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Predicting Geomagnetic Activity: The Dst Index
Robert L. McPherron and Paul O’Brien
Institute of Geophysics and Planetary Physics, University of California Los Angeles, Los Angeles, California
Geomagnetic activity is usually characterized by magnetic indices. Most indices have long records that allow statistical studies of the causes of activity and of
related phenomena. Correlations between indices and possible drivers provide the
basis for empirical prediction. Here we examine solar wind control of Dst, an index that is thought to be linearly proportional to the total energy in the terrestrial
ring current. We use linear prediction filtering, a technique in which an autoregressive (AR) filter maps past values of the index to the next value, and a moving average (MA) filter maps current and past values of the solar wind input to
the next value of the index. These ARMA filters may be determined from historical records by least square optimization. Nonlinear systems can be approximated
in a piecewise fashion by localizing the filter. We do this by using narrow bins of
the solar wind electric field; VBs. Our model utilizes 37 years of hourly observations to estimate the coefficients representing the quiet time ring current, the solar wind dynamic pressure, the ring current decay rate, and the rate of ring current injection in a simple differential equation. We find that pressure and decay
coefficients are fit by exponential functions of VBs, decreasing as VBs increases,
but ring current injection is a linear function of VBs. Integration of our model using observations of the solar wind and analytic fits to the coefficients produces a
time series that contains 76% of the variance in the original data. The prediction
residuals have a Gaussian distribution with zero mean and rms error of 10.6 nT.
1. INTRODUCTION
Space weather consists of a variety of phenomena driven
by the solar wind such as substorms, magnetic storms, acceleration of relativistic electrons, and ULF waves. In this
paper we report an empirical study of magnetic storms as
characterized by the Dst index. Magnetic storms occur
when the number and energy of positive ions and electrons
drifting in the outer radiation belts increase significantly.
Since electrons and protons drift in opposite directions they
produce a ring current around the earth. The direction of
this current is westward causing a decrease in the surface
field. The Dst index is a measure of the total energy of
these drifting particles. Dst is obtained by finding the instantaneous average of the deviations from a quiet day in
the horizontal component of the magnetic field at a number
of low latitude magnetic observatories.
A magnetic storm typically consists of three phases. The
initial phase is a result of an increase in solar wind dynamic pressure. This increase presses the magnetopause current
closer to the earth causing a positive perturbation in H. The
main phase is a consequence of a southward turning of the
interplanetary magnetic field (IMF). When the IMF turns
southward magnetic reconnection occurs on the dayside
allowing a fraction of the solar wind electric field to penetrate the magnetosphere [Reiff and Luhmann, 1986]. This
field transports ions from the tail to the inner magnetosphere where they are trapped in the ring current, causing
the Dst index to become more negative. The recovery phase
is a consequence of the IMF turning northward shutting off
the magnetospheric electric field. Particle injection decreases while the drifting ions charge exchange with atmospheric neutral particles losing their energy and thereby
decreasing the strength of the ring current.
The purpose of this paper is to illustrate how the strength
of the ring current as measured by the Dst index can be
predicted by the method of local linear filters. To do this
we utilize 37 years of solar wind and geomagnetic data to
produce filters for a variety of states of the magnetosphere.
We demonstrate that the coefficients of these models can
be represented by analytic functions of a single variable,
the solar wind electric field, VBs. We then show that these
functions may be used to make multi-step predictions of
the index from observations of the solar wind. We evaluate
the quality of these predictions showing that they generally
provide accurate predictions.
2. PREDICTION FILTERS
A linear prediction filter is written in the following way.
N
M
i 1
j 0
O(t )   ai O(t  it )  b j I (t  jt )
(1)
The output of a system at the next time step is the sum of
two parts. The first part is a weighted sum of previous values of the output. This self-prediction in called auto regression and it represents internal dynamics of the system. The
second part is a weighted sum of the current and past values of the input. This part represents the external dynamics. Together the autoregressive (AR) filter coefficients, ai,
and the moving average (MA) coefficients, bj, constitute an
autoregressive moving average (ARMA) filter. With a single set of filter coefficients the representation is completely
linear. Such filters can approximate even nonlinear systems, but the more nonlinear the system, the lower the accuracy of the predictions.
