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canopygrid.py
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canopygrid.py
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# -*- coding: utf-8 -*-
"""
Created on Fri Mar 24 11:01:50 2017
@author: slauniai
******************************************************************************
CanopyGrid:
Gridded canopy and snow hydrology model for SpaFHy -integration
Based on simple schemes for computing water flows and storages within vegetation
canopy and snowpack at daily or sub-daily timesteps.
(C) Samuli Launiainen, 2016-
last edit: Oct 2018 / Samuli
******************************************************************************
"""
import numpy as np
eps = np.finfo(float).eps
class CanopyGrid():
def __init__(self, cpara, state, outputs=False):
"""
initializes CanopyGrid -object
Args:
cpara - parameter dict:
state - dict of initial state
outputs - True saves output grids to list at each timestep
Returns:
self - object
NOTE:
Currently the initialization assumes simulation start 1st Jan,
and sets self._LAI_decid and self.X equal to minimum values.
Also leaf-growth & senescence parameters are intialized to zero.
"""
epsi = 0.01 # small number
self.Lat = cpara['loc']['lat']
self.Lon = cpara['loc']['lon']
# physiology: transpi + floor evap
self.physpara = cpara['physpara']
# phenology & LAI cycle
self.phenopara = cpara['phenopara']
# canopy parameters and state
self.hc = state['hc'] + epsi
self.cf = state['cf'] + epsi
#self.cf = 0.1939 * ba / (0.1939 * ba + 1.69) + epsi
# canopy closure [-] as function of basal area ba m2ha-1;
# fitted to Korhonen et al. 2007 Silva Fennica Fig.2
spec_para = cpara['spec_para']
ptypes = {}
LAI = 0.0
for pt in list(spec_para.keys()):
ptypes[pt] = spec_para[pt]
ptypes[pt]['LAImax'] = state['LAI_' + pt]
self.ptypes = ptypes
# compute gridcell average LAI and photosynthesis-stomatal conductance parameters:
LAI = 0.0
Amax = 0.0
q50 = 0.0
g1 = 0.0
for pt in self.ptypes.keys():
if self.ptypes[pt]['lai_cycle']:
pt_lai = self.ptypes[pt]['LAImax'] * self.phenopara['lai_decid_min']
else:
pt_lai = self.ptypes[pt]['LAImax']
LAI += pt_lai
Amax += pt_lai * ptypes[pt]['amax']
q50 += pt_lai * ptypes[pt]['q50']
g1 += pt_lai * ptypes[pt]['g1']
self.LAI = LAI + epsi
self.physpara.update({'Amax': Amax / self.LAI, 'q50': q50 / self.LAI, 'g1': g1 / self.LAI})
del Amax, q50, g1, pt, LAI, pt_lai
# - compute start day of senescence: starts at first doy when daylength < self.phenopara['sdl']
doy = np.arange(1, 366)
dl = daylength(self.Lat, self.Lon, doy)
ix = np.max(np.where(dl > self.phenopara['sdl']))
self.phenopara['sso'] = doy[ix] # this is onset date for senescence
del ix
# snow model
self.wmax = cpara['interc']['wmax']
self.wmaxsnow = cpara['interc']['wmaxsnow']
self.Kmelt = cpara['snow']['kmelt']
self.Kfreeze = cpara['snow']['kfreeze']
self.R = cpara['snow']['r'] # max fraction of liquid water in snow
# --- for computing aerodynamic resistances
self.zmeas = cpara['flow']['zmeas']
self.zground =cpara['flow']['zground'] # reference height above ground [m]
self.zo_ground = cpara['flow']['zo_ground'] # ground roughness length [m]
self.gsoil = self.physpara['gsoil']
# --- state variables
self.W = np.minimum(state['w'], self.wmax*self.LAI)
self.SWE = state['swe']
self.SWEi = self.SWE
self.SWEl = np.zeros(np.shape(self.SWE))
