## APPENDIX          Definition of Magnetic Cloud Quality, Qo

For measurement of quality (Qo) of the magnetic cloud (MC) fitting using the technique of Lepping et al.  we define some useful quantities:

"Check" ≡ (RΔT - Ro)/Ro,     where     RΔT =√[Yo2+(sin βCA VCΔT/2)2],

and where R is the radius, ΔT is the duration of cloud-passage, VC is the center speed of the cloud (being close to the average speed across the cloud), βCA is the angle between the cloud's axis and the Sun-Earth line (where cos βCA = cos φA cos θA, and where φA, θA are the longitude and latitude in GSE of the clouds axis), and Yo is the closest approach distance. That is, the value of the quantity "check" tests for consistency between two different means of obtaining estimates of the cloud's radius; RΔT uses cloud speed, duration, and attitude, and Ro is from the fitting program. Other useful quantities are:

ASF = |(1-2to/Duration)| x 100%, (Called the asymmetry factor, where ASF = 0% is excellent, and where to is the estimated cloud center-time),

and consideration of the average field components (taken across the cloud) in Cloud coordinates, <BX>Cl, <BY>Cl, <BZ>Cl. Ideally <BX>Cl should be always positive and <BY>Cl should be zero, because of the definition of the cloud coordinate system and the fundamental field geometry of the force free structure. Other factors are given below.

Qo = 3 category
We determine those MC's that fall into the Qo = 3 category first. This category arises from satisfying any one of the following:

|check| ≥ 55%, |CA| ≥ 97%, <BX>Cl ≤ -1.5 nT, f flag = NOT OK, Diameter ≥ 0.45 AU, ASF ≥ 40%, Cone angle (βCA) ≤ 25% of βCA ≥ 155o, and χR ≥ 0.215 (χR is defined in section 2 of Lepping et al. [2004b]).

The remaining cases, comprising designated "set 1,2," are examined next in order to differentiate the best cases (Qo = 1) from the intermediated (Qo = 2) ones.

Qo = 1 category
The Qo = 1 cases must satisfy all of the following criteria; |check| ≤ 20%, |<BY>Cl| ≤ 3.0 nT, ASF ≤ 30%, 45o ≤ βCA ≤ 135o, and χR ≤ 0.165. These are the "Qo = 1 set."

Qo = 2 category
The remaining cases within set 1,2, i.e., those not satisfying the Qo = 1 criteria, are put into category Qo = 2.

With these definitions we can reasonably designate "quality" in terms of Qo = 1 for excellent/good, 2 for fair, and 3 for poor. Discriminating features among Qo = 1, 2, and 3 were mainly developed from experience in applying the MC model of Lepping et al. .

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