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.

Abstract

This study investigates a shear-flow instability observed in the stably stratified nighttime boundary layer on 6 October 1999 during the Cooperative Atmosphere–Surface Exchange Study (CASES-99) in south-central Kansas. A scanning Doppler lidar captured the spatial structure and evolution of the instability, and high-rate in situ sensors mounted on a nearby 60-m tower provided stability and turbulence data with excellent vertical resolution. Data from these instruments are analyzed and linear stability analysis (LSA) is employed to carefully characterize the wave field, its interaction with the mean flow, and its role in turbulence generation.

The event persisted for about 30 min and was confined within the shear zone between the surface and a low-level jet (LLJ) maximum. Eigenvalues corresponding to the fastest growing mode of the LSA showed good agreement with the basic wave parameters determined from the lidar data. Good qualitative agreement was also obtained between the eigenfunction of the fastest growing mode and the vertical profile of the dominant Fourier mode in wavenumber spectra from spatially resolved lidar data. The height of the measured momentum flux divergence associated with the wave motion was consistent with the LSA prediction of the height of the critical level.

Data show that the instability was triggered by an increase in shear due to a slowing of the flow below the LLJ maximum. This low-level slowing produced a local maximum in the shear profile, which was elevated above the surface. The speed and height of the LLJ remained relatively constant before, during, and after the event. Prior to the event turbulent momentum flux increased as the shear increased and as the gradient Richardson number decreased. With the onset of wave activity, a sudden increase in downward wave-momentum flux was accompanied by a sharp reduction in shear near the critical level.

Abstract

A series of trials are performed to evaluate the sensitivity of a 4DVAR algorithm for retrieval of microscale wind and temperature fields from single-Doppler lidar data. These trials use actual Doppler lidar measurements to examine the sensitivity of the retrievals to changes in 1) the prescribed eddy diffusivity profile, 2) the first-guess or base-state virtual potential temperature profile, 3) the phase and duration of the assimilation period, and 4) the grid resolution.

The retrieved fields are well correlated among trials over a reasonable range of variation in the eddy diffusivity coefficients. However, the retrievals are quite sensitive to changes in the gradients of the first-guess or base-state virtual potential temperature profile, and to changes in the phase (start time) and duration of the assimilation period. Retrievals using different grid resolutions exhibit similar larger-scale structure, but differ considerably in the smaller scales. Increasing the grid resolution significantly improved the fit to the radial velocity measurements, improved the convergence rate, and produced variances and fluxes that were in better agreement with tower-based sonic anemometers.

Horizontally averaged variance and heat flux profiles derived from the final time steps of all the retrievals are similar to typical large-eddy-simulation (LES) results for the convective boundary layer. However, all retrieved statistics show significant nonstationarity because fluctuations in the initial state tend to be confined within the boundaries of the scan.

Abstract

One year of coherent Doppler lidar data collected at the U.S. Department of Energy’s Atmospheric Radiation Measurement site in Oklahoma was analyzed to provide profiles of vertical velocity variance, skewness, and kurtosis for cases of cloud-free convective boundary layers. The variance was normalized by the Deardorff convective velocity scale, which was successful when the boundary layer depth was stationary but failed in situations in which the layer was changing rapidly. In this study, the data are sorted according to time of day, season, wind direction, surface shear stress, degree of instability, and wind shear across the boundary layer top. The normalized variance was found to have its peak value near a normalized height of 0.25. The magnitude of the variance changes with season, shear stress, degree of instability, and wind shear across the boundary layer top. The skewness was largest in the top half of the boundary layer (with the exception of wintertime conditions). The skewness was also found to be a function of the season, shear stress, and wind shear across the boundary layer top. Like skewness, the vertical profile of kurtosis followed a consistent pattern, with peak values near the boundary layer top. The normalized altitude of the peak values of kurtosis was found to be higher when there was a large amount of wind shear at the boundary layer top.