# deciduous leaf growth stage
# NOTE: this assumes simulations start 1st Jan each year !!!
self.DDsum = 0.0
self.X = 0.0
self._relative_lai = self.phenopara['lai_decid_min']
self._growth_stage = 0.0
self._senesc_stage = 0.0
# phenological state
self.fPheno = self.phenopara['fmin']
# create dictionary of empty lists for saving results
if outputs:
self.results = {'PotInf': [], 'Trfall': [], 'Interc': [], 'Evap': [],
'ET': [], 'Transpi': [], 'Efloor': [], 'SWE': [],
'LAI': [], 'Mbe': [], 'LAIfract': [], 'Unload': []
}
def run_timestep(self, doy, dt, Ta, Prec, Rg, Par, VPD, U=2.0, CO2=380.0,
Rew=1.0, beta=1.0, P=101300.0):
"""
Runs CanopyGrid instance for one timestep
IN:
doy - day of year
dt - timestep [s]
Ta - air temperature [degC], scalar or (n x m) -matrix
prec - precipitatation rate [mm/s]
Rg - global radiation [Wm-2], scalar or matrix
Par - photos. act. radiation [Wm-2], scalar or matrix
VPD - vapor pressure deficit [kPa], scalar or matrix
U - mean wind speed at ref. height above canopy top [ms-1], scalar or matrix
CO2 - atm. CO2 mixing ratio [ppm]
Rew - relative extractable water [-], scalar or matrix
beta - term for soil evaporation resistance (Wliq/FC) [-]
P - pressure [Pa], scalar or matrix
OUT:
updated CanopyGrid instance state variables
flux grids PotInf, Trfall, Interc, Evap, ET, MBE [mm]
"""
# Rn = 0.7 * Rg #net radiation
Rn = np.maximum(2.57 * self.LAI / (2.57 * self.LAI + 0.57) - 0.2,
0.55) * Rg # Launiainen et al. 2016 GCB, fit to Fig 2a
""" --- update grid-cell phenology, LAI and average Amax, g1 and q50: self.ddsum & self.X ---"""
self.update_daily(Ta, doy)
""" --- aerodynamic conductances --- """
Ra, Rb, Ras, ustar, Uh, Ug = aerodynamics(self.LAI, self.hc, U, w=0.01, zm=self.zmeas,
zg=self.zground, zos=self.zo_ground)
""" --- interception, evaporation and snowpack --- """
PotInf, Trfall, Evap, Interc, MBE, unload = self.canopy_water_snow(dt, Ta, Prec,
Rn, VPD, Ra=Ra)
"""--- dry-canopy evapotranspiration [mm s-1] --- """
Transpi, Efloor, Gc = self.dry_canopy_et(VPD, Par, Rn, Ta, Ra=Ra, Ras=Ras,
CO2=CO2, Rew=Rew, beta=beta, fPheno=self.fPheno)
