A reanalysis for the seasonal and longer-period cycles and the trends in middle-atmosphere temperature from the Halogen Occultation Experiment

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112,, doi: /2006jd007489, 2007 A reanalysis for the seasonal and longer-period cycles and the trends in middle-atmosphere temperature from the Halogen Occultation Experiment Ellis E. Remsberg 1 Received 8 May 2006; revised 24 October 2006; accepted 20 November 2006; published 15 May [1] Remsberg and Deaver (2005) reported on multiple linear regression (MLR) analyses of time series of middle-atmosphere temperature versus pressure (or T(p)) profiles from the Halogen Occultation Experiment (HALOE) for its seasonal and longer-period cycles. Their results are extended herein to just over 14 years and updated to properly account for the effects of autocorrelation in their time series of zonally averaged data. The updated seasonal and annual average terms are provided, and they can be used to generate near-global, temperature distributions from 2 to hpa that are representative of the period Quasi-biennial oscillation (QBO-like; 853-day) and subbiennial (640-day) terms are also resolved and provided, and they exhibit good consistency across the range of latitudes and pressure altitudes. Further, somewhat exploratory analyses of the residuals from each of the 208 time series yield significant 11-year solar cycle (or SC-like) and linear trend terms at a number of latitudes and levels. Where significant, those terms are included in the final MLR models. The amplitudes of the SC-like terms for the mesosphere agree reasonably with calculations of the direct solar radiative effects for T(p). Those SC-like amplitudes increase by about a factor of 2 from the lower to the upper mesosphere and are larger at the middle than at the low latitudes. The diagnosed T(p) cooling trends from HALOE for the low latitudes are in the range of 0.5 to 1.0 K/decade, which is in good agreement with the findings from models of the radiative effects on pressure surfaces due to known increases in atmospheric CO 2. The diagnosed HALOE trends are somewhat larger than those predicted with models for middle latitudes of the upper mesosphere. Cooling trends also are found to be increasing from about 0.5 to 1.0 K/decade from 1 to 2 hpa of the upper stratosphere, also in reasonable agreement with modeled results. Citation: Remsberg, E. E. (2007), A reanalysis for the seasonal and longer-period cycles and the trends in middle-atmosphere temperature from the Halogen Occultation Experiment, J. Geophys. Res., 112,, doi: /2006jd Introduction [2] Time series of zonal-average temperature versus pressure or T(p) from the Halogen Occultation Experiment (HALOE) were analyzed for their seasonal and longerperiod terms in the upper stratosphere and mesosphere, as reported by Remsberg et al. [2002a] and Remsberg and Deaver [2005]. HALOE made its last measurements on 21 November 2005, and its parent UARS spacecraft was de-activated in mid-december The seasonal and interannual terms reported by Remsberg et al. [2002a] were based on 9.5 years of data; the results in the present paper are based on just over 14 years of data. The longer-period terms in the work of Remsberg and Deaver [2005] were based on 12.5 years of data, and those analyses are now 1 Science Directorate, NASA Langley Research Center, Hampton, Virginia, USA. This paper is not subject to U.S. copyright. Published in 2007 by the American Geophysical Union. extended to 14 years, too. However, both of their analyses did not account properly for the effects of autoregression in the time series; they included a term bt(n-1) in their equation (1) that had the incorrect effect of fitting a slightly shifted time series with itself (by one point) and thereby accounting for part of the variance in the data series. As a result, their periodic and polynomial terms only accounted for the variance that remained, and the coefficients that they reported for the seasonal and longer-period terms were underestimated. At times their fitted 11-year solar cycle (SC) terms were not quite in-phase with independent measurements of the solar flux variations. Their approach also led to undue difficulties for the fitting of the associated trend term in the presence of an SC term. Still, their assertions about the adequate sampling and excellent calibration of solar occultation measurements remain valid for obtaining the seasonal and longer-term variations of middle atmospheric T(p). [3] The reanalyses herein account for the first-order autoregression (AR1) term properly, leading to seasonal and longer-period terms of larger amplitude. Terms are 1of13

