# Presentation: 562551

## Mesoscale Modeling

- Robert Rozumalski
- National SOO Science and Training Resource CoordinatorNOAA/NWS/OCWWS/FDTB

## Tour of Talk

- Introduction and mesoscale primer
- Model Resolution
- Hydrostatic vs. Non-Hydrostatic
- Mesoscale Model Physics
- Mesoscale Model Boundaries
- Simple Model Experiments

## A Very Brief Mesoscale Primer

- NWP is  the application of the Navier-Stokes equations that have been adapted to atmospheric flow
- But are mesoscale models simply NWP models applied at a smaller grid spacing?

- Yes – mesoscale models are simply NWP systems that have been designed to simulate mesoscale atmospheric phenomena

## A Very Brief Mesoscale Primer

- Term “mesoscale” attributed to Lidga (1951) to classify phenomena that were observed on radar but not from conventional observation
- Since then a number of classification schemes have been proposed (Orlanski, 1975; Fujita, 1981, etc.)
- Traditional definition of mesoscale – from 2 to 2,000 km (Orlanski, 1975)
- 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

- The horizontal scale must be sufficiently small so that the Coriolis term is small relative to the advective and pressure gradient forces
- Defines the upper bound
- Definition is a function of latitude
- Near equator much larger meteorological features are considered “mesoscale” than at the poles

## A Very Brief Mesoscale Primer

- The horizontal scale must be sufficiently large so that the hydrostatic approximation can be applied
- Defines the lower bound

- Q:	If you are running non-hydrostatic dynamics are you still using a mesoscale model?

- 	Given the above definition of “mesoscale”:

- 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 x * y * z 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:
- 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 4x (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 well-resolved

## Horizontal Resolution

- Feature A: Covers an area spanning > 5 grid points: May appear in model fieldsFeature B: Covers an area spanning  1-2 grid points: Will not appear

## Horizontal Resolution

**Notes:**

The “+”s represent a grid pont with a 30km grid spacing that is superimposed on a clod scale simulation

## Vertical Resolution

## Vertical Resolution

- 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

- When deciding how to define the vertical resolution in an NWP model:

## Vertical Resolution

- Most model configurations attempt to place the highest vertical resolution where it is needed most, near the earth surface
- This allows the model to better resolve the transfer of heat and moisture into the boundary layer

## Vertical Resolution

- Similar resolution is generally not necessary in the middle troposphere (~600 to 300 mb) since vertical mixing has a longer length scale
- An increase in resolution is preferable within the upper troposphere to accurately resolve the jet stream circulations

## Vertical Resolution

- 21 Levels

- 31 Levels

- 61 Levels

- Model Top

- Model Top

- Model Top

## 3 km simulation

- 15 levels

- 61 levels

- Vertical Resolution

**Notes:**
A comparison between two 3km simulations over southern Florida depicting the diurnal cycle of the sea/land breeze circulation 

The Simulation on the left has 15 vertical levels while the one on the right used 61  note some of the differences between the 
Simulation:

Lake breeze development over lake Okeechobee in 61 level run
 Stronger on shore flow in S. Florida

## 15 levels

- 61 levels

- 3 km simulation

- Vertical Resolution

**Notes:**
A comparison between two 3km simulations over southern Florida depicting the diurnal cycle of the sea/land breeze circulation 

Better resolved PBL top in 61 level run
2.Stonger vertical motion along leading edge of sea breeze fonts in 61 level run
3. Improved resolution of vertically propagating energy

## Temporal Resolution

- An NWP model moves (integrates) forward in time by discrete time steps using a finite difference scheme
- Leap Frog - 1st order accuracy (faster)
- Runge-Kutta – 3rd order accuracy (slower: ARW)
- One limitation is that a trade-off exists between numerical accuracy and computational efficiency
- Type of scheme used: higher order -> more accuracy -> slower
- Smaller time step, more numerical accuracy, slower model runs
- Larger time steps, less numerical accuracy, faster model runs

## Temporal Resolution

- Generally, the need for computational efficiency overrides that of computational accuracy; however, there is a limit:
- A fundamental governing condition for the integration of time in a numerical model is the Courant, Friedrichs, and Lewy (CFL) condition
- 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 (x)

## Temporal Resolution

- 	A violation of the CFL condition is most commonly manifested as numerical “noise” often followed by a model crash (Bummer).

