A Closed-Form Statistical Expression for Evaluating Wind Speed and Direction Prediction Intervals from Doppler Lidar Arc Scans

Low-elevation Doppler wind lidar scans, known as arc scans, extend traditional vertical-profile measurements to horizontal, off-site locations. This technique is designed to enable measurements at multiple distant locations relative to the instrument. Arc-scan methods have been widely utilized in wind energy applications and are also a promising tool for environmental monitoring for hazard assessment. This method introduces specific challenges absent in traditional vertical profile scans. The limited scan angle restricts the number of wind orientations available for reliable vector extraction. A reliable method of estimating the uncertainty intervals for retrieved wind speed and direction in operational configurations is thus of interest. Here, we developed a closed-form statistical expression for evaluating wind speed and direction prediction intervals. Because rapid-update operational scenarios (such as real-time dispersion modeling) yield a limited number of scans, the framework is specifically designed to remain mathematically robust and computable using only diagonal variance terms, bypassing the need for numerically unstable cross-covariance matrices. The expression was tested against a lidar and sonic anemometry measurement campaign. The wind-arc alignment emerges as a major influencing parameter impacting uncertainty of both direction and speed retrievals. Conclusions regarding scan parameters and siting considerations are drawn.