Bulk Richardson Number Method Research Articles

Wind Turning in the Planetary Boundary Layer in CMIP6 Models

Abstract A set of CMIP6 models is evaluated for the turning of the wind over the planetary boundary layer (PBL) and the corresponding cross-isobaric mass flux. The bulk Richardson number method is used to calculate the height of the PBL to allow for comparisons with a climatology of observed wind-turning angles documented by Lindvall and Svensson based on more than 800 stations in the Integrated Global Radiosonde Archive. Wind-turning angles are found to be underestimated in all models, with the GFDL CM4 model having the closest distribution to the observations. Large, negative cross-isobaric mass fluxes (flow toward higher pressure) are found over high-terrain areas and the North Atlantic storm-track region in all models and the ERA-Interim reanalysis. Bulk Richardson number–derived PBLs are particularly shallow in the Norwegian Earth System Model, medium atmosphere-medium ocean resolution (NorESM2-MM), likely caused by a change in the turbulence and cloud scheme as compared to the CESM2 model that uses the same atmospheric model, leading to small wind-turning angles and cross-isobaric mass fluxes. Using the 850-hPa level as the upper boundary broadens the wind-turning angle distribution and increases the amount of cross-isobaric mass flux for all models. This makes the models closer to the observations, although substantial differences are still present. The assumption of a constant geostrophic wind throughout the PBL possibly affects the calculated mass fluxes.

Hurricane boundary layer height distribution from dropsonde composites based on the bulk Richardson number method

The distribution of hurricane boundary layer heights (HBLHs) relative to the hurricane center is investigated in a composite framework, using total 2674 dropsondes collected within four times the radius of maximum wind speed (RMW) of 61 hurricanes during 2002–2020. The HBLH is computed by the bulk Richardson number (Rib) method, which is sensitive to the critical Rib choice and more reasonable when the surface friction effect is considered. The sea surface friction velocity is derived from the 10-m wind speed through an air-sea drag relation. The results show that the HBLH is significantly low in the eye zone (0–0.5 RMW), out of which the HBLH is highest in the gale region (0.5–1.5 RMW) and decreases with the radius to the hurricane center. Similar to the hurricane wind field asymmetry, the HBLH is generally higher in the right than in the left in relation to the hurricane motion direction. ERA5 generally overestimates the HBLH, but substantially underestimates the higher HBLHs around the RMW, showing different variation of HBLHs along with the radius compared to dropsonde observations. According to linear regression analyses, the HBLH at least determined by the Rib method is importantly affected by the hurricane boundary layer dynamic factor, while has no significant correlation with the thermal factor.

The influence of different parameterizations on diurnal cycle of land precipitation in CAS-ESM

The impacts of physical parameterizations on the diurnal cycle of precipitation (DCP) over land are investigated by comparing long-term simulations of the Chinese Academy of Sciences Earth System Model (CAS-ESM). Significant improvements in the DCP occur when the model replaces the Community Atmosphere Model version 4 (CAM4) physics package with the CAM5 package at both global and regional scales. Globally, the reduced amplitudes and delayed phases of DCP with the CAM5 package can be explained by the diurnal variations in convective available potential energy (CAPE). Regionally, the improvements in the DCP are caused by the decreased daytime convergence at 850 hPa, smaller vertically integrated water vapor transport, weakened vertical velocity, and smaller stratus cloud liquid water amount simulated by the CAM5 package. Besides, CAS-ESM with the CAM5 package produces the decreased amplitudes and delayed phases of the diurnal variation of the convective cloud, which is closely related to the planetary boundary layer (PBL) processes. CAS-ESM with the CAM5 package exhibits a significantly lower PBL height than with the CAM4 package for both direct model outputs and estimates with the bulk Richardson number method. The peaks of lifting condensation level (LCL) deficit (difference between PBL height and LCL height) occur later (∼1–3 h) and are lower with the CAM5 package than with the CAM4 package. Consequently, CAS-ESM with the CAM5 package decreases the probability of cloud formation and produces more realistic DCP. This study underscores the importance of PBL schemes to the simulated convective clouds and DCP.