## 3 km simulation

- 18s Timestep

- Temporal Resolution

- 9s Timestep

**Notes:**

Note lack of  difference in simulations

## Resolution Vs. Computational Speed

- The computational cost of increasing vertical resolution is less than increasing the horizontal resolution
- 2-fold increase in levels ~ 2x increase in computation time
- 2-fold decrease in horizontal grid spacing ~ 8x increase in computation time *(3-fold = 27x increase!)*
- However, the potential benefit from a decrease in the grid spacing may be much greater than an increase in vertical levels
- There is generally little value in decreasing the model timestep to increase numerical accuracy

## Hydrostatic Vs. Non-Hydrostatic

**Surface heating**

**Surface heating**

**Solar Radiation**

**Moisture Fluxes**

**Turbulence**

**Convection**

**Evaporation**

**Condensation**

**Fluxes**

**Fluxes**

**Solar Radiation**

## Hydrostatic Vs. Non-Hydrostatic

- Until recently, running an NWP model at resolutions capable of resolving non-hydrostatic phenomena was very computationally expensive
- Small scale feature => small x => small t
- Additional cost in predicting vertical motion

- Most users accepted the hydrostatic approximation

## Hydrostatic Vs. Non-Hydrostatic

- Vertical Equation of Motion

- 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

- So, when do you *need* to go non-hydrostatic?
- Traditional rational is x < 10 km
- Some have noted that NH contribution not important until x ~ 1km
- Depends upon the phenomenon of interest!
- Explicitly resolved convection with x=4 km  ~  NH
- Outflow boundary from convection with x=4 km  ~  NH
- Sea breeze circulation with x=3 km ~ HY or NH
- Gravity wave simulation with x=5 km ~ HY or NH
- Large scale baroclinic wave with x=5 km ~ HY
- Flow over topography with x=2 km ~ Depends on topography

- Cost of NH dynamics with ARW WRF ~ 5%

## Hydrostatic Vs. Non-Hydrostatic

- 100 km

- 10 km

- 1km

- 10 m/s

- x = 10 km : Hydro or NH dynamics?

- x = 1km : Hydro or NH dynamics?

- Obviously not to scale

- Probably does not make a difference since forcing is of the scale where hydrostatic dynamics dominate

- Lx (100 km) >> Lz (1 km)

**Notes:**

For both grid spacing hydrostatic dynamics is sufficient.

It’s the scale of the forcing that is important

## Hydrostatic Vs. Non-Hydrostatic

- Hydrostatic

- Non-Hydrostatic

- 3 km simulation

**Notes:**

Minor differences between Hydrostatic and NH runs

## Hydrostatic Vs. Non-Hydrostatic

- Hydrostatic

- Non-Hydrostatic

- 3 km simulation

**Notes:**

Little difference between runs

## Mesoscale Model Physics

- How are physics schemes handled in a mesoscale model?

## Mesoscale Model Physics

** In WRF ARW Core*

- Typical call order within an NWP system

- (Also possibly Turbulence, TKE, Diffusion, others)

## Atmospheric Radiation

- Typically handled by separate shortwave (solar) and longwave (terrestrial) radiation schemes

## Atmospheric Radiation

- Model radiation schemes estimate the bulk effect of all absorbers, scatterers, and reflectors of radiation to determine:
- The total amount of shortwave radiation reaching the surface
- The amount of longwave radiation emitted from the earth into space
- The amount of downward longwave radiation reemitted back towards earth from clouds
- Largest errors result from predictions and diagnosing of clouds and cloud composition
- Schemes provide atmospheric temperature tendencies within a column

## Atmospheric Radiation

- Schemes are usually 1-d (column) with assumptions valid as long as x >> z
- Radiation schemes are typically run less frequently than other physics schemes due to the computational costs
- 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

- Includes infrared radiation absorbed and emitted by gases and surfaces
- Upward radiation flux from the ground determined by surface emissivity, which is a function of
- Land-use type
- Skin Temperature and near-surface temperature gradient

## Shortwave Radiation

- Shortwave radiation schemes typically include visible and surrounding wavelengths that make up the solar spectrum

