An observational climatology of the planetary boundary layer height (PBLH) diurnal cycle, specific to surface characteristics, is derived from 58 286 fine-resolution soundings collected in 14 major field campaigns around the world. An objective algorithm determining PBLH from sounding profiles is first developed and then verified by available lidar and sodar retrievals. The algorithm is robust and produces realistic PBLH as validated by visual examination of several thousand additional soundings. The resulting PBLH from all existing data is then subject to various statistical analyses. It is demonstrated that PBLH occurrence frequencies under stable, neutral, and unstable regimes follow a narrow, intermediate, and wide Gamma distribution, respectively, over both land and oceans. Over ice all exhibit a narrow distribution. The climatological PBLH diurnal cycle is strong over land and oceans, with a distinct peak at 1500 and 1200 LT, whereas the cycle is weak over ice. Relative to midlatitude land, the PBLH variability over tropical oceans is larger during the morning and at night but much smaller in the afternoon. This study provides a unique observational database for critical model evaluation on the PBLH diurnal cycle and its temporal/spatial variability.
The planetary boundary layer (PBL) is directly coupled with the earth’s surface, at a response time scale of about an hour or less (Stull 1988; Garratt 1992). Through the PBL, rapid exchanges of momentum, heat, moisture, natural, and anthropogenic chemical constituents take place between the free atmosphere and surface characteristics, including soil, vegetation of different varieties, water, ice, and snow. A fundamental variable of the PBL is its top height (PBLH) that determines many tropospheric processes critical to air pollution, such as aerosol distributions, convection activity, and cloud and fog formation. Thus, PBLH has been used as a key length scale in weather, climate, and air quality models to determine turbulence mixing, vertical diffusion, convective transport, cloud/aerosol entrainment, and atmospheric pollutant deposition (Deardorff 1972; Arakawa and Schubert 1974; Suarez et al. 1983; Wesely et al. 1985; Holtslag and Nieuwstadt 1986; Seibert et al. 2000; Stevens 2002; Lin et al. 2008; Konor et al. 2009).
The PBLH variability is dominated by its strong diurnal cycle (Stull 1988; Garratt 1992). It is typically shallow (<500 m) at night, as the surface layer becomes stable because of infrared radiative cooling; however, it grows deep (penetrating a few kilometers) in daytime when solar heating causes convective unstable conditions. The PBLH, however, is not directly observed by routine meteorological measurements. It is often diagnosed from vertical profiles of temperature, humidity, and wind. These profiles are conventionally measured with radiosondes only twice a day at specified synoptic times (0000 and 1200 UTC), and most data are reported only for the significant pressure levels with at most six records below 500 hPa (<6 km). The soundings often are insufficient in vertical resolution to estimate PBLH with an acceptable uncertainty and in temporal resolution to capture the diurnal structure. The two soundings correspond to evening (1600–1800) and morning (0400–0600 LST) over the United States. They miss not only the midafternoon peak but also the important morning and early-evening transitions (Angevine 2008). This explains why there exists no climatology of observed PBLH variations.
Recently, remote sounding systems such as lidar, sodar, wind profiler, and Radio Acoustic Sounding System (RASS; Clifford et al. 1994) have emerged to provide promising alternatives for continuous direct measurements or estimates of PBLH (Seibert et al. 2000). Yet, their operational use and data availability are still very limited. Most studies have focused on algorithm development and cross validation (Marsik et al. 1995; Grimsdell and Angevine 1998; Cohn and Angevine 2000; Hennemuth and Lammert 2006; Lammert and Bösenberg 2006; Wiegner et al. 2006; Münkel et al. 2007). Systematic documentation of the observed PBLH climatological variations has not been feasible because of relatively limited data records. In addition to those just cited, several more studies presented the PBLH diurnal cycle observations (Coulter 1979; Beyrich and Görsdorf 1995; Vogelezang and Holtslag 1996; Martano 2002; Asimakopoulos et al. 2004; Bretherton et al. 2004; Dandou et al. 2009). These studies, however, illustrated the PBLH diurnal evolution based on a few days of measurements at specific sites. There are two exceptions, both using sodar data: Argentini et al. (2005) showed the mean cycle and daily deviation from two summer months over the snow/ice surface at the Antarctic plateau station and Piringer et al. (2007) depicted the monthly-mean cycles of four seasons in the city center of Hannover, northern Germany.
The main objective of this study is, therefore, to establish an observational climatology of the PBLH diurnal cycle across a wide range of geographical locations with various surface characteristics. Here PBLH is diagnosed from fine-resolution sounding data of 58 286 samples collected in 14 major field campaigns during 1987–2008 around the world. In this regard, special recognition is given to Norton and Hoidale (1976), for the first and only documented climatological PBLH diurnal cycle and its seasonal variation based on 8236 radiosonde soundings irregularly released during 1961–72 at a high-elevation site over White Sands Missile Range (32°24′N, 106°22′W; 1216 m MSL), New Mexico. The soundings included here were mostly taken on a fixed schedule during the observational campaigns. Section 2 describes all the data used, while section 3 depicts the method to determine PBLH from sounding profiles as compared with available lidar and sodar retrievals. Section 4 shows the PBLH characteristic frequency distributions, while section 5 presents the climatology of the PBLH diurnal cycle, contrasting land, ocean, and ice surfaces as well as different seasons. A summary follows in section 6.
