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At least 487 records · Page 27

An atmospheric energy analysis of the impact of satellite lidar winds and TIROS temperatures in global simulations

A study of the effects on forecast accuracy of adding wind-profiler data is conducted. An observing system simulation test is employed that assumes a sufficient concentration of aerosols to provide global wind profiles (a best case scenario). The simulated data for the series of five day forecasts are produced from a twenty day integration utilizing the ECMWF model, which is also employed to produce the verification forecast for the five day period.

Keller, Linda M.↗

Analysis of Rapidly Developing Low Cloud Ceilings in a Stable Environment

This report describes the work done by the Applied Meteorology Unit (AMU) in developing a database of days that experienced rapid (< 90 minutes) low cloud formation in a stable atmosphere, resulting in ceilings at the Shuttle Landing Facility (TTS) that violated Space Shuttle Flight Rules (FR). The meteorological conditions favoring the rapid formation of low ceilings include the presence of any inversion below 8000 ft, high relative humidity beneath the inversion, and a clockwise turning of the winds from the surface to the middle troposphere (approx. 15000 ft). The AMU compared and contrasted the atmospheric and thermodynamic conditions between days with rapid low ceiling formation and days with low ceiling resulting from other mechanism. The AMU found that the vertical wind profile is the probable discerning factor between the rapidly-forming ceiling days and other low ceiling days at TTS. Most rapidly-developing low ceiling days had a clockwise turning of the winds with height, whereas other low ceiling days typically had a counter-clockwise turning of the winds with height or negligible vertical wind shear. Forecasters at the Space Meteorology Group (SMG) issue 30 to 90 minute forecasts for low cloud ceilings at TTS to support Space Shuttle landings. Mission verification statistics have shown ceilings to be the number one forecast challenge. More specifically, forecasters at SMG are concerned with any rapidly developing clouds ceilings below 8000 ft in a stable, capped thermodynamic environment, Therefore, the AMU was tasked to examine archived events of rapid stable cloud formation resulting in ceilings below 8000 ft, and document the atmospheric regimes favoring this type of cloud development. The AMU examined the cool season months of November to March during the years of 1993-2003 for days that had low-level inversions and rapid, stable low cloud formation that resulted in ceilings violating the Space Shuttle FR. The AMU wrote and modified existing code to identify inversions from the morning Cape Canaveral, FL rawinsonde (XMR) during the cool season and output pertinent sounding information. They parsed all days with cloud ceilings below 8000 ft at TTS, forming a database of possible rapidly-developing low ceiling events. Days with precipitation or noticeable fog bum-off situations were excluded from the database. Only the daytime hours were examined for possible ceiling development events since low clouds are easier to diagnose with visible satellite imagery. Follow-on work would expand the database to include nighttime cases, using a special enhancement of the infrared imagery for identifying areas of low clouds. The report presents two sample cases of rapidly-developing low cloud ceilings. These cases depict the representative meteorological and thermodynamic characteristics of such events. The cases also illustrate how quickly the cloud decks can develop, sometimes forming in 30 minutes or less. The report also summarizes the composite meteorological conditions for 20 event days with rapid low cloud ceiling formation and 48 non-events days consisting of advection or widespread low cloud ceilings. The meteorological conditions were quite similar for both the event and non-event days, since both types of days experienced low cloud ceilings. Both types of days had a relatively moist environment beneath the inversion based below 8000 ft. In the 20 events identified, de onset of low ceilings occurred between 1200-1800 UTC in every instance. The distinguishing factor between the event and non-event days appears to be the vertical wind profile in the XMR sounding. Eighty-five percent of the event days had a clockwise turning of the winds with height in the lower to middle troposphere whereas 83% of the non-events had a counter-clockwise turning of the winds with height or negligible vertical wind shear. A clockwise turning of the winds with height indicates a warm advection regime, which supports large-scale rising motn and possible cloud formation. Meanwhile, a counter-clockwise turning of the winds with height indicates cold advection or sinking motion in a post-cold frontal environment.

Wheeler, Mark M.↗

Analysis of wind perturbation activity for the NSTS launches

A method for statistical analysis of wind perturbation activity is proposed for application in NSTS prelaunch assessment of the wind environment. Methods for comparing day-of-launch wind perturbation standard deviations with historical data at the launch site are described. A statistical model based on the Gumbel extreme value distribution is developed for the largest vector and component perturbations in a wind profile as a function of high-pass filter cutoff wavelength. Application of the model is proposed for assessing extreme perturbations within prelaunch sequential Jimsphere wind profiles.