Transpi = Transpi * dt
Efloor = Efloor * dt
ET = Transpi + Efloor + Evap
# append results to lists; use only for testing small grids!
if hasattr(self, 'results'):
self.results['PotInf'].append(PotInf)
self.results['Trfall'].append(Trfall)
self.results['Interc'].append(Interc)
self.results['Evap'].append(Evap)
self.results['ET'].append(ET)
self.results['Transpi'].append(Transpi)
self.results['Efloor'].append(Efloor)
self.results['SWE'].append(self.SWE)
self.results['LAI'].append(self.LAI)
self.results['Mbe'].append(np.nanmax(MBE))
self.results['LAIfract'].append(self._relative_lai)
self.results['Unload'].append(unload)
return PotInf, Trfall, Interc, Evap, ET, Transpi, Efloor, MBE
def update_daily(self, T, doy):
"""
updates temperature sum, leaf-area development, phenology and
computes effective parameters for grid-cell
Args:
T - daily mean temperature (degC)
doy - day of year
Returns:
None
"""
self._degreeDays(T, doy)
self._photoacclim(T)
# deciduous relative leaf-area index
self._lai_dynamics(doy)
# canopy effective photosynthesis-stomatal conductance parameters:
LAI = 0.0
Amax = 0.0
q50 = 0.0
g1 = 0.0
for pt in self.ptypes.keys():
if self.ptypes[pt]['lai_cycle']:
pt_lai = self.ptypes[pt]['LAImax'] * self._relative_lai
else:
pt_lai = self.ptypes[pt]['LAImax']
LAI += pt_lai
Amax += pt_lai * self.ptypes[pt]['amax']
q50 += pt_lai * self.ptypes[pt]['q50']
g1 += pt_lai * self.ptypes[pt]['g1']
self.LAI = LAI + eps
#print(doy, LAI, Amax / self.LAI, g1 / self.LAI)
self.physpara.update({'Amax': Amax / self.LAI, 'q50': q50 / self.LAI, 'g1': g1 / self.LAI})
def _degreeDays(self, T, doy):
"""
Calculates and updates degree-day sum from the current mean Tair.
INPUT:
T - daily mean temperature (degC)
doy - day of year 1...366 (integer)
"""
To = 5.0 # threshold temperature
if doy == 1: # reset in the beginning of the year
self.DDsum = 0.
else:
self.DDsum += np.maximum(0.0, T - To)
def _photoacclim(self, T):
"""
computes new stage of temperature acclimation and phenology modifier.
Peltoniemi et al. 2015 Bor.Env.Res.
IN: object, T = daily mean air temperature
OUT: None, updates object state
"""
self.X = self.X + 1.0 / self.phenopara['tau'] * (T - self.X) # degC
S = np.maximum(self.X - self.phenopara['xo'], 0.0)
fPheno = np.maximum(self.phenopara['fmin'],
np.minimum(S / self.phenopara['smax'], 1.0))
self.fPheno = fPheno
def _lai_dynamics(self, doy):
"""
Seasonal cycle of deciduous leaf area
Args:
self - object
doy - day of year
Returns:
none, updates state variables self._relative_lai, self._growth_stage,
self._senec_stage
"""
lai_min = self.phenopara['lai_decid_min']
ddo = self.phenopara['ddo']
ddur = self.phenopara['ddur']
sso = self.phenopara['sso']
sdur = self.phenopara['sdur']
# growth phase
if self.DDsum <= ddo:
f = lai_min
self._growth_stage = 0.
self._senesc_stage = 0.
elif self.DDsum > ddo:
self._growth_stage += 1.0 / ddur
f = np. minimum(1.0, lai_min + (1.0 - lai_min) * self._growth_stage)
# senescence phase
if doy > sso:
self._growth_stage = 0.
self._senesc_stage += 1.0 / sdur
f = 1.0 - (1.0 - lai_min) * np.minimum(1.0, self._senesc_stage)
self._relative_lai = f
def dry_canopy_et(self, D, Qp, AE, Ta, Ra=25.0, Ras=250.0, CO2=380.0,
Rew=1.0, beta=1.0, fPheno=1.0):
"""
Computes ET from 2-layer canopy in absense of intercepted precipitiation,
i.e. in dry-canopy conditions
IN:
self - object
D - vpd in kPa
Qp - PAR in Wm-2
AE - available energy in Wm-2
Ta - air temperature degC
Ra - aerodynamic resistance (s/m)
Ras - soil aerodynamic resistance (s/m)
CO2 - atm. CO2 mixing ratio (ppm)
Rew - relative extractable water [-]
beta - relative soil conductance for evaporation [-]
fPheno - phenology modifier [-]
Args:
Tr - transpiration rate (mm s-1)
Efloor - forest floor evaporation rate (mm s-1)
Gc - canopy conductance (integrated stomatal conductance) (m s-1)
SOURCES:
Launiainen et al. (2016). Do the energy fluxes and surface conductance
of boreal coniferous forests in Europe scale with leaf area?
Global Change Biol.
