5.13.2-dev0
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mHM
The mesoscale Hydrological Model
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mHM
The mesoscale Hydrological Model
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Module for calculating reference/potential evapotranspiration [mm d-1]. More...
Functions/Subroutines | |
| elemental pure real(dp) function, public | pet_hargreaves (harsamcoeff, harsamconst, tavg, tmax, tmin, latitude, doy) |
| Reference Evapotranspiration after Hargreaves. | |
| elemental pure real(dp) function, public | pet_priestly (prietayparam, rn, tavg) |
| Reference Evapotranspiration after Priestly-Taylor. | |
| elemental pure real(dp) function, public | pet_penman (net_rad, tavg, act_vap_pressure, aerodyn_resistance, bulksurface_resistance, a_s, a_sh) |
| Reference Evapotranspiration after Penman-Monteith. | |
| elemental pure real(dp) function, public | extraterr_rad_approx (doy, latitude) |
| Approximation of extraterrestrial radiation. | |
| elemental pure real(dp) function, public | slope_satpressure (tavg) |
| slope of saturation vapour pressure curve | |
| elemental pure real(dp) function, public | sat_vap_pressure (tavg) |
| calculation of the saturation vapour pressure | |
Module for calculating reference/potential evapotranspiration [mm d-1].
This module calculates PET [mm/d] based on one of the methods
COPYING and COPYING.LESSER provided with this software. The complete GNU license text can also be found at http://www.gnu.org/licenses/. | elemental pure real(dp) function, public mo_pet::extraterr_rad_approx | ( | integer(i4), intent(in) | doy, |
| real(dp), intent(in) | latitude | ||
| ) |
Approximation of extraterrestrial radiation.
Approximation of extraterrestrial radiation at the top of the atmosphere \( R_a \) after Duffie and Beckman (1980). \( R_a \) is converted from \( [J\;m^{-2}\;d^{-1}] \) in \( [mm\;d^{-1}]\) .
\[ R_a = \frac{86400}{ \pi \cdot \lambda} \cdot E_0 \cdot d_r \cdot (\omega \cdot \sin(latitude) \cdot \sin(\delta) + \cos(latitude) \cdot \cos(\delta) \cdot \sin(\omega) \]
where \( E_0=1367\;J\;m^{-2}\;s^{-1} \) is the solar constant and It is dependent on the following sub equations: The relative distance Earth-Sun:
\[ d_r = 1 + 0.033 \cdot \cos \left( \frac{2 \cdot \pi \cdot doy}{365} \right) \]
in which doy is the day of the year. The solar declination [radians] defined by
\[ \delta = 0.4093 \cdot \sin\left( \frac{2 \cdot \pi \cdot doy}{365} - 1.405 \right) \]
The sunset hour angle [radians]:
\[ \omega = \arccos( - \tan(latitude) * \tan(\delta) ) \]
< \( \lambda = 2.45 \cdot 10^6\;J\;m^{-2}\;mm^{-1} \) is the latent heat of vaporization.
| [in] | integer(i4) :: doy | day of year [-] |
| [in] | real(dp) :: latitude | latitude [rad] |
Definition at line 314 of file mo_pet.f90.
References mo_mhm_constants::duffiedelta1, mo_mhm_constants::duffiedelta2, mo_mhm_constants::duffiedr, and extraterr_rad_approx().
Referenced by extraterr_rad_approx(), and pet_hargreaves().
| elemental pure real(dp) function, public mo_pet::pet_hargreaves | ( | real(dp), intent(in) | harsamcoeff, |
| real(dp), intent(in) | harsamconst, | ||
| real(dp), intent(in) | tavg, | ||
| real(dp), intent(in) | tmax, | ||
| real(dp), intent(in) | tmin, | ||
| real(dp), intent(in) | latitude, | ||
| integer(i4), intent(in) | doy | ||
| ) |
Reference Evapotranspiration after Hargreaves.
