PDF《数值模式内物理参数化》

10 * Physical process in the atmosphere Specification of heating, moistening and frictional terms in terms of dependent variables of prediction model →Each process is a specialized branch of atmospheric sciences. * Parameterization The formulation of physical process in terms of the model variables as parameters. (constants or functional relations) Schematic configuration

11 small amount of E E * Subgrid scale process Any numerical model of the atmosphere must use a finite resolution in representing continuum certain physical &

dynamical phenomena that are smaller than computational grid. - Subgrid process (Energy perspective) the energy dissipation takes place by molecular viscosity (smallest grid size idealized situation) ? Objective of subgrid scale parameterization To design the physical formulation of energy sink, withdrawing the equivalent amount of energy comparable to cascading energy down at the grid scale in an ideal situation. ?

12 E

1000 100

10 NWP model → Parameterization ← increasing scale ← hard truncation limit

1 1000

100 10 E Parameterization that are only somewhat smaller than the smallest resolved scales. If the real atmosphere was like that, Where truncation limit ;

spectral gap Unfortunately, there is no spectral gap

13 Consider prognostic water vapor equation In the real atmosphere, is neglected 2) Subgrid scale process &

Reynolds averaging

14 ① ② ① grid-resolvable advection (dynamical process) ② turbulent transport * Rule of Reynolds average : then eq.(1) becomes * how to parameterize the effect of turbulent transport a) b) c) obtain a prognostic equation for : 0th order closure : 1st order closure (K-theory) from (1), (2) taking Reynolds averaging, : 2nd order closure (HW: 4-1) Parameterizations are personal ? Since we may have different understandings of how the phenomenon we are parameterizing behaves, parameterization schemes are personal. I will primarily talk about how I view the various schemes. I hope my example will give you an idea how you might make a better scheme!! A classical case ? The surface layer parameterization using the similarity profile function is nearly universally adopted. ? Based on scaling argument, dimensionless profile functions can be formulated using local measurements. ? Problem is the applicability to situations not measured: under strong wind conditions in the typhoon environment. ? Boundary layer researcher have, for years, try to apply the same method to the boundary layer with little success.

17 1) Bulk method wind shear 2) Monin-Obukov similarity Integrate, : curving factor Surface layer

18 Profile function : and Dyer and Hicks formula for similarity (Businger formula : complex) - unstable (L <

0) - stable (L >

0) Given the Applying the surface layer formulation to the interface ? Over ocean: C H = ? cp Ch U (Ts C Ta) C LE = ? L Ch U (qs(Ts) C qa) ? Over land, the situation is much more complicated. The early effort to parameterize the heat flux is to apply the same formula as for ocean with an additional parameter (b) for evaporation C LE = b ? L Ch U (qs(Ts) C qa) Heat exchange over land ? Since the heat storage for land surface is much smaller than for ocean, the incoming and outgoing heat fluxes are nearly balanced. So we often use a surface heat budget to calculate the '

skin'

temperature Ts. ? The problem with using a single parameter b to handle evaporation over many different situations proved impossible. Land heat flux ? In fact, evaporation for most of the land area comes in the form of transpiration from vegetations. Trees are living entities and '