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Keywords:

  • global change;
  • thermosphere

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information

[1] The 1966–1987 Saint Santin/Nançay incoherent scatter radar database is analyzed to determine long-term trends beyond those associated with the “natural” variations of solar and magnetic activity, season, and time of day. Trends averaging some −3 K/yr are found in the F region. Positive trends in the E region may be explained by the subsidence of an overlying warmer regime of air. The trend line seems to change slope around the “breakpoint” year 1979, with the cooling changing from −0.8 K/yr before that time to −5.5 K/yr afterward at 350 km altitude. These trends greatly exceed those predicted by model simulations for increases in greenhouse gas concentrations. Further, carbon dioxide shows no such breakpoint year, but ozone does, near the time of the change in thermospheric trend, and a surface climatic regime shift has also been reported near this time. It is not clear that greenhouse gases are driving the long-term trend in thermospheric temperature. Restriction of analysis to a particular time of day results in greatly different trends, from near zero at midnight to −6 K/yr at noon at 350 km altitude. A separate analysis to determine the long-term trend in the amplitude of the 24 h tide at 350 km altitude shows a large change, with the amplitude diminishing from 136 K in 1966 to 89 K in 1988. Our results show the great need to remove all other natural variations from long-term data sets in determining long-term trends to avoid great ambiguity in trend interpretation.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information

[2] That atmospheric gases transmit short-wavelength visible solar radiations and absorb long-wavelength infrared Earth radiations, and thereby produce a “greenhouse” effect, has been known at least as far back as the time of Fourier [Fourier, 1824]. Tyndall [1863] realized that the asymmetric water vapor molecule is orders of magnitude more efficient at absorbing these Earth radiations than the dominant symmetric molecules N2 and O2. Arrhenius [1896, p. 267] undertook a numerical calculation of the effect of CO2 on atmospheric temperature owing to the extraordinary interest of the times in the question of the cause of ice ages, when “the countries that now enjoy the highest civilization were covered with ice.” Chamberlin [1899, p. 528], editor in general charge of the Journal of Geology, noted that further “abstraction of carbon dioxide from the atmosphere…would insure…the permanent and final winter of the Earth.” Callendar [1938, p. 236] claimed that fuel combustion in the previous 50 years was then raising atmospheric temperature; this result, he concluded, would be beneficial to man in the growth of plants and in the expansion of land cultivation poleward, and, “in any case the return of the deadly glaciers should be delayed indefinitely.” It was not until the 1950s that concern was voiced that such warming might damage our environment (see, e.g., Plass [1956, p. 387]: “The accumulation of carbon dioxide in the atmosphere from continually expanding industrial activity may become a real problem in several generations.”)

[3] Scant attention to the change in temperature aboveground level was given in these early considerations except insofar as conditions there may affect ground-level temperature. Manabe and Wetherald [1967] showed that raising CO2 concentration would raise temperatures in the troposphere but lower them at higher altitudes. While at low altitudes essentially all emissions from CO2 are reabsorbed by surrounding CO2 (or other greenhouse gases), in the higher thinner atmosphere upward emissions are more likely to be lost to space. Roble and Dickinson [1989] first investigated the cooling effects of increased CO2 and CH4 on the mesosphere and thermosphere, finding changes of some 50 K in the high thermosphere and resultant large compositional redistribution for a doubling of these gases. Rishbeth [1990] estimated from theoretical considerations that such a change in the thermosphere would lower the ionospheric E region by 2 km and F region by 15–20 km with small change in layer densities. Rishbeth and Roble [1992] performed model calculations to confirm these ionospheric predictions. Bremer [1992] detected an 8 km decrease in the height of the F region peak during the period 1957–1990. CO2 increased by about 12% over this period [see, e.g., Keeling et al., 1995], and Rishbeth's estimate of 15–20 km change in F layer height for a doubling of CO2 would scale to only 2 km for a 12% change. This result, that the measured change greatly exceeds that estimated on the basis of a change in greenhouse gases, anticipates our own results.