Adelfang, Stanley I.↗

Impact of Lidar Wind Sounding on Mesoscale Forecast

An Observing System Simulation Experiment (OSSE) was conducted to study the impact of airborne lidar wind sounding on mesoscale weather forecast. A wind retrieval scheme, which interpolates wind data from a grid data system, simulates the retrieval of wind profile from a satellite lidar system. A mesoscale forecast system based on the PSU/NCAR MM5 model is developed and incorporated the assimilation of the retrieved line-of-sight wind. To avoid the "identical twin" problem, the NCEP reanalysis data is used as our reference "nature" atmosphere. The simulated space-based lidar wind observations were retrieved by interpolating the NCEP values to the observation locations. A modified dataset obtained by smoothing the NCEP dataset was used as the initial state whose forecast was sought to be improved by assimilating the retrieved lidar observations. Forecasts using wind profiles with various lidar instrument parameters has been conducted. The results show that to significantly improve the mesoscale forecast the satellite should fly near the storm center with large scanning radius. Increasing lidar firing rate also improves the forecast. Cloud cover and lack of aerosol degrade the quality of the lidar wind data and, subsequently, the forecast.

Miller, Timothy L.↗

Design and Development of a Scanning Airborne Direct Detection Doppler Lidar System

In the fall of 2005 we began developing an airborne scanning direct detection molecular Doppler lidar. The instrument is being built as part of the Tropospheric Wind Lidar Technology Experiment (TWiLiTE), a three year project selected by the NASA Earth Sun Technology Office under the Instrument Incubator Program. The TWiLiTE project is a collaboration involving scientists and engineers from NASA Goddard Space Flight Center, NOAA ESRL, Utah State University Space Dynamics Lab, Michigan Aerospace Corporation and Sigma Space Corporation. The TWiLiTE instrument will leverage significant research and development investments made by NASA Goddard and it's partners in the past several years in key lidar technologies and sub-systems (lasers, telescopes, scanning systems, detectors and receivers) required to enable spaceborne global wind lidar measurement. These sub-systems will be integrated into a complete molecular direct detection Doppler wind lidar system designed for autonomous operation on a high altitude aircraft, such as the NASA WB57. The WB57 flies at an altitude of 18 km and from this vantage point the nadir viewing Doppler lidar will be able to profile winds through the full troposphere. The TWiLiTE integrated airborne Doppler lidar instrument will be the first demonstration of a airborne scanning direct detection Doppler lidar and will serve as a critical milestone on the path to a future spaceborne tropospheric wind system. In addition to being a technology testbed for space based tropospheric wind lidar, when completed the TWiLiTE high altitude airborne lidar will be used for studying mesoscale dynamics and storm research (e.g. winter storms, hurricanes) and could be used for calibration and validation of satellite based wind systems such as ESA's Aeolus Atmospheric Dynamics Mission. The TWiLiTE Doppler lidar will have the capability to profile winds in clear air from the aircraft altitude of 18 km to the surface with 250 m vertical resolution and < 2mls velocity accuracy.

Gentry, Bruce↗

The Profile Envision and Splice Tool (PRESTO): Developing an Atmospheric Wind Analysis Tool for Space Launch Vehicles Using Python

Tropospheric winds are an important driver of the design and operation of space launch vehicles. Multiple types of weather balloons and Doppler Radar Wind Profiler (DRWP) systems exist at NASA's Kennedy Space Center (KSC), co-located on the United States Air Force's (USAF) Eastern Range (ER) at the Cape Canaveral Air Force Station (CCAFS), that are capable of measuring atmospheric winds. Meteorological data gathered by these instruments are being used in the design of NASA's Space Launch System (SLS) and other space launch vehicles, and will be used during the day-of-launch (DOL) of SLS to aid in loads and trajectory analyses. For the purpose of SLS day-of-launch needs, the balloons have the altitude coverage needed, but take over an hour to reach the maximum altitude and can drift far from the vehicle's path. The DRWPs have the spatial and temporal resolutions needed, but do not provide complete altitude coverage. Therefore, the Natural Environments Branch (EV44) at Marshall Space Flight Center (MSFC) developed the Profile Envision and Splice Tool (PRESTO) to combine balloon profiles and profiles from multiple DRWPs, filter the spliced profile to a common wavelength, and allow the operator to generate output files as well as to visualize the inputs and the spliced profile for SLS DOL operations. PRESTO was developed in Python taking advantage of NumPy and SciPy for the splicing procedure, matplotlib for the visualization, and Tkinter for the execution of the graphical user interface (GUI). This paper describes in detail the Python coding implementation for the splicing, filtering, and visualization methodology used in PRESTO.

