Transcript Presentation - Copernicus.org

New Unifying Procedure for PC index calculations.
P. Stauning
Danish Meteorological Institute (e-mail: [email protected]/phone: + 45 39157473)
)
Abstract. The Polar Cap (PC) index is a controversial topic within the IAGA
scientific community. Since 1997 discussions of the validity of the index to be
endorsed as an official IAGA index have ensued.
• Currently, there are now the three separate PC index versions constructed
from the different procedures used at the three institutes: the Arctic and
Antarctic Research Institute (AARI), the Danish Meteorological Institute (DMI),
and the Danish National Space Institute (DTU Space).
• It is demonstrated in this presentation, that two consistent unifying procedures
can be built from the best elements of the three different versions. One
procedure uses a set of coefficients aimed at the calculation of final PC index
values to be accepted by IAGA. The other procedure uses coefficients aimed at
on-line real-time production of preliminary PC index values for Space Weather
monitoring applications.
• For each of the two cases the same procedure is used for the northern (PCN)
and the southern (PCS) polar cap indices, and the derived PCN and PCS
coefficients are similar.
1. Basics. A high degree of correlation exists between polar cap horizontal
magnetic field variations ΔF and the ”Geo-effective” (or “merging”) Electric
Field, Em, that controls the global energy input from the Solar wind to the
Earth’s Magnetosphere (Kan and Lee, 1979):
Em = VSW • BT • sin2(/2)
(1)
BT = (BY2 + BZ2)1/2 : IMF transverse magnetic field component
= arctan(BY/BZ) : IMF polar angle with respect to the GSM Z-axis
We may increase the correlation by projecting ΔF to an “optimum” direction in
a polar cap coordinate system fixed with respect to the Sun-Earth direction.
The optimum direction is characterized by the angle, φ, between the equivalent
horizontal transverse current and the direction to the Sun and varies with local
time and season.
ΔFPROJ is a scalar quantity. A further increase in the correlation is obtained by
displacing the projected horizontal variation by an amount, β (intercept), which
also varies with local time and season.
Hence we are looking for the correlation between the modified polar cap
horizontal magnetic field variations ΔF* and the Solar Wind ”Geo-effective
Electric Field” Em of the form:
ΔF* = ΔFPROJ – β = α • Em
(2)
where β (e.g. in units of nT) is the baseline shift (“intercept”), while the
proportionality constant α is the “slope” (e.g. in units of nT/(mV/m)). The
parameters are calculated on a statistical basis from cases of measured values
through an extended epoch.
From equivalence with Em the dimensionless Polar Cap Index PC is defined
by:
PC == (ΔFPROJ – β)/α
(3)
The PC index is a measure of the polar geomagnetic activity corrected for daily
and seasonal variations but also a proxy for the geo-effective electric field Em
measured in mV/m
2. Interpretation of α and β. Before entering a discussion of the current PC
index types, a few basic statements should be made. Eq. 3 could be written:
PC = ΔFproj /α – β/ α
(4)
In this version it is easy to see the two limiting cases:
Highly disturbed conditions:
PC ~ ΔFproj /α when ΔFproj is very large
(5a)
Very quiet conditions:
PC ~ – β/ α
when ΔFproj is very small
(5b)
With these limiting cases it is easy to arrive at a basic understanding of the
physical interpretation of the two scaling coefficients.
Specifically, it should be noted, that the value of the parameter α defines the PC
index’ “sensitivity” to magnetic variations, while the parameter β (in combination
with α) defines the PC index value at quiescent conditions where ΔFproj is very
small.
3. Definition of magnetic variation vector. In the calculation of magnetic
variations, three variants have developed to derive the magnetic variation
vector, ΔF, from the observed magnetic data, FOBS , which could be described
by the following defining equations:
ΔF = FOBS - FBL
…. DTU-S (formerly DMI#2)
(6a)
ΔF = (FOBS - FBL) - FQDC
…..DMI
(6b)
ΔF = (FOBS - FBL– ΔFY) - FQDC
.... AARI
(6c)
In these expressions FBL is the slowly (secularly) varying baseline vector for the
day in question; FQDC is the quiet day (QDC) variation vector for the time in
question; ΔFY is an IMF By-related (solar wind sector dependent) correction
vector for the day in question. The terms FBL+ ΔFY could be combined.
6. PC index coefficients at AARI, DTUS and DMI. The
different ways to calculate magnetic variations are not the only
difference between the three current PC index variants (AARI,
DTU-S, and DMI).
