April 29 – May 2, 20081Space Weather Workshop 2008, Boulder, CO JPL/USC GAIM: Assimilating COSMIC occultations & Sample Applications Jet Propulsion Laboratory California Institute of Technology M/S Oak Grove Drive Pasadena CA Brian Wilson, Attila Komjathy, Vardan Akopian, Xioaqing Pi, Chi Ao, and Byron Iijima

April 29 – May 2, 20082Space Weather Workshop 2008, Boulder, CO Outline Global Assimilative Ionosphere Model (JPL/USC GAIM) First-principles physics model, with an adjoint Assimilation by Kalman filter and 4DVAR Assimilating COSMIC TEC improves profile shapes Three case studies: Arecibo, Jicamarca and Millstone ISR Extensive validation using Jason VTEC, ISR profiles, ionosonde Storm Studies TEC and density profile perturbations during August 7, 2006 storm Ray Tracing Capability Added to GAIM Trace ray bending thru 3D electron density field Application: Improving neutral atmosphere retrievals from COSMIC Short-Term Forecast (2-6 hours) Adjust drivers using 4DVAR; feed improved drivers into Kalman filter For longer-term, must forecast or measure upstream drivers/couplings

April 29 – May 2, 20083Space Weather Workshop 2008, Boulder, CO Global Assimilative Ionospheric Model Data Assimilation Process Driving Forces Driving Forces Mapping State To Measurements Mapping State To Measurements Physics Model Physics Model Kalman Filter State and covariance Forecast State and covariance Analysis Adjustment Of Parameters 4DVAR Innovation Vector Kalman Filter Recursive Filtering Covariance estimation and state correction Optimal interpolation Band-Limited Kalman filter 4-Dimensional Variational Approach Minimization of cost function by estimating driving parameters Non-linear least-square minimization Adjoint method to efficiently compute the gradient of cost function Parameterization of model “drivers”

April 29 – May 2, 20084Space Weather Workshop 2008, Boulder, CO Forward Model with an Adjoint Driver Models NRL MSIS, HWM, Fejer-Scherliess ExB Drift (Fortran) Eulerian Solver Variable-resolution, magnetic grid Six ions: O +, H +, He +, N 2 +, O 2 +, NO + Computational Efficiency Adjoint computes all driver sensitivities in one pass Assim. cycle: Run forward model once & adjoint just once Multi-level physics cache: –Find in memory, pre-computed file, or generate Optimized C++ (2 nd generation code) Object-oriented, Templated Matrix classes High-performance numerics Kudos to our C++ expert, Vardan Akopian

April 29 – May 2, 20085Space Weather Workshop 2008, Boulder, CO Global Assimilative Ionospheric Model Data Assimilation Process Driving Forces Driving Forces Mapping State To Measurements Mapping State To Measurements Physics Model Physics Model Kalman Filter State and covariance Forecast State and covariance Analysis Adjustment Of Parameters 4DVAR Innovation Vector Kalman Filter Recursive Filtering Covariance estimation and state correction Optimal interpolation Band-Limited Kalman filter 4-Dimensional Variational Approach Minimization of cost function by estimating driving parameters Non-linear least-square minimization Adjoint method to efficiently compute the gradient of cost function Parameterization of model “drivers”

April 29 – May 2, 20086Space Weather Workshop 2008, Boulder, CO JPL/USC GAIM++ Forward Model With Adjoint 4DVAR Kalman Filter

April 29 – May 2, 20087Space Weather Workshop 2008, Boulder, CO Optimization Approach: 4DVAR Non-linear least squares minimization Cost function to compute model deviation from observations Adjoint method to compute gradient of cost function: computational efficiency Minimization: finding roots using Newton’s method by estimating driving parameters Parameterization of model drivers Estimate ionospheric drivers & optimize state

April 29 – May 2, 20088Space Weather Workshop 2008, Boulder, CO Better Drivers => Better Forecast Observation System Simulation Experiments (OSSE) to estimate “perturbed” drivers at low latitudes: Neutral winds E  B vertical drift velocity Production terms Synthetic ground GPS TEC data

April 29 – May 2, 20089Space Weather Workshop 2008, Boulder, CO Kalman Filter Equations State Model Measurement Model Noise Model

