def Epm(airtemp = scipy.array([]),\
rh = scipy.array([]),\
airpress = scipy.array([]),\
Rn = scipy.array([]),\
G = scipy.array([]),\
ra = scipy.array([]),\
rs = scipy.array([])):
'''
Function to calculate the Penman Monteith evaporation
(in mm) Monteith, J.L. (1965) Evaporation and environment.
Symp. Soc. Exp. Biol. 19, 205-224
Input (measured at 2 m height):
- airtemp: (array of) daily average air temperatures [C]
- rh: (array of) daily average relative humidity values[%]
- airpress: (array of) daily average air pressure data [hPa]
- Rn: (array of) average daily net radiation [J]
- G: (array of) average daily soil heat flux [J]
- ra: aerodynamic resistance [s/m]
- rs: surface resistance [s/m]
Output:
- Epm: (array of) Penman Monteith evaporation values [mm]
Examples:
>>> Epm_data = Epm(T,RH,press,Rn,G,ra,rs)
'''
# Calculate Delta, gamma and lambda
DELTA = meteolib.Delta_calc(airtemp) / 100. # [hPa/K]
airpress = airpress * 100. # [Pa]
gamma = meteolib.gamma_calc(airtemp, rh, airpress) / 100. # [hPa/K]
Lambda = meteolib.L_calc(airtemp) # [J/kg]
rho = meteolib.rho_calc(airtemp, rh, airpress)
cp = meteolib.cp_calc(airtemp, rh, airpress)
# Calculate saturated and actual water vapour pressures
es = meteolib.es_calc(airtemp) / 100. # [hPa]
ea = meteolib.ea_calc(airtemp, rh) / 100. # [hPa]
# Determine length of array
l = scipy.size(airtemp)
# Check if we have a single value or an array
if l < 2: # Dealing with single value...
Epm = (DELTA * Rn + rho * cp * (es - ea) * ra /
(DELTA + gamma * (1. + rs / ra))) / Lambda
else: # Dealing with an array
# Initiate output arrays
Epm = scipy.zeros(l)
for i in range(0, l):
Epm = (DELTA[i]*Rn[i]+rho[i]*cp[i]*(es[i]-ea[i])*ra[i]/(DELTA[i] \
+ gamma[i]*(1.+rs[i]/ra[i])))/Lambda[i]
return Epm # actual ET in mm
def Epm(airtemp = scipy.array([]),\
rh = scipy.array([]),\
airpress = scipy.array([]),\
Rn = scipy.array([]),\
G = scipy.array([]),\
ra = scipy.array([]),\
rs = scipy.array([])):
'''
Function to calculate the Penman Monteith evaporation
(in mm) Monteith, J.L. (1965) Evaporation and environment.
Symp. Soc. Exp. Biol. 19, 205-224
Input (measured at 2 m height):
- airtemp: (array of) daily average air temperatures [C]
- rh: (array of) daily average relative humidity values[%]
- airpress: (array of) daily average air pressure data [hPa]
- Rn: (array of) average daily net radiation [J]
- G: (array of) average daily soil heat flux [J]
- ra: aerodynamic resistance [s/m]
- rs: surface resistance [s/m]
Output:
- Epm: (array of) Penman Monteith evaporation values [mm]
Examples:
>>> Epm_data = Epm(T,RH,press,Rn,G,ra,rs)
'''
# Calculate Delta, gamma and lambda
DELTA = meteolib.Delta_calc(airtemp)/100. # [hPa/K]
airpress=airpress*100. # [Pa]
gamma = meteolib.gamma_calc(airtemp,rh,airpress)/100. # [hPa/K]
Lambda = meteolib.L_calc(airtemp) # [J/kg]
rho = meteolib.rho_calc(airtemp,rh,airpress)
cp = meteolib.cp_calc(airtemp,rh,airpress)
# Calculate saturated and actual water vapour pressures
es = meteolib.es_calc(airtemp)/100. # [hPa]
ea = meteolib.ea_calc(airtemp,rh)/100. # [hPa]
# Determine length of array
l = scipy.size(airtemp)
# Check if we have a single value or an array
if l < 2: # Dealing with single value...
Epm = (DELTA*Rn+rho*cp*(es-ea)*ra/(DELTA+gamma*(1.+rs/ra)))/Lambda
else: # Dealing with an array
# Initiate output arrays
Epm = scipy.zeros(l)
for i in range(0,l):
Epm = (DELTA[i]*Rn[i]+rho[i]*cp[i]*(es[i]-ea[i])*ra[i]/(DELTA[i] \
+ gamma[i]*(1.+rs[i]/ra[i])))/Lambda[i]
return Epm # actual ET in mm
def half_hour_evaporation(airtemp=sp.array([]),
rh=sp.array([]),
airpress=sp.array([]),
rs=sp.array([]),
rext=sp.array([]),
u=sp.array([]),
z=0.0):
"""
Function to calculate daily Penman open water evaporation (in mm/30min).
Equation according to
Shuttleworth, W. J. 2007. "Putting the 'Vap' into Evaporation."
Hydrology and Earth System Sciences 11 (1): 210-44. doi:10.5194/hess-11-210-2007.
