Robert L. McPherron ‐ Paper presented at
Celebration of 70th Birthday Christopher T. Russell
May 7, 2013 UCLA
May 7, 2013 UCLA
496 Citations
Russell, C., and R. McPherron (1973), S i
Semiannual Variation of Geomagnetic Activity, l V i ti
fG
ti A ti it
J. Geophys. Res., 78(1), 92‐108, doi:10.1029/JA078i001p00092.
The Semiannual Variation
SSabine, E. (1856), On Periodical Laws Discoverable in the Mean Effects of the bi
E (1856) O P i di l L
Di
bl i h M
Eff
f h
Larger Magnetic Disturbances. No. III, Philosophical Transactions of the Royal Society of London, 146, 357‐374, doi:10.1098/rstl.1856.0016.
•
Look for fractional kf f
i
l
deviations in the disturbance at Toronto magnetic observatory
magnetic observatory
•
There are peaks at the q
equinoxes!
•
“The conclusions which can be drawn from the observations at a single
observations at a single station are necessarily limited to the theory of the phenomena as they present themselves at a single point
themselves at a single point on the earth's surface.”
Axial Effect
Cortie, A.L. (1912), Sun‐spots and terrestrial magnetic phenomena, 1898‐1911: the Cause of the Annual Variation in Magnetic Disturbance, Monthly Notices of the Royal Astronomical Society, 73, 52‐60.
Astronomical Society, 73, 52
60.
•
More big magnetic storms More
big magnetic storms
are seen at the equinoxes!
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“… The equinoxes are not the condition of this inequality, but the diti
f thi i
lit b t th
Earth attains its maximum values of heliographic latitude when it gets into the region of the sun‐spots which happen to be near the equinoxes. … Th
The cause of the inequality is the f th i
lit i th
inclination of the Sun's axis.”
Equinoctial Effect
q
McIntosh, D.H. (1959), On the Annual Variation of Magnetic Disturbance, Philosophical Transactions of the Royal
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 251(1001), 525‐552, doi:10.1098/rsta.1959.0010.
•
“…Finally, comparison of the Finally comparison of the
phase, magnitude and other properties of the two components left no doubt that the obliquity of the earth's magnetic axis relative to the sun‐earth line offers a reasonable total explanation of the equinoxial maxima of disturbance ”
disturbance.
Magnetic Reconnection
(Dungey, J. W. (1961), Interplanetary magnetic field and the auroral zones, Phys. Res. Letters, 6, 47‐48.)
•
•
•
•
•
Resistivity develops at subsolar point
Solar wind field merges with earth’s field
Solar wind field merges with earth’s field
Solar wind transports flux over poles
Open field reconnects at distant x‐line
Magnetic flux returns to day side
Magnetic flux returns to day side
r
r r
E = −V × B ⇒ VBz
E
V
B
•
•
•
•
Open field lines continue in solar wind
Solar wind electric field is projected to l
d l
f ld
d
earth’s poles
Ionospheric plasma drifts in response
Pedersen and Hall rrents flo in
Pedersen and Hall currents flow in ionosphere
Three Explanations For Semiannual Variation
Three Explanations For Semiannual Variation
λ
March 5
Earth
Sun
ψ
June 21
Sun
Earth
ZGSM
Axial hypothesis: Axial
hypothesis:
λ =7.25° tilt of solar axis
Connects to active regions
Equinoctial hypothesis: ψ = ~34° tilt of dipole axis to Sun
Solar wind impacts at higher magnetic latitude
magnetic latitude
ZGSE ZGSEQ
YGSM
BY
YGSE
YGSEQ
BZ
View from Sun
Russell‐McPherron hypothesis: Russell‐McPherron
hypothesis:
φc = ~34° tilt of dipole axis
GSEQ IMF By projects as GSM Nz
Ey>0
Ey
0 as Predicted by Russell
as Predicted by Russell‐McPherron
McPherron
•
•
The projection
depends on UT and
season producing
g the
map shown in contours
White circle X shows
the times of maximum
projection
The R-M model
predicts ±100%
variation about a
mean of 1.0
Joint Dependence of R-M Ey>0 on Season and UT
24
2
1.8
16
1.6
18
1.4
1.2
12
1
0.8
06
0.6
6
0.4
0.2
0
81
173
Day of Year
265
356
Predicted Ey (mV/m)
P
•
At equinox the IMF
GSEQ By
B has
h negative
ti
projection on GSM
according to the rule:
“Spring To Fall Away”
Hour of D
Day
•
GSM Ey>0
y as Observed
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•
Joint Dependence of Observed Ey>0 on Season and UT
24
Peaks of Ey occur at times
of day and days of year as
expected
Min, Mean, & Max Ey are:
0.8530, 1.0069, 1.2107
corresponding to an
±18% modulation
We expectt any magnetic
W
ti
variation to change over
the year proportional to
this modulation
12
1.2
1.15
18
1.1
1.05
12
1
0.95
6
0.9
0
81
173
Day of Year
265
356
0 85
0.85
Observed E
Ey (mV/m)
•
The map of Ey exhibits the
R-M pattern
Hour o
of Day
•
UT-Season
UT
Season Variation in AL Index
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•
Joint Dependence of Observed abs(AL) on Season and UT
24
160
Peaks occur near
equinoxes but not at right
equinoxes,
time of day
The min, mean, & max are:
67, 130, 177 nT
The range of variation
relative to mean has
amplitude 43%
170
150
18
140
130
120
12
110
100
6
90
80
•
The pattern does not
correspond to R-M
predictions!
