Molecular density retrieval and temperature climatology for 40–60 km from SAGE II



[1] The Stratospheric Aerosol and Gas Experiment (SAGE) II is a spaceborne solar occultation instrument that makes long-term stable measurements of atmospheric transmission at seven wavelengths between the ultraviolet and the near infrared. It provides near-global coverage (from about 75°S to 75°N latitude) and a data record spanning over 18 years starting in late 1984. Recently, a self-consistent molecular density retrieval was developed which uses SAGE II version 6.10 transmission data above 40 km altitude. Since at this altitude attenuation of solar radiation due to aerosols can be neglected, there is enough independent information in five SAGE II channels (386–600 nm) to separate the absorption due to ozone and nitrogen dioxide from Rayleigh scattering. Vertical inversion to obtain profiles of these quantities from 40 to 60 km proceeds as in the standard SAGE II algorithm, using a matrix of refracted path lengths. The density gradient information for averaged profiles is converted to temperature. The data are sorted into 20° latitude bands from 70°S to 70°N latitude, and the time series are fitted to provide a mean climatology and long-term trend estimates. The climatology agrees well with published climatologies for the northern midlatitudes and includes results for the other latitude bands as well. Analysis of long-term variation finds no statistically significant effect from the solar cycle or quasi-biennial oscillation and no statistically significant trend. An upper bound on a possible cooling trend of 3 or 4 K/decade is derived for high and middle latitudes between 40 and 45 km altitude.

1. Introduction

[2] In recent years there is a degree of consensus concerning climate change in the stratosphere below 50 km. Surface warming and lower stratospheric cooling has occurred in the decades from the mid 1960s to the mid 1990s. Stratospheric cooling is attributed largely to decreases in stratospheric ozone and, to a lesser extent, increases in well-mixed greenhouse gases [Ramaswamy et al., 2001]. However, there is an ongoing need for temperature trend measurements in the upper stratosphere and mesosphere. Early 1-D radiative-photochemical model simulations suggested that cooling trends due to increased trace gas concentrations would peak between 40 and 50 km [World Meteorological Organization (WMO), 1990]. More recent models show cooling that increases with height at least up to 50 km [e.g., Forster and Shine, 1999]. The region near and above the stratopause is thus highlighted as a bellwether for atmospheric response to anthropogenic increases in carbon dioxide.

[3] Measurement-based estimates have been derived from rocketsonde and Rayleigh lidar data for the local and regional scale. Dunkerton et al. [1998] obtain a significant cooling of 1.7 K/decade for 30–60 km from rocketsonde data for northern midlatitudes in the western hemisphere for 1962–1991. A later analysis of low latitude U. S. rocketsonde data by Keckhut et al. [1998] indicates cooling of 1.7 ± 0.7 K/decade for 30–50 km and 3.3 ± 0.9 K/decade near 60 km. Rayleigh lidar at the Observatoire de Haute Provence yield mesospheric cooling of 0.4 K/year for 1979–1993, with no significant trend in the stratosphere [Keckhut et al., 1995].

[4] Global measurements of mesospheric temperature trends will likely only come from satellite observations. Long-term variability has been analyzed from the SSU series of satellite measurements [e.g., Lambeth and Callis, 1994], though trend analysis is complicated by discontinuities in the time series caused by changes in instrumentation [Finger et al., 1993] and by tidal influence manifested through abrupt changes in the local time of measurements [Keckhut et al., 2001]. A trend analysis on HALOE satellite data for just under one solar cycle resulted in significant cooling trends of 1.0 to 1.6 K/decade at 1 hPa in the tropics and at 0.2 and 0.3 hPa in a 10° latitude band centered at 20°N [Remsberg et al., 2002]. Wang et al. [1992], in a previous study using a smaller amount of SAGE II data, derived temperature measurements using a substantially different algorithm. The current study examines a newly released set of density and temperature data between 40 km and 60 km from SAGE II for 1984–2002.

