calculating the microstructure of atmospheric …calculating the microstructure of atmospheric...
TRANSCRIPT
Calculating the Microstructure ofAtmospheric Optical Turbulence
ARL-MR-419 December 1998
Arnold Tunick
Approved for public release; distribution unlimited.
The findings in this report are not to be construed as anofficial Department of the Army position unless so designatedby other authorized documents.
Citation of manufacturer’s or trade names does not constitutean official endorsement or approval of the use thereof.
Destroy this report when it is no longer needed. Do notreturn it to the originator.
Calculating the Microstructureof Atmospheric OpticalTurbulence
ARL-MR-419 December 1998
Army Research LaboratoryAdelphi, MD 20783-1197
Arnold Tunick Information Science and Technology Directorate
Approved for public release; distribution unlimited.
Turbulent fluctuations in air density can cause significant distortionsof an electromagnetic signal or image. Density fluctuations can bedescribed in terms of air temperature, air pressure, water vapor, andCO2 content. We can calculate the refractive index structure constant,Cn
2, with the fine-scale dynamics of heat, moisture, and momentumdiffusion. This helps us to quantify the intensity ofturbulence-induced refraction. A better understanding ofturbulence-induced refraction can provide a means of evaluatingsensors under various atmospheric conditions or be used in thedevelopment of turbulence-compensation adaptive optic systems.This paper annotates one set of equations for the refractive indexstructure constant, C n
Abstract
2, taken from the literature.
ii
iii
Contents
1. Introduction ........................................................................................................................................... 1
2. Model Equations ................................................................................................................................... 32.1 Refractive Index Structure Constant .............................................................................................. 32.2 Refractive Index of Air and Its Partial Derivatives ........................................................................ 4
3. A Model of the Microstructure of Atmospheric Optical Turbulence ......................................... 7
4. Summary ................................................................................................................................................ 8
References .................................................................................................................................................. 9
Distribution ............................................................................................................................................. 11
Report Documentation Page ................................................................................................................. 17
Figure
1. CN2 model output compared to scintillometer data taken at 2 m over a horizontalpath of 450 m........................................................................................................................................ 2
Tables
1. Microstructure of atmospheric optical turbulence model physical constants .............................. 72. Microstructure of atmospheric optical turbulence model input and output ................................ 8
1
1. IntroductionAtmospheric optical turbulence can modify the refractive index in air in away that can significantly alter the transmission and propagation of anelectromagnetic image or signal [1]. Even through weak turbulence, alaser beam can become highly scintillated and exhibit strong intensityfluctuations if propagated over a long distance [2]. Also, optical turbu-lence can reduce the efficiency of laser systems propagated from theground to an object in space [3]. In this regard, Walters [4] presented theresults of an investigation to develop a data-reduction algorithm forsequences of balloon-borne data aimed at providing vertical profiles ofthe refractive index structure constant. Walters asserts that knowledge ofboth turbulence and wind speed profiles could be helpful for the develop-ment of turbulence-compensation adaptive optic systems.
Andreas [5] defines the problem of estimating the refractive index struc-ture constant from meteorological point measurements and raises thequestion of whether or not point measurements can be used to predict apath-averaged assessment of turbulence-induced refraction. He citesDavidson et al [6] for an example of a bulk-layer method applied toestimating overwater optical turbulence. Also, Tunick et al [7] reported onan experiment wherein radiation and energy budget-derived turbulencedata are compared to scintillometer-retrieved data taken over a bare soilpath of 450 m. The semi-empirical models presented in Rachele andTunick [8] and Tunick [9] have also made estimates of the refractive indexstructure constant for comparison to observed turbulence (scintillometer)data. However, these types of first-order difference routines can result insignificant and sometimes extreme errors when point data in space andtime are used to represent area or path averages (see fig. 1), particularlythroughout periods before or after sunrise and sunset.
However, with increasing interest in high-performance computing,modeling the intensity turbulence-induced refraction is beingre-investigated through the use of large eddy simulations [10,11]. Therefractive index structure constant is recast as a variable that can bedetermined locally, given values for the heat and momentum flux andgradients of pressure, temperature, wind speed, and specific humidity. Asa means of illustrating a calculation of atmospheric optical turbulence ofthis type, an algorithm could be derived from equations collated fromdifferent articles in the open literature and tested using field experimentdata. In this report, the algorithm MAOT (Microstructure of AtmosphericOptical Turbulence), derived from equations collated from differentarticles in the open literature, is presented and the calculation is testedusing data generated from observations [12,7].