0
70
81
173
Day of Year
265
356
Observed -A
AL (nT)
•
AL varies with UT and
season,, but not in R-M
pattern
Hour of Day
•
2
0.8
5
0.
8
0.
75
18
0.
8
0.9
1
0. 8
0.85
12
0.
95
0.75
0.
95
59
0.80.
0
0.
9
5
0.7
6
5
0.9
12
5
0.9
Hour of Day
y
0.7
0.85
18
<psi(deg)>
24
9
0.
0.
95
24
<SIN(TILT) VERSUS UT & SEASON
85
0. 0.8
5
0.7
0.
95
0
spring
summer
fall
winter
<sin(tilt)2>=0.906
0.9
0.8
6
spring
summer
Day of Year
fall
winter
0.88
0.9
0.92
<psi(deg)>
UT‐Season Variation in AL Index
24
3. 3
3.1
24
<ABS(Δ(Dst))> AS FUNCTION OF UT & SEASON
2.9
2
2.5
3.1
3.1
3.3
summer
summer
2.
7
fall
fall
winter
winter
3.5
3
2.5
<|(Δ (Dst))|>=3.074 nT
spring
<|(Δ (Dst))|>=3.074 nT
spring
summer
Day of Year
summer
Day of Year
12
12
6
3.3
spring
spring
<ABS(Δ (D
Dst))>
<AB
BS(Δ (Dst))>
3
3.5
1
3.
3.5
3.
1
1
3.
0
0
3
3.3.3
2.9
1
3.
6
3.
1
3.1
1
3.
6 3.5
3.3
3.3
Hour of Day
H
Hour of Day
H
12
3.1
2. 7
2.7
12
3.1
18
7
2.
18
3. 1
18
7
2.
3.5
3
3.
6
2.
7
18
24
3.1
3. 3
<ABS(Δ(Dst))> AS FUNCTION OF.3 UT & SEASON
3
24
3.5
fall
fall
winter
winter
0
2.9
3
3.1
3.2
0 <ABS(Δ(Dst))>
2.9
3
3.1
Analysis Interval
1963-1999
<ABS(Δ (Dst))>
3.2
Total
T
t l Number
N b = 317,016
016
Analysis317
Interval
1963-1999
Total Good = 181,476
Number/hour = 15,697
Number/day = 6,796
Total Number = 317,016
Num/(hr*day) = 2,734
Total Good = 181,476
Number/hour = 15,697
Number/day = 6,796
Num/(hr*day) = 2,734
Linear Prediction Filters
m
I(t)
g(τ)
O(t)
On = ∑ b j I n − j1 ∀ n
j =0
Create a set of equations relating output at various
time to input series. Represent by matrix equation.
Matrix form
Local Linear Filter
Output (Y
O
Y)
s2
s1
Solution
CP2
CP1
Input (X)
X0
Prediction
Efficiency
Constant
Input
Coupling
p g
Strength
r
r
O = [X ]* b
r r
−1
( X '⋅ X ) X '⋅O = b
(
)
Var (Data − Model )
PEF = 1 −
Var (Data )
m
On >m = I 0 ∑ b j
j =0
Seasonal Variation of
Coupling
p g Strength
g
•
•
Use hourly averages from 1963-2012
to create hourly coupling functions
Mask coupling function and AL index
by day of year over all years
Calculate filters for each day
y of year
y
and determine prediction efficiency
and coupling strength
72.786
Prediction Efficiency (%)
•
Seasonal Variation of Prediction Efficency 1963-2012
67.155
60
50
•
S i
Spring
-91
S
Summer
0
F ll
Fall
91
182
Day w/o Summer Solstice
Seasonal Variation of Coupling Strength 1963-2012
160
Coupling S
Strength
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Prediction efficiency summer high
OPT is best with UCF second. Es
has much lower efficiency
Functions peak around equinox
with minima near solstice
Summer solstice higher than
winter solstice
Es
UCF
Opt
-182
170
•
•
70.990
70
150
140
130
120
-182
Es
UCF
Opt
Spring
-91
Summer
0
Day w/o Summer Solstice
Fall
91
182
Seasonal Variation of eys Coupling Strength
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•
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Light gray curve shows
the seasonal variation of
eys about mean (147)
The annual harmonic
(dashed green) peaks in
summer (10.95)
The second harmonic
(d h d red)
(dashed
d) peak
k
shortly after the
equinoxes with
amplitude (13.51)
The 2nd harmonic
modulation is ±9.2%
about mean
Season Variation of Harmonic Fit to eys
eys-AL
AL Coupling Strength
170
160
Coupling S
Strength
•
150
140
130
120
-182
eys
1+2
1
2
Avg
Spring
-91
Summer
0
Day w/o Summer Solstice
Fall
91
182
Semiannual Variation of Es & AL
27-d Run Avg In, Out, Coup vs Day of Year for Ey to AL
0.6
A vg E s (mV /m)
•
The observed
modulation of Es
has amplitude 8.5%
The modulation of
AL is 24%
0.5
±8 5%
±8.5%
0.4
A vg A L (nT)
•
140
130
±24.1%
120
110
100
90
-182
-91
0
91
Day w/o Summer Solstice
182
Conclusions
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The semiannual variation of geomagnetic activity is well established
Four hypothesis have been put forward:
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–
–
–
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Axial effect
Equinoctial effect
Russell-McPherron effect
Ionization by solar illumination
It is likely that all of these affect magnetic activity
The Russell-McPherron effect is not the primary cause of the
semiannual variation
There exist a variety of explanations for why the dipole tilt away from
the ecliptic pole might reduce the strength of solar wind coupling but
none has been definitely shown to be the cause of the semiannual
variation
Th E
The
End!
d!