SecondBEST is a simplified implementation of the Bare Essentials for Surface Transfer (BEST) land surface model. The main simplifications are that SecondBEST does not incorporate the effects of vegetation, which reduces a lot of calculations within BEST. We also assume each grid cell is either fully bare soil or snow/ice, i.e, there are no fractional land types. The implementation here follows the description in Pitman et al.
This notebook is a ready reference to the equations used in SecondBEST so that interested users don't have to read the above reference if they don't wish to. However, if you plan on making heavy use of SecondBEST, you are encouraged to do so!
Surface types:
Spectral regions, phases of water
Water content
Certain soil properties are calculated initially based on the soil and area types.
Currently, SecondBEST recognises two soil types: clay and sand.
claysandclaysandland_iceland_ice.The albedo calculation is described in section 5.0 of Pitman et al. SecondBEST calculates albedo in the near-infraread and shortwave separately. This is also quite convenient since RRTMG, the radiative transfer code also uses two separate albedos.
The albedo for bare soil is calculated as (Eqns. 5.5, 5.6): $$\alpha_{SW,u} = 0.10 + 0.1clr + 0.06(1-W_{L,u})\\ \alpha_{LW,u} = 2\alpha_{SW,u}$$
where $clr$ is the soil colour defined above.
$W_{L,u}$ is the soil wetness factor, and is defined as the ratio of the liquid soil water content in the upper soil layer to its porosity.
$$W_{L,u} = X_{w,u}/X_v$$The albedo of Land Ice is calculated as (Eqns. 5.7, 5.8): $$\alpha_{SW,u} = 0.60 + 0.06(1-W_{L,u}) \\ \alpha_{LW,u} = \frac{1}{3}\alpha_{SW,u}$$
SecondBEST calculates the drag parameters as in section 6 of Pitman et al.
where $z_m$ is the hydrostatic mid-level height of the lowest atmosphere level and $\kappa$ is the von Karman constant.
Where $U_m$ is the magnitude of the wind speed at the lowest model level and the other notation is as before. $U_m$ has a minimum value that can be set during initialisation of SecondBEST.
A negative Richardson number indicates unstable conditions.
where $\epsilon$ is 0.01 for land and 1.0 for oceans.
The equations are from Section 8. in Pitman et al.
is given by the relatively well known bulk aerodynamic formula.
$$SHF = \rho_s C_{pd} U_m C_{Dh} (T_u - T_s)$$is also given by the bulk formula
$$LHF = L_v\rho_s U_m C_{Dh} \beta_u(q^*_u - q_s) $$where $q^*_u$ is the saturation specific humidity at the soil surface. A "wetness factor", $\beta_u$, is also required, defined as
$$\beta_u = \left \{ \begin{array}{1} 1,\ snow\\ \frac{W_{F,u}L_v}{L_i} + \frac{E_{usmax}}{E_{usP}},\ soil\end{array} \right .$$$L_v$ is the latent heat of vapourisation, $L_i$ is the latent heat of sublimation, $W_{F,u}$ is the frozen soil moisture in the upper soil layer. The first term containing these terms represents the rate at which frozen soil can sublimate.
$E_{usP}$ is the potential evaporation rate at the soil surface,
$$E_{usP} = \rho_s c_u (q^*_u - q_s)$$where $c_u$ is the soil conductance, defined as (Eq. 7.22)
$$c_u = C_{Dh}U_m.$$$E_{usmax}$ is the exfiltration rate given by
$$E_{usmax} = K_{HD}\Theta_u^{0.5B + 2} - K_{H0}\Theta_u^{2B + 3}$$Where
$$B = \left \{ \begin{array} 10,\ clay\\ 4,\ sand\end{array} \right .$$$$K_{H0} = \left \{ \begin{array} 0.001,\ clay\\ 0.1,\ sand \end{array} \right .$$and $$K_{HD} = \left ( \frac{-4K_{H0}B\Psi_0\rho_wX_v(1 - W_{F,u})}{\pi\Delta t}\right )$$
where
$\Theta_u$ is defined as
$$\Theta_u = \frac{W_{L,u} - 0.01}{1 - W_{F,u}}$$The wetness factors $W_{L,x}$ in the soil in the upper and lower layers is NOT allowed to fall below 0.01 due to physical and numerical issues.
are directly calculated from the momentum bulk coefficient $$U_s = -\rho_s C_{Dm}U_mu$$