def stability(temp, lev, zdim, punit=100.):
"""
P level coordinates stability (Brunt-Vaisala).
:param temp: array_like, temperature.
:param lev: array_like, pressure level.
:param zdim: vertical dimension axis.
:param punit: pressure unit.
:return: ndarray.
"""
temp = np.asarray(temp)
ndim = temp.ndim
p = arr.expand(lev, ndim, axis=zdim) * punit
theta = pottemp(temp, lev, zdim, punit=punit)
alpha = Rd * temp / p
N = -alpha * grid.dvardp(np.log(theta), lev, zdim, punit=punit)
return N
def pottemp(temp, lev, zdim, punit=100., p0=100000.):
"""
Calculate potential temperature.
:param temp: array_like, temperature [K].
:param lev: array_like, level [punit*Pa].
:param zdim: vertical dimensions.
:param punit: pressure level punit.
:param p0: reference pressure.
:return: ndarray.
"""
temp = np.asarray(temp)
ndim = temp.ndim
p = arr.expand(lev, ndim, axis=zdim)
out = temp * ((p0 / p / punit)**kappa)
return out
def ertelpv(uwnd,
vwnd,
temp,
lon,
lat,
lev,
xdim,
ydim,
zdim,
cyclic=True,
punit=100.,
sphere=True):
"""
Calculate Ertel potential vorticity.
Hoskins, B.J., M.E. McIntyre and A.E. Robertson, 1985:
On the use and significance of isentropic potential
vorticity maps, `QJRMS`, 111, 877-946,
<http://onlinelibrary.wiley.com/doi/10.1002/qj.49711147002/abstract>
:param uwnd: ndarray, u component wind [m/s].
:param vwnd: ndarray, v component wind [m/s].
:param temp: ndarray, temperature [K].
:param lon: array_like, longitude [degrees].
:param lat: array_like, latitude [degrees].
:param lev: array_like, pressure level [punit*Pa].
:param xdim: west-east axis
:param ydim: south-north axis
:param zdim: vertical axis
:param cyclic: west-east cyclic boundary
:param punit: pressure level unit
:param sphere: sphere coordinates.
:return:
"""
u, v, t = np.ma.getdata(uwnd), np.ma.getdata(vwnd), np.ma.getdata(temp)
mask = np.ma.getmask(uwnd) | np.ma.getmask(vwnd) | np.ma.getmask(temp)
ndim = u.ndim
# potential temperature
theta = pottemp(t, lev, zdim, punit=punit)
# partial derivation
dthdp = dvardp(theta, lev, zdim, punit=punit)
dudp = dvardp(u, lev, zdim, punit=punit)
dvdp = dvardp(v, lev, zdim, punit=punit)
dthdx = dvardx(theta, lon, lat, xdim, ydim, cyclic=cyclic, sphere=sphere)
dthdy = dvardy(theta, lat, ydim, sphere=sphere)
# absolute vorticity
vor = rot(u, v, lon, lat, xdim, ydim, cyclic=cyclic, sphere=sphere)
f = arr.expand(constants.earth_f(lat), ndim, axis=ydim)
avor = f + vor
out = -g * (avor * dthdp - (dthdx * dvdp - dthdy * dudp))
out = np.ma.array(out, mask=mask)
out = arr.mrollaxis(out, ydim, 0)
out[0, ...] = np.ma.masked
out[-1, ...] = np.ma.masked
out = arr.mrollaxis(out, 0, ydim + 1)
return out
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