Geomagnetic Field Modeling Lessons learned from Ørsted and CHAMP and prospects for Swarm

Geomagnetic Field Modeling Lessons learned from Ørsted and CHAMP and prospects for Swarm Nils Olsen RAS Discussion Meeting on Swarm October 9 th 2009 Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 1 / 43

Outline of Talk 1 Exploring Earth s Magnetic Field from Space 2 Previous Missions: POGO and Magsat 3 Present Missions: Ørsted, CHAMP and SAC-C 4 Near Future: Swarm 5 Recent Core Field Changes Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 2 / 43

Outline of Talk Exploring Earth s Magnetic Field from Space 1 Exploring Earth s Magnetic Field from Space 2 Previous Missions: POGO and Magsat 3 Present Missions: Ørsted, CHAMP and SAC-C 4 Near Future: Swarm 5 Recent Core Field Changes Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 3 / 43

Exploring Earth s Magnetic Field from Space Why should we measure magnetic field from space? Global coverage with ground observatories... and with 3 days of satellite data Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 4 / 43

Exploring Earth s Magnetic Field from Space Magnetic Field Model From Satellite Data B = grad V V = N n a + V ext n=1 m=0 r, θ, φ are spherical coordinates ( a ) n+1 [gn m cos mφ + hn m sin mφ] P m r n (cos θ) a is Earth s radius g m n and h m n are the spherical harmonic expansion coefficients of the internal magnetic field Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 5 / 43

Exploring Earth s Magnetic Field from Space Expansion Coefficients g m n, h m n of the Internal Field Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 6 / 43

Exploring Earth s Magnetic Field from Space Model Resolution Vector data 10,000 observations No external field Static internal field Perfectly polar orbit (inclination = 90 ) Vector data at all latitudes Ideal case: Perfect satellite, perfect environment,... Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 7 / 43

Outline of Talk Previous Missions: POGO and Magsat 1 Exploring Earth s Magnetic Field from Space 2 Previous Missions: POGO and Magsat 3 Present Missions: Ørsted, CHAMP and SAC-C 4 Near Future: Swarm 5 Recent Core Field Changes Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 8 / 43

Previous Missions: POGO and Magsat Satellite Missions: POGO Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 9 / 43

Previous Missions: POGO and Magsat Model Resolution Scalar data 10,000 observations No external field Static internal field Perfectly polar orbit (inclination = 90 ) Only intensity data strong Backus effect! Sectorial coefficients g n n, h n n are poorly determined Example: data from POGO satellite series (1965-72) Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 10 / 43

Previous Missions: POGO and Magsat Model Resolution Vector and scalar data 10,000 observations No external field Static internal field Perfectly polar orbit (inclination = 90 ) Vector data at non-polar latitudes (below ±60 ), else intensity data Vector data only needed at low latitudes to avoid Backus effect Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 11 / 43

Previous Missions: POGO and Magsat Satellite Missions: Magsat Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 12 / 43

Previous Missions: POGO and Magsat Model Resolution Vector and scalar data 10,000 observations No external field Static internal field Near polar orbit (inclination = 97 ) Vector data at non-polar latitudes (below ±60 ), else intensity data Zonal coefficients poorly determined due to polar gap Example: data from Magsat satellite (1979-80) Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 13 / 43

Outline of Talk Present Missions: Ørsted, CHAMP and SAC-C 1 Exploring Earth s Magnetic Field from Space 2 Previous Missions: POGO and Magsat 3 Present Missions: Ørsted, CHAMP and SAC-C 4 Near Future: Swarm 5 Recent Core Field Changes Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 14 / 43

Present Missions: Ørsted, CHAMP and SAC-C Satellite Missions: Ørsted, CHAMP and SAC-C Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 15 / 43

Present Missions: Ørsted, CHAMP and SAC-C Present Satellites Satellites of the International Decade of Geopotential Research Ørsted Launched on 23th February 1999 Polar orbit, 650-850 km altitude all local times within 790 days (2.2 years) CHAMP Launched on 15th July 2000 low altitude (350-450 km) all local times within 130 days SAC-C Copy of Ørsted experiment Launched on 21th November 2000 700 km altitude, fixed local time 1030/2230 (no high-precision vector data due to payload failure) Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 16 / 43

Present Missions: Ørsted, CHAMP and SAC-C Single satellites: Space-Time Ambiguity A low-earth-orbiting satellite moves with 8 km/s. It is difficult to distinguish whether an observed field change is due to a temporal field change or due to the movement of the satellite. Multi-point observations in space can resolve this ambiguity Satellite Constellation Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 17 / 43

