The Relationship Between Atmospheric Boundary Layer Structure and Refractivity Robert E. Marshall, PhD Atmospheric Scientist / RF Engineer NSWCDD Q32 10 March 2011 Distribu(on Statement A: Approved for public release; distribu(on is unlimited.
Dr. Robert E. Marshall, Q32 - Radio Frequency Engineer - Meteorologist Our Team 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 2
Our R&D Structure 3
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 10 3 deficits on applicable radio frequency engineering solutions 4
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. sin sin n θ 1 θ 2 = n n 2 1 index of refraction Snells Law θ 1 n 1 n 2 θ 2 5
Index of Refraction n v ε r µ r index of refraction = relative permittivity relative permeability c n = v c speed of ε r light in a vacumm phase speed in the medium µ r Distribution Statement A: Approved for public release, distribution is unlimited. 6
Refractivity n 1.000300 in the atmosphere N refractivity N = ( n N p 1)10 6 77.6 4810e = P + T T atmospheric pressure (mb) T atmospheric temperature (K) e vapor pressure (mb) 7
R Refractivity and Boundary Layer Structure Modified Refractivity M modified refractivity N + an earth curvature term M = N + R 10 z height above the surface e z radius of the earth M = N + 0.157z e 6 8
The vertical gradient of modified refractivity defines the radio frequency refraction regime. 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. 9
10 z T e P T M 157 0. 4810 77.6 + + = temperature (K) potential ) water vapor mixing ratio (kg kg 0.157 0.286 0.622 4810 0 286 77 6-1 1000 1000 + + = θ θ w z wp P. θ. M p p = p T 1000 286 0. θ = p e e p e w 622 0. 0.622 Introduce the Conserved Variables
dm = + dp 1.336X 10 7 w + 2 0.572 p θ dw 3.106X 10 7 θ 2 P dθ 6.212X 10 7 w 3 θ + 0.157 m 1 θ 399.54 0.286 0.428 p p 0.428 + 559.6 The Vertical Gradient θ 0.714 2 p 11
Well Mixed Layer dθ = dw = 0 dm = dp 1.336X10 7 w 2 0.572 p θ + 3.995X10 2 0.286 θ p + 0.157 12
Well Mixed Layer 13
dm 0.128 + dw 5.97 X10 5 T 2 p dθ p 1.286 T 3 [ ] 2.57 X10 5 w+ 10.76T 14
dm dw 0.128+ c 1 c 2 dθ 15
dm dw 0.128+ c 1 c 2 dθ 16
Stable Internal Boundary Layers (SIBL) Offshore Flow of Warm and Drier Air over a Colder Sea Surface dm dw 0.128+ c 1 c 2 dθ SIBLs eventually advect into well mixed layers a distance (d) Offshore. 17
Evolution of stable internal boundary layers over a cold sea Smedman, Bergstrom, Grisogono, Journal of Geophysical Research, January, 1997 Δθ θ r velocity Δ θ 5625V d f θ r d offshore distance to mixed layer V f Coriolis parameter 10 4 potential temperature difference acrosssibl surfacepotential temperature 2 18
v On the formation of a stably stratified internal boundary layer by advection of warm air over a cooler sea Mulhearn, Boundary Layer, Meteorology, 1981 h 0.0146x h height of SIBL x offshore θ 1 T T T 0 wind speed land s1 r SST distance surface land surface gx ( θ1 T 2 v T r potential averagesibl temperature 0 ) ( T 0.1 temperature s1 T T potential dewpoint temperature r 0 ) 0.47 19
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 20
Measured data off Wallops Island Surface duct Offshore flow of warm air over cooler ocean dm dw 0.128+ c 1 c 2 dθ Distribution Statement A: Approved M for public release: distribution is unlimited. 21
Stable Internal Boundary Layers COAMPS profiles every 100km from A to B w d / > 0, warmer air advecting up and over colder air at the sea surface dm c c2 0.128 dθ + 1 dw dw/ < 0, drier air advecting up and over saturated air at the sea surface M dm/ < 0, advection ducts, bi-linear ducts, or surface ducts 1100UTC on 14 May, 2009 Advection ducts can extend hundreds of km offshore 22
Height (m, ASL) 500 450 400 350 300 250 200 150 100 50 0 Refractivity and Boundary Layer Structure 286 288 290 292 294 296 298 300 302 304 Potential Temperature (K) Height (m, ASL) 500 450 400 350 300 250 200 150 100 50 Entrainment Layers dm Modified Refractivity Standard Free Atmosphere Entrainment Layer Mixed Layer dw 0.128+ c 1 Height (meter, ASL) dθ 500 450 400 350 300 250 200 150 100 0 315 320 325 330 335 340 345 350 355 360 365 Modified Refractivity c 2 50 0 0.000 0.002 0.004 0.006 0.008 0.010 w Water Vapor Mixing Ratio (kgkg -1 ) Free Atmosphere Entrainment Layer Mixed Layer ELT 23
Sea Breeze Circulations Well mixed layer up to 400m, ASL 50m deep entrainment layer d / > 0 in the stable entrainment layer Dry tongue above the entrainment layer dw/ < 0 enhanced by dry tongue dm/ < 0 in the entrainment layer Sub-refractive layer above entrainment layer Entrainment layers are breeding grounds for radio frequency ducts 24
Sea Breeze Circulations Bay of CA 2000UTC 28 June 2005 Bay of CA 2000UTC 28 June 2005 Bay of CA 2000UTC 28 June 2005 COAMPS modeling Well mixed layer up to 80m, ASL 80m deep entrainment layer d / > 0 in the stable entrainment layer Dry tongue above the entrainment layer dw/ < 0 enhanced by dry tongue dm/ < 0 in the entrainment layer Sub-refraction above the entrainment layer 25
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 26
Engineering Significance of Refractivity P P r t G 2 λ 2 σ π 3 4 ( 4 ) R 4 = F Two way propagation factor in the Radar equation P P r t = G G λ 2 T R ( 4πR) F 2 2 One way propagation factor in the Communications link equation Propagation factor due to non standard refraction 0dB in free space F 2 potentially greater than +/- 30dB in real near surface atmospheres 27
Refractivity and Boundary Layer Structure Engineering Significance of Refractivity Standard Atmosphere (multipath nulls) Strong Ducting 28
Engineering Significance of Refractivity 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 29
Engineering Significance of Refractivity S band notional radar in the Persian Gulf 1100UTC, 14 May 2009 (validated refractivity field) Energy escapes the duct as critical angle ( c ) decreases with range 310 deg 150km Critical angle ( c ) increases with duct strength ( M) 30
Engineering Significance of Sub-refraction Wallops Synoptic Sounding Comparison EDAS 15 APR 2006 Place a ship based radar In Chesapeake Bay Sub-refraction creates expensive engineering demands 31
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. 32