## Shortwave Radiation

- Only source of shortwave radiation is the sun
- Processes simulated within the model atmosphere and at the surface include:
- Absorption
- Reflection
- Scattering
- Upward flux is due to reflection (surface albedo)
- Atmospheric shortwave radiation responds to:
- Cloud distributions
- Water vapor distributions
- Carbon dioxide, ozone, and trace gas concentrations

## Atmosphere Radiative Processes

## Surface Physics

## Surface Layer Physics

- Surface layer schemes typically
- Calculate friction velocities and exchange coefficients for the LSM
- Calculate surface stress for the PBL scheme
- Calculate surface fluxes over water only
- Provides no tendencies to the model state variables

## Land-Surface Model

- Uses information from:
- Surface layer scheme
- Atmospheric radiation scheme
- Precipitation from cumulus and microphysics schemes (from previous timestep)
- Surface boundary information
- Outputs:
- Heat and moisture fluxes over land and sea-ice points to PBL scheme

## Surface Physics

- Vegetation Type
- Vegetation fraction
- Soil Type
- Soil moisture
- Snow and ice cover
- Water location

- Static information typically needed for surface physics schemes includes:

## Vegetation Type

- The vegetation type is necessary to simulate the effects of vegetation on surface processes
- The vegetation type in a model acts to control
- Evapotranspiration from the soil
- Surface albedo => available solar radiation
- Near surface temperature and humidity
- Soil temperature

## Vegetation Type

## Vegetation Fraction

- The vegetation fraction is the portion of the grid box that is covered by vegetation
- The vegetation fraction acts to modify
- The amount of moisture evaporation from the soil
- Surface albedo
- Available solar radiation
- Partitioning of the surface fluxes
- Surface roughness

## Vegetation Fraction

## Soil Type

- The soil type acts to modify
- The amount of moisture evaporation from the soil
- The albedo of the surface => available solar radiation
- Heat conductivity of the surface

## Soil Moisture

- The amount of soil moisture acts to modify:
- The partitioning of available surface energy into heating and evaporation of moisture
- The amount of moisture available for evapotranspiration

## Water Surfaces

- Typically handled independent of land surfaces and physics are greatly simplified

## Water Surfaces

- Some issues to remember:
- Sub-grid scale bodies of water are not well-represented in a model simulation
- Small 1-point lakes are often removed from the model domain
- Temperature data for initialization of small scale water features are often not available.

## Water Surfaces

- More issues to remember:
- Skin temperatures over water are generally fixed during forecast
- Potential problem: Water skin temperature does respond to diurnal solar cycle, which can influence:
- 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:
- Sea and lake temperature gradients (*Sweet et al., 1981*)
- Wind speeds over water (*Sweet et al., 1981*)
- Intensity of lake and sea breeze circulations (*Mizzi and Pielke, 1984*)
- Cloud cover and low level stability (*Sweet et al., 1981*)

## Snow and Ice Cover

- Some issues to remember:
- 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:
- Water points that are considered ice covered are usually treated as snow covered land points and given a predefined skin temperature value
- Small, frozen lakes may not be well-resolved within a computational domain
- 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

- Responsible for the vertical sub grid-scale mixing due to eddy transports through the entire atmospheric column
- It is during the vertical mixing process in the model that the PBL develops

## Illustration of PBL Processes

## Planetary Boundary Layer Scheme

- Surface fluxes used to drive the vertical mixing are provided by the land surface scheme
- The PBL development in the model is largely controlled by the accuracy of predicted
- Model skin temperature
- 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

- Some newer schemes explicitly handle the entrainment layer (YSU scheme)
- Vertical model diffusion is handled with the PBL scheme
- 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)
- Assumptions that justify the use of a PBL scheme begin to break down when x < 1 km.

