3D complex refractivity using air quality and propagation models Theoretical Basis
Biswadev Roya,b, Saswati Dattab, and B. Vlahovica a
CREST Center Mary Townes Science Building, North Carolina Central University Durham, NC 27707
[email protected] b DIPCON LLC Morrisville, NC 27560
Abstract—Electromagnetic radiation (EMR) propagation through atmosphere is a function of temperature, pressure and composition. The composition of atmosphere will include natural and anthropogenic obscurants that alter radio refractive index. For the first time, we are using an air quality prediction model in retrospective mode for studying 3-dimensional complex refractive index profiles of the lower atmosphere from the surface up to the tropopause height. Since atmospheric obscurant concentration at any given geographic location and time, is dependent on history and dynamics of the air mass, and sources of emissions, it is important and realistic to consider a regional scale air quality model to infer time-varying 3 dimensional radio wave attenuation and seeing parameters. We will discuss methods to compute complex refractive index involving calculation of real and imaginary part of the refractive index which includes dispersion and total attenuation due to absorption and elastic scattering by gases, aerosols, and hydrometeors for the radio spectrum, and the free-space optical (FSO) propagation regime (20 THz to 375 THz). Our approach will adhere closely to past proven techniques, and following directions from most recent literature. For complex refractivity computation we will proceed using scattering extinction efficiencies and also use the line-by-line absorption coefficient calculations using Van Vleck-Weiskopf shape functions and linestrengths for resonant, non-resonant and continuum spectra as needed using Radiative Transfer Model (RTM). Keywords—EM propagation; Refractivity; particle scattering; absorption; extinction
I. INTRODUCTION The current state of Millimeter-wave Propagation Model (MPM) does not provide attenuation (rotational) due to weak spectral lines of gases[1,2,3,4] such as O3, CO, N2O, N2, and there is no dynamic input for the CO2 content. Such assumptions cause uncertainty in refractivity virials [5]. Anomalous Refractivity (AR) cases used by the geodetic community are not properly included currently, necessitating studies on the significance of the differences between signal group- and phase velocity in geodetic measurements through the atmosphere. This will entail studying effects of the absorption lines on phase- and group refractive indices (anomalous refraction) so as to compute instrument specific AR. There is also a need in the community for well defined Sellmeir equation relating the refractive index with wavelength and to study dispersion (continuum refractivity) in detail. Since atmospheric obscurant concentration at any given geographic location and time, is dependent on history and dynamics of the air mass, and sources of emissions, it is important and realistic to consider a regional scale air quality model to infer time-varying 3 dimensional radio wave attenuation and seeing parameters. We will employ an oneatmosphere air quality modeling framework [6,7] that includes initialization and boundary conditions from observations and global models to create a 3-dimensional hourly gridded refractivity and absorptivity map and its gradient. The air quality model predicts natural and anthropogenic atmospheric constituents and respective profiles with a high degree of accuracy by using a chemical transport model (CTM) with emissions data coupled with NCAR developed non-hydrostatic Weather Research Forecast (WRF) model [8] v3.6 with a built-in meteorology-chemistry interface processor. The CTM ingests gridded surface emissions using a very reliable and state of the art National Emissions Inventory (NEI) Database. This model is known in air quality
community as Community Multiscale Air Quality Chemical Transport Model (CMAQ-CTM abbreviated as CCTM). Our main objective here is to create a gridded complex refractivity mapping system with 35 layer configuration [9,10] using CCTM outputs in an Eulerian frame of reference over the CONUS. This paper outlines the theoretical basis for computing the total power attenuation using non-dispersive, dispersive, resonant and non-resonant spectra of water vapor, O2, liquid water and for each of the gaseous species CO, CO2, N2O, O3 and N2, and for hydrosol scattering coefficients.
