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National Geomagnetism Program
geomag-algorithms
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3ee9aa05
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3ee9aa05
authored
9 years ago
by
Eddie McWhirter
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Josh rewrote the readme to be much more concise.
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Solar Quiet and Disturbance
Algorithm
Geomagnetic Secular Variation,
Solar Quiet
,
and Disturbance
=====================================
=====================================
Algorithm Theoretical Basis for "Geomag Solar Quiet and Disturbance"
E. Joshua Rigler
<
[erigler@usgs.gov](mailto:erigler@usgs.gov)
>
E. Joshua Rigler
<
[erigler@usgs.gov](mailto:erigler@usgs.gov)
>
## Summary
Mathematical underpinnings and general algorithm considerations are presented
for estimating Solar Quiet (SQ), Secular Variation (SV) and Magnetic
Disturbance (DIST) data streams. SV describes the geomagnetic trend line
at a given moment, and is usually assumed to be a measure of the Earth’s
internal field. SQ is used to describe daily variations that result from the
Earth’s rotation beneath geospace electric currents that are mostly fixed
with respect to the sun. Finally, the value often of most interest in
space weather applications is DIST, or the remainder of the signal when SV
and SQ are removed. This is typically assumed to represent Earth’s magnetic
response to aperiodic solar storms.
## Background and Motivation
## Background and Motivation
The magnetic field measured at a given point on Earth’s surface is often
The magnetic field measured at a given point on Earth’s surface is often
assumed to be static. However, this localized geomagnetic field actually
assumed to be static, but in reality it is constantly changing, and on a
varies over time. Historically, SV has been modeled as a low-order polynomial.
variety of time scales associated with distinct physical phenomena. These are:
After removing SV (i.e., detrending), a set of Fourier terms were fit to the
data to model SQ. The problem with such an approach is that it assumes
-
Secular variation (SV) - slow variations in the geomagnetic field associated
knowledge of future observations, and is not directly useful for real time
with changes in Earth's interior.
operations. As such, an exponential smoothing algorithm was chosen as a more
-
Solar quiet variation (SQ) - shorter-term periodic variations in the
robust method to predict evolving periodic signals.
geomagnetic field associated with Earth's rotation beneath quasi-static
geospace electric currents that are phase-locked with the sun.
-
Disturbance (DIST) - shorter-term non-periodic variations in the geomagnetic
field, typically associated with episodic events like geomagnetic storms and
substorms.
SV is fairly easily separated from higher frequency variations using low-order
polynomials to
*detrend*
the data. SQ and DIST have similar time scales, and
are therefore more difficult to separate. Fourier series can be fit to data to
estimate SQ, which works well in non-real time situations. This approach
suffers in real time situations for both practical and theoretical reasons
that we won't discuss in detail here.
## Exponential Smoothing
Real time decomposition of geomagnetic time series into SV, SQ, and DIST should
explicitly acknowledge and address time-causal nature of real time
observations. To this end, we employ a form of exponential smoothing, with
"seasonal" adjustments, that updates estimates of SV and SQ based only on past
observations, weighting older observations less and less as time passes. In
effect, SV and SQ adapt to changing conditions at a predictable rate that can
be specified by the user.
In addition, this approach is significantly less computationally expensive than
traditional Fourier techniques. No Fourier transform of months-to-years-long
data series is required, and memory requirements are comparably reduced, since
a description of the state of the system at any given moment is only 1+m, where
m is the number of data points in an SQ cycle, nominally 1 day.
Finally, exponential smoothing is generally more robust to common issues with
real time data series; it easily extrapolates SV and SQ across gaps in the
data; it provides a running estimate of the variance of DIST, which can be used
to set a threshold for spike detection; and it adjusts SV to accommodate DC
offsets at rate specified by the user.
## Example
## Example
...
...
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