2 Figure 1. Time series of zonally averaged sunrise (SR, open circles) and sunset (SS, solid circles) temperatures (in K) from Halogen Occultation Experiment (HALOE) measurements at 30 N and the 0.02-hPa level (near 75 km) of the mesosphere. Points have been adjusted to first order for the average diurnal difference at SS versus SR. Terms for the multiple linear regression (MLR) model fit are listed at the lower left (see text). The oscillating curve is the fit for the complete MLR model, while the straight line is the value of the constant term. reported for 10 wide latitude zones from 60 S to 60 N and for pressure levels from 2 hpa to hpa. Analyses are conducted for some additional levels, too 1.5, 0.7, 0.15, 0.07, and hpa. A total of 208 separate time series are analyzed, and the results are shown to be coherent with latitude and pressure altitude. Subbiennial (IA) and quasibiennial oscillation (QBO)-like terms are evaluated for each of the time series. The zonal mean and seasonal values can be used to generate a climatology of T(p) that is representative of the time span of October 1991 through November Section 2 briefly reviews the updates that are applied to the original method of analysis. Section 3 contains a tabulation of the findings for the seasonal and then the interannual, solar cycle, and linear trend terms. Some of the phase anomalies from the earlier studies are corrected now. The longer-period and trend terms from HALOE are also briefly compared with some other published results from data sets and from models. Section 4 is a summary of the findings for the time series of the HALOE T(p) data herein. 2. Time Series Reanalysis Approach [4] The procedure for assembling the time series of zonally averaged sunrise (SR) and sunset (SS) points from the HALOE Version 19 (V19) Level 2 profiles is unchanged from that described by Remsberg and Deaver [2005, and references therein]. For example, Figure 1 is an update of their original plot for 30 N and 0.02 hpa (near 75 km). Multiple linear regression (MLR) techniques are used for fitting the significant periodic and polynomial terms to the time series data. The terms for Figure 1 include annual (AO), semiannual (SAO), and quasi-biennial oscillation (QBO of average period 853 days) terms, an assumed 11-year SC (or 4015-day) term, and a linear trend term. As before, the periods and phases of the QBO and/or other interannual (IA) terms are determined by a Fourier fit to the residuals after accounting for the seasonal terms. This approach of examining the structure in the residuals is in accord with a basic tenet for the analysis of time series data, especially if the true causes of its variances are not fully known. That is why proxies were not used for the QBO and SC terms in this study, and why the analyses herein are considered exploratory for the longer-period and trend terms. A Fourier fit for structure in the residuals means that the QBO, IA, and SC terms are assumed to be sinusoidal. However, the predominant periods for the QBO and IA terms are 853 days and 640 days, respectively, and they were imposed for the evaluation of the set of terms for the final MLR models. An 11-year period for the SC term was imposed, too. The phase of the SC-like term was determined from the MLR fit, primarily to see whether it was truly in-phase with an SC proxy, as opposed to some other decadal-scale forcing mechanism. Only those terms that are clearly indicated in the residuals are retained for the final MLR model of a given latitude and pressure level. In summary, separate analyses were necessary for each level and latitude zone, rather than assuming that the same terms are present and significant at all locations. The fit to the points in Figure 1 is based on the combination of all the reanalyzed terms, as shown by the oscillating curve, and it includes the linear trend term. The straight line fit is based on just the constant term (198.7 K) after accounting for the first-order effects of the autocorrelation. [5] The average separation in time for the points in the HALOE time series is about 25 days. Even so, because the temperature value at time n has considerable memory of the atmospheric state of time n-1 for zonal means, the time series points have autoregressive characteristics. The correct MLR result for that situation is obtained by a two-step process (see Appendix A of Tiao et al. [1990]). Initially, a model of the form Tn ðþ¼aþbx þ e sinðzþþf cosðzþþ...þ Nn ð Þ ð1þ 2of13

3 Figure 2. Contour plot of the autocorrelation coefficients at lag-1 (or AR1) from the analyses of the HALOE temperature time series in terms of latitude versus pressure altitude. The altitude scale on the right is approximate and is based on a pressure scale-height of 16.5 km for the range of the HALOE T(p) profiles. is used, where T(n) is the temperature at the nth point in the time series. The model has a constant term a and a linear term in X = (t n t 1 )/T, where t n is the time of the nth observation point, t 1 is the first point in the time series, T is the total length of the time series, and b is the coefficient of the linear term. The model also has seasonal and longerperiod terms that are represented by Fourier components in Z, where Z = 2pt n /P, and P is the period of a given cycle. Periodic terms that are considered are AO, SAO, QBO-like, subbiennial (IA), and an 11-year SC-like term. Only those terms with a high probability of being present were retained