def tnflux3d(U, V, T, strm, lon, lat, lev, xdim, ydim, zdim,
cyclic=True, limit=100, punit=100.):
"""
Takaya & Nakamura (2001) 计算等压面上的波活动度.
Takaya, K and H. Nakamura, 2001: A formulation of a phase-independent
wave-activity flux for stationary and migratory quasigeostrophic eddies
on a zonally varying basic flow, `JAS`, 58, 608-627.
http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%282001%29058%3C0608%3AAFOAPI%3E2.0.CO%3B2
:param U: u component wind [m/s].
:param V: v component wind [m/s].
:param T: climate temperature [K].
:param strm: stream function bias [m^2/s]
:param lon: longitude degree.
:param lat: latitude degree.
:param lev: level pressure.
:param xdim: longitude dimension index.
:param ydim: latitude dimension index.
:param zdim: level dimension index.
:param cyclic: east-west cyclic boundary.
:param limit:
:param punit: level pressure unit.
:return: east-west, south-north, vertical component.
"""
U, V, T = np.asarray(U), np.asarray(V), np.asarray(T)
ndim = U.ndim
S = stability(T, lev, zdim, punit=punit)
f = arr.expand(constants.earth_f(lat), ndim, axis=ydim)
dstrmdx = dvardx(strm, lon, lat, xdim, ydim, cyclic=cyclic)
dstrmdy = dvardy(strm, lat, ydim)
dstrmdp = dvardp(strm, lev, zdim, punit=punit)
d2strmdx2 = d2vardx2(strm, lon, lat, xdim, ydim, cyclic=cyclic)
d2strmdy2 = d2vardy2(strm, lat, ydim)
d2strmdxdy = dvardy(dstrmdx, lat, ydim)
d2strmdxdp = dvardx(dstrmdp, lon, lat, xdim, ydim, cyclic=True)
d2strmdydp = dvardy(dstrmdp, lat, ydim)
tnx = U * (dstrmdx ** 2 - strm * d2strmdx2) + \
V * (dstrmdx * dstrmdy - strm * d2strmdxdy)
tny = U * (dstrmdx * dstrmdy - strm * d2strmdxdy) + \
V * (dstrmdy ** 2 - strm * d2strmdy2)
tnz = f ** 2 / S ** 2 * (
U * (dstrmdx * dstrmdp - strm * d2strmdxdp) -
V * (dstrmdy * dstrmdp - strm * d2strmdydp))
tnx = 0.5 * tnx / np.abs(U + 1j * V)
tny = 0.5 * tny / np.abs(U + 1j * V)
tnxy = np.sqrt(tnx ** 2 + tny ** 2)
tnx = np.ma.asarray(tnx)
tny = np.ma.asarray(tny)
tnz = np.ma.asarray(tnz)
tnx[(U < 0) | (tnxy > limit)] = np.ma.masked
tny[(U < 0) | (tnxy > limit)] = np.ma.masked
tnz[(U < 0) | (tnxy > limit)] = np.ma.masked
return tnx, tny, tnz
def tnflux2d(U, V, strm, lon, lat, xdim, ydim, cyclic=True, limit=100):
"""
Takaya & Nakamura (2001) 计算水平等压面上的波活动度.
Takaya, K and H. Nakamura, 2001: A formulation of a phase-independent
wave-activity flux for stationary and migratory quasigeostrophic eddies
on a zonally varying basic flow, `JAS`, 58, 608-627.
http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%282001%29058%3C0608%3AAFOAPI%3E2.0.CO%3B2
:param U: u component wind [m/s].
:param V: v component wind [m/s].
:param strm: stream function [m^2/s].
:param lon: longitude degree.
:param lat: latitude degree.
:param xdim: longitude dimension index.
:param ydim: latitude dimension index.
:param cyclic: east-west cyclic boundary.
:param limit:
:return:
"""
U, V = np.asarray(U), np.asarray(V)
ndim = U.ndim
dstrmdx = dvardx(strm, lon, lat, xdim, ydim, cyclic=cyclic)
dstrmdy = dvardy(strm, lat, ydim)
d2strmdx2 = d2vardx2(strm, lon, lat, xdim, ydim, cyclic=cyclic)
d2strmdy2 = d2vardy2(strm, lat, ydim)
d2strmdxdy = dvardy(
dvardx(strm, lon, lat, xdim, ydim, cyclic=cyclic),
lat, ydim)
tnx = U * (dstrmdx ** 2 - strm * d2strmdx2) + \
V * (dstrmdx * dstrmdy - strm * d2strmdxdy)
tny = U * (dstrmdx * dstrmdy - strm * d2strmdxdy) + \
V * (dstrmdy ** 2 - strm * d2strmdy2)
tnx = 0.5 * tnx / np.abs(U + 1j * V)
tny = 0.5 * tny / np.abs(U + 1j * V)
tnxy = np.sqrt(tnx ** 2 + tny ** 2)
tnx = np.ma.asarray(tnx)
tny = np.ma.asarray(tny)
tnx[tnxy > limit] = np.ma.masked
tny[tnxy > limit] = np.ma.masked
tnx[U < 0] = np.ma.masked
tny[U < 0] = np.ma.masked
return tnx, tny