1. Introduction to Mesoscale Meteorology

2. Defining the Scales of Atmospheric Science
Scale Definitions
Synoptic
Synoptic derived from Greek “synoptikos” meaning general view of the whole. Also has grown to imply “at the same time” or “simultaneous”.
Synoptic Scale
The scales of fronts and cyclones studied by the early Norwegian scientists. The classic synoptic scale are the time and space scales resolved by observations taken at major European cities having a mean spacing of about 100 km. Hence weather systems having scales of a few hundred kilometers or more and time scales of a few days are generally what is accepted to be “synoptic scale” phenomena.

3. Overview Scale Definitions Cumulus
Defined by the rise of RADAR meteorology in the late 1940’s to be the scale of individual thunderstorm and cumulus cell echos, this became the second important scale of meteorology research. This scale is on the order of a couple of kilometers to about 50 km and time scales of a few minutes to several hours.

4. Overview Scale Definitions Mesoscale (original definition)
Coined by Lidga (1951), mesoscales are the “Middle Scales” between synoptic scale and cumulus scale. This original definition hence refered to weather phenomena of scales between what were thought to be the two primary energy containing scales of cumulus and synoptic scale. The Modern Definition is much more robust.

5. Overview Scale Definitions Mesoscale (modern definition)
Orlanski (1975) proposed a new set of scales (ignoring synoptic and cumulus) that include the micro-, meso- and macro- scales. Figure 1 depicts these three definitions. All three definitions have gained wide acceptance, despite an even newer proposal by Fugita (1981). His definition of the “mesoscale” was scales between 2 km and 2000 km. Scales larger than 2000 km are “macroscale” and scales smaller than 2 km are “microscale”

6. Mesoscale Over The Years

8. Overview Scale Definitions Mesoscale (modern definition, continued)
Orlanski divides the “mesoscale” into three “sub-mesoscales”:
Meso- : 2-20 km
Meso- : km
Meso- : km
We will attach a physical significance to these three mesoscales.

9. Force Balance Inertial Balance _________________________ | |
Rotation
Hydrostatic Balances
Irrotational

10. Equations of Motion (Boussinesq Form) a=F/m
Force 1:
Pressure Gradient
Force 2: Buoyancy |
Advection
Coriolis

11. Force Balance Form Balance Equation|

12. Force Balance Balances or primary drivers depend on what the dominant frequencies are|

13. Physical Significance of Mesoscale
Two Major Categories of Dynamic Force Balances Result
Hydrostatic: Gravity versus Pressure Gradient
Inertial: Inertial Force Versus Gravity
Geostrophic (Horizontal Pressure Gradient versus vertical Coriolis effect)
Cyclostrophic (Pressure Gradient versus rotational and irrotational inertial)
Gradient (Horizontal Pressure gradient versus all inertial)

14. Perturbations from Balance
For stable balance, i.e. stability restores balance, perturbations initiate oscillations that result in waves
For unstable balance, perturbations produce a growing disturbance

15. Perturbations from Hydrostatic Balance
Perturbations from stable balance lead to:
Gravity or Buoyancy waves
Horizontal phase speed is
Perturbations from unstable balance lead to:
Convection

16. Perturbations from Geostrophic Balance
Stable Balance Produces
Oscillation frequency is f
Wave speed is on order of :
Unstable Balance produces:
Inertial Instability

17. If both hydrostatic and inertial balances occur and the flow is perturbed,what is the result?
Depends on which adjustment dominates.
Determine dominant adjustment from ratio of gravity wave phase speed to inertial wave phase speed:

18. The Rossby Radius of Deformation
Scale at Which There is Equal Inertial and Gravity Wave Response
The definition of Rossby Radius (disregarding inertia of the flow) is:

19. Taking into Account Inertia of the Flow Rossby Radius for axi-symmetric vortex having tangential wind “V” and Radius “R”

20. Scale Based on Physical Mechanism
Small Scales
Frequency of gravity waves, ie Brunt-Visalia Frequency, larger than frequency of inertial waves
Tendency toward hydrostatic balance with “g” dominate
Large Scales
Frequency of inertial wave involving Coriolis larger than gravity wave
Balance against inertial acceleration dominates

21. But Wait! What is a Rossby wave?
A wind (inertial) anomaly in balance with mass field
Variation of Coriolis effect creates asymmetric advection of the balanced inertial wave causing it to propagate westward relative to the flow
A Rossby wave can exist only when there is an inertial/mass balance
The beta (Rossby) effect can occur with large gravity waves, such as tropical mixed Rossby-gravity waves, that do not maintain a balance with the mass field

22. Back to Mesoscale Definitions
At middle latitudes (40 N) :
For a disturbance depth of 7 km:
Hence Rossby radius is typically:

23. Equatorially trapped Kelvin waves
Mixed Rossby-gravity waves
Extratropical cyclone
Planetary waves
Squall lines
Downslope wind storm
MCSs
Tropical cyclone
Inertial turbulence
supercells
tornadoes

24. Scales from 2-20 km
Disturbances characterized by Gravity (Buoyancy) Waves (stable) or Deep Convection (unstable).
Coriolis effect generally negligible, although local inertial effects can arise to change character of disturbances (i.e. rotating thunderstorms, tornadoes, dust devils, etc)