2. Description of observational data
Figure 1 illustrates the geographic locations and the name abbreviations of the 14 field campaigns, from which fine-resolution sounding data were collected for use in this study. Table 1 lists their site specifications, including elevation, surface characteristics, climate regime, data period, vertical resolution, temporal interval, and total number of records. All records include vertical profiles for pressure, temperature, relative humidity, and wind. Depending on the campaign, the vertical resolution of the available data ranges from 1 to 10 s per balloon rising or at 5-hPa intervals interpolated on constant pressure levels [only for the Cooperative Atmosphere–Surface Exchange Study of 1997 (CASES-97) and the First International Satellite Cloud Climatology Project (ISCCP) Field Experiment (FIFE)]. A sensitivity analysis is conducted to choose the suitable sounding vertical resolution from the range of 1–10 hPa or ∼10–100 m. It shows that a resolution of 5 hPa is appropriate for our purpose, balancing resultant accuracy with uncertainty due to raw data noise. As such, each raw sounding is resampled to obtain a profile starting from the second reading and stepping upward at every nearest 5-hPa decrement, within which data are discarded. The first reading is taken here to represent the surface air state. The resulting profile has a vertical resolution in the boundary layer of approximately 50 m, which is considered the truncation error in this study. The temporal interval also differs largely between campaigns or even within a same campaign, typically 3, 6, or 12 h. Some campaigns [CASES, FIFE, Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX)] have soundings every 1 h during intensive observation periods, while others contain only one record in a day.
The field campaigns are grouped into three major surface characteristics: land, ocean, and ice. The land category includes the Atmospheric Radiation Measurement Program (ARM)’s Southern Great Plains (SGP; Stokes and Schwartz 1994), CASES (LeMone et al. 2000; Poulos et al. 2002), FIFE (Sellers et al. 1992), Upper Missouri River Basin Pilot Project (UMRBPP) (Smith and Farwell 1997), and VORTEX (Rasmussen et al. 1994). Located in Oklahoma with relatively homogeneous topography, SGP measurements were taken continuously for more than 15 yr with a typical 3-h interval. It provides the best dataset for studying PBLH variations, especially with respect to diurnal cycle and seasonal changes, and for a wide variety of climate conditions, including mesoscale convection and low-level jets (LLJs). Observations in both CASES and FIFE were made over plain surfaces under fair-weather conditions at a high temporal (1–3 h) resolution. They also are ideal for depicting the representative PBLH diurnal evolution. Soundings from CASES were selected to illustrate physical definitions and numerical procedures for diagnosing PBLH of different regimes or phases. Given the availability of concurrent PBLH retrievals from lidar and sodar measurements, FIFE soundings were used to objectively verify our method for determining PBLH from radiosonde profiles. UMRBPP was conducted in the Black Hills of South Dakota and Wyoming, where terrain features are complex and surface elevations range from 505 to 1768 m. This campaign enables a comparison with others to identify the topographic effect. VORTEX was designed to test tornado theories and environmental regulations on storm structure. Thus, soundings were collected in the main updraft of the target storm and the surrounding near-storm environment over the southern Great Plains from Kansas to Texas. This campaign facilitates a comparison of PBLH between severe and fair weather conditions.
The ocean category includes the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE; Webster and Lukas 1992), the ARM tropical western Pacific (TWP; Mather et al. 1998), the East Pacific Investigation of Climate (EPIC; Weller et al. 1999; Raymond et al. 2004), the Variability of American Monsoon Systems (VAMOS) Ocean–Cloud–Atmosphere–Land Study (VOCALS; Wood et al. 2007), and the Indian Ocean Experiment (INDOEX; Ramanathan et al. 2001). Both TOGA and TWP were conducted in the western Pacific warm pool, identified with prevailing deep convections in the intertropical convergence zone (ITCZ). TOGA includes intensive observations for the 1992/93 winter [December–February (DJF)] from an array of 15 islands, seven ships, and two airplanes, while TWP consists of continuous measurements for more than 10 yr from three islands. Two islands (Manus, Nauru) were the common sites for TOGA and TWP, facilitating direct comparison of their results. Soundings from EPIC were mostly made during numerous ship cruises across a wide area over the eastern Pacific cold tongue/ITCZ complex, in the presence of prevailing trade stratus clouds. VOCALS soundings were taken over the southeast Pacific, where cold sea surface temperatures (SSTs) in combination with warm and dry air aloft support the largest and most persistent subtropical stratocumulus deck in the world (Wood et al. 2007). INDOEX also covered a wide area but focused on the northeast dry monsoon in the Indian Ocean, including ship cruises and observations from two islands. To our knowledge, only Zeng et al. (2004) and Bretherton et al. (2004) analyzed PBLH variations based on the EPIC data; however, none documented the PBLH diurnal cycle climatology over oceans from these campaigns. In addition, the Lake-Induced Convection Experiment (LAKE-ICE; Kristovich et al. 2000) was carried out over and near Lake Michigan during the 1997/98 winter when the water surface was mostly ice free. Results from this study are discussed separately to contrast PBLH characteristics over the midlatitude lake water from the tropical oceans.
The ice category includes the ARM North Slope of Alaska (NSA; Stamnes et al. 1999), the Surface Heat Budget of the Arctic Ocean (SHEBA; Uttal et al. 2002), and the Baltic Sea Experiment (BALTEX; Raschke et al. 2001). NSA and SHEBA were conducted in the Arctic but over land and ocean, respectively. BALTEX took place over the Baltic Sea, which experiences a seasonal ice cover. Only winter (December–February) soundings were selected to focus on the ice-covered surface. To our knowledge, there exists no previous study that has presented PBLH characteristics over ice from these campaigns.
