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Copy pathTurbulence_PrognosticTKE.pyx
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Turbulence_PrognosticTKE.pyx
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#!python
#cython: boundscheck=False
#cython: wraparound=False
#cython: initializedcheck=True
#cython: cdivision=False
import numpy as np
include "parameters.pxi"
import cython
import sys
cimport EDMF_Updrafts
from Grid cimport Grid
cimport EDMF_Environment
from Variables cimport VariablePrognostic, VariableDiagnostic, GridMeanVariables
from Surface cimport SurfaceBase
from Cases cimport CasesBase
from ReferenceState cimport ReferenceState
from TimeStepping cimport TimeStepping
from NetCDFIO cimport NetCDFIO_Stats
from thermodynamic_functions cimport *
from turbulence_functions cimport *
from utility_functions cimport *
from libc.math cimport fmax, sqrt, exp, pow, cbrt, fmin, fabs
from cpython.mem cimport PyMem_Malloc, PyMem_Realloc, PyMem_Free
cdef class EDMF_PrognosticTKE(ParameterizationBase):
# Initialize the class
def __init__(self, namelist, paramlist, Grid Gr, ReferenceState Ref):
# Initialize the base parameterization class
ParameterizationBase.__init__(self, paramlist, Gr, Ref)
# Set the number of updrafts (1)
try:
self.n_updrafts = namelist['turbulence']['EDMF_PrognosticTKE']['updraft_number']
except:
self.n_updrafts = 1
print('Turbulence--EDMF_PrognosticTKE: defaulting to single updraft')
try:
self.use_steady_updrafts = namelist['turbulence']['EDMF_PrognosticTKE']['use_steady_updrafts']
except:
self.use_steady_updrafts = False
try:
self.use_local_micro = namelist['turbulence']['EDMF_PrognosticTKE']['use_local_micro']
except:
self.use_local_micro = True
print('Turbulence--EDMF_PrognosticTKE: defaulting to local (level-by-level) microphysics')
try:
self.calc_tke = namelist['turbulence']['EDMF_PrognosticTKE']['calculate_tke']
except:
self.calc_tke = True
try:
self.calc_scalar_var = namelist['turbulence']['EDMF_PrognosticTKE']['calc_scalar_var']
except:
self.calc_scalar_var = False
if (self.calc_scalar_var==True and self.calc_tke==False):
sys.exit('Turbulence--EDMF_PrognosticTKE: >>calculate_tke<< must be set to True when >>calc_scalar_var<< is True (to calculate the mixing length for the variance and covariance calculations')
try:
if str(namelist['turbulence']['EDMF_PrognosticTKE']['entrainment']) == 'inverse_z':
self.entr_detr_fp = entr_detr_inverse_z
elif str(namelist['turbulence']['EDMF_PrognosticTKE']['entrainment']) == 'dry':
self.entr_detr_fp = entr_detr_dry
elif str(namelist['turbulence']['EDMF_PrognosticTKE']['entrainment']) == 'inverse_w':
self.entr_detr_fp = entr_detr_inverse_w
elif str(namelist['turbulence']['EDMF_PrognosticTKE']['entrainment']) == 'b_w2':
self.entr_detr_fp = entr_detr_b_w2
elif str(namelist['turbulence']['EDMF_PrognosticTKE']['entrainment']) == 'entr_detr_tke':
self.entr_detr_fp = entr_detr_tke
elif str(namelist['turbulence']['EDMF_PrognosticTKE']['entrainment']) == 'entr_detr_tke2':
self.entr_detr_fp = entr_detr_tke2
elif str(namelist['turbulence']['EDMF_PrognosticTKE']['entrainment']) == 'suselj':
self.entr_detr_fp = entr_detr_suselj
elif str(namelist['turbulence']['EDMF_PrognosticTKE']['entrainment']) == 'none':
self.entr_detr_fp = entr_detr_none
else:
print('Turbulence--EDMF_PrognosticTKE: Entrainment rate namelist option is not recognized')
except:
self.entr_detr_fp = entr_detr_b_w2
print('Turbulence--EDMF_PrognosticTKE: defaulting to cloudy entrainment formulation')
if(self.calc_tke == False and 'tke' in str(namelist['turbulence']['EDMF_PrognosticTKE']['entrainment'])):
sys.exit('Turbulence--EDMF_PrognosticTKE: >>calc_tke<< must be set to True when entrainment is using tke')
try:
self.similarity_diffusivity = namelist['turbulence']['EDMF_PrognosticTKE']['use_similarity_diffusivity']
except:
self.similarity_diffusivity = False
print('Turbulence--EDMF_PrognosticTKE: defaulting to TKE-based eddy diffusivity')
if(self.similarity_diffusivity == False and self.calc_tke ==False):
sys.exit('Turbulence--EDMF_PrognosticTKE: either >>use_similarity_diffusivity<< or >>calc_tke<< flag is needed to get the eddy diffusivities')
if(self.similarity_diffusivity == True and self.calc_tke == True):
print("TKE will be calculated but not used for eddy diffusivity calculation")
try:
self.extrapolate_buoyancy = namelist['turbulence']['EDMF_PrognosticTKE']['extrapolate_buoyancy']
except:
self.extrapolate_buoyancy = True
print('Turbulence--EDMF_PrognosticTKE: defaulting to extrapolation of updraft buoyancy along a pseudoadiabat')
try:
self.mixing_scheme = str(namelist['turbulence']['EDMF_PrognosticTKE']['mixing_length'])
except:
self.mixing_scheme = 'tke'
print 'Using tke mixing length formulation as default'
# Get values from paramlist
# set defaults at some point?
self.surface_area = paramlist['turbulence']['EDMF_PrognosticTKE']['surface_area']
self.max_area_factor = paramlist['turbulence']['EDMF_PrognosticTKE']['max_area_factor']
self.entrainment_factor = paramlist['turbulence']['EDMF_PrognosticTKE']['entrainment_factor']
self.detrainment_factor = paramlist['turbulence']['EDMF_PrognosticTKE']['detrainment_factor']
self.pressure_buoy_coeff = paramlist['turbulence']['EDMF_PrognosticTKE']['pressure_buoy_coeff']
self.pressure_drag_coeff = paramlist['turbulence']['EDMF_PrognosticTKE']['pressure_drag_coeff']
self.pressure_plume_spacing = paramlist['turbulence']['EDMF_PrognosticTKE']['pressure_plume_spacing']
# "Legacy" coefficients used by the steady updraft routine
self.vel_pressure_coeff = self.pressure_drag_coeff/self.pressure_plume_spacing
self.vel_buoy_coeff = 1.0-self.pressure_buoy_coeff
if self.calc_tke == True:
self.tke_ed_coeff = paramlist['turbulence']['EDMF_PrognosticTKE']['tke_ed_coeff']
self.tke_diss_coeff = paramlist['turbulence']['EDMF_PrognosticTKE']['tke_diss_coeff']