2. The SAGE II Instrument

[5] The Stratospheric Aerosol and Gas Experiment (SAGE II) is an orbiting solar occultation instrument. It generally observed fifteen sunrise and fifteen sunset events per day, about 40 weeks a year from October 1984 until a problem with the instrument pointing system forced operations to stop temporarily in July 2000. Reduced coverage was resumed in November 2000 and continues to the present, with up to sixteen events of only one type occurring per day. Coverage is nearly global, ranging from 75 S to 75 N latitude, with a full sweep taking from 25 to 40 days [Mauldin et al., 1985].

[6] The SAGE II instrument primarily measures ozone and NO2 number density, aerosol extinction at four wavelengths and water vapor mixing ratio in the stratosphere down to the middle troposphere or cloud top. The optical depth is measured in seven wavelength channels as the apparent path to the Sun descends through the atmosphere during sunset or ascends during sunrise. For calibration, exoatmospheric measurements are made before sunset and after sunrise when the path to the Sun is above the atmosphere, giving the solar occultation technique the advantage of automatic self-calibration. In the primary algorithm that is used to generate the SAGE II standard products, the attenuation due to Rayleigh scattering is removed using temperature data from the National Centers for Environmental Prediction (NCEP). Linear systems of equations are solved to determine the optical depth due to each species. Finally, the slant path optical depth is inverted into vertical profiles using a matrix of path lengths for the refracted light. The current study involves the result of a secondary algorithm that differs in its treatment of Rayleigh scattering, as described below.

[7] The primary motivation for the retrieval of molecular number density above 40 km is to improve the SAGE II ozone data, by removing the dependence on the NCEP data, especially at high altitudes, where the measurement uncertainties are large and systematic errors are also present [Finger et al., 1993]. The calculation is independent of any external temperature and pressure database. The density results were released for the first time in version 6.10, the newest version of SAGE II data. These data can be obtained through the Langley Atmospheric Sciences Data Center (ASDC) ( The retrieval of molecular density is possible because aerosol is a negligible contributor to atmospheric extinction at altitudes above 40 km. With no need to account for aerosol, the SAGE II measurements provide enough independent information to separate Rayleigh scattering from ozone and NO2. This measurement is an early return on a long-term development effort. It presents the opportunity to study middle atmosphere density and temperature over the past eighteen years.

[8] SAGE II provides the benefit of a long-term record of approximately one and a half solar cycles without discontinuities caused by changes in instrumentation and analysis. In contrast, radiosonde measurements often suffer from discontinuities of this type [Ramaswamy et al., 2001] and even after corrections [Finger et al., 1993], the multi-instrument SSU satellite record does as well [Keckhut et al., 2001]. Furthermore, SAGE II observations are nearly global in coverage, another important strength compared to radiosondes and lidar systems. In addition, the solar occultation technique avoids some systematic problems common to other satellite measurements. For example, since all the measurements used in this study occur at the time of local sunset, diurnal effects [Keckhut et al., 1996] are less critical [Remsberg et al., 2002]. Also, heating and cooling of the radiometer due to solar shadowing, an issue with some satellite instruments [Ramaswamy et al., 2001], is not problematic for SAGE II, since the solar occultation technique is self-calibrating.

[9] However, the task of obtaining temperature from SAGE II measurements is a challenging one. The upper stratospheric and lower mesospheric regime where this measurement is possible corresponds to the least robust usable transmission data. At these altitudes, the signal to noise ratio is small and the resulting temperature data is noisy. The noise results in a narrow vertical range of measurements, from 40 to 60 km, and in a vertical resolution that is practically much coarser than the nominal value of 0.5–1.0 km for standard SAGE II version 6.1 measurements, because of the large error bars on the density profiles. The horizontal resolution is 2.5 arcminute, corresponding to approximately 2.5 km [Mauldin et al., 1985]. Time series analysis is also complicated by uneven temporal sampling, due to the orbit characteristics and the solar occultation geometry. Nevertheless, derivation of temperature near the stratopause from SAGE II is worthwhile because this data set is long term, nearly global in coverage, and free from discontinuities.