Compilation of these geographically and seasonally diverse collections of soundings provides a unique and valuable opportunity to evaluate PBLH climatological characteristics in an unprecedented comprehensiveness.
3. Determination of PBLH from soundings
The PBL structure during a diurnal cycle can be classified into three major regimes (Stull 1988): convective boundary layer (CBL), stable boundary layer (SBL), and residual layer (RL). The CBL usually occurs in daytime and is driven by convective thermals generated as a result of heat transfer from a warm ground or radiative cooling from a cloud top. Strong turbulence mixing causes nearly uniform vertical distributions of potential temperature and constituents within the CBL. Conversely, the SBL forms often in nighttime because of radiative cooling of the ground or sometimes as warm air is advected over a colder surface. Both conditions create a boundary layer of air that is warmer than the underlying surface, and turbulence mixing is largely suppressed in the SBL. At the evening or morning transition, the RL is disconnected from the ground by the underlying SBL while maintaining the atmospheric state of the former CBL. Thus, the RL is not affected by turbulent transport from the surface but allows turbulence to decay homogenously in all directions.
Accordingly, the PBLH is defined for the CBL at the base of the overlying inversion layer that caps the rising convective thermals. For the SBL, the PBLH is defined as the top of the underlying inversion layer, where turbulence decreasing from the surface nearly ceases (Stull 1988). In both cases, the PBLH restrains the vertical domain in which turbulent transport from the surface has a significant influence. Note that the PBLH definition, although clear for the CBL, is less clear for the SBL as its top may blend into the RL above. During the evening and morning transitions where the RL may occur, we determine the PBLH as defined by the SBL if present or otherwise by that for the CBL excluding the entrainment zone at the top. The latter case is generally identified with near-neutral conditions in the surface layer (see below). Therefore, we consider only the neutral RL that starts from the ground surface, hereafter referred as to NRL.
Figure 2 illustrates the three PBL regimes in the real atmosphere under fair-weather conditions. The soundings were observed on 28 April 1997 from CASES. A CBL was fully developed at about 1630 LST, where potential temperature and water vapor mixing ratio were well mixed throughout the entire PBL. It was capped by a strong inversion layer of very dry air. The CBL then decayed into an NRL starting from the ground evident at about 1800 LST as the surface temperature was reduced, while potential temperature and water vapor mixing ratio structures were almost unchanged. As surface temperature further decreased, a SBL grew from the ground, with a clear surface inversion layer at 1930 LST, while the overlying RL was still obvious. By definition, the PBLH for the CBL, NRL, and SBL was determined at 1737, 1475, and 86 m above ground level (AGL), respectively. The PBLH so defined includes the midentrainment zone at the top for the CBL but excludes that for the NRL.
One key task of this study is to first develop a robust numerical procedure that automates the PBLH determination from all available soundings. This is sketched in Fig. 3. The procedure starts with the regime identification by examining the near-surface thermal gradient between the fifth and second levels, which are chosen specifically to remove the raw data noises:
where θ is potential temperature (Kelvin) and its subscript number denotes for the data level index assuming surface air at l = 1; δs is the θ increment for the minimum strength of the stable (inversion) layer above the CBL top or below the SBL top. The value of δs can be set to zero for idealized cases but in practice is specified as small positive by this study depending on surface characteristics (see below).
Since buoyancy is the dominant mechanism driving turbulence in the CBL, we determine the PBLH as the height at which an air parcel rising adiabatically from the surface becomes neutrally buoyant (Stull 1988). In practice, for the unstable regime, we first scan upward to find the lowest level l = k (Fig. 3) that meets the condition
where δu is the θ increment for the minimum strength of the unstable layer. This first-guess level k is then corrected by another upward scan to search for the first occurrence of
where θ̇ is the θ vertical gradient per height z and θ̇r is its minimum strength for the overlying inversion layer (Fig. 3). Here θ̇r can be considered as the overshooting threshold of the rising parcel and thus defines the scope of the entrainment zone for the CBL. The same procedure is adopted to determine the PBLH of the NRL for the neutral regime (Fig. 3).
Note that the virtual potential temperature is not used in the above formulations, because it contains larger uncertainties due to errors in measuring humidity and hence causes significant fluctuations in the resulting PBLH. Similarly, the two vertical scans start from the data level right above 150 m AGL for the CBL and NRL to avoid noisy readings near the surface. This corresponds to the fifth level for most sounding records. The above procedure requires the specification of three bound parameters: δs, δu, and θ̇r. Through visual validation with trial and error, these parameters are 1.0 K, 0.5 K, and 4.0 K km−1 over land, and 0.2 K, 0.1 K, and 0.5 K km−1 over oceans and ice, respectively. The distinction of the surface categories is necessary, since the diurnal cycle of the thermodynamic structure is much stronger over land than over oceans or ice.
Figure 4 compares the PBLH determined by the above procedure from radiosonde soundings and derived from lidar measurements in FIFE (available online at http://daac.ornl.gov/FIFE/guides/lidar_height_data.html). The height values are paired when the difference in observational times is less than 30 min and the lidar values are averaged over all available records during this interval. There are 51 pairs in total, of which 22 and 29 are identified with the unstable and neural regimes, respectively. The two results are in excellent agreement, with a correlation coefficient of 0.96, root-mean-square error of 211 m, and a Nash and Sutcliffe (1970) efficiency of 0.83. The PBLH from this procedure tends to be somewhat higher, mainly because the lidar detects the immediate top of the well-mixed layer, excluding the entrainment zone. This zone may extend 5%–100% of the underlying mixed layer (Cohn and Angevine 2000). The method used here determines the CBL height at about the middle to the top of the entrainment zone. Nonetheless, our comparison reaches a conclusion similar to Hennemuth and Lammert (2006), who found that the PBLH based on radisonde and lidar data deviates between ±200 m.
