Long-Term Evaluation of the Scintec Boundary-Layer Scintillometer and the Wageningen Large-Aperture Scintillometer: Implications for Scintillometer Users

Abstract

We compare the structure parameter of the refractive index, $C_{nn}$, measured simultaneously with two large-aperture scintillometers: the WagLAS (Wageningen University, Wageningen, the Netherlands) and the BLS900 (Scintec, Rottenburg, Germany). A 3.5-year dataset shows a bias in $C_{nn}$ of about 17 % between the instruments. Analysis of these data reveals firstly that the logarithmic amplifiers in the WagLAS exhibit a strong dependence on temperature, resulting in an overestimation of $C_{nn}$ of up to 35 % for temperatures $<$0 $^{\circ }\hbox {C}$. Secondly, high-pass filtering of the WagLAS and BLS900 intensity data artificially reduces $C_{nn}$ for crosswinds $<$2 $\hbox {m\,s}^{-1}$ (error $\le$25 and $\le$5 % respectively). Thirdly, the BLS900 increasingly underestimates $C_{nn}$ (up to 10–15 %) with increasing signal saturation. We demonstrate that Scintec’s data processing relies too heavily on the assumption that the intensity data obey a log-normal distribution, which they do not in the case of saturation. Fourthly, both instruments ignore the dissipation range of the refractive-index spectrum, which leads to an overestimation of $C_{nn}$ of up to 30 % for friction velocity $<$0.2 $\hbox {m\, s}^{-1}$. Implications of these findings are discussed and placed into perspective for other scintillometer users. Furthermore, we present a tool for revealing saturation and other violations of Rytov theory for any given scintillometer type, including microwave scintillometers.

Appendices

Appendix 1

Scintillometer theory describes the relation between $\sigma _{\mathrm{ln}\left( I \right) }^2$ and $C_{nn}$ by combining wave-propagation and turbulence theory through directly solving the wave equation for a scattered wave. In a charge-free atmosphere with constant magnetic permeability and neglecting polarisation effects, the wave equation becomes (Tatarskii 1961; Lawrence and Strohbehn 1970),

$$\begin{aligned} \Delta E\left( {\left| {\vec {r}} \right| } \right) +\kappa ^{2}n^{2}\left( {\left| {\vec {r}} \right| } \right) E\left( {\left| {\vec {r}} \right| } \right) =0, \end{aligned}$$

(11)

where $E(\left| {\vec {r}} \right| )$ is the vertical component of the electric field belonging to the electromagnetic wave, defined as $E=A\hbox {e}^{iS}$, with $A$ the amplitude and $S$ the phase, $\left| {\vec {r}} \right|$ is the distance between two observation points in the field, and $n(\left| {\vec {r}} \right| )$ is the refractive-index field.

For solving Eq. 11, the Rytov method is used, which consists of applying a perturbation technique to the exponent of $E$ (Vetelino et al. 2007). Hence, substituting $E = \hbox {e}^{\varPsi }$ into Eq. 11 and writing $\varPsi = \chi + iS$, the wave equation becomes the Riccati equation (Tatarskii 1961; Strohbehn 1968),

$$\begin{aligned} \Delta \psi \left( {\left| {\vec {r}} \right| } \right) +\nabla \psi \left( {\left| {\vec {r}} \right| } \right) \cdot \nabla \psi \left( {\left| {\vec {r}} \right| } \right) +\kappa ^{2}n^{2}\left( {\left| {\vec {r}} \right| } \right) =0, \end{aligned}$$

(12)

where the logarithmic amplitude, $\chi \equiv \hbox { ln}(A)$, is the real and $S$ is the imaginary part of $\varPsi$ (Obukhov 1953; Strohbehn 1968).

Subsequently, perturbation technique is applied, whereby $\varPsi$ is expanded into a linear series $\varPsi =\varPsi _{0} + \varPsi _{1} + {\cdots } + \varPsi _{\infty }$. Under the assumption that only single scattering occurs, i.e. neglecting the higher order terms $\varPsi _{2}, \varPsi _{3}$, etc., the Ricatti equation becomes (Tatarskii 1961)

$$\begin{aligned} \Delta \psi _1 \left( {\left| {\vec {r}} \right| } \right) +2\nabla \psi _0 \left( {\left| {\vec {r}} \right| } \right) \cdot \nabla \psi _1 \left( {\left| {\vec {r}} \right| } \right) +2\kappa ^{2}n_1 ^{2}\left( {\left| {\vec {r}} \right| } \right) =0, \end{aligned}$$

(13)

where $n_1 \left( {\left| {\vec {r}} \right| } \right) =n\left( {\left| {\vec {r}} \right| } \right) -1$ (assuming $\overline{n} \left( {\left| {\vec {r}} \right| } \right) =1$ and $n_1 \left( {\left| {\vec {r}} \right| } \right) < < 1)$. Equation 13 has a solution, from which one may derive Eq. 1 with a few more assumptions regarding atmospheric turbulence (Tatarskii 1961, 1971). Note, that the derivation is done for $\sigma _\chi ^2$, but that $\sigma _{\mathrm{ln}\left( I \right) }^2$ is measured. Since $I=A^{2}$, they relate to each other through the equality $\sigma _\chi ^2 = 0.25\sigma _{\mathrm{ln}\left( I \right) }^2$ (Lawrence and Strohbehn 1970).

Appendix 2

For achieving the desired scaling of the WagLAS instrument’s output signal, four steps are involved (the following is adapted from Meijninger 2003, see p.143 onwards for the original text and diagram): first, the intensity signal passes a logarithmic amplifier for conversion from $I$ to $\hbox {ln}(I)$. Second, after the logarithmic amplifier the signal is amplified or debilitated by an amplifier, the gain of which depends on the length of the scintillometer path, each WagLAS instrument has a potentiometer to set the correct gain for this amplifier. Third, the signal is band-pass filtered between 0.1 and 400 Hz to remove noise from the carrier frequency and demodulator, and to remove fluctuations due to undesired scattering and absorption (Nieveen et al. 1998). Finally, the signal passes through a second logarithmic amplifier in root-mean-square mode, giving the logarithm of the variance of its input signal. Consequently, the final output is a voltage proportional to $C_{nn}$.