Dynamic Balance of Cloud Vertical Velcoty

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Dynamic Balance of Cloud Vertical Velcoty Yuanfu Xie FAB/GSD/ESRL

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Dynamic Balance of Cloud Vertical Velcoty. Yuanfu Xie FAB/GSD/ESRL. A variational balance (LAPS). Written in a Lagrangian function,. Poisson Equation for λ (McGinley 1987). Take a perturbation of the Lagrangian function in terms of u, v, ω ,. Poisson Equation for λ ( cont ’). - PowerPoint PPT Presentation

Transcript of Dynamic Balance of Cloud Vertical Velcoty

Dynamic Balance of Cloud Vertical Velcoty

Dynamic Balance of Cloud Vertical VelcotyYuanfu XieFAB/GSD/ESRLA variational balance (LAPS)

Written in a Lagrangian function,

Poisson Equation for (McGinley 1987)Take a perturbation of the Lagrangian function in terms of u, v, ,

Poisson Equation for (cont) Integration by part yields

Or,

Issues with the Poisson EqnNeed 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 2878-2881);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.Evidence of Incorrect vertical finite difference formulation

New adjustment of windLAPS balanceA simple trickAfter LAPS/STMAS analysis, the balance package adds cloud to wind. Instead of a 3D Poisson solver, a simple scheme is used to adjust wind

An Approximation of the BalanceIt 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.Experiments at the CI DomainThere 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.Forecast at 2011-09-04 00ZETSBias

Forecast at 2011-09-04 00ZETSBias

Forecast at 2011-09-04 00ZETSBias

Divergence, cloud omega and reflectivity plots: 2011-09-04 06Z

Preliminary ConclusionsLAPS 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!14Evidence of inconsistency between analysis anf WRF forecast 0

Vertical Finite DifferenceWhen 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.