The Relationship Between Atmospheric Boundary Layer Structure …seminar/data/y11spring/umd... · 2011-03-10 · Refraction Distribution Statement A: Approved for public release:

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The Relationship Between Atmospheric Boundary Layer Structure and Refractivity

Robert E. Marshall, PhD Atmospheric Scientist / RF Engineer

NSWCDD Q32 10 March 2011

Refractivity and Boundary Layer Structure

2 Distribution Statement A: Approved for public release: distribution is unlimited.

Our Team •  Dr. Robert E. Marshall, Q32 - Radio Frequency Engineer - Meteorologist

•  Victor Wiss, Q32

- Radio Frequency Engineer - Meteorological Measurements Engineer

•  Katherine Horgan, Q32

- Mesoscale and Numerical Weather Prediction Meteorologist - Meteorological Instrumentation Technician

•  Isha Renta, Q32

- Mesoscale and Numerical Weather Prediction Meteorologist - Radio Frequency Propagation Analyst

•  William Thornton, Q32

- Computer Programmer - Radio Frequency Propagation Analyst



Our R&D Structure


Refraction


  Atmospheric refraction bends radio frequency energy away from intended destinations.   The direction of refraction is dependent on the vertical thermodynamic structure of the atmospheric boundary layer.

- surface layers - mixing layers - internal boundary layers - entrainment layers

  Within 100km of the coast, mesoscale circulations can produce significant refraction   Refraction can introduce 103 deficits on applicable radio frequency engineering solutions


Snells Law


n1

n2

refraction ofindex sinsin

1

2

2

1

≡

=

nnn

θθ

θ 1

θ 2

Dutch scientist Willebrørd Snell (1591–1626), who first stated the law in a manuscript in 1621. In French, however, the same law is often called “la loi de Descartes” because it was René Descartes (1596–1650) who first put the law into widespread circulation in his Discourse on Method, published in 1637.


6 Distribution Statement A: Approved for public release, distribution is unlimited.

medium thein speed phaseva vacumm inlight of speed

typermeabili relative

typermittivi relative

refraction ofindex

≡≡

=

≡

≡

=≡

cvcn

n

r

r

rr

µε

µε

Index of Refraction



(mb) pressurevapor (K) re temperatucatmospheri

(mb) pressure catmospheri

48106.7710)1(

ty refractiviatmosphere in the 000300.1

6

≡≡≡

⎟⎠⎞⎜

⎝⎛ +⎟⎠⎞⎜

⎝⎛=

−=≡≈

eTp

TeP

TN

nNNn

Refractivity



Modified Refractivity

0.157zearth theof radiusR

surface theaboveheight

10R

termcurvatureearth an tyrefractivi modified

e

6

e

+=≡

≡

+=

+≡

NM

z

zNM

NM



Standard: Short lived in the littorals. Radar energy gently curves away from earth curvature. Super-refraction: Radar energy follows the curvature of the earth. Extended radar horizon and folded land clutter. Trapping: Radar energy trapped in a shallow duct formed by the sea surface and a positive vertical gradient of refractivity above the surface. Extended and separated areas of sea clutter. Sub-refraction: Radar energy abruptly curves away from earth curvature. Ameliorating engineering costs are very high.

The vertical gradient of modified refractivity defines the radio frequency refraction regime.



zTeP

TM 157.048106.77 +⎟

⎠⎞⎜

⎝⎛ +⎟⎠⎞⎜

⎝⎛=

(K) re temperatupotential)kg (kg ratio mixingr water vapo

157.0286.0622.0

4810

2860677

1-

10001000

≡≡

+

⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

+

⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

=

⎥⎦⎤

⎢⎣⎡

⎥⎦⎤

⎢⎣⎡

θ

θ

w

z

wP

P.

θ

.Mpp

⎟⎠⎞⎜

⎝⎛

=p

T1000

286.0

θ⎟⎟⎠

⎞⎜⎜⎝

⎛≈⎟⎟⎠

⎞⎜⎜⎝

⎛−

=pe

epew 622.0622.0

Introduce the Conserved Variables



1157.0

2

714.06.5593

428.0107212.6

2

428.0107106.3

286.054.399

572.02107336.1

−+

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+−

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+=

m

wXdzd

Xdzdw

wXdzdp

dzdM

pp

P

pp

θθ

θ

θθ

θ

The Vertical Gradient



157.0286.0

210995.3572.02

710336.1

0

+⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+=

==

ppXwX

dzdp

dzdM

dzdw

dzd

θθ

θ

Well Mixed Layer



Well Mixed Layer



[ ]⎟⎟⎠⎞

⎜⎜⎝

⎛+

≈

−

⎟⎟

⎠

⎞⎜⎜

⎝

⎛+

TwTp

dzd

Tp

dzdw

dzdM

X

X

76.1010557.23

286.1

2

51097.5

128.0

θ



dzd

cdzdwcdz

dM θ21

128.0 −+≈



dzd

cdzdwcdz

dM θ21

128.0 −+≈



dzd

dzdw

dzdM cc θ

21128.0 −+≈

SIBLs eventually advect into well mixed layers a distance (d)

Offshore.