Modified from: Leuning et al. 2008. A Simple surface conductance model
to estimate regional evaporation using MODIS leaf area index and the
Penman-Montheith equation. Water. Resources. Res., 44, W10419
Original idea Kelliher et al. (1995). Maximum conductances for
evaporation from global vegetation types. Agric. For. Met 85, 135-147
Samuli Launiainen, Luke
Last edit: 13.6.2018: TESTING UPSCALING
"""
# ---Amax and g1 as LAI -weighted average of conifers and decid.
rhoa = 101300.0 / (8.31 * (Ta + 273.15)) # mol m-3
Amax = self.physpara['Amax']
g1 = self.physpara['g1']
kp = self.physpara['kp'] # (-) attenuation coefficient for PAR
q50 = self.physpara['q50'] # Wm-2, half-sat. of leaf light response
rw = self.physpara['rw'] # rew parameter
rwmin = self.physpara['rwmin'] # rew parameter
tau = np.exp(-kp * self.LAI) # fraction of Qp at ground relative to canopy top
"""--- canopy conductance Gc (integrated stomatal conductance)----- """
# fQ: Saugier & Katerji, 1991 Agric. For. Met., eq. 4. Leaf light response = Qp / (Qp + q50)
fQ = 1./ kp * np.log((kp*Qp + q50) / (kp*Qp*np.exp(-kp * self.LAI) + q50 + eps) )
# the next formulation is from Leuning et al., 2008 WRR for daily Gc; they refer to
# Kelliher et al. 1995 AFM but the resulting equation is not exact integral of K95.
# fQ = 1./ kp * np.log((Qp + q50) / (Qp*np.exp(-kp*self.LAI) + q50))
# soil moisture response: Lagergren & Lindroth, xxxx"""
fRew = np.minimum(1.0, np.maximum(Rew / rw, rwmin))
# fRew = 1.0
# CO2 -response of canopy conductance, derived from APES-simulations
# (Launiainen et al. 2016, Global Change Biology). relative to 380 ppm
fCO2 = 1.0 - 0.387 * np.log(CO2 / 380.0)
# leaf level light-saturated gs (m/s)
gs = 1.6*(1.0 + g1 / np.sqrt(D)) * Amax / CO2 / rhoa
# canopy conductance
Gc = gs * fQ * fRew * fCO2 * fPheno
Gc[np.isnan(Gc)] = eps
""" --- transpiration rate --- """
Tr = penman_monteith((1.-tau)*AE, 1e3*D, Ta, Gc, 1./Ra, units='mm')
Tr[Tr < 0] = 0.0
"""--- forest floor evaporation rate--- """
# soil conductance is function of relative water availability
# gcs = 1. / self.soilrp * beta**2.0
# beta = Wliq / FC; Best et al., 2011 Geosci. Model. Dev. JULES
Gcs = self.gsoil
Efloor = beta * penman_monteith(tau * AE, 1e3*D, Ta, Gcs, 1./Ras, units='mm')
Efloor[self.SWE > 0] = 0.0 # no evaporation from floor if snow on ground or beta == 0
return Tr, Efloor, Gc
def canopy_water_snow(self, dt, T, Prec, AE, D, Ra=25.0, U=2.0):
"""
Calculates canopy water interception and SWE during timestep dt
Args:
self - object
dt - timestep [s]
T - air temperature (degC)
Prec - precipitation rate during (mm d-1)
AE - available energy (~net radiation) (Wm-2)
D - vapor pressure deficit (kPa)
Ra - canopy aerodynamic resistance (s m-1)
Returns:
self - updated state W, Wf, SWE, SWEi, SWEl
PotInf - potential infiltration to soil profile (mm)
