STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK REPORT ON WP2X00: TIDAL SIGNAL RECOVERY USING THE COMPREHENSIVE INVERSION (CI) RESULTS FROM CHAMP AND SWARM Nils Olsen, Terence J Sabaka, Lars Tøffner-Clausen

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Study Work Breakdown Structure

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Outline Extension of CI code to estimate M2 tidal field Non-gradient version: CM5 Including NS (alongtrack) and EW gradients Results obtained using CHAMP satellite data Published in Sabaka et al 2015 (CM5) Some experiments on spherical harmonic truncation level Results obtained from 18 months of Swarm satellite data Only field data (no gradient) Field and NS gradient data (”single satellite solution”) Field and EW gradient data Field and NS + EW gradient data

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Results obtained with CHAMP satellite data First successful determination of the spatial structure of the M2 tidal signal Tyler et al (2003) had filter CHAMP data on an orbit-by-orbit basis is order to be able to extract the M2 tidal signal No need for this processing step when using CI results have been published as CM5 (Sabaka et al 2015) M 2 tidal field is described by scalar magnetic potential which is expanded in spherical harmonics up to d/o 36, assuming a M2 period of hrs

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Spatial Power spectrum

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Maps of |Br| at 430 km altitude

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Maps of phase(Br) at 430 km altitude

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Experiments with Different SH Truncation Levels n = n = n =

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Extension of CI code Swarm data selection and data use Data selection 1 Hz data downsampled to 15 sec data |dDst/dt| < 3 nT/hr Kp ≤3 0 East-West/North-South (EW/NS) scalar sums/differences (s/d) for all local times and all latitudes EW/NS vector s/d for all local times and |QD lat| < 55° Scalar data nightside for all latitudes Vector data nightside for |QD lat| < 55° No observatory data

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Extension of CI code Model Parameterization (1) Degree/order (d/o) 90 static (core+crustal) field d/o 13 linear SV d/o 1 magnetospheric/induced fields in 1 hr bins "usual" CI ionospheric parameterization accounting for 3D induction via Q-matrices d/o 36 M 2 tidal field (period hrs)

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Extension of CI code Model Parameterization (2) (Nominal) core determined by all data except low-latitude dayside (Nominal) crust determined by all field data and all difference data except low-latitude dayside Ionosphere determined by all data Magnetosphere/induced determined by all data (Nominal) M 2 determined (mostly) by all difference data

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Extension of CI code Major differences from "old" CI model “Old” CI code: developed and tested during Swarm SCARF development phase Direct Huber weighting of s/d rather than formal covariance propagation from scalar or vector constituents Component-only s/d used (like SIFM+) rather than full covariant forms The addition of scalar/vector data to s/d data rather than only s/d data No vector data for |QD lat| > 55° rather than using vector at all latitudes (no toroidal field estimated yet) Day as well as night data for crust and M2 rather than nightside only M 2 determined mostly by gradient data Core field now varies linearly rather than quadratically

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Results obtained from 18 months of Swarm satellite data Four models have been derived: Only field data (no gradient) Field and NS gradient data (”single satellite solution”) Field and EW gradient data Field and NS + EW gradient data

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Spatial Power spectrum

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK M2 Tidal Field 18 months of Swarm data allows for an astonishing determination of the M 2 tidal signal, comparable to what has been obtained using 10 years of CHAMP data (at lower altitude) |B r | of M 2 tide Model prediction CM5 (CHAMP) CI (Swarm) Sabaka et al., GJI (2015)Sabaka et al., in preparation for GRL

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK |Br| at 430 km altitude

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Phase(Br) at 430 km altitude

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Comparison of M 2 Amplitudes and Phases B r at ground, from CHAMP (CM5, top) and Swarm (CI, bottom)

STSE Tides to Sense Earth, MTR 25 January 2016DTU, Lyngby/DK Conclusions New version of CI model derived, using only Swarm data and solving for core, crust, ionosphere, magnetosphere and M2 tidal field Major improvement compared to version 01 (determined in May 2015) M2 Tidal signal determination from 18 months of Swarm data is “almost as good as” what is possible from 10 years of CHAMP, thanks to the novel Swarm constellation gradient concept Gradient data is what is responsible for the resolving power of the oceanic M2 magnetic signal from Swarm data EW gradients are doing most of the resolving as compared to the NS gradients. There seems to be little degradation when NS gradients are not used