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Approximate Kalman: Save only part of covariance matrix based on physical correlation lengths. Tested extensively with real data: Ground GPS TEC from global sites. Validate densities against: Vertical TEC obs. From TOPEX Ionosonde FoF2, HmF2, & bottomside profiles Slant TEC obs. from independent ground GPS sites. Density profiles retrieved from space-based GPS occultations Band-Limited Kalman Filter

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO JPL/USC Real-Time GAIM: RT TEC Map & Density Slices Three Installations: JPL, AFRL, DoD

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Outline Global Assimilative Ionosphere Model (GAIM) First-principles physics model, with an adjoint Assimilation by Kalman filter and 4DVAR Assimilating COSMIC TEC improves profile shapes Three case studies: Arecibo, Jicamarca and Millstone ISR Extensive validation using Jason VTEC, ISR profiles, ionosonde Storm Studies TEC and density profile perturbations during August 7, 2006 storm Ray Tracing Capability Added to GAIM Trace ray bending thru 3D electron density field Application: Improving neutral atmosphere retrievals from COSMIC Short-Term Forecast (2-6 hours) Adjust drivers using 4DVAR; feed improved drivers into Kalman filter For longer-term, must forecast or measure upstream drivers/couplings

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO GAIM Input Data Types Ground GPS Data (Absolute TEC) >150 5-min. to Hourly Global GPS Ground Stations Assimilate >300,000 TEC points per day 5 min rate) per day Space GPS Data (Relative TEC) CHAMP 440 km) SAC-C 700 km) IOX 800 km) GRACE 350 km) Topex/Poseidon km) (Upward looking only) Jason 1 km) (Upward looking only) C/NOFS & COSMIC constellation UV Airglow: Limb & Nadir Scans LORAAS on ARGOS, GUVI on TIMED SSUSI/SSULI on DMSP and NPOESS Other Data Types TEC from TOPEX & JASON Ocean Altimeters Ionosonde DMSP, CHAMP, C/NOFS in situ density C/NOFS Electric fields GRACE Cross links ISR

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Coverage of Daily IGS Network and Regional Networks (10 degree elevation mask; 450 km shell height)

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Six-satellite COSMIC constellation Launched April 14, 2006 Low-Earth Orbiter GPS Electron Density Profile COSMIC coverage: 2500 profiles/day COSMIC Ionospheric Weather Constellation

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Occultation TEC Links

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Kalman Assimilation Runs: Three Case Studies (Attila Komjathy) Three runs: GAIM Climate (no data) Ground GPS TEC (200 sites) Ground + COSMIC links (upward & occultation) Medium and Low Resolution runs: 2.5 Vs. 5.0 Lat. In Deg Vs Lon. in Deg. 40 Vs. 80 Alt. in km 100,000 Vs. 18,000 voxels Sparse Kalman filter: Update & propagate covariance Truncate off-diagonal covariance that is beyond physical correlation lengths Magnetic equator Eccentric tilted dipole Intersections of : - magnetic field lines, - magnetic geopotential lines - and magnetic longitudes

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Arecibo FM2 FM5 GPS15 20:05 20:09 20:21 20:25 CRO1 JAMA SCUB CRO1 UT 20:00 Case 1: Arecibo ISR Study for June 26, 2006 UT 20:00 UT 20:12UT 20:24

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO GAIM versus Abel Profiles

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO GAIM Validation Using Jason-2 Vertical TEC for June 26 Ground-data only Ground and space data COSMIC

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Case 2: Ground, COSMIC and Jicamarca ISR Coverage for Sept 21, 2006 Ground GPS COSMIC Jicamarca ISR dense but unevenly distributed coverage less dense yet evenly distributed coverage

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO UCAR and JPL Raw GPS Data Processing Results for Sept 21, 2006 Comparison of UCAR and JPL calibrated TEC near Jicamarca Ground and COSMIC data availability near Jicamarca Ground and COSMIC ground tracks near Jicamarca

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO An Example of COSMIC Impact on Profile Shape 2. UT 15:48 3. UT 16:36 COSMIC UT 15:30 UT hours Elevation angle 1. UT 15: UT 15:36

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Illustration for TEC data, GAIM Prefit and Postfit Residuals

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Medium Resolution GAIM VTEC Difference Maps for Case 2 Ground minus Climate Ground+COSMIC Minus Climate Ground+COSMIC Minus Ground-Only Profile shape at Jicamarca using medium resolution run improves compared to low resolution