3. Molecular Density Measurement

[10] The input measurements for the calculation of Rayleigh scattering are transmission as a function of altitude, from five of the seven SAGE II channels, from 386 nm to 600 nm. Transmission is reported on a 0.5 km grid, reflecting a vertical resolution of approximately 0.75 km. The altitude registration is estimated to be precise to at least 100 m, though errors will be correlated from level to level. (J. Zawodny, manuscript in preparation, 2003). Because the attenuation due to Rayleigh scattering is proportional to the fourth power of the wavelength, the high altitude signals from the longer wavelength channels are too small to be useful and are excluded. The version of transmission data is 6.10 [Zawodny and Thomason, 2001]. Figure 1a shows the total optical depth observed in the 386 nm channel for each sunset event on 1 January 1985.

Figure 1.

Stages of density retrieval for 15 sunset events on 1 January 1985. (a) Total optical depth in the 386 nm channel and the 600 nm channel, the shortest and longest wavelengths used here. (b) After species separation, the optical depth due to Rayleigh scattering, or “slant path density.” (c) After vertical peeling, the number density.

[11] The altitude range of the retrieval is 40–60 km. The lower limit of the range is constrained by the requirement that the contribution of aerosol to the optical depth be negligible. In the region where this assumption is valid, above approximately 40 km, the total optical depth in each of the five channels consists solely of contributions by ozone, NO2, and Rayleigh scattering:

equation image

where τij is the total optical depth in channel i at altitude level j, njRay represents the Rayleigh optical depth for the jth altitude level, and the σis are the Rayleigh, ozone and NO2 cross sections for channel i. The effectiveness of the retrieval is limited at the upper end by instrument noise. Although the calculation is performed for every level up to 75 km, the range over which measurements are sufficiently robust to allow time series analysis is smaller.

[12] The relative attenuation of a given species in each channel is determined by the cross sections. These are derived from published spectra: ozone cross sections from MODTRAN [Shettle and Anderson, 1995], NO2 cross sections from Harder et al. [1997], and Rayleigh cross sections from the analytic formula by Bucholtz [1995]. These spectra must be integrated over the SAGE II channels to derive effective cross sections for each channel. The computation is a convolution of the published figures for each species with the instrument frequency response and the solar spectrum. Additionally, the nominal 448-nm channel is adjusted for an apparent time-dependent evolution of the channel response, just as in the standard SAGE II processing [Hofmann et al., 1998]. However, the potential effect of this wavelength correction on the derived temperature data and trend is very small, much smaller than the uncertainty of the temperature trend calculations.

[13] The five equations, one for each instrument channel, are inverted using a straightforward matrix inversion. Figure 1b shows the optical depth due to Rayleigh scattering for the sunset events on 1 January 1985. The resulting species slant path optical depth functions then undergo vertical inversion using the same process as in the primary SAGE II algorithm, a Twomey-Chahine nonlinear inversion algorithm [Chu et al., 1989; Thomason et al., 2000] with the matrix of refracted slant path lengths as input. No smoothing is performed on the profiles during the vertical inversion. The final result is a vertical profile of molecular number density as a function of altitude from 40 to 75 km. Figure 1c shows these results for 1 January 1985.

[14] Only satellite sunset measurements are included in the analysis. Examination of sunrise measurements reveal a systematic offset believed to be due to a transient signal that has been observed in other SAGE II measurements [Hofmann et al., 1998]. This signal apparently originates in the instrument electronics. The maximum magnitude is about 0.3% in the NO2 channels (J. Zawodny, personal communication, 2003). In the standard processing, both sunrise and sunset measurements are corrected for this signal. However, since the atmospheric attenuation observed in the current experiment is very small, the electronic transient signal is a potential source of significant systematic error even after correction, in sunrise events. It is negligible for sunset observations because of the longer time lapse between turning on the instrument and observations at these altitudes.