Orcutt, John M.↗

Development of a laser Doppler system for the detection and monitoring of atmospheric disturbances

A description is presented of a scanning laser Doppler velocimeter system (SLDVS) which can be used for the determination and the monitoring of the velocity structure of atmospheric disturbances. The described system has been successfully employed to detect and study the velocity structure of aircraft wake vortices. Vertical wind profiles in a single plane in the atmosphere have also been investigated with the SLDVS. Attention is given to system operational aspects, approaches of vortex data collection, and questions of wind profile data collection.

Bilbro, J. W.↗

Observational and numerical studies of extreme frontal scale contraction

The general objective of this effort is to increase understanding of how frontal scale contraction processes may create and sustain intense mesoscale precipitation along intensifying cold fronts. The five-part project (an expansion of the originally proposed two-part project) employed conventional meteorological data, special mesoscale data, remote sensing measurements, and various numerical models. First an idealized hydrostatic modeling study of the scale contraction effects of differential cloud cover on low-level frontal structure and dynamics was completed and published in a peer-reviewed journal. The second objective was to complete and publish the results from a three dimensional numerical model simulation of a cold front in which differential sensible heating related to cloud coverage patterns was apparently crucial in the formation of a severe frontal squall line. The third objective was to use a nonhydrostatic model to examine the nonlinear interactions between the transverse circulation arising from inhomogeneous cloud cover, the adiabatic frontal circulation related to semi-geostrophic forcing, and diabatic effects related to precipitation processes, in the development of a density current-like microstructure at the leading edge of cold fronts. Although the development of a frontal model that could be used to initialize such a primitive equation model was begun, we decided to focus our efforts instead on a project that could be successfully completed in this short time, due to the lack of prospects for continued NASA funding beyond this first year (our proposal was not accepted for future funding). Thus, a fourth task was added, which was to use the nonhydrostatic model to test tentative hypotheses developed from the most detailed observations ever obtained on a density current (primarily sodar and wind profiler data). These simulations were successfully completed, the findings were reported at a scientific conference, and the results have recently been submitted to a peer-reviewed journal. The fifth objective was to complete the analysis of data collected during the Cooperative Oklahoma Profiler Studies (COPS-91) field project, which was supported by NASA. The analysis of the mesoscale surface and sounding data, Doppler radar imagery, and other remote sensing data from multi frequency wind profiler, microwave radiometer, and the Radio Acoustic Sounding System has been completed. This study is a unique investigation of processes that caused the contraction of a cold front to a microscale zone exhibiting an undular bore-like structure. Results were reported at a scientific conference and are being prepared for publication. In summary, considerable progress has been achieved under NASA funding in furthering our understanding of frontal scale contraction and density current - gravity wave interaction processes, and in utilizing models and remotely sensed data in such studies.

Koch, Steven E.↗

GLOW: The Goddard Lidar Observatory for Winds

GLOW (Goddard Lidar Observatory for Winds) is a mobile Doppler lidar system which uses direct detection Doppler lidar techniques to measure wind profiles from the surface into the lower stratosphere. The system is contained in a modified van to allow deployment in field operations. The lidar system uses a Nd:YAG laser transmitter to measure winds using either aerosol backscatter at 1064 nm or molecular backscatter at 355 nm. The receiver telescope is a 45 cm Dall-Kirkham which is fiber coupled to separate Doppler receivers, one optimized for the aerosol backscatter wind measurement and another optimized for the molecular backscatter wind measurement. The receivers are implementations of the 'double edge' technique and use high spectral resolution Fabry-Perot etalons to measure the Doppler shift. A 45 cm aperture azimuth-over-elevation scanner is mounted on the roof of the van to allow full sky access and a variety of scanning options. GLOW is intended to be used as a deployable field system for studying atmospheric dynamics and transport and can also serve as a testbed to evaluate candidate technologies developed for use in future spaceborne systems. In addition, it can be used for calibration/validation activities following launch of spaceborne wind lidar systems. A description of the mobile system is presented along with the examples of lidar wind profiles obtained with the system.

