### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Methodology
- 4. Results and Discussion
- 5. Summary and Conclusions
- Acknowledgments
- References
- Supporting Information

[1] The characteristics of atmospheric tides in the upper troposphere and lower stratosphere region are investigated using radio occultation (RO) measurements performed by the Formosa Satellite Mission-3/Constellation Observing System for Meteorology, Ionosphere, and Climate (FORMOSAT-3/COSMIC) satellite constellation and compared to tides observed in short-term forecast model fields of European Centre for Medium-Range Weather Forecasts (ECMWF) and National Centers for Environmental Prediction (NCEP). Spectral analysis of 2 years of monthly data (2007 to 2008) yields the migrating diurnal tide to be the largest spectral component. This diurnal tide shows similar temporal, latitudinal, and altitudinal characteristics in all data sets equatorward of 50°. Beyond 50°, COSMIC local time sampling is insufficient within 1 month, which prevents space-time spectral analysis from isolating atmospheric waves. Diurnal tides of temperature are characterized by largest amplitudes in the tropics (0.8 K to 1.0 K at an altitude of 30 km). Amplitudes of diurnal tides analyzed in model data are more pronounced by ∼20%. An annual cycle of the amplitudes, characteristically linked to the movement of the intertropical convergence zone, is clearly revealed. Tropical diurnal phase features downward progression of waves fronts with a vertical wavelength of 20 km. Extratropical diurnal tides are most pronounced in the model data sets with amplitudes of up to 0.5 K at 30 km. In this analysis we also see the influence of high-altitude initialization of RO data by background information in using data processed by two different centers (University Corporation for Atmospheric Research (UCAR) and Wegener Center (WEGC)). UCAR data, initialized by a climatology without tidal information, exhibit no appreciable extratropical diurnal tides, while WEGC data, initialized by ECMWF forecasts, show more pronounced ones. Overall the results underpin the utility of the local-time resolving COSMIC RO constellation data for monitoring diurnal tide dynamics in the stratosphere. The agreement between observational and model data further confirms that the tidal dynamics is appropriately captured in the models, which is important for other (middle/upper) atmosphere models relying on ECMWF or NCEP dynamics.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Methodology
- 4. Results and Discussion
- 5. Summary and Conclusions
- Acknowledgments
- References
- Supporting Information

[2] In April 2006 the satellite constellation FORMOSAT-3/COSMIC (Formosa Satellite Mission-3/Constellation Observing System for Meteorology, Ionosphere, and Climate) [*Anthes et al.*, 2008], COSMIC hereafter, was launched into orbit. The constellation consists of six platforms, which are evenly distributed in space (approximately 30° orbit plane separation). One single COSMIC satellite is able to perform more than 10,000 Global Positioning System (GPS) radio occultation (RO) measurements per month. GPS RO measurements are known to be intrinsically calibrating and long-term stable [*Ho et al.*, 2009; *Steiner et al.*, 2009]. They feature best quality in the upper troposphere and lower stratosphere region (UTLS, ∼5 km to 35 km altitude) where they have a very high vertical resolution (∼0.5 km to ∼1.5 km) as well as high accuracy and precision (e.g., for temperature <1 K) [*Kursinski et al.*, 1997; *Steiner et al.*, 2001; *Hajj et al.*, 2002; *Schreiner et al.*, 2007; *Anthes et al.*, 2008].

[3] RO climatologies (e.g., monthly, seasonal, or annual) are obtained by “binning” and averaging over a large number of vertical profiles [*Foelsche et al.*, 2008]. The quality of a climatology depends on the quality of the measurement itself and of its retrieval [*Ho et al.*, 2009] as well as on the sampling characteristic of the satellite [*Pirscher et al.*, 2007a]. The satellite orbits, the number of measurements, and atmospheric variability determine the sampling error of a climatology. High atmospheric variability (e.g., at high latitudes during wintertime) demands a large number of measurements to minimize the sampling error, whereas low atmospheric variability (e.g., in the tropics) is captured by a smaller number of measurements. The satellite orbits of transmitters and receivers determine the global distribution of RO events and the local time when measurements are taken [*Pirscher et al.*, 2007a; *Foelsche et al.*, 2009a].