The PBLH is more difficult to quantify for the stable than unstable regime, and there is no unique algorithm to determine the SBL top accurately without actual observations of the turbulence kinetic energy profile in the boundary layer (Stull 1988; Seibert et al. 2000). In particular, the SBL turbulence can result from two dominant mechanisms: buoyancy forced and/or shear driven. At night, wind usually calms down near the ground but may sometimes accelerate aloft to form a nocturnal LLJ. The stable stratification reduces surface buoyancies that suppress turbulence, while the developing LLJ enhances wind shear that generates turbulence. Thus, for the stable regime, the PBLH is defined at either the top of the bulk stable layer starting from the ground or at the level of the LLJ nose if present, whichever is lower (Fig. 3).
In the case where the SBL is forced primarily by buoyancy, we first scan upward to find the lowest level at which θ̇k reaches a minimum and then determine the PBLH at that level if either of the following conditions is met:
where the first condition ensures that θk is a local peak with a curvature parameter δ̇ of 40 K km−1 and the second condition constrains that an inversion layer is not evident in the upper two layers. The PBLH so defined represents the transition from the stable layer to a neutral or unstable condition above.
In the case where the SBL turbulence generation is dominated by shear, the LLJ nose is identified at the level where wind speed reaches a maximum that is at least 2 m s−1 stronger than the layers above and below while decreasing monotonically toward the surface (Bonner 1968; Stull 1988). In many events, especially at night, the bulk stable layer can be deep, extending from the surface to above 2 km, whereas the LLJ can also be strong, with the nose closer to the ground. For such cases, the PBLH is defined at the lower height of the two diagnosed from the thermal (θ stability) and dynamic (wind shear) profiles.
Figure 5 illustrates the procedure to diagnose the PBLH from radiosonde measurements for three typical SBL cases. The soundings were observed on 29 and 30 November and 3 October 2000 from ARM SGP. They respectively depict an SBL 1) driven primarily by surface buoyancy with weak wind, 2) having a strong but shallow surface inversion layer with a clear LLJ structure aloft, and 3) dominated by shear turbulence generation with a pronounced LLJ nose in a deep inversion layer. The PBLH is determined by the vertical structure of θ for the first and second cases (as the LLJ nose exists at a higher level) but by that of wind in the third case (since the bulk stable layer penetrates above the LLJ nose).
Figure 6 compares the PBLH determined by the above procedure from radiosonde soundings and derived from sodar retrievals in FIFE (available online at http://daac.ornl.gov/FIFE/guides/sodar_bndry_layer_hts.html). The heights are paired with the difference in observational times less than 30 min and the sodar values are averaged over all available records during this interval. There are 23 pairs in total, of which 11 stable and 12 neutral regimes are identified. Relative to those for CBL versus lidar measurements (Fig. 4), the results for SBL versus sodar retrievals (Fig. 6a) are in poor agreement, with a correlation coefficient of 0.6, root-mean-square error of 167 m, and Nash–Sutcliffe efficiency of −0.49. To better understand the differences, Fig. 6b illustrates the θ profiles of all 23 records with concurrent radiosonde and sodar data. Each successive profile is displaced by 5 K for a clear view and marked by two symbols for the sounding-diagnosed and sodar-retrieved PBLH values. A visual examination indicates that our diagnostic approach based on radiosonde profiles performs well and is generally more accurate than the sodar method. Only 3 out of the 23 soundings show the sodar retrievals are better. For the NRL, our diagnosed PBLH closely matches the lidar result (Fig. 4), which has been established as a reliable observation (Seibert et al. 2000). Thus, the large discrepancy revealed for the NRL in Fig. 6 may indicate that the sodar method is relatively unreliable.
The PBLH results have been visually evaluated for thousands of sounding profiles, by examining plots such as Figs. 2, 5, and 6b, and have confirmed that the diagnostic approach outlined above is realistic and robust. Given this established approach, the following documents the observed diurnal cycle climatology of the PBLH from all available field campaign data.
4. PBLH statistical characteristics
This section examines gross statistical characteristics of PBLH variations, distinguishing land, ocean, and ice surfaces. Figure 7 compares the frequency distributions for occurrences of the stable (SBL), neutral (NRL), and unstable (CBL) regimes at 3-h intervals (LST) across the diurnal cycle. Most of the campaigns were based on multiple sites, covering a wide area. Each record is identified with a specific LST that corresponds to the actual time and location (longitude) of the observation. All records that fall within the 3-h window are counted at the respective center LST. Over land, data records are dominated by ARM SGP (Table 1), which alone has the number of soundings approximately 12.5 times the total of all the other four campaigns (CASES, FIFE, UMRBPP, VORTEX). The SGP and non-SGP results are shown separately to depict how representative the SGP statistics are for land. From the other campaigns, all available data are grouped into ice and water categories. For each category, the total number of records is plotted as a measure of sampling adequacy.
Over land from SGP alone (Fig. 7a), the number of available records is 485 (522) at 0300 (2100) LST and much larger at other times, varying between 1248 and 4411. They are sufficient to provide a robust statistics for each time interval. The SGP and non-SGP data indicate that the CBL regime over land mainly occurs in daytime from 0900 to 1800 LST, peaking at 1500 LST. In contrast, the SBL regime dominates at nighttime: evenly distributed at 0300, 0600, 2100, 2400 LST with occurrence exceeding 70% but declining to about 20% at 0900 and 1800 LST and below 5% at 1200 and 1500 LST. The NRL regime accounts for the remaining portion, identified with approximately 25% of the soundings at nighttime and more than 60% at daytime.
