Transcript WRF Physics Options

Mesoscale Modeling
Robert Rozumalski
National SOO Science and Training Resource Coordinator
NOAA/NWS/OCWWS/FDTB
Tour of Talk
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Introduction and mesoscale primer
Model Resolution
Hydrostatic vs. Non-Hydrostatic
Mesoscale Model Physics
Mesoscale Model Boundaries
Simple Model Experiments
A Very Brief Mesoscale Primer
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NWP is the application of the Navier-Stokes
equations that have been adapted to atmospheric
flow
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But are mesoscale models simply NWP models
applied at a smaller grid spacing?
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Yes – mesoscale models are simply NWP systems
that have been designed to simulate mesoscale
atmospheric phenomena
A Very Brief Mesoscale Primer
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Term “mesoscale” attributed to Lidga (1951) to classify
phenomena that were observed on radar but not from
conventional observation
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Since then a number of classification schemes have been
proposed (Orlanski, 1975; Fujita, 1981, etc.)
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Traditional definition of mesoscale – from 2 to 2,000 km
(Orlanski, 1975)
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
500 km grid spacing - mesoscale model?

2 km grid spacing - mesoscale model?
The model results differ but may still be classified as
mesoscale by the above definition
A Very Brief Mesoscale Primer
An alternative mesoscale definition (Emanuel,
Pielke):
1.
The horizontal scale must be sufficiently small so that
the Coriolis term is small relative to the advective and
pressure gradient forces
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Defines the upper bound
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Definition is a function of latitude
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Near equator much larger meteorological features
are considered “mesoscale” than at the poles
A Very Brief Mesoscale Primer
An alternative mesoscale definition (Emanuel,
Pielke):
2.
The horizontal scale must be sufficiently large so that
the hydrostatic approximation can be applied
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Defines the lower bound
Given the above definition of “mesoscale”:
Q:
If you are running non-hydrostatic dynamics are
you still using a mesoscale model?
Q:
Is a model running at a 1 km grid spacing considered
mesoscale?
Resolution and Grid Spacing
Basics: A value at a model grid point represents
the mean within a Dx * Dy * Dz grid cell or box
Resolution and Grid Spacing
Basics: A model forecast at a grid point does not represent
an actual maximum or minimum value unless:
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There is no variability within the grid cell
The grid cell is infinitesimal => point
Wind Speeds
Resolution and Grid Spacing
Basics: Grid-point models can adequately
resolve features that are 4Dx (5 grid points) or
greater
Basics: The 12 km NAM can resolve features
on a scale of 48 km or greater
Resolution and Grid Spacing
Basics: “adequately resolve” does not mean wellresolved
Horizontal Resolution
Feature A: Covers an area spanning > 5 grid points: May appear in model fields
Feature B: Covers an area spanning 1-2 grid points: Will not appear
Horizontal Resolution
Vertical Resolution
Vertical Resolution
When deciding how to define the vertical
resolution in an NWP model:
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The vertical structure should be prescribed to
fully resolve the critical vertical circulations in a
simulation
A greater tilt to the system being simulated
requires increased vertical resolution
Vertical Resolution
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Most model configurations attempt to place the
highest vertical resolution where it is needed most,
near the earth surface
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This allows the model to better resolve the transfer
of heat and moisture into the boundary layer
Vertical Resolution
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Similar resolution is generally not necessary in the
middle troposphere (~600 to 300 mb) since vertical
mixing has a longer length scale
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An increase in resolution is preferable within the
upper troposphere to accurately resolve the jet
stream circulations
Vertical Resolution
21 Levels
Model Top
31 Levels
61 Levels
Model Top
Model Top
Vertical Resolution
3 km simulation
15 levels
61 levels
Vertical Resolution
3 km simulation
15 levels
61 levels
Temporal Resolution
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An NWP model moves (integrates) forward in time
by discrete time steps using a finite difference
scheme
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Leap Frog - 1st order accuracy (faster)
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Runge-Kutta – 3rd order accuracy (slower: ARW)
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One limitation is that a trade-off exists between
numerical accuracy and computational efficiency
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Type of scheme used: higher order -> more accuracy -> slower
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Smaller time step, more numerical accuracy, slower model runs
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Larger time steps, less numerical accuracy, faster model runs
Temporal Resolution
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Generally, the need for computational efficiency
overrides that of computational accuracy; however,
there is a limit:
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A fundamental governing condition for the integration of
time in a numerical model is the Courant, Friedrichs, and