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO TEC Comparison with Jicamarca ISR

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO NmF2 Comparison with Jicamarca ISR Medium resolution GAIM NmF2 with COSMIC data matches well during the dense data period UT

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO HmF2 Comparison with Jicamarca ISR Medium resolution GAIM HmF2 with COSMIC matches best with truth

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Summary of Results TEC NmF2

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Summary of Results GO = Ground-GPS only GD = Ground + down-looking COSMIC

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Case 3: Millstone Hill Radar Validation for Dec 20, 2006 Ground-Based GPS Coverage COSMIC FM1 Measurements COSMIC FM3 Measurements

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO GAIM Millstone Hill Radar Validation for Dec 20, 2006 FM3 TracksFM1 Tracks UT 15:00 UT 15:12 UT 15:00UT 15:12UT15:24UT 15:36

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Millstone Hill Radar Validation for Dec 20, 2006 UT 15:24 UT 15:36 UT 15:00UT 15:12UT15:24UT 15:36 FM3 Tracks

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO NmF2 Comparison: Bear Lake

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO GAIM w/ COSMIC versus JASON VTEC

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Detail for JASON Track off Australia on 06/26/2006 Nearby COSMIC data crucial for achieving accuracy.

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO MeanSigmaRMS GIM /26/06Ground Ground+COSMIC MeanSigmaRMS GIM /21/06Ground Ground+COSMIC MeanSigmaRMS GIM /21/06Ground Ground+COSMIC GAIM w/ COSMIC versus JASON VTEC Statistics over Three ISR Periods

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO GAIM Driven By Ground GPS Only versus JASON VTEC June – Nov. 2004: 137 days

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Outline Global Assimilative Ionosphere Model (GAIM) First-principles physics model, with an adjoint Assimilation by Kalman filter and 4DVAR Assimilating COSMIC TEC improves profile shapes Three case studies: Arecibo, Jicamarca and Millstone ISR Extensive validation using Jason VTEC, ISR profiles, ionosonde Storm Studies (Xiaoqing Pi) TEC and density profile perturbations during August 7, 2006 storm Ray Tracing Capability Added to GAIM Trace ray bending thru 3D electron density field Application: Improving neutral atmosphere retrievals from COSMIC Short-Term Forecast (2-6 hours) Adjust drivers using 4DVAR; feed improved drivers into Kalman filter For longer-term, must forecast or measure upstream drivers

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Drivers of the Ionosphere: Coupling with Magnetosphere and Thermosphere Solar EUV radiation  Cause of the ionization  Solar flares Auroral particle precipitation  Cause of the ionization at high latitudes  Significant variations during storms and substorms Thermospheric composition & temperature  Gas to be ionized  Loss of ionization due to chemical reactions  Global thermospheric circulation changes during storms Dynamics  Electric fields: originated from the magnetospheric and wind dynamo processes  Thermospheric winds  Controlled by the geomagnetic field  Magnetospheric convection, penetration, and disturbance wind dynamo Ionospheric data assimilation combines first-principles physics-based modeling and global-scale observations. For long-term forecast of ionospheric weather, must deal with the drivers and magnetospheric & thermospheric couplings.

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Magnetic Storm: August 7, 2006 AUG 4 AUG 5 AUG6 AUG 7 AUG 8 AUG 9 AUG 10 AUG nT -80 nT

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Global Ionospheric Maps 04:00 & 07:15 UT

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Global Ionospheric Maps: 10:30 & 23:00 UT

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Validation of GAIM Using JASON Altimeter TEC Measurements Storm Day Tracks of COSMIC occul. tangent points Jason orbit tracks GPS ground stations Statistics for the entire day TEC along Jason orbit tracks

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO COSMIC RO and JASON Comparison ~ 1 hour Comparisons between GAIM, IRI, and Jason

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Effect of Assimilating Space GPS Data With grnd GPS Data Only With both Space & grnd GPS data Difference %

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Disturbed Ionosphere at 9 UT TEC perturbations in the west Pacific longitudes COSMIC coverage in the regions of perturbations

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Ne Disturbance in the Pacific Longitudes

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO TEC perturbations in the west Pacific longitudes COSMIC coverage in the regions of perturbations Disturbed Ionosphere at 10 UT

