in
if len(lats_in) == JM_i:
if spherical:
lat_edges_in = np.zeros(JM_i + 1)
lat_edges_in[0] = max(-maxlat,
lats_in[0] - 0.5 * (lats_in[1] - lats_in[0]))
lat_edges_in[JM_i] = min(
maxlat, lats_in[JM_i - 1] + 0.5 *
(lats_in[JM_i - 1] - lats_in[JM_i - 2]))
lat_edges_in[1:JM_i] = (lats_in[0:JM_i - 1] + lats_in[1:JM_i]) / 2.
else:
lat_edges_in = np.zeros(JM_i + 1)
lat_edges_in[0] = lats_in[0] - 0.5 * (lats_in[1] - lats_in[0])
lat_edges_in[JM_i] = lats_in[JM_i - 1] + 0.5 * (lats_in[JM_i - 1] -
lats_in[JM_i - 2])
lat_edges_in[1:JM_i] = (lats_in[0:JM_i - 1] + lats_in[1:JM_i]) / 2.
elif len(lats_in) == JM_i + 1:
lat_edges_in = lats_in
else:
raise RuntimeError
#
####### lats_out
if centers_out:
JM_o = len(lats_out)
if spherical:
lat_edges_out = np.zeros(JM_o + 1)
lat_edges_out[0] = max(
-maxlat, lats_out[0] - 0.5 * (lats_out[1] - lats_out[0]))
lat_edges_out[JM_o] = min(
maxlat, lats_out[JM_o - 1] + 0.5 *
(lats_out[JM_o - 1] - lats_out[JM_o - 2]))
lat_edges_out[1:JM_o] = (lats_out[0:JM_o - 1] +
lats_out[1:JM_o]) / 2.
else:
lat_edges_out = np.zeros(JM_o + 1)
lat_edges_out[0] = lats_out[0] - 0.5 * (lats_out[1] - lats_out[0])
lat_edges_out[JM_o] = lats_out[
JM_o - 1] + 0.5 * (lats_out[JM_o - 1] - lats_out[JM_o - 2])
lat_edges_out[1:JM_o] = (lats_out[0:JM_o - 1] +
lats_out[1:JM_o]) / 2.
else:
JM_o = len(lats_out) - 1
lat_edges_out = lats_out
#
####### lons_in
if len(lons_in) == IM_i:
lon_edges_in = np.zeros(IM_i + 1)
lon_edges_in[0] = lons_in[0] - 0.5 * (lons_in[1] - lons_in[0])
lon_edges_in[IM_i] = lons_in[IM_i - 1] + 0.5 * (lons_in[IM_i - 1] -
lons_in[IM_i - 2])
lon_edges_in[1:IM_i] = (lons_in[0:IM_i - 1] + lons_in[1:IM_i]) / 2.
elif len(lons_in) == IM_i + 1:
lon_edges_in = lons_in
else:
raise RuntimeError
#
####### lons_out
if centers_out:
IM_o = len(lons_out)
lon_edges_out = np.zeros(IM_o + 1)
lon_edges_out[0] = lons_out[0] - 0.5 * (lons_out[1] - lons_out[0])
lon_edges_out[IM_o] = lons_out[IM_o - 1] + 0.5 * (lons_out[IM_o - 1] -
lons_out[IM_o - 2])
lon_edges_out[1:IM_o] = (lons_out[0:IM_o - 1] + lons_out[1:IM_o]) / 2.