Lewy (CFL) condition
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The CFL condition states that the time step between
intermediate forecasts must be less than the time it takes
the fastest moving wave in the model to travel one grid
space (Dx)
Temporal Resolution
A violation of the CFL condition is most commonly
manifested as numerical “noise” often followed by a
model crash (Bummer).
Temporal Resolution
3 km simulation
18s Timestep
9s Timestep
Resolution Vs. Computational Speed
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The computational cost of increasing vertical
resolution is less than increasing the horizontal
resolution
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2-fold increase in levels ~ 2x increase in computation time
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2-fold decrease in horizontal grid spacing ~ 8x increase in
computation time (3-fold = 27x increase!)
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However, the potential benefit from a decrease in
the grid spacing may be much greater than an
increase in vertical levels
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There is generally little value in decreasing the
model timestep to increase numerical accuracy
Hydrostatic Vs. Non-Hydrostatic
Examples of Processes with NH Effects
Solar Radiation
Fluxes
Convection
Solar Radiation
Moisture
Fluxes
Turbulence Evaporation
Condensation
Fluxes
Surface heating
Surface heating
Hydrostatic Vs. Non-Hydrostatic
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Until recently, running an NWP model at
resolutions capable of resolving non-hydrostatic
phenomena was very computationally expensive
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Small scale feature => small Dx => small Dt
Dw
Additional cost in predicting vertical motion
Dt
Most users accepted the hydrostatic approximation
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Dw
1 or
Dt
L x  L z
Hydrostatic Vs. Non-Hydrostatic
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Vertical Equation of Motion
 Dw   1 p  g  1 p    g  gq
Dt
 z
 z 
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At large horizontal scales, i.e, Lx >> Lz, the
gravitational term is very large compared to
buoyancy
As scale becomes smaller, the buoyancy term may
become more important
Hydrostatic Vs. Non-Hydrostatic
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So, when do you need to go non-hydrostatic?
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Depends upon the phenomenon of interest!
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Traditional rational is Dx < 10 km
Some have noted that NH contribution not important until
Dx ~ 1km
Explicitly resolved convection with Dx=4 km ~ NH
Outflow boundary from convection with Dx=4 km ~ NH
Sea breeze circulation with Dx=3 km ~ HY or NH
Gravity wave simulation with Dx=5 km ~ HY or NH
Large scale baroclinic wave with Dx=5 km ~ HY
Flow over topography with Dx=2 km ~ Depends on
topography
Cost of NH dynamics with ARW WRF ~ 5%
Hydrostatic Vs. Non-Hydrostatic
10 m/s
Probably
does
not make
a difference
Dx = 10 km
: Hydro
or NH
dynamics?
since forcing is of the scale where
Dx = 1km : Hydro
or NH
dynamics?
hydrostatic
dynamics
dominate
1km
10 km
Lx (100 km) >> Lz (1 km)
100 km
Obviously not to scale
Hydrostatic Vs. Non-Hydrostatic
3 km simulation
Hydrostatic
Non-Hydrostatic
Hydrostatic Vs. Non-Hydrostatic
3 km simulation
Hydrostatic
Non-Hydrostatic
Mesoscale Model Physics
How are physics schemes handled
in a mesoscale model?
Mesoscale Model Physics
Typical call order within an NWP system
Call Order*
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Atmospheric Radiation
Surface Layer and Land-Surface Model
Planetary Boundary Layer
Cumulus
Microphysics
(Also possibly Turbulence, TKE, Diffusion, others)
* In WRF ARW Core
Atmospheric Radiation
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Typically handled by separate shortwave (solar)
and longwave (terrestrial) radiation schemes
Atmospheric Radiation
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Model radiation schemes estimate the bulk effect
of all absorbers, scatterers, and reflectors of
radiation to determine:
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The total amount of shortwave radiation reaching the surface
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The amount of longwave radiation emitted from the earth
into space
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The amount of downward longwave radiation reemitted back
towards earth from clouds
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Largest errors result from predictions and
diagnosing of clouds and cloud composition
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Schemes provide atmospheric temperature
tendencies within a column
Atmospheric Radiation
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Schemes are usually 1-d (column) with
assumptions valid as long as Dx >> Dz
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Radiation schemes are typically run less
frequently than other physics schemes due to
the computational costs
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The radiation schemes are usually called first in
a mesoscale model because the radiative fluxes
output are needed for the land-surface scheme
Longwave Radiation
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Includes infrared radiation absorbed and emitted
by gases and surfaces
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Upward radiation flux from the ground
determined by surface emissivity, which is a
function of
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Land-use type
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Skin Temperature and near-surface temperature gradient
Shortwave Radiation
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Shortwave radiation schemes typically include
visible and surrounding wavelengths that