for the final model. Note that the seasonal terms almost always reach a probability of 99%. The QBO, IA, and SC terms were allowed to have lower probabilities, in order to provide a better judgment about their existence in the time series across all latitudes and pressure altitudes. Probabilities for the linear terms are noted as part of their tabulated findings. Finally, the term N(n) is the autoregressive (AR) noise residual that is given by Nn ðþ¼8nðn 1ÞþEn ð Þ; for a first-order (AR1) process. The factor 8 is the autocorrelation of the noise residual and E(n) is the white noise component. In practice, the estimates of 8 are based on the residuals that are found from a fit of the dominant seasonal (AO and SAO) and QBO-like terms. Thus the current MLR method consists of a fit for those terms of equation (1) and the generation of its model residuals N(n). The autocorrelation coefficient 8 for this model is found, and a search is made for any remaining significant interannual and SC terms in N(n). Then, a refitting is conducted for the complete set of significant and transformed model terms of equation (3), Tn ðþ 8Tðn 1Þ ¼ a1 ½ 8ŠþbXn ½ ðþ 8Xðn 1ÞŠ þ e½sinðzðnþþ 8 sinðzðn 1ÞÞŠ þ f½cosðzðþ n Þ 8 cosðzðn 1ÞÞŠþ...þ En ð Þ: ð2þ ð3þ [6] Equation (3) yields a new residual E(n) that is closer to having a white noise character. The terms of equation (3) have the same coefficients as equation (1), except with different and now more appropriate estimates of significance and/or uncertainty. The present reanalysis employs the sequence of operations from equation (1) through equation (3). The updated model terms have larger amplitudes and somewhat larger uncertainties than before; terms whose amplitudes are sufficiently greater than the noise are still highly significant. Further, because MLR provides for a combined fitting of all the model terms, the absolute temperature uncertainties are nearly the same for each term of the model. The percentage deviations and their probabilities depend on the amplitudes of the respective terms. [7] As an example, the reanalysis for 30 N, 0.02 hpa is shown in Figure 1 and yields an autocorrelation coefficient 8 of The AO and SAO terms have amplitudes of 6.8 K and 3.5 K, respectively, both with a partial rank order correlation (its PROC or probability of being present) of greater than 99.99%. There is also a significant 853-day QBO cycle of amplitude 0.8 K (98%). The SC term has amplitude 2.1 K (99.9%), and its maxima occur in January of 1992 and 2003 or very near to those of the variations of the F10.7 cm solar flux. Note that this SC amplitude is analogous to a max minus min variation of 4.2 K over the solar cycle. In addition, there is a cooling trend term with a slope of 2.4 K (99.7%) over 14+ years or 1.7 K/decade. Remsberg and Deaver [2005] did not report a QBO term for this level and latitude, and the amplitudes of their AO, SC, and trend terms were smaller. [8] Figure 2 is a contour plot of the absolute values of the AR1 coefficient 8 as a function of latitude and pressure altitude. Those values are generally small in the mesosphere, and, in fact, the signed values are occasionally negative in the subtropical upper mesosphere of the Southern Hemisphere and in the middle mesosphere at tropical latitudes. Small values for 8 indicate very little memory for the time series points, even in a zonal mean sense. The smallest values occur in the middle mesosphere at subtropical latitudes, where the amplitudes of the seasonal cycles are also small compared with the longer-period waves and the residual effects of the temperature tides (see next paragraph). Values of 8 are larger at the higher latitudes, where the amplitude of the annual cycle is increasing. Values of 8 are also enhanced slightly in the middle mesosphere at the equator, where the amplitude of the SAO term is largest. It was expected that there would be larger values of 8 in the stratosphere, and one can see that they increase from 1 to 2 hpa across most latitudes. [9] Prior to performing an MLR fit to the time series of the SS and SR data points, the means of the time series of just the SS points and then just the SR points were obtained, as in the work of Remsberg et al. [2002a]. The two series of separate SS and SR points were adjusted by half the difference of those means. In this way the SS (solid circles) and SR (open circles) points for Figure 1 have had the firstorder variations of the average diurnal variation at SS versus SR removed before combining them into a single time series, even though tidal variations do not alias onto the longer-period seasonal terms. However, because the SS and SR points are nearly alternating in time at most latitudes, what one gains by this diurnal adjustment is a reduction of 3of13

