1. Coupling Between the Lower Atmosphere and Thermosphere as Revealed in GOCE and Swarm Accelerometer Measurements Jeffrey M. Forbes, Xiaoli Zhang and Jesse Zhang Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO 80309, Eelco Doornbos Delft University of Technology, Delft, The Netherlands Sean Bruinsma Centre National d’Etudes Spatiales (CNES), Toulouse, France Brief review of wave coupling between the lower and upper atmosphere Deriving tides from quasi-Sun-synchronous satellite measurements GOCE, CHAMP, GRACE, Swarm and solar tides GOCE and the lunar tide 1 Conclusions

2. Wave Coupling The primary mechanism through which energy and momentum are transferred from the lower atmosphere to the upper atmosphere and ionosphere is through the generation and propagation of waves. 2

3. Atmospheric Tides Nomenclature 3 Solar tides are atmospheric oscillations that are periodic in time and longitude: diurnal, (n = 1), semidiurnal (n = 2), etc. tides s = zonal wavenumber λ = longitude implying zonal phase speeds DE3 -- “Diurnal Eastward-propagating tide with with zonal wavenumber 3” (s = -3) SW2 – “Semidiurnal Westward-propagating tide with zonal wavenumber 2” (s = +2) Nomenclature, e.g.,

4. Land-Sea Differences Modulate Diurnal cycle of Latent heating The longitude variation of land vs. ocean near the equator modulates the latent heating that is released in deep convective clouds. Land-sea modulation of the diurnal cycle gives rise to a spectrum of solar thermal tides with periods of 24 hours, 12 hours, 8 hours, etc. The predominant longitudinal Fourier component of land-sea difference in the tropics is m = 4 cos4λ cos(2Ωt + 2λ) (SW2) X = cos(2Ωt + 6λ) + cos(2Ωt - 2λ) = SW6 + SE2 cos4λ cos(Ωt + λ) (DW1) X = cos(Ωt + 5λ) + cos(Ωt - 3λ) = DW5 + DE3 “sum and difference waves” 4 westward  2π/24h

5. Additional waves are generated by interactions with other land-sea difference zonal wavenumbers DW5 is dissipated before it reaches the ionosphere-thermosphere (IT), but DE3, SE2 and SW6 are observed there. This talk will mainly concentrate on DE3 and SE2. CHAMP, GRACE, GOCE, Swarm are all either Sun-synchronous or quasi-Sun- synchronous Tides Observed from Sun-Synchronous Orbit - 1 Converting from UT to local time, (s-n) = 4 for DW5, DE3, SW6, SE2 in general, (s-n) = ±m From Sun-synchronous orbit (t LT = constant), a tide with frequency n day -1, and zonal wavenumber s generated by wave-m topography appears as a wave-m longitude variation. 5

6. “Snapshots” of sums and differences of ascending (A) and descending (D) orbital data, ~12h apart, can be used to separate diurnal and semidiurnal tides, (A-D)/2, (A+D)/2. However, ambiguity remains as to the mixture of waves, since more than one wave can give rise to the same longitudinal wave structure. In this case other constraints can sometimes be applied to narrow the choices. wave-4 probably implies dominance of DE3 wave-4 probably implies dominance of SE2 GRACE 10d-means, wave-1 removed, September, 2006 (A-D)/2  all diurnal, terdiurnal (odd- frequency) waves (A+D)/2  all stationary planetary, semidiurnal, (even-frequency) waves Tides Observed from Sun-Synchronous Orbit - 2 This is the situation for GOCE, which is in a dawn/dusk orbit 6

7. Separating Into Symmetric and Antisymmetric Parts can be Useful for Wave Interpretation (A-D)/2(A+D)/2 Symmetric Antisymmetric DE3-like SW6-like SE2-like 7

8. (A-D)/2, June 2010, 10-day means, co-planar event Wave-1 Prominent at “Low Altitudes” During 2010 GOCE ~270 km Dominance of wave-1 unexpected Due to displaced geomagnetic & geographic coordinates? DE3 suppressed at these altitudes CHAMP ~320 km DE3 SE2 GSWM model 8