Present Missions: Ørsted, CHAMP and SAC-C N Single Satellites vs. Constellation of N Satellites Data treated as multiple single-satellite observations Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 18 / 43

Present Missions: Ørsted, CHAMP and SAC-C N Single Satellites vs. Constellation of N Satellites Data treated as multiple single-satellite observations N satellites increase of number of data by N reduction of model error by N (if data are independent) Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 18 / 43

Present Missions: Ørsted, CHAMP and SAC-C N Single Satellites vs. Constellation of N Satellites Data treated as multiple single-satellite observations N satellites increase of number of data by N reduction of model error by N (if data are independent) improvement less than N if data are not independent Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 18 / 43

Present Missions: Ørsted, CHAMP and SAC-C N Single Satellites vs. Constellation of N Satellites Data treated as multiple single-satellite observations N satellites increase of number of data by N reduction of model error by N (if data are independent) improvement less than N if data are not independent Take advantage of constellation: potential of improvement better than N Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 18 / 43

Outline of Talk Near Future: Swarm 1 Exploring Earth s Magnetic Field from Space 2 Previous Missions: POGO and Magsat 3 Present Missions: Ørsted, CHAMP and SAC-C 4 Near Future: Swarm 5 Recent Core Field Changes Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 19 / 43

Near Future: Swarm After Ørsted and CHAMP: Swarm Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 20 / 43

Near Future: Swarm The Swarm Concept ESA mission, to be launched in 2010 3 satellites: 2 side-by-side in low orbit 1 in higher orbit Three orbital planes with two different near-polar inclinations Science objectives Monitoring of core field changes after Ørsted and CHAMP Improved determination of the small-scale crustal field 3D mantle conductivity Magnetospheric and ionospheric current systems Magnetic forcing of the upper atmosphere Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 21 / 43

Near Future: Swarm Lower Pair of Swarm Satellites Measures Magnetic Field Gradient Pair of Swarm Satellites Measures Magnetic Field Gradient B r B θ B φ Swarm allows to measure the East-West Gradient, which is more sensitive to the small-scale lithospheric field Magnetic field East-West Gradient of Magnetic field 02.11.2007 Geophysical Colloquium, ETH Zurich page 32 Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 22 / 43

Near Future: Swarm Advantage of two satellites flying side-by-side Quasi-complex representation of crustal field: B = Re{grad V } V = a ( a ) n+1 γ m r n Pn m e imφ n,m γ m n = g m n ih m n Difference of B at two satellites separated by φ in longitude: B = B(r, θ, φ) B(r, θ, φ + φ) 0 0 50 100 150 order m = Re{grad V } γn m = γn m ( 1 e im φ ) 1 e im φ m φ Sensitive to higher order m Filter gain 1 exp(i m φ) 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 φ = 1 o φ = 1.4 o φ = 2 o Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 23 / 43

Near Future: Swarm Model Resolution East-West gradient data 10,000 observations No external field Static internal field Near polar orbit (inclination = 97 ) East-West gradient data Zonal coefficients undetermined Enhanced resolution of sectorial coefficients Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 24 / 43

Near Future: Swarm End-To-End Mission Simulation Generation of synthetic orbits simulation starts on July 1, 1998 (one solar cycle before anticipated launch) simulation length of 4.5 years 24 18 Swarm A Swarm C Swarm C Swarm A 550 500 450 Local Time [hrs] 12 altitude [km] 400 350 6 300 Swarm C Swarm A 0 1998.5 1999 1999.5 2000 2000.5 2001 2001.5 2002 2002.5 2003 year 250 1998.5 1999 1999.5 2000 2000.5 2001 2001.5 2002 2002.5 2003 year 24 Swarm A Swarm C Swarm C Swarm A 18 Local Time [hrs] 12 6 0 1998.5 1999 1999.5 2000 2000.5 2001 2001.5 2002 2002.5 2003 year Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 25 / 43

Near Future: Swarm End-To-End Mission Simulation Magnetic Field Generation Core field time changes up to n = 19 Crustal field (static) up to n = 250 Ionospheric field, daily + seasonal periodicity Amplitude modulated by daily values of F10.7 Induced field by means of 1D conductivity model Magnetospheric field Time dependence of external coefficients up to n = 3, m = 0, 1 given by observatory data (hourly mean values) Induced field (up to n = 45) calculated using 3D mantle conductivity, including oceans Toroidal (non-potential) field daily + seasonal periodicity Instrument noise Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 26 / 43

Near Future: Swarm Crustal Field Recovery from B alone Single satellite approach degree error at ground 1 degree correlation 10 1 0.99 0.98 0.97 [nt] 10 0 degree correlation ρ n 0.96 0.95 0.94 10 1 0.93 0.92 10 2 signal Field only 20 40 60 80 100 120 140 degree n 0.91 0.9 20 40 60 80 100 120 140 degree n Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 27 / 43

