Environ. Sci. Technol. 2003, 37, 4336-4342
Variability of Apparent Particle Density of an Urban Aerosol M I K E P I T Z , * ,†,‡ J O S E F C Y R Y S , †,‡ ERWIN KARG,§ ALFRED WIEDENSOHLER,| H . - E R I C H W I C H M A N N , †,‡ A N D JOACHIM HEINRICH‡ Biometrics and Epidemiology, Institute of Medical Data Management, Ludwig-Maximilians-University, Munich, D-85758 Germany, Institute of Epidemiology, GSF National Research Center for Environment and Health, Efurt, D-99096 Germany, Institute for Inhalation Biology, GSF National Research Center for Environment and Health, Neuherberg/ Munich, D-85758 Germany, and Institute for Tropospheric Research, Leipzig, D-04318 Germany
The day to day and diurnal variation of apparent particle density was studied using highly time-resolved measurements of particle number distribution and fine-particle mass concentration. The study was conducted in Erfurt, Germany, from January 1, 1999, to November 22, 2000. A setup consisting of a differential mobility particle spectrometer and a laser aerosol spectrometer was used for particle number distribution measurements. PM2.5 particle mass was measured in parallel on an hourly basis using a tapered element oscillating microbalance (TEOM) and on daily base by using a Harvard marple impactor (HI). For the estimation of the mean apparent density of particles, number size distributions were converted into volume size distributions, assuming that the particles were spherically shaped. The volume size distributions were integrated over the range of 10 nm to 2.03 µm Stokes equivalent diameter to obtain volume concentrations. Mean apparent particle density was calculated as ratio of mass concentration and volume concentration. The mean apparent particle density, determined from HI and number size distribution on a daily basis was 1.6 ( 0.5 g cm-3. We found a strong dayto-day variation of apparent density ranging from 1.0 to 2.5 g cm-3 (5th and 95th percentile). Furthermore, the apparent density showed pronounced diurnal pattern both in summer and in winter and also on weekdays and weekends. The apparent density was lowest in the morning and highest in the afternoon. The mean apparent density on an hourly basis was 1.4 ( 0.5 and 1.5 ( 0.5 g cm-3 for PM2.5TEOM and corrected PM2.5TEOM using regression equation between daily mass concentration of HI and TEOM, respectively. The strong diurnal variation of apparent particle density was associated predominantly with the vertical temperature inversion and with traffic intensity. Thus, the apparent particle density depends on the physical particle properties and might be related to chemical composition of the sampled particle. * Corresponding author telephone: +49-361-3460-631; fax: +49361-3460-639; e-mail:
[email protected]. † Ludwig-Maximilians-University. ‡ Institute of Epidemiology, GSF National Research Center for Environment and Health. § Institute for Inhalation Biology, GSF National Research Center for Environment and Health. | Institute for Tropospheric Research. 4336
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Introduction Time-series studies have shown that increased daily means of fine-particle mass concentrations are associated with increased mortality rates and hospital emergency room visits, increases in respiratory symptoms, and lung function decrements as well as cardiovascular end points. Particularly in asthmatics and children, associations were observed with respiratory illnesses and with decreases in lung function (1). Studies on short-term effects have shown that high particulate air pollution exposures are associated with changes in plasma viscosity, heart rate, and lung function (2-4). All these studies used in general daily averages of mass concentration and, more rarely, number concentration to assess the association between ambient air pollutant levels and health effects. However, other aerosol parameters such as particle surface or chemical composition are also discussed as being relevant for toxicological and epidemiological studies (5-7). Particle density is a parameter that directly controls particle deposition in the lungs by inertial and sedimentational processes. The knowledge of particle size, shape, and density would improve the output of model deposition calculation results. In the environment, particle density is influenced by physical and chemical particle composition and by the generation processes. Thus, particle density may play a prominent role in the consideration of the associations between health effects and particulate air pollutants. When PM2.5 mass concentration and particle size are measured in parallel, density data are available as the ratio between mass concentration and integrated volume concentration for the overlay size range of both instrumental setups. Consequently, this parameter includes the errors of both setups; it is associated with a high uncertainty due to error propagation. The density calculated in this study is an average density for all spherical particles up to an aerodynamic diameter of 2.5 µm; therefore, it is addressed as “apparent density”. It may be totally different from the bulk density of the particulate material itself as indexed in handbooks. It depends on the physical and chemical composition of the particle populations sampled. For instance: (i) Particles from the earth’s crustal erosion processes such as wind erosion, industrial sources, or road dust events are expected to consist of dispersed bulk material with a bulk densitiy of about 2.7 g cm-3 as indicated by Ha¨nel and Thudlum (8) for desert dust or 1.6-3.2 g cm-3 as indicated by Ghosal and Self (9) for coal combustion. (ii) Hygroscopic particles from local industrial sources or adverted by long-distance atmospheric transport may have performed condensation and evaporation processes with liquefaction and amorphous crystallization. They are expected to consist of a mixture of materials and amorphous crystals. They have an effective density of 1.6 g cm-3 (10) as measured at a suburban site, of 1.6-1.8 g cm-3 as indicated by Stein et al. (11) for background aerosol particles, and of 1.7 g cm-3 as calculated by Putaud et al. (12) for maritime sulfate aerosols. (iii) Freshly emitted combustion particles consisting of nano-nuclei loosely aggregated to clusters of various diameters are expected to result in an apparent density below 1 g cm-3, whereas the bulk density of coal is indexed as 1.4 g cm-3. Lapuerta et al. (13) found an effective density of diesel exhaust particles of 0.6-0.4 g cm-3 for an engine load rising from 30 to 70%, and Park et al. (14) reported effective densities of diesel particles for 50-220 nm (mobility size) ranging from 10.1021/es034322p CCC: $25.00
2003 American Chemical Society Published on Web 09/06/2003
1.2 to 0.55 g cm-3 and from 0.95 to 0.39 g cm-3 for the engine running at 10% and 50% loads, respectively. (iv) Most urban spherical hygroscopic particles of ∼0.1and ∼0.3 µm have several distinct masses, resulting in 1.54-1.77 g cm-3 at 3-6% relative humidity (RH) and 0.25-0.64 and 1.7-2.2 g cm-3 “effective densities” for less massive particles (chain agglomerate soot) and more massive particles, respectively (15). The apparent particle density depends on many parameters. During the generation process, initial number concentration, coagulation status, and vapor condensation form the emitted particles. During atmospheric transport, temperature and humidity, condensation and evaporation, radiation, wind conditions, and mixing with other particle populations transform the aerosol and result in a modification of the initial density. During sampling, the transmission efficiency of the sampling line and the instruments individual analysis methods additionally change the density for instance by drying and heating. Thus, apparent density is expected to be very variable and uncorrelated to a single meteorological or particulate measurement parameter. However, some basic aspects of particle composition and behavior can be derived from our data, for example, to convert number distributions to mass distributions and to determine the relationship between aerodynamic and Stokes diameter. There are only a few studies investigating the daily and hourly variation of particle density. Morawska et al. (16) reported a 4-h mean particle density over a 12-d period in the summer of 1.7 ( 1.0 g cm-3 for ambient air and a variation of 1.2-1.8 g cm-3 depending on the time of day for Queensland, Australia. Kuhlbusch et al. (17) reported the variation of the so-called “potential” density, defined as the ratio of PM2.5 and aerosol particle sizer data, assuming unit density, for 14 weekdays in a rural area of Voerde-Spellen, Germany. The potential density varied from 0.4 to 1.0 g cm-3. In this study, we calculate the apparent particle density as the ratio between hourly PM2.5 measurements and number distribution derived hourly volume concentrations, assuming the particles to be spherically shaped. Furthermore, we show the day-to-day variation of the apparent fine-particle density from daily PM2.5 gravimetric measurements. To find out the correlations between the calculated apparent density on one hand with the meteorological parameters and traffic intensity on the other hand, we consider the diurnal pattern of those parameters for weekdays and weekends and for summer and winter separately.
Methodology Study Area and Period. The measurements were conducted in Erfurt (population approximately 200 000 individuals), the capital city of the state of Thuringia, Germany. Erfurt is situated on a flat plain, approximately 200 m above sea level, surrounded by a 100 m high ridge on all sides, except toward the north. The measurement site was located approximately 1 km south of the town center and 40 m from the nearest major road. The measurements were conducted for a period of 692 d from January 1, 1999, to November 22, 2000. Measurement Methods. Number Size Distribution. The equipment used for the number size distribution measurement consisted of two instruments covering different size ranges. Particle number size distribution on a continuous basis was measured with a temporal resolution of 255 s (1821). The ambient air was sampled continuously at a flow velocity of 1 m s-1 through a stack located 4 m above the ground. Particles with a mobility diameter between 10 and 500 nm were measured with a differential mobility particle spectrometer (DMPS), consisting of a differential electrical mobility analyzer (DMA, TSI type 3071) and a condensation
particle counter (CPC, TSI type 3010). Note that the mobility diameter corresponds to the Stokes equivalent diameter. The measuring process was automatically controlled by a PC. The ratio of aerosol and sheath flow of the DMPS was 1/10, resulting in a flow rate of 0.61l and 6.1l min-1, respectively. Particles with a Stokes equivalent diameter between 100 nm and 3 µm were measured with a laser aerosol spectrometer (PMS model LAS-X). Flow rate of the LAS was 60 cm3 min-1. Three size ranges of 0.09-0.2, 0.2-0.5, and 0.5-3 µm are cyclically analyzed for 85 s to adapt the entire cycle to the measuring cycle of the DMPS. The three size ranges are divided into 15 channels each. DMPS and LAS operated at cabinet temperature (20 ( 3 °C), and the relative humidity of the sheath air flow was 45 ( 10%. Number concentration (NC) for the total size range and for different subranges were calculated from each spectrum. The subranges are quoted by the subscripts X-Y, which denote lower and upper integration threshold in microns. PM2.5 Mass Concentration. For hourly PM2.5 mass concentration measurements, we used the tapered element oscillating microbalance (TEOM) series 1400a monitor with an URG PM2.5 cyclone inlet (22). The TEOM is a gravimetricbased, cost-effective method to measure particle mass concentration nearly continuously. The TEOM measures the mass collected on an exchangeable filter cartridge by monitoring the corresponding frequency changes of a tapered element. The sample flow passes through the filter, where particulate matter is collected. As particle mass accumulates on the filter, the natural frequency of oscillation decreases. A direct relationship exists between the tube’s change in frequency and the mass on the filter. The inlet of the sampler and the filter were kept at 50 °C so that the sample filter always collects under conditions of very low (and therefore, relatively constant) humidity. The sample flow rate was 3 L min-1. Flow rate was regulated by a mass flow controller. We used the Harvard impactor (HI) operated at 10 L min-1 (23) for the determination of the mean daily PM2.5 mass concentration. The sample volume was determined with a gas meter, and sample time was set with a radio-controlled clock. The 24-h samples were collected on Teflon membrane filter (PTFE) with a pore size of 2 µm. The filters were weighed using a Sartorius M5P V001 microbalance with a resolution of 1 µg. Before weighing, the filters were equilibrated at 21 ( 2 °C and 35 ( 5% RH for 24 h. Meteorology. Ambient temperature and relative humidity were measured using a combined PT100 thermocouple (model FT3205-M, RCI, Ro¨sler, Germany). Quality Control. Size Spectrometer. Because the intensity of the scattered light emitted from the particles depends on their optical characteristics, the manufacturer-provided calibration of the LAS was corrected according to the mobility diameter of monodisperse ambient particles selected by the DMPS in the size range from 0.1 to 0.5 µm (24, 25). The mobility-derived diameters were used to shift the entire calibration curve of the LAS along the diameter axis (mobility calibration). The mobility calibration was done once per week and usually resulted in a shift of 10-15% of the original LAS-derived optical diameter. Also periodic tests of LAS function with 0.304-µm latex particles, permitting slight fluctuations of one channel from target, and leak checks were done. HI. To account for humidity and temperature fluctuations during the weighting procedure, the filter status was checked by weighing two blank and two aged Teflon filters as a reference. If the balance showed a difference of more than 5 µg from the long-term average weight, gravimetric analysis was canceled for this day. To check for balance stability and electrostatic effects, reference and particle filters were VOL. 37, NO. 19, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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weighed twice. Results were accepted if the difference between first and second measurements was below 5 µg. Data Analyses. Spherical shape of the particles was assumed for the conversion of number size distribution into volume size distribution. The volume concentration (VCX-Y) was calculated by integrating of the volume size distribution from 10 nm to 2.03 µm Stokes equivalent diameter (the upper integration threshold corresponds to an aerodynamic diameter of 2.5 µm, assuming an apparent density of 1.5 g cm-3 (26) and particle shape factor of 1). The apparent density of particles with an aerodynamic diameter smaller than 2.5 µm was calculated as the ratio of the particle mass concentration obtained by TEOM (FTEOM) on an hourly basis or by HI (FHI) on a daily basis to the corresponding volume concentration. Daily or hourly average was considered valid if 66% of the data were available and apparent density ranges from 0.6 to 3 g cm-3. The outliers were traced back to incorrect mobility calibration of the LAS alternatively to measurements of nonspherical particles. Weekdays are Monday-Friday; the weekend is Saturday and Sunday. Season summer is defined from April to September, and winter is from October to March. Vehicle density was used as the hourly mean of classified automotive of the year 2001, as there were no data available for 1999 and 2000. Heavy-duty vehicle traffic is the sum of trucks, buses, and vans. Spearman rank correlation coefficients and linear regression models were computed. All the analyses were carried out using SPSS (SPPS Base 10, SPSS Inc., Chicago, IL).
Results and Discussion The results presented here below are limited for several reasons: (i) A shift in apparent particle density due to the TEOM heating at 50 °C causes a loss of semivolatile particle mass of approximately 20-30% (27-30). (ii) The mobility calibration of the LAS was usually conducted once per week and is basically valid only for the specific air mass conditions at calibration time. A permanent calibration would be necessary to follow the rapid changes in particle properties depending on meteorology and emission sources. This may result in a biased size selection of particles due to the different optical characteristics. (iii) The apparent average density does not include particles below 10 nm in diameter. As their contribution to mass and volume is low, their influence is considered as negligible. (iv) The upper size threshold for particle volume integration is fixed at a Stokes diameter of 2.03 µm. If particle density is 1.5 g cm-3, this coincides with the 50% cutoff aerodynamic diameter of 2.5 µm. If the actual particle density deviates from this value, the integrated volume is misadjusted, and the apparent average density will be estimated too high for low-density particles and vice versa. (v) Several factors such as the vicinity of our measurement site to a major road (only 40 m), local sources of ambient particulate matter, wind speed and prevailing wind direction, orography of the city of Erfurt, and the moderate climate limit the generalization of the results of this study to other places. Descriptive statistical characteristics of hourly and daily averaged concentrations are summarized in Table 1. The mean number concentration of particles with a Stokes diameter smaller than 30 nm (NC0.01-0.03 ) 8047 cm-3) contributed for the most part (62%) to the number concentration of particles between 10 nm and 2.03 µm (NC0.01-2.03 ) 13 033 cm-3). However, the volume concentration of this smallest particle fraction (NC0.01-0.03) was negligible. In the size range of 100-500 nm, the mean volume concentration (VC0.1-0.5 ) 8.1 µm3 cm-3) accounts for 76% of the total VC0.01-2.03 but contributes only about 10% to NC0.01-2.03. Daily mean of PM2.5 measured by TEOM and HI was 13 and 16 µg 4338
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TABLE 1. Descriptive Statistical Characteristics of Hourly and Daily Averaged Concentrations during the Measurement Period January 1, 1999, to November 22, 2000, in Erfurt, Germanya N
AM
median
5th-95th percentile
SD
Number Concentration (cm-3) (hourly) NC0.01-0.03 NC0.03-0.05 NC0.05-0.1 NC0.1-0.5 NC0.5-1.0 NC1.0-2.03 NC0.01-2.03
14 229 14 229 14 229 14 229 14 229 14 229 14 229
8047 2169 1332 1471 12.8 0.5 13033
6044 1552 1021 1196 5.8 0.4 10 219
7138 1954 1122 1064 18.6 0.7 10 020
1550-21 215 544-5934 326-3422 375-3517 0.8-48.2 0.05-1.3 3544-31 927
Volume Concentration (µm3 cm-3) (hourly) VC0.01-0.03 VC0.03-0.05 VC0.05-0.1 VC0.1-0.5 VC0.5-1.0 VC1.0-2.03 VC0.01-2.03
14 229 14 229 14 229 14 229 14 229 14 229 14 229
PM2.5TEOMb PM2.5HIc
13 891 657
FTEOMb FHIc
10 907 573
tempe (°C) RH (%)
15 983 16 022
0.02 0.05 0.19 8.1 1.5 0.7 10.6
0.02 0.04 0.15 6.5 0.8 0.5 8.2
0.02 0.05 0.16 6.2 2.2 0.8 8.4
0.004-0.05 0.01-0.15 0.046-0.49 1.7-19.6 0.1-5.6 0.1-1.9 2.4-26.5
Mass Concentration (µg m-3) 13.1 16
10.7 13.5
8.6 9.9
4.5-29.4 5.4-35.5
Particle Density (g cm-3) 1.4 1.6
1.3 1.5
0.5 0.5
0.7-2.4 1.0-2.5
7.9 15.9
-1.3-24.5 46.9-98.3
Meteorology (hourly) 10.7 78.3
10.4 82.2
a N, number of measurements; AM, arithmetic mean; SD, standard deviation; RH, relative humidity. b Hourly. c Daily.
m-3, respectively (Spearman correlation coefficient between PM2.5TEOM and PM2.5HI was 0.92). The hourly mean apparent particle density FTEOM was 1.4 g cm-3, and it ranged from 0.7 to 2.4 g cm-3 (5th and 95th percentile). The ratio of the daily PM2.5 means TEOM/HI was 0.81 and the regression equation is TEOM ) 0.579HI + 3.66. The distinctions describe different sampling conditions of the two instruments. The TEOM measures at a constant temperature of 50 °C to negate the effects of particle-bound water, associated with hygroscopic salts, on the measurements. At this temperature, some particulate semivolatile material will not be detected. Taking this into account, corrected hourly PM2.5TEOM using daily regression equation between TEOM and HI resulting in FTEOM ) 1.5 g cm-3 and 5th and 95th percentiles of 0.8 and 2.5 g cm-3, respectively. The day-to-day variation of FHI is shown in Figure 1. The loss of the data from the beginning of April till the end of June 2000 was due to the yearly technical services of the MAS. The arithmetic daily mean of apparent density up to an aerodynamic diameter of 2.5 µm FHI ) 1.6 g cm-3 was strongly pronounced within a range from 1.0 to 2.5 g cm-3 (5th and 95th percentile), indicating different factors and emission sources affecting the particle formation. No differences between winter and summer and between weekdays and weekends were found. Table 2 shows the inter-correlations between ambient air particulates stratified by weekdays/ weekends and by summer/winter on hourly and daily basis. Both PM2.5 (determined by TEOM and HI) are strongly correlated with NC0.1-2.03 (r approximately 0.8) both for weekdays and weekends and for summer and winter. The means of ultrafine particle number concentration NC0.01-0.1 are less correlated with PM2.5 (e.g., on weekdays r ) 0.6 for the daily means and r ) 0.4 for the hourly means). Apparent particle density is weakly negative and positive correlated with particle mass concentration on hourly and daily basis,
FIGURE 1. Day to day variation of fine apparent particle density GHI during January 01, 1999, to November 22, 2000, in Erfurt, Germany.
TABLE 2. Spearman Rank Correlation for (A) Weekday (Monday-Friday) versus Weekend (Saturday/Sunday) and (B) Winter (October-March) versus Summer (April-September) of Hourly and Daily Particle Concentrations and Meteorological Parameters during January 1, 1999, to November 22, 2000, in Erfurt, Germanya Section A: Weekday/Weekend hourly means GTEOM FTEOM PM2.5TEOM NC0.01-0.1 NC0.1-2.03 temp RH
PM2.5TEOM NC0.01-0.1 NC0.1-2.03 -0.12*
-0.18* -0.16* -0.48* 0.13* -0.27*
0.40* 0.79* 0.03 0.04*
daily means temp (°C)
RH (%)
GHI
PM2.5HI NC0.01-0.1 NC0.1-2.03
-0.12* -0.43* 0.12* -0.22* FHI 0.22 0.17 -0.08 0.34* 0.82* 0.09* 0.07* PM2.5HI 0.14 0.46* 0.80* 0.47* -0.28* 0.16* NC0.01-0.1 0.19* 0.56* 0.52* 0.57* 0.05 0.11* NC0.1-2.03 -0.11 0.88* 0.61* -0.29* -0.06* -0.61* temp -0.11 -0.04 -0.38* -0.01 0.15* 0.12* -0.61* RH 0.02 0.10 0.16 -0.01
temp (°C)
RH (%)
-0.03 -0.02 -0.23 0.15
-0.02 0.17 0.02 -0.08 -0.66*
-0.65*
Section B: Winter/Summer hourly means GTEOM FTEOM PM2.5TEOM NC0.01-0.1 NC0.1-2.03 temp RH
PM2.5TEOM NC0.01-0.1 NC0.1-2.03 -0.14*
-0.18* -0.22* -0.52* 0.17* -0.25*
0.43* 0.80* -0.18* 0.17*
-0.00 0.35* 0.61* -0.22* 0.06*
daily means temp (°C)
RH (%)
GHI
PM2.5HI
NC0.01-0.1 NC0.1-2.03
-0.37* 0.12* -0.27* FHI 0.19 0.34* 0.80* 0.14* -0.00 PM2.5HI 0.14 0.47* 0.50* -0.22* 0.15* NC0.01-0.1 0.01 0.56* -0.01 0.06* NC0.1-2.03 -0.15 0.87* 0.69* -0.22* -0.73* tempe -0.14 -0.29* -0.23* 0.22* -0.44* RH 0.03 0.31* 0.04
temp (°C)
-0.05 0.08 0.83* 0.24* 0.53* -0.12 0.22* -0.18 0.20* -0.34*
RH (%) -0.12 -0.05 -0.16 -0.27* -0.39*
a Winter values are given in boldface type. Summer values are given in regular type. An asterisk (*) indicates that correlation is significant at the 0.001 level.
respectively. The same was observed for the correlation between FHI and particle number concentration NC0.01-0.1. The apparent density FTEOM and NC0.1-2.03 are negatively correlated for all periods. The meteorological parameters temperature and relative humidity are not significantly correlated with particle density, particle mass, or number concentration. Figure 2a,b characterizes the diurnal variation of PM2.5TEOM and NC0.01-2.03 in any period. In the course of the day similar patterns were observed for PM2.5TEOM, peaking at around 10: 00 and 20:00. The morning peak on weekdays and in summer was more pronounced as compared with the afternoon peak. This is not the case on weekends and in winter. NC0.01-2.03 peaked at around 08:00 on weekdays,in summer and in winter
other than on weekends. Only in winter was an afternoon peak observed for particle number concentration, peaking at around 18:00. Figure 3a shows the diurnal variation of apparent density FTEOM classified by weekdays and weekends as well as by summer and winter. It has a similar pattern for both seasons and for weekends in comparison with weekdays. In the early morning, the apparent particle density decreased rapidly from approximately 1.4 g cm-3 at 0:00 to 1.1 g cm-3 at 6:00. After 6:00 a strong increase occurs up to 1.6 g cm-3 in the early afternoon. During weekends, the morning minimum is clearly less pronounced. Note that the mentioned hourly FTEOM raises to an average of 0.1 g cm-3 in consequence of the loss of the TEOM mass concentration. Several processes are assumed to form this minimum. First, the daily minimum VOL. 37, NO. 19, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Diurnal variation of (a) fine particle mass concentration PM2.5TEOM and (b) fine-particle number concentration NC0.01-2.03, showing weekdays (Monday-Friday), weekends (Saturday and Sunday), summer (April-September), and winter (March-October) during January 01, 1999, to November 22, 2000, in Erfurt, Germany. temperature, short before sunrise, results in water vapor condensation on hygroscopic particles, which drives the density toward 1 g cm-3. Particles change composition by incorporation of crystal water or by amorphous crystallization. Additionally, hygroscopically grown particles and droplets are predominantly washed out from the air. Second, the vertical temperature inversion suppresses convection and entrainment and conserves all moisture and particulates in a stratified Erfurt basin layer. Figure 3b shows the vertical temperature difference between the sampling station and the official German meteorological weather station (which is situated at 316 m above sea level, e.g., approximately 100 m higher than our measurement site and 5 km away). It is used as an indicator for a vertical temperature inversion in the Erfurt basin. The average temperature measured at our site was usually about 1 °C higher than the average temperature observed at the weather station. This value is close to the theoretical adiabatic temperature gradient of -1 K/100 m. During inversion events, if the difference is