Comparison of planetary boundary layer height from ceilometer with ARM radiosonde data

Abstract. Ceilometer measurements of aerosol backscatter profiles have been widely used to provide continuous planetary boundary layer height (PBLHT) estimations. To investigate the robustness of ceilometer-estimated PBLHT under different atmospheric conditions, we compared ceilometer- and radiosonde-estimated PBLHTs using multiple years of U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) ceilometer and balloon-borne sounding data at ARM fixed-location atmospheric observatories and from ARM mobile facilities deployed around the world for various field campaigns. These observatories cover from the tropics to the polar regions and over both ocean and land surfaces. Statistical comparisons of ceilometer-estimated PBLHTs from the Vaisala CL31 ceilometer data with radiosonde-estimated PBLHTs from the ARM PBLHT-SONDE Value-added Product (VAP) are performed under different atmospheric conditions including stable and unstable atmospheric boundary layer, low-level cloud-free conditions, and cloudy conditions at these ARM observatories. Under unstable conditions, good comparisons are found between ceilometer- and radiosonde-estimated PBLHTs at ARM low- and mid-latitude land observatories. However, it is still challenging to obtain reliable PBLHT estimations over ocean surfaces even using radiosonde data. Under stable conditions, ceilometer- and radiosonde-estimated PBLHTs have weak correlations. We compare different PBLHT estimations utilizing the Heffter, the Liu–Liang, and the bulk Richardson number methods applied to radiosonde data with ceilometer-estimated PBLHT. We find that ceilometer-estimated PBLHT compares better with the Liu–Liang method under unstable conditions and compares better with the bulk Richardson number method under stable conditions.

Testing the efficacy of atmospheric boundary layer height detection algorithms using uncrewed aircraft system data from MOSAiC

Abstract. During the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition, meteorological conditions over the lowest 1 km of the atmosphere were sampled with the DataHawk2 (DH2) fixed-wing uncrewed aircraft system (UAS). These in situ observations of the central Arctic atmosphere are some of the most extensive to date and provide unique insight into the atmospheric boundary layer (ABL) structure. The ABL is an important component of the Arctic climate, as it can be closely coupled to cloud properties, surface fluxes, and the atmospheric radiation budget. The high temporal resolution of the UAS observations allows us to manually identify the ABL height (ZABL) for 65 out of the total 89 flights conducted over the central Arctic Ocean between 23 March and 26 July 2020 by visually analyzing profiles of virtual potential temperature, humidity, and bulk Richardson number. Comparing this subjective ZABL with ZABL identified by various previously published automated objective methods allows us to determine which objective methods are most successful at accurately identifying ZABL in the central Arctic environment and how the success of the methods differs based on stability regime. The objective methods we use are the Liu–Liang, Heffter, virtual potential temperature gradient maximum, and bulk Richardson number methods. In the process of testing these objective methods on the DH2 data, numerical thresholds were adapted to work best for the UAS-based sampling. To determine if conclusions are robust across different measurement platforms, the subjective and objective ZABL determination processes were repeated using the radiosonde profile closest in time to each DH2 flight. For both the DH2 and radiosonde data, it is determined that the bulk Richardson number method is the most successful at identifying ZABL, while the Liu–Liang method is least successful. The results of this study are expected to be beneficial for upcoming observational and modeling efforts regarding the central Arctic ABL.

Trends of Planetary Boundary Layer Height Over Urban Cities of China From 1980–2018

Boundary layer height (BLH) is an important parameter in climatology and air pollution research, especially in urban city. We calculated the BLH with a bulk Richardson number (Ri) method over urban cities of China during 1980–2018 using European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-interim data after carefully validation with sounding data obtained from two meteorology stations in eastern China during 2010–2018. The values of BLH between these two types of data have correlation coefficients in the range of 0.65–0.87, which indicates that it is reasonable to analyze long-term trends of the BLH from ERA data sets. Using ERA-interim calculated BLH, we found that there is an increasing trend in the daytime BLH in most cities of eastern China, particularly during the spring season. A correlation analysis between the BLH and temperature, wind speed, relative humidity and visibility revealed that the variability in meteorological parameters, as well as in aerosol concentrations over highly polluted eastern China, play important roles in the development of the BLH.

