High-Resolution Retrieval of Atmospheric Boundary Layers with Nonstationary Gaussian Processes

TL;DR

This work tackles the challenge of retrieving the time-varying ABL height from Doppler lidar measurements by moving beyond empirical variance-thresholds to a nonstationary Gaussian process framework. It introduces a two-regime GP mixture in which the ABL height $\alpha(t)$ is embedded in the weight function $w(t,x)$ and the processes $Z_1, Z_2$ obey a multivariate Matérn covariance with cross-covariance $K_{12}$, while $\alpha(t)$ is expanded as $\alpha(t)=\sum_{j=1}^m c_j \psi_j(t)$ using wavelets or splines for multi-scale inference. Scalability to large daily datasets (≈$5$ million measurements) is achieved with Vecchia's approximation, a space-first conditioning scheme, and gradient-enabled optimization aided by automatic differentiation. Demonstrations on Doppler lidar data show the framework recovers rapid ABL evolution, handles data gaps and cloud contamination, and delivers high-temporal-resolution ABL-height estimates suitable for real-time monitoring and improved boundary-layer diagnostics.

Abstract

The atmospheric boundary layer (ABL) plays a critical role in governing turbulent exchanges of momentum, heat moisture, and trace gases between the Earth's surface and the free atmosphere, thereby influencing meteorological phenomena, air quality, and climate processes. Accurate and temporally continuous characterization of the ABL structure and height evolution is crucial for both scientific understanding and practical applications. High-resolution retrievals of the ABL height from vertical velocity measurements is challenging because it is often estimated using empirical thresholds applied to profiles of vertical velocity variance or related turbulence diagnostics at each measurement altitude, which can suffer from limited sampling and sensitivity to noise. To address these limitations, this work employs nonstationary Gaussian process (GP) modeling to more effectively capture the spatio-temporal dependence structure in the data, enabling high-quality -- and, if desired, high-resolution -- estimates of the ABL height without reliance on ad-hoc parameter tuning. By leveraging Vecchia approximations, the proposed method can be applied to large-scale datasets, and example applications using full-day vertical velocity profiles comprising approximately $5$M measurements are presented.

Figures (9)

• Figure 1: The ABL height estimation for three days with variance threshold 0.04 $m^2 \cdot s^{-2}$.
• Figure 2: An example of simulated data from the ABL-mixture process given by \ref{['eq:model']}.
• Figure 3: An example of selecting the conditioning set of the red point, where the black points are previous ones, and the gray points have higher indices in the enumeration.
• Figure 4: Daubechies wavelets of order 8 at three different resolution levels.
• Figure 5: The evolution of a signal with wavelets from low to high frequencies with vertical lines indicating the support of functions $\psi_j$ as the level is decreased.