Trfall - throughfall to snow / soil surface (mm)
Evap - evaporation / sublimation from canopy store (mm)
Interc - interception of canopy (mm)
MBE - mass balance error (mm)
Unload - undloading from canopy storage (mm)
Samuli Launiainen & Ari Laurén 2014 - 2017
Last edit 12 / 2017
"""
# quality of precipitation
Tmin = 0.0 # 'C, below all is snow
Tmax = 1.0 # 'C, above all is water
Tmelt = 0.0 # 'C, T when melting starts
# storage capacities mm
Wmax = self.wmax * self.LAI
Wmaxsnow = self.wmaxsnow * self.LAI
# melting/freezing coefficients mm/s
Kmelt = self.Kmelt - 1.64 * self.cf / dt # Kuusisto E, 'Lumi Suomessa'
Kfreeze = self.Kfreeze
kp = self.physpara['kp']
tau = np.exp(-kp*self.LAI) # fraction of Rn at ground
# inputs to arrays, needed for indexing later in the code
gridshape = np.shape(self.LAI) # rows, cols
if np.shape(T) != gridshape:
T = np.ones(gridshape) * T
Prec = np.ones(gridshape) * Prec
AE = np.ones(gridshape) * AE
D = np.ones(gridshape) * D
Ra = np.ones(gridshape) * Ra
Prec = Prec * dt # mm
# latent heat of vaporization (Lv) and sublimation (Ls) J kg-1
Lv = 1e3 * (3147.5 - 2.37 * (T + 273.15))
Ls = Lv + 3.3e5
# compute 'potential' evaporation / sublimation rates for each grid cell
erate = np.zeros(gridshape)
ixs = np.where((Prec == 0) & (T <= Tmin))
ixr = np.where((Prec == 0) & (T > Tmin))
Ga = 1. / Ra # aerodynamic conductance
# resistance for snow sublimation adopted from:
# Pomeroy et al. 1998 Hydrol proc; Essery et al. 2003 J. Climate;
# Best et al. 2011 Geosci. Mod. Dev.
Ce = 0.01*((self.W + eps) / Wmaxsnow)**(-0.4) # exposure coeff (-)
Sh = (1.79 + 3.0*U**0.5) # Sherwood numbner (-)
gi = Sh*self.W*Ce / 7.68 + eps # m s-1
erate[ixs] = dt / Ls[ixs] * penman_monteith((1.0 - tau[ixs])*AE[ixs],
1e3*D[ixs], T[ixs], gi[ixs],
Ga[ixs], units='W')
# evaporation of intercepted water, mm
gs = 1e6
erate[ixr] = dt / Lv[ixr] * penman_monteith((1.0 - tau[ixr])*AE[ixr],
1e3*D[ixr], T[ixr], gs,
Ga[ixr], units='W')
# ---state of precipitation [as water (fW) or as snow(fS)]
fW = np.zeros(gridshape)
fS = np.zeros(gridshape)
fW[T >= Tmax] = 1.0
fS[T <= Tmin] = 1.0
ix = np.where((T > Tmin) & (T < Tmax))
fW[ix] = (T[ix] - Tmin) / (Tmax - Tmin)
fS[ix] = 1.0 - fW[ix]
del ix
# --- Local fluxes (mm)
Unload = np.zeros(gridshape) # snow unloading
Interc = np.zeros(gridshape) # interception
Melt = np.zeros(gridshape) # melting
Freeze = np.zeros(gridshape) # freezing
Evap = np.zeros(gridshape)
""" --- initial conditions for calculating mass balance error --"""
Wo = self.W # canopy storage
SWEo = self.SWE # Snow water equivalent mm
""" --------- Canopy water storage change -----"""
# snow unloading from canopy, ensures also that seasonal LAI development does
# not mess up computations
ix = (T >= Tmax)
Unload[ix] = np.maximum(self.W[ix] - Wmax[ix], 0.0)