the Boltzmann’s constant and T is temperature. We will use WRF-CCTM derived atmospheric states and constituent profiles to estimate n. Sfi(T) is the transition line intensity at temperature T of a single line for the single molecule, and F(ν, νfi) is normalized line-shape function. Subscripts f and i are the final and initial energy levels respectively. Total absorption coefficient for all species at frequency ν is given as
M ( )
m
m ( )
(6)
The line-intensity can be written as II. THEORETICAL BASIS
(7)
A. Microwave Region Electromagnetic radiation (EMR) propagation through atmosphere depends on temperature (T), pressure (P) and composition (C) [11]. The composition of atmosphere will include natural and anthropogenic obscurants that alter radio refractive index (N). The phase and amplitude for plane EM wave is written as,
E ( z ) exp[ikz(1 Nx10 6 )]E (0)
(1)
where E(0) is the initial field strength, k=2π/λ wave number in free space, c is speed of light in vacuum, and N is the refractivity. Refractivity, according to [1] could be decomposed, N = N0 + N’(ν) + iN’’
(2)
where [N0 + N’(ν)] is the real part of refractivity that alters the phase velocity upon interacting with the atmosphere and which includes a frequency independent non-dispersive term N0 and a dispersive term N’(ν). The real part could be related to the delay rate (ps km-1). N’’ is the imaginary part that accounts for energy absorption, and can be related to the specific power attenuation (α in dB km-1). Following [1] the power attenuation term can be written as α = 0.1820 ν N’’
dB/km
(3)
The total attenuation coefficient from first principles at a frequency ν and at a height z can be written as α (ν,z) = αM (ν,z) + βM (ν,z) + αA (ν,z) + βA (ν,z) + αP(ν, z) + (4) βP(ν, z) Throughout this section, α denotes the absorption coefficient dB km-1 and β denotes scattering related extinction (also having unit dB km-1). The subscripts M and A are used to denote contributions due to molecular and aerosol constituents respectively. The Subscript P refers to other hydrosol particles in the atmosphere. The power absorption coefficient for a molecular specie (based on M-B distribution) could be written as [11]
m ( ) n
S
fi F ( , fi )
(5)
f ,i
n is the number of molecules of the specie per unit volume, n= ap/kT, where p is the partial pressure of absorbing gas, a is fractional abundance of isotopic variant of the molecule, k is
Where, h is Plank’s constant, c is velocity of light in vacuum, gi is the statistical weight due to nuclear spin in state i, Ei and Ef are the energy level of the ith and fth state respectively, μfi is the reduced molecular dipole-moment and Q(T) is the internal partition function. If there is a table of line intensities available at a specified temperature T0 along with associated energy levels, then Sfi(T) can be estimated as, (8) Where Q(T) can be separated as Q(T) = Qelec(T)Qvib(T)Qrot(T)
(9)
Qelec and Qvib for terrestrial atmosphere for most species can be approximated as unity. For asymmetric (H2O, O3) or symmetric-top molecules (NH3) Qrot can be approximated as (10a) Since linear molecules has fewer rotational states, in this case, we can write, Qrot(T)/Qrot(T0) = T/T0
(10b)
In the microwave region, gaseous O2, water vapor (H2O) and suspended liquid water (hydrosols) are considered principal absorbers [12]. There are two important water vapor transitions at 22.235 GHz and one at 183.310 GHz. CO is a linear molecule, and its rotational spectra is simple, occurring at 115.3 GHz. N2O also has a linear structure with rotational transitions at multiples of 25.1 GHz. In this region, thermal broadening is negligible and the shape function F is mainly determined by the pressure broadening. Tropospheric absorption in microwave region is dominated by oxygen and water vapor. For water vapor, the Van VleckWeisskopf shape factor [11] will be used. There is also a continuum term given by (11) Where, Cs = 1.50 X 10-7 cm-1bar-2GHz-2; Cf = 4.74 X 10-9 cm1 bar-2GHz-2; PH2O = partial pressure of water vapor; Pdry = partial pressure of dry air; and θ = 300K/T The first term in the continuum equation is the self-broadening term and the second term is the foreign-broadened term.