make up the solar spectrum
Shortwave Radiation
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Only source of shortwave radiation is the sun
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Processes simulated within the model atmosphere
and at the surface include:
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Absorption
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Reflection
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Scattering
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Upward flux is due to reflection (surface albedo)
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Atmospheric shortwave radiation responds to:
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Cloud distributions
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Water vapor distributions
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Carbon dioxide, ozone, and trace gas concentrations
Atmosphere Radiative Processes
Surface Physics
Surface Layer Physics
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Surface layer schemes typically
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Calculate friction velocities and exchange coefficients
for the LSM
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Calculate surface stress for the PBL scheme
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Calculate surface fluxes over water only
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Provides no tendencies to the model state variables
Land-Surface Model
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Uses information from:
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Surface layer scheme
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Atmospheric radiation scheme
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Precipitation from cumulus and microphysics schemes
(from previous timestep)
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Surface boundary information
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Outputs:
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Heat and moisture fluxes over land and sea-ice points
to PBL scheme
Surface Physics
Static information typically needed for
surface physics schemes includes:
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Vegetation Type
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Vegetation fraction
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Soil Type
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Soil moisture
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Snow and ice cover
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Water location
Vegetation Type
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The vegetation type is necessary to simulate the
effects of vegetation on surface processes
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The vegetation type in a model acts to control
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Evapotranspiration from the soil
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Surface albedo => available solar radiation
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Near surface temperature and humidity
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Soil temperature
Vegetation Type
Vegetation Fraction
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The vegetation fraction is the portion of the
grid box that is covered by vegetation
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The vegetation fraction acts to modify
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The amount of moisture evaporation from the soil
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Surface albedo
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Available solar radiation
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Partitioning of the surface fluxes
Surface roughness
Vegetation Fraction
Soil Type
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The soil type acts to modify
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The amount of moisture evaporation from the soil
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The albedo of the surface => available solar radiation
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Heat conductivity of the surface
Soil Moisture
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The amount of soil moisture acts to modify:
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The partitioning of available surface energy into
heating and evaporation of moisture
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The amount of moisture available for
evapotranspiration
Water Surfaces
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Typically handled independent of land surfaces
and physics are greatly simplified
Water Surfaces
Some issues to remember:
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Sub-grid scale bodies of water are not wellrepresented in a model simulation
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Small 1-point lakes are often removed from the
model domain
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Temperature data for initialization of small
scale water features are often not available.
Water Surfaces
More issues to remember:
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Skin temperatures over water are generally fixed
during forecast
Potential problem: Water skin temperature does respond
to diurnal solar cycle, which can influence:
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Turbulent fluxes over water (Zeng and Dickenson, 1998)
Most mesoscale models do not allow for coupled
water-atmosphere interactions
Potential problem: Wind flow along coast lines may
enhance or suppress upwelling, which can modify:
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Sea and lake temperature gradients (Sweet et al., 1981)
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Wind speeds over water (Sweet et al., 1981)