[15] Because the SAGE II density measurements tend to be noisy, the molecular density profiles are combined by calculating the mean profile for each pass through a 10° latitude band. The number of measurements in a pass depends on the latitude band, with between approximately 20 and 80 measurements per pass from the 40°S to 40°N bands, and generally about 150 measurements per pass for the 60°N and 60°S bands. The time lapse between passes is not constant, varying approximately between four and eleven weeks at a given latitude. The total number of points in each time series, after averaging, ranges from 72 in the 60°S band to 133 in the latitude band centered at the Equator.

4. Conversion to Temperature

[16] Although molecular number density is measured in this experiment, temperature is of greater interest scientifically. Accordingly, the SAGE II median density profiles are converted to temperature.

[17] Various researchers discuss calculating a temperature profile from measured density data [e.g., Hauchecorne and Chanin, 1980]. In these methods, the temperature is bootstrapped downward from a climatological starting point at the ceiling, at 65.5 km in our case. At each level, hydrostatic equilibrium and the ideal gas law are assumed. In the present study, those basic equations are combined to yield the following:

equation image

T, the temperature at geometric altitude H, is the only unknown variable in the equation. Consecutive levels are spaced 0.5 km apart. The quantities Tb, Hb, and Nb are the temperature, height, and number density for the level 0.5 km above the current level and N is the number density at the current level. The quantities M0, the molecular weight of dry air, and R*, the gas constant, are constants as described in the U.S. Standard Atmosphere [National Oceanic and Atmospheric Administration (NOAA), 1976], and g(H) is the altitude-dependent acceleration of gravity. The temperature T is found using Müller's root finding method [Press et al., 1992].

[18] Equation 2 is based on the assumption that the temperature varies linearly with height between two consecutive levels. The equation is left in the root-solving form shown, rather than isolating T, so that no other simplifying equations are needed. There is no assumption that the density can be represented as a single mean density over the layer [e.g., Wang et al., 1992] nor are any corrections needed for the variation of density [e.g., Clancy and Rusch, 1989].

[19] The GRAM 95 model [Justus et al., 1995] provides the climatological value of temperature for the uppermost level. As in the work by Hauchecorne and Chanin [1980] and other studies, bootstrapping downward was found to be preferable to working upward. This is so even though the temperature is more accurately known at the lower end of the region because the influence of the endpoint dissipates quickly when working downward. The relatively greater robustness of this method is demonstrated by Figure 2. However, because some contamination from the initialization value may still be expected between five and ten kilometers below the ceiling, the top five kilometers of the resulting profile are discarded and further analysis includes profiles only up to 60 km.

Figure 2.

A number of starting values were chosen with which to initialize the temperature conversion for a single event at (a) the lower boundary or at (b) the upper boundary of the data. The temperatures were calculated by bootstrapping from one level to the next. When bootstrapping upward, the results show instability, with the temperatures at the upper boundary varying more than the starting temperatures. Conversely, the results in Figure 2b are much closer than the starting temperatures.

[20] The uncertainty in the temperature is obtained through an error propagation analysis. It is assumed that the uncertainty at each level depends on the density error for the current level, taken to be the standard error in the mean, and the temperature error from the level above. The two uncertainty sources are added in quadrature to obtain the temperature uncertainty for each level. The uppermost level is assigned an error bar of 12 K, the value quoted for the GRAM 95 model [Justus et al., 1995].

5. Results

[21] The daily profile data, for temperature and density separately, are sorted into multiple time series, one for each 20° latitude band and for each 1/2-km altitude level. To improve the quality of the time series fits, data during a low battery period in 1993 and 1994 are removed before fitting. During this period, the duration of each event was shortened to save power, resulting in less opportunity to perform calibration measurements between powering on and the solar occultation. In consequence, the calibration scans were fewer and lower in altitude than normal, and the data quality tends to be relatively poor. Events with this problem can easily be identified and excluded using data quality flags that were released along with the data [Zawodny and Thomason, 2001].