Over oceans with all the campaigns combined (Fig. 7c), the number of available records is 593 (699) at 1800 (0600) LST and much larger at other times, varying between 1324 and 8423. They are also sufficient to provide a robust statistics at each time interval. The CBL regime over oceans can occur during the whole day; however, its frequency has a distinct diurnal cycle that maximizes (54%) at local noon, minimizes (2%) at midnight, and is high (37%–47%) at 0900, 1500, 1800 LST. In contrast, the SBL regime has an opposite diurnal cycle: its frequency of occurrence minimizes (15%) at 1200 and 1500 LST, medium (21%) at 0900 and 1800 LST; high (53%, 57%) at 0300 and 0600 LST; and maximizes (76%, 77%) at 2100 and 2400 LST. As compared with land (Fig. 7a), the CBL regime over oceans occurs more frequently and during a longer period, enhanced especially at 0900 and 1800 LST. Also, the frequency of the SBL regime over the oceans increases by 14% at 1200 and 1500 LST; decreases by 15% and 20% at 0300 and 0600 LST, respectively; and changes little at other times in comparison with land. The NRL regime over oceans is not predominant in daytime, with its frequency reduced from that over land by 20%–33% at 0900, 1200, 1500, and 1800 LST. These land–ocean contrasts result from the much stronger diurnal variation of surface temperature over land than oceans.
Over ice with all the campaigns combined (Fig. 7d), the number of available records varies from 45 at 0300 LST to 2037 at 1200 LST. The statistics are less robust because of the limited data available. The CBL regime is generally less frequent, that is, all the percentages were less than 10%. The NRL regime is predominant at 0600, 2400, 1800, 0900, 1200 LST with increasing frequency from 55 to 64. At 0300 LST, the SBL regime dominates. For all regimes, the diurnal variations are less obvious than those over land or oceans.
Figure 8 compares the frequency distributions of PBLH variations under the SBL, NRL, and CBL regimes, using all available data records. They are calculated for bins of every 50-m PBLH interval, from 25 to 75 to 2975 to 3025 m. Clearly, none follow a Gaussian distribution. All have longer tails on the right and thus are positively skewed. They can be well fitted by a Gamma distribution. The probability density function of a Gamma-distributed random variable x is defined as
where parameters (k, s), both positive, depict the shape and scale of the distribution; Γ is the Gamma function. By such a distribution, the mean, deviation, and skewness of x are ks, ks, and 2/k, respectively. It is found by trial and error that x = PBLH/50 gives the best overall fit. The fitted Gamma distributions and corresponding parameters are illustrated in Fig. 8 for different surface categories.
Over land from SGP alone (Fig. 8a), the PBLH frequency distributions differ significantly between the stable, neutral, and unstable regimes. The SBL frequency follows well a narrow Gamma distribution (k = 3.0, s = 1.6), except for greater occurrences at the peak (150 m). In contrast, the CBL frequency is more closely depicted by a broad Gamma distribution (k = 3.5, s = 7.2), which has a quite flat shape with a wider PBLH range of similar occurrences around the peak (900 m). The peak occurrence drops substantially from 21% for SBL to 4% for CBL, while the PBLH variability (measured by deviation from its mean) increases by a factor of 4. The NRL frequency is intermediate of the two and defined mostly by a Gamma distribution (k = 1.7, s = 8.7), except for greater occurrences below 250 m. These features are generally captured by other land campaigns combined (Fig. 7b), with relatively small departures in the fitting parameters and larger fluctuations due to very limited data samples.
Over oceans with all the campaigns combined (Fig. 8c), the SBL frequency is approximated by a narrow Gamma distribution (k = 3.5, s = 1.0). As compared with those over land from SGP alone, the SBL occurrences over oceans are fewer between 200 and 600 m but more frequent for both lower and higher PBLH. In contrast, the CBL frequency follows well a broad Gamma distribution (k = 6.6, s = 2.6). Relative to SGP land, this distribution has smaller skewness (0.78 versus 1.15), identified with a much sharper peak frequency (7.3% at 800 m versus 4.0% at 900 m), and systematically greater (fewer) occurrences below (above) 1150 m. The NRL frequency is in between the other two and is estimated reasonably by a Gamma distribution (k = 2.3, s = 3.9), except for fewer (greater) occurrences between 250 and 450 m (below 250 m). This pattern resembles that over SGP land but with greater (fewer) occurrences below (above) 850 m. Thus, under all conditions, the PBL is generally shallower over oceans than land, because SST has a much weaker diurnal variation (Chen and Houze 1997). Conversely, stable conditions are also identified with deeper PBL over oceans than land, because of more frequent occurrences of warm air advecting over the colder water surface.
Over ice with all the campaigns combined (Fig. 8d), the SBL frequency closely follows a narrow Gamma distribution of (k = 2.0, s = 2.4). This resembles that over land, albeit with a tighter fit. The CBL frequency can be approximated by a very similar Gamma distribution (k = 2.2, s = 2.1), except for more frequent occurrences at a lower peak height (150–200 m). This is different from that over land and ocean. The NRL frequency also exhibits a similar feature, with a reasonable fit by a Gamma distribution (k = 3.5, s = 1.9). This is even narrower than that over oceans, with more occurrences at a lower PBLH. The similarity across the regimes results from weaker diurnal variations than those over land and ocean (Fig. 7d).