self.W = self.W - Unload
del ix
# dW = self.W - Wo
# Interception of rain or snow: asymptotic approach of saturation.
# Hedstrom & Pomeroy 1998. Hydrol. Proc 12, 1611-1625;
# Koivusalo & Kokkonen 2002 J.Hydrol. 262, 145-164.
ix = (T < Tmin)
Interc[ix] = (Wmaxsnow[ix] - self.W[ix]) \
* (1.0 - np.exp(-(self.cf[ix] / Wmaxsnow[ix]) * Prec[ix]))
del ix
# above Tmin, interception capacity equals that of liquid precip
ix = (T >= Tmin)
Interc[ix] = np.maximum(0.0, (Wmax[ix] - self.W[ix]))\
* (1.0 - np.exp(-(self.cf[ix] / Wmax[ix]) * Prec[ix]))
del ix
self.W = self.W + Interc # new canopy storage, mm
Trfall = Prec + Unload - Interc # Throughfall to field layer or snowpack
# evaporate from canopy and update storage
Evap = np.minimum(erate, self.W) # mm
self.W = self.W - Evap
""" Snowpack (in case no snow, all Trfall routed to floor) """
ix = np.where(T >= Tmelt)
Melt[ix] = np.minimum(self.SWEi[ix], Kmelt[ix] * dt * (T[ix] - Tmelt)) # mm
del ix
ix = np.where(T < Tmelt)
Freeze[ix] = np.minimum(self.SWEl[ix], Kfreeze * dt * (Tmelt - T[ix])) # mm
del ix
# amount of water as ice and liquid in snowpack
Sice = np.maximum(0.0, self.SWEi + fS * Trfall + Freeze - Melt)
Sliq = np.maximum(0.0, self.SWEl + fW * Trfall - Freeze + Melt)
PotInf = np.maximum(0.0, Sliq - Sice * self.R) # mm
Sliq = np.maximum(0.0, Sliq - PotInf) # mm, liquid water in snow
# update Snowpack state variables
self.SWEl = Sliq
self.SWEi = Sice
self.SWE = self.SWEl + self.SWEi
# mass-balance error mm
MBE = (self.W + self.SWE) - (Wo + SWEo) - (Prec - Evap - PotInf)
return PotInf, Trfall, Evap, Interc, MBE, Unload
""" *********** utility functions ******** """
# @staticmethod
def degreeDays(dd0, T, Tbase, doy):
"""
Calculates degree-day sum from the current mean Tair.
INPUT:
dd0 - previous degree-day sum (degC)
T - daily mean temperature (degC)
Tbase - base temperature at which accumulation starts (degC)
doy - day of year 1...366 (integer)
OUTPUT:
x - degree-day sum (degC)
"""
if doy == 1: # reset in the beginning of the year
dd0 = 0.
return dd0 + max(0, T - Tbase)
# @staticmethod
def eq_evap(AE, T, P=101300.0, units='W'):
"""
Calculates the equilibrium evaporation according to McNaughton & Spriggs,\
1986.
INPUT:
AE - Available energy (Wm-2)
T - air temperature (degC)
P - pressure (Pa)
units - W (Wm-2), mm (mms-1=kg m-2 s-1), mol (mol m-2 s-1)
OUTPUT:
equilibrium evaporation rate (Wm-2)
"""
Mw = 18e-3 # kg mol-1
# latent heat of vaporization of water [J/kg]
L = 1e3 * (2500.8 - 2.36 * T + 1.6e-3 * T ** 2 - 6e-5 * T ** 3)
# latent heat of sublimation [J/kg]
if T < 0:
L = 1e3 * (2834.1 - 0.29 * T - 0.004 * T ** 2)
_, s, g = e_sat(T, P)