4 Table 1. HALOE Sunset Minus Sunrise Temperature a a Temperatures are given in K. HALOE, Halogen Occultation Experiment. the short-period, noise-like character of the residuals, particularly in the mesosphere. This reduction in geophysical noise is important for subtropical latitudes of the middle mesosphere, where the amplitudes of the seasonal and longer-period terms are small and near the noise level. In addition, the combined time series have twice as many points, which allows for a more adequate sampling of the SAO cycle from the solar occultation measurements. The fact that there is some seasonal variation to the tidal behavior becomes part of the seasonal terms for the final T(p) models but is of secondary importance to those terms. [10] Table 1 contains the SS minus SR differences from those respective means, and they have a pattern with altitude at low latitudes that is similar to that of the diurnal tide. Figure 3 shows the average SS minus SR variations in T(p) for selected latitudes. Upon assuming that each decade of pressure altitude occurs over 16.5 km, the vertical wavelength for the tide is about 33 km at the equator and at 30 N, but nearly reversed in phase between those two zones, as calculated from linear theory [Lindzen, 1967] and as reported from other observations [e.g., Dudhia et al., 1993]. Tidal amplitudes inferred from HALOE are largest at the equator. There is evidence for some interfering effects of the tidal signatures of the equator and 30 N in the average SS minus SR profile at 20 N. [11] Another physically important characteristic of Table 1 is the large amount of symmetry in the mesosphere for the pattern and magnitude of the SS/SR differences between the two hemispheres, even at the latitude zones of 40 60, where the effects of the 3-day per year orbital precession and the changes for the seasonal sampling over the 14-year period of HALOE, have been of some concern. Still, the SS/SR differences at those higher latitude zones are rather large (of order 5 K) near the stratopause and are viewed with skepticism because of the subtle effects of that long-term precession and of the marginal sampling rates for the large-amplitude, seasonal cycles from the SS and SR orbital segments. As will be shown in section 3, the reanalysis results for the seasonal and longer-period terms from HALOE data set exhibit good coherence across the entire range of latitudes and pressure altitudes. However, the trend terms at 50 and 60 latitude appear to have biases because of the inadequate seasonal sampling and slow precession; those results are not retained. 3. Results of the Reanalyses 3.1. Seasonal and Annual-Mean Terms [12] Table 2 and Figure 4 present the amplitudes of the annual cycles (AO) as a function of latitude and pressure level. AO amplitudes are weak at the low latitudes and in the middle mesosphere at all latitudes. Much larger AO variations are found at the higher latitudes, especially near the stratopause and mesopause. As a result of properly accounting for the autoregressive effects in the zonal mean temperature data, it is noted that the AO amplitudes are larger than those reported by Remsberg et al. [2002a] for those regions where the values of 8 are relatively large. AO amplitudes are also similar for the same latitudes of each hemisphere, as expected. An exception occurs for the Figure 3. Average profiles of the HALOE SS minus SR temperatures (in K) for selected latitude zones. 4of13

5 Table 2. Amplitude of Annual Cycle a a Amplitudes are given in K latitude region, where the AO amplitudes in the upper mesosphere are larger in the NH than in the SH. Conversely, the AO amplitudes at high latitudes of the SH are larger than in the NH for the lower and upper mesosphere and for the upper stratosphere. [13] Table 3 contains the day of the year of the AO maximum, and there is excellent continuity in its timing across latitude and pressure altitude. There is an outof-phase relationship for the AO cycle at middle and high latitudes of the two hemispheres, indicating good seasonal symmetry for the AO. For example, at 1 hpa the AO maximum occurs on day 173 at 60 N, while it is on day 349 at 60 S, or 176 days (nearly 6 months) later. Even though the HALOE sampling occurs fairly infrequently at the higher latitudes, it appears to be adequate for resolving its large-amplitude AO cycles with reasonable accuracy. One can see the nearly 180-degree change in the AO phase that occurs in the middle mesosphere (between 0.10 and 0.15 hpa) for the middle to higher latitudes. The AO phase changes more gradually with pressure altitude for the lower latitudes. [14] Table 4 and Figure 5 contain the average amplitude of the two SAO cycles. No attempt was made to distinguish between the first and second cycles, although it is likely that there are slight differences in their magnitudes and phases. There is more hemispheric similarity for the amplitudes for the SAO than for the AO. However, there is less certainty for the SAO than the AO amplitudes at 50 and 60 of latitude because of the relative sparseness of the sampling from HALOE for at least one season. Table 5 shows the day of year for the SAO temperature maximum in terms of its first SAO cycle, even though the SAO amplitudes and phases are obtained from the fit to both the first and second cycles of every year. As with the AO, there is good