Gentry, Bruce M.↗

GLOW- The Goddard Lidar Observatory for Winds

GLOW (Goddard Lidar Observatory for Winds) is a mobile Doppler lidar system which uses direct detection Doppler lidar techniques to measure wind profiles from the surface into the lower stratosphere. The system is contained in a modified van to allow deployment in field operations. The lidar system uses a Nd:YAG laser transmitter to measure winds using either aerosol backscatter at 1064 nm or molecular backscatter at 355 nm. The receiver telescope is a 45 cm Dall-Kirkham which is fiber coupled to separate Doppler receivers, one optimized for the aerosol backscatter wind measurement and another optimized for the molecular backscatter wind measurement. The receivers are implementations of the 'double edge' technique and use high spectral resolution Fabry-Perot etalons to measure the Doppler shift. A 45 cm aperture azimuth-over-elevation scanner is mounted on the roof of the van to allow full sky access and a variety of scanning options. GLOW is intended to be used as a deployable field system for studying atmospheric dynamics and transport and can also serve as a testbed to evaluate candidate technologies developed for use in future spaceborne systems. In addition, it can be used for calibration/validation activities following launch of spaceborne wind lidar systems. A description of the mobile system is presented along with the examples of lidar wind profiles obtained with the system.

Gentry, Bruce M.↗

Optimal control laws for microburst encounter

Simplified structures for longitudinal control laws that reduce an aircraft's response to the strong head-tailwind and downdraft variations associated with microbursts are presented. They are based on non-zero-set-point linear-quadratic regulators that command throttle setting and angle of attack as functions of velocity and flight path angle, and they can incorporate direct measurements of the wind profile if available. Selection of cost functions to be minimized by feedback control has been aided by a prior study of classical control laws and exact nonlinear-optimal flight paths through realistic microburst wind profiles. The resulting optimal control laws have an adaptive, dual-mode structure that can be implemented either in flight-director logic or in an autopilot.

Stengel, R. F.↗

Low-altitude coverage of ST radars

Clear air ST (stratosphere troposphere) radars are now widely used for atmospheric research and wind profiling. Most attention to date has been directed toward extending the altitude coverage as high as possible. It is also desirable to extend the coverage as low as possible. Any improvement in the low altitude coverage of existing wind profiling radars would be useful. The approximate lower limits of some existing ST radars are listed and what set these limits are briefly examined.

Ecklund, W. L.↗

Influence of aerodynamic roughness length on aeolian processes: Earth, Mars, Venus

The aerodynamic roughness length (z sub 0) is the height at which a wind profile assumes a zero velocity. The lower part of the atmospheric boundary layer will be impeded by friction with the surface. An increase in surface roughness will also increase the shear stress required to initiate particle entrainment by the wind. Bagnold (1941) estimated z sub 0 as being 1/30 of the mean particle size. In Nature, surface roughness is composed of nonerodible elements as well as sand-size erodible particles. To assess z sub 0 values as a function of terrain, field experiments were conducted to obtain wind profiles monitored over natural surfaces at 15 sites in the Mojave Desert, Death Valley, and Nye County, Nevada. These sites span a variety of arid-land terrains, including smooth playas, alluvial fans, and lava flows; z sub 0 values ranged from 0.0001 cm to 1 cm. These values were incorporated in a threshold model and a flux model to assess transport efficiency over such terrains in three planetary environments (Venus, Earth, and Mars), and for particle sizes ranging from 60-500 micron. Threshold and flux are a function of planetary environment, particle density and size (Dp), and z sub 0, and the shear velocity of 1.2 x U sub *t (for Dp = 250 micron and z sub 0 = 0.84). Results show that flux on Mars is approximately 14 g/(cm x s), on Earth it is approximately 3 g/(cm x s), and on Venus 0.5 g/(cm x s). Under all planetary environments, the results also show a dramatic decrease in the flux for particles greater than 200 microns when z sub 0 increases above 0.0085 cm (corresponding to sites consisting of alluvium). When z sub 0 approaches 0.03 cm (corresponding to a mantled pahoehoe lava), the flux diminishes.

