Suggestions for Now casting of
the optical environment
Ove Gustafsson, FOI
[email protected]
Abstract
The use of optical och electro-optical system within society both the
military part and the civil society are expanding continuously. The
environmental influence on the optical signals are evinced as reduction of
the signal and turbulence disturbance, with data loss, enlarged nominal
optical hazard distances (NOHD) and disturbed images as consequences.
The signal reduction due to absorption and scattering for active and
passive system can be deduced out of weather parameters as humidity,
temperature, wind, visual range etc. The important of the influence on
atmospheric attenuation and optical turbulence on laser propagation and
images as function of weather parameters as for instance the structure
parameter of refractive index will be discussed. With the use of mesoscale
numerical weather prediction methods there are also possibilities to
deduce for instance the structure parameter for refractive index (Cn2) as
function of heights.
Introduction
Lidar measurement
Nominal Ocular Hazard Distance, NOHD
Atmospheric influence on NOHD  OHD
Examples of effects due to turbulence
Turbulence influence on laser safety range
Structurfunction of refraction, Cn2
Cloud characterization
Discussion and conclusions
Lidar instrument
Receiver:
APD module diam. 1 mm
(Licel S11518-10)
focal length of 615 mm
FOV of 1.6 mrad
filter FWHM 12 nm
Licel TR40:
sample rate 40 MHz
Laser:
230 mJ,
1064 nm,
pulse length 5 ns,
PRF 10 Hz,
beam divergence 0.5 mrad
beam diameter 3 mm
IR-lidar measurement and comparison
Lidarsondering 2014-09-10 (lokal tid) kl 10:28:42 - 10:33:45
Hm: 6975 Su: 50, H1: 2000, Sm: 50, H2: 10000, So: 50, ak: 8/100
Lidar sounding 2015-03-09 (local time) 15:30 - 16:00
9000
10000
1.064 µm
355 nm
9000
8000
7000
Altitude [m asl] (resolution 75 m)
Altitude [m asl] (resolution 75 m)
8000
7000
6000
5000
4000
3000
5000
4000
3000
2000
2000
1000
1000
0
6000
0
2
4
6
8
Aerosol backscatter [1/(m sr)]
10
12
x 10
-7
0
0
2
4
6
Aerosol backscatter [1/(m sr)]
8
10
x 10
-7
Nominal Ocular Hazard Distance, NOHD
𝐸=
4𝑃𝑜
𝜋 𝑎+𝜃∙𝑟
2
a

16,43
3,75
1
𝑁𝑂𝐻𝐷 = 𝜃
4𝑃𝑜
𝜋∙𝑀𝑃𝐸
−𝑎
rNOHD
NOHD
331,96
Gustafsson etal. “Visual appearance
of wind turbine tower at long range
measured using imaging system”
SPIE88921Y, 2013
Laser Energy
[J]
Divergence
[mrad]
MPE
[J/m2]
NOHD [km]
Designator Laser, single pulse
0,180
0,08
0,050
26,5
Designator Laser, pulse train
0,180
0,08
0,013
51,6
Influence of atmospheric attenuation
on laser safety range
4𝑃𝑜 ∙ 𝒆− µ∙𝒅𝒙
4𝑃𝑜 ∙ 𝒆−µ∙𝑟
𝐸=
=
𝜋 𝑎+𝜃∙𝑟 2 𝜋 𝑎+𝜃∙𝑟 2
Lambert W function
𝜔𝑒 𝜔 = 𝑧
𝑊(𝑧)𝑒 𝑊(𝑧) = 𝑧
Lambert W function
2
10
Steinvall, 2009
Coreless, et al 1996
Valluri et. al 2000
Chapeua-Blondeau
et. al, 2002
y=z
1
Lambert W
10
 W(z)
0
10
-1
10
 W(z)/z
-2
10
-2
10
0
10
2
10
4
10
Parameter z
6
10
8
10
10
10
Atmospheric influence on laser safety
range, NOHD OHD
𝜇 𝑎 + 𝜃𝑟
𝜇 𝑎 + 𝜃𝑟 ∙ exp(
)
2𝜃
2𝑊(
) 𝑎
2𝜃
𝑂𝐻𝐷𝜇 =
−
μ
𝜃
Extinction coefficient [km-1]
60
Inf
0.00458
0.00229
0.00153
0.00115
0.000916
0.000763
0.000654
0.000573
NOHD-multiple
Laser Safe Range [km]
50
OHD-multiple
40
30
NOHD-single
OHD-single
20
10
0
0
50
100
150
Visibility [km]
200
250
300
Exemple of laser spots
Turbulence, effects on image
high
low
high turbulence
low turbulence
Från Baltic ´99 mätningarna
FOA-R--00-0171-615--SE
a
b
Intensity distributions in two
64 x 64 pixel image selections
Visual images,
range 18.6 km
Turbulence influence on laser safety
range, horizontal path
Sannolikheten för skada vers avstånd, NOHD = 1261 m
Irradians vs avstånd , NOHD = 1261 m
1
1
10
C2
=2e-15 m-2/3
n
Sannolikheten för skada [-]
Radiant exponering (irradians) [J/m 2]
0.9
0
10
-1
10
-2
10
C2
=2e-14 m-2/3
n
0.8
C2
=2e-13 m-2/3
n
0.7
0.6
0.5
0.4
0.3
0.2
0.1
-3
10
0
0.5
1
1.5
2
2.5
Avstånd [km]
3
3.5
Nd:YAG laser
Laser Energy 5 mJ
Puls frequence 20 Hz,
Laser divergence 0,5 mrad
4
0
0
0.5
1
1.5
2
2.5
3
Avstånd [km]
Gustafsson etal. “Lidar measurement as
support to the ocular hazard distance
calculation using atmospheric
attenuation ” SPIE, Toulouse, 2015.