[22] Data were also filtered for exceptionally large error bars. Characteristic of the high altitude density data set is that it includes large enough noise that many legitimately small data points approach zero with nonnegligible probability. Therefore it is vulnerable to being biased by the more common method of filtering all data having an uncertainty equal to one half of the data value. Instead, two other criteria were used here for filtering. First, all data having a one-sigma uncertainty of greater than 300% are removed. The uncertainty for each datum is also compared to the average data value in the latitude/altitude bin. If the uncertainty for an individual point is greater than this average value, the point is removed. These criteria were chosen to eliminate data for which the error bars clearly indicate poor quality, but to avoid biasing the data by removing large numbers of small-valued points. Example time series are displayed in Figure 3 for the 40°N latitude band for three altitude levels and in Figure 4 for the latitude band centered at the equator for the same altitude levels.

Figure 3.

SAGE II temperature time series for three altitude levels for the 30–50°N latitude band. Also shown is the climatological fit which includes constant, annual, and semiannual terms.

Figure 4.

SAGE II temperature time series for three altitude levels for the 10°S–10°N latitude band. Also shown is the climatological fit which includes constant, annual, and semiannual terms.

5.1. Mean Climatology

[23] Initial analysis is focused on obtaining a mean climatology. For this purpose, the time series for each altitude and latitude band are fit using singular value decomposition [Press et al., 1992]. The analysis employed the following model for the temperature, T, for a given altitude and latitude band, xi, as a function of time in years, tj.

equation image

In this equation, b and c are the coefficients for the odd and even parts of the annual term, respectively, and d and f are those for the semiannual terms. Including even and odd parts is equivalent to solving for both the amplitude and phase constant of the periodic terms. N(xi, tj) represents the portion of the variability not explained by the model.

[24] The results are shown in Figure 5 for the latitude band from 30°N to 50°N and in Figure 6 for the 20° band centered at the equator. They are also represented in Table 1 for all bands for five altitude levels. In general, the stratopause appears between 46 km and 51 km altitude. At midlatitudes, the maximum temperature is approximately 275 K in the summer, and about 15–20 K cooler in the winter. At the equator, the stratopause exhibits a clear semiannual cycle, with the warmest temperature of 275 K in April and a secondary maximum a few degrees cooler in October, and with stratopause minimum temperatures of approximately 267 K in January and July. The phase of the annual cycle, as shown in Table 1, indicates the time of year of the maximum temperature. The phase shown for the semiannual cycle indicates the first maximum in the calendar year.

Figure 5.

SAGE II average climatology is shown for the latitude band from 30°N to 50°N. It is derived from the SAGE II analysis using a constant term and annual and semiannual periodic terms.

Figure 6.

Like Figure 5 but for the latitude band from 10°S to 10°N.

Table 1. SAGE II Average Climatology Derived Using a Constant Term and Annual and Semiannual Periodic Termsa
  • a

    Units are in Kelvin.