Blumberg, Dan G.↗

Jupiter's Turbulent Power Spectra from Hubble Space Telescope

Turbulence in Jupiter's atmosphere was investigated with archival and ongoing observations from the Hubble Space Telescope. Data sets that include one full rotation (360° longitude coverage) were used to produce complete maps of the planet's upper cloud layer. The global maps were analyzed to generate the passive tracer power spectrum of cloud features for single rotation observations, while successive rotations produced pairs of maps such that zonal winds were calculated. An atmosphere's dimensionality and dynamics are reflected in the slopes of such turbulent power spectra. Many of the retrieved passive tracer power spectra have a shallow spectral index over wave numbers k∼1 − 30 and transition to the well‐known Kolmogorov k(exp −5/3) relation at smaller scales between wave numbers k∼30 − 1,000. The transition scale is similar to the number of jets in Jupiter's zonal wind profile and is related to the Rhines scale and the beta effect induced anisotropy scale. We also report on differences found in anticyclonic and cyclonic shear region power spectra and how they correlate to latitudinal changes in the zonal wind profile. We found that properties of Jupiter's power spectra are consistent with quasi‐geostrophic turbulence for shallow fluids.

Richard G. Cosentino↗

Stochastic model of temporal changes of wind spectra in the free atmosphere

Data for wind profile spectra changes with respect to time from Cape Kennedy, Florida for the time period from 28 November 1964 to 11 May 1967 have been analyzed. A universal statistical distribution of the spectral change which encompasses all vertical wave numbers, wind speed categories, and elapsed time has been developed for the standard deviation of the time changes of detailed wind profile spectra as a function of wave number.

Huang, Y. H.↗

Radar - ARL Wind Profilerwith RASS, Boardman - Raw Data

**Winds** A radar wind profiler measures the Doppler shift of electromagnetic energy scattered back from atmospheric turbulence and hydrometeors along 3-5 vertical and off-vertical point beam directions. Back-scattered signal strength and radial-component velocities are remotely sensed along all beam directions and combined to derive the horizontal wind field over the radar. These data typically are sampled and averaged hourly and usually have 6-m and/or 100-m vertical resolutions up to 4 km for the 915 MHz and 8 km for the 449 MHz systems. **Temperature** To measure atmospheric temperature, a radio acoustic sound system (RASS) is used in conjunction with the wind profile. These data typically are sampled and averaged for five minutes each hour and have a 60-m vertical resolution up to 1.5 km for the 915 MHz and 60-m up to 3.5k m for the 449 MHz.

17 WIND ENERGY↗

Benchmarking Near-Surface Winds in the HRRR Analyses Using Multisource Observations over Complex Terrain in the Southeastern United States

Wind energy plays a crucial role in sustainable power generation, yet its full potential in the southeast United States (SEUS) remains underexplored. This study advances wind resource assessment in the SEUS using existing regional modeling and multisource observations. We find that terrain complexity, influenced by orography and forest canopy, significantly impacts the accuracy of modeled wind speed. While the High-Resolution Rapid Refresh (HRRR) model effectively simulates wind profiles over flat, nonforested terrain, larger errors are produced above forest canopies, and particularly for those stands in hilly and mountainous terrain where there are no observations aloft that could be used by HRRR’s data assimilation software. Seasonal variations, e.g., changes in the leaf area index, further complicate the relationship between terrain complexity and simulation errors. Here, our findings emphasize the critical need for comprehensive wind profile measurements, extending from below the canopy to height above the canopy and through the lower planetary boundary layer, to fully quantify model performance over and near forests, and for improving wind resource assessment, planning, and management. This study provides valuable insights not only for further model development but also for future field campaign deployment with the goal of further improving our understanding of wind resources in the region.

