comp_friction_vel Subroutine

public subroutine comp_friction_vel(friction_vel, iter, mp, CVONK, CUMIN, CPI_C, zetar, zref_uv, zref_tq, z0m, ua)

Purpose

This SUBROUTINE evaluates the value of the friction velocity $u_*$ as used during the iteration loop of the Monin-Obukhov (MO) similarity theory in define_canopy. $u_*$ is used when quantifying the stability parameter canopy%zetar in update_zetar, and when evaluating the resistance network components rt0 and rt1 in define_canopy. The friction velocity quantifies the magnitude of turbulent mixing that is occurring as well as the flux of momentum from the atmosphere to the land.

The output friction_vel is known as canopy%us elsewhere in the code.

Method

The basic formula is derived from the modified log-law for the vertical profile of wind speed near to the ground namely

$u_{*} = U(z_{ref}) / ( \log [z_{ref}/z_{0m}] - \psi_m[\xi * z_{ref}/z_{refTq}] + \psi_m[\xi * z_{0m}/z_{refTq}] )$

with $\psi_m$ the integrated similarity function given by psim, $U$ the wind speed at height $z_{ref}$, $\xi$ the current value of the stability parameter, and $z_{0m}$ the roughness length.
A minimum value is applied to the input wind speed, ua= $U(z_{ref})$, to assist with convergence of the MO iteration in light wind conditions. Small and large value limits are applied to the evaluated $u_*$.

NOTE Most literature references assume that the reference levels for wind and temperature are equal inside the arguments to the stability functions $\psi_m$ and $\psi_s$ - in CABLE this need not be true. $\xi$ is always defined relative to the reference level for temperature, in $\psi_m$ the reference height for wind is needed. Consequently the calls to psim include conversion factors to account for the different reference levels. zref_uv and zref_tq passed to comp_friction_vel are the heights above the displacement height rough%disp.

References

Kowalczyk et al. (2006) - section 3.1, equations 1-9.

Arguments

Type	Intent	Optional	Attributes		Name
real,	intent(out)			::	friction_vel(mp)	friction velocity (ms$^{-1}$)
integer,	intent(in)			::	iter	MO iteration counter (-)
integer,	intent(in)			::	mp	size of cable vector of land points (-)
real,	intent(in)			::	CVONK	von Karman constant (-)
real,	intent(in)			::	CUMIN	minimum value of wind speed (ms$^{-1}$)
real,	intent(in)			::	CPI_C	$\pi$ (-)
real,	intent(in)			::	zetar(mp,iter)	stability parameter - see update_zetar canopy%zetar (-)
real,	intent(in)			::	zref_uv(mp)	reference height for wind rough%zref_uv (m)
real,	intent(in)			::	zref_tq(mp)	reference height for temperature and humidity rough%zref_tq (m)
real,	intent(in)			::	z0m(mp)	roughness length rough%z0m (m)
real,	intent(in)			::	ua(mp)	wind speed met%ua (ms$^{-1}$)