# Need to code up as paramlist option?
self.minimum_area = 1e-3
# Create the updraft variable class (major diagnostic and prognostic variables)
self.UpdVar = EDMF_Updrafts.UpdraftVariables(self.n_updrafts, namelist,paramlist, Gr)
# Create the class for updraft thermodynamics
self.UpdThermo = EDMF_Updrafts.UpdraftThermodynamics(self.n_updrafts, Gr, Ref, self.UpdVar)
# Create the class for updraft microphysics
self.UpdMicro = EDMF_Updrafts.UpdraftMicrophysics(paramlist, self.n_updrafts, Gr, Ref)
# Create the environment variable class (major diagnostic and prognostic variables)
self.EnvVar = EDMF_Environment.EnvironmentVariables(namelist,Gr)
# Create the class for environment thermodynamics
self.EnvThermo = EDMF_Environment.EnvironmentThermodynamics(namelist, paramlist, Gr, Ref, self.EnvVar)
# Entrainment rates
self.entr_sc = np.zeros((self.n_updrafts, Gr.nzg),dtype=np.double,order='c')
#self.press = np.zeros((self.n_updrafts, Gr.nzg),dtype=np.double,order='c')
# Detrainment rates
self.detr_sc = np.zeros((self.n_updrafts, Gr.nzg,),dtype=np.double,order='c')
# Pressure term in updraft vertical momentum equation
self.updraft_pressure_sink = np.zeros((self.n_updrafts, Gr.nzg,),dtype=np.double,order='c')
# Mass flux
self.m = np.zeros((self.n_updrafts, Gr.nzg),dtype=np.double, order='c')
# mixing length
self.mixing_length = np.zeros((Gr.nzg,),dtype=np.double, order='c')
# Near-surface BC of updraft area fraction
self.area_surface_bc= np.zeros((self.n_updrafts,),dtype=np.double, order='c')
self.w_surface_bc= np.zeros((self.n_updrafts,),dtype=np.double, order='c')
self.h_surface_bc= np.zeros((self.n_updrafts,),dtype=np.double, order='c')
self.qt_surface_bc= np.zeros((self.n_updrafts,),dtype=np.double, order='c')
# Mass flux tendencies of mean scalars (for output)
self.massflux_tendency_h = np.zeros((Gr.nzg,),dtype=np.double,order='c')
self.massflux_tendency_qt = np.zeros((Gr.nzg,),dtype=np.double,order='c')
# (Eddy) diffusive tendencies of mean scalars (for output)
self.diffusive_tendency_h = np.zeros((Gr.nzg,),dtype=np.double,order='c')
self.diffusive_tendency_qt = np.zeros((Gr.nzg,),dtype=np.double,order='c')
# Vertical fluxes for output
self.massflux_h = np.zeros((Gr.nzg,),dtype=np.double,order='c')
self.massflux_qt = np.zeros((Gr.nzg,),dtype=np.double,order='c')
self.diffusive_flux_h = np.zeros((Gr.nzg,),dtype=np.double,order='c')
self.diffusive_flux_qt = np.zeros((Gr.nzg,),dtype=np.double,order='c')
if self.calc_tke:
self.massflux_tke = np.zeros((Gr.nzg,),dtype=np.double,order='c')
# Added by Ignacio : Length scheme in use (mls), and smooth min effect (ml_ratio)
self.mls = np.zeros((Gr.nzg,),dtype=np.double, order='c')
self.ml_ratio = np.zeros((Gr.nzg,),dtype=np.double, order='c')
return
cpdef initialize(self, GridMeanVariables GMV):
self.UpdVar.initialize(GMV)
return
# Initialize the IO pertaining to this class
cpdef initialize_io(self, NetCDFIO_Stats Stats):
self.UpdVar.initialize_io(Stats)
self.EnvVar.initialize_io(Stats)
Stats.add_profile('eddy_viscosity')
Stats.add_profile('eddy_diffusivity')
Stats.add_profile('entrainment_sc')
Stats.add_profile('detrainment_sc')
Stats.add_profile('massflux')
Stats.add_profile('massflux_h')
Stats.add_profile('massflux_qt')
Stats.add_profile('massflux_tendency_h')
Stats.add_profile('massflux_tendency_qt')
Stats.add_profile('diffusive_flux_h')
Stats.add_profile('diffusive_flux_qt')
Stats.add_profile('diffusive_tendency_h')
Stats.add_profile('diffusive_tendency_qt')
Stats.add_profile('total_flux_h')
Stats.add_profile('total_flux_qt')
Stats.add_profile('mixing_length')
Stats.add_profile('updraft_qt_precip')
Stats.add_profile('updraft_thetal_precip')
if self.calc_tke:
Stats.add_profile('tke_buoy')
Stats.add_profile('tke_dissipation')
Stats.add_profile('tke_entr_gain')
Stats.add_profile('tke_detr_loss')
Stats.add_profile('tke_shear')
Stats.add_profile('tke_pressure')
Stats.add_profile('tke_interdomain')
if self.calc_scalar_var:
Stats.add_profile('Hvar_dissipation')
Stats.add_profile('QTvar_dissipation')
Stats.add_profile('HQTcov_dissipation')
Stats.add_profile('Hvar_entr_gain')
Stats.add_profile('QTvar_entr_gain')
Stats.add_profile('Hvar_detr_loss')
Stats.add_profile('QTvar_detr_loss')
Stats.add_profile('HQTcov_detr_loss')
Stats.add_profile('HQTcov_entr_gain')
Stats.add_profile('Hvar_shear')
Stats.add_profile('QTvar_shear')
Stats.add_profile('HQTcov_shear')
Stats.add_profile('Hvar_rain')
Stats.add_profile('QTvar_rain')
Stats.add_profile('HQTcov_rain')
Stats.add_profile('Hvar_interdomain')
Stats.add_profile('QTvar_interdomain')
Stats.add_profile('HQTcov_interdomain')
return
cpdef io(self, NetCDFIO_Stats Stats):
cdef:
Py_ssize_t k, i
Py_ssize_t kmin = self.Gr.gw
Py_ssize_t kmax = self.Gr.nzg-self.Gr.gw
double [:] mean_entr_sc = np.zeros((self.Gr.nzg,), dtype=np.double, order='c')
double [:] mean_detr_sc = np.zeros((self.Gr.nzg,), dtype=np.double, order='c')
double [:] massflux = np.zeros((self.Gr.nzg,), dtype=np.double, order='c')
double [:] mf_h = np.zeros((self.Gr.nzg,), dtype=np.double, order='c')
double [:] mf_qt = np.zeros((self.Gr.nzg,), dtype=np.double, order='c')
self.UpdVar.io(Stats)
self.EnvVar.io(Stats)
Stats.write_profile('eddy_viscosity', self.KM.values[self.Gr.gw:self.Gr.nzg-self.Gr.gw])
Stats.write_profile('eddy_diffusivity', self.KH.values[self.Gr.gw:self.Gr.nzg-self.Gr.gw])
with nogil:
for k in xrange(self.Gr.gw, self.Gr.nzg-self.Gr.gw):
mf_h[k] = interp2pt(self.massflux_h[k], self.massflux_h[k-1])