Complex terrain↗

Understanding and Utilizing PBL Height Data from Multiple Observing Systems in the GEOS System

The accuracy of PBL height simulation is a key issue in many applications including forecasting near surface meteorology and air quality, however, it is a very challenging problem due to the lack of not only comprehensive, global Planetary Boundary Layer (PBL) observations but also a strategy and infrastructure to utilize PBL height data from a variety of sensors. Following the designation of PBL as an incubation class observable in the 2017 Decadal Survey, the PBL Incubation Study Team Report [14] made clear that “a future global PBL observing system requires modeling and data assimilation as essential components.” There is an urgent need for global modeling development in order to utilize Program of Record (POR) observations, assess their impacts, and identify gaps to be filled by future PBL missions. Our overall objective is to develop PBL data assimilation capabilities in the NASA Global Earth Observing System (GEOS), focusing on PBL height from multiple observing systems, to support the assessment and use of future PBL observations. The NASA GEOS system is composed of the GEOS global atmospheric general circulation model (AGCM) and the atmospheric data assimilation system (ADAS). The PBL parameterizations include the “Lock” K-profile scheme driven by surface and cloud-top buoyancy fluxes ([4]), and the “Louis” local scheme for stable conditions based on the Richardson number ([5]). Above the mixed layer defined by the Lock surface plume, shallow cumulus convection is represented by the mass flux scheme of [9]. Additional parameterizations are summarized in [1]. The ADAS employs the hybrid 4D Ensemble- Variational (EnVar) configuration ([15]), with the ensemble providing flow-dependent background error covariance information. The resultant analysis increments are fed back to the forecast model through the 4D incremental analysis update (IAU) approach ([11]). In this study, PBL height data are being or have been generated from radiosondes, GNSS RO, satellite (CATS, CALIPSO and ICESat-2) and ground-based (MPLNET) lidars, and wind profiler. Investigations have been conducted to specify quality marks for PBL height retrievals for the data assimilation purpose. These PBL height data have different strengths and weaknesses ([2], [3], [6], [7], [8], [10]), and the satellite PBL height data provide better global coverage and complement in-situ PBL height data. Radiosondes offer high accuracy and in situ measurement of temperature and humidity profiles, but with poor spatio-temporal sampling. The in-situ observing systems like MPLNET and wind profiler provide long history of PBL height records at each station. The GNSS RO based PBL height is retrieved based on the sharp gradients in refractivity profile that represent the fine vertical structure of temperature and moisture changes above the PBL. However, not all RO refractivity profiles reach the surface depending on location and regime, and RO refractivity retrievals can be negatively biased below 2km. The PBL height data from satellite lidars provide high resolution along track PBL height retrievals, but over land they are affected by previous day convective PBL aerosol and strongly associated with mixing layer and retrievals cannot be made below thick, attenuating clouds. A successful assimilation of PBL height data requires a thorough understanding of the observing method and the retrieval algorithm for each observing system in order to use the PBL height data from multiple observing systems properly. Due to the sensitivity of PBL height data to the observing method and choice of algorithm, it is important to use a model definition appropriate for each observation type to compute differences between PBL height data and model PBL height (OmFs). The GEOS model currently includes two PBL height definitions suitable for direct comparison with observed PBL height, and additional definitions are being added in this study. Evaluation of different model PBL height definitions is underway. Meanwhile, efforts have been made in the GEOS data assimilation system to develop PBL height data assimilation capability. PBL height data can be assimilated using two different approaches. The traditional approach is to construct an observation operator and its tangent linear and adjoint, which link control variables to PBL height data from each observing system. This observation operator can be very complicated, e.g., the lidar-based PBL height observation operator includes the backscatter lidar forward observation operator, the algorithm to derive PBL height from attenuated total backscatter, interpolation, and calculations handling the mismatch between observed and model scales. The other approach is to augment PBL height to the control variable vector, and it is adopted in this study. The latter approach was also used in previous studies, e.g., the assimilation of PBL height data from radiosonde and aircraft in the Real Time Mesoscale Analysis (RTMA) system for a dispersion modelling study ([13]); the PBL height assimilation study using lidar PBL height data at Greensburg, Kansas for a field campaign ([12]). The PBL height assimilation from multiple observing systems in this study allows us to take advantage of the diverse PBL height data that provide much better global coverage collectively under different meteorological conditions and with different temporal and spatial scales. As all the PBL heights are tightly coupled with the PBL thermodynamic variables, the strong correlations, which are provided by the 4D ensemble forecast, enable PBL height data from various sources to interact and combine coherently and provide additional information for PBL temperature and moisture fields. The results of comparisons among PBL height data from different sources and the evaluation of the model PBL height definitions with the PBL height data will be presented, and the PBL height data synergy strategies and preliminary results will also be discussed at the conference.

Y. Zhu↗