[4] Since that time, investigators have scoured upper atmosphere data for evidence of long-term trends. The reports of many of these investigations may be found in the proceedings of conference sessions held on the topic of “Long-term changes and trends in the atmosphere” (or similar names) in Moscow, Russia, in 1998 [Golitsyn, 1998], Pune, India, in 1999 [Beig, 2000], Prague, Czech Republic, in 2001 (Second IAGA-ICMA-PSMOS Workshop, “Long-Term Changes and Trends in the Atmosphere,” Phys. Chem. Earth, 27(6–8), 397–615, 2002), Sozopol, Bulgaria, in 2004 (Long-Term Changes and Trends in the Atmosphere, Phys. Chem. Earth, 31(1–3), 1–128, 2006), Toulouse, France, in 2005 (Long-Term Trends and Short-Term Variability in the Upper, Middle and Lower Atmosphere, J. Atmos. Sol. Terr. Phys., 68(17), 1853–2052, 2006), Sodankyla, Finland, in 2006 (Fourth IAGA-ICMA-CAWSES Workshop, “Long-Term Changes and Trends in the Atmosphere,” Ann. Geophys., 26, 1171–1326, 2008), and Perugia, Italy, in 2007 (Long-Term Changes and Solar Impacts in the Atmosphere-Ionosphere System, J. Atmos. Sol. Terr. Phys., 71(13), 1413–1510, 2009); conferences on this topic are planned for Boulder, Colorado, and Berlin, Germany, in 2010. Recent review articles on this topic include those of Beig et al. [2003], Beig [2006], Lastovicka et al. [2008], and Lastovicka [2009]. While these works include a number of reports related to ionospheric density, works concerning direct measurements of temperature above the mesopause are scarce. Holt and Zhang [2008] have reported the long-term trend in noontime temperature at 375 km altitude above Millstone Hill, apparently the only direct measurement of temperature above 110 km. The consensus of these measurements gives the consistent picture of slow cooling with time at all altitudes above the troposphere, but with little trend in the mesopause region, and very strong cooling in the high thermosphere.

[5] In the present paper we use measurements made with the French Saint Santin/Nançay incoherent scatter radar to show the long-term trend in ion temperature Ti. Ti begins its daytime upward divergence from the neutral temperature toward the electron temperature at about 250 km altitude but does not separate greatly in our altitude range of emphasis, so our results essentially apply to the neutral temperature also.

2. Data Set

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information

[6] We use the entire data set of the Saint Santin/Nançay bistatic incoherent scatter radar facility [e.g., Bauer et al., 1974], collected during the years 1966–1987 and deposited in the Coupling, Energetics, and Dynamics of Atmospheric Regions (CEDAR) database at the National Center for Atmospheric Research in Boulder, Colorado (http://cedarweb.hao.ucar.edu). This data set consists of 131,959 records distributed in altitude between 90 and 800 km as shown in Figure 1. The ion temperature exhibits patterns of “natural” behavior with solar and magnetic activity, season, and local time which are much larger than the small long-term trends sought. We have chosen to remove these natural variations by fitting a model of all variations to the entire data set, independently at each altitude, and then subtracting from each data value all model variations except that of the long-term trend. Indeed we have found it necessary to remove these other modelable variations, and a primary message of our work is that failure to do so leads to great ambiguity in the interpretation of any long-term trend obtained. We omit altitudes above 500 km because of their poor radar signal strength. We also omit altitudes with fewer than 298 total measurements; altitudes with fewer measurements did not cover the range of independent-variable values needed for a successful model fit to the data.

image

Figure 1. Height distribution of Saint Santin/Nançay database.

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[7] There is always a concern, when looking for smallish trends, that changes in instrumentation or data processing over the span of the data set could lend a time-varying bias that could be confused with the trend sought. We cannot irrefutably verify the lack of such a bias in our data set, but we can speculate on its presence. First, most such changes to system or processing occur at discrete times, leading to step-like shifts in the time series. We see no such steps in our time series. Second, the Saint Santin/Nançay system experienced no change in system or experiment design during its existence owing largely to its continuous wave (CW) system design that allowed little flexibility in its operation. Third, the primary feature of the Saint Santin/Nançay system design that might have imparted a long-term trend to spectral shape was its use of a filter bank. A long-term trend in performance of one of these filters could have caused a long-term trend in deduced spectrum shape. But these filters were all calibrated to the same sky-noise power level to correct for any such gain between filters [Petit, 1968]. The upshot of these considerations is that we can conceive of no likely instrumental effect that would lend a long-term bias to the temperature data set considered in our present study.