ARMA filters are actually discrete representations of differential equations [Klimas et al., 1998]. Representation of
the relation between the input and output of a causal system by a linear prediction filter is equivalent to describing
it by a differential equation. Integration of this equation
from a known initial condition with a measured input as
driver is how prediction is accomplished. Note that the
current output cannot be calculated until the current input
is measured. If for example the time step is one day the
output for the day cannot be calculated until the end of the
day. Only if the actual input can be measured well in advance of its arrival, or the delay in the system response is
long compared to the time step, can this be considered a
“prediction” technique.
A representation of the behavior of the ring current in
terms of linear prediction filters is motivated by a consideration of the physical processes that produce the surface
magnetic fields. According to the D-P-S relation, Dst is
directly proportional to the total energy in the drifting ring
current particles [Dessler and Parker, 1959; Sckopke,
1966]. This implies that the Dst (a negative quantity) becomes more negative when energy is injected and less negative when energy is lost. It has been found that injection is
proportional to the solar wind electric field and decay is
proportional to the strength of Dst. Burton et al. [1975]
expressed these facts with the following equation.
dDst
D
 Q(t )  st
dt

(2)
The quantity Dst* is the component of the measured Dst
index that is caused by a symmetric ring current. However
it is well known that measured Dst is a superposition of the
effects of the ring current, the disturbed magnetopause
current, and the quiet time ring current present when the
baselines for the magnetic perturbations are determined.
These facts are summarized by the relation
Dst  Dst  b p  c
(3)
Here p is the dynamic pressure of the solar wind, b is the
constant of proportionality relating changes in Dst to
changes in pressure, and c is the effect of the quiet time
magnetopause. If we substitute this relation into equation
2, approximate the time derivatives with first differences,
and rearrange terms we obtain


ct 
  t 
 bt 

Dst  
 Dst  b  p  
 p  Q(t ) 
 (4)
 
  
  

The dependent variable in this difference equation is
Dst while Dst, p, p, and Q(t) are independent variables. The coefficients of the equation are , b, c, and whatever constants are required to describe the input function
Q(t). Measurements at a specific time define one instance
of the relation between the dependent and independent
variables. Taking many successive measurements we obtain an over-determined set of equations for the unknown
coefficients. Burton et al. [1975] assumed that all of these
coefficients were constants independent of the state of the
system and determined each constant separately by a different method. Their most important result was that Q(t)
was a linear function of the solar wind electric field, i.e.
Q(t) =VBs. Below we assume that injection is an arbitrary function of the solar wind, i.e. Q(t) = A(VBs). We
then show that this is a linear function except for details
near VBs = 0.
The work of Klimas et al. [1998] and Vassiliadis et al.
[1999a] makes quite different assumptions about both the
form of the differential equation and the constancy of the
coefficients. Instead of using a single feedback term they
use two (a1 and a2). This is equivalent to a second order
differential equation where a1 can be interpreted as the
damping constant and a2 as the resonant frequency of the
system. They also assume that the coefficients depend on
the state of the system. The two papers differ in how they
localize the ARMA filters, but both assume that the state of
the system depends on three variables: Dst, dDst/dt, and
VBs. Klimas et al. [1998] neglect the pressure correction
to Dst. Vassiliadis et al. [1999b] makes this correction prior
to calculating the state-dependent filter coefficients obtaining coefficients b and c that change with season. The authors justify the use of the second order equation by the
observation that the Dst index appears to oscillate after
pressure pulses and during the main phase decrease.
In this paper we continue to use the Burton equation (2)
because we see no compelling theoretical reason to believe
that the symmetric ring current should display oscillatory
behavior. Also, how well the Burton equation with state
dependent coefficients is able to explain the behavior of
the ring current has not been established. Finally, our use
of hourly averages precludes observation of any oscillations shorter than two-hour period, and this is the order of
the oscillations reported by Vassiliadis et al. [1999a]. Our
work also differs from that of Klimas and Vassiliadis because we assume that the system’s state is defined only by
the solar wind electric field, VBs.
A justification for our view is provided by our previous
work described in O'Brien and McPherron [2000a]. In this
work we used a new statistical procedure that does not involve linear filters to study the validity of the Burton equation. The entire 37-year history of solar wind measurements was examined creating a sequence of joint probability distributions corresponding to fixed bins of VBs. Each
distribution shows the probability of a particular Dst given
a specific Dst with VBs essentially constant. In each distribution we fit the median Dst versus Dst to a polynomial in
Dst. The fits are almost precisely straight lines. The slope
and intercepts of these lines depend on VBs allowing us to
obtain analytic fits to the parameters of the Burton equation. The absence of any quadratic or higher terms in the
polynomial fits implies that Dst is a linear function of Dst
throughout the Dst - Dst phase space. This is precisely the
relation implied by the Burton equation!
