NUMERICAL WEATHER PREDICTION (Model Physics Part) Dr Meral Demirtaş Turkish State Meteorological Service Weather Forecasting Department WMO, Training Course,

NUMERICAL WEATHER PREDICTION NUMERICAL WEATHER PREDICTION ((Model Model Physics Physics PPart)art)

Dr Meral DemirtaşDr Meral Demirtaş

Turkish State Meteorological ServiceTurkish State Meteorological Service

Weather Forecasting DepartmentWeather Forecasting Department

WMO, Training Course, 26-30 September 2011WMO, Training Course, 26-30 September 2011Alanya, TurkeyAlanya, Turkey

Outline

• Introduction• Basic concepts• Physical processes and interactions• Subgridscale processes and Reynolds averaging• Cumulus parameterizations• Planetary Boundary Layer (PBL)• Radiation• Surface Parameterization

A schematic illustration of atmospheric processes

1 10 100 km

Cumulus ParameterizationResolved Convection

LES PBL Parameterization

Two Stream Radiation3-D Radiation

Model Physics in Various Resolutions

Physics“No Man’s Land”

Physical ParameterizationPhysical Parameterization

Physical parameterization is how we include the effects of physical processes implicitly when we cannot include the processes themselves explicitly. The method of accounting for physical effects without directly forecasting them is called physical parameterization. Physical parameterizations are done for the following areas:

• Planetary boundary layer • Radiation• Surface/sub-surface processes• Cumulus parameterization• Sub-grid scale orography• Microphysics• Turbulence/diffusion

Radiation Processes Convective Motions

Surface Processes Microphysical Processes

• Hydrometeor phase, cloudoptical properties, cloud overlap assumptions, & cloud fractions

• Precipitation (incl. phases)and clouds

• Subgrid transports, stabilization, detrainment

• Surface energy fluxes, land & ocean surface models

• Convection (deep & shallow), PBL evolution, precipitation

Every little counts….

Parameterizing Physical Processes

A physical process that cannot be directly predicted requires a parameterization scheme. The scheme must derive information about the processes from the variables in the forecast equations using a set of assumptions. Several types of assumptions are used to provide information.

Parameterizing Sub-Grid Scale Processes

The key problem of parameterization is trying to predict with incomplete information; such as the effects of sub grid-scale processes with information at the grid scale. Say using the wind forecast in a grid box to predict boundary-layer turbulence without knowing topography details, vegetation characteristics, or the details of structures at the surface.

Vertical re-distribution of heat and moisture by convection may easily occur between meso-scale grid boxes. The animation shows the development of the rain shaft (white and gray) and the accompanying cold pool (blue shading). Notice that sub grid-scale variations in the convection will have an effect on the moisture and heating in some of the model grid boxes.

Convective Processes

Even in very high-resolution models, microphysical processes occur on a scale too small to be modeled explicitly. There are important variations in both the horizontal and vertical. In this example, the cloud microphysical processes of condensation and droplet growth are occurring inside a 1-km model grid box.

Microphysical Processes

The effects that model physics parameterizations attempt to address are generally unresolvable at grid scales and can be categorized as follows:

• Shortwave (solar) and long wave (terrestrial) radiation in the atmosphere; it includes effects of clouds, water vapor and trace gases.

• Land and sea surface characteristics and their effect on the absorption and partitioning of solar radiation reaching on the surface; it includes effects of vegetation type, soil type, soil moisture quantities, and snow.

• Transfer of heat, moisture and momentum between the ground and the planetary boundary layer (PBL) and between the PBL and the free atmosphere by turbulence; this is affected by the treatment of radiation in the atmosphere and at the ground.

Physics interactions

Subgrid-scale Processes and Interaction Between Them and Resolved Processes

Subgrid-scale processes are all the processes that cannot be resolved explicitly by the model.

These subgrid-scale processes depend on and in turn, affects the large-scale fields and processes that are explicitly resolved by numerical models.

Prognostic equation for water vapour:

Subgrid-Scale Processes and Reynolds Averaging

u and q contain model grid scale and subgrid-scale processes

The overbar represents the spatial average over a grid, and the primes notes the subgrid-scale perturbations.

The Reynolds averaging rule:

Combine the equations and apply the Reynolds averaging

• The first three terms of the right-hand side (in blue) are the resolvable grid-scale advection –which is explicitly computed in the dynamical process.

• The next three terms (in red) are the turbulent moisture transports -which are not resolvable by dynamical equation-, need to be parameterized.

• The last two terms (in green) are evaporation and condensation need to be parameterized, since they are not resolvable by dynamical equation.

