Title: Determining the refractive index structure constant using high-resolution radiosonde data




НазваниеTitle: Determining the refractive index structure constant using high-resolution radiosonde data
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2. High resolution radiosonde data



High quality, high-resolution radiosonde data is increasingly becoming available for scientific applications. Some research organisations have started to store and archive the full resolution data (instead of only the standard and significant levels) from the operational radiosonde launches. The acquisition of these data is justified when the quality and response time of the equipment and sensors is adequate.

The British Atmospheric Data Centre has been archiving the high-resolution data of the Vaisala RS80L radiosondes performed by the UK Met Office for around twenty sites. This data is in the Vaisala PC-CORA binary format.

These data yield values for pressure, temperature, humidity, wind speed and direc­tion. Wind speed and direction are not directly measured by the radiosonde. These are calculated from the position of the sonde at successive time intervals. The equipment used to obtain the data is the Vaisala RS80L radiosonde. A short overview of its technical specifications is shown below


The RS80L data employs Loran-C to determine wind speed and direction. The estimated accuracies are 1-2 m/s and 5-10 degrees respectively. The resolution is 0.1 m/s and one degree respectively. With its sampling rate of 7 samples per 10 seconds for each parameter it is ideally suited for this work, as this yields a data point approximately every 8 meters of altitude, on average, given a typical radiosonde ascent rate of about 5 meters per second. This resolution would allow in principle allow the identification of turbulent layers, as thin as 8 meters, with no statistical assumptions regarding the their occurrence.

Data from four stations has been used, their locations spread out latitudinally. As the aim was to characterise the Cn2 for different climate types, stations were chosen at latitudes ranging from the most northern to the most southern available. The BADC dataset covers a wider range of years that that used here however a subset was selected based on the availability of a maximum number of launches per day with no gaps throughout the years.


3. METHODOLOGY


To derive Cn2 we first identify, within the data for each individual radiosonde launch, the turbulent layers. This is done through the calculation of the Reynolds and Richardson (Ri) numbers for each high-resolution data point.

The Potential refractive Index Gradient is derived for all layers but is only used to derive Cn2 in those identified as turbulent (i.e. where Ri is smaller than the critical value).

In summary the following step-by-step approach was used for each high-resolution radiosonde data point:


  1. Calculate Reynolds number.

  2. Calculate Richardson number.

  3. Calculate Potential Refractive Index Gradient.

  4. Create data subset based on (Ri < Ricr), this contains only measurements where the layers are turbulent.

  5. Calculate structure constant (Cn2 ) for all turbulent layers and set its value for stable layers to 10-21 m-2/3.


Figure 1 illustrates this methodology.

3.1 Reynolds number


The Reynolds number is used to determine whether a flow is laminar or turbulent. Considered to be the most important dimensionless number in fluid dynamics it yields the ratio between inertial and viscous forces. When Re exceeds a critical value a transition of the flow from laminar to turbulent or chaotic occurs. For the atmosphere the critical Reynolds number is around 106, 107.




(6)


where V is the wind speed, l the characteristic length and ν = 1.1ּ10-5 m2/s is the kinematic viscosity.

For the atmosphere the characteristic length has been taken to be equal to the resolution of the radiosonde measurement. It has been included more as a measure of completeness than as a conclusive method to determine whether or not a measurement was turbulent. In fact, what the results show is that by definition of the Reynolds number the entire atmosphere can be considered turbulent, which is of course the basis for Kolmogorov's universal equilibrium theory.

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