x = np.divide((AE * s), (s + g)) # Wm-2 = Js-1m-2
if units == 'mm':
x = x / L # kg m-2 s-1 = mm s-1
elif units == 'mol':
x = x / L / Mw # mol m-2 s-1
x = np.maximum(x, 0.0)
return x
# @staticmethod
def e_sat(T, P=101300):
"""
Computes saturation vapor pressure (Pa), slope of vapor pressure curve
[Pa K-1] and psychrometric constant [Pa K-1]
IN:
T - air temperature (degC)
P - ambient pressure (Pa)
OUT:
esa - saturation vapor pressure in Pa
s - slope of saturation vapor pressure curve (Pa K-1)
g - psychrometric constant (Pa K-1)
"""
NT = 273.15
cp = 1004.67 # J/kg/K
Lambda = 1e3 * (3147.5 - 2.37 * (T + NT)) # lat heat of vapor [J/kg]
esa = 1e3 * (0.6112 * np.exp((17.67 * T) / (T + 273.16 - 29.66))) # Pa
s = 17.502 * 240.97 * esa / ((240.97 + T) ** 2)
g = P * cp / (0.622 * Lambda)
return esa, s, g
# @staticmethod
def penman_monteith(AE, D, T, Gs, Ga, P=101300.0, units='W'):
"""
Computes latent heat flux LE (Wm-2) i.e evapotranspiration rate ET (mm/s)
from Penman-Monteith equation
INPUT:
AE - available energy [Wm-2]
VPD - vapor pressure deficit [Pa]
T - ambient air temperature [degC]
Gs - surface conductance [ms-1]
Ga - aerodynamic conductance [ms-1]
P - ambient pressure [Pa]
units - W (Wm-2), mm (mms-1=kg m-2 s-1), mol (mol m-2 s-1)
OUTPUT:
x - evaporation rate in 'units'
"""
# --- constants
cp = 1004.67 # J kg-1 K-1
rho = 1.25 # kg m-3
Mw = 18e-3 # kg mol-1
_, s, g = e_sat(T, P) # slope of sat. vapor pressure, psycrom const
L = 1e3 * (3147.5 - 2.37 * (T + 273.15))
x = (s * AE + rho * cp * Ga * D) / (s + g * (1.0 + Ga / Gs)) # Wm-2
if units == 'mm':
x = x / L # kgm-2s-1 = mms-1
if units == 'mol':
x = x / L / Mw # mol m-2 s-1
x = np.maximum(x, 0.0)
return x
# @staticmethod
def aerodynamics(LAI, hc, Uo, w=0.01, zm=2.0, zg=0.5, zos=0.01):
"""
computes wind speed at ground and canopy + boundary layer conductances
Computes wind speed at ground height assuming logarithmic profile above and
exponential within canopy
Args:
LAI - one-sided leaf-area /plant area index (m2m-2)
hc - canopy height (m)
Uo - mean wind speed at height zm (ms-1)
w - leaf length scale (m)
zm - wind speed measurement height above canopy (m)
zg - height above ground where Ug is computed (m)
zos - forest floor roughness length, ~ 0.1*roughness element height (m)
Returns:
ra - canopy aerodynamic resistance (sm-1)
rb - canopy boundary layer resistance (sm-1)
ras - forest floor aerod. resistance (sm-1)
ustar - friction velocity (ms-1)
Uh - wind speed at hc (ms-1)
Ug - wind speed at zg (ms-1)
SOURCE:
Cammalleri et al. 2010 Hydrol. Earth Syst. Sci
Massman 1987, BLM 40, 179 - 197.
Magnani et al. 1998 Plant Cell Env.