:param airtemp: average air temperature [Celsius]
:param rh: relative humidity[%]
:param airpress: average air pressure[Pa]
:param rs: Incoming solar radiation [MJ/m2/30min]
:param rext: Extraterrestrial radiation [MJ/m2/30min]
:param u: average wind speed at 2 m from ground [m/s]
:param z: site elevation, default is zero [metre]
:return: Penman open water evaporation values [mm/30min]
Examples:
>>> half_hour_evaporation = E0(T,RH,press,Rs,N,Rext,u,1000.0) # at 1000 m a.s.l
"""
# Set constants
albedo = 0.06 # open water albedo
# Stefan boltzmann constant = 5.670373*10-8 J/m2/k4/s
# http://en.wikipedia.org/wiki/Stefan-Boltzmann_constant
# sigma = 5.670373*(10**-8) # J/m2/K4/s
sigma = (1.02066714 * (10**-10)
) # Stefan Boltzmann constant MJ/m2/K4/30min
# Calculate Delta, gamma and lambda
delta = delta_calc(airtemp) # [Kpa/C]
# Lambda = met.L_calc(airtemp)/(10**6) # [MJ/Kg]
# gamma = met.gamma_calc(airtemp, rh, airpress)/1000
# Lambda = 2.501 -(0.002361*airtemp) # [MJ/kg]
# gamma = (0.0016286 *(airpress/1000))/Lambda
# Calculate saturated and actual water vapour pressure
es = met.es_calc(airtemp) # [Pa]
ea = met.ea_calc(airtemp, rh) # [Pa]
# Determine length of array
l = sp.size(airtemp)
# Check if we have a single value or an array
if l < 2:
lambda_mj_kg = 2.501 - (0.002361 * airtemp) # [MJ/kg]
gamma = (0.0016286 * (airpress / 1000)) / lambda_mj_kg
rns = (1.0 - albedo) * rs # shortwave component [MJ/m2/30min]
# calculate clear sky radiation Rs0
rs0 = (0.75 + (2E-5 * z)) * rext
f = (1.35 * (rs / rs0)) - 0.35
epsilom = 0.34 - (-0.14 * sp.sqrt(ea / 1000))
rnl = f * epsilom * sigma * (
airtemp + 273.16)**4 # Longwave component [MJ/m2/30min]
rnet = rns - rnl
Ea = (1 + (0.536 * u)) * ((es / 1000) - (ea / 1000))
E0 = ((delta * rnet) + gamma * (6.43 * Ea)) / (lambda_mj_kg *
(delta + gamma))
else:
# Inititate output array
E0 = sp.zeros(l)
rns = sp.zeros(l)
rs0 = sp.zeros(l)
f = sp.zeros(l)
epsilom = sp.zeros(l)
rnl = sp.zeros(l)
rnet = sp.zeros(l)
Ea = sp.zeros(l)
lambda_mj_kg = sp.zeros(l)
gamma = sp.zeros(l)
for i in range(0, l):
lambda_mj_kg[i] = 2.501 - (0.002361 * airtemp[i])
gamma[i] = (0.0016286 * (airpress[i] / 1000)) / lambda_mj_kg[i]
# calculate longwave radiation (MJ/m2/30min)
rns[i] = (1.0 - albedo) * rs[i]
# calculate clear sky radiation Rs0
rs0[i] = (0.75 + (2E-5 * z))
f[i] = (1.35 * (rs[i] / rs0[i])) - 0.35
epsilom[i] = 0.34 - (-0.14 * sp.sqrt(ea[i] / 1000))
rnl[i] = f[i] * epsilom[i] * sigma * (
airtemp[i] + 273.16)**4 # Longwave component [MJ/m2/30min]
rnet[i] = rns[i] - rnl[i]
Ea[i] = (1 + (0.536 * u[i])) * ((es[i] / 1000) - (ea[i] / 1000))
E0[i] = ((delta[i] * rnet[i]) + gamma[i] *
(6.43 * Ea[i])) / (lambda_mj_kg[i] *
(delta[i] + gamma[i]))
return E0
def half_hour_E0(
airtemp=sp.array([]),
rh=sp.array([]),
airpress=sp.array([]),
Rs=sp.array([]),
Rext=sp.array([]),
u=sp.array([]),
Z=0.0,
):
"""
Function to calculate daily Penman open water evaporation (in mm/30min).
Equation according to
Shuttleworth, W. J. 2007. "Putting the 'Vap' into Evaporation."
Hydrology and Earth System Sciences 11 (1): 210-44. doi:10.5194/hess-11-210-2007.
:param airtemp: average air temperature [Celsius]
:param rh: relative humidity[%]
:param airpress: average air pressure[Pa]
:param Rs: Incoming solar radiation [MJ/m2/30min]
:param Rext: Extraterrestrial radiation [MJ/m2/30min]
:param u: average wind speed at 2 m from ground [m/s]
:param Z: site elevation, default is zero [metre]
:return: Penman open water evaporation values [mm/30min]
"""
# Set constants
albedo = 0.06 # open water albedo
# Stefan boltzmann constant = 5.670373*10-8 J/m2/k4/s
# http://en.wikipedia.org/wiki/Stefan-Boltzmann_constant
# sigma = 5.670373*(10**-8) # J/m2/K4/s
sigma = 1.02066714 * (10 ** -10) # Stefan Boltzmann constant MJ/m2/K4/30min
# Calculate Delta, gamma and lambda
DELTA = delta_calc(airtemp) # [Kpa/C]
# Lambda = met.L_calc(airtemp)/(10**6) # [MJ/Kg]
# gamma = met.gamma_calc(airtemp, rh, airpress)/1000
# Lambda = 2.501 -(0.002361*airtemp) # [MJ/kg]
# gamma = (0.0016286 *(airpress/1000))/Lambda
# Calculate saturated and actual water vapour pressure
es = met.es_calc(airtemp) # [Pa]
ea = met.ea_calc(airtemp, rh) # [Pa]
# Determine length of array
l = sp.size(airtemp)
# Check if we have a single value or an array
if l < 2:
Lambda = 2.501 - (0.002361 * airtemp) # [MJ/kg]
gamma = (0.0016286 * (airpress / 1000)) / Lambda
Rns = (1.0 - albedo) * Rs # shortwave component [MJ/m2/30min]
# calculate clear sky radiation Rs0
Rs0 = (0.75 + (2e-5 * Z)) * Rext
f = (1.35 * (Rs / Rs0)) - 0.35
epsilom = 0.34 - (-0.14 * sp.sqrt(ea / 1000))
Rnl = f * epsilom * sigma * (airtemp + 273.16) ** 4 # Longwave component [MJ/m2/30min]
Rnet = Rns - Rnl
Ea = (1 + (0.536 * u)) * ((es / 1000) - (ea / 1000))
E0 = ((DELTA * Rnet) + gamma * (6.43 * Ea)) / (Lambda * (DELTA + gamma))
else:
# Inititate output array
E0 = sp.zeros(l)
Rns = sp.zeros(l)
Rs0 = sp.zeros(l)
f = sp.zeros(l)
epsilom = sp.zeros(l)
Rnl = sp.zeros(l)
Rnet = sp.zeros(l)
Ea = sp.zeros(l)
Lambda = sp.zeros(l)
gamma = sp.zeros(l)
for i in range(0, l):
Lambda[i] = 2.501 - (0.002361 * airtemp[i])
gamma[i] = (0.0016286 * (airpress[i] / 1000)) / Lambda[i]
# calculate longwave radiation (MJ/m2/30min)
Rns[i] = (1.0 - albedo) * Rs[i]
# calculate clear sky radiation Rs0
Rs0[i] = 0.75 + (2e-5 * Z)
f[i] = (1.35 * (Rs[i] / Rs0[i])) - 0.35
epsilom[i] = 0.34 - (-0.14 * sp.sqrt(ea[i] / 1000))
Rnl[i] = f[i] * epsilom[i] * sigma * (airtemp[i] + 273.16) ** 4 # Longwave component [MJ/m2/30min]
Rnet[i] = Rns[i] - Rnl[i]
Ea[i] = (1 + (0.536 * u[i])) * ((es[i] / 1000) - (ea[i] / 1000))
E0[i] = ((DELTA[i] * Rnet[i]) + gamma[i] * (6.43 * Ea[i])) / (Lambda[i] * (DELTA[i] + gamma[i]))
return E0
def Epm(airtemp = scipy.array([]),\
rh = scipy.array([]),\
airpress = scipy.array([]),\
Rn = scipy.array([]),\
G = scipy.array([]),\
ra = scipy.array([]),\
rs = scipy.array([])):
'''
Function to calculate the Penman Monteith evaporation.