Apply the same procedures onto momentum and thermal dynamical equations:

How to tackle unresolved parameters?

Parameterization of the turbulent flux terms (1)

1. Bulk parameterization (aka “slab model”)

It is assumed that the grid-scale field is well mixed in the boundary layer.

In real life, convective boundary layer is topped by a stable layer, and that:

- Over land, during the day when surface heating is strong.

- Over ocean, when the air near the sea surface is colder than the surface water temperature.

Parameterization of the turbulent flux terms (2)

2. K Theory (aka the Eddy Theory)

It is assumed that turbulent mixing acts in a way analogous tomolecular diffusion. The flux of a given field is proportional tothe local gradient of the mean.

Where K is the Eddy diffusivity.

In real life, neutrally or stably stratified boundary layer with moisture does vary significantly with height!

3. Directly obtain a prognostic equation for the flux term

Consider vertical motion, w equation:

Multiply this equation with ρq

and multiply prognostic equation of water vapour with w :

Sum up the above two equations and apply Reynolds Averaring rule on the resulting equation, and come up with a neat prognostic equation:

(Moeng and Wyngaard, 1989)

Model Equations

Momentum Eqn.:

Continuity Eqn.:

Hydrostatic Eqn.:

Surface Pressure Eqn.:

Atmosphetic State Eqn.:

Thermo dynamics Eqn.::

Water vapour conservation Eqn.:

Notes on notations used in the equations

The overbar noted terms are the grid-averaged quantities computed by the model dynamics, and the tilde noted terms represent subgrid scale processes that are need to be parameterized.

• Momentum equation has the effect of eddy fluxes,• Thermal dynamics equation includes radiative heating and cooling,

sensible heat fluxes, condensation and evaporation.• The water vapour equation includes the condensation and evaporation, and the moisture flux.

Types of parameterization processes:

• Vertical flux terms:

• Radiative heating and cooling:

• Condensation and evaporation:

Vertical flux terms

Eddy flux terms of momentum equation, -sensible heat and moisture- may be written as:

(Note that horizontal turbulence is neglected due to scales.)

These terms can be represented using K-Theory in the boundarylayer and neglected in the free atmosphere above boundary bysetting K=0

Radiation

It is determined from the vertical divergence of the upward and downward fluxes of short- and long- wave radiation, obtained using the radiative transfer equation. (Kiehl, 1992)

The interactions between clouds and radiation are important. How to determine clouds?

• Cloud from climatology (Manabe et al., 1965),• Cloud cover is based on relative humidity (Slingo 1987),• Cloud and rain water were predicted using budget equations and cloud

cover was derived from the amount of cloud water (Zhao et al., 1997).Cloud properties are also important

• Clouds are represented in plane slab structure? Not really…• Clouds have a fractal structure?

Derivation of surface flux termsThe vertical derivative of the lower boundary turbulent fluxes requiresurface fluxes of heat, moisture, and momentum. One of the most used surface flux parameterization scheme is the bulk parameterization based on the Monin-Obukhov (1954) similarity theory. The theory suggests that the flux is constant with height in the surface layer. The wind and temperature in the surface layer can be described by a set of equations that depends only on a few parameters (e.g, roughness length).

are the velocity, potential temperature, and mixing ratio at the surface layer, respectively, and the variables with an s subscript are the corresponding values at the underlying ocean or land surface (vs = 0)

are transfer coefficients and they depend on the stability of the surface layer.

Cloud processes interwoven the dynamical and hydrological processes in the atmosphere. Cloud processes play a central role in the interaction between different processes.

Cloud processes;

• couple radiative and dynamical-hydrological processes in the atmosphere through the reflection, absorption, and emission of radiation.

• through the heat of condensation and the re-distribution of sensible and latent heat, it changes the temperature field and the momentum (dynamical processes). Via condensation and evaporation, it changes the humidity field (dynamical processes).

• influence hydrological process in the ground through precipitation

Interactions between grid and subgrid scale processes

Precipitation Processes:Cumulus Parameterization

• Atmospheric heat • Moisture/cloud tendencies• Surface precipitation

• Convective initiation

• Deep/shallow convection

• Vertical heating/cooling

• Vertical drying and moistinening (entrainment/detrainment)

• Precipitation types

Cumulus parameterization schemes include

Convective parameterization (CP) schemes are designed to address:

• The vertical transport of latent heat.• Reducing thermodynamic instability so the grid-scale precipitation

and cloud parameterization (CP) schemes do not try to create unrealistic large-scale convection.

