FLUXES AT INTERFACES

• Thus far, we've discussed the importance of mean and eddy fluxes for transporting heat, moisture, and momentum through the boundary layer.
• We also just finished a discussion of surface forcing mechanisms, noting the heat and radiation budgets at the earth's surface.
• These forcing mechanisms create fluxes of heat, moisture and momentum from the ground to the air directly above it.
• For example, (u'w')_s  represents the vertical flux of horizontal momentum at the earth's surface
• Likewise, (q'w')_s represents the vertical heat flux at the earth's surface.
• Remember, these fluxes represent the combined effects of molecular and turbulent transport (see section 5).
• Q:  how does a numerical weather model compute the above two quantities, or others similar to them????????????????????????

• These quantities need to be approximated (parameterized) since they can not be explicitly calculated by the current NWP or research models.

How is this done you ask???  Let's discuss fluxes at interfaces.

Fluxes at Interfaces

The vertical flux (F_z), of any variable z, is assumed to be driven by the difference in z across the interface.  Thus: 

F_z = -U_T (z_top - z_bottom)    (1)

where U_T represents a transport velocity across the interface, while z_top and  z_bottom are the values just above and below the boundary.

Hence, we can write the following equations for the surface fluxes of momentum, heat, and moisture.

(u'w')_s = -C_D M (U_air - U_ground) = -C_D M (U_air)    (1)

(v'w')_s = -C_D M (V_air - V_ground) = -C_D M (V_air)    (2)

where M is the mean horizontal wind speed and C_D is the bulk drag coefficient.  C_D, M , and U_air should all be calculated at the same height, usually 10 meters is used.

For heat and moisture:

(w'q')_s = -C_H M (q_air - q_ground)    (3)

(w'q')_s = -C_E M (q_air - q_ground)     (4)

where C_H and C_E are the bulk transfer coefficients for heat and moisture, respectively.  Typical values for these coefficients are 1x10^-3 to 5 x 10^-3 (they are dimensionless).

• Notice from (3) and (4) that to calculate surface heat and moisture fluxes, one needs the values of theta and mixing ratio at the ground, within the top 1 mm of soil or sea.  These ground values of theta and mixing ratio are called the skin values.

• How in the world does an NWP model figure out skin values of temperature and moisture?????  Answer:  many of the newer, more sophisticated models have soil-layer models that are coupled to the atmospheric model.

  • typical soil layer models contain a few (on order of 5) vertical layers of soil and describe the transfer and storage of heat and moisture within the ground. 

  • They also contain detailed information about the land use and type over the model domain.

• Now you can understand the need for a soil-layer model for NWP. 

• Let's discuss the basics of a soil layer model in more detail