.. math::
E_{pm} = \\frac{\\Delta \\cdot (R_n-G)+\\rho \\cdot c_p \\cdot (e_s-e_a)/r_a}{\\lambda \\cdot (\\Delta + \\gamma \\cdot (1+\\frac{r_s}{r_a}))}
The function can be used with different time intervals, such as commonly
used hourly or daily time intervals are used. When a plant canopy is wet,
the surface resistance (rs) becomes zero (stomatal resistance irrelevant,
as evaporation is directly from wet leaf surface). Function ra() in this
module can be used to calculate the aerodynamic resistance (ra) from wind
speed and height parameters.
Parameters:
- airtemp: (array of) daily average air temperatures [Celsius].
- rh: (array of) daily average relative humidity values [%].
- airpress: (array of) daily average air pressure data [hPa].
- Rn: (array of) net radiation input over time interval t [J t-1].
- G: (array of) soil heat flux input over time interval t [J t-1].
- ra: aerodynamic resistance [s m-1].
- rs: surface resistance [s m-1].
Returns:
- Epm: (array of) Penman Monteith evaporation values [mm t-1].
References
----------
J.L. Monteith (1965). Evaporation and environment. Symp. Soc. Exp. Biol.
19: 205-224.
Examples
--------
>>> Epm(21.67,67.0,1013.0,14100000.,500000.,104.,70.)
3.243341146049407
'''
# Test input array/value
airtemp, rh, airpress, Rn, G, ra, rs = meteolib._arraytest(
airtemp, rh, airpress, Rn, G, ra, rs)
# Calculate Delta, gamma and lambda
DELTA = meteolib.Delta_calc(airtemp) / 100. # [hPa/K]
airpress = airpress * 100. # [Pa]
gamma = meteolib.gamma_calc(airtemp, rh, airpress) / 100. # [hPa/K]
Lambda = meteolib.L_calc(airtemp) # [J/kg]
rho = meteolib.rho_calc(airtemp, rh, airpress) # [kg m-3]
cp = meteolib.cp_calc(airtemp, rh, airpress) # [J kg-1 K-1]
# Calculate saturated and actual water vapour pressures
es = meteolib.es_calc(airtemp) / 100. # [hPa]
ea = meteolib.ea_calc(airtemp, rh) / 100. # [hPa]
# Calculate Epm
Epm = ((DELTA * (Rn - G) + rho * cp * (es - ea) / ra) /
(DELTA + gamma * (1. + rs / ra))) / Lambda
return Epm # actual ET in mm
def ET0pm(airtemp = scipy.array([]),\
rh = scipy.array([]),\
airpress = scipy.array([]), \
Rs = scipy.array([]),\
Rext = scipy.array([]),\
u = scipy.array([]), \
Z=0.0):
'''
Function to calculate daily Penman Monteith reference evaporation estimates.
Parameters:
- airtemp: (array of) daily average air temperatures [Celsius].
- rh: (array of) daily average relative humidity values [%].
- airpress: (array of) daily average air pressure data [hPa].
- Rs: (array of) total incoming shortwave radiation [J m-2 day-1].
- Rext: Incoming shortwave radiation at the top of the atmosphere\
[J m-2 day-1].
- u: windspeed [m s-1].
- Z: elevation [m], default is 0 m a.s.l.
Returns:
- ET0pm: (array of) Penman Monteith reference evaporation (short\
grass with optimum water supply) values [mm day-1].
Notes
-----
Meteorological measuements standard at 2 m above soil surface.
References
----------
R.G. Allen, L.S. Pereira, D. Raes and M. Smith (1998). Crop
evapotranspiration - Guidelines for computing crop water requirements -
FAO Irrigation and drainage paper 56. FAO - Food and Agriculture
Organization of the United Nations, Rome, 1998.
(http://www.fao.org/docrep/x0490e/x0490e07.htm)
Examples
--------
>>> ET0pm(20.67,67.0,101300.0,22600000.,42000000.,3.2)
4.7235349721073039
'''
# Test input array/value
airtemp, rh, airpress, Rs, Rext, u = meteolib._arraytest(
airtemp, rh, airpress, Rs, Rext, u)
# Set constants
albedo = 0.23 # short grass albedo
sigma = 4.903E-3 # Stefan Boltzmann constant J/m2/K4/d
# Calculate Delta, gamma and lambda
DELTA = meteolib.Delta_calc(airtemp) # [Pa/K]
gamma = meteolib.gamma_calc(airtemp, rh, airpress) # [Pa/K]
Lambda = meteolib.L_calc(airtemp) # [J/kg]
# Calculate saturated and actual water vapour pressures
es = meteolib.es_calc(airtemp) # [Pa]
ea = meteolib.ea_calc(airtemp, rh) # [Pa]
Rns = (1.0 - albedo) * Rs # Shortwave component [J/m2/d]
# Calculate clear sky radiation Rs0
Rs0 = (0.75 + 2E-5 * Z) * Rext # Clear sky radiation [J/m2/d]
f = 1.35 * Rs / Rs0 - 0.35
epsilom = 0.34 - 0.14 * scipy.sqrt(ea / 1000)
Rnl = f * epsilom * sigma * (airtemp +
273.15)**4 # Longwave component [J/m2/d]
Rnet = Rns - Rnl # Net radiation [J/m2/d]
ET0pm = (DELTA/1000.*Rnet/Lambda+900./(airtemp+273.16)*u*(es-ea)/1000\
*gamma/1000)/(DELTA/1000.+gamma/1000*(1.+0.34*u))
return ET0pm # FAO reference evaporation [mm/day]
def E0(airtemp = scipy.array([]),\
rh = scipy.array([]),\
airpress = scipy.array([]),\
Rs = scipy.array([]),\
Rext = scipy.array([]),\
u = scipy.array([]),\
alpha = 0.08,\
Z = 0.0):
'''
Function to calculate daily Penman (open) water evaporation estimates:
.. math::
E_0 = \\frac{R_n \\cdot \\Delta}{\\lambda \cdot (\\Delta + \\gamma)} + \\frac{6430000 \\cdot E_a \\cdot \\gamma}{\\lambda \\cdot (\\Delta+\\gamma)}
Parameters:
- airtemp: (array of) daily average air temperatures [Celsius].