2
–12 –8 –4 0 4 8 12 16 2010–23
10–22
10–21
10–20
10–19
10–18
10–17
10–16
10–15
10–14
10–13
10–12
10–11
Cn
(m–2
/3)
Local time
2
Scintillometer dataCN2 model (input data: 1 and 4 m)CN2 model (input data: 2 and 4 m)CN2 model (input data: 4 and 8 m)
Source: A. Tunick, The Refractive Index Structure Parameter/Atmospheric Optical Turbulence Model: CN2, U.S. Army Research Laboratory, ARL-TR-1615 (1998).
Figure 1. CN2 modeloutput compared toscintillometer datataken at 2 m over ahorizontal path of450 m.
3
2. Model Equations
2.1 Refractive Index Structure Constant
Hill [13] gives an expression for the refractive index structure constant as
Cn
2 =n(x) – n(x + r) 2
r2 32 3=
Dn(r)r2 32 3
, (1)
where n is the refractive index in air, (x) and (x + r) denote position inspace, and the ensemble mean variance n(x) – n(x + r) 2 is the scalarstructure function. Batchelor [14] gives a connection between the function,Dn(r), in r space, and the spectrum for the scalar, Γn(k), in k space as
Dn(r) = 2 1 – sin (rk)
rkΓn(k) dk ,
0
∞(2)
where k is the wave number. Through dimensional analysis, the scalarstructure function and the scalar spectrum can be expressed in terms ofthe dissipation rate of turbulent kinetic energy, ε, and the diffusive dissi-pation rate of the scalar variance, χn. Hill [13] gives χn as
χn = 2 dn ∇n 2 , (3)
where, dn ≈ dh, assuming that the diffusion coefficients for the scalarsrefractive index and potential temperature are effectively the same [15].Then
dn = dh = w′ θ′ / ∂θ/∂z . (4)
The variable ε can be expressed as
ε = g/θ w′ θ′ – u′ w′ ∂U/∂z , (5)
where g is the acceleration due to gravity, u′ w′ is the ensemble meaneddy transport of horizontal momentum, w′ θ′ is the ensemble meankinetic heat flux, ∂θ/∂z is the vertical gradient of potential temperature,and ∂U/∂z is the vertical gradient of the total horizontal wind [16].
The resulting expressions for the scalar structure function and the scalarspectrum are
Dn(r) = b n χn ε– 1 3– 1 3 r2 32 3 , (6)
and
Γn(k) = β n χn ε– 1 3– 1 3 k– 5 3– 5 3 , (7)
4
given the Kolmogorov 2/3- and –5/3-dependencies for r and k, respec-tively, where bn and βn are constants (Hill [17,18] gives βn = 0.72). Whenequations (6) and (7) are substituted into equation (2), bn is given as
bn = – 65 βn
cos (x)(x)
5 35 3dx = 9
10 Γ(1/3) β n . (8)
Relationships among the gamma functions, Γ(p) , for 0 < p < 1 are givenby Weast et al [19]. Finally, the expression for the structure constant inequation (1) can be rewritten as
Cn2 = 2 bn dh ε– 1 3– 1 3 ∂n/∂z 2 , (9)
where bn = 1.736.
2.2 Refractive Index of Air and Its Partial Derivatives
The refractive index of air for the visible and near-infrared (3650 to6328 Å) region of the electromagnetic spectrum is expressed [20,21] interms of wavelength (in micrometers), barometric pressure (P, in milli-bars), temperature (T, in degrees Kelvin), and vapor pressure (e, thepartial pressure of the atmosphere due to water vapor content, also inmillibars) in the form presented by Andreas [5]:
nvi = 1.0 + m1PT + m1 + m2
eT × 10– 6 , (10)
where temperature, T, is defined as T = θ (P/Ps)(2⁄7); Ps is normally de-fined as sea level barometric pressure,
m1 = 23.7134 + 6839.397130.0 – σ 2 + 45.473
38.9 – σ 2 , (11)
and
m2 = 64.8731 + 0.58058 σ2 – 0.007115 σ 4 + 0.0008851 σ 6 , (12)
where σ = 1.0/λ (µm–1).