3.5
4
Turbulence influence on laser safety
range, slant path
Sannolikheten för överskrida MTE vers avstånd, NOHD = 48,4 km
Irradians vs avstånd , NOHD = 48 km
2
1
10
C2n=5e-17 m-2/3
Sannolikheten för skada [-]
Radiant exponering (irradians) [J/m 2]
0.9
1
10
0
10
-1
10
C2n=5e-16 m-2/3
0.8
C2n=2e-15 m-2/3
0.7
0.6
0.5
0.4
0.3
0.2
0.1
-2
10
0
10
20
30
Avstånd [km]
40
50
Nd:YAG laser
laser Energy 0.180 J
puls frequence 11.5 Hz,
laser divergence 0,08 mrad
60
43
44
45
46
47
48
49
Avstånd [km]
50
51
52
53
Structurfunction of refraction, Cn2, is
influenced by weather and environment
Sun
time on the day
season
Cloud cover
Meteorological parameters
temperature
humidity
wind
pressure
Latitude
Altitude
convection
wind shear
Ground characteristics
absorption och reflection
vegetation
buildings
Cn2
Brytningsindex fluktuationer
Täthets fluktuationer
Temperatur fluktuationer,
Temperatur gradient,
Strålnings flöde
Breddgrad
Tid på dygnet
och året
Höjd över marken, z
Ytan råhetsstruktur, zo
Ytegenskaper
Molnighet
Luftfuktighet
Markegenskap
Vertikal Vindhastiget
Marktäckning
Vindhastighet
Strukturfunktionen, Cn2
Strukturfunktionen, Cn2, mått på statistiska medelvärdet
𝐶𝑛2 (𝑟12 ) =
𝑛1 − 𝑛2
2
2 3
𝑟12
Kolmogorov spektrum och gäller for skalära vågtalet, k, inom området mellan
inre och yttre skallängden.
Φ𝑛 (𝜅) = 0,00330𝐶𝑛2 𝜅 11
3
Modeller av Cn2
Tatarskiimodell
2 𝑧 −𝑥
𝐶𝑛2 (𝑧) = 𝐶𝑛𝑜
där
x = 4/3, dagtid
x = 2/3, natt
Fried’s och Brookner’s modeller
2 −𝑏 −𝑧
𝐶𝑛2 (𝑧) = 𝐶𝑛𝑜
𝑧 𝑒
𝑧𝑜
Fried’s modell,
b = 1/3, zo = 3200 m samt Cno2 = 4,22·10-14 m-1/3
Brookner’s modell,
zo = 320 m samt Cno2 = 3,6·10-13 m-1/3
b = 2/3, vid soluppgång och solnedgång
b = 5/6, vid sol och dag klart väder
b = 1, nattetid
forts. Modeller av Cn2
Kaimal/Walters-Kunkels modell
𝐶𝑛2 𝑧
=
2
𝐶𝑛𝑜
𝑧0
𝑧
4
−3
𝑧0
𝑧, 𝑧0 ≤ 0,7𝑧𝑖
4
−3
0,5𝑧𝑖 𝑧0
2,9
4
−3
0,5𝑧𝑖 𝑧0
0,5𝑧𝑖 ≤ 𝑧 ≤ 0,7𝑧𝑖
𝑧 𝑧𝑖
3
0,7𝑧𝑖 ≤ 𝑧 ≤ 𝑧𝑖
Kukharets-Tsvangs modell (K-T)
𝐶𝑛2
2
𝐶𝑛𝑜
𝑧
0,046 𝑧
=
𝑧0
4
−3
𝑧𝑖
+ 0,6 ∙ 𝑒𝑥𝑝 −12 𝑧 𝑧𝑖 − 1,1
0,046
4
−3
𝑧𝑜 𝑧𝑖
2
forts. Modeller av Cn2
Similaritetsmodeller
2
𝜕𝑛
𝑃
= 78 ∙ 10−6 2
𝜕𝑇
𝑇
𝜕𝑛