3. Fitting Function

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information

[8] To model our data, we have chosen a formula based on that used in the MSIS models [e.g., Hedin, 1987] reduced to apply to a single geographic location. Our formula is shown in Table 1. It consists of a constant, variations with solar activity, magnetic activity, day of year, and time of day, plus a long-term trend not in the MSIS model. The “solar cycle” variation is modeled as a quadratic function of the three solar rotation average equation image of the solar 10.7 cm flux intensity F in units of 10−22 W m−2 s−1. The “solar rotation” variation is modeled as a quadratic function of Fequation image. The magnetic variation is modeled as a linear function of the magnetic activity index Ap (a more detailed functional form was not found to be warranted for this location of rather low magnetic latitude). The “seasonal” variation consists of 12 month and 6 month sinusoids, with the 12 month component allowed to have a linear solar activity dependence. The “temporal” variation consists of 24 h, 12 h, and 8 h sinusoids, each allowed to have compound linear seasonal and solar activity dependences. The formula shown in Table 1 has 31 parameters, p1p31, that we adjust to give best fit to the data in a least squares sense. The least squares technique used is that of Bevington [1969] in which the fitting formula is linearized and the fitting is iterated until convergence is obtained. The error estimates on the p parameters come from joint consideration of the uncertainties of the data and the chi-square goodness of fit of the function to the data.

Table 1. Model Fitting Function
 Value
yyear
dday of year, Ω = 2π/365.2422 days
thour, ω = 2π/24 h
F10.7 cm solar flux intensity (10−22 W/m2)
equation imagethree-solar-rotation average of F
Favaverage F for our data set (133.5407)
Apavaverage Ap for our data set (14.1611)
Fitconstant + solar + magnetic + seasonal + temporal + long term
Constantp1
Solarsolar cycle + solar rotation
Solar cyclep3 (equation imageFav) + p4 (equation imageFav)2
Solar rotationp5 (Fequation image) + p6 (Fequation image)2
Magneticp9 (ApApav)
Seasonalannual + semiannual
Semiannualp10 cos 2Ωd + p11 sin 2Ωd
Annual(p12 cos Ωd + p13 sin Ωd) × (1 + p7 × solar)
Temporal(diurnal + semidiurnal + terdiurnal) × (1 + p8 × solar)
Diurnal(p14 + p15 cos Ωd + p16 sin Ωd) cos ωt + (p17 + p18 cos Ωd + p19 sin Ωd) sin ωt
Semidiurnal(p20 + p21 cos Ωd + p22 sin Ωd) cos 2ωt + (p23 + p24 cos Ωd + p25 sin Ωd) sin 2ωt
Terdiurnal(p26 + p27 cos Ωd + p28 sin Ωd) cos 3ωt + (p29 + p30 cos Ωd + p31 sin Ωd) sin 3ωt
Long termp2 (y - 1977)

4. Modification of Time-of-Day Function for Low Altitudes

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information

[9] At night the electron density in the E and lower F regions decreases to values too low to provide useful radar measurements. This lack of nighttime data poses a serious difficulty in determining the form of the full-day variation from a “half day” of data. Crary and Forbes [1983] have evaluated this issue quantitatively. While the ability to extract the values of the daily mean and diurnal harmonics depends on the quality and quantity of the data, they give a practical value of coverage of at least 15.5 h out of 24 needed for reliable extraction, i.e., no data gap of 8.5 h or longer. Figure 2 shows all of the measurements of the Saint Santin/Nançay database plotted versus local time and height of measurement. It is clear that we have a good 16 h of data at altitudes below 200 km and so should be able to extract the diurnal harmonics. Of course, these 16 h of data are possible only for midsummer while midwinter must yield data spans correspondingly shorter than 12 h. The summer data constrain the diurnal harmonics and the winter data do not, so we cannot determine any seasonal dependence of the harmonic components in the formula shown in Table 1 and are forced to set pi to zero for i = 15, 16, 18, 19, 21, 22, 24, 25, 27, 28, 30, and 31 and ignore seasonal variations in the tides for these altitudes. The lack of full nighttime data provides the greatest source of uncertainty in determination of the model parameters p1 and p2 for our analysis for altitudes below 200 km.

image

Figure 2. Time-height distribution in Saint Santin/Nançay database.

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5. Weighting the Data

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information

[10] We use “clipped weighting” in the fit. To data value yi with uncertainty Δyi, we assign the weight 1/Δyi2 for Δyi > median(Δy), 1/median(Δy)2 for Δyi < median(Δy). Such weighting provides three safeguards needed with our data set: It gives little influence to poor data, it prevents excessive control of the fit by a small minority of well-determined data, and it guards against control by data with erroneously small uncertainties. This latter category consists of a number of apparent printout-to-punched-card transcription errors, such as an error bar of 1 K in the midst of a time series of measurements with error bars of 10 K or more. Blind use of the 1 K error bar would be equivalent to duplicating this data point 100 times or more and risk skewing the model fit.