[4] Atmospheric tides are known to have strongest impact on the local-time component of the sampling error. The local-time component of the sampling error of a Sun-synchronous receiving satellite is constant with time if the diurnal tide is constant. A changing diurnal tide or a slowly drifting satellite yields a change in the local time component, in the sampling error, and consequently in the climatology itself. A constellation of satellites in orbits with high drifting rates can overcome this problem by actually sampling diurnal tides. The orbit design of the COSMIC constellation allows the determination and also monitoring of atmospheric tides on a monthly basis, equatorwards of 50°N/S.

[5] Atmospheric tides are global-scale waves, which can be classified into thermal and gravitational tides [*Chapman and Lindzen*, 1970]. Absorption of solar radiation by tropospheric water vapor and stratospheric ozone as well as tropospheric latent heat release yield migrating thermal tides [*Hagan*, 1996; *Hagan and Forbes*, 2002, 2003]. These tides move westward with the apparent motion of the Sun. Zonal wave numbers *k* of migrating tides, where positive wave numbers correspond to westward motion, therefore equal their frequencies, *n*, in cycles per day (e.g., migrating tides DW1 and SW2, where DW1 is the westward propagating diurnal tide with *k* = 1 and *n* = 1 cycle per day, and SW2 is the westward propagating semi-diurnal tide with *k* = 2 and *n* = 2 cycles per day).

[6] Any longitudinal variation in the absorbing medium such as large-scale regional cloudiness, diurnally varying latent heat release (convective heating), including variations in the Earth's surface (land-sea contrast and topography) give rise to additional non-migrating tidal components (*k* ≠ *n*, e.g., eastward propagating diurnal tides, DE) [e.g., *Tsuda and Kato*, 1989; *Lieberman*, 1991; *Williams and Avery*, 1996].

[7] The most prominent atmospheric tidal mode is the Sun-synchronous migrating diurnal tide, which has an amplitude of ∼1 K at 30 km at tropical latitudes [*Alexander and Tsuda*, 2008; *Zeng et al.*, 2008]. Amplitudes of other components are significantly smaller in the UTLS region, which limits the observation, especially of non-migrating tides. In the mesosphere and lower thermosphere (MLT), however, tidal amplitudes are larger. At 115 km, for example, the amplitude of the migrating diurnal tide is larger than 20 K, the amplitude of the migrating semi-diurnal tide amounts to ∼16 K, and the amplitude of the eastward propagating diurnal wave with wave number 3 (DE3) is ∼8 K [*Zhang et al.*, 2006].

[8] We investigate the diurnal tide of temperature in the UTLS region using RO data of the COSMIC satellite constellation. Our main focus lies on the analysis of the migrating diurnal tides at low- and mid-latitudes.

[9] Studies on diurnal tides within the UTLS region have been performed by, e.g., *Tsuda et al.* [1997], *Seidel et al.* [2005], *Alexander and Tsuda* [2008], and *Huang et al.* [2009] using radiosonde data and by, e.g., *Revathy et al.* [2001] and *Riggin et al.* [2002] using radar data. These ground-based data contain global and local signatures of atmospheric tides and it is not possible to separate migrating from non-migrating diurnal tides. *Zeng et al.* [2008] used CHAMP (CHAllenging Minisatellite Payload) RO measurements to detect migrating diurnal tides within the tropics. The single satellite RO mission CHAMP yields the longest available RO data set with data available from 2001 to 2008. The design of the CHAMP orbit leads to a local-time drift of three hours within one month. Consequently it is not possible to observe diurnal tides within one month or one season. For that reason it is necessary to synthetically merge data from a number of years. With this study we advance the work of *Zeng et al.* [2008] by investigating the comprehensive COSMIC RO data and applying the same method to isolate atmospheric tides (space-time spectral analysis). The main advantages of the COSMIC data set are the large number of measurements performed by six evenly distributed satellites and the resulting high local-time resolution of diurnal tide analyses, which is possible on a continuous monthly scale.

[10] To provide valuable context, comparisons are drawn to migrating diurnal tides analyzed in ECMWF (European Centre for Medium Range Weather Forecasts) and NCEP (National Centers for Environmental Prediction) data. In an early study, *Hsu and Hoskins* [1989] have shown that ECMWF analyses depict diurnal and semi-diurnal tides below 50 hPa. Since RO data are operationally assimilated at ECMWF and NCEP, we investigate short-term forecasts (24 h to 45 h forecasts) to look for diurnal tides rather than analyses, which avoids direct inter-dependencies and investigates the models' dynamics.