coherence for the timing of the SAO maximum with latitude and pressure altitude. [15] The annual-mean temperature distribution or constant term from the MLR analyses is given in Figure 6 and Table 6. This distribution together with the AO and SAO amplitude and phase information is all that one needs to assemble monthly or seasonal profiles of T(p) for scientific study. The annual-mean and seasonal terms compare favorably with the values presented by Barnett et al. [1985], although the amplitude of their SAO term is noticeably smaller in the mesosphere because of the much lower vertical resolution of their Pressure Modulated Radiometer (PMR) data set. Because the QBO, IA, and SC-like terms have been obtained as part of the MLR fits for the seasonal terms, one can be confident that the distributions of T(p) from Tables 2 6 are representative of the period, at least within the known estimates of absolute error for the retrievals of the HALOE V19 temperature profiles [Remsberg et al., 2002b]. [16] There are several instances of likely bias in the HALOE temperatures of the upper mesosphere. The signal-to-noise (S/N) in its CO 2 channel is becoming low at the level of hpa, and there is a blending of its retrieved profile with that of the MSIS model. As a result, the temperature at that level is often a combination of the model and the measurement, based on a weighting for the two as determined by that S/N. It is also likely that the values at 60 latitude for the levels of and 0.01 hpa are affected by absorption from polar mesospheric cloud (PMC) particles during the summer months. This interference effect will lead to summer season and annual-mean temperatures Figure 4. Contour plot of the zonal average temperature amplitude (in K) for the annual oscillation (AO) term of the MLR model. Contour interval is 2 K. 5of13

6 Table 3. Day of Year for the Maximum of the Annual Cycle that are too warm by a few degrees [McHugh et al., 2003]. The finite field of view (FOV) of the HALOE CO 2 channel also tends to smooth the true amplitudes of the vertical structures in a temperature profile that have been induced by tides and/or by the breaking of gravity and planetary waves, particularly in the upper mesosphere [LeBlanc and Hauchecorne, 1997; Remsberg et al., 2002b]. [17] Table 7 gives the hemispheric differences (SH minus NH) for the annual-mean temperatures. The subtropical upper mesosphere is slightly warmer in the SH than the NH. For the 40 through 60 latitude zones of the upper mesosphere the SH annual means are warmer than in the NH, which confirms the expected findings based on the model studies of Siskind et al. [2003]. At lower altitudes those HALOE differences are negative for the 40 and 50 zones. That finding is opposite to what Siskind et al. [2003] predicted, possibly because of the varying effects of the wave activity associated with the wintertime stratospheric warming events that they did not represent well in their model. Although the amplitude of the AO is larger in the upper mesosphere at 60 latitude for the SH versus the NH, the combination of the annual-mean and the AO terms still give summertime T(p) values that are colder in the NH. Such hemispheric differences imply that one ought to find more frequent occurrences of PMCs in the NH, as confirmed from separate analyses of the HALOE measurements at high latitudes in the work of Hervig and Siskind [2005] and Wrotny and Russell [2006] QBO and Subbiennial Terms [18] The seasonal residuals were Fourier-analyzed for QBO and/or other interannual (IA) terms, primarily in order to remove remaining structure in the time series before attempting to resolve the solar cycle and trend terms. In a 14-year data set one can expect to find 6 or 8 complete, QBO and subbiennial cycles, respectively. An 853-day QBO-like term emerged at many latitudes and pressure altitudes. When the probability of its presence was greater than 80%, it was included in the final MLR model. Initially, regression models with a QBO-wind proxy term were tried for low levels of the stratosphere, but that term did not fit as well even when allowing for its varying phase with latitude. [19] Table 8 shows the amplitudes (0.2 to 1.8 K) of the 853-day QBO terms at each level and latitude. Amplitudes exceed 1 K at tropical latitudes of the upper mesosphere and at middle latitudes of the mesosphere of both hemispheres (i.e., 40 N 60 N and 40 S 50 S). Of equal importance are the vertical variations of the relative phases, which are shown in Figure 7 from the diagnosed terms at 40 latitude of each hemisphere. Note that the negative phase is given in Table 4. Amplitude of Semiannual Cycle a a Amplitudes are given in K. 6of13