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Intensity of lake and sea breeze circulations (Mizzi and
Pielke, 1984)
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Cloud cover and low level stability (Sweet et al., 1981)
Snow and Ice Cover
Some issues to remember:
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The location, coverage, and depth of snow or ice
cover will directly impact the surface radiation
budget due to changes in the albedo
Snow and Ice Cover
Some potential issues to remember:
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Water points that are considered ice covered are
usually treated as snow covered land points and
given a predefined skin temperature value
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Small, frozen lakes may not be well-resolved
within a computational domain
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Smaller bodies of water that are resolved in the
model may not be properly characterized as
open or frozen
Planetary Boundary Layer Scheme
Planetary Boundary Layer Scheme
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Responsible for the vertical sub grid-scale
mixing due to eddy transports through the
entire atmospheric column
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It is during the vertical mixing process in the
model that the PBL develops
Illustration of PBL Processes
Planetary Boundary Layer Scheme
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Surface fluxes used to drive the vertical mixing
are provided by the land surface scheme
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The PBL development in the model is largely
controlled by the accuracy of predicted
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Model skin temperature
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Near-surface temperature, moisture, and wind
The height of the PBL top is typically diagnosed
using stability criteria (bulk Richardson number;
0.0 < Ri < 0.5)
Planetary Boundary Layer Scheme
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Some newer schemes explicitly handle the
entrainment layer (YSU scheme)
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Vertical model diffusion is handled with the PBL
scheme
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PBL schemes will determine the flux profiles within
the PBL and stable layer, and output tendencies for
the model state variables (T,Qv,Qc,V,U, etc)
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Assumptions that justify the use of a PBL scheme
begin to break down when Dx < 1 km.
Cumulus Scheme
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Cumulus schemes are responsible for the sub
grid-scale effects of convective and/or shallow
clouds
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Intended to represent vertical fluxes due to
unresolved up and downdrafts within clouds
and compensating motion outside the clouds
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Schemes typically provide:
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Vertical profiles of moistening tendencies
Vertical profiles of heating tendencies
Cloud water tendencies
Precipitation tendencies (convective component)
Future schemes may provide momentum
tendencies
Illustration of Cumulus Processes
Illustration of Cumulus Processes
Cumulus Scheme
Most schemes designed for Dx > 10 km
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Assumptions that convective eddies are sub grid-scale
break down when Dx < 10 km
Some schemes may help to trigger convection 5 to 10 km
Cumulus schemes probably should not be used for
Dx < 5 km
Microphysics Scheme
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Govern the characteristics of the clouds and
precipitation generated by the grid-scale scheme
Include the explicitly resolved water vapor, cloud
and precipitation processes
Often categorized as simple or complex
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Simple: diagnose precipitation from cloud water or ice
only (E.g. Kessler) ~ Dx > 10 km
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Complex: precipitation predicted through internal cloud
processes including hydrometeor types and multiple
clouds (E.g. Lin) ~ Dx <= 10 km
Microphysics Scheme
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Complex schemes are computationally more
expensive but often provide a better forecast for
grid spacing < 10 km.
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Complex schemes are often further subdivided by
the number of microphysical species and whether
ice and mixed-phase processes are included
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Mixed-phase processes are those in which there is
an interaction between ice and water particles
such as riming that produce graupel and hail
Illustration of Microphysical Schemes
Kessler
WSM3
Ferrier
Qv
Qi/Qs/
Qg
Qc
WSM5
Lin et al./WSM6
Qr
Microphysics Scheme
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For Dx > 10 km mixed phase schemes generally
not worth the expense
For 10km > Dx > 5 km mixed phase schemes may
be of value
For Dx < 5 km mixed phase schemes should be
used
Model Boundary Conditions
Z
4 Lateral Boundaries
X
Lower or Bottom Boundary
Top or Upper Boundary
Y
Y
Model Boundary Conditions
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Since a LAM domain is artificially enclosed with
sides, the various “state” or “dependent” variables
must be specified along the boundaries
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How the dependent variables are specified
constitutes the boundary conditions of a LAM
Model Boundary Conditions
All limited area Models have boundaries on 6 sides
Z
4 Lateral Boundaries
X
Lower or Bottom Boundary
Top or Upper Boundary
Y
Y
Model Boundary Conditions
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In a LAM, the top and lateral BCs are included
out of computational necessity