9. The Thermosphere Tidal Spectrum Evolves with Height The diurnal tidal spectrum evolves with height, the larger- scale waves penetrating to 400 km, while the shorter-scale waves are absorbed at intervening altitudes, giving up their energy and momentum to the mean atmosphere. There are also nonlinear interactions between the different wave components that give rise to secondary waves. Interactions with the longitudinally-varying ionosphere also give rise to additional wave components. GOCE provides a key “middle thermosphere” perspective, between lower thermosphere measurements up to 110 km by TIMED, and upper thermosphere measurements by CHAMP, GRACE & Swarm. 9

10. GOCE Provides New Insights Into Vertical Evolution of the Tidal Spectrum November, Wave-1 Removed Inter-annual consistency with GOCE Similar longitude structures for (A+D)/2 Vertical evolution of longitude structures for (A-D)/2 10

11. Tides Observed from Precessing Orbits For satellites like TIMED, which samples 24 hours of local time in 60 days (assuming both ascending and descending node sampling), mean tides within 60-day moving windows can be performed. For CHAMP and Swarm A/B, the window is 130 days; Swarm C, 160 days From CHAMP and GRACE density measurements, exospheric temperatures can be derived using empirical models, and used to derive tides within 72-day windows containing 24-hour local time coverage. The signatures of land-sea differences are seen at 400-500 km levels! 11

12. By combining CHAMP & GRACE data when orbital planes are > 3 hours LT apart, diurnal variations in exosphere temperature have been obtained on a daily basis. Daily Diurnal Tides From GOCE, CHAMP, GRACE, Swarm The minimum 3-h LT separation between Swarm A/B and Swarm C is exceeded after 18 months. GRACE and GOCE could provide additional data points early in the Swarm mission Similar analyses can be performed on electric fields measured by Swarm 12

13. Thermosphere Response to Solar Rotation 13

14. Lunar Semidiurnal Tide from GOCE - 1 Study of the lunar semidiurnal tide is important for several reasons: Since the forcing is well-known, observations of the lunar tide can serve as a good test of the veracity of theoretical models of wave propagation, dissipation, wave- mean flow interactions, etc. It is now known that the lunar tide can be considerably amplified during sudden stratospheric warmings, and produce significant low-latitude ionospheric effects by driving electric fields through the dynamo mechanism – “ionospheric space weather” GOCE provides a “middle thermosphere” perspective on the lunar tide, in terms of both density and wind variations. The lunar tide produces significant density variations at orbital altitudes – “thermospheric space weather” – that remain un- modeled, and yet are to a significant degree predictable. Lunar Tide from CHAMP orbit has a period of 13.28 days 14

15. Results to the left obtained by binning longitude- averaged residuals from 15-day running mean into lunar time bins covering Nov 2009 – May 2012, and extracting the amplitude of the semidiurnal lunar tide (top); only low magnetic activity days included. These are vector-average tides. high-latitude extent not well-captured by models Lunar Semidiurnal Tide from GOCE - 2

16. GOCE for Studying Vertical Wave Coupling Waves propagating upward from the lower atmosphere undergo “differential dissipation” in the thermosphere, and thus their relative importance varies with height; other factors also affect the wave spectrum. At ~270 km, GOCE provides insight into vertical evolution of tidal spectrum from ~110 km (SABER) to ~400-500 km (CHAMP, GRACE, Swarm). High-precision density and wind measurements enable investigation of smaller- amplitude waves, such as lunar tides and gravity waves emanating from the polar regions and from the lower atmosphere. Densities + winds provide additional constraints on decomposition of tidal components. With 2 local time measurements, GOCE will be used with CHAMP, GRACE, and Swarm in terms of obtaining sufficient local time coverage to unambiguously identify tidal components. GOCE data are already challenging theory and models. 16