Abstract

Two coherent Doppler lidars from the U.S. Army Research Laboratory (ARL) and Arizona State University (ASU) were deployed in the Joint Urban 2003 atmospheric dispersion field experiment (JU2003) held in Oklahoma City, Oklahoma. The dual-lidar data were used to evaluate the accuracy of a four-dimensional variational data assimilation (4DVAR) method and to identify the coherent flow structures in the urban boundary layer. The objectives of the study are threefold. The first objective is to examine the effect of eddy viscosity models on the quality of retrieved velocity data. The second objective is to determine the fidelity of single-lidar 4DVAR and evaluate the difference between single- and dual-lidar retrievals. The third objective is to inspect flow structures above some geospatial features on the land surface. It is found that the approach of treating eddy viscosity as part of the control variables yields better results than the approach of prescribing viscosity. The ARL single-lidar 4DVAR is able to retrieve radial velocity fields with an accuracy of 98% in the along-beam direction and 80%–90% in the cross-beam direction. For the dual-lidar 4DVAR, the accuracy of retrieved radial velocity in the ARL cross-beam direction improves to 90%–94% of the ASU radial velocity data. By using the dual-lidar-retrieved data as a reference, the single-lidar 4DVAR is able to recover fluctuating velocity fields with 70%–80% accuracy in the along-beam direction and 60%–70% accuracy in the cross-beam direction. Large-scale convective roll structures are found in the vicinity of the downtown airport and parks. Vortical structures are identified near the business district. Strong up- and downdrafts are also found above a cluster of restaurants.

Abstract

Radial velocity data measured by high-resolution Doppler lidar (HRDL) are assimilated with a four-dimensional variational data assimilation (4DVAR) method to retrieve microscale flow structures in an atmospheric boundary layer. The control variables of 4DVAR consist of initial three-dimensional velocity and temperature fields, as well as profiles of eddy viscosity and thermal diffusivity. The effects of lateral boundary conditions and buffer zones on the retrieval quality are evaluated using identical twin experiments with synthetic observational data prior to HRDL data retrieval. It is found that use of inflow/outflow boundary conditions in conjunction with buffer zones yields good results. HRDL field observations are then assimilated with 4DVAR, together with the above treatment of boundaries to recover microscale flow structures in a convective boundary layer. The uncertainty of the retrieved data is assessed by conducting a grid sensitivity test. A large-scale flow structure resembling a dry microburst is observed in the retrieved wind field. Characteristics of this structure are discussed and compared with those of a typical microburst.

Abstract

In the nighttime stable boundary layer (SBL), shear and turbulence are generated in the layer between the maximum of the low-level jet (LLJ) and the earth's surface. Here, it is investigated whether gross properties of the LLJ—its height and speed—could be used to diagnose turbulence intensities in this subjet layer. Data on the height and speed of the LLJ maximum were available at high vertical and temporal resolution using the high-resolution Doppler lidar (HRDL). These data were used to estimate a subjet layer shear, which was computed as the ratio of the speed to the height of the jet maximum, and a jet Richardson number Ri _J , averaged at 15-min intervals for 10 nights when HRDL LLJ data were available for this study. The shear and Ri _J values were compared with turbulence kinetic energy (TKE) values measured near the top of the 60-m tower at the Cooperative Atmosphere–Surface Exchange Study-1999 (CASES-99) main site. TKE values were small for Ri _J greater than 0.4, but as Ri _J decreased to less than ∼0.4, TKE values increased, indicating that Ri _J does have merit in estimating turbulence magnitudes. Another interesting finding was that shear values tended to cluster around a constant value of 0.1 s⁻¹ for TKE values that were not too small, that is, for TKE greater than ∼0.1 m² s⁻².