mf_qt[k] = interp2pt(self.massflux_qt[k], self.massflux_qt[k-1])
massflux[k] = interp2pt(self.m[0,k], self.m[0,k-1])
if self.UpdVar.Area.bulkvalues[k] > 0.0:
for i in xrange(self.n_updrafts):
mean_entr_sc[k] += self.UpdVar.Area.values[i,k] * self.entr_sc[i,k]/self.UpdVar.Area.bulkvalues[k]
mean_detr_sc[k] += self.UpdVar.Area.values[i,k] * self.detr_sc[i,k]/self.UpdVar.Area.bulkvalues[k]
Stats.write_profile('entrainment_sc', mean_entr_sc[self.Gr.gw:self.Gr.nzg-self.Gr.gw])
Stats.write_profile('detrainment_sc', mean_detr_sc[self.Gr.gw:self.Gr.nzg-self.Gr.gw])
Stats.write_profile('massflux', massflux[self.Gr.gw:self.Gr.nzg-self.Gr.gw ])
Stats.write_profile('massflux_h', mf_h[self.Gr.gw:self.Gr.nzg-self.Gr.gw])
Stats.write_profile('massflux_qt', mf_qt[self.Gr.gw:self.Gr.nzg-self.Gr.gw])
Stats.write_profile('massflux_tendency_h', self.massflux_tendency_h[self.Gr.gw:self.Gr.nzg-self.Gr.gw])
Stats.write_profile('massflux_tendency_qt', self.massflux_tendency_qt[self.Gr.gw:self.Gr.nzg-self.Gr.gw])
Stats.write_profile('diffusive_flux_h', self.diffusive_flux_h[self.Gr.gw:self.Gr.nzg-self.Gr.gw])
Stats.write_profile('diffusive_flux_qt', self.diffusive_flux_qt[self.Gr.gw:self.Gr.nzg-self.Gr.gw])
Stats.write_profile('diffusive_tendency_h', self.diffusive_tendency_h[self.Gr.gw:self.Gr.nzg-self.Gr.gw])
Stats.write_profile('diffusive_tendency_qt', self.diffusive_tendency_qt[self.Gr.gw:self.Gr.nzg-self.Gr.gw])
Stats.write_profile('total_flux_h', np.add(mf_h[self.Gr.gw:self.Gr.nzg-self.Gr.gw],
self.diffusive_flux_h[self.Gr.gw:self.Gr.nzg-self.Gr.gw]))
Stats.write_profile('total_flux_qt', np.add(mf_qt[self.Gr.gw:self.Gr.nzg-self.Gr.gw],
self.diffusive_flux_qt[self.Gr.gw:self.Gr.nzg-self.Gr.gw]))
Stats.write_profile('mixing_length', self.mixing_length[kmin:kmax])
Stats.write_profile('updraft_qt_precip', self.UpdMicro.prec_source_qt_tot[kmin:kmax])
Stats.write_profile('updraft_thetal_precip', self.UpdMicro.prec_source_h_tot[kmin:kmax])
if self.calc_tke:
self.compute_covariance_dissipation(self.EnvVar.TKE)
Stats.write_profile('tke_dissipation', self.EnvVar.TKE.dissipation[kmin:kmax])
Stats.write_profile('tke_entr_gain', self.EnvVar.TKE.entr_gain[kmin:kmax])
self.compute_covariance_detr(self.EnvVar.TKE)
Stats.write_profile('tke_detr_loss', self.EnvVar.TKE.detr_loss[kmin:kmax])
Stats.write_profile('tke_shear', self.EnvVar.TKE.shear[kmin:kmax])
Stats.write_profile('tke_buoy', self.EnvVar.TKE.buoy[kmin:kmax])
Stats.write_profile('tke_pressure', self.EnvVar.TKE.press[kmin:kmax])
Stats.write_profile('tke_interdomain', self.EnvVar.TKE.interdomain[kmin:kmax])
if self.calc_scalar_var:
self.compute_covariance_dissipation(self.EnvVar.Hvar)
Stats.write_profile('Hvar_dissipation', self.EnvVar.Hvar.dissipation[kmin:kmax])
self.compute_covariance_dissipation(self.EnvVar.QTvar)
Stats.write_profile('QTvar_dissipation', self.EnvVar.QTvar.dissipation[kmin:kmax])
self.compute_covariance_dissipation(self.EnvVar.HQTcov)
Stats.write_profile('HQTcov_dissipation', self.EnvVar.HQTcov.dissipation[kmin:kmax])
Stats.write_profile('Hvar_entr_gain', self.EnvVar.Hvar.entr_gain[kmin:kmax])
Stats.write_profile('QTvar_entr_gain', self.EnvVar.QTvar.entr_gain[kmin:kmax])
Stats.write_profile('HQTcov_entr_gain', self.EnvVar.HQTcov.entr_gain[kmin:kmax])
self.compute_covariance_detr(self.EnvVar.Hvar)
self.compute_covariance_detr(self.EnvVar.QTvar)
self.compute_covariance_detr(self.EnvVar.HQTcov)
Stats.write_profile('Hvar_detr_loss', self.EnvVar.Hvar.detr_loss[kmin:kmax])
Stats.write_profile('QTvar_detr_loss', self.EnvVar.QTvar.detr_loss[kmin:kmax])
Stats.write_profile('HQTcov_detr_loss', self.EnvVar.HQTcov.detr_loss[kmin:kmax])
Stats.write_profile('Hvar_shear', self.EnvVar.Hvar.shear[kmin:kmax])
Stats.write_profile('QTvar_shear', self.EnvVar.QTvar.shear[kmin:kmax])
Stats.write_profile('HQTcov_shear', self.EnvVar.HQTcov.shear[kmin:kmax])
Stats.write_profile('Hvar_rain', self.EnvVar.Hvar.rain_src[kmin:kmax])
Stats.write_profile('QTvar_rain', self.EnvVar.QTvar.rain_src[kmin:kmax])
Stats.write_profile('HQTcov_rain', self.EnvVar.HQTcov.rain_src[kmin:kmax])
Stats.write_profile('Hvar_interdomain', self.EnvVar.Hvar.interdomain[kmin:kmax])
Stats.write_profile('QTvar_interdomain', self.EnvVar.QTvar.interdomain[kmin:kmax])
Stats.write_profile('HQTcov_interdomain', self.EnvVar.HQTcov.interdomain[kmin:kmax])
return
# Perform the update of the scheme
cpdef update(self,GridMeanVariables GMV, CasesBase Case, TimeStepping TS):
cdef:
Py_ssize_t k
Py_ssize_t kmin = self.Gr.gw
Py_ssize_t kmax = self.Gr.nzg - self.Gr.gw
self.update_inversion(GMV, Case.inversion_option)
self.wstar = get_wstar(Case.Sur.bflux, self.zi)
if TS.nstep == 0:
self.initialize_covariance(GMV, Case)
with nogil:
for k in xrange(self.Gr.nzg):
if self.calc_tke:
self.EnvVar.TKE.values[k] = GMV.TKE.values[k]
if self.calc_scalar_var:
self.EnvVar.Hvar.values[k] = GMV.Hvar.values[k]
self.EnvVar.QTvar.values[k] = GMV.QTvar.values[k]
self.EnvVar.HQTcov.values[k] = GMV.HQTcov.values[k]
self.decompose_environment(GMV, 'values')
if self.use_steady_updrafts:
self.compute_diagnostic_updrafts(GMV, Case)
else:
self.compute_prognostic_updrafts(GMV, Case, TS)
# TODO -maybe not needed? - both diagnostic and prognostic updrafts end with decompose_environment
# But in general ok here without thermodynamics because MF doesnt depend directly on buoyancy
self.decompose_environment(GMV, 'values')
self.update_GMV_MF(GMV, TS)