Latitude 60.0
40.5251.7 ± 1.713.1 ± 2.721 Jun2.3 ± 2.406 Jan
45.0261.9 ± 2.713.9 ± 4.317 Jun1.1 ± 3.823 Jun
50.0264.6 ± 4.014.0 ± 6.419 Jun1.5 ± 5.513 Jun
55.0259.1 ± 5.512.8 ± 8.826 Jun3.7 ± 6.817 May
60.0252.2 ± 6.79.9 ± 10.410 Jun5.4 ± 8.311 May
Latitude 40.0
40.5254.6 ± 1.78.0 ± 2.201 Jun1.0 ± 2.331 Jan
45.0263.5 ± 2.17.6 ± 2.809 Jun0.2 ± 2.910 Mar
50.0265.1 ± 3.67.3 ± 4.723 Jun1.9 ± 5.010 May
55.0256.3 ± 5.04.3 ± 6.921 May0.8 ± 6.911 Apr
60.0244.9 ± 6.12.1 ± 8.326 Nov4.2 ± 8.514 May
Latitude 20.0
40.5256.8 ± 2.02.5 ± 2.905 May1.3 ± 2.819 Apr
45.0266.6 ± 3.02.0 ± 4.412 Apr1.5 ± 4.119 Apr
50.0267.6 ± 5.02.9 ± 7.311 Apr0.9 ± 6.917 Mar
55.0255.2 ± 6.81.6 ± 9.328 Jan0.4 ± 8.904 Apr
60.0245.4 ± 10.12.1 ± 13.807 Jan4.0 ± 13.918 Mar
Latitude 0.0
40.5257.3 ± 2.31.3 ± 3.324 May4.8 ± 3.425 Apr
45.0265.7 ± 3.40.9 ± 4.803 Jun3.3 ± 4.510 Apr
50.0267.3 ± 5.53.0 ± 7.729 May5.2 ± 7.414 Apr
55.0259.7 ± 7.45.9 ± 10.509 Dec1.6 ± 11.307 May
60.0247.2 ± 9.75.1 ± 13.910 Jan6.6 ± 14.918 May
Latitude −20.0
40.5255.9 ± 2.24.1 ± 3.023 Dec0.8 ± 3.120 Apr
45.0264.4 ± 3.34.2 ± 4.403 Jan2.2 ± 4.725 Apr
50.0267.1 ± 5.53.6 ± 7.429 Dec1.6 ± 8.204 May
55.0256.0 ± 5.62.9 ± 8.103 Mar1.9 ± 8.623 May
60.0238.4 ± 7.78.0 ± 10.524 Jan8.7 ± 10.311 Apr
Latitude −40.0
40.5252.9 ± 1.511.8 ± 2.120 Dec2.5 ± 2.108 Feb
45.0262.7 ± 2.511.2 ± 3.321 Dec2.1 ± 3.425 Jan
50.0263.3 ± 3.28.8 ± 4.222 Dec2.4 ± 4.423 Jan
55.0254.7 ± 4.76.6 ± 6.214 Dec3.4 ± 6.430 Jun
60.0244.0 ± 5.77.3 ± 8.508 Oct4.7 ± 7.928 May
Latitude −60.0
40.5253.0 ± 1.916.5 ± 3.112 Dec2.2 ± 2.209 Feb
45.0262.5 ± 2.815.6 ± 4.512 Dec1.8 ± 3.631 Jan
50.0265.8 ± 4.512.9 ± 7.319 Dec2.4 ± 6.308 Jan
55.0258.5 ± 5.79.5 ± 9.014 Dec2.7 ± 7.721 Jun
60.0249.4 ± 7.912.7 ± 12.411 Dec1.1 ± 10.208 Jun

5.2. Autocorrelation and Uncertainties

[25] Also quoted in Table 1 are uncertainties for each model term. These are the 95% confidence intervals, generated using the standard deviation and the student's t value for nm degrees of freedom where n is the number of data points in the time series and m is the number of terms in the fit. The standard deviations are obtained by propagating the uncertainty in the temperature data, discussed above, through the singular value decomposition algorithm. An additional correction is made for autocorrelation.

[26] Various authors [e.g., Woodward and Gray, 1993] point out the potential disadvantages of noise which contains autocorrelation. The noise term in a time series model represents the portion of the measurement that is not known or measurable. It is not necessarily random and independent; more often, consecutive values are partly correlated. Because a nonzero autocorrelation indicates that the residuals are not completely independent, neglecting it can inflate the apparent precision of derived parameters [Tiao et al., 1990; Weatherhead et al., 1998]. Therefore autoregression must be taken into account for the proper estimation of the precision of the calculated trend and other model coefficients.

[27] This study makes an adjustment to the standard error using an effective sample size ne [Santer et al., 2000]:

equation image

where nt is the number of measurements and r1 represents the correlation between successive residuals, ej.

equation image

[28] The autocorrelation coefficient tends to be small in this study. For 90% of the 280 time series at different altitude levels and latitude bands, the adjustment required by this procedure corresponds to less than a 19% increase in the size of the error bars. For example, an uncertainty of 1 K would be adjusted to approximately 1.2 K or less. For the remainder of the time series, the maximum adjustment to the uncertainty is approximately 40%.