Planetary Boundary-Layer Structure at an Inland Urban Site under Sea Breeze Penetration

We evaluated the performance of the Weather Research and Forecasting Model in simulating the boundary-layer structure at an urban site in Seoul on two clear summer days against observations made using a ceilometer, a Doppler wind lidar, and a microwave radiometer. The planetary boundary-layer height (PBLH) was estimated from two different methods using observations: the ceilometer-based method (CBM) and bulk Richardson number method (BRM). The maximum PBLH was well captured by the model but PBLH was underestimated in the late afternoon and evening. To examine the cause for underestimation of PBLH in the evening, we compared the wind and virtual potential temperature structure between the simulation and observations. The model captured the timing of the sea breeze well, but it considerably overestimated the intensity of the simulated sea breeze, resulting in an overestimated cold advection by a sea breeze. The effect of the overestimated cold advection on evening PBLH was greater when the sea breeze arrived in the late afternoon and hence the vertical extent of the sea breeze was shallow. This study underscores the importance of accurately simulating the sea breeze for PBLH prediction in the evening, over the inland urban areas under sea breeze penetration.

Climatology of the Boundary Layer Height and of the Wind Field over Greece

In this study, a climatology of two key boundary layer features, the Planetary Boundary Layer Height (PBLH) and the wind field over Greece is derived. The climatology is based on daily soundings collected in Athens, Thessaloniki and Heraklion and spanning a 32-year period. The PBLH is estimated using a method based on the gradient of potential temperature and a method based on the bulk Richardson number. The wind field is analyzed by calculating the wind shear and the turning angle of the wind vector between the surface and the top of the boundary layer. The PBLH of the daytime boundary layer over Athens and Thessaloniki is found to exhibit seasonal variability with summer maxima and winter minima and has annual median values in the range of 1.4–1.7 km estimated using the gradient method. The PBLH over Heraklion is found to exhibit weak seasonal variability with a lower median value of 1.2 km. The nighttime boundary layer over all three sites is found to be much shallower with PBLH values in the range of 150–200 m with no seasonal variations. In addition, the bulk Richardson number method is found to systematically underestimate the PBLH compared to the gradient method. The wind field in the daytime boundary layer at all three sites is found to have small shear of the order of 1 ms−1 and wind turning angles that are lower than 15 degrees, while in the nocturnal boundary layer it has larger shear of the order of 5–10 ms−1 with turning angles lower than 20 degrees. In addition, for both the daytime and the nighttime boundary layer there is no general preference for veering or backing.

Diurnal variability of the planetary boundary layer height estimated from radiosonde data

Diurnal variations in the planetary boundary layer height (PBLH) at different latitudes over different surface characteristics are described, based on 45 years (1973−2017) of radiosonde observations. The PBLH is determined from the radiosonde data by the bulk Richardson number (BRN) method and verified by the parcel method and the potential temperature gradient method. In general, the BRN method is able to represent the height of the convective boundary layer (BL) and neutral residual layer cases but has relatively large uncertainty in the stable BL cases. The diurnal cycle of the PBLH over land is quite different from the cycle over ocean, as are their seasonal variations. For stations over land, the PBLH shows an apparent diurnal cycle, with a distinct maximum around 15:00 LT, and seasonal variation, with higher values in summer. Compared with the PBLH over land, over oceans the PBLH diurnal cycles are quite mild, the PBLHs are much lower, and the seasonal changes are less pronounced. The seasonal variations in the median PBLH diurnal cycle are positively correlated with the near-surface temperature and negatively correlated with the near-surface relative humidity. Finally, although at most latitudes the daytime PBLH exhibits, over these 45 years, a statistically significant increasing trend at most hours between 12:00 LT and 18:00 LT over both land and ocean, there is no significant trend over either land or ocean in the nighttime PBLH for almost all the studied latitudes.