# (###)
# decompose_environment + EnvThermo.satadjust + UpdThermo.buoyancy should always be used together
# This ensures that:
# - the buoyancy of updrafts and environment is up to date with the most recent decomposition,
# - the buoyancy of updrafts and environment is updated such that
# the mean buoyancy with repect to reference state alpha_0 is zero.
self.decompose_environment(GMV, 'mf_update')
self.EnvThermo.satadjust(self.EnvVar, True)
self.UpdThermo.buoyancy(self.UpdVar, self.EnvVar, GMV, self.extrapolate_buoyancy)
self.compute_eddy_diffusivities_tke(GMV, Case)
self.update_GMV_ED(GMV, Case, TS)
self.compute_covariance(GMV, Case, TS)
# Back out the tendencies of the grid mean variables for the whole timestep by differencing GMV.new and
# GMV.values
ParameterizationBase.update(self, GMV, Case, TS)
return
cpdef compute_prognostic_updrafts(self, GridMeanVariables GMV, CasesBase Case, TimeStepping TS):
cdef:
Py_ssize_t iter_
double time_elapsed = 0.0
self.UpdVar.set_new_with_values()
self.UpdVar.set_old_with_values()
self.set_updraft_surface_bc(GMV, Case)
self.dt_upd = np.minimum(TS.dt, 0.5 * self.Gr.dz/fmax(np.max(self.UpdVar.W.values),1e-10))
while time_elapsed < TS.dt:
self.compute_entrainment_detrainment(GMV, Case)
self.solve_updraft_velocity_area(GMV,TS)
self.solve_updraft_scalars(GMV, Case, TS)
self.UpdVar.set_values_with_new()
time_elapsed += self.dt_upd
self.dt_upd = np.minimum(TS.dt-time_elapsed, 0.5 * self.Gr.dz/fmax(np.max(self.UpdVar.W.values),1e-10))
# (####)
# TODO - see comment (###)
# It would be better to have a simple linear rule for updating environment here
# instead of calling EnvThermo saturation adjustment scheme for every updraft.
# If we are using quadratures this is expensive and probably unnecessary.
self.decompose_environment(GMV, 'values')
self.EnvThermo.satadjust(self.EnvVar, False)
self.UpdThermo.buoyancy(self.UpdVar, self.EnvVar, GMV, self.extrapolate_buoyancy)
return
cpdef compute_diagnostic_updrafts(self, GridMeanVariables GMV, CasesBase Case):
cdef:
Py_ssize_t i, k
Py_ssize_t gw = self.Gr.gw
double dz = self.Gr.dz
double dzi = self.Gr.dzi
eos_struct sa
entr_struct ret
entr_in_struct input
double a,b,c, w, w_km, w_mid, w_low, denom, arg
double entr_w, detr_w, B_k, area_k, w2
self.set_updraft_surface_bc(GMV, Case)
self.compute_entrainment_detrainment(GMV, Case)
with nogil:
for i in xrange(self.n_updrafts):
self.UpdVar.H.values[i,gw] = self.h_surface_bc[i]
self.UpdVar.QT.values[i,gw] = self.qt_surface_bc[i]
# Find the cloud liquid content
sa = eos(self.UpdThermo.t_to_prog_fp,self.UpdThermo.prog_to_t_fp, self.Ref.p0_half[gw],
self.UpdVar.QT.values[i,gw], self.UpdVar.H.values[i,gw])
self.UpdVar.QL.values[i,gw] = sa.ql
self.UpdVar.T.values[i,gw] = sa.T
self.UpdMicro.compute_update_combined_local_thetal(self.Ref.p0_half[gw], self.UpdVar.T.values[i,gw],
&self.UpdVar.QT.values[i,gw], &self.UpdVar.QL.values[i,gw],
&self.UpdVar.QR.values[i,gw], &self.UpdVar.H.values[i,gw],
i, gw)
for k in xrange(gw+1, self.Gr.nzg-gw):
denom = 1.0 + self.entr_sc[i,k] * dz
self.UpdVar.H.values[i,k] = (self.UpdVar.H.values[i,k-1] + self.entr_sc[i,k] * dz * GMV.H.values[k])/denom
self.UpdVar.QT.values[i,k] = (self.UpdVar.QT.values[i,k-1] + self.entr_sc[i,k] * dz * GMV.QT.values[k])/denom
sa = eos(self.UpdThermo.t_to_prog_fp,self.UpdThermo.prog_to_t_fp, self.Ref.p0_half[k],
self.UpdVar.QT.values[i,k], self.UpdVar.H.values[i,k])
self.UpdVar.QL.values[i,k] = sa.ql
self.UpdVar.T.values[i,k] = sa.T
self.UpdMicro.compute_update_combined_local_thetal(self.Ref.p0_half[k], self.UpdVar.T.values[i,k],
&self.UpdVar.QT.values[i,k], &self.UpdVar.QL.values[i,k],
&self.UpdVar.QR.values[i,k], &self.UpdVar.H.values[i,k],
i, k)
self.UpdVar.QT.set_bcs(self.Gr)
self.UpdVar.QR.set_bcs(self.Gr)
self.UpdVar.H.set_bcs(self.Gr)
# TODO - see comment (####)
self.decompose_environment(GMV, 'values')
self.EnvThermo.satadjust(self.EnvVar, False)
self.UpdThermo.buoyancy(self.UpdVar, self.EnvVar, GMV, self.extrapolate_buoyancy)
# Solve updraft velocity equation
with nogil:
for i in xrange(self.n_updrafts):
self.UpdVar.W.values[i, self.Gr.gw-1] = self.w_surface_bc[i]
self.entr_sc[i,gw] = 2.0 /dz
self.detr_sc[i,gw] = 0.0
for k in range(self.Gr.gw, self.Gr.nzg-self.Gr.gw):
area_k = interp2pt(self.UpdVar.Area.values[i,k], self.UpdVar.Area.values[i,k+1])
if area_k >= self.minimum_area:
w_km = self.UpdVar.W.values[i,k-1]
entr_w = interp2pt(self.entr_sc[i,k], self.entr_sc[i,k+1])
detr_w = interp2pt(self.detr_sc[i,k], self.detr_sc[i,k+1])
B_k = interp2pt(self.UpdVar.B.values[i,k], self.UpdVar.B.values[i,k+1])
w2 = ((self.vel_buoy_coeff * B_k + 0.5 * w_km * w_km * dzi)
/(0.5 * dzi +entr_w + self.vel_pressure_coeff/sqrt(fmax(area_k,self.minimum_area))))
if w2 > 0.0:
self.UpdVar.W.values[i,k] = sqrt(w2)
else:
self.UpdVar.W.values[i,k:] = 0
break
else:
self.UpdVar.W.values[i,k:] = 0
self.UpdVar.W.set_bcs(self.Gr)
cdef double au_lim
with nogil:
for i in xrange(self.n_updrafts):
au_lim = self.max_area_factor * self.area_surface_bc[i]
self.UpdVar.Area.values[i,gw] = self.area_surface_bc[i]
w_mid = 0.5* (self.UpdVar.W.values[i,gw])
for k in xrange(gw+1, self.Gr.nzg):
w_low = w_mid
w_mid = interp2pt(self.UpdVar.W.values[i,k],self.UpdVar.W.values[i,k-1])
if w_mid > 0.0:
if self.entr_sc[i,k]>(0.9/dz):
self.entr_sc[i,k] = 0.9/dz
self.UpdVar.Area.values[i,k] = (self.Ref.rho0_half[k-1]*self.UpdVar.Area.values[i,k-1]*w_low/
(1.0-(self.entr_sc[i,k]-self.detr_sc[i,k])*dz)/w_mid/self.Ref.rho0_half[k])
# # Limit the increase in updraft area when the updraft decelerates
if self.UpdVar.Area.values[i,k] > au_lim:
self.UpdVar.Area.values[i,k] = au_lim
self.detr_sc[i,k] =(self.Ref.rho0_half[k-1] * self.UpdVar.Area.values[i,k-1]
* w_low / au_lim / w_mid / self.Ref.rho0_half[k] + self.entr_sc[i,k] * dz -1.0)/dz
else:
# the updraft has terminated so set its area fraction to zero at this height and all heights above
self.UpdVar.Area.values[i,k] = 0.0
self.UpdVar.H.values[i,k] = GMV.H.values[k]
self.UpdVar.QT.values[i,k] = GMV.QT.values[k]
self.UpdVar.QR.values[i,k] = GMV.QR.values[k]
#TODO wouldnt it be more consistent to have here?