- rh: (array of) daily average relative humidity [%].
- airpress: (array of) daily average air pressure data [Pa].
- Rs: (array of) daily incoming solar radiation [J m-2 day-1].
- Rext: (array of) daily extraterrestrial radiation [J m-2 day-1].
- u: (array of) daily average wind speed at 2 m [m s-1].
- alpha: albedo [-] set at 0.08 for open water by default.
- Z: (array of) site elevation, default is 0 m a.s.l.
Returns:
- E0: (array of) Penman open water evaporation values [mm day-1].
Notes
-----
Meteorological parameters measured at 2 m above the surface. Albedo
alpha set by default at 0.08 for open water (Valiantzas, 2006).
References
----------
- H.L. Penman (1948). Natural evaporation from open water, bare soil\
and grass. Proceedings of the Royal Society of London. Series A.\
Mathematical and Physical Sciences 193: 120-145.
- H.L. Penman (1956). Evaporation: An introductory survey. Netherlands\
Journal of Agricultural Science 4: 9-29.
- J.D. Valiantzas (2006). Simplified versions for the Penman\
evaporation equation using routine weather data. J. Hydrology 331:\
690-702.
Examples
--------
>>> # With single values and default albedo/elevation
>>> E0(20.67,67.0,101300.0,22600000.,42000000.,3.2)
6.6029208786994467
>>> # With albedo is 0.18 instead of default and default elevation
>>> E0(20.67,67.0,101300.0,22600000.,42000000.,3.2,alpha=0.18)
5.9664248091431968
>>> # With standard albedo and Z= 250.0 m
>>> E0(20.67,67.0,101300.0,22600000.,42000000.,3.2,Z=250.0)
6.6135588207586284
>>> # With albedo alpha = 0.18 and elevation Z = 1000 m a.s.l.
>>> E0(20.67,67.0,101300.0,22600000.,42000000.,3.2,0.18,1000.)
6.00814764682986
'''
# Test input array/value
airtemp, rh, airpress, Rs, Rext, u = meteolib._arraytest(
airtemp, rh, airpress, Rs, Rext, u)
# Set constants
sigma = 4.903E-3 # Stefan Boltzmann constant J/m2/K4/d
# Calculate Delta, gamma and lambda
DELTA = meteolib.Delta_calc(airtemp) # [Pa/K]
gamma = meteolib.gamma_calc(airtemp, rh, airpress) # [Pa/K]
Lambda = meteolib.L_calc(airtemp) # [J/kg]
# Calculate saturated and actual water vapour pressures
es = meteolib.es_calc(airtemp) # [Pa]
ea = meteolib.ea_calc(airtemp, rh) # [Pa]
# calculate radiation components (J/m2/day)
Rns = (1.0 - alpha) * Rs # Shortwave component [J/m2/d]
Rs0 = (0.75 + 2E-5 * Z) * Rext # Calculate clear sky radiation Rs0
f = 1.35 * Rs / Rs0 - 0.35
epsilom = 0.34 - 0.14 * scipy.sqrt(ea / 1000)
Rnl = f * epsilom * sigma * (airtemp +
273.15)**4 # Longwave component [J/m2/d]
Rnet = Rns - Rnl # Net radiation [J/m2/d]
Ea = (1 + 0.536 * u) * (es / 1000 - ea / 1000)
E0 = (DELTA / (DELTA + gamma) * Rnet / Lambda + gamma /
(DELTA + gamma) * 6430000 * Ea / Lambda)
return E0
def E0(airtemp = scipy.array([]),\
rh = scipy.array([]),\
airpress = scipy.array([]),\
Rs = scipy.array([]),\
# N = scipy.array([]),\
Rext = scipy.array([]),\
u = scipy.array([]),\
Z=0.0):
'''
Function to calculate daily Penman open water evaporation (in mm/day).
Equation according to J.D. Valiantzas (2006). Simplified versions
for the Penman evaporation equation using routine weather data.
J. Hydrology 331: 690-702. Following Penman (1948,1956). Albedo set
at 0.06 for open water.
Input (measured at 2 m height):
- airtemp: (array of) daily average air temperatures [Celsius]
- rh: (array of) daily average relative humidity [%]
- airpress: (array of) daily average air pressure data [Pa]
- Rs: (array of) daily incoming solar radiation [J/m2/day]
- N: (array of) maximum daily sunshine hours [h]
- Rext: (array of) daily extraterrestrial radiation [J/m2/day]
- u: (array of) daily average wind speed at 2 m [m/s]
- Z: (array of) site elevation [m a.s.l.], default is zero...
Output:
- E0: (array of) Penman open water evaporation values [mm/day]
Examples:
>>> # T, RH, etc. are arrays of data...
>>> E0_data = E0(T,RH,press,Rs,N,Rext,u) # for zero elevation
>>> E0_data = E0(T,RH,press,Rs,N,Rext,u,1000.0) # at 1000 m a.s.l
>>> # With single values and default elevation...
>>> E0(20.67,67.0,101300.0,22600000,14.4,42000000,2.0)
6.3102099052283389
>>> # for elevation of 1.0 m a.s.l.
