Comparison between single- andthree-station IPS measurements
Munetoshi Tokumaru（Solar-Terrestrial Environment
Laboratory, Nagoya University）

Solar Wind Speed Measurements byIPS• Cross Correlation Method– Multi-station measurements– STEL (Kakinuma et al., 1973), Cambridge(Denission & Hewish, 1967), UCSD
(Armstrong & Coles, 1972), EISCAT(Bougois et al.)• Spectral Fit Method– Single-station measurements– ORT (Ananthkrishnan & Manoharan,1990), Kashima (Tokumaru et al., 1991),
Pushchino, MEXART, Jeju/Korea, …

• Co-spectrum Method– Dual-frequency measurements– (Scott et al., 1983), Kashima (Tokumaruet al., 1994)

This Work
• Preliminary results fromcomparison between crosscorrelation and spectral fitting
methods– Simultaneous observations at thesame site/system and the samefrequency– To explore potential of thespectral fitting method for filling
multi-station data gap of STEL
during winter• I intend to develop a fullyautomated data processing software

Comparison between Ooty andSTEL IPS observations at 327 MHz(Manoharan & Ananthakrishnan,MNRAS, 1990)

Observations• Solar wind speeds derived
from STEL IPS observations
at 327 MHz– V1: Single-station(Toyokawa) observations:Spectral fitting method– V3: Three-station
observations; i.e. Cross
correlation method• Source: 3C273– Solar offset distance:
16~180 Rs• Period: 2012 Aug.4-Dec.1– Strong scattering region(<0.2 AU): Sep.18~Oct.9• No. Data: 78– Weak scattering data: 64
Strong scatteringModels• Model 1: Thin screen at the point P /2k  2 f2
P1 (kx )  CN   kx  2  VAR 

22kk2sin  2   exp   2  dky
 kF  kc – Free parameters: CN, kF(=2πfF/V), α, AR– Fixed parameter: kc (fc=6Hz)– point-P-Earth distance: z, wavelength: λ2y• Model 2: Spherically symmetric distribution– Free parameters: CN, V, α, AR– Solar elongation: ε, Sun-Earth distance rSErSE3 sin3 1 2 f 
P2 ( f )   dz
P k 
3/2 1  x
022VVx r  z  2r z cos SESEfF V z

Spectral Fitting Analysis(left) Model 1, (right) Model 2

Addition of white noise

V=459 km/s, AR=1.07, α= 3.8
1. Least Squares Fitting: Marquardt Method
2. Fitting in Log-Log Space
3. Weighting Function: 1/N

V=462 km/s, AR=0.88, α= 3.4
N2W(log(O)log(C)) min
 iiii 1

Initial Values for CN, fF (V), AR, αand Fixed Values for fC (Si)
• CN: Level of the flat part at low frequencies• Fresnel Frequency (Model 1) fF=400km/s/(πλz)1/2,Speed (Model 2) V=400km/s• AR=1.5– Kojima & Kakinuma, 1988 for 0.3AU– Cf. Scott et al., 1983, 1.3±0.3 for >35 Rs• α=11/3 (Kolmogorov)– Woo & Armstrong, 1979 for >15 Rs• Inner scale (fixed parameter)– (Model 1) fC = 6 Hz
– (Model 2) Si =213.9458×sinε or 90 km, kC=3/Si

Dependence on Initial Values:
Model 1 with Different Initial Fresnel freq.; i.e. V
Strong scattering region
No significant
difference isfound except forthe strong
scattering region,
where singlestation data tend
to higher speeds.

Dependence on Initial Values:
Model 2 with Different Initial V
Strong scattering region
Systematicdifference exists
betweendifferent initialvalues of V.

Initial value
dependence
is thought toresult fromstrong
coupling
betweenparameters.

Correlation between V1 and V3
Model 1(a) 4 para: CN, fF(V), AR, α
ρ= 0.465258
The best correlation isobtained.
(b) 3 para: CN, fF(V), AR(α=11/3)
ρ= 0. 266111(c) 3 para: CN, fF(V), α(AR=1.5)
ρ= 0. 228365(d) 2 para: CN, fF(V)(α=11/3, AR=1.5)
ρ= 0. 433643
Note that V1 issystematically higher thanV3. →Owing to bad fixedvalues for AR.

Dependence of Radial Distance R andIPS Level: Model 1• No systematic trend isfound in the IPS level vsV1/V3 plot.

– Note that 3C273 is a verystrong source.

• No systematic trend isfound in the R vs V1/V3
plot for R>0.2 AU.
– In the strong scattering,
V1/V3 tends to be >1.

• Cf. No dependence on
initial values of thespectral fitting method

Relation between errors of multi-andsingle-station measurements: Model 1VERR: Error estimates from cross-correlation
method. VERR < 0 means two-station
measurements.
• No systematic trend in VERR/V vs V1/V3
or |V1-V3|/V3• When VERR < 0 , V1/V3 shows a larger
scatter.

Histograms of AR and α determinedfrom spectral fitting analysis
Model 1: 4 free parameters

AR=1.17011±0.337964
Initial values

α=3.48149±0.479286
Initial values

Summary• The spectral fitting analysis with Model-1 and 4 freeparameters yields the best result, while its correlation
coefficient is 0.47 (meaningful but poor).
• The effect of strong scattering biases V1 to higherspeed.
• No significant dependence on either radial distance orIPS level is found.
• Discrepancy between V1 and V3 does not correlatewith VERR. However, large discrepancy occurs for V3
derived with two-station measurements (VERR = -999).
• AR ~ 1.0 (isotropic) and α~3.5 (~Kolmogorov)• Further improvement is needed.