else:
IM_o = len(lons_out) - 1
lon_edges_out = lons_out
#
#
#
### first define ranges to loop over that map overlapping lat and lons
lon_looplist = [[]]
for i in range(IM_o):
if i > 0:
lon_looplist.append([])
### figure out which lon quadrant to normalize the data to. if -90<lon<90 then normalize to option 1, otherwise to zero
if (Ngl.normalize_angle(lon_edges_out[i], 1) <
90.) and (Ngl.normalize_angle(lon_edges_out[i], 1) > -90.):
lon_sector = 1
else:
lon_sector = 0
min_cell_lon_o = Ngl.normalize_angle(lon_edges_out[i], lon_sector)
max_cell_lon_o = Ngl.normalize_angle(lon_edges_out[i + 1], lon_sector)
for ii in range(IM_i):
min_cell_lon_i = Ngl.normalize_angle(lon_edges_in[ii], lon_sector)
max_cell_lon_i = Ngl.normalize_angle(lon_edges_in[ii + 1],
lon_sector)
overlap_interval_lon = min(max_cell_lon_i, max_cell_lon_o) - max(
min_cell_lon_i, min_cell_lon_o)
if overlap_interval_lon > 0.:
lon_looplist[i].append(ii)
#
#
#
lat_looplist = [[]]
for j in range(JM_o):
if j > 0:
lat_looplist.append([])
min_cell_lat_o = lat_edges_out[j]
max_cell_lat_o = lat_edges_out[j + 1]
for jj in range(JM_i):
min_cell_lat_i = lat_edges_in[jj]
max_cell_lat_i = lat_edges_in[jj + 1]
overlap_interval_lat = min(max_cell_lat_i, max_cell_lat_o) - max(
min_cell_lat_i, min_cell_lat_o)
if overlap_interval_lat > 0.:
lat_looplist[j].append(jj)
#
#
#
### now begin looping over output grid
total_weights = np.zeros([JM_o, IM_o])
total_weights_inputmasked = np.zeros([JM_o, IM_o])
if ndims == 2:
total_value = np.zeros([JM_o, IM_o])
elif ndims == 3:
total_value = np.zeros([shape[0], JM_o, IM_o])
elif ndims == 4:
total_value = np.zeros([shape[0], shape[1], JM_o, IM_o])
else:
raise RuntimeError
for i in range(IM_o):
### figure out which lon quadrant to normalize the data to. if -90<lon<90 then normalize to option 1, otherwise to zero
if (Ngl.normalize_angle(lon_edges_out[i], 1) <
90.) and (Ngl.normalize_angle(lon_edges_out[i], 1) > -90.):
lon_sector = 1
else:
lon_sector = 0
min_cell_lon_o = Ngl.normalize_angle(lon_edges_out[i], lon_sector)
max_cell_lon_o = Ngl.normalize_angle(lon_edges_out[i + 1], lon_sector)
for j in range(JM_o):
min_cell_lat_o = lat_edges_out[j]
max_cell_lat_o = lat_edges_out[j + 1]
for ii in lon_looplist[i]:
for jj in lat_looplist[j]:
if not (mask_in[jj, ii]) or dilute_w_masked_data:
min_cell_lat_i = lat_edges_in[jj]
max_cell_lat_i = lat_edges_in[jj + 1]
min_cell_lon_i = Ngl.normalize_angle(
lon_edges_in[ii], lon_sector)
max_cell_lon_i = Ngl.normalize_angle(
lon_edges_in[ii + 1], lon_sector)
overlap_interval_lat = min(
max_cell_lat_i, max_cell_lat_o) - max(
min_cell_lat_i, min_cell_lat_o)
overlap_interval_lon = min(
max_cell_lon_i, max_cell_lon_o) - max(
min_cell_lon_i, min_cell_lon_o)
if overlap_interval_lat > 0. and overlap_interval_lon > 0.:
fractional_overlap_lat = overlap_interval_lat / (
max_cell_lat_i - min_cell_lat_i)
fractional_overlap_lon = overlap_interval_lon / (
max_cell_lon_i - min_cell_lon_i)
fractional_overlap_total = fractional_overlap_lat * fractional_overlap_lon
if spherical:
weight = fractional_overlap_total * weights_in[
jj, ii] * Ngl.gc_qarea(min_cell_lat_i,
min_cell_lon_i,
max_cell_lat_i,
min_cell_lon_i,
max_cell_lat_i,
max_cell_lon_i,
min_cell_lat_i,
max_cell_lon_i,
radius=radius)
else:
weight = fractional_overlap_total * weights_in[
jj, ii]
total_weights[j, i] = total_weights[j, i] + weight
if not (mask_in[jj, ii]):
total_weights_inputmasked[
j,
i] = total_weights_inputmasked[j,
i] + weight
if ndims == 2:
total_value[j, i] = total_value[
j, i] + weight * data_in[jj, ii]
elif ndims == 3:
total_value[:, j,
i] = total_value[:, j,
i] + weight * data_in[:,
jj,
ii]
elif ndims == 4:
total_value[:, :, j,
i] = total_value[:, :, j,
i] + weight * data_in[:, :,
jj,
ii]
#
if ndims > 2:
total_weights_bc, total_value_bc = np.broadcast_arrays(
total_weights, total_value)
total_weights_inputmasked_bc, total_value_bc = np.broadcast_arrays(
total_weights_inputmasked, total_value)
else:
total_weights_bc = total_weights
total_weights_inputmasked_bc = total_weights_inputmasked
#
if total_weights_inputmasked.min() > 0.:
mean_value = total_value[:] / total_weights_bc[:]
fraction_maskedinput = total_weights_inputmasked[:] / total_weights[:]
else:
mean_value = np.ma.masked_array(
total_value[:] / total_weights_bc[:],
mask=total_weights_inputmasked_bc[:] == 0.)
fraction_maskedinput = np.ma.masked_array(
total_weights_inputmasked[:] / total_weights[:],
mask=total_weights_inputmasked[:] == 0.)
#
#
if not return_frac_input_masked:
return mean_value
else:
return mean_value, fraction_maskedinput