>>> E0(21.65,67.0,101300.0,24200000,14.66,42200000,1.51,1.0)
6.5991748573832343
>>>
'''
# Set constants
albedo = 0.06 # Open water albedo
sigma = 4.903E-3 # Stefan Boltzmann constant J/m2/K4/d
# Calculate Delta, gamma and lambda
DELTA = meteolib.Delta_calc(airtemp) # [Pa/K]
gamma = meteolib.gamma_calc(airtemp,rh,airpress) # [Pa/K]
Lambda = meteolib.L_calc(airtemp) # [J/kg]
# Calculate saturated and actual water vapour pressures
es = meteolib.es_calc(airtemp) # [Pa]
ea = meteolib.ea_calc(airtemp,rh) # [Pa]
# Determine length of array
l = scipy.size(airtemp)
# Check if we have a single value or an array
if l < 2: # Dealing with single value...
Rns = (1.0-albedo)*Rs # Shortwave component [J/m2/d]
# Calculate clear sky radiation Rs0
Rs0 = (0.75+2E-5*Z)*Rext
f = 1.35*Rs/Rs0-0.35
epsilom = 0.34-0.14*scipy.sqrt(ea/1000)
Rnl = f*epsilom*sigma*(airtemp+273.15)**4 # Longwave component [J/m2/d]
Rnet = Rns-Rnl # Net radiation [J/m2/d]
Ea = (1+0.536*u)*(es/1000.-ea/1000.)
E0 = DELTA/(DELTA+gamma)*Rnet/Lambda+gamma/(DELTA+gamma)*6430000*Ea/Lambda
else: # Dealing with an array
# Initiate output arrays
E0 = scipy.zeros(l)
Rns = scipy.zeros(l)
Rs0 = scipy.zeros(l)
f = scipy.zeros(l)
epsilom = scipy.zeros(l)
Rnl = scipy.zeros(l)
Rnet = scipy.zeros(l)
Ea = scipy.zeros(l)
for i in range(0,l):
# calculate longwave radiation component Rln (J/m2/day)
Rns[i] = (1.0-albedo)*Rs[i] # Shortwave component [J/m2/d]
# Calculate clear sky radiation Rs0
Rs0[i] = (0.75+2E-5*Z)*Rext[i]
f[i] = 1.35*Rs[i]/Rs0[i]-0.35
epsilom[i] = 0.34-0.14*scipy.sqrt(ea[i]/1000)
Rnl[i] = f[i]*epsilom[i]*sigma*(airtemp[i]+273.15)**4 # Longwave component [J/m2/d]
Rnet[i] = Rns[i]-Rnl[i] # Net radiation [J/m2/d]
Ea[i] = (1+0.536*u[i])*(es[i]/1000-ea[i]/1000)
E0[i] = DELTA[i]/(DELTA[i]+gamma[i])*Rnet[i]/Lambda[i]+gamma[i]/(DELTA[i]+gamma[i])* \
6430000*Ea[i]/Lambda[i]
return E0
def ET0pm(airtemp = scipy.array([]),\
rh = scipy.array([]),\
airpress = scipy.array([]), \
Rs = scipy.array([]),\
N = scipy.array([]),\
Rext = scipy.array([]),\
u = scipy.array([]), \
Z=0.0):
'''
Function to calculate daily Penman Monteith reference evaporation
(in mm/day). Source: R.G. Allen, L.S. Pereira, D. Raes and M. Smith
(1998). Crop evapotranspiration - Guidelines for computing crop
water requirements - FAO Irrigation and drainage paper 56. FAO -
Food and Agriculture Organization of the United Nations, Rome, 1998
Input (measured at 2 m height):
- airtemp: (array of) daily average air temperatures [Celsius]
- rh: (array of) daily average relative humidity values[%]
- airpress: (array of) daily average air pressure data [hPa]
- Rs: (array of) total incoming shortwave radiation [J/m2/day]
- N: daylength [h]
- Rext: Incoming shortwave radiation at the top of the atmosphere [J/m2/day]
- u: windspeed [m/s]
- Z: elevation [m], default is 0.0 m
Output:
- ET0pm: (array of) Penman Monteith reference evaporation (short grass with optimum water supply) values [mm]
Examples:--
>>> Eref_data = ET0pm(T,RH,press,Rs,N,Rext,u)
'''
# Set constants
albedo = 0.23 # short grass albedo
sigma = 4.903E-3 # Stefan Boltzmann constant J/m2/K4/d
# Calculate Delta, gamma and lambda
DELTA = meteolib.Delta_calc(airtemp) # [Pa/K]
gamma = meteolib.gamma_calc(airtemp,rh,airpress) # [Pa/K]
Lambda = meteolib.L_calc(airtemp) # [J/kg]
# Calculate saturated and actual water vapour pressures
es = meteolib.es_calc(airtemp) # [Pa]
ea = meteolib.ea_calc(airtemp,rh) # [Pa]
# Determine length of array
l = scipy.size(airtemp)
# Check if we have a single value or an array
if l < 2: # Dealing with single value...
Rns = (1.0-albedo)*Rs # Shortwave component [J/m2/d]
# Calculate clear sky radiation Rs0
Rs0 = (0.75+2E-5*Z)*Rext # Clear sky radiation [J/m2/d]
f = 1.35*Rs/Rs0-0.35
epsilom = 0.34-0.14*scipy.sqrt(ea/1000)
Rnl = f*epsilom*sigma*(airtemp+273.15)**4 # Longwave component [J/m2/d]
Rnet = Rns-Rnl # Net radiation [J/m2/d]
ET0pm = (DELTA/1000.*Rnet/Lambda+900./(airtemp+273.16)*u*(es-ea)/1000\
*gamma/1000)/(DELTA/1000.+gamma/1000*(1.+0.34*u))
else: # Dealing with an array
# Initiate output arrays
ET0pm = scipy.zeros(l)
Rns = scipy.zeros(l)
Rs0 = scipy.zeros(l)
f = scipy.zeros(l)
epsilom = scipy.zeros(l)
Rnl = scipy.zeros(l)
Rnet = scipy.zeros(l)
for i in range(0,l):
# calculate longwave radiation component Rln (J/m2/day)
Rns[i] = (1.0-albedo)*Rs[i] # Shortwave component [J/m2/d]
# Calculate clear sky radiation Rs0
Rs0[i] = (0.75+2E-5*Z)*Rext[i]
f[i] = 1.35*Rs[i]/Rs0[i]-0.35
epsilom[i] = 0.34-0.14*scipy.sqrt(ea[i]/1000)
Rnl[i] = f[i]*epsilom[i]*sigma*(airtemp[i]+273.15)**4 # Longwave component [J/m2/d]
Rnet[i] = Rns[i]-Rnl[i] # Net radiation [J/m2/d]
ET0pm[i] = (DELTA[i]/1000.*Rnet[i]/Lambda[i]+900./(airtemp[i]+273.16)* \
u[i]*(es[i]-ea[i])/1000*gamma[i]/1000)/ \
(DELTA[i]/1000.+gamma[i]/1000*(1.+0.34*u[i]))
return ET0pm # FAO reference evaporation [mm/day]
def E0(airtemp = scipy.array([]),\
rh = scipy.array([]),\
airpress = scipy.array([]),\
Rs = scipy.array([]),\
# N = scipy.array([]),\
Rext = scipy.array([]),\
u = scipy.array([]),\
Z=0.0):
'''
Function to calculate daily Penman open water evaporation (in mm/day).