## Cumulus Scheme

- Cumulus schemes are responsible for the sub grid-scale effects of convective and/or shallow clouds
- Intended to represent vertical fluxes due to unresolved up and downdrafts within clouds and compensating motion outside the clouds
- Schemes typically provide:
- 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 x > 10 km
- Assumptions that convective eddies are sub grid-scale break down when x < 10 km
- Some schemes may help to trigger convection 5 to 10 km
- Cumulus schemes probably should not be used for x < 5 km

## Microphysics Scheme

- 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
- Simple: diagnose precipitation from cloud water or ice only (E.g. Kessler) ~ x > 10 km
- Complex: precipitation predicted through internal cloud processes including hydrometeor types and multiple clouds (E.g. Lin) ~ x <= 10 km

## Microphysics Scheme

- Complex schemes are computationally more expensive but often provide a better forecast for grid spacing < 10 km.
- Complex schemes are often further subdivided by the number of microphysical species and whether ice and mixed-phase processes are included
- 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

## Microphysics Scheme

- For x > 10 km mixed phase schemes generally not worth the expense
- For 10km > x > 5 km mixed phase schemes may be of value
- For x < 5 km mixed phase schemes should be used

## Model Boundary Conditions

## Model Boundary Conditions

- Since a LAM domain is artificially enclosed with sides, the various “state” or “dependent” variables must be specified along the boundaries
- 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

- Lower or Bottom Boundary

- Y

- Z

- Y

- X

- Top or Upper Boundary

- 4 Lateral Boundaries

## Model Boundary Conditions

- In a LAM, the top and lateral BCs are included out of computational necessity
- The bottom or lower boundary is a *real* boundary with physical significance
- For the most part, it is impossible to specify correct values on the LAM boundaries, especially for the lateral and top boundaries
- Thus, it is critical that LAM be configured to minimize the impact

## Upper Boundary Conditions

- The primary goal of a well-specified upper boundary condition is to stop vertically propagating wave energy from reflecting back towards the surface
- 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*
- An alternative is to place the model top above a layer of deep thermodynamic stratification, such as within the stratosphere
- Assumptions are that Lz << Lx
- Vertical circulations are relatively small
-  Vertical motions are ~ 0

## Upper Boundary Conditions

- Common Upper BC formulations
- 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
- Porous model top
- Impervious lid

## Lateral Boundary Conditions

- Lateral boundary conditions are designed similar to those of the upper boundary in order to reduce reflection. Examples for idealized simulations include:
- Constant flow – Flow entering and exiting the lateral boundaries is held constant
- Zero Gradient – Values along periphery of the grid are defined such that n) – (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

- Most models used for weather simulation purposes use NWP or analysis-specified lateral boundary conditions

- LBCs are typically provided by a coarser run
- 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

**Computational Domain**

- South

- East

- West

- 1

- 2

- 3

- 4

- 5

- 5

- 4

- 3

- 2

- 1

- 5

- 4

- 3

- 2

- 1

- 5

- 4

- 3

- 2

- 1

**BCs (Qv, ********, V, U) Specified from other data source**

**BCs determined through relaxation**

** ****Inner computational domain**

## Lateral Boundary Conditions

- The benefits of specified lateral boundary conditions
- Act to constrain solution – Unlike global model
- Influence on forecast is somewhat controllable

## Lateral Boundary Conditions

- Specified lateral boundary conditions can degrade a forecast through
- Errors in spatial interpolation from external grid
- Temporal aliasing of information
- Inability to feedback information to larger scale (1-way nests)
- An incompatibility between physical-process parameterization
- Errors propagate via advection and inertial gravity wave modes

## Lower Boundary Conditions

- 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:
- 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

- 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

- Sea breeze circulation
- Topographically forced circulations

## Simple NWP experiments

- Data sets used for the initial and boundary conditions were constructed to isolate the response to the local forcing
- 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 + Zsfc

## Simple NWP experiments

- Characteristic values for vegetation and soil type were also applied uniformly over the domain
- Atmospheric moisture, as defined by RH, was set to be uniform over the entire domain
- A simple 2-layer atmospheric stability profile was constructed where the lapse rate was defined by Brunt-Väisälä frequency (N):
- N =
- Nstratosphere > Ntroposphere

## Sea Breeze Experiments

## Sea Breeze Experiments

## Sea Breeze Experiment #1

- 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

## Sea Breeze Experiment #2

- 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

- 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

## Complex Terrain Experiment

## Summary of Talk

- Introduction and mesoscale primer
- Model Resolution
- Hydrostatic Vs. Non-Hydrostatic
- Mesoscale Model Physics
- Mesoscale Model Boundary Conditions
- Simple Model Experiments

## Mesoscale Modeling

- The End