Error analysis of divergence and vorticity from aircraft-measured winds in a cloud-capped boundary layer

Errors in divergence and vorticity estimates from airborne-measured wind during DYCOMS-II are analyzed. Two main errors have been identified: a random (sampling) error due to the turbulent fluctuations in the measured wind field, and a systematic bias due to uncertainties in the offsets in the airplane-relative airflow angles. The vorticity is affected only by the random error, but less strongly than the divergence that is roughly an order of magnitude smaller.

The random error was evaluated from the synthetic wind fields. For simulated turbulent fluctuations with an rms amplitude of 1 m s^-1 and an integral time scale of 10 s, commensurate with the observed winds, the absolute error in divergence per flight leg (circle) is ∼ 6⋅10^-6 s^-1. This value is similar to the expected divergence value for the region, but can be significantly reduced by flying multiple circles.

The systematic bias was evaluated from the observed winds altered for the offsets in the airflow angles. The divergence error due to an offset in the sideslip angle of 1 deg is large, ∼ 10^-4 s^-1, but it effectively cancels by flying circles in opposite directions. The divergence error due to an offset in the attack angle is proportional to both the attack angle offset and the roll angle, and it does not cancel when flying in opposite directions. For the roll angle of 2 deg (corresponding to a half an hour flight time around the circle) and the attack angle offset of 1 deg this error has a value of ∼ 4⋅10^-6 s^-1. The latter error has not previously been identified and is believed to be the cause of the negative divergence reported in previous analyses of the DYCOMS-II data.