6. Display of the Data

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information

[11] Our current interest is in the long-term change in the background temperature stripped of all other variations. For display purposes we therefore subtract from each data point the fitted formula (evaluated for the solar, magnetic, seasonal, and diurnal conditions of that point) to obtain “cleaned data,” free of variations not of interest. It is these cleaned data that we show in this report. All error bars shown represent uncertainties of one standard deviation.

[12] Owing to the large number of data available to display, we often bin-average the data into years, 1966 through 1987. Such binning is done only after fitting, and it is the cleaned data that are binned, giving them approximately the same expectation value in a given bin. All data in a bin are considered independent estimates of the bin average, and the uncertainty of the bin average is computed as the standard deviation of the bin data divided by the square root of the number of data averaged. The true independence of those data is commented on as those results are discussed.

7. Ion Temperature Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information

[13] We fitted the ion temperature data independently at each altitude with the formula shown in Table 1 and as explained above. Figure 3 shows the constant term p1 in the formula plotted versus altitude. Error bars are included and become visible for the highest and lowest altitudes of weaker signal strength, for altitudes of relatively fewer measurements, and for the lower altitudes at which nighttime data are lacking. Figure 4 shows the data, cleaned of all variations except the long-term trend, bin averaged and plotted at 3 month intervals, plus the long-term trend line p1 + p2 (year - 1977), determined for the altitude of 350 km. The long-term cooling trend is evident in this plot. The scatter of the bin-averaged data points here is much larger than the size of the error bars. This effect results from the campaign nature of incoherent scatter radar operation in which many measurements are taken in a short period of time rather than randomly over the solar cycle. There is much weather in the thermosphere, just as there is on the surface, with periods during which the mean temperature may vary considerably from the climatological mean. The year 1982 (no data were taken during 1983), for example, seems to have been some 50 K cooler than average. The small error bars associated with the 1982 data points show the internal consistency of the data for that year, but for determination of the long-term trend these data may be viewed to be highly correlated in their deviation from the norm, and hence not independent estimates of the norm, and so warrant a larger error bar on their binned averages.

image

Figure 3. Mean Ti plotted versus altitude above Saint Santin.

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image

Figure 4. Long-term trend in Ti at 350 km above Saint Santin.

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[14] Figure 5 shows the per annum change in temperature (parameter p2 in our fitting formula) plotted versus height as the solid dots. The overall pattern of long-term change in the Saint Santin data is clear: falling temperatures from 90 km to 105 or 110 km, then rising temperatures into the E region, then a steadily strengthening rate of temperature decline with increasing altitude throughout the F region. The results from 250 to 350 km have small uncertainties yet differ height to height by much more than these uncertainties. We have been unable to identify any problem with these data or their fits and must leave these differences unexplained.

image

Figure 5. Height profile of the long-term trend in Ti above Saint Santin (solid dots). The summary profiles of Semenov et al. [2002] and She et al. [2009] and the result of Holt and Zhang [2008] are shown for comparison. The She et al. data are shown inside the box at 85–105 km, drawn to encompass the range of these data.

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[15] Included in Figure 5 are three results for comparison: (1) a summary of trend results compiled by Semenov et al. [2002] from Russian rocket, airglow, and radiophysical measurements, (2) a summary of Na lidar measurements at Fort Collins developed by She et al. [2009] (both read from their published graphs), and (3) the single point of Holt and Zhang [2008] determined from incoherent scatter radar measurements made at Millstone Hill. The result of Holt and Zhang agrees with ours fortuitously well. We consider this comparison further later in this paper. All three sets of lower thermosphere measurements indicate a transition from falling temperatures to rising temperatures as one rises from the mesopause into the thermosphere, though details of transition height and magnitude of the trend differ substantially. Striking here is the rapidly strengthening negative trend of the Saint Santin data as one descends below 105 km (the data points are shown in 5 km increments from 90 to 120 km altitude), culminating at 90 km in a temperature change over 22 years that would exceed the temperature itself as shown in Figure 3. These Saint Santin E region temperatures have been the subject of many papers written on the subject of tides, but we have found no such study that used the data from 90 km altitude; all have started at 95 km. The radar signal strength is decreasing rapidly with decreasing altitude at this level, and the effect of collisions on the signal spectrum is likewise rapidly removing the unique signature of temperature. We surmise that the data from 90 km altitude are unreliable. But this trend forms a consistent pattern as we ascend in altitude: 90, 95, 100, 105, 110, 115 km. We wonder if the problem that presumably afflicts the data at 90 km also afflicts higher-altitude data to smaller and smaller degree until it becomes negligible at 105 km, where the Saint Santin trend agrees better with the others shown. But even if these data are so afflicted, that does not explain why this affliction should have a long-term change. These apparently spurious results remain unresolved.