#self.UpdVar.QL.values[i,k] = GMV.QL.values[k]
#self.UpdVar.T.values[i,k] = GMV.T.values[k]
sa = eos(self.UpdThermo.t_to_prog_fp,self.UpdThermo.prog_to_t_fp, self.Ref.p0_half[k],
self.UpdVar.QT.values[i,k], self.UpdVar.H.values[i,k])
self.UpdVar.QL.values[i,k] = sa.ql
self.UpdVar.T.values[i,k] = sa.T
# TODO - see comment (####)
self.decompose_environment(GMV, 'values')
self.EnvThermo.satadjust(self.EnvVar, False)
self.UpdThermo.buoyancy(self.UpdVar, self.EnvVar, GMV, self.extrapolate_buoyancy)
self.UpdVar.Area.set_bcs(self.Gr)
self.UpdMicro.prec_source_h_tot = np.sum(np.multiply(self.UpdMicro.prec_source_h, self.UpdVar.Area.values), axis=0)
self.UpdMicro.prec_source_qt_tot = np.sum(np.multiply(self.UpdMicro.prec_source_qt, self.UpdVar.Area.values), axis=0)
return
cpdef update_inversion(self,GridMeanVariables GMV, option):
ParameterizationBase.update_inversion(self, GMV,option)
return
cpdef compute_mixing_length(self, double obukhov_length):
cdef:
Py_ssize_t k
Py_ssize_t gw = self.Gr.gw
double tau = get_mixing_tau(self.zi, self.wstar)
double l1, l2, z_
double grad, grad2, H
with nogil:
for k in xrange(gw, self.Gr.nzg-gw):
l1 = tau * sqrt(fmax(self.EnvVar.TKE.values[k],0.0))
z_ = self.Gr.z_half[k]
if obukhov_length < 0.0: #unstable
l2 = vkb * z_ * ( (1.0 - 100.0 * z_/obukhov_length)**0.2 )
elif obukhov_length > 0.0: #stable
l2 = vkb * z_ / (1. + 2.7 *z_/obukhov_length)
else:
l2 = vkb * z_
self.mixing_length[k] = fmax( 1.0/(1.0/fmax(l1,1e-10) + 1.0/l2), 1e-3)
return
cpdef compute_eddy_diffusivities_tke(self, GridMeanVariables GMV, CasesBase Case):
cdef:
Py_ssize_t k
Py_ssize_t gw = self.Gr.gw
double lm
double we_half
double pr_vec[2]
double ri_thl, shear2
if self.similarity_diffusivity:
ParameterizationBase.compute_eddy_diffusivities_similarity(self,GMV, Case)
else:
self.compute_mixing_length(Case.Sur.obukhov_length)
with nogil:
for k in xrange(gw, self.Gr.nzg-gw):
lm = self.mixing_length[k]
self.KM.values[k] = self.tke_ed_coeff * lm * sqrt(fmax(self.EnvVar.TKE.values[k],0.0) )
# Prandtl number is fixed. It should be defined as a function of height - Ignacio
self.KH.values[k] = self.KM.values[k] / self.prandtl_number
return
cpdef set_updraft_surface_bc(self, GridMeanVariables GMV, CasesBase Case):
self.update_inversion(GMV, Case.inversion_option)
self.wstar = get_wstar(Case.Sur.bflux, self.zi)
cdef:
Py_ssize_t i, gw = self.Gr.gw
double zLL = self.Gr.z_half[gw]
double ustar = Case.Sur.ustar, oblength = Case.Sur.obukhov_length
double alpha0LL = self.Ref.alpha0_half[gw]
double qt_var = get_surface_variance(Case.Sur.rho_qtflux*alpha0LL,
Case.Sur.rho_qtflux*alpha0LL, ustar, zLL, oblength)
double h_var = get_surface_variance(Case.Sur.rho_hflux*alpha0LL,
Case.Sur.rho_hflux*alpha0LL, ustar, zLL, oblength)
double a_ = self.surface_area/self.n_updrafts
double surface_scalar_coeff
# with nogil:
for i in xrange(self.n_updrafts):
surface_scalar_coeff= percentile_bounds_mean_norm(1.0-self.surface_area+i*a_,
1.0-self.surface_area + (i+1)*a_ , 1000)
self.area_surface_bc[i] = self.surface_area/self.n_updrafts
self.w_surface_bc[i] = 0.0
self.h_surface_bc[i] = (GMV.H.values[gw] + surface_scalar_coeff * sqrt(h_var))
self.qt_surface_bc[i] = (GMV.QT.values[gw] + surface_scalar_coeff * sqrt(qt_var))
return
cpdef reset_surface_covariance(self, GridMeanVariables GMV, CasesBase Case):
flux1 = Case.Sur.rho_hflux
flux2 = Case.Sur.rho_qtflux
cdef:
double zLL = self.Gr.z_half[self.Gr.gw]
double ustar = Case.Sur.ustar, oblength = Case.Sur.obukhov_length
double alpha0LL = self.Ref.alpha0_half[self.Gr.gw]
#double get_surface_variance = get_surface_variance(flux1, flux2 ,ustar, zLL, oblength)
if self.calc_tke:
GMV.TKE.values[self.Gr.gw] = get_surface_tke(Case.Sur.ustar,
self.wstar,
self.Gr.z_half[self.Gr.gw],
Case.Sur.obukhov_length)
if self.calc_scalar_var:
GMV.Hvar.values[self.Gr.gw] = get_surface_variance(flux1*alpha0LL,flux1*alpha0LL, ustar, zLL, oblength)
GMV.QTvar.values[self.Gr.gw] = get_surface_variance(flux2*alpha0LL,flux2*alpha0LL, ustar, zLL, oblength)
GMV.HQTcov.values[self.Gr.gw] = get_surface_variance(flux1*alpha0LL,flux2*alpha0LL, ustar, zLL, oblength)
return
# Find values of environmental variables by subtracting updraft values from grid mean values
# whichvals used to check which substep we are on--correspondingly use 'GMV.SomeVar.value' (last timestep value)
# or GMV.SomeVar.mf_update (GMV value following massflux substep)
cpdef decompose_environment(self, GridMeanVariables GMV, whichvals):
# first make sure the 'bulkvalues' of the updraft variables are updated
self.UpdVar.set_means(GMV)
cdef:
Py_ssize_t k, gw = self.Gr.gw
double val1, val2, au_full
if whichvals == 'values':
with nogil:
for k in xrange(self.Gr.nzg-1):
val1 = 1.0/(1.0-self.UpdVar.Area.bulkvalues[k])
val2 = self.UpdVar.Area.bulkvalues[k] * val1
self.EnvVar.QT.values[k] = val1 * GMV.QT.values[k] - val2 * self.UpdVar.QT.bulkvalues[k]
self.EnvVar.H.values[k] = val1 * GMV.H.values[k] - val2 * self.UpdVar.H.bulkvalues[k]
