def gms_like_ratio(weights, tracer, dp):
"""Compute ratio of integrals in the style of gross moist stability."""
# Integrate weights over lower tropospheric layer
dp = to_pascal(dp)
denominator = field_vert_int_max(weights, dp)
# Integrate tracer*weights over whole column and divide.
numerator = np.sum(weights*tracer*dp, axis=-3) / grav
return numerator / denominator
def gms_like_ratio(weights, tracer, dp):
"""Compute ratio of integrals in the style of gross moist stability."""
# Integrate weights over lower tropospheric layer
dp = to_pascal(dp)
denominator = field_vert_int_max(weights, dp)
# Integrate tracer*weights over whole column and divide.
numerator = np.sum(weights * tracer * dp, axis=-3) / grav
return numerator / denominator
def field_vert_int_max(arr, dp):
"""Maximum magnitude of integral of a field from surface up."""
dp = to_pascal(dp)
# 2015-05-15: Problem: Sigma data indexing starts at TOA, while pressure
# data indexing starts at 1000 hPa. So for now only do for
# sigma data and flip array direction to start from sfc.
arr_dp_g = (arr*dp)[::-1] / grav
# Input array dimensions are assumed ([time dims,] level, lat, lon).
pos_max = np.amax(np.cumsum(arr_dp_g, axis=0), axis=-3)
neg_max = np.amin(np.cumsum(arr_dp_g, axis=0), axis=-3)
# Flip sign because integrating from p_sfc up, i.e. with dp negative.
return -1*np.where(pos_max > -neg_max, pos_max, neg_max)
def field_vert_int_max(arr, dp):
"""Maximum magnitude of integral of a field from surface up."""
dp = to_pascal(dp)
# 2015-05-15: Problem: Sigma data indexing starts at TOA, while pressure
# data indexing starts at 1000 hPa. So for now only do for
# sigma data and flip array direction to start from sfc.
arr_dp_g = (arr * dp)[::-1] / grav
# Input array dimensions are assumed ([time dims,] level, lat, lon).
pos_max = np.amax(np.cumsum(arr_dp_g, axis=0), axis=-3)
neg_max = np.amin(np.cumsum(arr_dp_g, axis=0), axis=-3)
# Flip sign because integrating from p_sfc up, i.e. with dp negative.
return -1 * np.where(pos_max > -neg_max, pos_max, neg_max)
def msf(lats, levs, v):
"""Meridional mass streamfunction."""
# Compute half level boundaries and widths.
p_top = 5.
p_bot = 1005.
p_half = 0.5*(levs[1:] + levs[:-1])
p_half = np.insert(np.append(p_half, p_top), 0, p_bot)
dp = to_pascal(p_half[:-1] - p_half[1:])[np.newaxis, ::-1, np.newaxis]
geom_factor = (2.*np.pi*r_e/grav *
np.cos(np.deg2rad(lats))[np.newaxis, np.newaxis, :])
# Integrate from TOA down to surface.
msf_ = geom_factor * np.cumsum(v.mean(axis=-1) * dp, axis=1)[::-1]
# Average the values calculated at half levels; flip sign by convention.
msf_[:,:-1] = -0.5*(msf_[:,1:] + msf_[:,:-1])
# Uppermost level goes to 0 hPa (so divide by 2); surface value is zero.
msf_[:,-1]*=0.5
msf_[:,0] = 0.
return msf_
def msf(lats, levs, v):
"""Meridional mass streamfunction."""
# Compute half level boundaries and widths.
p_top = 5.
p_bot = 1005.
p_half = 0.5 * (levs[1:] + levs[:-1])
p_half = np.insert(np.append(p_half, p_top), 0, p_bot)
dp = to_pascal(p_half[:-1] - p_half[1:])[np.newaxis, ::-1, np.newaxis]
geom_factor = (2. * np.pi * r_e / grav *
np.cos(np.deg2rad(lats))[np.newaxis, np.newaxis, :])
# Integrate from TOA down to surface.
msf_ = geom_factor * np.cumsum(v.mean(axis=-1) * dp, axis=1)[::-1]
# Average the values calculated at half levels; flip sign by convention.
msf_[:, :-1] = -0.5 * (msf_[:, 1:] + msf_[:, :-1])
# Uppermost level goes to 0 hPa (so divide by 2); surface value is zero.
msf_[:, -1] *= 0.5
msf_[:, 0] = 0.
return msf_