7 Figure 5. As in Figure 4 but for the amplitude of the semiannual oscillation (SAO) term. Contour interval is 1 K. order to provide for continuity with altitude at 40 N in the upper mesosphere. There is an offset of about days for the cycles at 40 N versus 40 S, perhaps an indication of an asymmetry for the latitudinal extent of the QBO forcing in the two hemispheres. Nonetheless, both cycles exhibit a slow advance in their phase as they proceed toward lower altitudes. This coherent character for the phase of the QBO term for T(p) is in reasonable accord with the rate of descent for the alternating mean QBO easterlies and westerlies of the middle atmosphere, and it is a useful check on the quality of the separate MLR determinations of this cycle with latitude and pressure altitude from the HALOE data set. [20] Shepherd et al. [2004] found a QBO signature in the upper mesosphere from 45 S to 65 N from their satellite experiment WINDII on UARS. Periods for their diagnosed cycles are in the range of days. The corresponding signals from HALOE for the upper mesosphere are strongest in the tropics and at latitude; amplitudes are generally small or not resolvable in the subtropics. Crooks and Gray [2005] and Pascoe et al. [2005] report on the interactions between the QBO and the solar cycle (and other decadal-scale forcings) based on their analyses of the ERA-40 data set, which extends into the lower mesosphere. Thus it is clear that there is interannual structure in a time series of T(p) and that one must account for it when trying to resolve other long-period terms. [21] A significant subbiennial term with a period of about 640 days is also present in the HALOE results at many latitudes and altitudes. The amplitudes (0.2 to 1.7 K) of those terms are given in Table 9 for the range of latitudes and pressure altitudes. Largest amplitudes are found in the tropical upper mesosphere and at middle to high latitudes of the middle mesosphere, although this IA term is significant at many other locations, too. A subbiennial term can arise owing to the nonlinear interaction between the annual and the QBO cycles [e.g., Dunkerton, 2001]. However, qualitative checks of the maximum amplitudes of the various terms from the HALOE MLR analyses indicate a better correspondence between the SAO and the QBO. Such interactions have been reported from studies with both data and models [e.g., Garcia and Sassi, 1999; Shepherd et al., 2005]. They find that the SAO/QBO interactions are more pronounced just after equinox and in alternating years. However, the HALOE data set does not provide for a frequent sampling of the SAO that is required to resolve such subtle interactions with the QBO. Further observational studies of the source of these subbiennial terms must be conducted with satellite data sets having more frequent sampling over the near-global domain of the mesosphere Solar Cycle or SC-like Term [22] The MLR model in Figure 1 shows the results of the reanalysis of the extended time series for 30 N and 0.02 hpa. The model includes a significant QBO-like term, plus a prescribed, periodic 4015-day or 11-year SC term. A linear trend term also emerged and is included; it has a rate of cooling of 1.7 K/decade and a 99% probability of being present (see section 3.4, too). [23] Table 10 displays the amplitude of the significant SC-like terms from the reanalyses. Note that these amplitudes are equivalent to one-half the solar max minus solar min values reported by most analysts and modelers. SC-like terms are not reported for a HALOE time series, when their probability of occurrence or confidence interval is less than 75%. That is why no corresponding contour plot Table 5. Day of Year for the Maximum of the First Semiannual Cycle of13

8 Figure 6. Contour plot of the annual-mean, zonal-average temperature distribution from the MLR model. Contour interval is 5 K. is provided for the amplitudes of these terms, as one might wish for purposes of comparisons with results from numerical models. The largest SC-like temperature responses are found at middle latitudes of the upper mesosphere. Where significant, the amplitudes in the middle mesosphere are about half as strong. [24] Table 11 contains the phase of the maximum T(p) of the SC-like terms, as measured in years past 1 January Because the approach for the analyses of the SC term herein was merely to find the best fit for a term of 11-year period, it was expected that there would not be an exact match to the time of the rather broad maximum from the traditional solar flux proxies. That is why the present results for the SC-like term are considered somewhat exploratory, rather than strictly definitive. Still, its phases are almost always within ±2 years of January Exceptions occur in the upper mesosphere at 60 S and in the lower mesosphere and upper stratosphere at 60 N. Those anomalies may be due to the high latitudes not being sampled as well, such that the rather large amplitudes of its seasonal cycles have biases that impact the diagnosed SC term. A somewhat out-of-phase relationship at high latitudes may also be an indication of a dynamically induced, decadal-scale term in the T(p) time series, perhaps related indirectly to the solar cycle [e.g., Hampson et al., 2006]. [25] In order to illustrate the direct SC-like variations of T(p) with latitude and pressure altitude, average SC responses were generated as follows. First, the amplitudes of the SC-like terms in Table 