[16] There are other results reported in the literature for the mesopause region, many of which are summarized in reviews by Beig et al. [2003] and Beig [2006]. Beig reports a growing consensus of results that there is little trend at all at the mesopause, with several sources citing 92 km as being an altitude of zero trend, in conflict with the Saint Santin results shown.

8. Interpretation of Long-Term Temperature Trend

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information

[17] The long-term increase in temperature in the ∼110–170 km altitude region shown in Figure 5 could possibly be interpreted as a long-term increase in heating in that region. On the other hand, Akmaev and Fomichev [1998] have shown that even if there were cooling at all pressure levels, one may measure an increase in temperature at constant altitude if the cooling should cause subsidence of a warmer overlying atmosphere to the height of observation, such as might be expected above the mesopause where we find the steep temperature gradients leading upward to the thermosphere. These gradients approach 10 K/km, and so a 1 km shift in profile would have a large effect.

[18] We may attempt to unfold the true cooling and subsidence effects from our p1 and p2 results. Knowing the mean temperature profile and the true cooling profile, we could calculate the subsidence profile and the apparent temperature increase associated with the downward shift of the mean profile. Ours is the inverse problem, which must be carried out iteratively, for we know neither the cooling nor the subsidence values required in the calculation. We must make some initial assumption about either true cooling or subsidence to start the iteration. Make the following definitions of change of temperature T and height h over a given period of time, all functions of h:

[19] ΔTmeas = T change at constant height;

[20] ΔTwarm = T change due to warming;

[21] ΔTshift = T change due to profile shift;

[22] Δh = atmospheric expansion due to ΔTwarm.

[23] The measured trend is the sum of trends of true warming and profile shift,

  • equation image

[24] Iterate as follows:

[25] 1. Initialize ΔTwarm = 0 K at all h.

[26] 2. Δh(h) = equation image.

[27] 3. ΔTshift = T(h − Δh) − T(h).

[28] 4. ΔTwarm = ΔTmeas − ΔTshift.

[29] 5. Go to step 2 until ΔTwarm converges.

[30] In this analysis we use the fact that the expansion of the thickness of a slab of air is proportional to the increase of absolute temperature (Charles's law), and the expansion Δh experienced at any height h is the sum of the expansions of all air slabs below h. We have chosen to initialize ΔTwarm to zero at all altitudes; a wide range of choices of initialization yielded the same final result. Our deduction of Twarm, being an inverse procedure, is prone to amplify the noise present in the data. For this reason we have fit sixth-degree polynomials to our T and ΔTmeas profiles and used these fits in the deduction. The results of this exercise are shown in Figure 6, where the ΔTmeas data and their polynomial fit and the deduced ΔTwarm profiles are shown. It is clear that all of the apparent warming seen in the ΔTmeas profile comes from subsidence of the overlying warmer atmosphere and that true cooling prevails at all altitudes above 90 km. The amount of subsidence Δh deduced is shown in Figure 7. We assumed no subsidence at our lowest height of 90 km, and the deduced true cooling would be greater if there should be subsidence there. This factor is somewhat compensated for by the likely excessive cooling shown from 90 to 100 km, as discussed earlier. The only importance that we place on this plot is to confirm that cooling and subsidence prevail throughout and to obtain rough estimates of the magnitudes of the cooling and subsidence.

image

Figure 6. Height profile of measured temperature increase and of true heating.

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image

Figure 7. Height profile of subsidence deduced from the measured long-term temperature changes.

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9. Data and Model Selectivity

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information

[31] Our technique of modeling all variations for our complete data set and then removing those variations not of immediate concern avoids ambiguities in interpretation that can otherwise plague a search for smallish trends. If, for example, a long-term data set should happen to have a preponderance of summer data at the beginning of a data set and/or winter data at the end, failure to remove the seasonal variation from the data set would likely result in a false finding of a long-term cooling. It is a question of the distribution of data as a function of all solar geophysical variables involved. A small unremoved imbalance in the distribution of any solar geophysical factor influencing the data could be misinterpreted as a “global change” trend.