[11] Section 2 gives a description of the COSMIC RO data set and of the ECMWF and NCEP forecast data. A brief introduction in space-time spectral analysis, used to extract the tidal modes, and an error analysis are given in section 3. Results are presented in section 4 and section 5 closes with a summary and conclusions.

### 3. Methodology

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Methodology
- 4. Results and Discussion
- 5. Summary and Conclusions
- Acknowledgments
- References
- Supporting Information

[26] Information on global atmospheric waves is present in RO data. The spatial and temporal scales of the waves as well as characteristics of the data set determine the method used to extract the waves. This section describes the methodology used to obtain information on atmospheric diurnal tides using COSMIC RO and model data.

[27] Diurnal tides are investigated in different latitudinal regions, where the mean atmospheric profile of each region has to represent typical atmospheric characteristics and the variation of corresponding single measurements must not be too large. Therefore, the optimal extent of the regions to detect diurnal tides is a tradeoff between a sufficiently large number of RO profiles and small atmospheric variability. We found both, a sufficient number of measurements and reasonably similar atmospheric characteristics, in selecting 5° zonal bands. These bands range from 90°S to 90°N resulting in 36 zonal bands. At low- and mid-latitudes the number of profiles available within one band varies between 1000 and 2500; at high latitudes, the number of profiles is significantly less.

[28] Monthly averaged local-time variations of dry temperature (“diurnal temperature variations”) enable a first view of diurnal tides [*Pirscher et al.*, 2009]. First of all, in data preparation for this purpose, any RO event is allocated to the appropriate 5° zonal bin. To remove synoptic atmospheric variability, the daily-mean 5° zonal mean ECMWF forecast profile is subtracted from each single COSMIC profile. Finally, diurnal temperature variations are calculated by averaging over all profiles belonging to the same local-time bin (we chose eight local-time bins with three hours width) and subtracting the mean profile of all local-time bins. This approach does not contain any confining assumption but it strongly depends on the number of profiles and atmospheric variability. Furthermore, it does not split particular modes of total oscillation but represents the superposition of all waves.

[29] Figure 2 shows diurnal temperature variations of WEGC COSMIC and ECMWF data. Northern hemispheric winter is accompanied by strong atmospheric variability. An unequally distributed number of profiles for each local-time bin (Figure 2, left; see also Figure 1f) results in inhomogeneous diurnal temperature variations. Otherwise, a regular number of measurements and comparably low variability unveil patterns, which are similar to diurnal tides determined with a more sophisticated method.

[30] We use space-time spectral analysis [*Hayashi*, 1971] to decompose atmospheric tides into zonal wave number and direction (space) and period (time). The space dimension of the data set covers zonal bands with 5° width and is analyzed with respect to wave numbers *k*. We use 64 grid points in longitude (spatial resolution: 5.625°) for the RO data sets and 32 grid points for the model data sets (spatial resolution: 11.25°). Time is gridded in 64 points in the RO data sets (UTC resolution: 0.375 h) and 8 points (only 8 time layers available, UTC resolution: 3 h) in the model data sets. To sum up, the RO data set *X*_{ϕ}(*λ*, *t*), with geographical latitude ϕ, longitude *λ*, and time *t*, is gridded into 64 × 64 points and the forecast model data are gridded into 32 × 8 points. Sensitivity tests with different resolutions showed that the results of space-time spectral analysis are stable with these resolutions, i.e., changes of grid density have little effect (±0.05 K) on the analysis results.

[31] Space-time spectral analysis is applied separately for each month, each zonal latitude band, and each height level. Again, the daily mean ECMWF forecast profile is subtracted from each single COSMIC profile. The mean longitude-UT field is calculated by averaging over all profiles, which are available in each grid cell. Grid cells, which do not contain any data, are filled applying bilinear interpolation from neighborhood cells. Mean longitude-UT fields of ECMWF and NCEP are calculated in the same way.

[32] The space dimension is analyzed with Fourier analysis for each single time step *t*, yielding Fourier coefficients *C*_{t}(*k*) and *S*_{t}(*k*), which correspond to the data series *x*_{t}(*λ*). Examination of temporal variations of one wave number (*k* fixed) enables us to find temporal periodic behavior. Fourier analyses of the time series *C*_{k}(*t*) and *S*_{k}(*t*) yield the Fourier coefficients *A*_{k}(*ω*) and *B*_{k}(*ω*) and *a*_{k}(*ω*) and *b*_{k}(*ω*), respectively.

