Parameterization

The representation of the effects of sub-grid scale processes in terms of grid-scale variables predicted by the model

• NWP models cannot resolve features and/or processes within a grid box realistically

• Parameterization has its greatest impact on predictions of sensible weather at the surface

• Physical processes typically parameterized

• Soil moisture/temperature

• Long wave radiation

• Solar isolation/reflection

• Evaporation

• Convection

• Cloud and precipitation processes

• Friction/turbulence

Convective Parameterization Schemes

• Most NWP models use these parameterization Schemes

• Designed to reduce atmospheric instability in the model

• Prediction of precipitation is a by-product of how the scheme reduces instability

• Expectations of schemes to accurately predict location and timing of convective precipitation is usually low

Planetary Boundary Layer in NWP

3 reasons processes need to be parameterized

1. Phenomena are too small or too complex to be resolved numerically – computers aren’t powerful enough to directly treat them

2. Processes are often not understood well enough to be represented by an equation

3. Effects profoundly impact model fields and are crucial for making realistic forecasts

Problems associated with using parameterizations result from:

1. Increasing complexity of parameterization

2. Interactions between parameterization schemes – these are harder to trace than errors occurring in a single scheme

Dynamics and Numerics of Shallow Water Flows

Outline:

• governing equations

• dimensionles s parameters

• wave propagation, Tsunamis

• hydraulic jumps

• vortex shedding

• Seiche waves

• numerical implementation

Shallow water equations

1. Commonly used in large-scale ocean models

2. Start with Euler’s equations

Phase speed of shallow-water waves

Hydraulic jumps

Shallow-Water Flow Past a Ridge

Atmospheric flow past a ridge

Shallow water equations

• Neglect vertical accelerations

→ Hydrostatic pressure in fluid

−        Assume no vertical variation in (u, v)

a) Advantages

• Allows variable depth in natural way

• Three coupled, hyperbolic PDEs

• The equations admit (weak) discontinuous solutions, which approximate breaking waves

b) Disdvantages

• Equations admit no wave dispersion and no smooth waves of permanent form

• Actual breaking waves create significant vertical variation in horizontal velocity. These equations give vertically averaged velocities, at best.

OR IN COMPUTER CODE:

>> Du/Dt = (f0 + beta*y)v - g*Deta/Dx

>> Dv/Dt = -(f0 + beta*y)u - g*Deta/Dy

>> Deta/Dt = -H*(Du/Dx + Dv/Dy)

Can be derived from primitive equations based on a number of assumptions:

1) The fluid is barotropic

2) The hydrostatic or shallow water assumption based on H<<L

3) Boussinesq assumption

4) neglect vertical component of Coriolis term

5) neglect small advection and diffusion terms

6) eta << H

Periods of seiche waves

Dimensionless Formulation of Shallow-Water Equations

Dimensional formulation                                                    dimensionless formulation

                                                                        With

Numerical Implementation

Staggered Grid

Array Structure

Numerical Integration of Momentum Equation

Dimensionless Formulation

Centered Differences in space and time

Solve for time level n+1

Numerical Integration of Mass Equation

Dimensionless Formulation

Centered Differences in space and time

Solve for time level n+1

tambahan :

1. Lower-tropospheric WRF sounding overlays from (a) nonlocal (YSU and MRF) and hybrid local and nonlocal (ACM2) schemes, and from (b) local (MYJ and QNSE) and hybrid local–nonlocal (ACM2) schemes, plotted around and below the 600-mb level at 0400 UTC 1 Jan 2011 for JAN, plotted beside soundings from the observed JAN sounding and corre-spondingRUC–SFCOA sounding (Cohen et al. 2015)

2. The velocity decreases with increasing distance from the point of impact (due to mass conservation).This provokes the transition from super critical to subcritical condition. The transition is accompanied by a Hydraucalic Jump, where some of the kinetic energy is dissipated in turbulence.

3. Constituents of the PBL and their evolution through the diurnal and nocturnal cycles [from Kis and Straka (2010) and Stull (1988)].