Specifying Instantaneous Currents and Electric Fields in the High-Latitude Ionosphere FESD-ECCWES Meeting, 21 July 20141/15 Ellen Cousins 1, Tomoko Matsuo 2,3, Art Richmond 1 1 NCAR-HAO, 2 CU-CIRES, 3 NOAA-SWPC  Implemented assimilative mapping procedure for SuperDARN+AMPERE  Evaluated options for specifying conductance  Demonstrate benefit of using two data sets together J || Φ

High-latitude Ionospheric Electrodynamics  Currents from magnetosphere close through high-latitude ionosphere  Drive currents parallel to and perpendicular to ionospheric electric field E E E E  Satellites sample magnetic perturbations (  field-aligned currents)  SuperDARN radars sample plasma drifts (  electric fields)  Goal: Combine the two data sets and estimate complete (2D) current & electric field distribution FESD-ECCWES Meeting, 21 July 20142/15

 Assimilative technique with Empirical Orthogonal Function (EOF) – based error covariance  Traditionally solved in terms of electrostatic potential; can also be solved in terms of magnetic vector potential FESD-ECCWES Meeting, 21 July 20143/15 Mapping Procedure SuperDARN Obs Magnetic vector potential AMPERE Obs SuperDARN Obs Electrostatic potential Local: Global:

AMPERE EOFs  EOFs calculated independently for North/Winter & South/Summer hemispheres  Universal EOFs obtained by combing results from North & South North mean EOF 1 EOF 2 South EOF 3 EOF 4 Both FESD-ECCWES Meeting, 21 July 20144/15

Noon 45° Ionospheric Conductance  Height-integrated conductivity (tensor)  Assumed infinite along magnetic field lines Solar  Solar-produced component  Empirical model – assumed to be reasonably accurate Auroral  Auroral component unknown  Highly variable in space and time  Estimated using empirical model  Can try to estimate/adjust using information from observations Night-side  Night-side background level  Less well known than day-side  Use as tuning parameter FESD-ECCWES Meeting, 21 July 20145/15

FESD-ECCWES Meeting, 21 July 20146/15 Evaluating Conductance Models Solar Noon 45° Auroral Night-side O-PFAC adj>2, O-P>4, O-P>4, O-SM>4, no aur>6, O-P Med |err| [m/s] Med |err| [nT] ΔB  E: E  ΔB: Best results: diffuse aurora from Ovation Prime or SM [Newell et al., 2010; Mitchell et al., 2013], w/ night-side Σ p = 4 S  Want quantitative metric for selecting ‘best’ conductance model  Evaluate by using mapping procedure with just one data type, predict observations of other type  e.g., fit electrostatic potential with SuperDARN data, predict AMPERE observations (using assumed conductance),  Compare predictions with actual observations  Pick conductance model that minimizes discrepancy between E obs & ΔB obs

 Solving with both data sets together  Electrostatic potential map based on solving in terms of electrostatic potential (more weight for SuperDARN data)  Field-aligned current map based on solving in terms of magnetic vector potential (more weight for AMPERE data) Assimilative Mapping Example J || Φ J || from Φ,Σ FESD-ECCWES Meeting, 21 July 20147/15

Analysis Error  Optimal interpolation method provides estimate of uncertainty in mapped result (“analysis error”)  Takes into account background model error & observational error  Useful for judging reliability of results  Evaluate accuracy of analysis error by comparing with errors in predicting independent observations  Predicting SuperDARN:median = 1.2; 80% < 3  Predicting AMPERE:median = 0.5; 97% < 3 y – observations Hx a – predicted observations σ r 2 – obs. error variance σ a 2 – analysis error variance FESD-ECCWES Meeting, 21 July 20148/15

Assimilative Mapping – Benefits of using data sets together  Analysis error decreases by 10% for Φ, 40% for A  AMPERE fills in SuperDARN coverage gaps & vice versa  Electric potential & FAC maps more compatible?  feature correspondence mV/m nT mW/m FESD-ECCWES Meeting, 21 July 20149/15

Assimilative Mapping – Benefits of using data sets together  Analysis error decreases by 10% for Φ, 40% for A  AMPERE fills in SuperDARN coverage gaps & vice versa  Electric potential & FAC maps more compatible?  feature correspondence mV/m nT mW/m FESD-ECCWES Meeting, 21 July /15

Example Results FESD-ECCWES Meeting, 21 July /15  Cross-polar cap potential typically (but not always) similar between hemispheres  Field-aligned currents and Poynting flux larger in Southern Hemisphere  Seasonal conductance effect (summer in South, winter in North)

Example Results kV μA/m 2 mW/m FESD-ECCWES Meeting, 21 July /15

Example Results kV μA/m 2 mW/m FESD-ECCWES Meeting, 21 July /15

Example Results FESD-ECCWES Meeting, 21 July /15

Summary  Mapping ionospheric electrodynamics using optimal interpolation data assimilation method  Model error covariances based on EOF analysis  Solving for both electrostatic potential & magnetic vector potential  Using magnetic potential improves specification of FACs  Various conductance models evaluated  Best results using Ovation Prime & night-side Σ p = 4 mho  Working with SuperDARN & AMPERE together gives improvements over using data sets independently  Decreased analysis error (increased confidence in results)  AMPERE fills in gaps in SuperDARN coverage & vice versa  More compatible electric potential & FAC maps? FESD-ECCWES Meeting, 21 July /15

FESD-ECCWES Meeting, 21 July 2014 Empirical Orthogonal Function (EOF) analysis  A variant of principal component analysis (PCA)  Technique to estimate dominant modes of variability in a data set (Decompose into eigenmodes & eigenvalues)  Calculated in terms of magnetic vector potential: A J mean EOF 1 EOF 2