[33] After the computation of temporal variations of all wave numbers, the Fourier coefficients of *C*(*k*, *t*) are represented by the matrices *A*(*k*, *ω*) and *B*(*k*, *ω*), combined in the complex quantity *F*_{c}; the Fourier coefficients of *S*(*k*, *t*) are represented by the matrices *a*(*k*, *ω*) and *b*(*k*, *ω*), combined in the complex quantity *F*_{s}.

[34] The power spectra *P*_{ω}(*C*) = and *P*_{ω}(*S*) = denotes the complex conjugate), and the quadrature spectrum (imaginary part of the cross spectrum) *Q* = Im() enable the calculation of the power spectra of the separated waves:

*P*_{+ω} is the power spectrum for westward traveling waves and *P*_{−ω} for eastward traveling ones. The corresponding waves' phase is calculated from

where phase denotes local-time of maximum temperature, (i.e., phase of wave crests).

[35] The RO data set is decomposed into 32 wave numbers and 32 frequencies and the ECMWF and NCEP model data are decomposed into 16 wave numbers and 4 frequencies (recall that corresponding longitude-UT resolutions were 64 × 64 and 32 × 8 for the RO and the model data sets, respectively). Waves with wave number *k* = +1 and period *T* = 24 h (frequency *n* = 1 cycle d^{−1}) travel westward and are called migrating diurnal tides, DW1. The SW2 wave is equal to the migrating semi-diurnal tide, wave number *k* = +2 traveling westward with the period *T* = 12 h (frequency *n* = 2 cycles d^{−1}).

[36] A Hovmöller diagram shown in Figure 3a, presents the temperature anomaly of COSMIC data in January 2008 at an altitude of 30 km between the equator and 5°N. This 64 × 64 longitude-UT field is decomposed with spectral analysis. The dashed line corresponds to midnight local-time. It is obvious that the positive temperature anomalies lie close to the dashed line. This corresponds to the tide DW1 with temperature maximum close to midnight. Confirmation is obtained by calculating the spectrum (Figure 3b). The wave with *k* = 1 and *T* = 24 h, DW1, exhibits the maximum spectral amplitude, all other components show negligible contribution. Figures 3c and 3d depict the diurnal tides (*T* = 24 h) in terms of altitude and latitude dependence, respectively. In Figure 3c, the height cross-section near the equator shows that the spectral amplitude of DW1 increases with height and all other components yield a negligible spectral amplitude at all height levels. Figure 3d shows that beyond 50°N, spectral amplitude is large for all wave numbers −8 ≤ *k* ≤ 8. This only means, however, that atmospheric waves cannot be isolated because the spectral analysis fails.

[37] This indicates that high atmospheric variability during wintertime and the comparatively low number of measurements at high latitudes yield significant aliasing errors.

[38] To estimate the errors associated with COSMIC sampling, we extract profiles from ECMWF forecast fields, which are co-located to times and locations of COSMIC events. These profiles are used to estimated atmospheric tides using ECMWF data from a non-optimally sampled field. The sampling error of our atmospheric tides is estimated from the spectral components of the difference field, the co-located longitude-UT ECMWF field minus the full longitude-UT ECMWF field.

[39] Figure 4 depicts the spectral amplitude of the sampling error with *T* = 24 h as a function of wave number and latitude (Figure 4, left) and spectral amplitude of the sampling error with *k* = 1 and *T* = 24 h as a function of latitude and height (Figure 4, right) for January 2008. We find strongest spectral amplitudes of the sampling error in regions with high atmospheric variability (in winter polewards of 50° latitude). Non-negligible sampling errors occur also at mid and high latitudes below approximately 13 km. Spectral phase (not shown) does not show any regular pattern.

[40] Because of these findings we focus our analysis of diurnal and semi-diurnal tides equatorwards of 50°, where the sampling error generally remains smaller than 0.2 K.

[41] The systematic retrieval error of radio occultation measurements does not yield any error in spectral amplitudes and phases because it is eliminated when performing spectral analysis. However, the systematic difference originating from different retrieval algorithms is quantified comparing two COSMIC data sets from such different retrievals (CDAAC and WEGC).

