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The existence of magnetized turbulence in the interstellar HI is wellaccepted. A number of techniques to obtain turbulence spectrum and magneticfield direction and strength have been developed and successfully applied to HIspectroscopic data. To better separate the imprints of density and velocityfluctuations to the channel maps, a new theory-based technique, the VelocityDecomposition Algorithm (VDA,Yuen et.al 2021), has been created. The techniquedemonstrates that the intensity fluctuations are separated into a component pvthat mostly arises from velocity fluctuations and pd that mostly arise fromdensity fluctuations. The VDA helps to clarify the nature of the filamentarystructure observed in channel maps. A recent publication (Kalberla et.al2022,K22) claims that the application of VDA to HI4PI data provides negativecorrelation of pv and pd,which according to the authors invalidates thetechnique since it requires that pv and pd have zero correlation. However, thequantities pv and pd given by VDA are naturally orthogonal which can betrivially checked analytically or numerically. That means the correctapplication of the VDA to any data must provide zero correlation. This is thepoint that we clarify in this paper and search for the cause of the mistake inthe application of the VDA in K22 that resulted in the erroneous conclusion. Weprove analytically that by construction pv and pd are not correlated. Weidentify the likely mistake in the VDA expression that K22 used and reproducetheir figures with the incorrect expression. We find that 14 out of 15 figuresin K22 are invalid, and thus their criticism of the VDA is ill-founded andarises from their use of incorrect expressions. We conclude that thedetrimental mistake that K22 made at their analysis completely invalidate theirscientific claim that Y21 isnt compatible to observation.

Correlation of velocity and density contributions to spectroscopic channel maps: Reality check on Kalberla et.al (2022)