In the infrared region of the electomagnetic spectrum from 78,000 to190,000 Å [20,22], the refractive index is expressed in the form
nir = 1.0 + m1P – e
T + nirw × 10– 6 , (13)
where the refractive index of water vapor is given as
nirw = Q
957.0 – 928.0 T/To0.4 (X – 1.0)
1.03 T/To0.17 – 19.8X2 + 8.2X4 – 1.7X8 + 3.747 × 106
12,449.0 –X2 , (14)
5
where Q = 0.2166847 e⁄T, absolute humidity is in kg/m3, and
X =10.0 (µm)
λ (µm). (15)
In equations (10) and (13), vapor pressure, e, in millibars, can beexpressed [23] in terms of specific humidity, q, in units of grams of watervapor content per kilogram of moist air (dry air and water vapor com-bined) in the following form:
e =P q
mw/ma + 1 – mw/ma q, (16)
where specific humidity is defined [24] as
q =es m w/m a
PRH
100.0exp
m wL v
R*1.0T o
– 1.0T
, (17)
where es = 6.1078 mbar is the saturation vapor pressure at 0.0 °C; mw andma are the molecular weights of water vapor and of dry air, respectively;Lv = 2.5008 × 106 + 2.3 × 103 T (T in degrees Celsius) is the latent heat ofvaporization; R* = 8314.32 J °K–1kmol–1 is the universal gas constant; andRH is relative humidity in percent.
The derivatives of the refractive index given by equations (10) and (13)take the form
∂n∂z = ∂n
∂T∂T∂z + ∂n
∂e∂e∂z , (18)
so that
∂nvi∂T = – m1
PT2 – m2 – m1
eT2
∂e∂T × 10– 6 , (19)
where
∂e∂T = – 1.0
T2L v
R*/mwexp
L vR*/mw
1.0To
– 1.0T × e2 – e
P q . (20)
The partial derivative of n with respect to vapor pressure takes the form
∂nvi∂e
=m 2 – m 1
T× 10– 6 . (21)
The partial derivative of vapor pressure takes the form
∂e∂z
= ∂e∂q
∂q∂z , (22)
6
where
∂e∂q
=m w/m a P
m w/m a + 1.0 – m w/m a q 2. (23)
The partial derivative of T in terms of the scalar potential temperaturetakes the form
∂T∂z
=
∂θ∂z
+ 2.07.0
TP s
P 2
P s
P
– 57
– 57 ∂P
∂z
P s
P
2 72 7.
(24)
Equations (13) and (14) can be rewritten as
nir = 1 + m1PT + 0.21668 f (T,X) – m1
eT × 10– 6 , (25)
where
[A] =
957.0 – 928.0 T/To0.4 (X – 1.0)
1.03 T/To0.17 – 19.8X2 + 8.2X4 – 1.7X8 + 3.747 × 106
12449.0 – X2 . (26)
The partial derivative of nir with respect to temperature can now take theform
∂nir∂T = – m1
PT2 – e
T2 0.21668[A] – m1∂[A]∂T × 10– 6 , (27)
where
∂[A]∂T
= –
0.1751T o
TT o
– 0.83957.0 – 928.0 T
T o
0.4(X – 1.0)
1.03 TT o
0.17– 19.8X 2 + 8.2X 4 – 1.7X 8
2
–
371.2273.15
TT o
0.6
1.03 TT o
0.17– 19.8X 2 + 8.2X 4 – 1.7X 8
.
(28)
Lastly, the partial derivative of nir with respect to vapor pressure takes theform
∂nir∂e =
0.21668[A] – m1T × 10– 6 . (29)
7
3. A Model of the Microstructure of Atmospheric OpticalTurbulence
The equations presented in sections 2.1 and 2.2 were programmed inFORTRAN to produce a computer model called MAOT. The MAOTmodel computes the refractive index structure constant, given values forthe heat and momentum flux and gradients of pressure, temperature,wind speed, and specific humidity as input. Table 1 gives values for themodel’s physical constants. Table 2 gives the results of testing the MAOTcalculation for different conditions of atmospheric stability. The modelinput is generated from observed surface layer data that were reported byTunick et al [7] except for the last column, which was derived from themicrometeorological data reported by Stenmark and Drury [12].