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The bottom or lower boundary is a real
boundary with physical significance
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For the most part, it is impossible to specify
correct values on the LAM boundaries,
especially for the lateral and top boundaries
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Thus, it is critical that LAM be configured to
minimize the impact
Upper Boundary Conditions
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The primary goal of a well-specified upper
boundary condition is to stop vertically
propagating wave energy from reflecting back
towards the surface
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The top of the model should be placed as far from
the area of interest as possible, ideally where
pressure = ~0mb – Not practical for most LAM
applications
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An alternative is to place the model top above a
layer of deep thermodynamic stratification, such
as within the stratosphere
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Assumptions are that Lz << Lx
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Vertical circulations are relatively small
Vertical motions are ~ 0
Upper Boundary Conditions
Common Upper BC formulations
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Sponge layer – Damps out vertically propagating waves within an
upper boundary buffer zone before reaching the top boundary by
using smoothing, filtering or some other approaches such as
adding frictional terms to model momentum equations.
Rigid Lid – Effective provided that model top is located well above
region of interest and Lx >> Lz; otherwise reflection of energy off
model top a possibility.
Radiative – Allows energy to exit through top of domain but must
be employed well away from model domain. Difficult to use since
it must be applied spectrally and vertical wave number and
frequency must be specified.
Other formulations
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Porous model top
Impervious lid
Lateral Boundary Conditions
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Lateral boundary conditions are designed
similar to those of the upper boundary in
order to reduce reflection. Examples for
idealized simulations include:
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Constant flow – Flow entering and exiting the lateral
boundaries is held constant
Zero Gradient – Values along periphery of the grid are
defined such that F(n) – F(n-1) = 0
Radiative – Similar to upper BC treatment. Used to
minimize reflection
Sponge – Similar to upper BC treatment. Uses damping
or diffusion along lateral boundaries
Lateral Boundary Conditions
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Most models used for weather simulation
purposes use NWP or analysis-specified
lateral boundary conditions
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LBCs are typically provided by a coarser run
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Operational NAM or GFS
Reanalysis
Previous WRF Model run
Previous analyses
Values for the dependent variables are obtained
and interpolated in time and space to the grid
points along the periphery of the LAM
computational domain
Lateral Boundary Conditions
1 2 3 4 5
Computational
Domain
5 4 3 2 1
East
West
North
1
2
3
4
5
5
4
3
2
1
South
BCs (Qv, q, V, U) Specified from other data source
BCs determined through relaxation
Inner computational domain
Lateral Boundary Conditions
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The benefits of specified lateral boundary
conditions
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Act to constrain solution – Unlike global model
Influence on forecast is somewhat controllable
Lateral Boundary Conditions
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Specified lateral boundary conditions can
degrade a forecast through
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Errors in spatial interpolation from external grid
Temporal aliasing of information
Inability to feedback information to larger scale (1way nests)
An incompatibility between physical-process
parameterization
Errors propagate via advection and inertial
gravity wave modes
Lower Boundary Conditions
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The lower boundary is the only one that has
physical significance
Formulation of the surface governs the generation
of many lower tropospheric phenomena
Specification of lower boundary conditions
include:
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Type of Surface (land, water, ice)
Surface skin temperature
Topographic information
Soil type
Land use information
Surface albedo
Snow cover and depth
Simple NWP experiments
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Mesoscale models can be an effective tool for
training and research on local forecasting problems
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One method for targeting a specific problem is to
run a model with a prescribed atmospheric
environment that allows for the manifestations of
the local forcing to be emphasized
Simple NWP experiments
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A series of simple NWP experiments were executed
to examine local forcing mechanisms
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Sea breeze circulation
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Topographically forced circulations
Simple NWP experiments
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All runs were made with the WRF EMS
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Data sets used for the initial and boundary
conditions were constructed to isolate the
response to the local forcing
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Surface pressure and temperature for the
initialization data sets were computed from a
prescribed base sea level pressure and
temperature where:

Psfc = Pslpe-(G*Zsfc)/(Rd*Tm)

Tsfc = To + G*Zsfc
Simple NWP experiments
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Soil moisture and temperature values were specified
as uniform over entire domain to eliminate
horizontal gradients in fluxes
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Characteristic values for vegetation and soil type
were also applied uniformly over the domain
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Atmospheric moisture, as defined by RH, was set to
be uniform over the entire domain
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A simple 2-layer atmospheric stability profile was
constructed where the lapse rate was defined by
Brunt-Väisälä frequency (N):
 g q 


 T Z 
1/ 2

N=

Nstratosphere > Ntroposphere
Sea Breeze Experiments
Sea Breeze Experiments
Sea Breeze Experiment #1
Purpose: To examine the evolution of the diurnallyforced sea breeze circulation

Base surface temperature set to a uniform
300K Tsfc = T(z)

Sea level pressure set to 1000mb, surface
pressure Psfc = P(Z)

N = 0.21 troposphere, 0.28 stratosphere
(200mb)

RH = 20% over entire domain

24 hour simulation initialized at 12 UTC 1
August
Sea Breeze Experiment #1
10m winds
Sea Breeze Experiment #1
Sea Breeze Experiment #1
Simulated
Reflectivity
Sea Breeze Experiment #1
Sea Breeze Experiment #1
X section of
Theta & Circ
Sea Breeze Experiment #1
coast
coast
Sea Breeze Experiment #2
Purpose: To examine the evolution of the diurnallyforced sea breeze circulation

Base surface temperature set to a uniform 300K
Tsfc = T(z)

Sea level pressure set to 1000mb, surface
pressure Psfc = P(Z)

N = 0.21 troposphere, 0.28 stratosphere
(200mb)

RH = 40% over entire domain

24 hour simulation initialized at 12 UTC 1
August
Sea Breeze Experiment #2
Simulated
Reflectivity
Sea Breeze Experiment #2
Complex Terrain Experiment
Purpose: To examine the impact of topography on
diurnally-forced local circulations

Base surface temperature set to a uniform 300K Tsfc
= T(z)

Sea level pressure set to 1000mb, surface pressure
Psfc = P(Z)

N = 0.21 troposphere, 0.28 stratosphere (200mb)

RH = 20% over entire domain

24 hour simulation initialized at 12 UTC 1 August
Complex Terrain Experiment
10m winds
Complex Terrain Experiment
Complex Terrain Experiment
X section of
Theta & Circ
Complex Terrain Experiment
Complex Terrain Experiment
Simulated
Reflectivity
Complex Terrain Experiment
Summary of Talk
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Introduction and mesoscale primer
Model Resolution
Hydrostatic Vs. Non-Hydrostatic
Mesoscale Model Physics
Mesoscale Model Boundary Conditions
Simple Model Experiments
Mesoscale Modeling
The End