MFACE Files

ÿþAuxiliary Material for Paper 2012gl053168



A high-resolution model of field-aligned currents through empirical orthogonal 

functions analysis (MFACE)



Maosheng He and Joachim Vogt 

School of Engineering and Science, Jacobs University Bremen, 

Bremen, Germany



Hermann Luhr 

Deutsches GeoForschungsZentrum Potsdam, 

Potsdam, Germany



Eugen Sorbalo 

School of Engineering and Science, Jacobs University Bremen, 

Bremen, Germany



Adrian Blagau 

School of Engineering and Science, Jacobs University Bremen, 

Bremen, Germany



Institute for Space Sciences, 

Bucharest-Magurele, Romania



Guan Le 

Heliophysics Science Division, NASA Goddard Space Flight Center, 

Greenbelt, Maryland, USA



Gang Lu

High Altitude Observatory, NCAR, 

Boulder, Colorado, USA





He, M., J. Vogt, H. Luhr, E. Sorbalo, A. Blagau, G. Le, and G. Lu (2012), A 

high-resolution model of field-aligned currents through empirical orthogonal 

functions analysis (MFACE), Geophys. Res. Lett., 39, L18105, 

doi:10.1029/2012GL053168. 



Introduction



This electronic supplement contains tables of MFACE coefficients for both 

the Northern and Southern hemisphere, and an additional figure presenting 

polar distributions of FACs at March Equinox. To unify the driving 

condition, MFACE is built with 30 minutes lag to solar winds driving, 

despite the FAC density (~20 minutes) responds quicker than FAC latitude 

dependence (~35-40 minutes) as indicated by Figure 2b. 



The current density jz (in units of mu Am-2) in the direction of 

geomagnetic field could be calculated through the following steps, for a 

given driving set of Geomagnetic Latitude (MLat), Geomagnetic Local Time 

(MLT), Day of Year (DoY), IMF clock angle  ¸IMF in GSM, IMF component in 

GSM y-z plane Bt (in units of nT), IMF magnitude B (in units of nT), 

solar wind speed  (in units of km/s) and AE index,.

1) Determination of latitude of Auroral Current Centre (ACC) MLatACC and 

the score sj,

MLatACC=Sigma_alpha_ACC*termAi*termBi

sj=Sigma_alpha_sj*termAi*termBi, j=1,2,...,12

Here, termAi and termBi are functions of . The specific functions are 

given in the first and second columns of the table contained in Tables S1 

and S3. alpha's are coefficients presented in Tables S2 and S4.

2) Calculation of jmean(dMLat) and EOFi(dMLat) through the discrete 

functions listed in Tables S1 and S3. Here, dMLat is the latitude with 

respect to the reference point of ACC, dMLat=MLat-MLatACC.

EOFs are basis functions determined from the profiles in such a way that 

the EOF1 accounts for the largest possible variance, and each succeeding 

EOF in turn accounts for maximum variance possible under the constraint 

that it be orthogonal to the preceding EOFs. Only the first twelve EOFs 

are provided here, since they are the least set that accounts for more 

than 95% variance.

3)  Estimation of current density,

jz=jmean+Sigma_si*EOFi

Users could cut off the model at lower order than 12, because the 

variance captured by the regression decreases rapidly with EOF order, as 

shown in Figure 2a. 



1. 2012gl053168-ts01.xls 

Table S1. EOFs for the Northern Hemisphere.

1.1 Column "dMLat", the latitude with respect to Auroral Current Centre.

1.2 Column "jmean", average FAC density of all profiles.

1.3 Columns "EOF1" ,...,"EOF12", the first twelve EOFs.



2. 2012gl053168-ts02.xls

Table S2. Coefficients for the Northern Hemisphere.

2.1 Column "termA", the first factor termAi .

2.2 Column "termB", the second factor termBi.

2.3 Column "MLat_ACC", alpha_ACC, coefficients for MLatACC.

2.4 Columns "s_1" ,..., "s_j",..., "s_12", 

alpha_s1,...,alpha_sj,...,alpha_s12, coefficients for s1,...,sj,..., s12.



3. 2012gl053168-ts03.xls 

Table S3. Same as Table S1 but for the Southern Hemisphere. 



4. 2012gl053168-ts04.xls 

Table S4. Same as Table S2 but for the Southern Hemisphere.



5. 2012gl053168-fs01.pdf 

Figure S1. Polar distribution of FACs at March Equinox for Northern 

(left) and Southern (right) Hemispheres, arranged by IMF clock angle. Bt 

equals 5nT for all patterns except equals 0nT for the central plots for 

each hemisphere. In each panel, numbers in corners show the maximum 

density (bottom corners, in units of mu Am-2) and hemispherical integrated 

density (top corners, in units of MA), for both the downward (right 

corners) and the upward current (left corners). Maximum upward and 

downward current peaks are marked by crosses.