Values of Cn2 have been generally observed to range from about 10–12 to
10–16 m–2/3. The values of Cn2 for the column labeled Unstable (approxi-
mately 10–12 m–2/3) imply that the turbulence is intense, and considerableimage blurring or signal distortion could occur (similar to that seen whenone looks over an open field or a paved lot on a hot day). In contrast,the values of Cn
2 for the column labeled Weakly stable (approximately10–16 m–2/3 ) imply that the intensity of the optical turbulence might beconsidered negligible, except for where a light beam is transmitted over along distance. Higher values of Cn
2 given in table 1 correlate with higher(absolute) values of kinematic heat flux and potential temperature gradi-ent. The lower values of Cn
2 given in table 1 correlate with higher valuesof momentum flux and wind speed gradient. This observation makes thepoint that surface layer stability and turbulence are generally lessened bythe effects of wind shear and surface stress.
Parameter Symbol Unit Amount
Kolmogorov or Corrsin constant bn — 1.736Acceleration due to gravity g m/s2 9.8Temperature scaling To °K 273.15Molecular weight of water vapor mw g/mol 18.016Molecular weight of dry air ma g/mol 28.966Universal gas constant R* J °K–1 kmol–1 8314.32Saturation vapor pressure at 0.0 °C es mbar 6.1078Reference level pressure Ps mbar 1013.25
Table 1.Microstructure ofatmospheric opticalturbulence modelphysical constants.
8
Table 2. Microstructure of atmospheric optical turbulence model input and output.*
Condition of atmospheric stability
Parameter Unit Unstable Weakly unstable Weakly stable Stable
Kinematic heat flux °K m/s –0.470 –0.055 0.014 0.073Momentum flux m2/s2 –0.164 –0.217 –0.042 –0.191Potential temperature gradient °K/m –0.670 –0.124 0.010 0.310
Wind speed gradient ms /m 0.330 0.510 0.303 0.812
Specific humidity gradient gg /m –1.133 × 10–4 –6.667 × 10–6 1.000 × 10–4 –2.500 × 10–4
Pressure gradient mbar/m –0.10 –0.10 –0.10 –0.10
Model outputCn
2 visible m–2/3 1.633 × 10–12 3.382 × 10–14 8.590 × 10–16 1.176 × 10–13
Cn2 IR m–2/3 1.763 × 10–12 3.479 × 10–14 5.283 × 10–15 1.154 × 10–13
*Electromagnetic wavelength—visible 0.94 µmElectromagnetic wavelength—IR 10.6 µm
4. SummaryThe propagation of a light beam through the atmosphere is affected byrandom fluctuations in the refractive index of air [24] and it is thesefluctuations or discontinuities that cause optical turbulence. The refrac-tive index structure parameter is the quantitative measure for such turbu-lence. In this report, I have presented the algorithm MAOT, derived fromequations collated from different articles in the open literature. TheMAOT calculation was tested using kinematic heat flux and momentumflux data generated from observations. MAOT was regarded as a steptaken toward enhancing calculations of refractivity in the surface layerthrough the diurnal cycle.
9
References1. Burk, S. D., and W. T. Thompson, “Mesoscale modeling of summertime
refractive conditions in the southern California Light,” J. Appl. Meteor. 36(1997), pp 22–31.
2. Primmerman, C. A., T. R. Price, R. A. Humphreys, B. G. Zollars, H. T.Barclay, and J. Herrmann, “Atmospheric-compensation experiments instrong-scintillation conditions,” Appl. Opt. 34 (1995), pp 2081–2088.
3. Fouche, D. G., C. H. Higgs, and C. F. Pearson, “Scaled AtmosphericBlooming Experiments (SABLE),” Lincoln Laboratory Journal 5 (2) (1992),pp 273–293.
4. Walters, D. L., “Measurements of optical turbulence with higher-orderstructure functions,” Appl. Opt. 34 (1995), pp 1591–1597.
5. Andreas, E. L., “Estimating Cn2 over snow and sea ice from meteorological
data,” J. Opt. Soc. Am. 5 (1988), pp 481–495.
6. Davidson, K. L, G. E. Schacher, C. W. Fairall, and A. K. Goroch, “Verifica-tion of the bulk layer method for calculating overwater optical turbu-lence,” Appl. Opt. 20 (1981), pp 2919–2924.