Near Future: Swarm Crustal Field Recovery from B and [ B] EW Constellation approach degree error at ground 1 degree correlation 10 1 0.99 0.98 0.97 [nt] 10 0 degree correlation ρ n 0.96 0.95 0.94 10 1 0.93 0.92 10 2 signal Field only Field + Gradient 20 40 60 80 100 120 140 degree n 0.91 0.9 20 40 60 80 100 120 140 degree n Same observations in both cases, but different arrangement of data subsets Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 27 / 43

Crustal Field Recovery Near Future: Swarm Sensitivity matrix: relative error in %, normalized by mean power at that degree n Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 28 / 43

Near Future: Swarm Map of Crustal Field Difference using B only B r at surface, in nt Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 29 / 43

Near Future: Swarm Map of Crustal Field Difference using B and [ B] EW B r at surface, in nt Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 30 / 43

Near Future: Swarm Improvement of Lithospheric Field Model POGO and Magsat... n 30, resolution: 1330 km Magnetic field of Earths crust radial component at 10 km altitude Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 31 / 43

Near Future: Swarm Improvement of Lithospheric Field Model POGO and Magsat... n 30, resolution: 1330 km... with present satellites Ørsted and CHAMP... n 60, resolution: 670 km Magnetic field of Earths crust radial component at 10 km altitude Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 31 / 43

Near Future: Swarm Improvement of Lithospheric Field Model POGO and Magsat... n 30, resolution: 1330 km... with present satellites Ørsted and CHAMP... n 60, resolution: 670 km... and with Swarm n 130, resolution: 300 km Magnetic field of Earths crust radial component at 10 km altitude Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 31 / 43

Outline of Talk Recent Core Field Changes 1 Exploring Earth s Magnetic Field from Space 2 Previous Missions: POGO and Magsat 3 Present Missions: Ørsted, CHAMP and SAC-C 4 Near Future: Swarm 5 Recent Core Field Changes Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 32 / 43

Core field changes Recent Core Field Changes Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 33 / 43

Recent Core Field Changes Core field changes Ground observatory data monitor field change in time at a fixed location in space The role of observatory data: help in separating spatial and temporal variations when analyzing satellite data help in bridging the gap between satellite missions Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 33 / 43

Recent Core Field Changes Observatory monthly means monitor field change at fixed locations but: contain internal and external field contribution challenge: extraction of core field signal dy/dt [nt/yr] dy /dt at Niemegk/Germany 20 15 10 5 0 5 10 15 observed 20 1950 1960 1970 1980 1990 2000 annual differences of monthly means Scatter (partly) due to magnetospheric ring-current contributions Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 34 / 43

Revised monthly means Recent Core Field Changes 50 years (1958-2007) of hourly mean values from Niemegk Traditional way: arithmetic mean (all days, all local times) σ = 13.3 nt/yr σ = 4.7 nt/yr 40 15 NGK 20 30 10 15 20 5 10 σ = 11.6 nt/yr dx/dt [nt/yr] 10 0 10 20 dy/dt [nt/yr] 0 5 10 15 20 dz/dt [nt/yr] 5 0 5 10 15 20 30 1960 1970 1980 1990 2000 year 1960 1970 1980 1990 2000 year New: robust (Huber) average of data after correction for ionospheric and magnetospheric contributions 40 30 20 σ = 4.9 nt/yr NGK 15 10 5 σ = 1.9 nt/yr 20 15 10 1960 1970 1980 1990 2000 year σ = 3.3 nt/yr dx/dt [nt/yr] 10 0 10 20 dy/dt [nt/yr] 0 5 10 15 20 dz/dt [nt/yr] 5 0 5 10 15 20 30 1960 1970 1980 1990 2000 year 1960 1970 1980 1990 2000 year 1960 1970 1980 1990 2000 year Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 35 / 43

Revised monthly means Recent Core Field Changes 50 years (1958-2007) of hourly mean values from Niemegk Traditional way: arithmetic mean (all days, all local times) σ = 13.3 nt/yr σ = 4.7 nt/yr 40 15 NGK 20 30 10 15 20 5 10 σ = 11.6 nt/yr dx/dt [nt/yr] 10 0 10 20 dy/dt [nt/yr] 0 5 10 15 20 dz/dt [nt/yr] 5 0 5 10 15 20 30 1960 1970 1980 1990 2000 year 1960 1970 1980 1990 2000 year New: robust (Huber) average of data after correction for ionospheric and magnetospheric contributions 40 30 20 σ = 4.9 nt/yr NGK 15 10 5 σ = 1.9 nt/yr 20 15 10 1960 1970 1980 1990 2000 year σ = 3.3 nt/yr dx/dt [nt/yr] 10 0 10 20 dy/dt [nt/yr] 0 5 10 15 20 dz/dt [nt/yr] 5 0 5 10 15 20 30 1960 1970 1980 1990 2000 year 1960 1970 1980 1990 2000 year 1960 1970 1980 1990 2000 year Standard deviation σ (wrt a GCV spline fit) is reduced by a factor of 3 Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 35 / 43