Equation according to J.D. Valiantzas (2006). Simplified versions
for the Penman evaporation equation using routine weather data.
J. Hydrology 331: 690-702. Following Penman (1948,1956). Albedo set
at 0.06 for open water.
Input (measured at 2 m height):
- airtemp: (array of) daily average air temperatures [Celsius]
- rh: (array of) daily average relative humidity [%]
- airpress: (array of) daily average air pressure data [Pa]
- Rs: (array of) daily incoming solar radiation [J/m2/day]
- N: (array of) maximum daily sunshine hours [h]
- Rext: (array of) daily extraterrestrial radiation [J/m2/day]
- u: (array of) daily average wind speed at 2 m [m/s]
- Z: (array of) site elevation [m a.s.l.], default is zero...
Output:
- E0: (array of) Penman open water evaporation values [mm/day]
Examples:
>>> # T, RH, etc. are arrays of data...
>>> E0_data = E0(T,RH,press,Rs,N,Rext,u) # for zero elevation
>>> E0_data = E0(T,RH,press,Rs,N,Rext,u,1000.0) # at 1000 m a.s.l
>>> # With single values and default elevation...
>>> E0(20.67,67.0,101300.0,22600000,14.4,42000000,2.0)
6.3102099052283389
>>> # for elevation of 1.0 m a.s.l.
>>> E0(21.65,67.0,101300.0,24200000,14.66,42200000,1.51,1.0)
6.5991748573832343
>>>
'''
# Set constants
albedo = 0.06 # Open water albedo
sigma = 4.903E-3 # Stefan Boltzmann constant J/m2/K4/d
# Calculate Delta, gamma and lambda
DELTA = meteolib.Delta_calc(airtemp) # [Pa/K]
gamma = meteolib.gamma_calc(airtemp, rh, airpress) # [Pa/K]
Lambda = meteolib.L_calc(airtemp) # [J/kg]
# Calculate saturated and actual water vapour pressures
es = meteolib.es_calc(airtemp) # [Pa]
ea = meteolib.ea_calc(airtemp, rh) # [Pa]
# Determine length of array
l = scipy.size(airtemp)
# Check if we have a single value or an array
if l < 2: # Dealing with single value...
Rns = (1.0 - albedo) * Rs # Shortwave component [J/m2/d]
# Calculate clear sky radiation Rs0
Rs0 = (0.75 + 2E-5 * Z) * Rext
f = 1.35 * Rs / Rs0 - 0.35
epsilom = 0.34 - 0.14 * scipy.sqrt(ea / 1000)
Rnl = f * epsilom * sigma * (airtemp +
273.15)**4 # Longwave component [J/m2/d]
Rnet = Rns - Rnl # Net radiation [J/m2/d]
Ea = (1 + 0.536 * u) * (es / 1000. - ea / 1000.)
E0 = DELTA / (DELTA + gamma) * Rnet / Lambda + gamma / (
DELTA + gamma) * 6430000 * Ea / Lambda
else: # Dealing with an array
# Initiate output arrays
E0 = scipy.zeros(l)
Rns = scipy.zeros(l)
Rs0 = scipy.zeros(l)
f = scipy.zeros(l)
epsilom = scipy.zeros(l)
Rnl = scipy.zeros(l)
Rnet = scipy.zeros(l)
Ea = scipy.zeros(l)
for i in range(0, l):
# calculate longwave radiation component Rln (J/m2/day)
Rns[i] = (1.0 - albedo) * Rs[i] # Shortwave component [J/m2/d]
# Calculate clear sky radiation Rs0
Rs0[i] = (0.75 + 2E-5 * Z) * Rext[i]
f[i] = 1.35 * Rs[i] / Rs0[i] - 0.35
epsilom[i] = 0.34 - 0.14 * scipy.sqrt(ea[i] / 1000)
Rnl[i] = f[i] * epsilom[i] * sigma * (
airtemp[i] + 273.15)**4 # Longwave component [J/m2/d]
Rnet[i] = Rns[i] - Rnl[i] # Net radiation [J/m2/d]
Ea[i] = (1 + 0.536 * u[i]) * (es[i] / 1000 - ea[i] / 1000)
E0[i] = DELTA[i]/(DELTA[i]+gamma[i])*Rnet[i]/Lambda[i]+gamma[i]/(DELTA[i]+gamma[i])* \
6430000*Ea[i]/Lambda[i]
return E0
def ET0pm(airtemp = scipy.array([]),\
rh = scipy.array([]),\
airpress = scipy.array([]), \
Rs = scipy.array([]),\
N = scipy.array([]),\
Rext = scipy.array([]),\
u = scipy.array([]), \
Z=0.0):
'''
Function to calculate daily Penman Monteith reference evaporation
(in mm/day). Source: R.G. Allen, L.S. Pereira, D. Raes and M. Smith
(1998). Crop evapotranspiration - Guidelines for computing crop
water requirements - FAO Irrigation and drainage paper 56. FAO -
Food and Agriculture Organization of the United Nations, Rome, 1998
Input (measured at 2 m height):
- airtemp: (array of) daily average air temperatures [Celsius]
- rh: (array of) daily average relative humidity values[%]
- airpress: (array of) daily average air pressure data [hPa]
- Rs: (array of) total incoming shortwave radiation [J/m2/day]
- N: daylength [h]
- Rext: Incoming shortwave radiation at the top of the atmosphere [J/m2/day]
- u: windspeed [m/s]
- Z: elevation [m], default is 0.0 m
Output:
- ET0pm: (array of) Penman Monteith reference evaporation (short grass with optimum water supply) values [mm]
Examples:--
>>> Eref_data = ET0pm(T,RH,press,Rs,N,Rext,u)
'''
# Set constants
albedo = 0.23 # short grass albedo
sigma = 4.903E-3 # Stefan Boltzmann constant J/m2/K4/d
# Calculate Delta, gamma and lambda
DELTA = meteolib.Delta_calc(airtemp) # [Pa/K]
gamma = meteolib.gamma_calc(airtemp, rh, airpress) # [Pa/K]
Lambda = meteolib.L_calc(airtemp) # [J/kg]
# Calculate saturated and actual water vapour pressures
es = meteolib.es_calc(airtemp) # [Pa]
ea = meteolib.ea_calc(airtemp, rh) # [Pa]
# Determine length of array
l = scipy.size(airtemp)
# Check if we have a single value or an array
if l < 2: # Dealing with single value...
