PDS_VERSION_ID = PDS3 RECORD_TYPE = STREAM OBJECT = TEXT INTERCHANGE_FORMAT = ASCII PUBLICATION_DATE = 2019-06-01 NOTE = "Description for Venus Climate Orbiter (VCO, also known as PLANET-C and AKATSUKI) RS data calculation including calibration" END_OBJECT = TEXT END calculation to derive the current product ========================================= This file is created by extracting texts from [IMAMURAETAL2011]. Schematic diagram of radio occultation experiments -------------------------------------------------- The following two diagrams, global view and close-up view, show the geometric relation among the Earth, Venus, Akatsuki, Venusian Atmosphere, and ray path of the transmitted wave using Ultra-Stable Oscillator from Akatsuki. Note that the bending of the ray path for each is exaggerated. global view ----------- (2) The wave propagates through the Venusian atmosphere and the ray path of the wave is bended. ..------------.. .'' _______ ``. / ..'' ``.. \ / .'' ray path ``. \ |.' _______ `.| .' / \ `. .' | | | | `. .__ .' | | Venus | | `. |`. (1) transmission .' | | | | `. `. of the wave Earth | \_______/ | `. `. \ / `. `. (3) The wave \ / Akatsuki is received `. .' by ground ``-------------'' station at the Earth. close-up view ------------- asymptotes `. .' `. .' `. .'\ `x' | ``alpha'' .' `. / .------.'-----`.--------. .-' .' `. `-. Venus' atmosphere .-' .' `. `-. .-' .' `. `-. / .'__..------+------..__`. \ .' ..'' ray path | ``.. `. / .' | `. .__ | .'\ | ``r0'' /`. |`. transmission .' \ ..--------|-------.. / `. `. of the wave .' \ ' Venus | ` / `. `. ray path .' \ body | / `. `. .' \ | / ray path `. `. .' \ | / `. .' \ | / to Akatsuki .' ``a'' \ | / ``a'' to Earth \ | / \ | / \ | / \ | / \ | / \ | / \ | / \|/ + center of Venus Note that the variables -- that are enclosed with `` '' -- are described in the next section. Variables, equations, and the parameters used --------------------------------------------- -- variables -- name label name if any description ----- --------------------- ------------------------------------------ r_0 RADIUS (L3) distance of the ray from the center of Venus at closest approach to Venus alpha BENDING_ANGLE (L3) asymptotic bending angle for a radially symmetric atmosphere. a IMPACT_PARAMETER (L3) ray impact parameter n REFRACTIVE_INDEX (L3) refractive index mu REFRACTIVITY (L3) refractivity -- equations -- n(r0) * r0 = a (Bouguer's rule) eq. (1) where r0 is function of a. /inf 1 dn 1 alpha = -2a | --- -- ------------------------- dr eq. (2) /r_0 n dr sqrt( (n * r)**2 - a**2 ) where dn/dr is partial derivative. 1 /inf [ a / ( a ) \ ] dalpha ln n(r) = - -- | ln [ --- + | (---)**2 - 1 |**(1/2) ] ------ da PI /a_1 [ a_1 \ (a_1) / ] da eq. (3) where a_1 is function of r. ``alpha'' and ``a'' are calculated from the measured atmospheric Doppler shift and the reconstructed velocity and position vectors of the spacecraft and the ground stations. The refractivity mu is related to the refractive index by mu = (n-1) x 10**6 eq. (4) and mu is the sum of the contributions from the neutral atmosphere and the ionosphere: beta * N_e mu = V * N - ---------- * 10**6 eq. (5) f**2 where V is the refractive volume, N is the number density of the neutral atmosphere, beta = e**2/(8*pi**2*epsilon*m_e) ~ 40.3 m**3 s**-2 with e, epsilon and m_e being the elementary charge, dielectric constant in vacuum and electron mass, respectively, c is the speed of light, N_e is the number density of electrons, and f is the frequency of the carrier signal. On the assumption that the neutral atmosphere is well mixed, we adopt a constant V of 1.81 x 10**-17 m**3 based on the composition of 96.5% CO2 and 3.5% N2 using the constants given in [FJELDBO&ESHLEMAN1968]. The neutral and ionospheric contributions are separated in altitude (see results of [PAETZOLDETAL2007]). This enables us to retrieve the vertical profiles of the neutral atmospheric density N and the electron density N_e separately. The vertical profile of the neutral atmospheric pressure, p(r), is derived from the density profile N(r) by integrating the equation of hydrostatic equilibrium: / r_top p(r) = p(r_top) + m | N(r') * g(r') dr' eq. (6) / r where m is the mean molecular mass, g is the acceleration due to gravity, and r_top is the adopted upper boundary. The ideal gas law relates p(r_top) to the atmospheric temperature T at this height as p(r_top) = N(r_top) * k * T(r_top), eq. (7) where k is the Boltzmann's constant. The boundary condition required for the integration is the value T(r_top). The temperature profile T(r) is calculated from N(r) and p(r) using the ideal gas law. The influence of the adopted T(r_top) on the calculated T(r) is almost negligible except at the uppermost 10 km [PAETZOLDETAL2007, TELLMANNETAL2009]. The received signal power varies during each occultation experiment due to atmospheric defocusing and absorption. The former must be taken into account when retrieving the vertical distribution of absorbing materials from the observed signal power. Atmospheric defocusing is caused by the radial gradient of the refractive index. The defocusing loss is estimated by [ESHLEMAN1973] L = ( cos alpha - D (d alpha / d a) )**-1 eq. (8) where D is the distance from the spacecraft to the crossing of the ray asymptotes. Once the defocusing loss is estimated as a function of time from trajectory information and the relationship between alpha and a from the Doppler measurements, one may calculate the total atmospheric absorption from the time series of the received signal power. This time series is converted to a height profile of the absorptivity with the aid of ray tracing on the assumption of a spherically symmetric atmosphere [JENKINS&STEFFES1991, JENKINSETAL1994]. The absorption due to CO2, N2, and SO2 is removed from the absorptivity profile based on its dependence on the ambient pressure and temperature. The remaining absorption will be principally due to H2SO4 vapor. -- Summary of the assumed parameters -- Venus radii: 6052 km GM: 3.24858592 x 10**5 km**3 s**-2 V: 1.81 x 10**-17 m**3