Calculates the Reference Evapotranspiration \( [mm\;d^{-1}] \) based on the Hargreaves-Samani (1982) model for a given cell by applying the equation
\[ PET = HarSamCoeff * R_a * (T_{avg} + HarSamConst) * \sqrt{ T_{max} - T_{min}} \]
where \( R_a\;[W\;m^{-2}]\) is the incoming solar radiation and \( T_{avg}, T_{max} \) and \( T_{min}\) \( [ ^{\circ}C]\) are the mean, maximum, and minimum daily temperatures at the given day, respectively.
| [in] | real(dp) :: HarSamCoeff | coefficient of Hargreaves-Samani equation [-] |
| [in] | real(dp) :: HarSamConst | constant of Hargreaves-Samani equation [-] |
| [in] | real(dp) :: tavg | daily men temperature \([^{\circ}C]\) |
| [in] | real(dp) :: tmax | daily maximum of temp \([^{\circ}C]\) |
| [in] | real(dp) :: tmin | daily minimum of temp \([^{\circ}C]\) |
| [in] | real(dp) :: latitude | latitude of the cell for Ra estimation \([radians]\) |
| [in] | integer(i4) :: doy | day of year for Ra estimation |
Definition at line 73 of file mo_pet.f90.
References extraterr_rad_approx(), and pet_hargreaves().
Referenced by mo_meteo_handler::get_corrected_pet(), and pet_hargreaves().
| elemental pure real(dp) function, public mo_pet::pet_penman | ( | real(dp), intent(in) | net_rad, |
| real(dp), intent(in) | tavg, | ||
| real(dp), intent(in) | act_vap_pressure, | ||
| real(dp), intent(in) | aerodyn_resistance, | ||
| real(dp), intent(in) | bulksurface_resistance, | ||
| real(dp), intent(in) | a_s, | ||
| real(dp), intent(in) | a_sh | ||
| ) |
Reference Evapotranspiration after Penman-Monteith.
Calculates the reference evapotranspiration \( [mm\;d^{-1}] \) based on the Penman-Monteith model for every given cell by applying the equation
\[ PET = \frac{1}{\lambda} \cdot \frac{\Delta \cdot R_n + \rho \cdot c_p \cdot (e_s-e) \cdot \frac{a_sh}{r_a}} {\Delta + \gamma \cdot \frac{a_sh}{a_s} \cdot \left( 1 + \frac{r_s}{r_a} \right) } \]
where \(R_n\;[W\;m^{-2}]\) is the net solar radiation, \(\Delta\;[kPa\;K^{-1}]\) is the slope of the saturation-vapour pressure curve, \( \lambda\;[MJ\;kg^{-1}] \) is the latent heat of vaporization, \( (e_s-e)\;[kPa] \) is the vapour pressure deficit of the air, \( \rho\;[kg\;m^{-3}] \) is the mean atmospheric density, \( c_p=1005.0\;J\;kg^{-1}\;K^{-1} \) is the specific heat of the air, \( \gamma [kPa\;K^{-1}] \) is the psychrometric constant, \( r_s [s m^{-1}] \) is the bulk canopy resistance, \( r_a [s m^{-1}] \) is the aerodynamic resistance, \( a_s [1] \) is the fraction of one-sided leaf area covered by stomata (1 if stomata are on one side only, 2 if they are on both sides) and \( a_{sh} [-] \) is the fraction of projected area exchanging sensible heat with the air (2) Implementation refers to the so-called Penman-Montheith equation for transpiration. Adjusting the arguments \( a_{sh} \) and \( a_s \) we obtain the corrected MU equation (for details see Schymanski and Or, 2017). If \( a_{sh} = 1 = a_s \) Penman-Montheith equation for transpiration is preserved. For reproducing characteristics of symmetrical amphistomatous leaves use \( a_{sh} = 2 = a_s \), in which case the classic PM equation is only missing a factor of 2 in the nominator, as pointed out by Jarvis and McNaughton (1986, Eq. A9). These analytical solutions eliminated the non-linearity problem of the saturation vapour pressure curve, but they do not consider the dependency of the long-wave component of the soil surface or leaf energy balance ( \( R_l \)) on soil or leaf temperature ( \( T_l \)). We assume that net radiation equals the absorbed short-wave radiation, i.e. \( R_N = R_s \) (p.79 in Monteith and Unsworth, 2013).