7. Tunick, A., H. Rachele, F. V. Hansen, T. A. Howell, J. L. Steiner, A.D.Schneider, and S. R. Evett, “REBAL ’92—A Cooperative Radiation andEnergy Balance Field Study for Imagery and EM Propagation,” Bull. Am.Meteorol. Soc. 75 (1994), pp 421–430.
8. Rachele, H., and A. Tunick, “Energy balance model for imagery andelectromagnetic propagation,” J. Appl. Meteor. 33 (1994), pp 964–976.
9. Tunick, A., The Refractive Index Structure Parameter/Atmospheric OpticalTurbulence Model: CN2, U.S. Army Research Laboratory, ARL-TR-1615,(1998).
10. Peltier, L. J., and J. C. Wyngaard, “Structure-function parameters in theconvective boundary layer from large-eddy simulation,” J. Atmos. Sci. 52(1995), pp 3641–3660.
11. Wyngaard, J. C., N. Seaman, K. Gilbert, and M. Otte, The refractivitystructure of the lower atmosphere: connecting turbulence and meterology, to bepublished in Proceedings of the 1998 Battlespace Atmospheric and CloudImpacts on Military Operations (BACIMO) Conference, Hanscom AirForce Base, MA (1–3 December 1998).
12. Stenmark, E. B., and L. D. Drury, Micrometeorological field data from Davis,California: 1966–1967 runs under non-advective conditions, U.S. Army Tech-nical Report, ECOM-6051 (1970), p 604 (available from U.S. Army Re-search Laboratory, Adelphi, MD).
10
13. Hill, R. J., “Structure functions and spectra of scalar quantities in theinertial-convective and viscous-convective ranges of turbulence,” J.Atmos. Sci. 46 (1989), pp 2245–2251.
14. Batchelor, G. K., “Small-scale variation of convective quantities liketemperature in a turbulent fluid, Part 1: General discussion and the caseof small conductivity,” J. Fluid Mech. 5 (1959), pp 113–133.
15. Tatarski, V. I., The Effects of the Turbulent Atmosphere on Wave Propagation,Israel Program for Scientific Translations, Jerusalem (1971), p 472, (avail-able as NTIS Technical Translation 68-50464).
16. Wyngaard, J. C., “On surface layer turbulence,” Workshop on Micrometeo-rology, D.A. Haugen, ed., Amer. Meteor. Soc. (1973), p 392.
17. Hill, R. J., “Models of the scalar spectrum for turbulent advection,” J.Fluid Mech. 88 (1978), pp 541–562.
18. Hill, R. J., “Spectra of fluctuations in refractivity, temperature, humidity,and the temperature-humidity cospectrum in the inertial and dissipationranges,” Radio Sci. 13 (1978), pp 953–961.
19. Weast, R. C., S. M. Selby, and C. D. Hodgman, eds., Handbook of Chemistryand Physics, 45th Edition, The Chemical Rubber Co., Cleveland, OH (1964),p A-142.
20. Owens, J. C., “Optical refractive index of air: dependence on pressure,temperature and composition,” Appl. Opt. 6 (1967), pp 51–59.
21. Ciddor, P. E., “Refractive index of air: new equations for the visible andnear infrared,” Appl. Opt. 35 (1996), pp 1566–1573.
22. Hill, R. J., and R. S. Lawrence, “Refractive index of water vapor in infra-red windows,” Infrared Phys. 26 (1986), pp 371–376.
23. Gill, A., Atmosphere-Ocean Dynamics, Academic Press (1982), p 662.
24. Kunkel, K. E., D. L. Walters, and G. A. Ely, “Behavior of the TemperatureStructure Parameter in a Desert Basin,” J. Appl. Meteorol. 20 (1981), pp130–136.