On the association between characteristics of the atmospheric boundary layer and air pollution concentrations

Air pollution in the lower atmosphere is a global concern. Characteristics of the planetary boundary layer (PBL) are considered important determinants of the dispersion and the concentrations of pollutants. This work explores the association between characteristics of the PBL and corresponding air pollution data, separately for different PBL states. Five years (2014–2018) of twice daily (01:30 and 13:30 local time) high resolution radiosonde data were used to estimate the convective and stable boundary layer heights (CBL and SBL, respectively), and the temperature lapse rate, in Bet Dagan, Israel. In 23% of the nights, mostly cloudy ones, no indication for an SBL was found but a clear top of a ground–based residual layer (RBL) was detected. The concentrations of NO, NO2, NOx and PM2.5 were negatively correlated with the heights of the CBL and RBL but positively correlated with the SBL height. Their association with the lapse rate was always negative, weak in daytime (CBL) but very strong during the night (SBL and RBL). The associations with the O3 concentrations were opposite in sign to those with the primary pollutants. The PBL height using the bulk Richardson number method was most strongly associated with the CBL and RBL concentrations but we found it unsuitable for estimating the height of the SBL. Our results demonstrate the importance of accounting for the different states of the PBL. In particular, they suggest that during SBL conditions, the common practice of using the PBL volume as a determinant of pollutant concentrations might not be appropriate.

The Characteristics of Spatial and Temporal Variations in the PBL during the Landfall of Tropical Cyclones across East China

AbstractThe planetary boundary layer (PBL) controls the exchange of momentum and energy between the ground surface and the free troposphere, but few studies have been involved in the connection of the PBL with the development and extinction of tropical cyclones (TCs). Studies on the PBL usually need high-resolution soundings in the lowest troposphere that are otherwise quite rare with traditional technology. Here, 1-s resolution L-band radiosonde data are acquired to study the variations in PBL characteristics associated with the development of TCs in eastern China. The strong variations in the vertical profiles of temperature, relative humidity, and wind speed in the PBL during the landfall of a TC are revealed. In addition, four typical methods, including the virtual potential temperature method, Holzworth method, bulk Richardson number method, and potential temperature gradient method, are applied to estimate the PBL height (PBLH). The results indicate that the PBLHs derived by these methods vary by several hundred meters, which may be related to their different definitions of kinetic or thermodynamic theories. Furthermore, the PBLH was found to display a slight upward tendency during the landfall of TC.

Climatological characteristics of planetary boundary layer height over Japan

Based on the 30‐year (1988–2017) radiosonde observations, the climatological characteristics of the planetary boundary layer height (PBLH) over Japan, as well as the long‐term changes, are investigated. We firstly compared four different methods to determine the PBLH. Results show that the bulk Richardson number method has the best performance among all these methods. At all studied stations, monthly median PBLHs in the morning are generally higher than the ones in the evening. Bimodal structure of seasonal PBLHs are found over Japan. Daytime PBLH peaks in spring and autumn and achieves the minimum in summer and winter. Night‐time PBLH shows less seasonal variations. It is found that the PBLHs in the central and southern part of Japan could be dominant by the variations of surface temperature, while the variations of surface relative humidity (RH) may be responsible for the PBLHs in the northern part of Japan. Moreover, sea fog which is associated with high RH and temperature inversion also has an obvious influence on PBLHs in northern Japan. Trend study shows that PBLHs in most stations slightly increased during the past 30 years.

Evaluation of methods for estimating atmospheric stability at two coastal sites

Understanding the atmospheric stability conditions is important in order to obtain accurate estimates of the vertical wind speed profile. This work compares and evaluates common methods for estimation of atmospheric stability using standard meteorological mast observations. Atmospheric stability distributions from three different met-masts located at two coastal sites are calculated and compared. The atmospheric stability parameter, L is estimated using the bulk Richardson number, the surface-layer Richardson number, and calculated directly from eddy covariance flux measurements. The resulting distributions vary depending on which method is used. The atmospheric stability measurements from two masts located 3 km apart in similar terrain are compared directly. The highest correlation is found for the surface-layer Richardson number method. This method it also less sensitive to variation of measurement heights than the bulk Richardson number method.

Estimating the planetary boundary layer height from radiosonde and doppler lidar measurements in the city of São Paulo - Brazil

This study aims to compare the planetary boundary layer height (PBLH) values estimated by radiosonde data through the bulk Richardson number (BRN) method and by Doppler lidar measurements through the Carrier to Noise Ratio (CNR) method, which corresponds to the maximum of the variance of CNR profile. The measurement campaign was carried during the summer of 2015/2016 in the city of São Paulo. Despite the conceptual difference between these methods, the results show great agreement between them.

