Uncertainty in Scatterometer-Derived Vorticity

Abstract

Abstract A more versatile and robust technique is developed for determining area-averaged surface vorticity based on vector winds from swaths of remotely sensed wind vectors. This technique could also be applied to determine the curl of stress, and it could be applied to any gridded dataset of winds or stresses. The technique is discussed in detail and compared to two previous studies that focused on early development of tropical systems. Error characteristics of the technique are examined in detail. Specifically, three independent sources of error are explored: random observational error, truncation error, and representation error. Observational errors are due to random errors in the wind observations and determined as a worst-case estimate as a function of averaging spatial scale. The observational uncertainty in the Quick Scatterometer (QuikSCAT)-derived vorticity averaged for a roughly circular shape with a 100-km diameter, expressed as one standard deviation, is approximately 0.5 × 10−5 s−1 for the methodology described herein. Truncation error is associated with the assumption of linear changes between wind vectors. Uncertainty related to truncation has more spatial organization in QuikSCAT data than observational uncertainty. On 25- and 50-km scales, the truncation errors are very large. The third type of error, representation error, is due to the size of the area being averaged compared to values with 25-km length scales. This type of error is analogous to oversmoothing. Tropical and subtropical low pressure systems from three months of QuikSCAT observations are used to examine truncation and representation errors. Representation error results in a bias of approximately −1.5 × 10−5 s−1 for area-averaged vorticity calculated on a 100-km scale compared to vorticity calculated on a 25-km scale. The discussion of these errors will benefit future projects of this nature as well as future satellite missions.