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Authors: M.G. Sterenborg^{1} J.P.V. Poiares Baptista^{2} S. Bühler^{3} Affiliations: ^{1} European Space Agency, ESTEC, Earth Observation Programme ^{2} European Space Agency, ESTEC, Wave Interaction and Propagation ^{3}Institute for Environmental Physics, University of Bremen Date of submission: Author address: J.P.V. Poiares Baptista ESTEC, European Space Agency Keplerlaan 1 – NL 2201 AZ Noordwijk ZH, Netherlands Email: Pedro.Baptista@esa.int ABSTRACT Within the framework of the Atmosphere and Climate Explorer (ACE+) radiooccultation mission work has been carried out to determine the effects of scintillation on its radio links. To that end a method to derive estimates of the refractive index structure constant (C_{n}^{2}) from highresolution radiosonde data has been developed. Data from four locations, from high to low latitudes, has been used, covering from one up to four years of radiosonde measurements. From north to south the locations are: Lerwick, Camborne, Gibraltar and St. Helena. A rigorous statistical analysis has been performed, which seems to confirm the usefulness of these data to determine C_{n}^{2} with no assumptions regarding the statistics of turbulent layers. 1. INTRODUCTIONThis work has been carried out within the context of the preparatory work of the Atmosphere and Climate Explorer (ACE+), ESA [2004]. ACE+ proposed to use 3 radio links in occultation to determine atmospheric temperature and water vapour. The frequencies proposed are 10, 17 and 23 GHz. The transmitter and receiver are located on two different Low Earth Orbit (LEO) satellites. From the attenuations measured at the receiving satellite, the water vapour and temperature can be retrieved due to the different absorption at the three frequencies. Since this technique uses the amplitude (or intensity) of the radio frequency signal, measured in a finite period of time, scintillation may have an impact in the accuracy of the estimation of the atmospheric attenuation. The time available for the attenuation measurement is limited due to the velocity of the two satellites and the required resolution of the temperature and water vapour profiles. Scintillation is an incoherent radio propagation effect brought on by the passage of the radio link through a random medium, such as Earth’s atmosphere. In essence the atmospheric turbulence introduces a stochastic component into the measured amplitude and phase of the radio signal. An important aspect of this effect is that it has no bias, meaning that, given an infinite observation time, the error due to scintillation would be zero after averaging and the measurement would suffer only from instrumental errors. The impact of scintillation was evaluated using models based on Woo & Ishimaru [1974] and Ishimaru [1973],that require, as input parameter the structure constant of the index of refraction C_{n}^{2} . This paper proposes a method to derive C_{n}^{2} profiles from currently available highresolution radiosonde data. To the authors’ knowledge this has never been attempted, even if proposed or suggested by many in the field mainly because of the lack of data, Warnock & VanZandt [1985], Vasseur [1999], VanZandt et al [1978]. 1.1 TurbulenceRichardson [1922] first proposed a qualitative description of turbulence by imagining it as a process of decay as it proceeds through an energy cascade, in which eddies subdivide into ever smaller eddies until they disappear by means of heat dissipation through molecular viscosity. This cascade begins at the outer scale wavenumber, with an eddy size equal to the outer scale length L_{0}, and continues on until the eddies are equal the inner scale length l_{0}.The main energy losses occur in the energy dissipation region, which is separated from the energy input region by the inertial range. All the energy is thus transmitted without any significant losses through the inertial range to the viscous dissipation region. The energy transfer through the spectrum from small to large wavenumbers, or from large scale eddies to smallscale ones, can be seen as a process of eddy division. If the Reynolds number, the dimensionless ratio of the inertial to the viscous forces, of the initial flow is high, it becomes unstable and the size of the resulting eddies is of the order of the initial scale of the flow L_{0}. The Reynolds number characterizing the motion of these eddies is smaller than that of the initial flow, but still sufficiently high to make these eddies unstable and cause further division into smaller eddies. During this process energy of a large decaying eddy is transferred to smaller eddies, i.e., a flow of energy is established from small to large wavenumbers. Each division reduces the Reynolds number of the product eddies. This continues on until the Reynolds number becomes subcritical. At that point the eddies are stable and have no tendency to decay any further. It is clear that the larger the Reynolds number of the initial flow is, the greater the number of successive divisions. Thus the inner scale length reduces with increasing Reynolds number corresponding to the outer scale length. A finite inertial range is observed when the viscous range is separated from the energy range. This occurs when Re >> Re_{cr}. In practice an inertial range is observed for Re > 10^{6} – 10^{7}, Tatarskii [1971] and can be described by a universal theory based on dimensional analysis as advanced by Kolmogorov [1941]. Assuming incompressible flow, Kolmogorov hypothesized that the velocity fluctuations are both isotropic and homogeneous in the inertial range. For this range, well removed from both the energy input and dissipation region, only the rate of transfer of energy, ε, is of importance. The structure function for the velocity component which is parallel to the separation vector ρ depends on ε as well as on the magnitude of the separation, Wheelon [2001]:
Employing dimensional analysis only one combination of ε and ρ is found to generate a squared velocity:
as the dimensions of the energy dissipation rate ε are m^{2}s^{3}. Here C_{v}^{2} is called the velocity structure constant. This is the famous ‘twothirds’ law derived by Kolmogorov. The same technique can be applied to describe the turbulent mixing of a passive scalar. This leads to a similar expression for the refractive index structure function:
where ρ is the separation between sensors, C_{n}^{2} the index of refraction structure constant, l_{0} and L_{0} the inner and outer scales respectively. 