10 were adjusted for the fact that the fitted SC-like terms were not exactly in-phase (coinciding with January 1991). Those adjustments were made by simply multiplying the amplitude by the factor, cos [2pp/11], where the phase p (in years) was taken from Table 11 and divided by the presumed 11-year SC period. The adjusted amplitudes were averaged within the latitude ranges of S, 20 S 20 N, and N at each pressure level, with only those terms having phases in Table 11 within ±2 years of January 1991 being retained. The adjusted amplitudes of the terms that meet that phase criterion were then multiplied by 2 to give an estimate of the observed max minus min values for comparison with the responses of the direct SC forcings that have been published by others from analyses of their data sets and/or from their model studies. Those average middle- and low-latitude profiles are shown in Figure 8. Their max minus min values are between K near the stratopause, K in the lower mesosphere, and then increasing to K in the upper mesosphere. The estimated, direct SC response for the low-latitude zone is about half that at the middle latitudes throughout the middle and upper mesosphere. It is also important to remember that the average profiles for each of the latitude zones are likely upper limits. That caveat is particularly true at levels of the middle mesosphere at the low latitudes and at the middle latitudes of the NH, where no significant SC-like term was resolved in some instances from the HALOE time series (see Table 10). [26] The HALOE adjusted, zonal-mean SC max minus min differences of 2.0 to 3.0 K for the upper mesosphere at 40 N 50 N are in good agreement with the combined, summer plus winter, results from the ground-based, Rayleigh lidar measurements at 44 N [Keckhut et al., Mail Stop 401B, 2005, Figure 3]. The qualitative HALOE results of Figure 8 also agree reasonably with the findings from the modeling studies of Garcia et al. [1984], Huang and Table 6. Annual Average Temperature Distribution From HALOE of13

9 Table 7. Annual-Mean Southern Hemisphere Minus Northern Hemisphere Temperature Difference by Latitude Zone a P, hpa a Temperatures are given in K. Brasseur [1993], and McCormack and Hood [1996], among others. However, the T(p) responses from the models vary more uniformly with latitude. The larger SC-like amplitudes at middle latitudes of the upper mesosphere from HALOE may be an indication of dynamical responses to the effects of breaking waves whose focus may vary in latitude with the solar cycle [Kodera and Kuroda, 2002]. [27] Model studies indicate a significant, secondary maximum for the SC response near the tropical stratopause. The model max minus min results have upper limits that vary from 2.2 K [Garcia et al., 1984; McCormack and Hood, 1996] to 1.4 K [Huang and Brasseur, 1993] and to 1.1 K [Matthes et al., 2004]. The upper limit from the HALOE reanalyses at the stratopause for 20 Sto20 N is in the range of 0.7 to 1.0 K or at the low end of the model results, although the individual, phase-adjusted HALOE values at the equator reach 1.4 K at 1.5 hpa and 1.8 K at 1.0 hpa. The somewhat weaker and more localized-in-latitude, SC-like response from HALOE versus the model values near the tropical stratopause may be an indication of interfering influences of wave activity associated with the QBO cycle Figure 7. Vertical variation of the relative phase (in days) for the quasi-biennial oscillation (QBO-like; 853-day) terms at 40 S and 40 N latitude. [e.g., Salby and Callaghan, 2006]. An SC/QBO interaction has been included in several recent model studies [e.g., Matthes et al., 2004]. [28] The HALOE values near the stratopause at low latitudes are somewhat smaller and more localized in latitude than those reported from the NCEP reanalyses, too [Hood, 2004]. The HALOE results agree better with those from the ERA-40 data set [Crooks and Gray, 2005] and with the SC analyses from the SSU satellite radiances when those latter results are scaled to the max-minus-min solar flux units [Scaife et al., 2000]. These published NCEP/ ERA-40/SSU results are based on data sets that extend from 1979 to either 1997 or 2001 and are not strictly representative of the period of HALOE. To first order though, such a mismatch in the respective time spans of the Table 8. Amplitude of QBO-Like Term a a Amplitudes are given in K. QBO, quasi-biennial oscillation (853-day). 9of13