Abstract

This study investigates the accuracy and calibration stability of temperature profiles derived from an operational Raman lidar over a 2-yr period from 1 January 2009 to 31 December 2010. The lidar, which uses the rotational Raman technique for temperature measurement, is located at the U.S. Department of Energy's Atmospheric Radiation Measurement site near Billings, Oklahoma. The lidar performance specifications, data processing algorithms, and the results of several test runs are described. Calibration and overlap correction of the lidar is achieved using simultaneous and collocated radiosonde measurements. Results show that the calibration coefficients exhibit no significant long-term or seasonal variation but do show a distinct diurnal variation. When the diurnal variation in the calibration is not resolved the lidar temperature bias exhibits a significant diurnal variation. Test runs in which only nighttime radiosonde measurements are used for calibration show that the lidar exhibits a daytime warm bias that is correlated with the strength of the solar background signal. This bias, which reaches a maximum of ~2.4 K near solar noon, is reduced through the application of a correction scheme in which the calibration coefficients are parameterized in terms of the solar background signal. Comparison between the corrected lidar temperatures and the noncalibration radiosonde temperatures show a negligibly small median bias of −0.013 K for altitudes below 10 km AGL. The corresponding root-mean-square difference profile is roughly constant at ~2 K below 6 km AGL and increases to about 4.5 K at 10 km AGL.

Abstract

Dual-Doppler lidar observations are used to assess the accuracy of single-Doppler retrievals of microscale wind and temperature fields in a shear-driven convective boundary layer. The retrieval algorithm, which is based on four-dimensional variational data assimilation, is applied by using dual- and single-Doppler lidar data that are acquired during the Joint Urban 2003 field experiment. The velocity field that was retrieved using single-Doppler data is compared directly with radial velocities that were measured by a second noncollocated lidar. Dual-Doppler retrievals are also performed and then compared with the single-Doppler retrieval. The linear correlation coefficient and rms deviation between the single-Doppler retrieval and the observations from the second lidar are found to be 0.94 and 1.2 m s⁻¹, respectively. The high correlation is mainly the result of good agreement in the mean vertical structure as observed by the two lidars. Comparisons between the single- and dual-Doppler retrieval indicate that the single-Doppler retrieval underestimates the magnitude of fluctuations in the crossbeam direction. Vertical profiles of horizontally averaged correlations between the single- and dual-Doppler retrievals also show a marginal correlation (0.4–0.8) between one of the horizontal velocity components. Again, this suggests that the retrieval algorithm has difficulty estimating the crossbeam component from single-Doppler data.

Abstract

This study combines the experimental measurements with large-eddy simulation (LES) data of a neutral planetary boundary layer (PBL) documented by a 60-m tower instrumented with eight sonic anemometers, and a high-resolution Doppler lidar during the 1999 Cooperative Atmospheric and Surface Exchange Study (CASES-99) experiment. The target of the paper is (i) to investigate the multiscale nature of the turbulent eddies in the surface layer (SL), (ii) to explain the existence of a −1 power law in the velocity fluctuation spectra, and (iii) to investigate the different nature of turbulence in the two sublayers within the SL, which are the eddy surface layer (ESL; lower sublayer of the SL lying between the surface and about 20-m height) and the shear surface layer (SSL; lying between the ESL top and the SL top). The sonic anemometers and Doppler lidar prove to be proper instruments for LES validation, and in particular, the Doppler lidar because of its ability to map near-surface eddies.

This study shows the different nature of turbulence in the ESL and the SSL in terms of organized eddies, velocity fluctuation spectra, and second-order moment statistics. If quantitative agreement is found in the SSL between the LES and the measurements, only qualitative similarity is found in the ESL due to the subgrid-scale model, indicating that the LES captures part of the physics of the ESL. The LES helps explain the origin of the −1 power-law spectral subrange evidence in the velocity fluctuation spectra computed in the SL using the CASES-99 dataset: strong interaction between the mean flow and the fluctuating vorticities is found in the SL, and turbulent production is found to be larger than turbulent energy transfer for k ₁ z > 1 (k ₁ being the longitudinal wavenumber and z the height), which is the condition of the −1 power-law existence.