5.3. Comparison With Other Data Sets

[29] In comparison with the recently published climatology of HALOE temperature data for the same latitude [Remsberg et al., 2002], reproduced here as Figure 7, the climatology in Figure 5 shows similar structure in the altitude region of overlap. The peak temperatures occur at the same altitude and time of year in both analyses, with SAGE II peak temperatures higher than HALOE by less than 5 K. The annual cycle observed in SAGE II data is larger than in HALOE, approximately 7–8 K in the 40°N latitude band compared to 5–6 K from HALOE [Remsberg et al., 2002]. The peak in Figure 5 covers a narrower altitude range, falling off faster at higher and lower altitudes.

Figure 7.

Climatology for a 10° band centered at 40°N derived from HALOE for the 1990s. This is Figure 7 from Remsberg et al. [2002] and is reproduced with permission.

[30] The SAGE II climatology for the 40°N latitude band is also compared with a lidar climatology from the Observatoire de Haute Provence [Leblanc et al., 1998], reproduced here in Figure 8. The agreement between the two climatologies is very good in the region of overlap. Both the shape and magnitude of the peak correspond closely. The agreement persists throughout much of the year, except for a few months in winter, where the climatology by Leblanc et al. [1998] exhibits a smaller secondary maximum in stratopause temperatures which is not present in the current work.

Figure 8.

Climatology from lidar measurements at the Observatoire de Haute Provence. This from Leblanc et al. [1998, Plate 1a] and is reproduced with permission.

5.4. Solar Cycle and QBO Terms

[31] Model simulations predict a 1-K effect on temperature at the stratopause over the course of the solar cycle [Ramaswamy et al., 2001] and solar cycle effects have been observed in temperature data sets [Labitzke and Chanin, 1988]. In the present study, SAGE II data were analyzed for trend and solar effects by repeating the singular value decomposition as described in section 4.1 with solar, QBO, and trend terms added to the model. The effect of the solar cycle was modeled by employing a simple eleven-year periodic term [Remsberg et al., 2002], similar to the annual and semiannual terms discussed above. This method allows for the possibility of a time lag between the solar forcing and the temperature data, an effect which was seen in the HALOE data [Remsberg et al., 2002]. In addition, a term was added to model the quasi-biennial oscillation, using the 30 hPa Singapore zonal wind index [Naujokat, 1986] as a proxy. The results of this fit are shown in Table 2. Two additional solar proxies, the 10.7-cm solar flux from Penticton and Ottawa and the Mg II index [Viereck and Puga, 1999], were separately tested (not shown). None of the solar or QBO terms is significant (95% confidence) in any of the three cases. Since uncertainties are larger than the 1 K effect predicted by models, the nonsignificance of the results should not be taken to imply that there are no solar or QBO effects present, but that it is not possible to measure them because of the noise present in the data set.

Table 2. SAGE II Derived Solar and QBO Amplitudes and Phases Plus Trend Coefficientsa
  • a

    All uncertainties are 95% confidence intervals. Units for the trend results are in Kelvin per year; for the amplitudes units are Kelvin, and phase is expressed in degrees from 0 to 360.