The scattering part of extinction is mostly governed by interaction of EM radiation with suspended sparsely distributed liquid and ice particles. Sometimes the hydrometeors can be mixed dielectrics like hail or graupel [13, 14] which consists of water in all three phases. The size, shape and number distribution of hydrometeors also vary widely. For small cloud droplets, diameter < 50μm, the scattering is negligible, but for larger particles there is significant scattering particularly at higher frequencies. Assuming shapes of all the particles to be spherical and assuming a size distribution of n(D), where D is the effective diameter, the aggregate hydrometeor absorption αe and scattering coefficient αs at wavelength λ, for poly-dispersed media can be written as [14], e
4
D
( ) D n( D)dD 2
e
(12)
0
Where P and T are the pressure in mb and temperature in deg. K respectively, P0 = 1013 mb and T0 = 273.15 K. Molecular scattering will have some effect in UV to visible wavelengths and is negligible at IR frequencies. Total molecular scattering at each level is obtained as, (20) Aerosols are extremely small suspended particulates mostly abundant in the lower atmosphere. Depending on the size, aerosols are generally grouped into 2 categories, fine particulate matter and coarse particulate matter. The aerosol absorption coefficient can be written as
D s s ( ) D 2 n( D )dD 4
(13)
0
where, the extinction cross section for mono-dispersed spherical particles can be written as (14) (15) where, x = 2πr/λ is the size parameter, m is the complex refractive index of the hydrometeor and an and bn are the Mie coefficients, and βP(ν,z) is given as P ( , z ) e s
(16)
B. Free Space Optical (FSO) link region For the case of terrestrial free space optical (FSO) links we will primarily focus on including atmospheric effects (pollution, haze, fog, rain/snow and cloud effects) as much as possible. Neglecting atmospheric turbulence effects [15] we will consider gaseous and aerosol attenuations along with rain and fog attenuations to derive the dynamic 3D complex refractivity field. We will consider CCTM concentration profiles for N2, O2, H2, H2O, CO2, O3 and Ar. MPM-93 like simulations will again be used for computing the absorption power coefficients accounted for refractivity with inputs on concentrations from the CCTM, as described in section A, rewriting this for FSO domain, (17) MFSO ( , z ) O2 ( , z ) N 2 ( , z ) ..... Ar ( , z ) Rayleigh scattering approach will be used. Extinction coefficient for a particular molecular specie can be written using Sellmeir formula following [16] as, mol ( )
where ρ is the molecular density and δ is the constant depolarization factor for air ≈ 0.03. This molecular scattering coefficient can be approximated as (19)
24 3
( n( ) 2 1 6 3 10 3 2 n( ) 2 6 7 4
(18)
-1 dN ( r ) 2r , n' ' r 2 dr km dr
A ( ) 105 Qa 0
(21)
Where, Qa is aerosol absorption cross sections, dN(r)/dr is particle size distribution per unit volume (cm-4), (log-normal distribution is assumed in CCTM outputs), n´´ is imaginary part of refractive index of the aerosol specie. A separate lookup table for refractive indices for all aerosol types will be considered, r is the radius of the particles (cm) and Qa(2πr/λ, n´´) is the absorption cross section which is function of size parameter and complex RI of the particle n´´. For the NIR spectra region imaginary part is very low and hence could be neglected. Aerosol scattering induced extinction is quite prominent in the atmosphere and limits electro-optical performance. The size parameter 2πr/λ in our case for PM2.5 for the upper frequency limit of EMR (375 THz or 0.8 μm) is ~19.6 hence we will deal with this meteorological optic as of haze and cloud scattering case determined by rules of Mie scattering class. We will be able to use CCTM for obtaining the particle size distribution and particle radii effectively considering particle shape to be spherical. For this extinction we will compute using the Equation (6) from [16]
A ( ) 105 Q (2r / , n' )r 2 0
dN (r ) dr km-1 dr
(22)
Essentially the scattering cross section Q(2πr/λ, n’) assumes an asymptotic magnitude of 2 when size parameters are very large (~ 20 in this case). CMAQ is a fairly good modeling tool to study spatio-temporal changes in βA(λ) since aerosol concentration, composition and size distribution can be obtained in 3 dimensional gridded fashion. Finally, we will derive the total FSO region extinction as, FSO ( , z ) M ( , z ) M ( , z ) A ( , z ) A ( , z ) P ( , z ) (23)
III. EXAMPLE EXTINCTIONS USING CCTM
There is a strong new interest in utilizing millimeter wave spectrum (28 GHz to 73 GHz) for cellular communication requiring to study the air-interface [19] for improving power efficiencies. Three dimensional mm-wave attenuation maps might prove to be beneficial there as well. REFERENCES [1]
[2]
[3]
[4]
[5] [6]
[7]
[8]
[9]
Figure 1. June-July-August 2001 (25 site-month averaged) comparison of surface nephelometer extinctions with CCTM derived extinctions at surface considering wildfire emissions into processing using satellite derived IR signatures of area burnt. Spatial plot on the bottom shows color dab comparison of extinctions for the same period [17]. IV.
