Airborne Studies of Atmospheric Dynamics

Thomas R. ParishDepartment of Atmospheric Science

University of Wyoming

Newton’s Second Law – The Equation of Motion

HHHHHH VkfpVVtV

dtVd

1

TotalDerivative

LocalDerivative

Advection(Inertia) Term

Horizontal Pressure Gradient Force

Coriolis Force

aggH VVV

Geostrophiccomponent

Ageostrophiccomponent

Geostrophic Wind

• Balanced flow state• Purely rotational (non-divergent)• Often the largest component of wind• Relatively inert component of the wind

kpf

V

Vkfp

Hg

HH

1

10

L H

Vg

P C

Ageostrophic Wind

• Unbalanced flow state• Often contains significant divergent component• Generally small component of wind• Isallobaric and inertia/advective components generally largest• Important forcing component of the wind

dtVdk

fV Hag

1

agHgH

HHH

VkfVkfVkfdtdV

VkfpdtdV

1

Measurement of Geostrophic Wind

HpH VkfzgdtVd

• Write Equation of Motion in isobaric coordinates

• Variation of height on a pressure surface proportional to horizontal pressure gradient force

• Airborne applications – use autopilot

Pre-GPS Era (before 2004)

• Radar Altimeter measurements provide height above surface• Terrain maps (digital) provide terrain height assuming

geographic position known with high accuracy• Height of isobaric surface is sum of above signals

Problems:

• Two signals (radar altimeter heights, terrain height) large and of opposite sign

• PGF is the sum of those terms, being quite small and noisy

• Potential errors in both radar altimeter height, terrain height

• “Artifact” problem for radar altimeter• Footprint issue for altimeter• Uncertainties in aircraft position estimates• Issues with terrain height data sets

Resulting uncertainty with “terrain registration”

600

700

800

900

10000 2 4 6 8 10 12 14

Wind Speed (m/s)

Pres

sure

(hPa

)

4 am

1 pm

7 am

10 pm

7 pm

1 am

Example: Great Plains Low-Level Jet• Nocturnal summertime jet maximum ~400 m agl

• Competing theories for LLJ formation• Blackadar frictional decoupling• Holton sloping terrain influence

Flight Strategy – Repeating isobaric legs

Results of PGF measurements at lowest level

Conclusions:

• Isallobaric component of wind ~4 m/s at level maximum wind

• Large changes in turbulent intensity at jet level

• Blackadar frictional decoupling dominant mechanism in forcing Great Plains LLJ

GPS Era

• Avoid “terrain registration” issues

• GPS provides a means to accurately map isobaric surface

• Position errors from standard GPS receiver insufficient to resolve isobaric slopes

• Differential GPS required• Requires fixed base station• Position errors at base station can be used to correct

position errors for rover platform (aircraft) • Importance of acceptable satellite constellation (5 or 6?)• Position accuracy on order of decimeters• Relative accuracy probably much better

GPS04 Study – Arcata CA

• Frequent summertime LLJ at top of marine boundary layer

• Comparison with altimetry-derived geostrophic wind

• Tested GrafNav differential processing software

GPS04 LLJ Example

• Isobaric east-west flight leg south of Cape Mendocino

• Nearly identical signals

• dGPS calculations of Vg from most legs within 1 m/s altimetry Vg

• GPS04 validated dGPS technique

Application of dGPS on atmospheric dynamics – Coastally Trapped Wind Reversals (CTWRs, also CTDs, southerly surges)

0000 UTC 22 June - 0000 UTC 26 June 2006

CTWR Forcing Issues• Kelvin Wave

• Cross-coast PGF• Variations in MBL Height

• Topographic Rossby Wave

• Topographically-Trapped Wave

• Density Current

• Synoptic-scale response• Ageostrophic acceleration• Importance of synoptic-scale pressure field

23 June 2006 Example

• Isobaric east-west flight leg

• Little detectable cross-coast PGF

23 June 2006 Example

23 June 2006 Example

23 June 2006 Example

24 June 2006 Example

24 June 2006 Example

23-25 June 2006 CTWR Conclusions

• CTWR density current

• No Kelvin-wave features observed during this event

• Active propagation phase highly ageostrophic

• Little detectable cross-coast PGF at any time during the life history

• Onset and propagation dependent on synoptic pressure field

Application: CloudGPS08

• May-June 2008, flights over high plains WY, NE, CO

• Measure horizontal perturbation pressures associated with clouds

• Clouds mostly in cumulus congestus phase

• Differential GPS dependent on accurate measurement of static pressure

Application: CloudGPS08 (May 21)

Liquid Water Content (g/kg)

Isobaric Height

W (m/s) u

v

Horizontal Pressure Perturbation (mb)

θV

Liquid Water Content (g/kg)

W (m/s)

Horizontal Pressure Perturbation (mb)

Application: CloudGPS08 (June 17)

Leg 1Liquid Water Content (g/kg)

W (m/s)

Horizontal Pressure Perturbation (mb)

u

v

θV

Isobaric Height

Leg 2Liquid Water Content (g/kg)

W (m/s)

Horizontal Pressure Perturbation (mb)

u

v

θV

Isobaric Height

Leg 3Liquid Water Content (g/kg)

W (m/s)

Horizontal Pressure Perturbation (mb)

u

v

θV

Isobaric Height

Leg 4Liquid Water Content (g/kg)

W (m/s)

Horizontal Pressure Perturbation (mb)

u

v

θV

Isobaric Height

Leg 5Liquid Water Content (g/kg)

W (m/s)

Horizontal Pressure Perturbation (mb)

u

v

θV

Isobaric Height

Leg 1

Leg 2

Leg 3

Leg 4

Leg 5

Application: Ocean Surface Topography

• Differences between GPS height, radar altimeter signal measure of ocean surface topography

Application: Ocean Surface Topography

• Reciprocal legs along 40.8°N

• Consistent pattern of height differences

• Validate using multiple altimeters?

• Gulf Stream flights?

Application: Ocean Surface Topography

• Reciprocal legs along 40.8°N

• Consistent pattern of height differences

• Validate using multiple altimeters?

• Gulf Stream flights?

Application: Ocean Surface Topography

Conclusions

• dGPS can provide precise mapping of aircraft height• Base station data rate 1 Hz• Baseline ~ 100 km?

• dGPS accuracy within decimeters?

• Relative accuracy higher?

• Accurate measurement of static pressure permits PGF calculations

• Assessment of atmospheric dynamics for a wide variety of flows

Thanks to Dave Leon, Larry Oolman, Dave Rahn and Eric Parish