3. ANALYSIS METHOD
Justified by our previous experience we continue our examination of the Burton equation with linear filters as expressed in (4). However, we now assume that the unknown
parameters in this equation are functions only of VBs. We
thus divide the 37-year history of solar wind observations
into subsets characterized by specific intervals of VBs. For
each bin , b, c, and A(VBs) are assumed constant. This fact
complicates the solution of (4) because the coefficients are
then constrained by linear relations between them, e.g. the
coefficient for Dst is fixed, while other coefficients are related to this one. If we ignore this fact for a moment (4)
can be written in the form
Dst  Dst   p  
p 
(5)
In this equation Dst and p are scalar time series with
one-hour time resolution. The first differences of these
[Dst and p] are easily calculated with due consideration
for flags denoting missing records. Equation 5 with fixed
coefficients applies to every unflagged hourly record in
each subset of the data. This collection of records defines
an over-determined set of equations for the unknown coefficients. Unfortunately, the coefficients are not independent
because the unknown  relates them. However, if we fix
which is possible since VBs is fixed, then the coefficients are related by linear constraints. We can use either
constrained least square or nonlinear optimization techniques to obtain the solution for the unknown parameters.
The two methods give identical results. It should be emphasized, however, that the parameters cannot be treated as
independent in a standard least square analysis. The constraints produce a significant correction.
3.1. Solution for Southward IMF
To define the filter coefficients for southward IMF we
must define a set of VBs bins. If these are too narrow then a
stable solution cannot be obtained. We find by experience
that 100 or more records are needed to accurately define
the coefficients for a specific VBs bin. However, the extreme values of VBs that create large storms are so rare that
it is impossible to obtain this many records for values of
VBs exceeding 10 mV/m. We have used a set of bins of
increasing width as the magnitude of VBs increases to partially compensate for the decreasing probability of a given
VBs. Even so, the extreme bins are quite wide and the calculated model coefficients are highly variable and somewhat suspect. In spite of this problem the coefficients display a systematic dependence on VBs.
Figure 1 presents four panels displaying graphs of various parameters as a function of VBs. The top left panel
contains the rate of ring current injection as a function of
VBs. The rate is clearly a linear function of VBs as shown
by the straight line fit. The slope of this line,
(4.65 nT/hr)/(mV/m), is close to the value obtained in previous studies. The top right panel presents the ring current
decay rate versus VBs. This rate decreases exponentially
from about 15 hours with northward IMF to approximately
Figure 1.
5 hours when VBs is greater than 10 mV/m. An analytic fit
to this curve is shown in the graph. The form of this function was derived from physical arguments by O'Brien and
McPherron [2000a], but the parameters were determined
by nonlinear inversion from the data plotted here. The bottom left panel shows the pressure constant versus VBs.
This function also decreases exponentially from its value
for northward field (>8 nT/(nP)) to a value close to 2. An
arbitrary function has been fit to the data with the results
shown in the graph. The fourth panel shows the number of
records used to determine the coefficients for each VBs bin.
For the most extreme bin near 20 mV/m there were only 10
occurrences in the 37 years of data.
3.2. Calculation of the Ring Current Injection Function
Previous work suggests that the rate of injection into the
ring current and its rate of decay are controlled by solar
wind VBs [Burton et al., 1975; O'Brien and McPherron,
2000a]. This assumption allows us to combine the injection
function Q(t) = A(VBs) and the quiet magnetopause correction (ct) into a single term in the regression equation
(4). We then sort our data into bins of constant VBs and use
the data from each bin to determine the coefficients of the
regression equation. The results plotted in Figure 1 indicate
that the offset term, VBs, in (5) is nearly a linear function of VBs. The injection function, A(VBs) can be calculated from the offset, , using the equation
A(VBs )   (VBs )  c
t
 (VBs )
(6)
If we assume that there is no ring current injection for
northward IMF, i.e. A(VBs=0) = 0, then the constant c in
(6) can be determined from our regression coefficients. We
find c = (0)/t = -4.6 nT. Substituting this value into
(6) gives us an equation for A(VBs), for any value of VBs.