25. Actinae

26. Bounadry Layer Convection

27. Thunderstorm

28. Thunderstorms

29. Supercells

30. Tornado

31. Scales of km
Less than but near to Rossby Radius
Gravity (Buoyancy) Waves govern system evolution and propagate relative to the wind
Inertial oscillation important to wave dynamics, i.e. Gravity-Inertia Waves

32. Sea Breeze Convection

33. Sea Breeze Convection

34. Meso-beta squall lines

36. Scales of km
Scales greater than but near to Rossby Radius of deformation
Characterized by Geostrophic Balance
Geostrophic disturbance determines evolution of the system
Vertical ageostrophic motions driven by geostrophic disturbance, ie quasi-geostrophic dynamics

37. Squall Line

38. MCC

39. MCC

40. ITCZ Cluster

41. Tropical Cyclone

42. Exceptions to these rules
These above rules are an approximate description of how the three mesoscales divide typical disturbances.
As we move to lower latitudes Coriolis effect decreases and the Rossby Radius scale increases, going to infinity at the equator! Hence relative to the Earth’s inertial effect, all disturbances around the equator are dynamically small, and are governed by gravity (buoyancy) waves. Hence, the Kelvin wave, a gravity type wave, is a global scale equatorial disturbance

43. Deeper disturbances lead to larger gravity wave phase speeds and so larger Rossby Radius and vise versa for shallow disturbances. Hence depth of the disturbance will affect its governing dynamics, the deeper disturbance less likely to be inertially balanced and the shallower disturbances more likely. Some examples:
Sea Breeze without deep convection: shallow, likely to achieve significant geostrophic balance
Sea Breeze with Deep convection: Deep, not likely to achieve inertial balance
Mesoscale Convective Complex: Deep convection parts of the system clearly less than Rossby Radius. Stratiform anvil has large horizontal scale shallow melting layer that may excite inertially balanced disturbance, ie an MCV (mesoscale convective vortex).

44. Rotation induced in the system may locally shrink the Rossby Radius, making the system dynamically large even on meso-beta scales. For example:
Mesocyclone or rotating thunderstorm with its forward flanking gust front and rear flanking gust fronts actually become quasi balanced and evolve very similar to a developing quasi-geostrophic baroclinic cyclone with warm and cold fronts respectively. This makes the supercell thunderstorm long lived.
The tropical cyclone eye wall becomes inertially stable from the strong storm rotation giving rise to Rossby wave disturbances (relative to cyclone rotation instead of Coriolis) that move around the eye, and play significant roles in horizontal momenum transport through their tilt!
Tornadoes survive relatively long periods for their size because of their inertial balance and locally vey small Rossby Radius of Deformation.

45. Special Observation and Analysis Problems of the Mesoscale
Synoptic observation systems have horizontal resolutions of 100 km and 1 hour at the surface and 400 km and 12 hours aloft and are clearly inadequate to capture all but the upper end of the meso
The dynamics of mesoscale disturbances contain important non-balanced or transient features that propagate rapidly.
The systems are highly three-dimensional where the vertical structure is equally important to the horizontal structure.

46. Mesoscale disturbances are more likely to be a hybrid of several dynamic entities interacting together to maintain the system.
Process Interaction is especially significant such as microphysical and radiative transfer interactions.
Scale Interactions are basic to the mesoscale problem and particularly interactions across the Rossby Radius of Deformation

47. Implications of Scale Interaction
Larger scales have long lifecycles and smaller scales have short lifecycles
Larger scales may go through 1 or less life cycles during a periods of interest while smallest scales may go through 10’s or 100’s of lifecycles
Small scales tend to be probabilistic rather than deterministic
Larger scales are sometimes deterministic (if not dependent on small scales)

48. Prediction of Probabilistic vs Deterministic Phenomena
An initial Value problem
Mostly linear exrtrapolation of initial condition
Non chaotic solution
Probabilistic
Chaotic , non-linear
Solution Basins
Solutions constrained by physical constraints
Entropy, energy conservation
Momentum, mass conservation
Potential vorticity consewrvation

49. How Can we Deal with This?
Use observations as clues to the analysis, and do not expect the data to ever be sufficient to reveal the process behind the observations.
Attach a strong dynamical model to the observations to fill in the gaps (assimilation). To the extent that the model reproduces the observations at points where it is coincident with the observations, it gains credibility.
Study the model to understand the dynamics. If the model is consistent with the few observations, then the model can be used (always with caution) to reveal the dynamics of the system.

50. What is a Model? Models range from simple to complex.
Simple model: Quasi-Geostrophic model: positive vorticity advection results in upward vertical motion. Its so simple we can do it in our heads! But it has many approximations and is likely to miss features that can be represented in more complex models.

51. Primitive Equation Forecast Model: Such as the NAM model, or GFS model or ECMWF model. Must be solved on the computer but much more precise than the simple PVA model. Why would anyone look at a 500mb map predicted by the GFS model and then disagree with its vertical motion pattern because it doesn‘t obey the mentally tractable PVA model?

52. Research Models: More precise physics, too big to execute in real time but able to provide a deeper understanding of specific processes causing an observed event.
Research Data Sets: Incorporate supplementary data during an Intensive Observation Period (IOP) in a field program setting
Compare to local model prediction
Assimilate the data to improve model simulation/forecast

53. What Makes a Good Mesoscale Model?
Handle deterministic part of forecast competently
Treat the probabilistic part competently