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Ne Disturbance in the Pacific Longitudes

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Outline Global Assimilative Ionosphere Model (GAIM) First-principles physics model, with an adjoint Assimilation by Kalman filter and 4DVAR Assimilating COSMIC TEC improves profile shapes Three case studies: Arecibo, Jicamarca and Millstone ISR Extensive validation using Jason VTEC, ISR profiles, ionosonde Storm Studies TEC and density profile perturbations during August 7, 2006 storm Ray Tracing Capability Added to GAIM (Chi Ao) Trace ray bending thru 3D electron density field Application: Improving neutral atmosphere retrievals from COSMIC Short-Term Forecast (2-6 hours) Adjust drivers using 4DVAR; feed improved drivers into Kalman filter For longer-term, must forecast or measure upstream drivers

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO GAIM++ 3D Raytracing Capability (Chi Ao) Adaptive Runge-Kutta solver Tricubic interpolation of electron density in (r,lat,lon) space [Lekien et al., 2004] IGRF magnetic field Refractive index from Appleton-Hartree formula “Homing” using the Subplex algorithm (generalization of the Nelder-Mead simplex method) [Rowan, 1990] 3D grid of Ne Rx/Tx Loc. & Freq Magnetic field GAIM 3D Raytracer TEC, Group path Ionosphere:

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Elevation Angles and Homing Geometric Path True Path Non-Homing Path STEC Nonhome > STEC True > STEC Geo

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Bending for Trans-Iono Raypaths 200 Mhz 30 Mhz 50 Mhz L1 See expected behavior: Much more bending at low frequencies

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Effect on Atmospheric Temperature Retrieval

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Error Study: Large-Scale Ionosphere L1 L2 Transmitter Receiver 11-year solar cycle “Ionosphere-free” linear combination Note: no assumptions made about ionospheric structure

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Magnitude of Different Effects From Bassiri and Hajj, 1993

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Bending Along L1 & L2 Signal Paths Need accuracy to 0.05 % in refractivity to get 0.1 degrees K.

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Effect on Atmospheric Temperature Retrieval

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Outline Global Assimilative Ionosphere Model (GAIM) First-principles physics model, with an adjoint Assimilation by Kalman filter and 4DVAR Assimilating COSMIC TEC improves profile shapes Three case studies: Arecibo, Jicamarca and Millstone ISR Extensive validation using Jason VTEC, ISR profiles, ionosonde Storm Studies TEC and density profile perturbations during August 7, 2006 storm Ray Tracing Capability Added to GAIM Trace ray bending thru 3D electron density field Application: Improving neutral atmosphere retrievals from COSMIC Short-Term Forecast (2-6 hours) Adjust drivers using 4DVAR; feed improved drivers into Kalman filter For longer-term, must forecast or measure upstream drivers/couplings

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Short-Term Forecast Issues Start with accurate iono. nowcast from data assimilation Exploit all global datasets, quantitative accuracy demonstrated Lots of science can be done with accurate 3D density fields Estimate improved drivers using 4DVAR Drivers: production, ExB drift, neutral winds, etc. Feed improved drivers into Kalman filter Forecast for 2-6 hours using physics propagator Continuous Forecast Validation Needed Unknown drivers or couplings drive iono. physics away from reality Simplest Benchmark: Must beat persistence Community should start comparing Skill Scores Iono. Assim. Complementary to T-I-M Coupled Models Couplings still incomplete, not quantitatively accurate, enough data? Use 4DVAR to invert for coupled boundary conditions

April 29 – May 2, Space Weather Workshop 2008, Boulder, CO Summary Global Assimilative Ionosphere Model (JPL/USC GAIM) First-principles physics model, with an adjoint Assimilation by Kalman filter and 4DVAR Assimilating COSMIC TEC improves profile shapes Extensive validation using Jason VTEC, ISR profiles, ionosonde Storm Studies using new level of global 3D accuracy Quantitatively-accurate science can be done Ray Tracing Capability Added to GAIM Looking for new iono. or atmo. applications for ray tracer Short-Term Forecast (2-6 hours) Adjust drivers using 4DVAR; feed improved drivers into Kalman filter High accuracy iono. forecast beyond 6 hours is HARD. Many approaches to hour forecast should be investigated.