Sensible Heat using Monin-Obukhov length — sensible

Calculates the sensible heat flux using the Monin-Obukhov length. Positive flux signifies flux away from the surface, negative values signify flux towards the surface. Monin-Obukhov outputs are diagnostic profile/stability estimates and are not expected to close $R_n - G$.

Usage

sensible_monin(...)

# Default S3 method
sensible_monin(
  t1,
  t2,
  z1 = 2,
  z2 = 10,
  v1,
  v2,
  elev,
  cap = NULL,
  surface_type = NULL,
  obs_height = NULL,
  ...
)

# S3 method for class 'weather_station'
sensible_monin(weather_station, cap = NULL, ...)

Arguments

...: Additional arguments.
t1: Air temperature at lower height in °C.
t2: Air temperature at upper height in °C.
z1: Lower height of measurement in m.
z2: Upper height of measurement in m (Use highest point of measurement as values are less disturbed).
v1: Windspeed at lower height (e.g. height of anemometer) in m/s.
v2: Windspeed at upper height in m/s.
elev: Elevation above sea level in m.
cap: The maximum absolute value for the stability parameter $s_1$. Default is NULL.
surface_type: Type of surface. Options: r surface_properties$surface_type
obs_height: Height of obstacle in meters (m).
weather_station: Object of class weather_station

Value

Sensible heat flux in W/m².

Details

The sensible heat flux ($Q_h$) using the Monin-Obukhov method is calculated as: $$Q_h = - \rho \cdot c_p \cdot \frac{k \cdot u_* \cdot z_2}{\phi_h} \cdot \frac{\Delta \theta}{\Delta z}$$ where: $\rho$ is the air density, $c_p$ is the specific heat capacity of air, $k$ is the von Kármán constant, $u_*$ is the friction velocity, $\phi_h$ is the stability correction function for heat, $\Delta \theta$ is the potential temperature gradient, and $\Delta z$ is the height difference between measurements.

The stability correction function for heat ($\phi_h$) is calculated using the gradient Richardson number ($Ri_g$) and the stability parameter ($s_1$). The stability parameter is the ratio of the higher measurement height and the Monin-Obukhov length. With Monin-Obukhov length values close to zero, the ratio can result in very high values, which is why the stability parameter ($s_1$) can be capped. The implemented potential-temperature gradient uses the measurement-height difference $z_2 - z_1$. Invalid heights, invalid wind speeds, and invalid numerical profile states are guarded elementwise and return NA with a warning. Zero potential-temperature gradient returns zero sensible heat flux. The default cap is set to NULL. These flux-gradient and Businger-type stability terms use Foken/Bendix method background.

References

Bendix 2004, p. 77, eq. 4.6,

Foken 2016, p. 362: Businger

Examples

# Calculate sensible heat flux using the Monin-Obukhov method
sensible_monin(t1 = 20, t2 = 15, z1 = 2, z2 = 10, v1 = 3, v2 = 5, elev = 100, surface_type = "lawn")
#> Warning: There are values above 600 W/m^2!
#> [1] 7215.479