1. The Subtropical Sea Breeze
John W. Nielsen-Gammon
Texas A&M University

2. Outline Preconceptions Observations Rotunno (1983) Theory
Niino (1987) Theory
Reconciling with Observations
Modeling Implications

3. Preconceptions
At what time of day (local standard time) does the sea breeze attain maximum strength?
00 LST (midnight) 12 LST (noon) Need more
03 LST 15 LST info
06 LST (sunrise) 18 LST (sunset) Don’t know
09 LST 21 LST

4. Land/Sea Breeze, Israel Coast
Peak sea breeze: 5 PM
SEA
LAND
Source:
Newman,
1977, JAS
Latitude: 31.6 N
Peak land breeze: 5 AM

5. Standard Conceptual Model
from Hsu 1970 MWR

6. Observations Coordinate definitions: u: along-coast, land to left
v: toward land

7. Surface Stations

8. SRST2: C-MAN platform, Sabine, Texas

9. SRST2 ubar,vbar (yellow, cyan); u’, v’ (blue, violet): August 2000

10. 42002, August 2000

11. Sea Breeze
Land Breeze
Sunset
Midnight
Sunrise
Midday
Sunset

17. Rotunno (1983) Linear theory Horizontal scale of sea breeze
Dependence on f

18. The Coriolis Force Caused by Earth’s rotation
Accelerates air parcels to the right (in NH) of their current motion
Force proportional to velocity
If no other forces, parcel will trace a complete circle
Force stronger (& circle faster) at high lats

19. Equations of Motion Linear, hydrostatic, boussinesq
ut – f v = - px + Fx
vt + f u = + Fy
wt – b = -pz + Fz
bt + N2 w = Q
ux + wz = 0

20. Reduce to one equation for the two-dimensional streamfunction:
N2 yxx + yzztt + f2 yzz = - Qx
Assume e-iwt time dependence:
N2 yxx + (f2 – w2) yzz = - Qx

21. N2 yxx + (f2 – w2) yzz = - Qx Elliptic if (f2 – w2) > 0
Latitudes greater than 30o
Solution decays with distance from forcing
Aspect ratio L = NH/ (f2 – w2)1/2

22. Rotunno model: imposed heating-2 2
Sea
Land

23. Streamfunction at midday: high latitudes [(f2 – w2) > 0]

24. N2 yxx + (f2 – w2) yzz = - Qx
Hyperbolic (wavelike solutions) if (f2 – w2) < 0 – within 30o of equator

25. Streamfunction at dawn: low latitudes [(f2 – w2) < 0]

26. Streamfunction at midday: low latitudes [(f2 – w2) < 0]

27. Streamfunction at sunset: low latitudes [(f2 – w2) < 0]

28. Why the difference? Role of f as damping at high latitudes
Undamped oscillations at low latitudes

29. Magic Latitudes (f2 – w2)1/2 is normally of order 7x10-5
For typical H and N, L = 150 km
At 30+/- 1 degrees, (f2 – w2)1/2 is of order 2x10-5
For typical H and N, L = 500 km

30. Phase relationships Inviscid case north of 30: In phase with heating
Inviscid case south of 30: Out of phase with heating
Add viscosity: In quadrature with heating

31. Phase relationships Time of strongest sea breeze Increasing friction 
midnight
Time of strongest
sea breeze
sunset
Low latitudes
High latitudes
midday
Increasing friction 

32. Niino (1987) Heating produced by vertical diffusion
Prandtl number unity
All vertical diffusion terms remain at leading order
Really ugly equation

33. Niino (1987) {(d/dt – k d2/dz2) * [(d/dt – n d2/dz2)2 + f2]} d2b/dz2 +
N2(d/dt – n d2/dz2) d2b/dx2 = 0
n=momentum diff., k = heat diff.
(reduces to Rotunno if k = n = 0)

34. Niino (1987) Vertical scale: (k/w)1/2
Horizontal scale: N/w (k/w)1/2 F(f)
F(f) ranges from 0.7 (high latitudes) to 2.2 (low latitudes)

35. Niino with friction: maximum onshore wind
High latitude
Equator
30 North

36. Niino without friction: maximum onshore wind
0 North
29.7 North
15 North
50 North

37. Compromise (2000) Theory Viscosity matters in neutral boundary layer
Viscosity important over land, not water
Internal inertia-gravity waves extending to sea
Seaward scale much larger than landward scale

39. Summary
Observations show sea-breeze-like oscillations extending well into Gulf of Mexico
Observations show wavelike wind oscillations above the boundary layer over land

40. Summary (continued)
Inviscid theory predicts large horizontal extent near 30o
Viscous theory predicts limited (100 km) horizontal extent everywhere
Compromise theory:
Viscous wavemaker over land
Nearly inviscid waves over water

41. Implications for Atmosphere
Enhanced heat/moisture fluxes over water
Diurnally-dependent transport over Gulf
Layered diurnal dispersion of plumes over land
Away from sea breeze front, “simple” oscillatory behavior

42. Implications for Air Quality Modeling
Model must resolve freely-propagating waves within and above the boundary layer
Vertical grid spacing?
Horizontal grid boundaries?
Spinup time?

43. Future Directions Horizontal structure with profiler data
Time-dependent viscosity over land
Full MM5 simulation of sea breeze
PBL parameterization?
Vertical resolution?
Role of basin shape?

44. Acknowledgments
Supported by the state of Texas through the Texas Air Research Center (but what I said is not necessarily what they would say)
Profiler data: Dick McNider
Buoy data: National Oceanographic and Atmospheric Administration