[32] Data selectivity, perhaps forced by conditions of an experiment, comprises a more subtle difficulty in interpretation of long-term trends, for if one does not have the data to define all solar geophysical variations affecting the data, one cannot remove them. The analysis of Holt and Zhang [2008], for example, limited analysis to times within half an hour of noon. One can imagine a number of scenarios in which a long-term trend determined from noontime data may yield ambiguous interpretation. If the true long-term trend consisted of no change in the daily mean but a decreasing amplitude of the diurnal amplitude, than looking at noontime data would show a long-term temperature decrease while the daily average temperature would be unchanged (and midnight data would show a corresponding increase). Alternatively, if both the daily mean and the diurnal amplitude remained unchanged but the phase of the diurnal variation should drift with time, then one would again see a long-term temperature rise at one time of day but a temperature fall at another. We are able to check these possibilities with our Saint Santin data by dropping the entire diurnal component from our fitting formula (p8 and p14p31) and separately fitting the data for the twenty-four 1 h periods of the day. The result is shown in Figure 8. It is clear that the trend ranges from near zero at midnight to some 6 K per year near midday. Clearly the diurnal function is experiencing large long-term variation. We suggest that this diurnal variation of the long-term trend reflects the diurnal variation in the density of the primary cooling gas at these altitudes; there is more cooling by day because there is more coolant. Beig [2002] warns of the dangers in long-term trend analysis from use of data at different hours. We further warn of the dangers of using data at the same hour. Any long-term trend analysis that does not remove the diurnal variation is subject to ambiguous interpretation; selection of any specific time of day guarantees that ambiguity. Those techniques that measure only at night (optical techniques), or only by day, or only in certain seasons owing to weather constraints, all incur this ambiguity of interpretation.

image

Figure 8. Temperature trend for the twenty-four 1 h periods of the day.

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[33] We have made an additional analysis to determine the long-term trend of the diurnal tide. We have modified our formula in Table 1 to let the diurnal sine and cosine terms p14 and p17 each acquire a long-term trend. We have modified p14 to p14 [1 + p32 (year - 1977)] and p17 to p17 [1 + p33 (year - 1977)] and determined a new set of parameters p1p33. By allowing the sine and cosine terms to have independent trends, we allow the amplitude and phase to vary independently. The results of this test, applied at 350 km altitude, are p32 = −0.0233 ± 0.0013/yr and p33 = −0.0075 ± 0.0019/yr, well-determined parameters showing decided long-term changes. Table 2 shows what these results mean for diurnal amplitude and phase (hour of maximum) for 3 years, 1966, 1977, and 1988, at the beginning, middle, and end of our data span, all with seasonal, solar activity and magnetic activity variations removed. The diurnal amplitude changes from 136 K to 89 K over that period. These are rather startling changes, but, again, well determined by fit to the data. One must understand, however, that this is just the 24 h “tide,” which, at this altitude, may not be an independently propagating wave but just a mathematical decomposition of an in situ generated waveform. Changes in the 12 h and 8 h components must be included to judge total change. If propagating tides should materially affect behavior at this altitude, Jacobi and Kürschner [2006] note that tidal wavelengths become smaller in a cooler atmosphere, leading directly to changes of phase as the tides propagate to higher altitudes, so change in phase should be expected in the thermosphere too. Our goal in this paper has been to determine the long-term trend in the mean temperature (p1 in our formula). Our test with the diurnal term shows that all such p terms need long-term trend analysis.

Table 2. Long-Term Trend in Ti Diurnal Amplitude and Phase at 350 km Altitude
YearAmplitude (K)Phase (h)
1966136.0 ± 1.714.03 ± 0.05
1977112.4 ± 0.914.25 ± 0.03
198889.4 ± 1.814.47 ± 0.08

10. Episodic Trends

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information

[34] The required length in years for long-term trend analysis has been brought up in the literature. Bremer [1992] notes that he needed 25 years of ionosonde data to articulate an accurate trend in the altitude of the F layer peak. Lastovicka [2002] claims that two solar cycles of data are needed. Danilov [2006] claims that 30–35 years of data are necessary for stable results. In his overview on such trends and their uncertainties, Beig [2002, p. 510] comes to the most reasonable conclusions that “a prerequisite for trend study is a detailed knowledge of the variations due to natural sources,” and “the length of the data time series may not be a deciding factor…unless the time series is too short (less than a decade or so).” If one wishes to detect a linear long-term trend, one must have a solar activity trend over the data span that differs sufficiently from a line, preferably a full cycle. Holt and Zhang [2008] have determined and removed solar activity and magnetic activity variations from a 30 year timeline of incoherent scatter radar data from Millstone Hill and have shown stable trend detection. Our Saint Santin database is 22 years long, and we experience no difficulty with the stability of our long-term trend. Further, additional exercises reported below show stable detection over shorter periods.