"""
zm = hc + zm # m
zg = np.minimum(zg, 0.1 * hc)
kv = 0.4 # von Karman constant (-)
beta = 285.0 # s/m, from Campbell & Norman eq. (7.33) x 42.0 molm-3
alpha = LAI / 2.0 # wind attenuation coeff (Yi, 2008 eq. 23)
d = 0.66*hc # m
zom = 0.123*hc # m
zov = 0.1*zom
zosv = 0.1*zos
# solve ustar and U(hc) from log-profile above canopy
ustar = Uo * kv / np.log((zm - d) / zom)
Uh = ustar / kv * np.log((hc - d) / zom)
# U(zg) from exponential wind profile
zn = np.minimum(zg / hc, 1.0) # zground can't be above canopy top
Ug = Uh * np.exp(alpha*(zn - 1.0))
# canopy aerodynamic & boundary-layer resistances (sm-1). Magnani et al. 1998 PCE eq. B1 & B5
#ra = 1. / (kv*ustar) * np.log((zm - d) / zom)
ra = 1./(kv**2.0 * Uo) * np.log((zm - d) / zom) * np.log((zm - d) / zov)
rb = 1. / LAI * beta * ((w / Uh)*(alpha / (1.0 - np.exp(-alpha / 2.0))))**0.5
# soil aerodynamic resistance (sm-1)
ras = 1. / (kv**2.0*Ug) * (np.log(zg / zos))*np.log(zg / (zosv))
#print('ra', ra, 'rb', rb)
ra = ra + rb
return ra, rb, ras, ustar, Uh, Ug
def wind_profile(LAI, hc, Uo, z, zm=2.0, zg=0.2):
"""
Computes wind speed at ground height assuming logarithmic profile above and
hyperbolic cosine profile within canopy
INPUT:
LAI - one-sided leaf-area /plant area index (m2m-2)
hc - canopy height (m)
Uo - mean wind speed at height zm (ms-1)
zm - wind speed measurement height above canopy (m)
zg - height above ground where U is computed
OUTPUT:
Uh - wind speed at hc (ms-1)
Ug - wind speed at zg (ms-1)
SOURCE:
Cammalleri et al. 2010 Hydrol. Earth Syst. Sci
Massman 1987, BLM 40, 179 - 197.
"""
k = 0.4 # von Karman const
Cd = 0.2 # drag coeff
alpha = 1.5 # (-)
zm = zm + hc
d = 0.66*hc
zom = 0.123*hc
beta = 4.0 * Cd * LAI / (k**2.0*alpha**2.0)
# solve ustar and U(hc) from log-profile above canopy
ustar = Uo * k / np.log((zm - d) / zom) # m/s
U = np.ones(len(z))*np.NaN
# above canopy top wind profile is logarithmic
U[z >= hc] = ustar / k * np.log((z[z >= hc] - d) / zom)
# at canopy top, match log and exponential profiles
Uh = ustar / k * np.log((hc - d) / zom) # m/s
# within canopy hyperbolic cosine profile
U[z <= hc] = Uh * (np.cosh(beta * z[z <= hc] / hc) / np.cosh(beta))**0.5
return U, ustar, Uh
def daylength(LAT, LON, DOY):
"""
Computes daylength from location and day of year.
Args:
LAT, LON - in deg, float or arrays of floats
doy - day of year, float or arrays of floats
Returns:
dl - daylength (hours), float or arrays of floats
"""
CF = np.pi / 180.0 # conversion deg -->rad
LAT = LAT*CF
LON = LON*CF
# ---> compute declination angle
xx = 278.97 + 0.9856*DOY + 1.9165*np.sin((356.6 + 0.9856*DOY)*CF)
DECL = np.arcsin(0.39785*np.sin(xx*CF))
del xx
# --- compute day length, the period when sun is above horizon
# i.e. neglects civil twilight conditions
cosZEN = 0.0
dl = 2.0*np.arccos(cosZEN - np.sin(LAT)*np.sin(DECL) / (np.cos(LAT)*np.cos(DECL))) / CF / 15.0 # hours
return dl
#def read_ini(inifile):
# """read_ini(inifile): reads canopygrid.ini parameter file into pp dict"""
#
# cfg = configparser.ConfigParser()
# cfg.read(inifile)
#
# pp = {}
# for s in cfg.sections():
# section = s.encode('ascii', 'ignore')
# pp[section] = {}
# for k, v in cfg.items(section):
# key = k.encode('ascii', 'ignore')
# val = v.encode('ascii', 'ignore')
# if section == 'General': # 'general' section
# pp[section][key] = val
# else:
# pp[section][key] = float(val)
#
# pp['General']['dt'] = float(pp['General']['dt'])
#
# pgen = pp['General']
# cpara = pp['CanopyGrid']
# return pgen, cpara