Recent Core Field Changes The CHAOS Field Model Series CHAOS 6.5 years of satellite data (March 1999 and December 2005) Order 4 splines up to spherical harmonic degree n = 14, static up to n = 50 Regularization of < B 2 > at Earth s surface CHAOS-2 10 years of satellite data (March 1999 and March 2009) Observatory monthly means (1997-2006) Order 6 splines up to n = 20, static for n = 21 60 Regularization of < B 2 > at Core-Mantle Boundary (CMB) CHAOS-3 10.5 years of satellite data (March 1999 and August 2009) Revised observatory monthly means (1997-2009) Order 6 splines up to n = 20, static for n = 21 60 Regularization of < d 3 B/dt 3 2 > at CMB Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 36 / 43

Recent Core Field Changes CHAOS-3 Data Selection Distribution of non-polar data 16000 14000 CHAMP scalar CHAMP vector Oersted scalar Oersted vector SAC C scalar total number of data points per month 12000 10000 8000 6000 4000 2000 0 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 year stacked histogram Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 37 / 43

Recent Core Field Changes Spectrum of first and second time derivative at t = 2005.0 10 4 10 3 CHAOS 2 CHAOS 3 [(nt/yr) 2 or (nt/yr 2 ) 2 10 2 10 1 10 0 first time derivative 10 1 second time derivative 10 2 10 3 0 2 4 6 8 10 12 14 16 18 20 degree n CHAOS-3 shows less secular acceleration power at n = 1, more power at n > 6 Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 38 / 43

Fit to observatory data Recent Core Field Changes CHAOS-2 CHAOS-3 component mean rms mean rms Ẋ [nt/yr] -2.74 13.42 0.02 7.35 Ẏ [nt/yr] 0.17 11.41-0.02 5.02 Ż [nt/yr] 0.92 9.91-0.10 7.02 CHAOS-3 rms misfit reduced by factor 2 for X and Y, and by 30% for Z The non-zero mean values of CHAOS-2 are not present in CHAOS-3 Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 39 / 43

Fit to observatory data Recent Core Field Changes CHAOS-2 CHAOS-3 component mean rms mean rms Ẋ [nt/yr] -2.74 13.42 0.02 7.35 Ẏ [nt/yr] 0.17 11.41-0.02 5.02 Ż [nt/yr] 0.92 9.91-0.10 7.02 CHAOS-3 rms misfit reduced by factor 2 for X and Y, and by 30% for Z The non-zero mean values of CHAOS-2 are not present in CHAOS-3 Also satellite rms misfit data is slightly lower for CHAOS-3 compared to CHAOS-2 Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 39 / 43

Recent Core Field Changes Fit to observatory data dx/dt [nt/yr] 5 0 5 10 15 20 25 KAK X 1998 2000 2002 2004 2006 2008 2010 dy/dt [nt/yr] 0 5 10 15 KAK Y CHAOS 2 CHAOS 3 1998 2000 2002 2004 2006 2008 2010 dz/dt [nt/yr] 35 KAK Z 30 25 20 15 10 5 0 5 1998 2000 2002 2004 2006 2008 2010 dx/dt [nt/yr] 0 5 10 15 20 25 HER X 1998 2000 2002 2004 2006 2008 2010 dy/dt [nt/yr] 8 10 12 14 16 18 20 22 24 HER Y 26 1998 2000 2002 2004 2006 2008 2010 dz/dt [nt/yr] HER Z 80 70 60 50 40 1998 2000 2002 2004 2006 2008 2010 Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 40 / 43

Conclusions Conclusions Bright future for space magnetometry (until 2015?) Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 41 / 43

Conclusions Conclusions Bright future for space magnetometry (until 2015?) Constellation aspect: 1+1+1 is sometimes more than 3 Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 41 / 43

Conclusions Conclusions Bright future for space magnetometry (until 2015?) Constellation aspect: 1+1+1 is sometimes more than 3 changed role of ground observatory data Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 41 / 43

Conclusions Nils Olsen (DTU Space) Ørsted, CHAMP, and Swarm 42 / 43