[35] It may well be argued that Figure 4 shows little long-term trend until about 1980. A tendency to episodic intervals in cooling rate has been noted before. Rozelot and Lefebvre [2006] say that there have been periods of warming and cooling since 1861 in surface temperature, with 1910–1945 showing a 0.13 K/decade warming, 1946–1975 showing a 0.01 K/decade cooling, and 1976–2001 showing a 0.21 K/decade warming, with the period 1861–1975 showing remarkable correlation with solar irradiance but the period 1976–2001 showing a complete break in that relationship. Labitzke and Kunze [2005] found that stratospheric temperature trends changed around year 1979, though, remarkably, the change was from positive to negative in the time series of March data but from negative to positive in the times series of December data. Bremer and Peters [2008] identify 1979 as a “breakpoint” year in the long-term O3 trend observed in data collected at Arosa, Switzerland, and relate this same year with a breakpoint in the trend of LF (low-frequency) reflection height measurements as seen above Collm, Germany. Danilov [2009, p. 1433] finds that the correlation between daytime and nighttime values of foF2 shows a clear change in trend “in the vicinity of 1980.” Merzylokov et al. [2009] discuss the current state of the art of breakpoint determination in time series. They note that complex nonlinear systems like the atmosphere may well transition from one quasi-stable state to another. They found a breakpoint in the mean wind above Obninsk close to year 1977, when a climatic regime shift was observed in many features of the global climate system [see, e.g., Seidel and Lanzante, 2004], and in the semidiurnal tide above both Obninsk and Collm close to year 1979, when the O3 trend changed. Concerning the mesopause, Beig [2006] notes that some models indicate the trend seen before year 1980 was different from the trend after that year, and during long periods even opposite in nature.

[36] We have tried one additional exercise with the Saint Santin data at 350 km altitude. We have allowed two trend lines, one before and one after the year of intersection of the two lines, and we have determined the two slopes and year of intersection that gives best fit to the data. The result was a trend of −0.8 ± 0.2 K/yr before year 1978.8 ± 1.0 and −5.5 ± 0.7 K/yr after that date, as shown in Figure 9 for yearly averaged data. This year of episodic change in trend line does not differ greatly from those noted above.

image

Figure 9. Long-term trend with two trend lines allowed.

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[37] The cooling seen above Saint Santin is far greater than that predicted by models. Roble and Dickinson [1989] predicted a 50 K increase for a doubling of greenhouse gases. Keeling et al. [1995] show CO2 concentration to have risen from 320 to 349 parts per million from 1966 to 1988, only 9%, implying less than 5 K cooling over 22 years from the model simulation. Even our shallow slope of 0.8 ± 0.2 K/yr seen before 1979 far exceeds 5 K over 22 years.

[38] Figure 10 shows an interesting result for O3 over the 1966–1988 time period. The O3 data are Halley Bay mean October column thickness values taken from www.faqs.org/faqs/ozone-depletion/antarctic, and they have been fitted just as the Saint Santin Ti data were to determine two slopes and year of slope change. The year of slope change here is 1975.9 ± 3.3. O3 exhibited both greater fractional density change than did CO2 and an episodic change that CO2 did not during this period. O3 is not acting as a greenhouse gas in the thermosphere, for the temperature and O3 trends would be anticorrelated if it were. But changes in O3 should have a major effect in the stratosphere-mesosphere layer, where O3 is responsible for the temperature bulge in that region, on top of which the thermosphere rests.

image

Figure 10. Long-term trend in ozone concentration.

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11. Ion Composition Considerations

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information

[39] Incoherent scatter radars measure Doppler shifts, or temperature-to-mass ratio for thermal motions. All “temperature” deductions are made under some assumption about the actual ion species present in the scattering volume. The temperatures in the Saint Santin database were derived under the assumption of a specific height profile of ion composition fixed for all time. The long-term trends in temperature shown in this paper must be affected by the inevitable change in ion composition that must accompany the long-term changes in the atmosphere. We do not attempt to assess the degree of that change below but only to recognize its bounds.