10 Table 9. Amplitude of Subbiennial Term a a Amplitudes are given in K. Subbiennial is 640 days. data sets should not be a problem for a truly repeating SC term, unless there are other underlying, long-period and/or trend terms that were changing but were not accounted for in their analyses Linear Trend Term [29] Table 12 contains the diagnosed temperature trends and their probabilities of being present from the MLR analyses. There are significant cooling trends for the HALOE time series data at a number of latitudes and pressure levels. Those effects are largest and most clearly resolved for middle latitudes of the middle to upper mesosphere, although they are somewhat larger than predicted (see below). In order to obtain trend terms for more of the latitudes and pressure levels of Table 12, the lower limit for their probability values was reduced to 60%. Even so, many of the terms in Table 12 have a probability that exceeds 90%. Because the HALOE sampling was marginal for the large seasonal amplitudes of 50 and 60 latitude, the diagnosed trends for those higher latitudes are necessarily less certain; they have not been included in Table 12. [30] Figure 9 is an assembly of the overall results from Table 12. The averages of the trends are shown for the two middle latitude ranges of S and of N, and they agree well with each other. The trends for the low latitudes have also been averaged and are shown by the solid curve of Figure 9. They vary from 0.5 K/decade from the stratopause to the middle mesosphere, increasing slowly to about 1.0 K/decade in the upper mesosphere. It is the low-latitude result that may be the most representative of the radiative cooling effects due to the steady increases of CO 2 in the atmosphere. That range of values from HALOE agrees well with the trends of 0.6 K/decade at the stratopause and of 0.8 K/decade in the lower mesosphere that were obtained for the simulated responses of temperature versus pressure owing to the observed increases in CO 2 from 1955 to 1995 (from Figure 2 of Akmaev and Fomichev [2000]). The larger HALOE trends of the middle to upper mesosphere at middle latitudes agree reasonably well with those diagnosed from long series of ground-based lidar measurements at 44 N [see Keckhut, 2001, and references therein], especially when one considers that the lidar results are in terms of temperature changes at constant altitudes that Table 10. Amplitude of SC-Like Term a a Amplitudes are given in K. SC, solar cycle. 10 of 13

11 Table 11. Time of Maximum Past 1 January 1991 for SC Term a a Time is given in years. would also be affected by the contraction of the deep mesospheric layer due to a radiative cooling. The apparently larger trends at middle versus low latitudes may be because of added effects in the mesosphere of long-term changes in the planetary and gravity wave activity [Gruzdev and Brasseur, 2005]. [31] Table 12 and Figure 9 also indicate that the cooling trend is increasing from about 0.5 to 1.0 K/decade from 1 to 2 hpa, most likely due to associated effects of trends in upper stratospheric ozone during this 14-year period. Shine et al. [2003] review the results of several model studies of the effects of increasing greenhouse gases for the temperature trends of the mesosphere and stratosphere. All the models indicate a cooling trend that attains a maximum rate between 1 to 3 hpa and of nearly the same magnitude as indicated from the present HALOE analyses. However, the temperatures at 3 hpa are affected slightly by their tie-in at 4 to 5 hpa in the HALOE T(p) algorithm to the temperature fields from the operational NOAA/CPC analyses that were supplied to the UARS Project. Remsberg and Deaver [2005, Figure 4] noted an effect in the HALOE T(p) data set at 5 hpa, presumably due to a change in the NOAA operational analysis procedures that was implemented in May They showed an apparent discontinuity at 5 hpa in 2001; the HALOE T(p) results may also be affected slightly at 3 hpa, but should be free of that bias at 2 hpa. That is why the long-term results for the 3-hPa level are not shown here. Therefore, from the HALOE data set it is difficult to know whether the atmospheric cooling trends become smaller from 2 or 3 hpa to 5 hpa, as predicted from the models. 4. Summary Findings [32] A reanalysis was conducted of time series of zonal averages of the temperature versus pressure profile data (or T(p)) provided by the 14+ years of HALOE measurements from the UARS satellite. The findings from the reanalyses are now more definitive because of a proper accounting for the effects of autoregression for the adjacent points of the time series and because of the addition of several more years of data. One can generate monthly or seasonal climatologies of T(p) for the middle-atmosphere levels from 2 hpa to hpa and for the period on the basis of the seasonal and annual-mean terms of Tables 2 6 herein; the effects of the interannual and solar cycle variations are already removed for those tables. In addition, the amplitudes, phases, and periods of the primary QBO-like (853-day) and subbiennial (640-day) terms are also considered definitive (where those terms emerged). Their amplitudes are of the order of 0.5 to 1.5 K, and their phases vary coherently with latitude and pressure altitude. It is believed that this is the first time that these interannual terms have been obtained from a single satellite data set covering such a large region of the mesosphere and the uppermost stratosphere and for a time span of more than a decade. Figure 8. Average profiles of the adjusted, max minus min differences of the T(p) response of the 11-year solar cycle (or SC-like) term of the MLR models for three separate latitude zones. 11 of 13