Adjoint Retrieval of Wind and Temperature Fields from a Simulated Convective Boundary Layer

The applicability of a four-dimensional variational data assimilation model to the retrieval of turbulent eddies in a convective boundary layer is assessed. The observation data were generated by the model itself. The period of assimilation is taken to be five minutes, about half of the averaged lifetime of coherent structures. We start with an ideal experiment, which uses information from thirteen instantaneous three-dimensional radial velocity data sets with each twenty-five seconds apart. The correlation coefficients of velocity and temperature fields between retrieved data and exact data for this ideal case are 0.99 and 0.97, respectively, after 400 iterations.

To emulate the data measured by lidar, the thirteen three-dimensional data sets are used to construct two volume data with each horizontal slice of data taken from different instantaneous data sets. Thus it resembles two volume scans of data taken in a period of 5 minutes. The correlation coefficients between retrieved data and exact data for velocity and temperature fields can still reach as high as 0.9 and 0.7 after 400 iterations. It is found that the height-dependent eddy viscosity and diffusivity do not lead to better retrieval quality. Yet the quality of retrieved data can be improved by doubling the value of eddy diffusivity. The temporal and spatial smoothness penalty constraints also improve significantly the retrieval quality in the presence of different types of errors.