Assimilating Coherent Doppler Lidar Measurements into a Model of the Atmospheric Boundary Layer. Part I: Algorithm Development and Sensitivity to Measurement Error

Abstract

A four-dimensional variational data assimilation (4DVAR) algorithm for retrieval of spatially and temporally resolved velocity and thermodynamic fields within the atmospheric boundary layer (ABL) is described and applied to a coherent Doppler lidar dataset. The adjoint method is used to find the initialization of an ABL model that gives the best fit to radial velocity measurements from the Doppler lidar. The adjoint equations are derived by assuming that subgrid-scale fluxes can be represented as general functions of the resolved-scale rates of strain and potential temperature gradients. For this study, particular attention is paid to the treatment of real measurement error. Radial velocity precision as a function of the signal-to-noise ratio (SNR) is estimated from time series analysis of real fixed beam data, and this information is used in the evaluation of the cost function. The cost function is evaluated by interpolating the model output to the observation coordinates. As a result, the error covariance matrix retains its diagonal structure and the form of the cost function is simplified. The retrieval method is applied to Doppler lidar data collected under convective conditions during the Cooperative Atmosphere/Surface Exchange Study (CASES-99) field program. The impact of the SNR-dependent measurement error is investigated by comparing a retrieval using equally weighted data to a retrieval using the estimated velocity precisions. At near range the fields are well correlated. However, at longer range, as the velocity precision exceeds the standard deviation of the measurements, the correlation decreases rapidly. Furthermore, retrievals using equally weighted data produce higher variances.