8. Effects of reverse convection on PC indices. With the slope and intercept
data presented in the above figures (Figs. 2a-c), the formula for the PC index
(Eqs.3 and 4) and the approximations (Eqs. 5a and 5b), it is easy to see the
effect of including/excluding reverse convection cases.
The AARI and DTU-S (=old DMI) versions include reverse
convection cases in the data set used for calculation of
coefficients, which is why the intercept values tend to become
strongly negative during local summer days (Fig.2c below).
Including reverse convection cases makes the intercept more negative. Thus a
positive term is added to the PC index value. The slope is increased, which
reduces the PC index values. The combined effect is an increase of PC index
values at low disturbance levels and a decrease of PC index values at high
disturbance levels. In the example below PCN-DMIA are PCN values calculated
using AARI coefficients and DMI QDC procedure. The other index values are
contributed from their respective producers.:
The DMI version excludes reverse convection cases in the
calculation of coefficients (not in the calculation of PC index
values). Accordingly, the β-value is close to zero.
In the present DMI method the IMF By-related (solar wind sector related) The coefficients: optimum angle, slope, and intercept values
derived
for
PCN
in
the
three
versions
are
displayed
below.
contribution is included in the calculation of the QDC vector.
Each monthly segment (1/12 of the diagram width) displays
In the AARI version the QDC is found by averaged over an interval much the monthly average daily variation in the selected parameter.
longer than the sector structure and the IMF By-related contribution is
calculated separately.
Fig.2a
4. Intercept parameter. For extremely quiescent conditions, where the
merging electric field, Em, is zero, we would expect that the magnetic
deflection shall resort to just depict the QDC variation.
Fig.4
Hence, according to Eq. 2, the so-called intercept value, β, must be equal to
ΔFPROJ , i.e., the variation vector projected to the optimum direction.
If the QDC vector has already been subtracted from the total variation vector
(AARI and DMI procedure), then the resulting variation is zero, and thus the
intercept value, β, must also be zero. Since the β value should be zero for
each case of Em=0, then the smoothing over long time should not change the
result, i.e.: β = = 0.
Fig.2b
If the QDC has not been subtracted from the variation vector (DTU-S
procedure), then the intercept value, β, must be equal to the projected QDC
vector according to Eq. 2. Since the value of β is formed by averaging over
some time (several years) then the resulting β-value should equal the average
value of the projected QDC vector.
Fig.2c
5. Reverse convection. When actual calculations give another result, then the
calculations are possibly influenced by cases of reverse convection.
Figs. 1a,b illustrate the consequences of reverse convection cases for the
calculation of regression coefficients. We consider observations made at the
same UT time on several consecutive days.
For these days the projected QDC level is assumed to be Fq at the selected
UT time. For the 3 days we assume that corresponding values of Em and
ΔFproj are known and they are marked in the plots. The QDC value, Fq, is
subtracted to provide a set of three corrected magnetic variation values.
Hence, from these three days we can calculate the slope and intercept
parameters, for instance, with QD correction. Now, we assume that one day is
a reverse convection case (ΔFproj <0) while on the two remaining days
conditions are normal forward convection cases (ΔFproj >0).
7. Test of effects of reverse convection on intercept. Data
from Thule were used to derive the PCN coefficients (angle,
slope, intercept) with exactly the same calculations (QDC
subtracted) except the inclussion/omission of reverse convection
cases. The results for the intercept are shown below.
It is now easy to see that including reverse convection cases makes the slope
steeper (i.e., α larger) and the intercept more negative (i.e., β more negative)
Fig. 1a
Fig. 1b
Fig. 3a
Fig. 3b
The new procedure:
Calculation of coefficients for final PC index (black lines in Fig.2a-c):
• Remove reverse convection cases from reference data set.
• Calculate QDC and correct all magnetic variation samples.
• Calculate optimum angles, φ (as usual) and project all samples to optimum
direction.
• Set intercept parameters, β=0 (is small anyway) and calculate best slope, α values.
Calculation of final PC index values (QDC calculations needed):
• Calculate QDC and correct all magnetic variation samples.
• Project all samples to optimum direction using φ.
• Divide QDC-corrected, projected magnetic variation samples by α. (β=0)
Calculation of coefficients for temporary PC index (for on-line applications):
• Remove reverse convection samples from reference data set.
• Project all samples to optimum direction using above φ angles (from final case).
• Set slope, α, to above final case values and calculate best intercept, β values.
Calculation of temporary PC index values (no need to derive actual QDC):
• Project all samples to optimum direction using optimum angle , φ, from final case.
• Subtract intercept, β, from projected variation samples and divide result by slope, α.