Rns = (1.0 - albedo) * Rs # Shortwave component [J/m2/d]
# Calculate clear sky radiation Rs0
Rs0 = (0.75 + 2E-5 * Z) * Rext # Clear sky radiation [J/m2/d]
f = 1.35 * Rs / Rs0 - 0.35
epsilom = 0.34 - 0.14 * scipy.sqrt(ea / 1000)
Rnl = f * epsilom * sigma * (airtemp +
273.15)**4 # Longwave component [J/m2/d]
Rnet = Rns - Rnl # Net radiation [J/m2/d]
ET0pm = (DELTA/1000.*Rnet/Lambda+900./(airtemp+273.16)*u*(es-ea)/1000\
*gamma/1000)/(DELTA/1000.+gamma/1000*(1.+0.34*u))
else: # Dealing with an array
# Initiate output arrays
ET0pm = scipy.zeros(l)
Rns = scipy.zeros(l)
Rs0 = scipy.zeros(l)
f = scipy.zeros(l)
epsilom = scipy.zeros(l)
Rnl = scipy.zeros(l)
Rnet = scipy.zeros(l)
for i in range(0, l):
# calculate longwave radiation component Rln (J/m2/day)
Rns[i] = (1.0 - albedo) * Rs[i] # Shortwave component [J/m2/d]
# Calculate clear sky radiation Rs0
Rs0[i] = (0.75 + 2E-5 * Z) * Rext[i]
f[i] = 1.35 * Rs[i] / Rs0[i] - 0.35
epsilom[i] = 0.34 - 0.14 * scipy.sqrt(ea[i] / 1000)
Rnl[i] = f[i] * epsilom[i] * sigma * (
airtemp[i] + 273.15)**4 # Longwave component [J/m2/d]
Rnet[i] = Rns[i] - Rnl[i] # Net radiation [J/m2/d]
ET0pm[i] = (DELTA[i]/1000.*Rnet[i]/Lambda[i]+900./(airtemp[i]+273.16)* \
u[i]*(es[i]-ea[i])/1000*gamma[i]/1000)/ \
(DELTA[i]/1000.+gamma[i]/1000*(1.+0.34*u[i]))
return ET0pm # FAO reference evaporation [mm/day]
def Epm(airtemp = scipy.array([]),\
rh = scipy.array([]),\
airpress = scipy.array([]),\
Rn = scipy.array([]),\
G = scipy.array([]),\
ra = scipy.array([]),\
rs = scipy.array([])):
'''
Function to calculate the Penman Monteith evaporation.
.. math::
E_{pm} = \\frac{\\Delta \\cdot (R_n-G)+\\rho \\cdot c_p \\cdot (e_s-e_a)/r_a}{\\lambda \\cdot (\\Delta + \\gamma \\cdot (1+\\frac{r_s}{r_a}))}
The function can be used with different time intervals, such as commonly
used hourly or daily time intervals are used. When a plant canopy is wet,
the surface resistance (rs) becomes zero (stomatal resistance irrelevant,
as evaporation is directly from wet leaf surface). Function ra() in this
module can be used to calculate the aerodynamic resistance (ra) from wind
speed and height parameters.
Parameters:
- airtemp: (array of) daily average air temperatures [Celsius].
- rh: (array of) daily average relative humidity values [%].
- airpress: (array of) daily average air pressure data [hPa].
- Rn: (array of) net radiation input over time interval t [J t-1].
- G: (array of) soil heat flux input over time interval t [J t-1].
- ra: aerodynamic resistance [s m-1].
- rs: surface resistance [s m-1].
Returns:
- Epm: (array of) Penman Monteith evaporation values [mm t-1].
References
----------
J.L. Monteith (1965). Evaporation and environment. Symp. Soc. Exp. Biol.
19: 205-224.
Examples
--------
>>> Epm(21.67,67.0,1013.0,14100000.,500000.,104.,70.)
3.243341146049407
'''
# Test input array/value
airtemp,rh,airpress,Rn,G,ra,rs = meteolib._arraytest(airtemp,rh,airpress,Rn,G,ra,rs)
# Calculate Delta, gamma and lambda
DELTA = meteolib.Delta_calc(airtemp)/100. # [hPa/K]
airpress=airpress*100. # [Pa]
gamma = meteolib.gamma_calc(airtemp,rh,airpress)/100. # [hPa/K]
Lambda = meteolib.L_calc(airtemp) # [J/kg]
rho = meteolib.rho_calc(airtemp,rh,airpress) # [kg m-3]
cp = meteolib.cp_calc(airtemp,rh,airpress) # [J kg-1 K-1]
# Calculate saturated and actual water vapour pressures
es = meteolib.es_calc(airtemp)/100. # [hPa]
ea = meteolib.ea_calc(airtemp,rh)/100. # [hPa]
# Calculate Epm
Epm = ((DELTA*(Rn-G)+rho*cp*(es-ea)/ra)/(DELTA+gamma*(1.+rs/ra)))/Lambda
return Epm # actual ET in mm
def ET0pm(airtemp = scipy.array([]),\
rh = scipy.array([]),\
airpress = scipy.array([]), \
Rs = scipy.array([]),\
Rext = scipy.array([]),\
u = scipy.array([]), \
Z=0.0):
'''
Function to calculate daily Penman Monteith reference evaporation estimates.
Parameters:
- airtemp: (array of) daily average air temperatures [Celsius].
- rh: (array of) daily average relative humidity values [%].
- airpress: (array of) daily average air pressure data [hPa].
- Rs: (array of) total incoming shortwave radiation [J m-2 day-1].
- Rext: Incoming shortwave radiation at the top of the atmosphere\
[J m-2 day-1].
- u: windspeed [m s-1].
