Presentation on theme: "Dynamic Balance of Cloud Vertical Velcoty"— Presentation transcript:
1 Dynamic Balance of Cloud Vertical Velcoty Yuanfu XieFAB/GSD/ESRL
2 A variational balance (LAPS) Written in a Lagrangian function,
3 Poisson Equation for λ (McGinley 1987) Take a perturbation of the Lagrangian function in terms of u, v, ω,
4 Poisson Equation for λ (cont’) Integration by part yields Or,
5 Issues with the Poisson Eqn Need a efficient 3D solver;It is complicated for vertical finite difference as vertical levels are non-uniform (McGinley 1987 uses a uniform grid; unfortunately, LAPS balance uses a uniform grid even it is not (e.g. LAPS_ci domain)!! See qbalpe.f line );LAPS uses a relaxation method:A relaxation is convergent but extremely slow;Most iterations tries to push shorter waves except the first few iterations;It usually results in high frequency noise (balance package shows a lot of noise in divergence).STMAS multigrid is a designed scheme for this;A simple trick to see if the minimization is right.
6 Evidence of Incorrect vertical finite difference formulation New adjustment of windLAPS balance
7 A simple trickAfter LAPS/STMAS analysis, the balance package adds cloud ω to wind. Instead of a 3D Poisson solver, a simple scheme is used to adjust wind
8 An Approximation of the Balance It keeps all wind information from previous analysis except adding vertical gradient of cloud omega to wind divergence;Fish package can be easily and efficiently used for solving these 2D Poisson equations;A quick verification for improving the forecast scores;An simple quick fix of the balance before a more sophisticated implementation.
9 Experiments at the CI Domain There are two STMAS runs set on the convective initiation domain, (stmas_ci and stmas_ci_cyc) for experimenting;The two runs are identical except the cloud and omega adjustmentLinear increment for cloud omega analysis;Smoothed cloud omega;Added cloud omega to the horizontal wind.LAPS uses the linear increment and smoothed cloud omega and is better than STMAS HWT forecasts without adding the cloud omega;More experiments are needed to evaluate the simple scheme comparing to the linear increment cloud omega and smoothed scheme.
13 Divergence, cloud omega and reflectivity plots: 2011-09-04 06Z
14 Preliminary Conclusions LAPS balance uses an incorrect finite difference formula in Poisson equation (vertical) if the vertical is non-uniform;The simple trick shows the minimization of balance package indeed improves ETS; but this simple trick brings in too strong reflectivity forecasts;It adjusts wind only but not other fields and is too simple;It shows that the relaxation scheme in the balance package can be improved;A more sophisticated multigrid minimization technique should be considered in STMAS development.The wide forecast bias may also warn us on the cloud omega computation; some sensitivity study is needed;A correct 3D Poisson equation and multigrid will be applied in STMAS for improving the balance!
15 Evidence of inconsistency between analysis anf WRF forecast 0
16 Vertical Finite Difference When a uniform vertical grid is used, a center finite difference is correct, such as for a stagger grid, for example, a first derivative,This is incorrect if the vertical is not uniform.