**APPENDIX Definition of Magnetic Cloud Quality, Q**_{o}

For measurement of quality (Q_{o}) of the magnetic cloud (MC) fitting using the technique of Lepping et al. [1990] we define some useful quantities:

"Check" ≡ (R_{ΔT} - R_{o})/R_{o}, where R_{ΔT} =√[Y_{o}^{2}+(sin β_{CA} V_{C}ΔT/2)^{2}],

and where R is the radius, ΔT is the duration of cloud-passage, V_{C} is the center speed of the cloud (being close to the average speed across the cloud), β_{CA} is the angle between the cloud's axis and the Sun-Earth line (where cos β_{CA} = cos φ_{A} cos θ_{A}, and where φ_{A}, θ_{A} are the longitude and latitude in GSE of the clouds axis), and Y_{o} 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; R_{ΔT} uses cloud speed, duration, and attitude, and R_{o} is from the fitting program. Other useful quantities are:

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

and consideration of the average field components (taken across the cloud) in __Cl__oud coordinates, <B_{X}>_{Cl}, <B_{Y}>_{Cl}, <B_{Z}>_{Cl}. Ideally <B_{X}>_{Cl} should be always positive and <B_{Y}>_{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.

**Q**_{o} = 3 category

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

|check| ≥ 55%, |CA| ≥ 97%, <B_{X}>_{Cl} ≤ -1.5 nT, f flag = NOT OK, Diameter ≥ 0.45 AU, ASF ≥ 40%, Cone angle (β_{CA}) ≤ 25% of β_{CA} ≥ 155^{o}, and χ_{R} ≥ 0.215 (χ_{R} 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 (Q_{o} = 1) from the intermediated (Q_{o} = 2) ones.

**Q**_{o} = 1 category

The Q_{o} = 1 cases must satisfy all of the following criteria; |check| ≤ 20%, |<B_{Y}>_{Cl}| ≤ 3.0 nT, ASF ≤ 30%, 45^{o} ≤ β_{CA} ≤ 135^{o}, and χ_{R} ≤ 0.165. These are the "Q_{o} = 1 set."

**Q**_{o} = 2 category

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

With these definitions we can reasonably designate "quality" in terms of Q_{o} = 1 for excellent/good, 2 for fair, and 3 for poor. Discriminating features among Q_{o} = 1, 2, and 3 were mainly developed from experience in applying the MC model of Lepping et al. [1990].

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