- Z: elevation [m], default is 0 m a.s.l.
Returns:
- ET0pm: (array of) Penman Monteith reference evaporation (short\
grass with optimum water supply) values [mm day-1].
Notes
-----
Meteorological measuements standard at 2 m above soil surface.
References
----------
R.G. Allen, L.S. Pereira, D. Raes and M. Smith (1998). Crop
evapotranspiration - Guidelines for computing crop water requirements -
FAO Irrigation and drainage paper 56. FAO - Food and Agriculture
Organization of the United Nations, Rome, 1998.
(http://www.fao.org/docrep/x0490e/x0490e07.htm)
Examples
--------
>>> ET0pm(20.67,67.0,101300.0,22600000.,42000000.,3.2)
4.7235349721073039
'''
# Test input array/value
airtemp,rh,airpress,Rs,Rext,u = meteolib._arraytest(airtemp,rh,airpress,Rs,Rext,u)
# Set constants
albedo = 0.23 # short grass albedo
sigma = 4.903E-3 # Stefan Boltzmann constant J/m2/K4/d
# Calculate Delta, gamma and lambda
DELTA = meteolib.Delta_calc(airtemp) # [Pa/K]
gamma = meteolib.gamma_calc(airtemp,rh,airpress) # [Pa/K]
Lambda = meteolib.L_calc(airtemp) # [J/kg]
# Calculate saturated and actual water vapour pressures
es = meteolib.es_calc(airtemp) # [Pa]
ea = meteolib.ea_calc(airtemp,rh) # [Pa]
Rns = (1.0-albedo)*Rs # Shortwave component [J/m2/d]
# Calculate clear sky radiation Rs0
Rs0 = (0.75+2E-5*Z)*Rext # Clear sky radiation [J/m2/d]
f = 1.35*Rs/Rs0-0.35
epsilom = 0.34-0.14*scipy.sqrt(ea/1000)
Rnl = f*epsilom*sigma*(airtemp+273.15)**4 # Longwave component [J/m2/d]
Rnet = Rns-Rnl # Net radiation [J/m2/d]
ET0pm = (DELTA/1000.*Rnet/Lambda+900./(airtemp+273.16)*u*(es-ea)/1000\
*gamma/1000)/(DELTA/1000.+gamma/1000*(1.+0.34*u))
return ET0pm # FAO reference evaporation [mm/day]
def E0(airtemp = scipy.array([]),\
rh = scipy.array([]),\
airpress = scipy.array([]),\
Rs = scipy.array([]),\
Rext = scipy.array([]),\
u = scipy.array([]),\
alpha = 0.08,\
Z = 0.0):
'''
Function to calculate daily Penman (open) water evaporation estimates:
.. math::
E_0 = \\frac{R_n \\cdot \\Delta}{\\lambda \cdot (\\Delta + \\gamma)} + \\frac{6430000 \\cdot E_a \\cdot \\gamma}{\\lambda \\cdot (\\Delta+\\gamma)}
Parameters:
- airtemp: (array of) daily average air temperatures [Celsius].
- rh: (array of) daily average relative humidity [%].
- airpress: (array of) daily average air pressure data [Pa].
- Rs: (array of) daily incoming solar radiation [J m-2 day-1].
- Rext: (array of) daily extraterrestrial radiation [J m-2 day-1].
- u: (array of) daily average wind speed at 2 m [m s-1].
- alpha: albedo [-] set at 0.08 for open water by default.
- Z: (array of) site elevation, default is 0 m a.s.l.
Returns:
- E0: (array of) Penman open water evaporation values [mm day-1].
Notes
-----
Meteorological parameters measured at 2 m above the surface. Albedo
alpha set by default at 0.08 for open water (Valiantzas, 2006).
References
----------
- H.L. Penman (1948). Natural evaporation from open water, bare soil\
and grass. Proceedings of the Royal Society of London. Series A.\
Mathematical and Physical Sciences 193: 120-145.
- H.L. Penman (1956). Evaporation: An introductory survey. Netherlands\
Journal of Agricultural Science 4: 9-29.
- J.D. Valiantzas (2006). Simplified versions for the Penman\
evaporation equation using routine weather data. J. Hydrology 331:\
690-702.
Examples
--------
>>> # With single values and default albedo/elevation
>>> E0(20.67,67.0,101300.0,22600000.,42000000.,3.2)
6.6029208786994467
>>> # With albedo is 0.18 instead of default and default elevation
>>> E0(20.67,67.0,101300.0,22600000.,42000000.,3.2,alpha=0.18)
5.9664248091431968
>>> # With standard albedo and Z= 250.0 m
>>> E0(20.67,67.0,101300.0,22600000.,42000000.,3.2,Z=250.0)
6.6135588207586284
>>> # With albedo alpha = 0.18 and elevation Z = 1000 m a.s.l.
>>> E0(20.67,67.0,101300.0,22600000.,42000000.,3.2,0.18,1000.)
6.00814764682986
'''
# Test input array/value
airtemp,rh,airpress,Rs,Rext,u = meteolib._arraytest(airtemp,rh,airpress,Rs,Rext,u)
# Set constants
sigma = 4.903E-3 # Stefan Boltzmann constant J/m2/K4/d
# Calculate Delta, gamma and lambda
DELTA = meteolib.Delta_calc(airtemp) # [Pa/K]
gamma = meteolib.gamma_calc(airtemp,rh,airpress) # [Pa/K]
Lambda = meteolib.L_calc(airtemp) # [J/kg]
# Calculate saturated and actual water vapour pressures
es = meteolib.es_calc(airtemp) # [Pa]
ea = meteolib.ea_calc(airtemp,rh) # [Pa]
# calculate radiation components (J/m2/day)
Rns = (1.0-alpha)*Rs # Shortwave component [J/m2/d]
Rs0 = (0.75+2E-5*Z)*Rext # Calculate clear sky radiation Rs0
f = 1.35*Rs/Rs0-0.35
epsilom = 0.34-0.14*scipy.sqrt(ea/1000)
Rnl = f*epsilom*sigma*(airtemp+273.15)**4 # Longwave component [J/m2/d]
Rnet = Rns-Rnl # Net radiation [J/m2/d]
Ea = (1+0.536*u)*(es/1000-ea/1000)
E0 = (DELTA/(DELTA+gamma)*Rnet/Lambda+gamma/(DELTA+gamma)*
6430000*Ea/Lambda)
return E0