5. PBLH diurnal cycle climatology
This section presents the climatology of the PBLH diurnal cycle based on observations from individual campaigns providing data for different seasons and synoptic conditions. Since the PBLH frequency distribution, as discussed in section 4, is non-Gaussian, the conventional use of mean and variance is less meaningful. Instead, the 25%, 50%, and 75% quantiles along with the average of PBLH temporal variations are shown. Following the previous analysis of the PBL regimes (Fig. 7), we construct the PBLH diurnal cycle at every 3-h interval, within which all corresponding data records are counted in the statistics. There are eight windows, centered at 0000, 0300, 0600, 0900, 1200, 1500, 1800, and 2100 LST, at which the subsequent result is displayed. For each campaign or its subset, the result at a specific LST is illustrated only when the respective number of data records exceeds 15 and represents at least 1% of the total across the entire day.
Figure 9 compares the statistics of the PBLH diurnal cycles over land among individual campaigns: ARM SGP, CASES, FIFE, VORTEX, and UMRBPP. Irrespective of different observational seasons and statistical measures, all campaigns reveal a well-defined PBLH diurnal cycle, having a distinct peak at 1500 LST and a morning (afternoon) transition at 0600 (2100) LST. The nighttime (2100–0600 LST) is almost exclusively under the stable regime for the PBLH below the 25% quantile and is replaced more by the neutral regime for higher quantiles. Without the unstable regime, the PBLH differences between the 75% and 25% quantiles are all less than 250 m, indicating small fluctuations at night. Conversely, the daytime PBLH varies in much larger magnitudes, where the 75% minus 25% quantile differences increase from 300 to 600, 400 to 800, 600 to 1000, 800 to 1200 m at 0900, 1200, 1500, and 1800 LST, respectively. The PBL evening transition is more distinct at 1800 LST and more abrupt than the morning rise at 0900 LST. The range at each time interval depicts the contrast between the campaigns.
Differences are found between CASES and FIFE from SGP, even though observational sites are close to each other. This is mainly attributable to the limited data records in shorter periods for CASES and FIFE. The SGP soundings were taken regularly, often at every 3-h interval and continuously over 15 yr, and thus are sufficient to construct a robust seasonal climatology of the PBLH diurnal cycle. As shown by the 50% quantile (Fig. 9f), the daytime PBLH at SGP exhibits large seasonal changes from winter to autumn [September–November (SON)] to spring [March–May (MAM)] to summer [June–August (JJA)] in an increasing order, while little variation occurs at night. The annual statistics (Fig. 9a) falls between those of autumn and spring. Since CASES was conducted under fair-weather conditions in April and May, its PBLH diurnal cycle of the 75% quantile agrees well with that for the SGP spring. FIFE was also conducted under fair-weather conditions but in summer, with warmer surface temperature causing stronger turbulence mixing, and hence its PBLH is generally higher than CASES.
Conversely, VORTEX soundings were collected under severe weather conditions inside and surrounding several target storms in March–June. As compared with FIFE and CASES, the PBLH is much higher in the morning (0900 LST) but systematically lower from noon onward (1200, 1500, 1800 LST). Deeper morning PBL mixing distributes surface convective energy throughout a thicker column, providing a favorable environment for severe storms to develop. The developing storms then produce clouds and precipitation, reducing surface solar and thermal heating and thus suppressing the PBLH.
While these previous campaigns were taken at low elevation (315–576 m) with relatively flat terrain, UMRBPP was conducted in April and May over a high mountain (1220 m) with heterogeneous topography. As such, it has much a larger surface roughness and acts as an elevated (sensible) heat source, both causing stronger turbulence mixing and convective instability. Because of this orographic enhancement effect, the PBLH over UMRBPP, as compared with other campaigns, typically rises much faster in the morning and penetrates into higher levels at noon and during the afternoon (especially for the peak at 1500 LST). The PBLH is identified more frequently with the convective regime in the daytime, while it resembles other campaigns at night. Note that our UMRBPP result resembles that of Norton and Hoidale (1976) for a high-elevation site over White Sands Missile Range, except for somewhat lower PBLH values. The discrepancy may arise from the different sampling method used.
Figure 10 compares the statistics of the PBLH diurnal cycles over oceans from ARM TWP, TOGA COARE, EPIC, VOCALS, and INDOEX. During the analysis, it was found necessary to separate measurements based on islands and ship cruises. In particular, site C2 on Nauru in TWP and TOGA and two sites on Kaashidhoo and Hulule in INDOEX have PBLH diurnal cycles that are very different from the rest of the respective campaigns. These three island sites have been singled out for the statistics in Fig. 10. Without them, TWP, TOGA, and EPIC all reveal a well-defined PBLH diurnal cycle that has a distinct peak at 1200 LST, in phase with solar heating and also that of near-surface atmospheric conditions. On the basis of the data from TOGA COARE and improved meteorological (IMET) instruments’ moored buoys, Chen and Houze (1997) found that both surface air temperature and SST maximize at ∼1200 LST over open tropical oceans. It is not clear whether such a PBLH diurnal cycle is linked with the atmospheric tides. But the peak of the surface wind convergence explained by the tide theory in Ueyama and Deser (2008) is not consistent with that of the PBLH. As compared with land, this peak over oceans occurs about three hours earlier and the diurnal range is weaker. All statistical measures show that PBLH decreases from TWP to TOGA to EPIC.