11
Distribution
AdmnstrDefns Techl Info CtrAttn DTIC-OCP8725 John J Kingman Rd Ste 0944FT Belvoir VA 22060-6218
Mil Asst for Env SciOfc of the Undersec of Defns for Rsrch &
Engrg R&AT E LSPentagon Rm 3D129Washington DC 20301-3080
Ofc of the Dir Rsrch and EngrgAttn R MenzPentagon Rm 3E1089Washington DC 20301-3080
Ofc of the Secy of DefnsAttn ODDRE (R&AT)Attn ODDRE (R&AT) S GontarekThe PentagonWashington DC 20301-3080
OSDAttn OUSD(A&T)/ODDDR&E(R) R J TrewWashington DC 20301-7100
ARL Chemical Biology Nuc Effects DivAttn AMSRL-SL-COAberdeen Proving Ground MD 21005-5423
Army Corps of Engrs Engr Topographics LabAttn CETEC-TR-G P F Krause7701 Telegraph RdAlexandria VA 22315-3864
Army Dugway Proving GroundAttn STEDP 3Attn STEDP-MT-DA-L-3Attn STEDP-MT-M BiltoftAttn STEDP-MT-M BowersDugway UT 84022-5000
Army Field Artillery SchoolAttn ATSF-TSM-TAFT Sill OK 73503-5000
Army Foreign Sci Tech CtrAttn CM220 7th Stret NECharlottesville VA 22901-5396
Army InfantryAttn ATSH-CD-CS-OR E DutoitFT Benning GA 30905-5090
Army Materiel Sys Analysis ActivityAttn AMXSY-AT CampbellAttn AMXSY-CS BradleyAberdeen Proving Ground MD 21005-5071
Army Rsrch OfcAttn AMXRO-GS BachPO Box 12211Research Triangle Park NC 27709
Army Strat Defns CmndAttn CSSD-SL-L LillyPO Box 1500Huntsville AL 35807-3801
Army TACOM-ARDECAttn AMSTA-AR-WEL-TLBldg 59 Phillips RdPicatinny Arsenal NJ 07806-5000
CECOMAttn PM GPS COL S YoungFT Monmouth NJ 07703
Hdqtrs Dept of the ArmyAttn DAMO-FDT D Schmidt400 Army Pentagon Rm 3C514Washington DC 20301-0460
Kwajalein Missile RangeAttn Meteorologist in ChargePO Box 57APO San Francisco CA 96555
Natl Security AgencyAttn W21 Longbothum9800 Savage RdFT George G Meade MD 20755-6000
Pac Mis Test CtrGeophysics DivAttn Code 3250 BattalinoPoint Mugu CA 93042-5000
Science & Technology101 Research DrHampton VA 23666-1340
Distribution (cont’d)
12
US Army Aviation and Missile CommandAttn AMSMI-RD-WS-PL G Lill JrBldg 7804Redstone Arsenal AL 35898-5000
US Army CECRLAttn CECRL-RG Boyne72 Lyme RdHanover NH 03755-1290
US Army Combined Arms CombatAttn ATZL-CAWFT Leavenworth KS 66027-5300
US Army CRRELAttn CEREL-GP R Detsch72 Lyme RdHanover NH 03755-1290
US Army Field Artillery SchlAttn ATSF-TSM-TA TaylorFT Sill OK 73503-5600
US Army Intel Ctr and FT HuachucaAttn ATSI-CDC-C ColantoFT Huachuca AZ 85613-7000
US Army Nuclear & Chem AgencyAttn MONA-ZBBldg 2073Springfield VA 22150-3198
US Army OECAttn CSTE-EFSPark Center IV 4501 Ford AveAlexandria VA 22302-1458
US Army Spc Technology Rsrch OfcAttn Brathwaite5321 Riggs RdGaithersburg MD 20882
US Army Topo Engrg CtrAttn CETEC-ZCFT Belvoir VA 22060-5546
US Army TRADOC Anlys Cmnd—WSMRAttn ATRC-WSS-RWhite Sands Missile Range NM 88002
US Army White Sands Missile RangeAttn STEWS-IM-IT Techl Lib BrWhite Sands Missile Range NM 88002-5501
US Military AcademyMathematical Sci Ctr of ExcellenceAttn MDN-A MAJ M D PhillipsDept of Mathematical Sci Thayer HallWest Point NY 10996-1786
USATRADOCAttn ATCD-FAFT Monroe VA 23651-5170
Nav Air War Cen Wpn DivAttn CMD 420000D C0245 A Shlanta1 Admin CirChina Lake CA 93555-6001
Nav Ocean Sys CtrAttn Code 54 RichterSan Diego CA 92152-5000
Nav Rsrch LabAttn Code 4110 RuhnkeWashington DC 20375-5000