# Have to account for staggering of W--interpolate area fraction to the "full" grid points
# Assuming GMV.W = 0!
au_full = 0.5 * (self.UpdVar.Area.bulkvalues[k+1] + self.UpdVar.Area.bulkvalues[k])
self.EnvVar.W.values[k] = -au_full/(1.0-au_full) * self.UpdVar.W.bulkvalues[k]
if self.calc_tke:
self.get_GMV_CoVar(self.UpdVar.Area,self.UpdVar.W, self.UpdVar.W, self.EnvVar.W, self.EnvVar.W, self.EnvVar.TKE, &GMV.W.values[0],&GMV.W.values[0], &GMV.TKE.values[0])
if self.calc_scalar_var:
self.get_GMV_CoVar(self.UpdVar.Area,self.UpdVar.H, self.UpdVar.H, self.EnvVar.H, self.EnvVar.H, self.EnvVar.Hvar, &GMV.H.values[0],&GMV.H.values[0], &GMV.Hvar.values[0])
self.get_GMV_CoVar(self.UpdVar.Area,self.UpdVar.QT,self.UpdVar.QT,self.EnvVar.QT,self.EnvVar.QT,self.EnvVar.QTvar, &GMV.QT.values[0],&GMV.QT.values[0], &GMV.QTvar.values[0])
self.get_GMV_CoVar(self.UpdVar.Area,self.UpdVar.H, self.UpdVar.QT,self.EnvVar.H, self.EnvVar.QT,self.EnvVar.HQTcov, &GMV.H.values[0],&GMV.QT.values[0], &GMV.HQTcov.values[0])
elif whichvals == 'mf_update':
# same as above but replace GMV.SomeVar.values with GMV.SomeVar.mf_update
with nogil:
for k in xrange(self.Gr.nzg-1):
val1 = 1.0/(1.0-self.UpdVar.Area.bulkvalues[k])
val2 = self.UpdVar.Area.bulkvalues[k] * val1
self.EnvVar.QT.values[k] = val1 * GMV.QT.mf_update[k] - val2 * self.UpdVar.QT.bulkvalues[k]
self.EnvVar.H.values[k] = val1 * GMV.H.mf_update[k] - val2 * self.UpdVar.H.bulkvalues[k]
# Have to account for staggering of W
# Assuming GMV.W = 0!
au_full = 0.5 * (self.UpdVar.Area.bulkvalues[k+1] + self.UpdVar.Area.bulkvalues[k])
self.EnvVar.W.values[k] = -au_full/(1.0-au_full) * self.UpdVar.W.bulkvalues[k]
if self.calc_tke:
self.get_GMV_CoVar(self.UpdVar.Area,self.UpdVar.W, self.UpdVar.W, self.EnvVar.W, self.EnvVar.W, self.EnvVar.TKE,
&GMV.W.values[0],&GMV.W.values[0], &GMV.TKE.values[0])
if self.calc_scalar_var:
self.get_GMV_CoVar(self.UpdVar.Area,self.UpdVar.H, self.UpdVar.H, self.EnvVar.H, self.EnvVar.H, self.EnvVar.Hvar,
&GMV.H.values[0],&GMV.H.values[0], &GMV.Hvar.values[0])
self.get_GMV_CoVar(self.UpdVar.Area,self.UpdVar.QT, self.UpdVar.QT, self.EnvVar.QT, self.EnvVar.QT, self.EnvVar.QTvar,
&GMV.QT.values[0],&GMV.QT.values[0], &GMV.QTvar.values[0])
self.get_GMV_CoVar(self.UpdVar.Area,self.UpdVar.H, self.UpdVar.QT, self.EnvVar.H, self.EnvVar.QT, self.EnvVar.HQTcov,
&GMV.H.values[0], &GMV.QT.values[0], &GMV.HQTcov.values[0])
return
# Note: this assumes all variables are defined on half levels not full levels (i.e. phi, psi are not w)
cdef get_GMV_CoVar(self, EDMF_Updrafts.UpdraftVariable au,
EDMF_Updrafts.UpdraftVariable phi_u, EDMF_Updrafts.UpdraftVariable psi_u,
EDMF_Environment.EnvironmentVariable phi_e, EDMF_Environment.EnvironmentVariable psi_e,
EDMF_Environment.EnvironmentVariable_2m covar_e,
double *gmv_phi, double *gmv_psi, double *gmv_covar):
cdef:
Py_ssize_t i,k
double [:] ae = np.subtract(np.ones((self.Gr.nzg,),dtype=np.double, order='c'),au.bulkvalues)
double phi_diff, psi_diff
double tke_factor = 1.0
#with nogil:
for k in xrange(self.Gr.nzg):
if covar_e.name == 'tke':
tke_factor = 0.5
phi_diff = interp2pt(phi_e.values[k-1]-gmv_phi[k-1], phi_e.values[k]-gmv_phi[k])
psi_diff = interp2pt(psi_e.values[k-1]-gmv_psi[k-1], psi_e.values[k]-gmv_psi[k])
else:
tke_factor = 1.0
phi_diff = phi_e.values[k]-gmv_phi[k]
psi_diff = psi_e.values[k]-gmv_psi[k]
gmv_covar[k] = tke_factor * ae[k] * phi_diff * psi_diff + ae[k] * covar_e.values[k]
for i in xrange(self.n_updrafts):
if covar_e.name == 'tke':
phi_diff = interp2pt(phi_u.values[i,k-1]-gmv_phi[k-1], phi_u.values[i,k]-gmv_phi[k])
psi_diff = interp2pt(psi_u.values[i,k-1]-gmv_psi[k-1], psi_u.values[i,k]-gmv_psi[k])
else:
phi_diff = phi_u.values[i,k]-gmv_phi[k]
psi_diff = psi_u.values[i,k]-gmv_psi[k]
gmv_covar[k] += tke_factor * au.values[i,k] * phi_diff * psi_diff
return
cdef get_env_covar_from_GMV(self, EDMF_Updrafts.UpdraftVariable au,
EDMF_Updrafts.UpdraftVariable phi_u, EDMF_Updrafts.UpdraftVariable psi_u,
EDMF_Environment.EnvironmentVariable phi_e, EDMF_Environment.EnvironmentVariable psi_e,
EDMF_Environment.EnvironmentVariable_2m covar_e,
double *gmv_phi, double *gmv_psi, double *gmv_covar):
cdef:
Py_ssize_t i,k
double [:] ae = np.subtract(np.ones((self.Gr.nzg,),dtype=np.double, order='c'),au.bulkvalues)
double phi_diff, psi_diff
double tke_factor = 1.0
if covar_e.name == 'tke':
tke_factor = 0.5
#with nogil:
for k in xrange(self.Gr.nzg):
if ae[k] > 0.0:
if covar_e.name == 'tke':
phi_diff = interp2pt(phi_e.values[k-1] - gmv_phi[k-1],phi_e.values[k] - gmv_phi[k])
psi_diff = interp2pt(psi_e.values[k-1] - gmv_psi[k-1],psi_e.values[k] - gmv_psi[k])
else:
phi_diff = phi_e.values[k] - gmv_phi[k]
psi_diff = psi_e.values[k] - gmv_psi[k]
covar_e.values[k] = gmv_covar[k] - tke_factor * ae[k] * phi_diff * psi_diff
for i in xrange(self.n_updrafts):
if covar_e.name == 'tke':
phi_diff = interp2pt(phi_u.values[i,k-1] - gmv_phi[k-1],phi_u.values[i,k] - gmv_phi[k])