Because of the nonlinear dependence of  on VBs this
equation is clearly nonlinear. However, note that the magnitude of the magnetopause correction term is always less
than 1.0 while the offset ranges from 0 to 100. Thus the
offset is important only near VBs = 0. Elsewhere A(VBs) is
well approximated by the linear relation shown in the figure. Despite this, any small departure from linearity near
zero is important. A linear fit to A(VBs) intercepts the VBs
axis at 0.53 (mV/m). Using the linear fit for smaller values
of VBs implies VBs causes a loss of energy from the ring
current. Thus, as did Burton et al. [1975] we introduce a
cutoff electric field Ec = -0.53 mV/m so that for weaker
fields we set A(VBs) = 0. A better approximation would be
to use a polynomial fit in the interval 0.0 to 1.0 mV/m.
3.3. Quality of the Dst Predictions
Solutions for the ARMA filter coefficients may be used
to model the data that defined them.
changes
 The predicted

for each VBs bin are given by Dst  ( X )c where (X) is
the matrix with columns containing the independent varia
bles in (5), and c is the vector of coefficients dependent
on VBs. Using the collection of solutions calculated for all
VBs bins we can generate a time series of Dst that may be
compared to the observed Dst. This change may then be
added to the current value of the observed Dst to predict the
next Dst. Note that this prediction utilizes the observed Dst
and solar wind parameters for each hour. This procedure is
referred to as one-step prediction.
A scatter plot of the predicted Dst versus observed Dst
shows a correlation of only 0.606. This average translates
to a prediction efficiency of only 37%. This means that
most of the variance in Dst is not predictable! None-theless, when the predicted change is added to the current
measured Dst, the predicted Dst for the next hour agrees
with the observed with a prediction efficiency of order
99%. The reason for this is that most of the predicted Dst
consists of the currently observed Dst so that the next Dst is
very close to that observed. This one-step prediction accuracy has little meaning since in an operational situation
measured Dst values are not available. Operationally we
must perform multi-step predictions as discussed in the
next section.
3.4. Multi-step Prediction of Dst Using Analytic Fits to
Model Coefficients
A multi-step prediction is achieved by integrating the regression equation (5) from a known initial condition. First
expand Dst to obtain
Dst (n  1)  (1   ) Dst (n)   p  
p 
(7)
If we start with a known value of Dst, now available
within about 24 hours, we can integrate forward in time to
the current time. In this integration we “feedback” the
previous prediction to calculate the next Dst that is added
to the previous prediction to obtain the next Dst. This is
referred to as multi-step prediction and provides a much
more stringent test of the model. Once the integration
reaches the current time it can be advanced only as fast as
data on the input are acquired. In this integration we use
the analytic fits to the various coefficients rather than the
tabular results of modeling. This assures more continuous
change in the coefficients as the state of the solar wind
changes.
Figure 2 presents illustrations of the results from this integration. Each panel contains a short segment of continuous solar wind data that has been integrated starting from a
Figure 2
measured value of Dst. Unfortunately, the main problem in
predicting geomagnetic activity is the presence of frequent
gaps in the solar wind input data. To perform the integration across such gaps it is necessary to assume the behavior
of the solar wind. These assumptions are almost always
wrong and introduce large errors in the predicted time series. It takes many hours for the prediction to converge
back to the correct solution. To avoid this problem here we
have scanned the entire 37-year record identifying all intervals with 12 or more hours of continuous data. For each
of these intervals we start the integration with the known
value of Dst and integrate to the end of the interval using
feedback of the prediction. This technique allows us to
determine the best possible prediction efficiency for the
method. The four examples were selected by the requirement that the interval contain more than 100 hours of data,
and the prediction efficiency for these intervals exceeds
89%. Thus the four intervals are the best possible illustrations of the quality of the predictions. Three curves are
plotted in each panel: the observed Dst, the 1-step prediction, and the multi-step prediction. The 1-step prediction is
indistinguishable from the original. The heavy line shows
the multi-step prediction is also very close to the observed
index for these intervals.
The average correlation for the entire data set is 0.872
corresponding to a prediction efficiency of 76%. The rms
error of the prediction relative to the data is only 10.6 nT!
