def thetal(press, Temp, rt):
"""
input: press in kPa (1d vector or scalar)
temp in K (1d vector or scalar
mixing ratio in kg/kg (1d vector or scalar)
# emanuel p. 121 4.5.15
"""
isscalar = test_scalar(press, Temp, rt)
press = np.atleast_1d(press)
Temp = np.atleast_1d(Temp)
rt = np.atleast_1d(rt)
rl = np.empty_like(rt)
rsat = rs_tp(Temp, press)
CPn = tc.RD + rt * tc.RV
chi = CPn / (tc.CPD + rt * tc.CPV)
gamma = (rt * tc.RV) / CPn
saturated = rt > rsat
rl[saturated] = rt[saturated] - rsat[saturated]
unsaturated = np.logical_not(saturated)
rl[unsaturated] = 0
LV = L_t(Temp)
theta = Temp * (tc.P0 / press)**chi
term1 = (1. - rl / (tc.EPS + rt))**chi
term2 = (1 - rl / rt)**(-gamma)
term3 = -LV * rl / (CPn * Temp)
term3 = np.exp(term3)
theThetal = theta * term1 * term2 * term3
if isscalar:
theThetal = theThetal[0]
return theThetal
def tro_trtp(t, rt, pressKpa):
"""in: t=temperature (K),pressKpa= pressure (kPa)
rt=mixing ratio (kg/kg)
out:tro=density temperature (K) (vector)
"""
isscalar = test_scalar(t, rt, pressKpa)
if not isscalar:
t = np.atleast_1d(t)
rt = np.atleast_1d(rt)
rv = np.empty_like(rt)
pressKpa = np.atleast_1d(pressKpa)
rs = rs_tp(t, pressKpa)
out = np.empty(rs.shape, dtype=np.float)
saturated = (rt >= rs)
unsaturated = np.logical_not(saturated)
rl = np.zeros(out.shape, dtype=np.float)
rl[saturated] = rt[saturated] - rs[saturated]
rl[unsaturated] = 0
rv[saturated] = rs[saturated]
rv[unsaturated] = rt[unsaturated]
out[saturated] = t[saturated] * (1. + 0.611 * rs[saturated] -
rl[saturated])
out[unsaturated] = t[unsaturated] * (1. + 0.611 * rt[unsaturated])
out = t * (1 + rv / tc.EPS) / (1. + rt)
if isscalar:
out = out[0]
return out
def tro_trtp(t,rt,pressKpa):
"""in: t=temperature (K),pressKpa= pressure (kPa)
rt=mixing ratio (kg/kg)
out:tro=density temperature (K) (vector)
"""
isscalar = test_scalar(t,rt,pressKpa)
if not isscalar:
t=np.atleast_1d(t)
rt=np.atleast_1d(rt)
rv=np.empty_like(rt)
pressKpa=np.atleast_1d(pressKpa)
rs=rs_tp(t,pressKpa)
out=np.empty(rs.shape,dtype=np.float)
saturated = (rt>=rs)
unsaturated=np.logical_not(saturated)
rl=np.zeros(out.shape,dtype=np.float)
rl[saturated]=rt[saturated] - rs[saturated]
rl[unsaturated]=0
rv[saturated]=rs[saturated]
rv[unsaturated]=rt[unsaturated]
out[saturated]=t[saturated]*(1.+0.611*rs[saturated]-rl[saturated])
out[unsaturated]=t[unsaturated]*(1.+ 0.611*rt[unsaturated])
out=t*(1 + rv/tc.EPS)/(1. + rt)
if isscalar:
out=out[0]
return out
def thetal(press,Temp,rt):
"""
input: press in kPa (1d vector or scalar)
temp in K (1d vector or scalar
mixing ratio in kg/kg (1d vector or scalar)
# emanuel p. 121 4.5.15
"""
isscalar = test_scalar(press,Temp,rt)
press=np.atleast_1d(press)
Temp=np.atleast_1d(Temp)
rt = np.atleast_1d(rt)
rl=np.empty_like(rt)
rsat=rs_tp(Temp,press)
CPn=tc.RD + rt*tc.RV
chi=CPn/(tc.CPD + rt*tc.CPV)
gamma=(rt*tc.RV)/CPn
saturated=rt > rsat
rl[saturated]=rt[saturated] - rsat[saturated]
unsaturated=np.logical_not(saturated)
rl[unsaturated]=0
LV=L_t(Temp)
theta=Temp*(tc.P0/press)**chi
term1=(1. - rl/(tc.EPS + rt))**chi
term2=(1 - rl/rt)**(-gamma)
term3= -LV*rl/(CPn*Temp)
term3=np.exp(term3)
theThetal=theta*term1*term2*term3
if isscalar:
theThetal = theThetal[0]
return theThetal
def alt_thetal(press, Temp, qt):
"""
quicker approximate version of thetal
input: press in kPa (1d vector or scalar)
temp in K (1d vector or scalar
mixing ratio in kg/kg (1d vector or scalar)
"""
isscalar = test_scalar(press, Temp, qt)
press = np.atleast_1d(press)
Temp = np.atleast_1d(Temp)
qt = np.atleast_1d(qt)
ql = np.empty_like(qt)
qsat = qs_tp(Temp, press)
ql = qt - qsat
ql[ql < 0] = 0.0
theta = Temp * (100.0 / press) ** 0.288
L = 2.5e6
cpd = 1004.0
the_thetal = theta - (theta / Temp) * (L / cpd) * ql
if isscalar:
the_thetal = the_thetal[0]
return the_thetal