def find_Tmoist(thetaE0, press):
"""
Calculates the temperatures along a moist adiabat.
Parameters
----------
thetaE0 : float
Initial equivalent potential temperature (K).
press : float or array_like
Pressure (Pa).
Returns
-------
Temp : float or array_like
Temperature (K) of thetaE0 adiabat at 'press'.
Examples
--------
>>> np.array([find_Tmoist(300., 8.e4)])
array([ 271.0638])
>>> find_Tmoist(330., 8.e4)
283.7226584032411
"""
Tstart = c.Tc
try:
brackets = rf.find_interval(thetaes_diff, Tstart, thetaE0, press)
Temp = rf.fzero(thetaes_diff, brackets, thetaE0, press)
except BracketError as e:
print("couldn't find bracket: debug info: ",e.extra_info)
Temp = np.nan
return Temp
def find_Tmoist(thetaE0, press):
"""
Calculates the temperatures along a moist adiabat.
Parameters
----------
thetaE0 : float
Initial equivalent potential temperature (K).
press : float or array_like
Pressure (Pa).
Returns
-------
Temp : float or array_like
Temperature (K) of thetaE0 adiabat at 'press'.
Examples
--------
>>> find_Tmoist(300., 8.e4)
270.59590841970277
>>> find_Tmoist(330., 800)
290.98965468303
"""
Tstart=c.Tc
brackets=rf.find_interval(thetaes_diff,Tstart,thetaE0,press)
Temp = rf.fzero(thetaes_diff,brackets,thetaE0,press)
return Temp
def temp_from_theta(theta,press):
"""
input: theta (K), press (Pa)
output: temp (K) found by rootfinder
"""
#
# use theta as guess for bracket and pass theta,press to theta_zero
#
brackets=rf.find_interval(theta_zero,theta,theta,press)
the_temp = rf.fzero(theta_zero,brackets,theta,press)
return the_temp
def tinvert_thetae(thetaeVal, rT, press):
"""
temp,rv,rl=tinvert_thetae(thetaeVal, rT, press)
Uses a rootfinder to determine the temperature for which the
pseudo equivilant potential temperature (thetaepress) is equal to the
equivilant potential temperature (thetae) of the parcel.
Parameters
----------
thetaeVal : float
Thetae of parcel (K).
rT : float
Total water mixing ratio (kg/kg).
press : float
Pressure of parcel in (Pa).
Returns
-------
theTemp : float
Temperature for which thetaep equals the parcel thetae (K).
rv : float
Vapor mixing ratio of the parcel (kg/kg).
rl : float
liquid water mixing ratio of the parcel (kg/kg) at 'press'.
Raises
------
IOError
If 'press' is larger than 100000 Pa.
Examples
--------
>>> tinvert_thetae(300., 0.001, 8.e4)
(278.4050485684102, 0.001, 0)
"""
if press > 1.e5:
raise IOError('expecting pressure level less than 100000 Pa')
# The temperature has to be somewhere between thetae
# (T at surface) and -40 deg. C (no ice).
Tstart = c.Tc
brackets = rf.find_interval(find_resid_thetae, Tstart, thetaeVal, rT,
press)
theTemp = rf.fzero(find_resid_thetae, brackets, thetaeVal, rT, press)
rv, rl = find_rvrl(theTemp, rT, press)
return theTemp, rv, rl
def tinvert_rsat(Tstart,rsat,press):
"""
rootfind the temp that produces rsat at press.
Parameters
----------
temp : float
temperature (K)
rsat : float
saturation mixing ratio (kg/kg)
press : float
pressure (hPa)
Returns
-------
Tdew : temperature (K) at with air is saaturated
"""
brackets=rf.find_interval(find_resid_rsat,Tstart,rsat,press)
temp = rf.fzero(find_resid_rsat,brackets,rsat,press)
return temp
cloud_vars['koehler_fun'] = koehler_fun
# ### find the equilibrium radius for each bin at saturation Sinit
# In[41]:
S_target = parcel.Sinit
logr_start = np.log(0.1e-6)
initial_radius = []
dry_radius = []
for mass in center_mass:
brackets = np.array(find_interval(find_diff,logr_start,S_target,mass,koehler_fun))
left_bracket, right_bracket = np.exp(brackets)*1.e6 #get brackets in microns for printing
equil_rad = np.exp(fzero(find_diff,brackets,S_target,mass,koehler_fun))
initial_radius.append(equil_rad)
dry_rad = (mass/(4./3.*np.pi*aero.rhoaero))**(1./3.)