Nav Surface Warfare CtrAttn Code B07 J Pennella17320 Dahlgren Rd Bldg 1470 Rm 1101Dahlgren VA 22448-5100
Naval Surface Weapons CtrAttn Code G63Dahlgren VA 22448-5000
AFCCC/DOCAttn Glauber151 Patton Ave Rm 120Asheville NC 28801-5002
Air ForceAttn Weather Techl LibAsheville NC 28801-5002
Hdqtrs AFWA/DNX106 Peacekeeper Dr Ste 2N3Offutt AFB NE 68113-4039
Phillips Lab Atmos Sci DivGeophsics DirctrtAttn McClatcheyHanscom AFB MA 01731-5000
Phillips Lab Atmospheric Sci DivGeophysics DirctrtKirtland AFB NM 87118-6008
13
Distribution (cont’d)
Phillips LaboratoryAttn AFRL-VSBE ChisholmAttn PL/LYP 3Attn PL/WE29 Randolph RdKirtland AFB NM 87118-6008
TAC/DOWPLangley AFB VA 23665-5524
USAF Rome Lab TechAttn Corridor W Ste 262 RL SUL26 Electr Pkwy Bldg 106Griffiss AFB NY 13441-4514
DARPAAttn B Kaspar3701 N Fairfax DrArlington VA 22203-1714
NASA Marshal Space Flt CtrAtmospheric Sciences DivAttn E501 FichtlHuntsville AL 35802
NASA Spct Flt CtrAtmospheric Sciences DivAttn Code ED 41 1Huntsville AL 35812
NASA/Marshall Spc Flight CtrAtmos Sci DivAttn Code ED-41Huntsville AL 35812
Colorado State UnivDept of Atmospheric SciAttn R A PielkeFT Collins CO 80523
Cornell UnivSchool of Civil & EnvAttn W H BrutsaertHollister HallIthica NY 14853-3501
Florida State UnivDept of MeteorologyAttn E A SmithTallahassee FL 32306
Iowa State UnivAttn E S TakleAttn R Arritt312 Curtiss HallAmes IA 50011
Iowa State UnivAttn M SegalAttn S E Taylor2104 Agronomy HallAmes IA 50011-1010
Michigan State UnivDept of Crop & Soil SciAttn J Ritchie8570 Plant & Soil Sciences BldgEast Lansing MI 48824-1325
Penn State UnivDept of MeteorologyAttn D Thompsom503 Walker BldgUniversity Park PA 16802
Rutgers Univ-Cook CampusEnvir & Natl Resources BldgAttn R AvissarNew Brunswick NJ 08903
Univ of Alabama at HuntsvilleRsrch InstitAttn R T McniderHuntsville AL 35899
Univ of California at DavisDept of Air, Land, & Water ResourcesAttn R H ShawDavis CA 95616
Univ of ConnecticutDept of Renewable Natural ResourcesAttn D R Miller1376 Storrs RdStorrs CT 06269-4087
Univ of NebraskaDept of Agrcltl MeteorologyAttn S B VermaLincoln NE 68583-0728
Distribution (cont’d)
14
University of KansasDept of Physics & AstronomyAttn J R EaglemanLawrence KS 66045
Washington State UnivDept of Agronomy & SoilsAttn G S CampbellPullman WA 99163
Agrclt Rsrch SvcConserve & Prodn Rsrch LabAttn A D SchneiderAttn S R EvettAttn T A HowellPO Drawer 10Bushland TX 79012
Dean RMDAttn GomezWashington DC 20314
Dept of Commerce CtrMountain AdministrationAttn Spprt Ctr Library R51325 S BroadwayBoulder CO 80303
Hicks & Associates, IncAttn G Singley III1710 Goodrich Dr Ste 1300McLean VA 22102
Natl Ctr for Atmospheric ResearchAttn NCAR Library SerialsPO Box 3000Boulder CO 80307-3000
NCARAttn T W HorstBoulder CO 80307-3000
NCAR/SSSFAttn S P OncleyBoulder CO 80307-3000
NCSUAttn J DavisPO Box 8208Raleigh NC 27650-8208
NTIA ITS S3Attn H J Liebe325 S BroadwayBoulder CO 80303
Pacific Missile Test CtrGeophysics DivAttn Code 3250Point Mugu CA 93042-5000
Raytheon CompanyEquip DivAttn Sonnenschein528 Boston Post Rd MS 1K9Sudbury MA 01776
Sigma Rsrch CorpAttn S R Hanna544 Hill RdBoxborough MA 01719