Latitude 60.0
40.50.1 ± 2.02860.3 ± 2.1−0.1 ± 0.3
45.00.7 ± 3.1109−0.3 ± 3.4−0.2 ± 0.4
50.01.5 ± 4.31920.8 ± 5.1−0.2 ± 0.6
55.01.5 ± 7.289−1.3 ± 7.80.1 ± 1.0
60.02.0 ± 8.22290.3 ± 9.3−0.4 ± 1.1
Latitude 40.0
40.50.4 ± 2.31440.5 ± 2.80.0 ± 0.3
45.00.3 ± 2.8157−0.8 ± 3.50.0 ± 0.4
50.00.7 ± 5.1281−0.5 ± 5.7−0.2 ± 0.7
55.02.4 ± 7.059−3.0 ± 8.0−0.1 ± 0.9
60.02.2 ± 8.075.3 ± 9.8−0.2 ± 1.2
Latitude 20.0
40.50.6 ± 2.9328−0.1 ± 3.50.0 ± 0.4
45.01.4 ± 4.43120.7 ± 5.10.0 ± 0.6
50.01.4 ± 7.43101.9 ± 8.50.0 ± 1.0
55.03.7 ± 9.23533.6 ± 11.40.1 ± 1.3
60.03.2 ± 13.824.7 ± 17.10.3 ± 2.0
Latitude 0.0
40.50.8 ± 3.8286−0.3 ± 4.1−0.1 ± 0.5
45.01.6 ± 5.6820.5 ± 6.00.0 ± 0.7
50.03.4 ± 8.0371.6 ± 9.5−0.1 ± 1.1
55.02.1 ± 10.3184−0.3 ± 13.20.1 ± 1.5
60.05.6 ± 13.13591.3 ± 16.80.5 ± 1.9
Latitude −20.0
40.50.6 ± 3.5258−0.7 ± 3.70.0 ± 0.4
45.00.8 ± 5.296−0.4 ± 5.7−0.1 ± 0.6
50.01.1 ± 8.61020.8 ± 9.4−0.2 ± 1.1
55.02.9 ± 8.2550.6 ± 9.3−0.5 ± 1.1
60.06.0 ± 11.7891.2 ± 13.0−0.8 ± 1.5
Latitude −40.0
40.50.7 ± 2.1490.4 ± 2.40.1 ± 0.3
45.00.6 ± 3.3100.0 ± 4.0−0.1 ± 0.5
50.01.5 ± 4.13340.7 ± 5.00.0 ± 0.6
55.04.2 ± 5.83421.6 ± 7.00.3 ± 0.8
60.04.9 ± 7.83022.7 ± 8.80.2 ± 1.1
Latitude −60.0
40.51.0 ± 2.1230.1 ± 2.50.1 ± 0.3
45.01.0 ± 3.215−1.2 ± 4.00.0 ± 0.5
50.01.7 ± 5.336−0.9 ± 6.4−0.1 ± 0.8
55.03.6 ± 7.072−2.4 ± 8.20.0 ± 1.0
60.02.9 ± 9.03500.8 ± 11.5−0.3 ± 1.3

5.5. Trend

[32] A linear trend term was added to the model as well, and the results are also presented in Table 2 along with the 95% confidence limits. Most of the derived trends are close to zero, and none are statistically significant. The 95% confidence limits allow us to place upper bounds on the size of a possible trend. The most precise estimates occur in the high and midlatitudes between 40 and 45 km, where the possible trend is limited to cooling of 3 or 4 K/decade. In these and all other altitudes and latitudes studied, the upper bound on the trend is consistent with previous work, such as the cooling of 1.0 to 1.6 K/decade in the tropics and subtropics observed by Remsberg et al. [2002], larger cooling amounts of 3.3 ± 0.9 K/decade near 60 km at stations between 8°S and 34°N estimated by Keckhut et al. [1998], and cooling of 4 K/decade in the northern midlatitude mesosphere reported by Keckhut et al. [1995].

6. Conclusion

[33] Version 6.10 of the SAGE II data set provides a new and potentially beneficial source of near-global density data in the stratopause region for 1984–2002. Since these data are free of discontinuities and nearly global in coverage, they provide a singular opportunity for middle atmosphere research. The present study converts those data to temperature and then derives mean climatologies and trend results for seven 20 latitude bands, from 70°S to 70°N. The mean climatology compares well with other published climatologies. The trend result shows no significant trend. It is expected that ongoing SAGE II development will result in improvements which should decrease the noisiness of the time series. Improved data would lead to heightened sensitivity to trends and other long-term variations and more detailed characterization of the stratopause region.


[34] S. P. Burton is supported by NASA contract NAS1-02058.