The PBLH differences of the 75% minus 25% quantiles (depicting temporal variability) are similar for TWP, TOGA, and EPIC, and they are quite symmetric about the peak at 1200 LST. They closely match the SGP land value at 1200 LST but differ widely for the rest. As compared with SGP, the variability over oceans is persistently larger during the morning and at night but much smaller in the afternoon. Since the daytime PBLH variability increases continuously until the transition at 1800 LST over SGP, while gradually decreasing after noon over TWP, TOGA, and EPIC, the land–ocean contrast increases from 1200 to 1800 LST.
Discrepancies among the campaigns over tropical oceans are larger than those over midlatitude land. This results partly from the weaker (than land) SST diurnal variation that enables atmospheric conditions to play a more dominant role in defining PBLH. The atmospheric conditions are more variable (than SST) among different climate regimes, because of synoptic and mesoscale processes of vertical motion and horizontal advection of different air masses. Conversely, warmer SST generally forces a PBL to penetrate into a higher level. EPIC was centered over the eastern Pacific cold tongue/ITCZ complex, while TWP was conducted over the western Pacific warm pool and consists mainly of island observations. As such, the former is identified with shallow trade wind cumulus, while the latter is associated with ITCZ deep convection. This explains why PBLH is systematically lower in EPIC than TWP. A similar reason applies to the daytime PBLH that is significantly lower in TOGA than TWP. Excluding Nauru, TWP consists of only two islands, while TOGA is mixed with islands and water. In the daytime, while receiving the same amount of solar radiation, SST warms much less than land surface temperature because of a greater heat capacity and strong turbulence mixing in the upper ocean.
Given similar SSTs, the PBL regimes are determined by near-surface air conditions. INDOEX was taken in winter, having SSTs close to TOGA. Yet the monsoonal northeasterly flow brings dry continental air over the ocean, producing low-level temperature inversions and mostly clear skies with scattered cumuli (Ramanathan et al. 2001). As such, INDOEX is dominated by the neutral regime (272 events versus 43 stable and 76 unstable cases), under which the PBLH is generally low. This explains why INDOEX, excluding the two islands, has the lowest PBLH with the smallest diurnal range among the five campaigns over oceans. Similarly, VOCALS was taken over cold SSTs, where large-scale subsidence (causing warm air) prevails aloft and southerly winds (advecting cold polar air) dominate the near-surface with frequent capping LLJ events (Garreaud and Muñoz 2005; Wood et al. 2007, 2009). As a result, VOCALS is also dominated by the neutral regime (588 cases of total 661 records) with a strikingly weak PBLH diurnal cycle under the persistent stratocumulus deck. The PBLH resembles the mean inversion height during 16–21 October 2001 from EPIC that took place at the same region (Bretherton et al. 2004).
On the basis of LAKE-ICE (Fig. 10h), the PBLH diurnal cycle over lake water (mostly unfrozen) resembles that for typical oceans, having a distinct peak at 1200 LST but with much weaker amplitude. This smaller diurnal range is caused mainly by weak thermal forcing from below, because the midlatitude Lake Michigan during winter has colder surface temperatures and smaller sensible heat fluxes than those over oceans near the equator.
Islands may have PBLH diurnal cycle characteristics that differ from both land and water. In particular, Nauru in TOGA and TWP exhibits a striking PBLH feature of double peaks at about 1200 and 1500–1800 LST (Fig. 10c). The former is coincident with the peak over water, while the latter is close to that over land. The two islands from INDOEX also show a peak at 1200 LST and maintain relatively high PBLH until 2100 LST (Fig. 10f). The superimposition of the continental and marine PBL processes may explain the feature at the islands. These results may be subject to an issue of data sample irregularity. The statistics for Nauru are based on a total of 7587 data records. The data, however, are unevenly distributed, with 470, 3144, 296, and 36 records at 0900, 1200, 1500, and 1800 LST, respectively. In contrast, the two islands in INDOEX contain only 301 samples. Hence, a more rigorous diagnostic analysis is needed to better understand the responsible physics processes if any or otherwise sampling errors.
Figure 11 compares the statistics of the PBLH diurnal cycles over ice from ARM NSA, SHEBA, and BALTEX. Both NSA and SHEBA were conducted in the Arctic, with land and seawater beneath ice cover, respectively. In contrast, BALTEX was mixed with ice and seawater. Because of weak thermal forcing from below, the PBLH over ice is generally much lower than that over land and oceans. All statistical measures, based on 2788 data records, show that NSA has very little diurnal variation in PBLH. PBLH remains at approximately the same level (with the mean of 240 m) from 0600 to 1800 LST and then drops by 50–150 m (depending on the measures) in about three hours. For comparison, as shown by Argentini et al. (2005) using sodar retrievals, the PBLH averaged in high summer over the Antarctica (always covered by snow and ice) remains around 100 m during 1800–0600 LST and reaches about 200 m at 1300–1500 LST. These two levels correspond to the height of the ground-based SBL at nighttime and the inversion capping the CBL in daytime, respectively. This PBLH diurnal variation resembles that of NSA, except for a shorter daytime high duration and a longer nighttime low duration.
SHEBA has only 815 records in total, with 298 samples at 1200 LST. Thus, the statistics are less robust than for NSA, especially for high quantiles having a small number of measurements. Nonetheless, the 25% and 50% quantiles over SHEBA both depict a flat PBLH all day long, resembling NSA at 0300–1800 LST. Conversely, BALTEX has 2341 records in total, quite evenly distributed among 0000, 0600, 1200, and 1800 LST. All statistical measures reveal an obvious PBLH diurnal cycle, which peaks at 1200 LST and gradually declines toward the minimum at 0600 LST. Except for the 25% quantile, all other measures indicate an asymmetric structure, where the PBLH is systematically higher at 1800 than 0600 LST. Perhaps this results from the enhanced solar heating in the late afternoon that warms the surface to produce larger sensible heat flux upward and hence higher PBLH. The associated ice melting process in BALTEX may play a major role in its PBLH characteristic differences from NSA and SHEBA.
