Numerical weather prediction models include parameterization schemes of the atmospheric boundary layer (ABL) which involve parameters such as ABL height, friction velocity, convective velocity scale, potential temperature scale, buoyancy heat flux, Obukhov length. These parameters contribute implicitly to the weather forecast.
Could some of these parameters be also of direct use to weather forecasters?
For specialty forecasting, like getting the winds at some level other than the surface, or estimating the winds at a grid scale roughness other than what is hardwired in the model, the friction velocity, boundary layer height and stability factors like Richardson number are helpful. These parameters are also useful for air quality forecasting.
Agree with Mark. If you want to go to the basic application all you can say is; as long as we keep trying to use parameters in a non-parametric system the forecasts will remain tenuous.
It depends on what you want to forecast, but let's suppose you just want to run a weather model with a well designed ABL component. The ABL is the part of the atmosphere directly influenced by interaction with the ground. The corollary is that the free atmosphere above is not directly influenced by the ground, but that is not the end of the story. The ABL has an indirect effect on weather systems by creating flow convergence or divergence near the ground (first km or so). This determines the rate of uplift or subsidence of the base of the weather system. It follows that the wind velocity field within the ABL, both its strength and direction, is highly important to larger-scale processes. Tracking back to what controls the wind within ABLs, we find the entrainment of momentum into the ABL at the heart of the question, so the parameters that control entrainment are of central interest. There is a substantial literature on this, and one takes ones pick. My own view is that we will have to solve the whole momentum, energy and heat budgets of the ABL if we are to do the job as well as it can be, and that entails finding all the parameters that control ABL dynamics. The relevant parameter set will vary according to turbulence regime..
I can't tell you that any of those parameters have any direct meaning to weather forecasters. I can tell you that having a good ABL forecast helps with aircraft turbulence and fog forecasting. If the truth be told, present day numerical weather models do a poor job with forecasting the ABL conditions observed in dense fog situations.
Apart from the already mentioned, the basic atmospheric parameters like surface pressure, temperature, relative humidity and are of prime importance. These have to be verified in temporal sequence and vertically also to estimate sensible heat flux, latent heat flux, moisture flux and momentum flux etc.