psi_diff = interp2pt(psi_u.values[i,k-1] - gmv_psi[k-1],psi_u.values[i,k] - gmv_psi[k])
else:
phi_diff = phi_u.values[i,k] - gmv_phi[k]
psi_diff = psi_u.values[i,k] - gmv_psi[k]
covar_e.values[k] -= tke_factor * au.values[i,k] * phi_diff * psi_diff
covar_e.values[k] = covar_e.values[k]/ae[k]
else:
covar_e.values[k] = 0.0
return
cpdef compute_entrainment_detrainment(self, GridMeanVariables GMV, CasesBase Case):
cdef:
Py_ssize_t k
entr_struct ret
entr_in_struct input
eos_struct sa
double transport_plus, transport_minus
long quadrature_order = 3
self.UpdVar.get_cloud_base_top_cover()
input.wstar = self.wstar
input.dz = self.Gr.dz
input.zbl = self.compute_zbl_qt_grad(GMV)
for i in xrange(self.n_updrafts):
input.zi = self.UpdVar.cloud_base[i]
for k in xrange(self.Gr.gw, self.Gr.nzg-self.Gr.gw):
input.quadrature_order = quadrature_order
input.b = self.UpdVar.B.values[i,k]
input.w = interp2pt(self.UpdVar.W.values[i,k],self.UpdVar.W.values[i,k-1])
input.z = self.Gr.z_half[k]
input.af = self.UpdVar.Area.values[i,k]
input.tke = self.EnvVar.TKE.values[k]
input.ml = self.mixing_length[k]
input.qt_env = self.EnvVar.QT.values[k]
input.ql_env = self.EnvVar.QL.values[k]
input.H_env = self.EnvVar.H.values[k]
input.b_env = self.EnvVar.B.values[k]
input.w_env = self.EnvVar.W.values[k]
input.H_up = self.UpdVar.H.values[i,k]
input.qt_up = self.UpdVar.QT.values[i,k]
input.ql_up = self.UpdVar.QL.values[i,k]
input.p0 = self.Ref.p0_half[k]
input.alpha0 = self.Ref.alpha0_half[k]
input.env_Hvar = self.EnvVar.Hvar.values[k]
input.env_QTvar = self.EnvVar.QTvar.values[k]
input.env_HQTcov = self.EnvVar.HQTcov.values[k]
if self.calc_tke:
input.tke = self.EnvVar.TKE.values[k]
input.tke_ed_coeff = self.tke_ed_coeff
input.T_mean = (self.EnvVar.T.values[k]+self.UpdVar.T.values[i,k])/2
input.L = 20000.0 # need to define the scale of the GCM grid resolution
## Ignacio
input.n_up = self.n_updrafts
input.thv_e = theta_virt_c(self.Ref.p0_half[k], self.EnvVar.T.values[k], self.EnvVar.QT.values[k],
self.EnvVar.QL.values[k], self.EnvVar.QR.values[k])
input.thv_u = theta_virt_c(self.Ref.p0_half[k], self.UpdVar.T.bulkvalues[k], self.UpdVar.QT.bulkvalues[k],
self.UpdVar.QL.bulkvalues[k], self.UpdVar.QR.bulkvalues[k])
input.dwdz = (self.UpdVar.Area.values[i,k+1]*
interp2pt(self.UpdVar.W.values[i,k+1],self.UpdVar.W.values[i,k]) +
(1.0-self.UpdVar.Area.values[i,k+1])*self.EnvVar.W.values[k+1] -
(self.UpdVar.Area.values[i,k-1]*
interp2pt(self.UpdVar.W.values[i,k-1],self.UpdVar.W.values[i,k-2]) +
(1.0-self.UpdVar.Area.values[i,k-1])*self.EnvVar.W.values[k-1]) )/(2.0*self.Gr.dz)
transport_plus = ( self.UpdVar.Area.values[i,k+1]*(1.0-self.UpdVar.Area.values[i,k+1])*
(interp2pt(self.UpdVar.W.values[i,k+1],self.UpdVar.W.values[i,k]) - self.EnvVar.W.values[k+1])*
(1.0-2.0*self.UpdVar.Area.values[i,k+1])*
(interp2pt(self.UpdVar.W.values[i,k+1],self.UpdVar.W.values[i,k]) - self.EnvVar.W.values[k+1])*
(interp2pt(self.UpdVar.W.values[i,k+1],self.UpdVar.W.values[i,k]) - self.EnvVar.W.values[k+1]) )
transport_minus = ( self.UpdVar.Area.values[i,k-1]*(1.0-self.UpdVar.Area.values[i,k-1])*
(interp2pt(self.UpdVar.W.values[i,k-1],self.UpdVar.W.values[i,k-2]) - self.EnvVar.W.values[k-1])*
(1.0-2.0*self.UpdVar.Area.values[i,k+1])*
(interp2pt(self.UpdVar.W.values[i,k-1],self.UpdVar.W.values[i,k-2]) - self.EnvVar.W.values[k-1])*
(interp2pt(self.UpdVar.W.values[i,k-1],self.UpdVar.W.values[i,k-2]) - self.EnvVar.W.values[k-1]) )
input.transport_der = (transport_plus - transport_minus)/2.0/self.Gr.dz
if input.zbl-self.UpdVar.cloud_base[i] > 0.0:
input.poisson = np.random.poisson(self.Gr.dz/((input.zbl-self.UpdVar.cloud_base[i])/10.0))
else:
input.poisson = 0.0
## End: Ignacio
ret = self.entr_detr_fp(input)
self.entr_sc[i,k] = ret.entr_sc * self.entrainment_factor
self.detr_sc[i,k] = ret.detr_sc * self.detrainment_factor
return
cpdef double compute_zbl_qt_grad(self, GridMeanVariables GMV):
# computes inversion height as z with max gradient of qt
cdef:
double qt_up, qt_, z_
double zbl_qt = 0.0
double qt_grad = 0.0
for k in xrange(self.Gr.gw, self.Gr.nzg-self.Gr.gw):
z_ = self.Gr.z_half[k]
qt_up = GMV.QT.values[k+1]
qt_ = GMV.QT.values[k]
if fabs(qt_up-qt_)*self.Gr.dzi > qt_grad:
qt_grad = fabs(qt_up-qt_)*self.Gr.dzi
zbl_qt = z_
return zbl_qt
cpdef solve_updraft_velocity_area(self, GridMeanVariables GMV, TimeStepping TS):
cdef:
Py_ssize_t i, k
Py_ssize_t gw = self.Gr.gw
double dzi = self.Gr.dzi
double dti_ = 1.0/self.dt_upd
double dt_ = 1.0/dti_
double whalf_kp, whalf_k
double au_lim
double anew_k, a_k, a_km, entr_w, detr_w, B_k, entr_term, detr_term, rho_ratio
double adv, buoy, exch, press, press_buoy, press_drag # groupings of terms in velocity discrete equation
with nogil:
for i in xrange(self.n_updrafts):
self.entr_sc[i,gw] = 2.0 * dzi
self.detr_sc[i,gw] = 0.0
self.UpdVar.W.new[i,gw-1] = self.w_surface_bc[i]