• CP schemes reduce instability by rearranging temperature and moisture in a grid column.

To accomplish both tasks, each scheme must define the following, using information averaged over entire grid boxes:

• What triggers convection in a grid column

• How convection, when present, modifies the sounding in the grid column

• How convection and model’s grid-scale dynamics affect each other

Types of Cloud Schemes

Parcel theory based cloud formation

DALR: dry adiabatic lapse rate (10C/km), lapse rate for sub-saturated parcels.

MALR: moist adiabatic lapse rate (5C/km), lapse rate for saturated parcels.

ELR: environmental lapse rate; taken as 7C/km in the troposphere.

LCL: lifting condensation level (cloud base).

LFC: level of free convection (parcel and environment temperatures same).

TOC: top of cloud (where air parcel again having the same T or colder than the environment).(Fovell, 2004)

Planetary Boundary Layer

• Boundary layer fluxes (heat, moisture, momentum)

• Vertical diffusion

Model Representation of the PBL (1)The PBL is defined as the layer between the surface and free atmosphere where the surface has a direct influence on heating, moisture and momentum. The PBL is determined by:

• The flux from the earth's surface into the atmosphere • Prescribe/diagnose the number of model layers where the surface

influence is felt.• Parameterize the transport of heat, moisture, and momentum through these

layers, which essentially constitute the model PBL.

Allocating the number of layers in the model PBL depends on:

• The predicted average grid-square skin temperature and first layer average grid-cube temperature, moisture, and wind.

• The lapse rate, vertical moisture gradient, and vertical wind shear between adjacent model layers moving up from the surface.

Vertical transport rates of momentum, heat, and moisture are based on these grid-scale gradients. The first model layer from the surface that does not meet the instability threshold is considered the PBL top.

PBL (2)

The PBL exhibits strong diurnal, synoptic (3-5days), and seasonal variations. Its depth depends on the amount of sensible and latent heating from the surface, which determines static stability and the growth of turbulent eddies.

The surface temperature, vertical temperature distribution and wind gradients in the lowest part of the atmosphere drive the diurnal development of the PBL. The observed PBL and associated vertical transport between the surface and free atmosphere are deepest on windy days and/or when the skin temperature is much warmer than the overlying atmosphere.

The PBL is shallow and stable with little or no vertical transport between the surface and free atmosphere (decoupled) in calm conditions and when the earth's surface is colder than the overlying atmosphere.

Radiation Longwave/Shortwave

• Atmospheric temperature tendency• Surface radiative fluxes

Model Representation of Radiation

Need to address uncertainties in the effects of the atmosphere and earth's surface on incoming solar and outgoing terrestrial radiation, which involves the following: In the atmosphere

• Transmission/Absorption

• Reemission (longwave radiation-LW)

• Reflection/Scattering At the earth's surface

• Transformation from shortwave radiation into other forms of energy at the earth's surface, based on the state of that surface over the area covered by the model grid box.

• Net emission of LW radiation from the earth's surface toward space.

A Schematic illustration of radiation processes

Surface Parameterization

• Surface layer of atmospheric diagnostics• Soil temperature, moisture, snow prediction

The earth's surface interacts with the incoming solar radiation that remains after scattering, reflection, and absorption by the atmosphere. The resulting surface energy balance depends on the surface's albedo, the availability of water to evaporate from the surface and/or its vegetation, the roughness of the surface, the surface type (soil, water, or ice), the presence of snow, and other characteristics. The net surface energy balance directly determines the surface temperature and the characteristics of the atmospheric layer directly influenced by the

planetary boundary layer (PBL).

Representation of Surface Characteristics (1)

A model that does not represent subgrid scale variability on the surface (a grid box containing an urban area within a generally forested or cultivated area, which is treated as one or the other) may not well capture subgrid scale surface air temperature/moisture variability.

Errors in simulated parameters resulting from large deviations from climatology (early emergence of live vegetation due to a warmer than normal spring) may result in errors in surface temperatures and surface energy and water fluxes.

Representation of Surface Characteristics (2)

Basics of Land-Surface Model (LSM) Physics

An LSM should provide following quantities:

• surface latent heat flux• surface sensible heat flux• upward long-wave radiation

(skin temperature and surface emissivity)• upward (reflected) shortwave radiation

(surface albedo, including snow effect)

Acknowledgements:

Thanks to documents/images of UCAR/COMET, Jimy Dudia (NCAR/MMM) and Mike Ek (NCEP/EMC) and Junjie Liu (UMD) that provided excellent starting point for this talk!

Thanks for attending…