𝐶𝑛2 =
𝐶𝑇2
𝜕𝑇
𝑔 𝑇 𝜕Θ 𝜕𝑧
𝑅𝑖 =
𝜕𝑈 𝜕𝑧 2
𝐶𝑇2 = 𝑧 4
3
𝜕Θ 𝜕𝑧 2 𝑓3 𝑅𝑖
forts. empiriska modeller av Cn2
Hufnagel modellen
𝐶𝑛2 𝑧 = 8,2 ∙ 10−56 𝑈 2 𝑧 10 𝑒 −𝑧
∙ 10−16 𝑒 −𝑧 𝑧𝑜2
𝑧𝑜1
+ 2,7
Hufnagel-Valley modellen
𝐶𝑛2 𝑧 = 8,2 ∙ 10−56 𝑈 2 𝑧 10 𝑒 −𝑧 𝑧𝑜1 + 2,7
∙ 10−16 𝑒 −𝑧 𝑧𝑜2 + 𝐴𝑒 −𝑧 𝑧𝑜3
forts. parametermodeller av Cn2
Sadot och Kopeika
𝐶𝑛2 = 3,8∙10−14 w+2∙10−15 T + 2,8∙10−15 𝑅𝐻 + 2,9∙10−17 𝑅𝐻 2
−1,1∙10−19 𝑅𝐻 3 −2,5∙10−15 𝑊𝑆 −1,2∙10−15 𝑊𝑆 2 −8,5∙10−17 𝑊𝑆
−5,3∙10−13
1
Viktsfunktion, w
0.8
0.6
0.4
0.2
0
-4
-2
0
2
4
6
temporal tid, th
8
10
12
14
3
Moln karaktärisering
Lidar med 1,5 µm laser kopplat till IR
ev. i kombination med avståndsmätare.
Studien “Lidaranvändning för EO system”
Karaktärisering
- moln fördelning
- molnbas
- molntjocklek
- molntäthet
- optisk täthet
- regn
Exempel på lidarmätningar
2000 vågformer
< 3 min
10 km
-2
10
-3
10
-4
10
-5
10
-6
10
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Avståndskompenserat
Elevation 22°, steg 2°
Other examples
Cloudy day (stratus) with ligh drizzle,
T = +14° C, RH = 60 %, Vis. about 45 – 50 km
Haze close to ground
Cloudy day (Cumulus) T = +14° C,
RH = 60 %, Vis. 45 – 50 km.
Cloudy day (stratus) with ligh drizzle,
T= 13° C, RH = 74 %, Vis. about 20 km
Clear, sun no clouds.
T= 17° C, RH = 55 %, Vis. 40 – 50 km
Clouds 2/8 cumulus.
T= 20° C, RH = 50 %,
Visibiility 25 – 40 km.
Visibility from pointmeter at the laser site
Diskussion
- 3D beskrivning av atmosfärsturbulens, Cn2 sfa
höjden, med numeriska modeller, ex SAF-WRF
(Masciadri et al. 1999)
- Mängden aerosol sfa höjd med NWP + CTM
(Kahnert 2008)
- Molntäckning, molnbas och tjocklek med NWP
Tack för uppmärksamheten!
Lidar station Vidsel
CALIPSO markspår 2014-09-30
69
68.5
68
67.5
67
66.5
66
65.5
65
16
17
18
19
20
21
22
23
24
25
JAS markspår vid , 2014-11-12 12:34:11 - 13:57:18
66.5
66.4
CALIPSO markspår 2014-09-30
66.19
66.3
66.18
Latitud
66.2
66.17
66.1
66.16
66.15
66
66.14
65.9
66.13
65.8
66.12
65.7
18.6
18.8
19
19.2
19.4
19.6
Longitud
19.8
20
66.11
20.2
20.4
19.56 19.58 19.6 19.62 19.64 19.66 19.68 19.7 19.72 19.74 19.76