Articles | Volume 35, issue 3
https://doi.org/10.5194/angeo-35-639-2017
https://doi.org/10.5194/angeo-35-639-2017
ANGEO Communicates
 | 
11 May 2017
ANGEO Communicates |  | 11 May 2017

Minimum variance projection for direct measurements of power-law spectra in the wavenumber domain

Yasuhito Narita, Yoshihiro Nishimura, and Tohru Hada

Abstract. Minimum variance projection is widely used in geophysical and space plasma measurements to identify the wave propagation direction and the wavenumber of the wave fields. The advantage of the minimum variance projection is its ability to estimate the energy spectra directly in the wavenumber domain using only a limited number of spatial samplings. While the minimum variance projection is constructed for discrete signals in the data, we find that the minimum variance projection can reasonably reproduce the spectral slope of the power-law spectrum if the data represent continuous power-law signals. The spectral slope study using the minimum variance projection is tested against synthetic random data with a power-law spectrum. The method is applicable even for a small number of spatial samplings. Conversely, the spatial aliasing causes a flattening of the spectrum.

Download
Short summary
An algorithm is proposed to estimate the spectral index of the turbulence energy spectrum directly in the wavenumber domain using multiple-sensor-array data. In contrast to the conventional method using time series data and Fourier transform of the fluctuation energy onto the frequency domain, the proposed algorithm does not require the assumption of Taylor's frozen inflow hypothesis, enabling direct comparison of the spectra in the wavenumber domain with various theoretical predictions.