### 5. Summary and Conclusions

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Methodology
- 4. Results and Discussion
- 5. Summary and Conclusions
- Acknowledgments
- References
- Supporting Information

[60] Radio occultation (RO) measurements from the six FORMOSAT-3/COSMIC satellites are of particular utility for observing and monitoring diurnal tides of temperature in the upper troposphere and lower stratosphere (UTLS). The orbit design of the satellite constellation allows the determination of diurnal tides on a monthly basis equatorwards of ∼50° latitude. Beyond 50° latitude, atmospheric variability in the winter hemisphere is too strong and COSMIC sampling too sparse to adequately resolve the tides. Within 50°S and 50°N the error associated with COSMIC sampling was estimated to be less than 0.2 K nearly everywhere.

[61] We performed space-time spectral analysis [*Hayashi*, 1971] to isolate atmospheric tides in COSMIC data (from January 2007 to December 2008) and draw comparisons to diurnal tides analyzed in ECMWF (European Centre for Medium-Range Weather Forecasts) and NCEP (National Centers for Environmental Prediction) short-term forecast fields (24 h to 45 h forecasts with a temporal resolution of 3 h). Differences in RO retrieval algorithms, which have an impact on diurnal tides, were investigated comparing two sets of COSMIC RO data: a data set retrieved by the Wegener Center (WEGC) and another one retrieved by the COSMIC Data Analysis and Archive Center (CDAAC) of the University Corporation for Atmospheric Research (UCAR). Spectral analysis yields the migrating diurnal tide (DW1) to be the most pronounced spectral component in all data sets. The difference between WEGC COSMIC and CDAAC COSMIC increases with height. At 30 km it reaches values of 0.2 K to 0.3 K.

[62] Typical features of diurnal tides are found in all four data sets and they are consistent with the theory of diurnal tides [*Chapman and Lindzen*, 1970]. On the one hand, this agreement confirms the utility of COSMIC RO data for monitoring diurnal tide dynamics, on the other hand it confirms that tidal dynamics is appropriately captured in the models, which is important for other (middle/upper) atmosphere models relying on ECMWF or NCEP dynamics.

[63] Best agreement is found at low latitudes. The ECMWF and NCEP model data show a more homogeneous diurnal tide at all latitudes than COSMIC observational data.

[64] Spectral amplitudes are largest at high altitudes since tidal amplitudes generally increase with altitude. At an altitude of 30 km, typical amplitudes of migrating diurnal tides at tropical latitudes amount to 0.8 K to 1.0 K but occasionally they can also become up to 1.5 K (in ECMWF data only).

[65] During solstice months tropical diurnal tides are characterized by a latitudinal shift with height. Below 27 km, maximum diurnal amplitudes follow the inter-tropical convergence zone (summer hemisphere); above that altitude maximum amplitudes shift to the other (winter) hemisphere. During equinox months, amplitudes are symmetric with respect to the equator. Focusing on a single confined low latitude band and on a constant altitude level, this latitudinal shift appears as an annual cycle of maximum amplitude. Below 27 km this cycle follows the annual cycle of the inter-tropical convergence zone, which is more pronounced in the Northern Hemisphere than in the Southern Hemisphere, above 27 km it is opposed to that.

[66] The phase at low latitudes shows the typical feature of downward progression of wave fronts, which corresponds to upward propagation of wave energy. The vertical wavelength seen in observational and model data sets amounts to ∼20 km.

[67] Extra-tropical diurnal tides are most pronounced in the model data sets with amplitudes up to 0.5 K at 30 km. At mid-latitudes, the RO data sets reflect the influence of retrieval differences on diurnal tides: CDAAC COSMIC data (high-altitude initialized with a climatology, which does not contain tidal information) do not show noticeable amplitudes of diurnal tide, while WEGC COSMIC data show a tide similar to that detected in the ECMWF data (initialized with ECMWF forecasts). Assuming that ECMWF overestimates the amplitude, we conclude that the actual amplitude of the extra-tropical diurnal tide lies between both observational data sets.

[68] Semi-diurnal tides become more apparent in the ECMWF data set than in the WEGC COSMIC data set, which is likely due to larger amplitudes in the model data set in general, and under-sampling problems in the observational data.

[69] The COSMIC satellite constellation is expected to deliver GPS RO measurements until 2012 and monitoring of diurnal tides utilizing COSMIC RO data can be extended until then (a follow-up multi-satellite mission is currently in planning stage). Inter-annual variations of diurnal tides, dependence on QBO (Quasi-Biennial Oscillation) or other atmospheric waves can be investigated in detail. The present study underpinned the utility of the data for such monitoring of diurnal-tide dynamics.