Atmospheric stability assessment for the characterization of offshore wind conditions

Based on the Fino-1 offshore met mast database, different instrument set-ups and methodologies for stability characterization have been tested using non-dimensional numbers like the gradient and bulk Richardson number, and their equivalences with the Obukhov parameter ζ = z/L, which can be measured locally with the use of a sonic anemometer. These equivalences depend to a large extent on the suitability of empirical stability functions obtained in horizontally-homogeneous conditions. The bulk Richardson number method, based on Grachev and Fairall (1997) empirical function, is the least demanding measurement method for stability characterization offering a more practical approach to wind farm designers than using the sonic method. Alternatively, the AMOK method, used by FUGA wake model and also based on the bulk Richardson number, assumes surface-layer theory and avoids using stability functions, which results in a more robust formulation. A 9-class stability classification based on Sorbjan and Grachev (2010) is used to generalize the categorization of wind conditions. Based on flux-profile analysis it was concluded that unfortunately the local ζ is not sufficient to describe the scaling behaviour of the stable boundary layer. Indeed, larger wind shear than predicted by classical onshore stability functions is found, probably as a result of lower boundary layer depths.

On the computation of planetary boundary-layer height using the bulk Richardson number method

Abstract. Experimental data from four field campaigns are used to explore the variability of the bulk Richardson number of the entire planetary boundary layer (PBL), Ribc, which is a key parameter for calculating the PBL height (PBLH) in numerical weather and climate models with the bulk Richardson number method. First, the PBLHs of three different thermally stratified boundary layers (i.e., strongly stable boundary layers, weakly stable boundary layers, and unstable boundary layers) from the four field campaigns are determined using the turbulence method, the potential temperature gradient method, the low-level jet method, and the modified parcel method. Then for each type of boundary layer, an optimal Ribc is obtained through linear fitting and statistical error minimization methods so that the bulk Richardson method with this optimal Ribc yields similar estimates of PBLHs as the methods mentioned above. We find that the optimal Ribc increases as the PBL becomes more unstable: 0.24 for strongly stable boundary layers, 0.31 for weakly stable boundary layers, and 0.39 for unstable boundary layers. Compared with previous schemes that use a single value of Ribc in calculating the PBLH for all types of boundary layers, the new values of Ribc proposed by this study yield more accurate estimates of PBLHs.

Comparison of GEOS-5 AGCM planetary boundary layer depths computed with various definitions

Abstract. Accurate models of planetary boundary layer (PBL) processes are important for forecasting weather and climate. The present study compares seven methods of calculating PBL depth in the GEOS-5 atmospheric general circulation model (AGCM) over land. These methods depend on the eddy diffusion coefficients, bulk and local Richardson numbers, and the turbulent kinetic energy. The computed PBL depths are aggregated to the Köppen–Geiger climate classes, and some limited comparisons are made using radiosonde profiles. Most methods produce similar midday PBL depths, although in the warm, moist climate classes the bulk Richardson number method gives midday results that are lower than those given by the eddy diffusion coefficient methods. Additional analysis revealed that methods sensitive to turbulence driven by radiative cooling produce greater PBL depths, this effect being most significant during the evening transition. Nocturnal PBLs based on Richardson number methods are generally shallower than eddy diffusion coefficient based estimates. The bulk Richardson number estimate is recommended as the PBL height to inform the choice of the turbulent length scale, based on the similarity to other methods during the day, and the improved nighttime behavior.