[40] In the E region the dominant ions are NO+ and O2+. The common assumption of a common mass of 31 amu for these molecular ions leaves an uncertainty of ±1/31, or ∼±13 K for a temperature of 400 K, depending on what the true ion composition should happen to be. Danilov [2002] suggests that a long-term increase in eddy diffusion should remove NO from the E region to the D region, thereby decreasing the importance of the O2 + NO [RIGHTWARDS ARROW] NO+ + O2 reaction and so increasing the O2+/NO+ density ratio. From rocket data he deduces a factor of 2.5 change in this ratio at 120 km altitude between the years 1970 and 1988. Such a change would impart an important apparent but false long-term trend to a temperature deduction based on a fixed ion composition.

[41] The situation is worse in the F1 region in which we see the transition between the “31+” molecular ions of the E region to the “16+” atomic oxygen ions of the F region. Here we have a factor of 2 change in mass and so a factor of 2 uncertainty in absolute temperature. The ion composition here is controlled by the composition of the main neutral species, which respond to long-term changes in temperature. We expect that the long-term temperature trends shown in this paper for the F1 region are affected by our use of a fixed F1 region ion composition profile in magnitude but not in sign.

[42] The further transition from O+ to H+ (and He+) ions at higher heights would introduce similar considerations in trend deduction. H+ ions are not important above Saint Santin at the altitudes considered in this paper but could become important at lower latitudes.

12. Concluding Remarks

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information

[43] Our analysis of the 1966–1987 Saint Santin/Nançay incoherent scatter radar database confirms the existence of long-term trends unassociated with the “natural” variations in solar or magnetic activity or season or time of day. These long-term trends are not just detectable, they are sufficiently determinable to enable a climatology to be derived and should be considered for inclusion in community models of the upper atmosphere and ionosphere.

[44] We have shown the great necessity to determine and remove all natural variations from the data in the process of determining the long-term trends. Failure to remove the diurnal variation, for example, resulted in our finding of a long-term trend of near zero from midnight data but 6 K cooling per year from noontime data. Analyses of data sets that cover only parts of the day or parts of the year, and hence cannot determine and remove these natural variations, inherently incur ambiguities in interpretation of their long-term trend results.

[45] The long-term trend in thermospheric cooling that we found far exceeds that predicted by model simulations based on greenhouse gas increases. Further, the observed trends have an apparent breakpoint in time, after which the cooling greatly accelerates. The greenhouse gas CO2 has experienced no such breakpoint year, but O3 has, close in time to the thermospheric-cooling breakpoint, and a climatic regime shift at the surface near that time has also been reported. It is not clear that CO2 is driving the long-term trend in thermospheric cooling.

[46] Our analysis has concentrated on the long-term trend of the mean temperature, but a test has also shown that the long-term trend in the diurnal amplitude is also well determined. Future analysis will investigate the long-term trends in all of the natural variations.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information

[47] This work used data accessed from the CEDAR database. The Saint Santin/Nançy facility was operated with financial support from the Centre National de la Recherche Scientifique. Discussions on the database with Christine Amory are gratefully acknowledged. This work was supported through NSF REU grant ATM-0327625; the research was conducted by undergraduates. Several students contributed to the project. Tyler Wellman first determined the global cooling trend for the altitude of 300 km in July 2006. Each student in the fall 2007 global change class at Boston University determined the global cooling trend at a different altitude in fall 2007. Jessica Donaldson first determined the entire height profile of global change in March 2008. Joanna Yoho and Ryota Yonezawa developed our in-house database, while Edgar Banguero developed our Web site for the database and Navin Narra helped to edit the data. We thank Jeffrey Forbes and Maura Hagan for helpful discussions on the data trends.

[48] Robert Lysak thanks Tony van Eyken and another reviewer for their assistance in evaluating this paper.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data Set
  5. 3. Fitting Function
  6. 4. Modification of Time-of-Day Function for Low Altitudes
  7. 5. Weighting the Data
  8. 6. Display of the Data
  9. 7. Ion Temperature Results
  10. 8. Interpretation of Long-Term Temperature Trend
  11. 9. Data and Model Selectivity
  12. 10. Episodic Trends
  13. 11. Ion Composition Considerations
  14. 12. Concluding Remarks
  15. Acknowledgments
  16. References
  17. Supporting Information
FilenameFormatSizeDescription
jgra20575-sup-0001-t01.txtplain text document1KTab-delimited Table 1.
jgra20575-sup-0002-t02.txtplain text document0KTab-delimited Table 2.

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