| [in] | real(dp) :: net_rad | net radiation \([W m^{-2}]\) |
| [in] | real(dp) :: tavg | average daily temperature \([^{\circ}C]\) |
| [in] | real(dp) :: act_vap_pressure | actual vapur pressure \([kPa]\) |
| [in] | real(dp) :: aerodyn_resistance | aerodynmaical resistance \(s\;m^{-1}\) |
| [in] | real(dp) :: bulksurface_resistance | bulk surface resistance \(s\;m^{-1}\) |
| [in] | real(dp) :: a_s | fraction of one-sided leaf area covered by stomata \(1\) |
| [in] | real(dp) :: a_sh | fraction of projected area exchanging sensible heat with the air \(1\) |
Definition at line 235 of file mo_pet.f90.
References pet_penman(), sat_vap_pressure(), and slope_satpressure().
Referenced by mo_meteo_handler::get_corrected_pet(), and pet_penman().
| elemental pure real(dp) function, public mo_pet::pet_priestly | ( | real(dp), intent(in) | prietayparam, |
| real(dp), intent(in) | rn, | ||
| real(dp), intent(in) | tavg | ||
| ) |
Reference Evapotranspiration after Priestly-Taylor.
Calculates the Reference Evapotranspiration \( [mm\;d^{-1}] \) based on the Priestly-Taylor (1972) model for every given cell by applying the equation
\[ PET = \alpha * \frac{\Delta}{(\gamma + \Delta)} * R_n \]
where \(R_n\;[W\;m^{-2}]\) is the net solar radiation \(\Delta = f(T_{avg})\) is the slope of the saturation-vapour pressure curve and \(\alpha\) is a emperical coefficient.
| [in] | real(dp) :: PrieTayParam | Priestley-Taylor coefficient \( \alpha [-] \) |
| [in] | real(dp) :: Rn | net solar radiation \( [W\;m^{-2}] \) |
| [in] | real(dp) :: Tavg |
Definition at line 149 of file mo_pet.f90.
References pet_priestly(), and slope_satpressure().
Referenced by mo_meteo_handler::get_corrected_pet(), and pet_priestly().
| elemental pure real(dp) function, public mo_pet::sat_vap_pressure | ( | real(dp), intent(in) | tavg | ) |
calculation of the saturation vapour pressure
Calculation of the saturation vapour pressure
\[ e_s(T_a) = 0.6108 \cdot \exp \left( \frac{17.27 \cdot T_a}{T_a + 237.3} \right) \]
| [in] | real(dp) :: tavg | temperature [degC] |
Definition at line 426 of file mo_pet.f90.
References sat_vap_pressure(), mo_mhm_constants::tetens_c1, mo_mhm_constants::tetens_c2, and mo_mhm_constants::tetens_c3.
Referenced by pet_penman(), sat_vap_pressure(), and slope_satpressure().
| elemental pure real(dp) function, public mo_pet::slope_satpressure | ( | real(dp), intent(in) | tavg | ) |
slope of saturation vapour pressure curve
slope of saturation vapour pressure curve after Tetens
\[ \Delta = \frac{0.6108 * e_s(T_a)}{e^(2 \cdot \log(T_a + 237.3))} \]
| [in] | real(dp) :: tavg | average daily temperature \([^{\circ}C]\) |
Definition at line 384 of file mo_pet.f90.
References sat_vap_pressure(), mo_mhm_constants::satpressureslope1, slope_satpressure(), and mo_mhm_constants::tetens_c3.
Referenced by mo_mrm_riv_temp_class::get_lat_heat(), pet_penman(), pet_priestly(), and slope_satpressure().
1.9.7