Stable Internal Boundary Layers (SIBL) Offshore Flow of Warm and Drier Air over a Colder Sea Surface



Evolution of stable internal boundary layers over a cold sea Smedman, Bergstrom, Grisogono, Journal of Geophysical Research, January, 1997

etemperaturpotentialsurfaceSIBLacrossdifferenceetemperaturpotential

parameterCoriolis

velocitylayermixedtodistanceoffshore

5625

10 4

2

≡≡Δ

≈≡

≡≡

≈

−

⎟⎠⎞⎜

⎝⎛ Δ

θ

θθ

θ

r

f

Vd

rfVd



On the formation of a stably stratified internal boundary layer by advection of warm air over a cooler sea Mulhearn, Boundary Layer, Meteorology, 1981

re temperatuSIBL average

emperaturedewpoint t potential surface land

SST

ure temperatpotential surface landspeed windv

distance offshorexSIBL ofheight

01012

0146.0

1

0

1

47.0

)(1.0)(

≡

≡

≡

≡≡≡≡

≈ ⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦⎤

⎢⎣⎡ −

−−

−

TTT

TTT

TT

vgx

r

s

hr

s

rxh

θ

θ



On the formation of a stably stratified internal boundary layer by advection of warm air over a cooler sea Mulhearn, Boundary Layer, Meteorology, 1981

SIBL Height is Duct Height


21 Distribution Statement A: Approved for public release: distribution is unlimited. M

Measured data off Wallops Island Offshore flow of warm air over cooler ocean

dzd

dzdw

dzdM cc θ

21128.0 −+≈

Surface duct



Stable Internal Boundary Layers

1100UTC on 14 May, 2009

dzdw

dzd

dzdM cc 21128.0 +−≈ θ

q w

M

  COAMPS® profiles every 100km from A to B   dq/dz > 0, warmer air advecting up and over colder air at the sea surface   dw/dz < 0, drier air advecting up and over saturated air at the sea surface   dM/dz < 0, advection ducts, bi-linear ducts, or surface ducts   Advection ducts can extend hundreds of km offshore



Entrainment Layers

050100150200250300350400450500

286 288 290 292 294 296 298 300 302 304

Potential Temperature (K)

Hei

ght (

m, A

SL)

0

50

100

150

200

250

300

350

400

450

500

0.000 0.002 0.004 0.006 0.008 0.010

Water Vapor Mixing Ratio (kgkg-1)

Heig

ht (m

eter

, ASL

)

050100150200250300350400450500

315 320 325 330 335 340 345 350 355 360 365Modified Refractivity

Hei

ght (

m, A

SL)

Modified Refractivity

Standard

Entrainment Layer

Entrainment Layer ELT

Free Atmosphere

Free Atmosphere

Mixed Layer

Mixed Layer

dzd

dzdw

dzdM cc θ

21128.0 −+≈q w



Sea Breeze Circulations

  Well mixed layer up to 400m, ASL   50m deep entrainment layer   dq/dz > 0 in the stable entrainment layer   Dry tongue above the entrainment layer   dw/dz < 0 enhanced by dry tongue   dM/dz < 0 in the entrainment layer   Sub-refractive layer above entrainment layer   Entrainment layers are breeding grounds for radio frequency ducts



Sea Breeze Circulations

  COAMPS ® modeling   Well mixed layer up to 80m, ASL   80m deep entrainment layer   dq/dz > 0 in the stable entrainment layer   Dry tongue above the entrainment layer   dw/dz < 0 enhanced by dry tongue   dM/dz < 0 in the entrainment layer   Sub-refraction above the entrainment layer

Bay of CA 2000UTC

28 June 2005

Bay of CA 2000UTC

28 June 2005

Bay of CA 2000UTC

28 June 2005



Surface Layer

  Surface Layer Model (Evaporation Duct Model) - atmospheric surface layer turbulence model for a thermally stratified layer - based on Monin-Obukhov similarity theory - assumes horizontal homogeneity of thermodynamic and wind variables - predicts the vertical profiles of wind speed, pressure, temperature, moisture and modified refractivity from the sea surface to the top of the atmospheric surface layer



Engineering Significance of Refractivity

( )

( ) FRGG

PP

FR

GPP

RT

t

r

t

r

22

2

4

43

22

4

4

πλ

πλ σ

=

= Two way propagation factor in the Radar equation One way propagation factor in the Communications link equation

• Propagation factor due to non standard refraction • 0dB in free space • F2 potentially greater than +/- 30dB in real near surface atmospheres




Standard Atmosphere (multipath nulls) Strong Ducting




150km 150km

150km

Notional S-band radar detection areas in white of a notional target at 100m ASL. The image on the left is an AREPS model in a standard atmosphere. The image on the right is a COAMPS®/AREPS model for 1100UTC on

14 May 2009




150km

S band notional radar in the Persian Gulf 1100UTC, 14 May 2009 (validated refractivity field)

310 deg

•  Energy escapes the duct as critical angle (ac) decreases with range

•  Critical angle (ac) increases with duct strength (DM)



Engineering Significance of Sub-refraction

EDAS 15 APR 2006 Place a ship based radar

In Chesapeake Bay

Wallops Synoptic Sounding Comparison

Sub-refraction creates expensive

engineering demands



Summary

  Refractivity in the PBL can significantly influence radio frequency

system performance.

  Refractivity is directly related to PBL thermodynamic structure.

  Mesoscale NWP has become a powerful tool for understanding the

four dimensional engineering demands placed on radio frequency

systems at specific locations.

  The potential exists for a 0 to 72 hour globally locatable radio

frequency system performance tool.

The Relationship Between Atmospheric Boundary Layer Structure …seminar/data/y11spring/umd... · 2011-03-10 · Refraction Distribution Statement A: Approved for public release:

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