6. Sample irregularity effect
For all 14 campaigns, the number of sounding samples differs greatly between times of day. For example, ARM SGP contains the smallest 485 (largest 4411) samples at 0300 (0600) LST. The corresponding numbers are 85 (1929) at 1800 (0900) LST for TOGA COARE excluding C2, and 50 (963) at 2100 (1200) LST for ARM NSA. Such sample irregularity may cause large uncertainty in the PBLH diurnal cycle documented in section 5. The following provides a statistical test based on 10 000 permutations from a random resampling procedure to depict the degree of that uncertainty for these three major surface categories (land, ocean, ice).
The procedure first defines the number of samples for a permutation (n) in all LST windows identical to the least value of the day for each campaign. This n equals 485 (SGP), 85 (TOGA), and 50 (NSA). For every LST, a permutation is then constructed by randomly selecting n samples from all the raw data available in that window. This random procedure is repeated to produce an ensemble of 10 000 permutation-mean PBLH values. The 5th and 95th percentiles of the ensemble are chosen to test the sample irregularity effect, or the uncertainty range of the average result using all available raw data. Figure 12 illustrates the effect for the three campaigns. Clearly, the uncertainty range for SGP is very narrow, generally less than 50 m, except for 79–104 m at 1200–1800 LST. The range for TOGA increases to 93 m on average and 117–145 m at 1200–1500 LST. For both SGP and TOGA, all three measures (the overall average, and the 5th and 95th percentiles) identify the diurnal cycle peak at the same LST. Conversely, the uncertainty range for NSA is 114–201 m, which is relatively large compared with its gross daytime mean of 240 m; the diurnal cycle is also more evident from the 5th and 95th percentiles, with a distinct peak at 1200 LST. This indicates that the NSA result is notably affected by the sample irregularity.
This study establishes an observational climatology of the PBLH diurnal cycle across a wide range of geographical locations with various surface characteristics. It is derived from 58 286 fine-resolution soundings collected in 14 major field campaigns around the world. An objective algorithm was developed to determine the PBLH from sounding profiles. The results are realistic compared with available lidar and sodar retrievals as well as visual validation against several thousand additional soundings. The PBLH occurrence frequencies were presented under stable, neutral, and unstable regimes. For both land and oceans, they followed a narrow, intermediate, and wide Gamma distribution, respectively. Over ice, all regimes exhibited a narrow distribution. Last, the climatology of the PBLH diurnal cycle was constructed, contrasting land, ocean, and ice surfaces as well as different seasons. Both land and oceans reveal a strong PBLH diurnal cycle, with a distinct peak at 1500 LST over land and 1200 LST over oceans. The diurnal range over ice is very small, except for BALTEX due to the mixture of water and ice. As measured by the differences of the 75% minus 25% quantiles, the daytime PBLH temporal variability increases sharply until the establishment of the SBL at 1800 LST over land. Over tropical oceans, the PBLH gradually increased and then decreases with symmetric rates around noon. Relative to midlatitude land, the PBLH variability over oceans is persistently larger during the morning and at night but much smaller in the afternoon.
Islands may have PBLH diurnal cycle characteristics that differ from those typical of land and water, exhibiting a feature like the superimposition of the continental and marine PBL processes. The actual mechanisms over islands are complex and warrant detailed studies combining satellite observations and numerical simulations (e.g., Yang et al. 2008b,a). The results, irrespective surface types, may also be subject to the influence of data sample irregularity. The statistical test based on a random resampling procedure reveals that the sample irregularity may cause notable uncertainties in the PBLH diurnal cycle if insufficient data are available (e.g., over ice) but otherwise insignificant effects on the result (e.g., over land at SGP and ocean at TWP or TOGA).
The general characteristics of PBLH diurnal variations during fair-weather events are well known (Stull 1988; Garratt 1992; Grossman and Gamage 1995). Yet there has been no observational study on the climatology of the PBLH diurnal cycle occurring over different surface characteristics and under various synoptic conditions. While some attempts addressed the PBLH climatology from numerical models (Randall et al. 1985; Medeiros et al. 2005; Konor et al. 2009), the simulation results validation against observations has been essentially lack. The present work provides a unique observational database not only for critical model evaluation but also for other applications, including satellite retrievals from radio occultation measurements (Ho et al. 2007). In this regard, all the PBLH data and statistics derived in this study will be made available upon request.
We thank Dave Kristovich and Michael Spinar for their constructive discussions on the PBL processes, and Nancy Westcott and James Angel for their detailed comments on the manuscript draft. We are grateful to Paquita Zuidema and other two anonymous reviewers for their instructive suggestions. We acknowledge NCAR for making available all the sounding data and NCSA/UIUC for the computing support. The research was supported in part by the NOAA Educational Partnership Program (EPP) COM Howard Grant 631017 and Climate Prediction Program for the Americas (CPPA) Grant NA08OAR4310875. The views expressed are those of the authors and do not necessarily reflect those of the sponsoring agencies and the Illinois State Water Survey.
* Additional affiliation: Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois
Corresponding author address: Dr. Xin-Zhong Liang, Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, 105 S. Gregory Street, Urbana, IL 61801. Email: firstname.lastname@example.org