self.UpdVar.Area.new[i,gw] = self.area_surface_bc[i]
au_lim = self.area_surface_bc[i] * self.max_area_factor
for k in range(gw, self.Gr.nzg-gw):
# First solve for updated area fraction at k+1
whalf_kp = interp2pt(self.UpdVar.W.values[i,k], self.UpdVar.W.values[i,k+1])
whalf_k = interp2pt(self.UpdVar.W.values[i,k-1], self.UpdVar.W.values[i,k])
adv = -self.Ref.alpha0_half[k+1] * dzi *( self.Ref.rho0_half[k+1] * self.UpdVar.Area.values[i,k+1] * whalf_kp
-self.Ref.rho0_half[k] * self.UpdVar.Area.values[i,k] * whalf_k)
entr_term = self.UpdVar.Area.values[i,k+1] * whalf_kp * (self.entr_sc[i,k+1] )
detr_term = self.UpdVar.Area.values[i,k+1] * whalf_kp * (- self.detr_sc[i,k+1])
self.UpdVar.Area.new[i,k+1] = fmax(dt_ * (adv + entr_term + detr_term) + self.UpdVar.Area.values[i,k+1], 0.0)
if self.UpdVar.Area.new[i,k+1] > au_lim:
self.UpdVar.Area.new[i,k+1] = au_lim
if self.UpdVar.Area.values[i,k+1] > 0.0:
self.detr_sc[i,k+1] = (((au_lim-self.UpdVar.Area.values[i,k+1])* dti_ - adv -entr_term)/(-self.UpdVar.Area.values[i,k+1] * whalf_kp))
else:
# this detrainment rate won't affect scalars but would affect velocity
self.detr_sc[i,k+1] = (((au_lim-self.UpdVar.Area.values[i,k+1])* dti_ - adv -entr_term)/(-au_lim * whalf_kp))
# Now solve for updraft velocity at k
rho_ratio = self.Ref.rho0[k-1]/self.Ref.rho0[k]
anew_k = interp2pt(self.UpdVar.Area.new[i,k], self.UpdVar.Area.new[i,k+1])
if anew_k >= self.minimum_area:
a_k = interp2pt(self.UpdVar.Area.values[i,k], self.UpdVar.Area.values[i,k+1])
a_km = interp2pt(self.UpdVar.Area.values[i,k-1], self.UpdVar.Area.values[i,k])
entr_w = interp2pt(self.entr_sc[i,k], self.entr_sc[i,k+1])
detr_w = interp2pt(self.detr_sc[i,k], self.detr_sc[i,k+1])
B_k = interp2pt(self.UpdVar.B.values[i,k], self.UpdVar.B.values[i,k+1])
adv = (self.Ref.rho0[k] * a_k * self.UpdVar.W.values[i,k] * self.UpdVar.W.values[i,k] * dzi
- self.Ref.rho0[k-1] * a_km * self.UpdVar.W.values[i,k-1] * self.UpdVar.W.values[i,k-1] * dzi)
exch = (self.Ref.rho0[k] * a_k * self.UpdVar.W.values[i,k]
* (entr_w * self.EnvVar.W.values[k] - detr_w * self.UpdVar.W.values[i,k] ))
buoy= self.Ref.rho0[k] * a_k * B_k
press_buoy = -1.0 * self.Ref.rho0[k] * a_k * B_k * self.pressure_buoy_coeff
press_drag = -1.0 * self.Ref.rho0[k] * a_k * (self.pressure_drag_coeff/self.pressure_plume_spacing
* (self.UpdVar.W.values[i,k] -self.EnvVar.W.values[k])**2.0/sqrt(fmax(a_k,self.minimum_area)))
press = press_buoy + press_drag
self.updraft_pressure_sink[i,k] = press
self.UpdVar.W.new[i,k] = (self.Ref.rho0[k] * a_k * self.UpdVar.W.values[i,k] * dti_
-adv + exch + buoy + press)/(self.Ref.rho0[k] * anew_k * dti_)
if self.UpdVar.W.new[i,k] <= 0.0:
self.UpdVar.W.new[i,k:] = 0.0
self.UpdVar.Area.new[i,k+1:] = 0.0
break
else:
self.UpdVar.W.new[i,k:] = 0.0
self.UpdVar.Area.new[i,k+1:] = 0.0
# keep this in mind if we modify updraft top treatment!
self.updraft_pressure_sink[i,k:] = 0.0
break
return
cpdef solve_updraft_scalars(self, GridMeanVariables GMV, CasesBase Case, TimeStepping TS):
cdef:
Py_ssize_t k, i
double dzi = self.Gr.dzi
double dti_ = 1.0/self.dt_upd
double m_k, m_km
Py_ssize_t gw = self.Gr.gw
double H_entr, QT_entr
double c1, c2, c3, c4
eos_struct sa
double qt_var, h_var
with nogil:
for i in xrange(self.n_updrafts):
self.UpdVar.H.new[i,gw] = self.h_surface_bc[i]
self.UpdVar.QT.new[i,gw] = self.qt_surface_bc[i]
self.UpdVar.QR.new[i,gw] = 0.0 #TODO
if self.use_local_micro:
# do saturation adjustment
sa = eos(self.UpdThermo.t_to_prog_fp,self.UpdThermo.prog_to_t_fp,
self.Ref.p0_half[gw], self.UpdVar.QT.new[i,gw], self.UpdVar.H.new[i,gw])
self.UpdVar.QL.new[i,gw] = sa.ql
self.UpdVar.T.new[i,gw] = sa.T
# remove precipitation (update QT, QL and H)
self.UpdMicro.compute_update_combined_local_thetal(self.Ref.p0_half[gw], self.UpdVar.T.new[i,gw],
&self.UpdVar.QT.new[i,gw], &self.UpdVar.QL.new[i,gw],
&self.UpdVar.QR.new[i,gw], &self.UpdVar.H.new[i,gw],
i, gw)
# starting from the bottom do entrainment at each level
for k in xrange(gw+1, self.Gr.nzg-gw):
H_entr = self.EnvVar.H.values[k]
QT_entr = self.EnvVar.QT.values[k]
# write the discrete equations in form:
# c1 * phi_new[k] = c2 * phi[k] + c3 * phi[k-1] + c4 * phi_entr
if self.UpdVar.Area.new[i,k] >= self.minimum_area:
m_k = (self.Ref.rho0_half[k] * self.UpdVar.Area.values[i,k]
* interp2pt(self.UpdVar.W.values[i,k-1], self.UpdVar.W.values[i,k]))
m_km = (self.Ref.rho0_half[k-1] * self.UpdVar.Area.values[i,k-1]
* interp2pt(self.UpdVar.W.values[i,k-2], self.UpdVar.W.values[i,k-1]))
c1 = self.Ref.rho0_half[k] * self.UpdVar.Area.new[i,k] * dti_
c2 = (self.Ref.rho0_half[k] * self.UpdVar.Area.values[i,k] * dti_
- m_k * (dzi + self.detr_sc[i,k]))
c3 = m_km * dzi
c4 = m_k * self.entr_sc[i,k]
self.UpdVar.H.new[i,k] = (c2 * self.UpdVar.H.values[i,k] + c3 * self.UpdVar.H.values[i,k-1]
+ c4 * H_entr)/c1
self.UpdVar.QT.new[i,k] = (c2 * self.UpdVar.QT.values[i,k] + c3 * self.UpdVar.QT.values[i,k-1]