Evapotranspiration calculated from flux tower data

[Benjamin-Maglio]

A couple of functions based on Penman-Monteith calculation for evapotranspiration from flux tower data. There are other methods depending on what data is available at the site. This method is adapted from [Allen, R. G., Pereira, L. S., Raes, D., & Smith, M. (1998). Crop evapotranspiration - Guidelines for computing crop water requirements. FAO Irrigation and drainage Paper 56.].

Latent heat (LE) and Air temperature (TA) are fed as arrays from the flux data.
month_days is a list created from the AmeriFlux (AF) timestamps to account for the number of days in each month, though this may be approximated.

Much of this may need to be adapted depending on the formatting of the monthly flux data.

month_days = []
for i in range(0, len(AF['TIMESTAMP'].values)):   
    tmp = str(AF['TIMESTAMP'].values[i])
    month_days.append(monthrange(int(tmp[0:4]), int(tmp[4:]))[1])


def evapotrans(LE, TA, month_days):
    '''
    Returns: ET (Evapotranspiration) [kgm^-2s-^1] --> [mm / month/ m2]
    ____________________________________________
    
    Inputs: LE (Latent heat flux) [W/m^2]
            TA (Air temperature)  [degC]
            month_days
            
            gamma (Latent heat of evaporation) [J/kg]
            rho (density of water) [kg/m^3]
            
    [Allen, R. G., Pereira, L. S., Raes, D., & Smith, M. (1998). 
    Crop evapotranspiration - Guidelines for computing crop water requirements. 
    FAO Irrigation and drainage Paper 56.]
    
    ''' 
    # latent heat of evaporation with temperature effects - [MJ / kg]
    gamma = 2.257 - (2.361e-3) * TA  
    
    # density of water [kg/m3]
    rho = 997
    
    # Converting LE [W/m2] --> [J / month / m^2]
    LE = LE * (np.asarray(month_days) * 86400)
    
    # Calculating ET [kg / month / m^2]
    ET_kg = LE / gamma
    
    # Converting ET [kg / month / m2] --> [m / month] 
    ET_m = (ET_kg / rho)
    
    # Converting ET [m / month] --> [mm / month]
    ET_mm = ET_m * 1e3
    
    # Converting ET [mm / month] --> [mm / m2 / month]
    ET = ET_mm / 1e6
    
    return ET

def pot_evapotrans(RS, TA, RPOT, VPD, month_days):
    '''
    Returns: Potential evapotranspiration [mm / month]
    ________________________________________
    
    Inputs: RS (incoming solar radiation) [MJ m2 / month] - SW_IN
            TA (air temperature) [degC]
            RPOT (potential i.e. extraterrestrial solar radiation) [MJ m2 / month] - SW_POT
            VPD (Vapor pressure deficit) [hPa]
    https://emf-creaf.github.io/meteolandbook/potentialevapotranspiration.html - Penman-Monteith
    https://www.sciencedirect.com/science/article/pii/S002216940600326X - Valiantzas
    '''
   
    # Converting radiation values into MJ / day / m2
    RS = 1e-6 * RS * (86400 * np.asarray(month_days)) 
    RPOT = 1e-6 * RPOT * (86400 * np.asarray(month_days)) 
    
    
    es = 6.11 * 10**((7.5*TA)/(273.3 + TA))#saturated vapor pressure [hPa] 
    RH = (VPD / es) * 100 # https://www.weather.gov/media/epz/wxcalc/vaporPressure.pdf
    
    PET = 0.047 * RS * (TA + 9.5)**(1/2) - 2.4 * (RS/RPOT)**2 + 0.09 * (TA - 20) * (1 - RH * 0.01)
        
    return PET