dry_radius.append(dry_rad)
print('mass = {mass:6.3g} kg'.format_map(locals()))
print('equlibrium radius at S={} is {:5.3f} microns\n'.format(S_target,equil_rad*1.e6))
# ### now add the intial conditions to the cloud_vars dictionary and make it a namedtuple
#
# the vector var_vec holds 30 droplet radii plus three extra variables at the
# end of the vector: the temperature, pressure and height.
# In[42]:
matplotlib.style.use('ggplot')
fig,ax = plt.subplots(1,1)
rvals=np.linspace(0.05,0.3,50)*1.e-6
Svals = find_S(rvals)
ax.plot(rvals*1.e6,(Svals -1)*1.e2)
out=ax.set(ylim=[-1,1],xlim = [0.05,0.3],
ylabel='Supersaturation (e/es - 1) %',xlabel='radius (microns)')
# ### 2. Find haze particle equilibrium radius at S=0.9
# In[21]:
def find_diff(r,S_target):
return S_target - find_S(r)
S_target = 0.90
r_start = 0.1e-6
from a405thermo.rootfinder import find_interval, fzero
brackets = np.array(find_interval(find_diff,r_start,S_target))
print('left bracket = {:8.3e} microns, right bracket={:8.3e} microns'.format(*(brackets*1.e6)))
equil_rad = fzero(find_diff,brackets,S_target)
print('equlibrium radius at S={} is {:5.3f} microns'.format(S_target,equil_rad*1.e6))
# In[ ]:
print(help(rf.find_interval))
# ### example -- find a bracket for sin(x)=0 near x=12 radians ~ 700 degrees
# In[8]:
brackets=rf.find_interval(np.sin,12)
brackets
# ## now use the fzero wrapper to find the root of sin(x)=0 (720 degrees)
# In[9]:
print(rf.fzero(np.sin,brackets)*180/np.pi)
# ## Redo theta example with find_interval
# In[39]:
import a405thermo.rootfinder as rf
from importlib import reload
reload(rf)
def theta_zero(Tguess,theta,press):
"""Function we want to find the root of
input: Tguess (K), target theta (K), press (Pa)
output: difference between guess and target -- should be zero when x is a root
"""
def zero_find_es(temp):
esguess=standard_es(temp)
brackets=rf.find_interval(zero_es,esguess,temp)
resid = rf.fzero(zero_es,brackets,temp)
return resid
def find_diff(logr,S_target,m):
"""
zero function for rootfinder
"""
r = np.exp(logr)
return S_target - koehler_fun(r,m)
S_target = parcel.Sinit
logr_start = np.log(0.1e-6)
initial_radius = []
for mass in center_mass:
brackets = np.array(find_interval(find_diff,logr_start,S_target,mass))
left_bracket, right_bracket = np.exp(brackets)*1.e6 #get brackets in microns for printing
equil_rad = np.exp(fzero(find_diff,brackets,S_target,mass))
Scrit=(4.*a**3./(27.*b*mass))**0.5
initial_radius.append(equil_rad)
print(('mass = {mass:6.3g} kg\n'
'left bracket = {left_bracket:8.3e} microns\n'
'right bracket={right_bracket:8.3e} microns\n'
'critical supersaturation: {Scrit:6.3g}')
.format_map(locals()))
print('equlibrium radius at S={} is {:5.3f} microns\n'.format(S_target,equil_rad*1.e6))
# In[ ]:
# In[4]:
def rv_diff(press,thetae_mix,rT_mix):
"""
the lcl is is the pressure where rv=rT_mix
we want a difference that changes sign at cloud base
so below cloud set rv = rsat(temp,press) and
rT_mix - rv will be negative below cloud base and
positive above cloud base
"""
Temp, rv, rl = tinvert_thetae(thetae_mix,rT_mix,press)
#
# below cloud rl ~ 0, so switch to rv=rsat
#
if rl < 1.e-5:
rv=find_rsat(Temp,press)
diff = rT_mix - rv
return diff
from a405thermo.rootfinder import find_interval,fzero
bracket=find_interval(rv_diff,7.e4,thetae_mix,rt_mix)
print('found bracket =',bracket)
lcl_press=fzero(rv_diff,bracket,thetae_mix,rt_mix)
print('the lcl pressure is {} hPa'.format(n(lcl_press*1.e-2)))
# In[ ]: