Sodium wind/temperature lidar measurements taken throughout the diurnal and annual cycles at Urbana, Illinois (40°N, 88°W), from February 1996 through January 1998 are used to characterize the seasonal variations of the mesospheric temperature structure between 80 and 105 km. By averaging data over several weeks and over the complete diurnal cycle, the significant effects of gravity waves, tides, and planetary waves are surpressed. The observed mean annual temperature structure is largely consistent with the assumption of radiative equilibrium between direct solar UV heating and radiative cooling by IR emission. Large seasonal variations of the mean thermal structure are observed. Below 91 km, there is strong adiabatic cooling in summer caused by the mean upward velocities associated with the diabatic circulation system. The maximum amplitude of the annual variation is 9.7 K at approximately 84 km. Above 98 km, increased UV absorption by O2 during summer drives an annual oscillation in this region with an amplitude of approximately 5 K. These two phenomena determine the seasonal variation of the mesopause altitude. The annual variation in solar UV heating in the lower thermosphere induces a modest 5-km peak to peak annual variation in the mesopause altitude. The mesopause is near 101 km in winter and ∼96 km in late summer. However, the summer cooling below 91 km is strong enough to define the minimum temperature, causing the mesopause altitude to fall to ∼87 km from about 7 May to about 15 July (∼70 days). The mesopause thickness, defined here as the altitude range where the temperature is within 5 K of the minimum, increases dramatically from approximately 7 km in winter to over 16 km in summer. Significant biases can occur in some parameters calculated from nighttime-only observations. The inversion layers that persist between 85 and 96 km in nighttime temperature profiles are virtually eliminated when data are averaged over the complete diurnal period. The strong annual temperature variation present around 84 km is overestimated by 40%, and the strong semiannual variation above 95 km is overestimated by as much as 150% when computed using only nighttime measurements. The low summer mesopause exists for a much longer period (∼126 days) in the nighttime observations. The mesopause temperature averaged over the annual cycle is 188 K compared to 190 K for the nighttime average. This bias is most pronounced during summertime, when the difference is 7 K.
Global circulation models predict that increasing emissions of greenhouse gases such as carbon dioxide and methane can have a profound effect on the temperature in the upper mesosphere and lower thermosphere (MLT) (Roble and Dickinson 1989). Studies also suggest a relationship between methane levels and mesospheric water vapor, which can facilitate the formation of noctilucent clouds (Thomas et al. 1989). Important chemical interactions involving odd-oxygen and odd-hydrogen species in the MLT are strongly temperature dependent. The MLT is an area of considerable dynamic activity. The short-term variability in temperature, wind, and density is dominated by gravity waves, tides, and planetary waves, which grow in amplitude as they propagate upward from sources in the troposphere and stratosphere. Tidal perturbations are related to stratospheric ozone and tropospheric water vapor. For these reasons, knowledge of the background thermal structure and dynamic behavior in the mesosphere is essential for developing accurate global circulation and chemical models of the middle atmosphere.
In situ rocket probes, airglow observations, and radars have been used for decades to characterize the mesosphere. During the past 15 years, Rayleigh and resonance fluorescence lidars have been developed to probe the thermal, wind, and density structure of the mesosphere with exceptional accuracy and resolution. Until now, most lidars were operated only at night to avoid the high background signal from the sun. Nighttime data are of limited utility when knowledge of longer period disturbances, such as tides and planetary waves, is desired. These waves can bias the measured thermal and wind structure when observations are only conducted over part of the diurnal cycle. To address this problem, the University of Illinois Na wind/temperature lidar system was modified for daytime operation, allowing observations throughout the diurnal cycle, weather permitting. The lidar technique has been described in detail in several papers (Bills et al. 1991; Bills and Gardner 1993; She et al. 1992; Papen et al. 1995), and the modifications of the Illinois lidar for daytime observations are addressed by Yu et al. (1997). In this paper, we describe the seasonal variations of the background temperature structure between 80 and 105 km derived from data collected over the complete diurnal cycle throughout the year. Because most lidars operate only at night, the bias introduced by analyzing only nighttime observations is also assessed. The analysis of solar tidal effects is presented in a companion paper (States and Gardner 2000).
2. Data processing technique
More than 1000 h of lidar observations were obtained from February 1996 through January 1998 at Urbana, Illinois. The data were obtained intermittently depending on weather. The goal was to obtain observations during three different days per month in each of the 24 1-h bins of the diurnal cycle. This goal was achieved over 80% of the time. The data are approximately uniformly distributed throughout both the diurnal and annual cycles. Both temperature and Na density profiles were derived from the photon count profiles. The temporal resolution was 20 min during daytime and 7.5 min during night. The vertical resolution was 960 m throughout the diurnal cycle. Radial wind velocities were also measured during nighttime.
A mean day temperature profile for each week of the year is calculated in the following way. The temperature data are first averaged into 1-h bins for each observation period. The vertical resolution of 960 m is retained. To produce the weekly mean day temperature structure, the data in each 1-h bin for each 24-h period are averaged using a Hamming window weighting function of 4 weeks full width at half maximum (FWHM) centered on a particular week. Smoothing the data over several weeks is sufficient to retain the seasonal and diurnal variations in temperature while eliminating or greatly reducing the effects of incoherent disturbances such as gravity and planetary waves. The resulting smoothed data consist of 52 weekly sets of 24 hourly temperature profiles covering the height range from about 80 to 105 km. The coherent tidal perturbations are eliminated by averaging each weekly set of profiles over the complete diurnal cycle (using uniform weighting). These 52 weekly diurnal mean profiles are plotted in contour form in Fig. 1a. During summer, the low sodium density and high background during daytime prevent accurate measurements of the diurnal mean temperature above 102 km. The annual mean temperature profile plotted in Fig. 2 is obtained by averaging the 52-weekly diurnal mean profiles (using uniform weighting).
The uncertainties in the averages vary considerably throughout the diurnal and annual cycles and with altitude. Each value in the weekly diurnal mean profiles is determined from an effective average of three samples in each of the 24-h bins for a total of approximately 72 samples. The uncertainty analysis described in the appendix lists typical errors for a vertical resolution of 960 m and a temporal resolution of 1 h (Table A2). Therefore, the rms error in the weekly mean day and diurnal mean temperatures can be estimated by dividing the errors listed in the appendix by 3 and 72, respectively.
To assess the biases in nighttime temperature observations caused by tides and in situ forcing, the temperature structure was also computed by using just the nighttime data. The data are weighted using a Hamming window centered at midnight with an annually varying full width that extends from sunset to sunrise. The data during daytime hours are given zero weight. The nonuniform weighting of the nighttime data simulates the temporal distribution of typical nighttime lidar observations. Observations do not start at sunset because the solar depression angle must be greater than about 5° and time is required to adjust the lidar equipment before a data run begins. Observations do not always extend till dawn because weather and equipment problems often terminate data runs prematurely. The result is fewer observations at the beginning and end of the nighttime period and more in the middle. The equivalent background temperature distribution for nighttime observations is shown in Fig. 1b. The main differences between the diurnal mean and nighttime mean profiles are 1) there is increased annual variability in the nighttime data below 96 km and increased semiannual variability above 96 km, and 2) inversion layers appear only in the nighttime data. Notice the warmer thermospheric temperatures during summer. This plot is very similar to one published by Plane et al. (1999), who combined nighttime lidar data from Urbana, Illinois, and Fort Collins, Colorado, to characterize the annual temperature structure. It is also similar to earlier datasets published by Senft et al. (1994), She et al. (1995), and Leblanc et al. (1998).
3. Mesopause temperature structure
Many dynamic, chemical, and radiative processes play important roles in establishing the thermal structure of the mesopause region. The mean background temperature is largely determined by radiative balance, that is, the balance between absorption and emission of solar radiation (e.g., Gavrilov and Roble 1994; Roble 1995). The annual mean temperature profile derived from our observations, and plotted in Fig. 2, illustrates this fundamental structure. Below 95 km mesospheric ozone absorbs UV radiation at wavelengths in the Hartley band between 200 and 300 nm and is the main source of solar heating in this region. Because the ozone concentration decreases above the stratopause (∼50 km), the mean temperature decreases monotonically with increasing altitude in the mesosphere. Above 95 km the absorption of solar UV radiation by molecular oxygen in the Schumann–Runge bands and continuum (135–200 nm) and the Lyman-α line (121.5 nm) is the dominant heat source so that in the thermosphere, temperature again increases monotonically with increasing altitude. The globally averaged, radiative equilibrium temperature distribution is similar to the annual mean profile illustrated in Fig. 2. However, near the mesopause there are several other important radiative, chemical, and dynamical processes that influence the temperature structure and complicate this overly simplified picture.
The energy budget of the mesopause region is dominated by the absorption of solar UV radiation by O2 and O3 (∼10 K day−1) (Mlynczak and Solomon 1993), by chemical heating from exothermic reactions involving odd-oxygen and odd-hydrogen species (∼10–20 K day−1) (Mlynczak and Solomon 1991, 1993; Reise et al. 1994; Meriwether and Mlynczak 1995), including quenching of excited photolysis products (Mlynczak and Solomon 1993; Shimazaki 1985); by radiative cooling associated with infrared emissions of CO2 (∼−15 K day−1) (Andrews et al. 1987; Wehrbein and Leovy 1982; Rodgers et al. 1992); by turbulent heating caused by breaking gravity waves (∼1–5 K day−1) (Fritts and van Zandt 1993; Lubken et al. 1993); and by dynamical cooling associated with the vertical transport of heat by dissipating waves (∼−30 K day−1) (Walterscheid 1981;Weinstock 1983; Gardner and Yang 1998). Several studies suggest that these effects are most pronounced near 90 km. Mlynczak and Solomon (1993) developed a global model of the chemical heating in the mesopause region arising from exothermic reactions involving the odd-oxygen and odd-hydrogen species created by UV photolysis of molecular oxygen and ozone. They found that the associated net heating rate at midlatitudes peaks near 90 km at values of approximately 10 K day−1. Quenching of the excited atomic and molecular products (such as OH, O, and O2) resulting from the photolysis of ozone and from the reaction of molecular oxygen and ozone, and ozone and atomic hydrogen, provides a peak heating rate of ∼5–10 K day−1 also at 90 km. The region of mildly warmer temperatures just below the mesopause, between about 87 and 92 km in Fig. 2, is most likely caused by these processes. Lubken et al. (1993) reported numerous measurements of turbulence generated by breaking gravity waves in the upper mesosphere and lower thermosphere. These measurements were made with rocket probes launched at Andoya, Norway (69°N). Although the typical value of the inferred heating rate due to wave dissipation is of the order of a few K day−1, Lubken’s (1997) most recent work shows that the heating can approach 10 K day−1 near the summer mesopause at 90 km. Balancing these effects are the dynamical cooling of ∼−30 K day−1 measured by Gardner and Yang (1998), which is also maximum between 90 and 95 km, and radiative cooling associated with infrared emissions of CO2 (∼−15 K day−1) (e.g., Rogers et al. 1992).
When these measured and estimated heating and cooling rates are summed, there is a net cooling near 90 km of about −15 K day−1. In contrast, the annual mean profile plotted in Fig. 2 suggests that there is a net heating in this region. This suggests that chemical heating in this region may be much larger than currently estimated. Accurate knowledge of the thermal budget is essential to understanding the temperature structure, chemistry, and dynamics in the MLT. The uncertainties in the measured and estimated heating and cooling rates quoted above illustrate the critical need for more observational data to improve our understanding of the thermal balance in this region and ultimately to improve model predictions.
Differential solar heating throughout the year imposes seasonal variations on this background thermal structure. This is illustrated in the observed diurnal mean temperature profiles plotted in Fig. 1a. The most striking feature in this plot is the significant summer cooling between 83 and 91 km. At these altitudes, the seasonal variation is significant. Above 98 km, temperature is maximum in the summertime when solar heating is greatest, but the annual variation is relatively small. The source of the summertime cooling below 91 km is breaking gravity waves (Garcia and Solomon 1985; McLandress 1998). Gravity wave momentum deposition creates a strong zonal force that reverses the zonal wind jets and induces a mean meridional flow from the summer to winter hemisphere to balance the zonal momentum budget. By continuity, this induces upward motion in the summer hemisphere and downward motion in the winter hemisphere. The associated adiabatic cooling and heating drives the observed seasonal variation in temperature, which is far from radiative equilibrium. When Garcia and Solomon (1985) included breaking gravity waves in their model, a strong summer increase in mean upward vertical wind velocities from 70 to 91 km was predicted at 40°N latitude. The mean vertical velocities are downward in the winter Southern Hemisphere. The result is significant adiabatic cooling during summer and heating during winter in this region.
The other significant seasonal effect occurs in the lower thermosphere (above 98 km). In situ solar UV absorption by O2 increases during summer and warms this region, providing a strong annual variation in the background temperature. This also has the effect of forcing the mesopause (temperature minimum) to a lower altitude during summer, resulting in a modest annual variation of mesopause height. However, the adiabatic cooling associated with the upwelling between 70 and 91 km is strong enough in midsummer to cool this region below the temperatures in the region above 95 km. Consequently, the mesopause altitude falls abruptly to about 87 km in early May. When the upwelling weakens after summer solstice and the lower mesopause region begins to warm, the mesopause altitude rises abruptly to about 96 km in mid-July. These dynamic processes result in mesopause temperatures far from that predicted by radiative equilibrium. The data from this campaign supports this description of the mesopause temperature structure and the controlling processes.
To clarify the annual variability in the background temperature, the data from Fig. 1a are averaged into monthly intervals. The monthly diurnal mean profiles are plotted in Fig. 3 and tabulated in Table 1. The diurnal mean, nighttime mean, and Committee on Space Research (COSPAR) International Reference Atmosphere (CIRA-86) temperature profiles are plotted for each month. The rms error in the mean plots varies with season but does not exceed 0.2 K at the peak of the Na layer (∼91.5 km) where the lidar signal levels are strongest or 1.2 K at the Na layer edges (91.5 ± 9 km) where the signal is weak. The CIRA profiles are in good agreement with the data in wintertime, but are significantly colder during summer. Nighttime inversion layers are clearly present during August through February. They are nonexistent or greatly attenuated when temperature is averaged over the complete diurnal cycle.
To quantify the seasonal variations, a fit to the annual and semiannual oscillations was computed at each altitude. The results for both the diurnal mean and nighttime mean are shown in Fig. 4. The annual amplitude in Fig. 4a is maximum (9.7 K) at 84 km and decreases to a minimum of 1.1 K between 97 and 99 km. Above 98 km the amplitude increases with altitude. Fitting just the nighttime data gives a larger diurnal amplitude around 84 km (13.6 K compared to 9.7 K). Similar studies by Plane et al. (1999) and She and von Zahn (1998), using nighttime data, predict annual amplitudes in this region of 16 and 19 K, respectively. Using only nighttime data significantly overestimates the annual variation. This discrepancy is explained by examining the phase (time of maximum temperature) of the diurnal tide and in situ solar forcing at this altitude. The phase of the diurnal tide is near noon from the spring to the fall equinoxes, yielding nighttime summer measurements with a cold bias. The diurnal tide phase increases clockwise from noon to midnight and then back to noon from the fall equinox to the spring equinox [see States and Gardner (2000, their Figs. 1a,b) while solar absorption weakens during winter. Because of the phase of the diurnal tide near midnight in winter, nighttime winter measurements have a warm bias. The combined effects of the cold summer bias and warm winter bias give a much larger annual amplitude in this region. However, the summertime cooling at these altitudes due to the dynamic effects of breaking gravity waves is unmistakable. The semiannual amplitudes for the nighttime and diurnal means differ only at high altitudes (Fig. 4c). The semiannual amplitude above 98 km is significantly overestimated in the nighttime data.
The phase of the annual temperature variations (Fig. 4b) is near December below 96 km, because of the summertime cooling in this region. Above 97 km the phase jumps abruptly to approximately day 210, the end of July. Both the analysis by Plane et al. (1999) and that by She and von Zahn (1998) reveal this jump in phase. This suggests that solar UV absorption by O2 is the controlling mechanism for temperature above 97 km, where heating is maximum in summer. The strength of this summertime solar heating is illustrated in the nighttime structure in Fig. 1b, and to a lesser extent in the diurnal profile (Fig. 1a). States and Gardner (1998, 2000) show that this thermospheric heating also has significant influence on the solar tidal structure in the mesosphere. The annual amplitude minimum between 97 and 99 km arises because solar heating in the lower thermosphere is approximately 180° out of phase with the adiabatic heating and cooling in the lower mesopause region.
The annual mean temperature structure derived from both the weekly diurnal and nighttime mean profiles is shown in Fig. 5. The most striking feature is the inversion layer from 87 to 97 km present in the nighttime profile. This phenomenon has been observed for years with rocketborne probes and nighttime lidar measurements. Temperature inversion layers appear most commonly between 65–70 and 90–95 km. Many papers have attributed the 90–95-km layers to chemical heating (Mlynczak and Solomon 1993; Meriwether and Mlynczak 1995), which is maximum during night, while the effects of breaking gravity waves has been suggested as the source of the 65–70-km layers (e.g., Hauchecorne et al. 1987; LeBlanc and Hauchecorne 1997). The annual diurnal and nighttime mean temperature profiles in Fig. 5 suggest that this phenomenon is an artifact caused by incomplete sampling of the diurnal tide and nighttime chemical heating. Recent observations reported by Dao et al. (1995), States and Gardner (1998), and Meriwether et al. (1998) also suggest that both the 65–70 and 90–95 km nighttime inversion layers are perturbations associated with the diurnal tide. The mild change in temperature gradient observed in the dirunal mean profile near 90 km is probably associated with chemical heating and quenching of excited species such OH (Mlynczak and Solomon 1993).
4. Characteristics of the mesopause
The mesopause is the boundary between the mesophere and thermosphere and is defined as the altitude of minimum temperature. Recent publications (She et al. 1993; von Zahn et al. 1996; She and von Zahn 1998) have reported a bistable, two-level mesopause that was observed over a wide range of latitudes. A high-altitude winter mesopause around 100 km transitions rapidly in late April or early May to a low summer mesopause around 87 km. The temperature difference between the levels depends on latitude, increasing as one travels poleward. For this paper, we define the mesopause “region” as the altitudes where the temperature is within 5 K of the minimum. The mesopause height, region width, and temperature derived from our data are illustrated in Fig. 6. The quasi-two-level mesopause observed in other datasets is clearly present here. The mesopause is near the high “winter state” (98–101 km) until about 7 May, when it abruptly switches to the low “summer state” (86–88 km) as shown in Fig. 6a (solid line). The mesopause remains in the summer state for a period of 70 days until about 15 July, when it abruptly moves to ∼96 km and then slowly increases over the next several months back to the winter state (∼101 km). Both transitions last less than a week. For the nighttime data (dotted line) the mesopause transitions to the summer state earlier in the spring and remains there longer. For our data, the nighttime mesopause transitions to the summer state on 9 April and returns to the winter state on 12 August, spending a total of 126 days at the low altitude, almost double that for the diurnal mean.
In section 3, it was suggested that thermospheric heating will force the mesopause to a lower altitude during summer. This is supported by the behavior of altitude for the diurnal mean in Fig. 6a (solid line). There is a general increase in the mesopause altitude from August to January as solar UV heating decreases to the winter minimum, and there is a general decrease in altitude from January to April as solar heating increases. This trend is interrupted when the adiabatic cooling in the lower mesopause region assumes control of the mesopause altitude in late spring. To investigate the effects of solar heating on the mesopause altitude in summer, the minimum temperature above 91 km was also identified and plotted in Fig. 6a (dashed line). Without the strong summer cooling below 90 km, the observations suggest that the mesopause altitude would oscillate between a winter maximum of about 101 km and a summer minimum of about 96 km.
It is also instructive to consider how well-defined the mesopause altitude is throughout the annual cycle. It is reasonable to assume that day-to-day variability caused by waves and tides could place the instantaneous mesopause anywhere within the mesopause region defined above. The width of this region is plotted in Fig. 6b. The mesopause width is approximately 7 km in winter and 16 km in summer. This broad summer mesopause region is associated with the dynamically induced cooling in the region between about 82 and 92 km.
The mesopause temperature is shown in Fig. 6c. As expected, temperature derived from the diurnal mean profiles is warmer than the nighttime data because of daytime solar heating. The mesopause temperature for the nighttime measurement averages 2.0 K colder than from the data covering the diurnal period, with the biggest deviation occurring, as expected, during summertime. The seasonal peak to peak variability of mesopause temperature is 10 K, which is much smaller than the 17 K reported by Plane et al. (1999) and the 19 K inferred from the nighttime data reported here.
The background temperature structure in the MLT is determined by a combination of radiative, chemical, and dynamic processes. Radiative balance establishes the fundamental background temperature structure. However, several indirect heating and cooling mechanisms force the MLT temperature structure far from radiative equilibrium. Several studies indicate that dynamic cooling from dissipating gravity waves is the most significant nonradiative effect in the MLT (Walterscheid 1981;Weinstock 1983). The latest experiments measured this cooling at about −30 K day−1 (Gardner and Yang 1998). This cooling is balanced by chemical heating, quenching, and, to a lesser extent, turbulent heating. Solar UV heating above 98 km and circulation-induced cooling below 91 km impose strong seasonal variations on the background temperature structure. Our observations illustrate that the most significant seasonal changes, a summertime cooling below 91 km due to the diabatic circulation sustained by breaking gravity waves and a summertime warming above 98 km due to increased solar UV absorption by O2, determine the behavior of the mesopause altitude. Direct solar heating by O2 absorption drives a peak to peak annual variation in the mesopause altitude of 5 km, with a winter maximum at ∼101 km and a late summer minimum at ∼96 km. The mesopause altitude is defined by this oscillation except for a 2-month period during summer. During this short period, the strong adiabatic cooling below 91 km assumes control of the mesopause altitude, placing it near 87 km. Our background temperature profiles are in good agreement with CIRA-86 during winter but in poor agreement during summer. The CIRA-86 is significantly cooler in the MLT during summer.
Our results demonstrate the importance of making observations over the complete diurnal period to determine the true background temperature structure in the mesopause region. Calculations from only nighttime lidar observations 1) significantly overestimate the magnitude of the annual temperature variations around 84 km; 2) significantly overestimate the magnitude of the semiannual temperature variations above 97 km; 3) create, or greatly enhance, temperature inversion layers near 90 km; 4) significantly overestimate the length of time the mesopause exists in the low altitude, summer state; 5) underestimate the mesopause temperature; and 6) overestimate the seasonal variability of the mesopause temperature. Incomplete sampling of the strong diurnal tide is responsible for most of this bias. Failure to average over an integer number of periods of the 12-, 8-, and 6-h tides can also contribute biases, albeit to a much lesser extent.
The only dynamic variation that was not eliminated from our dataset is year to year variability. This can contribute fluctuations or biases in the annual background structure. Even though our campaign lasted two years, sometimes the observations for a whole month were obtained exclusively in one year. We believe the enhanced April temperatures may be such an artifact because the April data were all obtained during 1996. It is desirable to have observations distributed over multiple years to minimize the effects of interannual variability. The choice of data combination and averaging can also yield different numerical results. The width of our Hamming window, 4 weeks FWHM, was chosen to eliminate short-term variations but retain seasonal trends and also avoid phase cancellation of solar tides. We also weighted the data using a 6-week FWHM Hamming window and a 4-week rectangular window. It was found that the background temperature profiles shown in Fig. 3 can deviate up to a worst-case value of approximately 5 K, depending on the choice of smoothing windows. However, none of the fundamental conclusions reached in this paper were compromised. The effects of different averaging methods and interannual variability can both be minimized by employing datasets larger than the ∼1000 h of observations used here.
To correct for the tidal bias in background structures derived from incomplete datasets, accurate knowledge of the tidal amplitude and phase behavior of temperature, density, and wind throughout the annual cycle is crucial. The seasonal tidal behavior of mesospheric temperature derived from this dataset is presented in the companion paper (States and Gardner 2000).
The authors thank Jirong Yu and Xinzhao Chu for their invaluable help in collecting the data. This work was supported by NSF Grants ATM 94-03036 and ATM 97-09921 and by NASA UARS Grant NAG 5-2746.
Data Acquisition and Error Analysis
Temperature, radial wind velocity, and Na density are determined by probing the Na D2 absorption line with a narrowband lidar. The outgoing laser pulse has a spectral width of only 140 MHz FWHM. The laser is tuned to different frequencies within the D2 line, effectively probing its spectral shape. The dependence of the D2 line shape and position on temperature (thermal broadening), radial wind (Doppler shifting), and Na density (amplitude) enables the inference of these parameters. Figure A1 illustrates the location of the frequencies used within the absorption line. During daytime, observations are made at the peak and crossover frequencies, and only temperature and Na density are measured. During night, the peak and two wing frequencies are used. Employing three frequencies instead of two enables a radial wind measurement to be calculated along with temperature and density. As stated in the introduction, a more detailed explanation of this technique is available in the literature (Bills et al. 1991; Bills and Gardner 1993; She et al. 1992; Papen et al. 1995).
The temperature metric used for each technique is given in Table A1. The normalized photo counts NNorm(f, z, t) in the metric formulas represent the detected sodium photocounts normalized by the Rayleigh (molecular) returns from 30 to 35 km. Normalizing in this way compensates for fluctuations in laser power and atmospheric transmittance. Application of the lidar equation reveals that the two-frequency metric can be expressed as the ratio of sodium cross sections:
The right side of Eq. (A1) is an analytic function of the temperature and radial wind, allowing these parameters to be calculated. The three-frequency metric can be expressed in a similar manner. The normalization procedure and the development of Eq. (A1) is described in detail in the lidar references listed above.
The temperature uncertainty formulas for each metric are also listed in Table A1. The derivation of the two-frequency formula is summarized below, but the same procedure can be applied to any metric. The first step is to determine the relative error:
where Nx is the sodium counts at frequency x, and Bx are the background counts at frequency x. The reason Bx does not appear in Eq. (A3) is that the mean background is subtracted from each profile before processing. However, the variance due to the background, ΔBx, remains. The next step is to take the mean square value of Eq. (A3) with the following considerations. The differentials on the right side of Eq. (A3) are independent, zero mean, Poisson-distributed random variables. This will cause the expected value of all the differential cross terms arising from squaring Eq. (A3) to be identically zero. Additionally, for a Poisson distribution, the mean is equal to the variance. Applying these identities, the mean square value of Eq. (A3) can be expressed as
Assuming the mean backgrounds are identical (Bc = Ba = B), after some algebraic manipulation, the rms relative error can be expressed as
To calculate approximate errors and for comparison of different metrics, the value of RT at typical values of temperature (200 K) and wind (0 m s−1) is used in the error formulas. This number (RT = 0.294) inserted into Eq. (A5) yields
where SNR = Na/B is the ratio of the signal counts to the background counts. The ratio between relative error and temperature error is determined by
This ratio is applied to Eq. (A6) to give the final rms uncertainty in the temperature measurement:
The only significant source of noise is the statistical nature of the photon-counting process so Eq. (A8) represents the total rms uncertainty in the temperature measurement.
The daytime background effect on the measurement error is evident in the uncertainty formulas. At night, due to virtually no background, the SNR is high, which drives the last square root term to 1. During daytime, the SNR varies considerably and depends on altitude, time of day, time of year, and atmospheric clarity. Hazy conditions alone can triple the background noise. Table A2 quantifies this effect for three parts of the annual cycle: winter solstice, equinox, and summer solstice. Typical values for the SNR at the peak of the layer (best case) at noon (worst case) observed at Urbana are shown. The factor of 8 between the solstice periods is a result of a summer increase in background due to sun angle, a summer decrease in sodium abundance, and a summer increase in atmospheric water vapor that usually provides much hazier conditions than during winter. At the edge of the layer (e−2 point), these SNR values will decrease approximately by a factor of 7.
The resulting measurement uncertainty for day and night at both the peak and edge of the Na layer are shown. These values reflect a temporal resolution of 1 h and a height resolution of 960 m. Errors from night and day cannot be compared directly because they reflect the use of different receivers. However, the background effect is easily calculated by direct application of the given SNR values to the uncertainty formulas. The result of seasonal variation in background can be seen by comparing the ratio of errors from the solstice periods. At night, the ratio of summer to winter is 1.4, a direct result of the doubling of the Na abundance during that period. For daytime, at the peak, the ratio is 3.0. The difference is due entirely to the daytime background and its enhanced level during the summer solstice. This effect is even worse with less signal. At the edge of the layer for daytime, the ratio increases to 3.75. These figures imply that approximately 9 times as much summer daytime data are needed as winter data for the same quality of measurement.
Corresponding author address: C. S. Gardner, University of Illinois, Department of Electrical and Computer Engineering, 1308 W. Main St., Urbana, IL 61801.