USEFULNESS OF THE APPROACH
This technique of Refractive index (RI) modeling from first principle will improve our ability to provide precise refractivity profile at a given CONUS location at any given hour. This research also offers basis for testing model based complex RI forecasting ability, and also explore opportunities to verify optical parameters by including real natural and anthropogenic emissions and meteorological fields in conjunction with state of the art radiative-transfer model, and a microwave/THz propagation models all combined into one system. With the current state of advanced visualization tools and diagnostic evaluation methods, this research may also provide opportunity to study time-dependent refractivity fields relevant to any geographic location and its response to natural and anthropogenic events.
[10]
[11]
[12] [13]
[14]
[15]
[16]
[17]
[18]
[19]
H.J. Liebe, et al., “Propagation modeling of moist air and suspended water/ice particles at frequencies below 1000 GHz”, AGARD Conf. Proc. 542: meeting on atmospheric propagation effects through natural and man-made obscurants for visible to mm-wave radiation, Palma de Mallorca, pp. 10 ,May 1993. H.J. Liebe, “MPM- An atmospheric millimeter wave propagation mode,” Int. J. Infrared and Millimeter Waves, vol. 10 (6), pp. 631-650, 1989. P.W. Rosenkranz, “Water vapor microwave continuum absorption: A comparison of measurements and model,” Radio Science, vol. 34(4), pp. 1025, 1999. J.C. Liljegren, et al., “The effect of the half-width of the 22 GHz water vapor line on retrievals of temperature and water vapor profiles with a twelve channel microwave radiometer,” IEEE Trans. Geosci. Rem. Sens., vol. 43(5), pp. 1102-1108, 2005. Philip Ciddor and Reginald Hill, “Refractive index of air. 2. Group index,” Applied Optics, Vol. 38(9), pp. 1663-1667, 1999. Daewon Byun, and Kenneth L. Schere, “Review of the governing equations, computational algorithms, and other components of the models-3 community multiscale air quality (CMAQ) modeling system,” Applied Mechanics Reviews, vol. 59, pp. 27, 2006. United States Environmental Protection Agency, Science Algorithms of the EPA Models-3 CMAQ Modeling System, EPA/600/R-99/030, March, 1999. ARW Version 3 Modeling System, Weather Research Forecasting System Model Users Guide, National Center for Atmospheric Research (NCAR), Version 3.6, pp.10, 2014. D.C. Wong, et al., “WRF-CMAQ two-way coupled system with aerosol feedback: software development and preliminary results,” Geosci. Model Dev., vol. 5, pp. 299-312, 2012. K. Wyat Appel, and Alice Gilliland, “Effects of vertical-layer structure and boundary conditions on CMAQ-v4.5 and v4.6 models,” Annual CMAS Conference, UNC-Chapel Hill, NC, pp. 5, 2006. P.W. Rosenkranz, “Absorption of microwaves by atmospheric gases in Atmospheric Remote Sensing by Microwave Radiometry,” M.A. Janssen (Ed.), Wiley & Sons, Inc., 1993, pp 37-90. Hans J. Liebe, “An updated model for millimeter wave propagation in moist air,” Radio Science, vol. 20(5), pp. 1069-1089, 1985. S. Datta, K. Goswami, and U.K. De, “Depth of surface layer over ice during riming in supercooled atmosphere”, Indian J. Radio & Space Phys., vol. 25(2) pp. 79., 1996 A.J. Gasiewski, “Microwave Radiative transfer in hydrometeors” in Atmospheric Remote Sensing by Microwave Radiometry, M.A. Janssen (Ed.), Wiley & Sons, Inc., 1993, pp 91-144. Hennes Henninger and Otakar Wilfert, “An introduction to free-space optical communications,” Radioengineering, vol. 19(2), pp. 203-212, 2010. International Telecommunication Union (ITU-R) recommendation ITUR P.1817-1, “Propagation data required for the design of terrestrial freespace optical links”, pp. 17, 2012. Biswadev Roy, et al., “A comparison of CMAQ-based aerosol properties with IMPROVE, MODIS and AERONET data,” J. Geophys. Res., vol. 112, pp. 17, 2007. International Telecommunication Union (ITU-R) recommendation ITUR P.834-6, “Effects of tropospheric refraction on radiowave propagation”, pp.12, 2007. Theodore S. Rappaport, et al., “Mobile’s millimeter-wave makeover,” IEEE Spectrum, pp. 35-38 and pp. 52-58, 2014.