This is close to the expected error in Dst produced by a
variety of problems in its generation. It is also better than
the second order fits obtained by Vassiliadis et al. [1999a]
assuming that the coefficients depend on Dst, Dst, and
VBs. However, this comparison is somewhat misleading
since they use 5-minute data that contains considerable
more variance than does hourly data.
4. DISCUSSION AND CONCLUSIONS
In this paper we have developed an algorithm for predicting the hourly Dst index from upstream observations of
the solar wind. Our technique is an extension of the work
of Burton et al. [1975] who derived a simple first order
differential equation for Dst based on physical principles.
This equation equates the rate of change of pressure corrected Dst to the difference between injection by the solar
wind and decay by charge exchange. Burton et al. [1975]
assumed that all coefficients in the differential equation
were constant with time and state of the magnetosphere,
and then determined their values empirically from small
datasets of 2.5-minute data. They demonstrated that an
integral of the equation from a known starting value, driven by measured inputs, provided a good fit to the data and
could be used as a forecast tool provided real time observations are available.
It is extremely difficult to compare our results to those
obtained by earlier workers. Some have used higher time
resolution, most have used smaller datasets, often authors
consider only a fixed point in the solar cycle, in some cases
they have used a second order differential equation (more
coefficients in the filters), and different methods of localization. Others have used alternative solar wind coupling
functions. Pressure correction are often ignored or not determined self-consistently with estimates of the ARMA
coefficients. A comparison of our prediction efficiency
(~76%), or rms error (~11 nT), with values quoted in previous papers suggests our method is equal or superior to
others. However, comparison with 5-minute Dst predictions
are misleading because these data have higher variance and
are therefore more difficult to predict. On the other hand,
other models use more parameters than does ours so that
should improve the quality of their fits.
Our results show that both the ring current decay time
and the dynamic pressure coefficients depend on the
strength of the solar wind electric field. The dependence of
 on VBs is consistent with previous reports that claim that
it is much shorter during the main phase than in the recovery phase. O'Brien and McPherron [2000a] have suggested
this variation is a consequence of changes in location of the
inner boundary of convection and the charge exchange
decay rate relevant to this location as a function of VBs.
The exponential decrease of b with VBs may have a simple explanation. As VBs increases a stronger tail current is
closer to the Earth. An increase in dynamic pressure will
increase the tail field thus increasing the tail current. The
effect of this current on the Earth is opposite to that of the
magnetopause current and so partially compensates for the
increase caused by an increase in the magnetopause current. Let us assume that the pressure contribution to Dst is
the difference between the effects of the magnetopause and
magnetotail, and that the effect of the magnetopause does
not change with VBs.
Dst  Magnetopause  Magnetotail
Dst  bMP p dyn  bTail VBs  p dyn
 bMP  bTail VBs  p dyn  b(VBs ) p dyn
Our value for b(VBs) during northward field is smaller
than the value expected theoretically (8 rather 16 nT/(nP))
suggesting that at quiet times the contribution to Dst from
the tail is half that expected from the magnetopause. When
VBs reaches –20 mV/m, b(VBs) appears to be about 2. If
this is the correct explanation of the apparent change in b
then the tail current must affect Dst far more than previously realized.
In conclusion we believe that we have improved our
ability to predict the hourly Dst index from upstream data.
The algorithm is simple, involving only three parametric
relations for the coefficient dependence on the solar wind
electric field. The method requires continuous tracking of
the solar wind and that the data be transferred to the Earth
in real time so as to provide sufficient time delay to allow a
calculation of the next hourly value prior to the end of the
hour. A version of this algorithm has been implemented at
www.igpp.ucla.edu/swcgag/. A predicted Dst index is updated hourly and past values are compared to the Kyoto
Sym-H index for validation. A brief description of the real
time algorithm will appear in O'Brien and McPherron
[2000b].
Acknowledgments. The authors would like to acknowledge frequent helpful discussions of the Dst prediction problem with A.
Klimas, D. Vassiliadis and T. Detman. This work has been supported by grants from the NSF under the space weather prediction
program [NSF ATM 96-13667 & NSF ATM 99-72069].
REFERENCES
Burton, R.K., R.L. McPherron, and C.T. Russell, An empirical
relationship between interplanetary conditions and Dst,
J. Geophys. Res., 80(31), 4204-4214, 1975.
Dessler, A.J., and E.N. Parker, Hydromagnetic theory of magnetic storms, J. Geophys. Res., 64(12), 2239-2259, 1959.
