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ground_template_from_modis.py
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from pyhdf.SD import SD, SDC
import healpy as hp
import numpy as np
from scipy import interpolate
h = 6.62e-34
c = 3e8
k_b = 1.38e-23
T_cmb = 2.72548
def tb2b(tb, nu):
#Convert blackbody temperature to spectral
x = h*nu/(k_b*tb)
return 2*h*nu**3/c**2/(np.exp(x) - 1)
def dBdT(tb, nu):
x = h*nu/(k_b*tb)
slope = 2*k_b*nu**2/c**2*((x/2)/np.sinh(x/2))**2
return slope
def modis_to_healpix(file, field, temp_scale=1., map_scale=0.05, nside=512):
"""
Changes modis data to a healpix map
Arguments:
----------
file : pyhdf.SD
A file with temperature data
Keyword arguments:
----------
map_scale : float
Separation between two points in the hd5 data in degrees (default : 0.05)
nside : int
Healpix nside of the outupt map (default : 512)
"""
data = file.select(field).get()/temp_scale
tht = np.radians(np.arange(0, 180, modis_map_scale))
phi = np.radians(np.arange(0, 360, modis_map_scale))
theta_modis, phi_modis = np.meshgrid(tht, phi)
healp_map = np.zeros(hp.nside2npix(512))
healp_map[hp.ang2pix(512, tht, phi)]=np.swapaxes(data, 1,0)
return healp_map
def rotate_to_point(inmap, lat, lon):
"""
Rotates healpy such that the North Pole is at the point defined by
(lat lon). Returns rotated map
Arguments:
----------
inmap : (12*N*N,) array of floats
Input map in the healpix RING format
lat : float
Latitude of point on the map [-90;90]
lon : float
Longitude of point on the map [-180;80]
"""
nside = hp.npix2nside(inmap.shape[0])
rlon = np.radians(lon)-np.pi
rlat = np.pi/2.-np.radians(lat)
x0, y0, z0 = hp.pix2vec(512, np.arange(hp.nside2npix(512)))
x1 = x0*np.cos(rlat)+z0*np.sin(rlat)
z = -x0*np.sin(rlat)+z0*np.cos(rlat)
x = x1*np.cos(rlon)-y0*np.sin(rlon)
y = x1*np.sin(rlon)+y0*np.cos(rlon)
pix_prime = hp.vec2pix(512, x,y,z)
return inmap[pix_prime]
def telescope_view_angles(nside, h, surf_h=0., R = 6.371e6):
"""
Calculates how the coordinates of a sphere of radius R with a given
nside project on the view of an outside observer located at a distance
h away from the north pole. Returns visible coordinates on the sphere
and corresponding coordinates for the observer.
Arguments:
----------
nside : int
Healpix nside of the input map
h : float
Altitude of observer above reference level in m
Keyword arguments:
----------
surf_h : float
Altitude of ground at pole above reference level (default : 0.)
R : float
Radius of sphere (default : Earth's Radius)
"""
r_ground = R+surf_h
h_abg = h - surf_h
theta_fov = np.arccos((r_ground) / (r_ground + h_abg))
theta, phi = hp.pix2ang(nside, np.arange(hp.nside2npix(nside)))
theta_visible = theta[theta<theta_fov]
phi_visible = phi[theta<theta_fov]
theta_from_tel = np.arctan2(r_ground*np.sin(theta_visible),
r_ground*(1 - np.cos(theta_visible)) + h_abg)
theta_from_tel = np.pi - theta_from_tel #Up is down
phi_from_tel = np.pi - phi_visible #Therefore left is right
return(theta_visible, phi_visible, theta_from_tel, phi_from_tel)
def ground_template(inmap, theta_visible, phi_visible, theta_from_tel,
phi_from_tel, nside_out=128, cmb=True, freq=95.,
frac_bwidth=.2):
"""
Creates a ground template given a world map and sets of coordinates
(see telescope_view_angles) Returns a filled-out ground template.
Arguments:
----------
inmap : (12*N*N,) array of floats
Input map in the healpix RING format
theta_visible : (M,) array of floats
Colatitude of the visible points of inmap in radians
phi_visible : (M,) array of floats
Longitude of the visible points of inmap in radians
theta_from_tel : (M,) array of floats
Correponding colatitude in other coordinate system
phi_from_tel : (M,) array of floats
Correponding longtitude in other coordinate system
Keyword arguments:
----------
nside_out : int
Healpix nside of the output ground template (default : 128)
cmb : bool
Convert the temperatures to CMB temperature units (default : True)
freq : float
Frequency at which temperature is measured, in GHz (default : 95)
frac_bwidth : float
Bandwidth of the measurement, as a fraction of freq (default : 0.2)
"""
nside_world = hp.npix2nside(inmap.shape[0])
ground_map = np.ones(hp.nside2npix(nside_out))*hp.UNSEEN
ground_pix = hp.ang2pix(nside_out, theta_from_tel, phi_from_tel)
ground_map[ground_pix] = inmap[hp.ang2pix(nside_world, theta_visible, phi_visible)]
if cmb:
freq_band=np.linspace(freq*(1-frac_bwidth/2.), freq*(1+frac_bwidth/2.),
201)
for i, tb in enumerate(ground_map):
if tb!=hp.UNSEEN:
bolo = np.trapz(tb2b(tb, freq_band), freq_band)
corr = np.trapz(dBdT(T_cmb, freq_band), freq_band)
ground_map[i] = bolo/corr*1e6
pix_pow = int(np.log2(nside_out))
map_low = hp.ud_grade(ground_map, 2)
for i in range(pix_pow+1):
nside = int(2**i)
map_normal = hp.ud_grade(ground_map, nside)
map_horizon = np.amin(hp.ang2pix(nside, theta_from_tel, phi_visible))
map_normal[map_horizon:] = np.where(
map_normal[map_horizon:]!=hp.UNSEEN, map_normal[map_horizon:],
hp.ud_grade(map_low, nside)[map_horizon:])
map_low = map_normal
return map_normal
def template_from_position(earth_map, lat, lon, h, nside_out=128,
cmb=True, freq=95., frac_bwidth=.2):
"""
Creates a ground template given a world map, a position and an altitude.
Returns a filled-out ground template.
Arguments:
----------
earth_map : (12*N*N,) array of floats
Input map in K, in the healpix RING format
lat : float
Latitude of point on the map [-90;90]
lon : float
Longitude of point on the map [-180;80]
h : float
Altitude of observer above reference level in m
Keyword arguments:
----------
nside_out : int
Healpix nside of the output ground template (default : 128)
cmb : bool
Convert the temperatures to CMB temperature units (default : True)
freq : float
Frequency at which temperature is measured, in GHz (default : 95)
frac_bwidth : float
Bandwidth of the measurement, as a fraction of freq (default : 0.2)
"""
nside_world = hp.npix2nside(earth_map.shape[0])
earth_rot = rotate_to_point(earth_map, lat, lon)
theta_visible, phi_visible, theta_from_tel, phi_from_tel = telescope_view_angles(
nside_world, h, surf_h=0, R=6.371e6)
ground_temp = ground_template(earth_rot, theta_visible, phi_visible,
theta_from_tel, phi_from_tel,
nside_out=nside_out, cmb=cmb, freq=freq,
frac_bwidth=frac_bwidth)
return ground_temp