USDA Agrcltl Rsrch SvcAttn W P KustasBARC0WEST Bldg 265Beltsville MD 20705
USDA Agrcltl Rsrch SvcAttn R D JacksonAttn S B Idso4331 E Broadway RdPhoenix AZ 85040
USDA Forest Svc Rocky Mtn Frst & RangeExprmnt Sta
Attn K F Zeller240 W Prospect StretFT Collins CO 80526
US Army Rsrch LabAttn AMSRL-IS-EA J HarrisAttn AMSRL-IS-EW D HoockBattlefield Envir DirWhite Sands Missile Range NM 88002-5001
US Army Rsrch LabAttn AMSRL-D J LyonsAttn AMSRL-DD J RocchioAttn AMSRL-CI-LL Techl Lib (3 copies)Attn AMSRL-CS-AS Mail & Records Mgmt
15
Distribution (cont’d)
US Army Rsrch Lab (cont’d)Attn AMSRL-CS-EA-TP Techl Pub (3 copies)Attn AMSRL-IS J D GanttAttn AMSRL-IS-E BrownAttn AMSRL-IS-EE A D Tunick (15 copies)Attn AMSRL-IS-EE D GarveyAttn AMSRL-IS-EE R MeyersAttn AMSRL-SE-EE Z G SztankayAdelphi MD 20783-1197
1. AGENCY USE ONLY
8. PERFORMING ORGANIZATION REPORT NUMBER
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
12a. DISTRIBUTION/AVAILABILITY STATEMENT
10. SPONSORING/MONITORING AGENCY REPORT NUMBER
5. FUNDING NUMBERS4. TITLE AND SUBTITLE
6. AUTHOR(S)
REPORT DOCUMENTATION PAGE
3. REPORT TYPE AND DATES COVERED2. REPORT DATE
11. SUPPLEMENTARY NOTES
14. SUBJECT TERMS
13. ABSTRACT (Maximum 200 words)
Form ApprovedOMB No. 0704-0188
(Leave blank)
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of thiscollection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 JeffersonDavis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.
12b. DISTRIBUTION CODE
15. NUMBER OF PAGES
16. PRICE CODE
17. SECURITY CLASSIFICATION OF REPORT
18. SECURITY CLASSIFICATION OF THIS PAGE
19. SECURITY CLASSIFICATION OF ABSTRACT
20. LIMITATION OF ABSTRACT
NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)Prescribed by ANSI Std. Z39-18298-102
Calculating the Microstructure of Atmospheric OpticalTurbulence
December 1998 March 1998 to August 1998
Turbulent fluctuations in air density can cause significant distortions of an electromagnetic signal or image.Density fluctuations can be described in terms of air temperature, air pressure, water vapor, and CO2 content.We can calculate the refractive index structure constant, Cn
2, with the fine-scale dynamics of heat, moisture, andmomentum diffusion. This helps us to quantify the intensity of turbulence-induced refraction. A betterunderstanding of turbulence-induced refraction can provide a means of evaluating sensors under variousatmospheric conditions or be used in the development of turbulence-compensation adaptive optic systems. Thispaper annotates one set of equations for the refractive index structure constant, Cn
2, taken from the literature.
Refractive index, heat flux
Unclassified
ARL-MR-419
7FEJ706110253A11
B53A61102A
ARL PR:AMS code:
DA PR:PE:
Approved for public release; distributionunlimited.
22
Unclassified Unclassified UL
2800 Powder Mill RoadAdelphi, MD 20783-1197
U.S. Army Research LaboratoryAttn: AMSRL-IS-EE [email protected]
U.S. Army Research Laboratory
17
Arnold Tunick
email:2800 Powder Mill RoadAdelphi, MD 20783-1197
DEP
AR
TMEN
T O
F TH
E A
RM
YU
.S.
Arm
y R
esea
rch
Labo
rato
ry28
00 P
owde
r M
ill R
oad
Ade
lphi
, M
D
2078
3-11
97
An
E qua
l O
ppor
tuni
ty E
mpl
oyer