Klimas, A.J., D. Vassiliadis, and D.N. Baker, Dst index prediction
using data-derived analogues of the magnetospheric
dynamics, J. Geophys. Res., 103(A9), 20,435-20,447,
1998.
O'Brien, T.P., and R.L. McPherron, An empirical phase-space
analysis of ring current dynamics: solar wind control of
injection and decay, J. Geophys. Res., 105(A4), 77077719, 2000a.
O'Brien, T.P., and R.L. McPherron, Forecasting the ring current
index Dst in real time, JASTP, in press, 2000b.
Reiff, P.H., and J.G. Luhmann, Solar wind control of the polarcap voltage, Solar Wind-Magnetosphere Coupling,
1986.
Sckopke, N., A general relation between the energy of trapped
particles and the disturbance field over the earth,, J.
Geophys. Res., 71(13), 3125-3130, 1966.
Vassiliadis, D., A.J. Klimas, and D.N. Baker, Models of Dst geomagnetic activity and of its coupling to solar wind parameters, Phys. Chem. Earth (C), 24(1-3), 107-112,
1999a.
Vassiliadis, D., A.J. Klimas, J.A. Valdivia, and D.N. Baker, The
Dst geomagnetic response as a function of storm phase
and amplitude and the solar wind electric field, J. Geophys. Res., 104(A11), 24,957-24,976, 1999b.
_____________
R. L. McPherron and Paul O’Brien, Institute of Geophysics
and Planetary Physics, University of California Los Angeles, Los
Angeles, CA 90095-1567
(e-mail:
[email protected]; [email protected])
FIGURE CAPTIONS
Figure 1. Graphs of the coefficients of the Dst prediction equation (4) versus VBs. Parametric fits to the relations are shown in
each panel. Clockwise from the upper left the panels present the
offset ( in equation 5), the decay time , the number of hourly
records used to make the fits in each VBs bin, and the pressure
constant b.
Figure 2. A comparison of the waveforms of the modeled and
observed changes in Dst. The four longest intervals of contiguous
data with prediction efficiencies above 89% were selected for the
illustration.
Figure 1. Graphs of the coefficients of the Dst prediction equation (4) versus VBs. Parametric fits to the relations are
shown in each panel. Clockwise from the upper left the panels present the offset ( in equation 5), the decay time , the
number of hourly records used to make the fits in each VBs bin, and the pressure constant b.
Figure 2. A comparison of the waveforms of the modeled and observed changes in Dst. The four longest intervals of
contiguous data with prediction efficiencies above 89% were selected for the illustration.
PREDICTING Dst
PREDICTING Dst
PREDICTING Dst
PREDICTING Dst
PREDICTING Dst
PREDICTING Dst
McPHERRON AND O’BRIEN
McPHERRON AND O’BRIEN
McPHERRON AND O’BRIEN
McPHERRON AND O’BRIEN
McPHERRON AND O’BRIEN
McPHERRON AND O’BRIEN
VBs COUPLING CONSTANT
DECAY TIME
15
0

-20
tau (hrs )
Offs et (nT)
Off=-4.65VBs -0.05
-40
-60
( 4.16/( 3.27+VBs))
 3.81e
10
5
-80
0
5
10
15
0
20
PRESSURE CONSTANT
10
15
20
10
b=2.26+9.47e-VBs/2.40
# s am ples
b (nt/s qrt(nP))
5
DATA STATISTICS
5
12
10
0
8
6
4
2
0
Figure 1
0
0
5
10
15
<VBs > (m V/m )
20
10
0
5
10
15
<VBs > (m V/m )
20
23-Sep-1981 12:00:00
01-Apr-1982 12:00:00
50
50
PEF=90.01
PEF=89.11
0
Dst(nt)
Dst(nt)
0
-50
-100
09/23
09/25
09/27
-50
-100
04/01
09/29
29-Mar-1973 21:00:00
04/03
04/05
04/07
25-Nov-1978 09:00:00
0
0
-50
-100
Dst(nt)
Dst(nt)
-50
-150
-200
PEF=94.48
-250
03/29
03/31
Date
Figure 2
-100
Obs Dst
1-step Pred
N-step Pred
PEF=93.51
04/02
04/04
-150
11/24 11/26 11/28 11/30 12/02
Date