Mixing layer height retrievals by multichannel microwave radiometer observations

Abstract. The mixing layer height (MLH) is a key parameter for boundary layer studies, including meteorology, air quality, and climate. MLH estimates are inferred from in situ radiosonde measurements or remote sensing observations from instruments like lidar, wind profiling radar, or sodar. Methods used to estimate MLH from radiosonde profiles are also used with atmospheric temperature and humidity profiles retrieved by microwave radiometers (MWR). This paper proposes an alternative approach to estimate MLH from MWR data, based on direct observations (brightness temperatures, Tb) instead of retrieved profiles. To our knowledge, MLH estimates directly from Tb observations have never been attempted before. The method consists of a multivariate linear regression trained with an a priori set of collocated MWR Tb observations (multifrequency and multi-angle) and MLH estimates from a state-of-the-art lidar system. The proposed method was applied to a 7-month data set collected at a typical midlatitude site. Results show that the method is able to follow both the diurnal cycle and the day-to-day variability as suggested by the lidar measurements, and also it can detect low MLH values that are below the full overlap limit (~200 m) of the lidar system used. Statistics of the comparison between MWR- and reference lidar-based MLH retrievals show mean difference within 10 m, root mean square within 340 m, and correlation coefficient higher than 0.77. Monthly mean analysis for daytime MLH from MWR, lidar, and radiosonde shows consistent seasonal variability, peaking at ~1200–1400 m in June and decreasing down to ~600 m in October. Conversely, nighttime monthly mean MLH from all methods are within 300–500 m without any significant seasonal variability. The proposed method provides results that are more consistent with radiosonde estimates than MLH estimates from MWR-retrieved profiles. MLH monthly mean values agree well within 1 standard deviation with the bulk Richardson number method applied at radiosonde profiles at 11:00 and 23:00 UTC. The method described herewith operates continuously and is expected to work with analogous performances for the entire diurnal cycle, except during considerable precipitation, demonstrating new potential for atmospheric observation by ground-based microwave radiometry.

Structure of the planetary boundary layer over Southeast England: Modeling and measurements

The Weather Research and Forecasting model was applied to analyze variations in the planetary boundary layer (PBL) structure over Southeast England including central and suburban London. The parameterizations and predictive skills of two nonlocal mixing PBL schemes, YSU and ACM2, and two local mixing PBL schemes, MYJ and MYNN2, were evaluated over a variety of stability conditions, with model predictions at a 3 km grid spacing. The PBL height predictions, which are critical for scaling turbulence and diffusion in meteorological and air quality models, show significant intra‐scheme variance (> 20%), and the reasons are presented. ACM2 diagnoses the PBL height thermodynamically using the bulk Richardson number method, which leads to a good agreement with the lidar data for both unstable and stable conditions. The modeled vertical profiles in the PBL, such as wind speed, turbulent kinetic energy (TKE), and heat flux, exhibit large spreads across the PBL schemes. The TKE predicted by MYJ were found to be too small and show much less diurnal variation as compared with observations over London. MYNN2 produces better TKE predictions at low levels than MYJ, but its turbulent length scale increases with height in the upper part of the strongly convective PBL, where it should decrease. The local PBL schemes considerably underestimate the entrainment heat fluxes for convective cases. The nonlocal PBL schemes exhibit stronger mixing in the mean wind fields under convective conditions than the local PBL schemes and agree better with large‐eddy simulation (LES) studies.

Evaluating Formulations of Stable Boundary Layer Height

Abstract Stable boundary layer height h is determined from eddy correlation measurements of the vertical profiles of the buoyancy flux and turbulence energy from a tower over grassland in autumn, a tower over rangeland with variable snow cover during winter, and aircraft data in the stable marine boundary layer generated by warm air advection over a cool ocean surface in summer. A well-defined h within the tower layer at the grass site (lowest 50 m) and the snow site (lowest 30 m) was definable only about 20% of the time. In the remaining stable periods, the buoyancy flux and turbulence energy either (a) remained constant with height, indicating a deep boundary layer, (b) increased with height, or (c) varied erratically with height. Approximately one-half of the tower profiles did not fit the traditional concepts of a boundary layer. The well-defined cases of h are compared with various formulations for the equilibrium depth of the stably stratified boundary layer based on the Richardson number or surface fluxes. The diagnostic models for h have limited success in explaining both the variance and mean magnitude of h at all three sites. The surface bulk Richardson number and gradient Richardson number approaches perform best for the combined data. For the surface bulk Richardson number method, the required critical value varies systematically between sites. The surface bulk Richardson number approach is modified to include a critical value that depends on the surface Rossby number, which incorporates the influence of surface roughness and wind speed on boundary layer depth.