Two geomagnetic regional models for Albania and south-east Italy from 1990 to 2010 with prediction to 2012 and comparison with IGRF-11

Abstract

Here we present a revised geomagnetic reference model for the region comprising Albanian territory, south-east part of Italian Peninsula and Ionian Sea from 1990 to 2010 with prediction to 2012. This study is based on the datasets of magnetic measurements taken during different campaigns in Albania and Italy in the time of concern, together with a total intensity data set from the Ørsted and CHAMP satellite missions. The model is designed to represent the Cartesian components, X , Y , Z and the total intensity F of the main geomagnetic field (and its secular variation) for the period of interest. To develop the model, we applied a Spherical Cap Harmonic Analysis (SCHA) of the geomagnetic potential over a 16 • cap with most of the observations concentrated in the central 4 • half-angle. The use of a larger cap than that containing the data was made to reduce the typical problems in SV modelling over small regions. Also a new technique, called "Radially Simplified Spherical Cap Harmonic Analysis" (RS-SCHA), was developed to improve the model especially in the radial variation of the geomagnetic field components. Both these models provide an optimal representation of the geomagnetic field in the considered region compared with the International Geomagnetic Reference Field model (IGRF-11) and can be used as reference models to reduce magnetic surveys undertaken in the area during the time of validity of the model, or to extrapolate the field till 2012.

Full text

Earth Planets Space,62, 1–9, 2010
Two geomagnetic regional models for Albania and south-east Italy
from 1990 to 2010 with prediction to 2012
and comparison with IGRF-11
Enkelejda Qamili1,2, Angelo De Santis1, Gianfranco Cianchini1,2, Bejo Duka3,
Luis R. Gaya-Piqu´
e4, Guido Dominici1, and Niko Hyka3
1Istituto Nazionale di Geofisica e Vulcanologia, Roma 2, Roma, Italy
2Scuola di Dottorato in Scienze Polari, Universit`
a degli studi di Siena, Siena, Italy
3Department of Physics, Faculty of Natural Sciences, University of Tirana, Albania
4On-Site Inspection Division, Comprehensive Nuclear-Test Ban Treaty Organization PrepCom, Vienna, Austria
(Received March 18, 2010; Revised June 23, 2010; Accepted July 20, 2010; Online published xxxx xx, 2010)
Here we present a revised geomagnetic reference model for the region comprising Albanian territory, south-
east part of Italian Peninsula and Ionian Sea from 1990 to 2010 with prediction to 2012. This study is based
on the datasets of magnetic measurements taken during different campaigns in Albania and Italy in the time of
concern, together with a total intensity data set from the Ørsted and CHAMP satellite missions. The model is
designed to represent the Cartesian components, X,Y,Zand the total intensity Fof the main geomagnetic field
(and its secular variation) for the period of interest. To develop the model, we applied a Spherical Cap Harmonic
Analysis (SCHA) of the geomagnetic potential over a 16◦cap with most of the observations concentrated in
the central 4◦half-angle. The use of a larger cap than that containing the data was made to reduce the typical
problems in SV modelling over small regions. Also a new technique, called “Radially Simplified Spherical Cap
Harmonic Analysis” (RS-SCHA), was developed to improve the model especially in the radial variation of the
geomagnetic field components. Both these models provide an optimal representation of the geomagnetic field in
the considered region compared with the International Geomagnetic Reference Field model (IGRF-11) and can
be used as reference models to reduce magnetic surveys undertaken in the area during the time of validity of the
model, or to extrapolate the field till 2012.
Key words: Regional geomagnetic modelling, spherical cap harmonic analysis, magnetic ground and satellite
data.
1. Introduction
There is a clear need to measure and model the values
of the main geomagnetic field and its secular variation at
global and regional scales. In this paper we present two ge-
omagnetic reference field models for the region comprising
Albania, south-east Italy and surrounding sea areas from
1990 to 2010 with a prediction to 2012 using data from
magnetic repeat station surveys and satellites. The repeat
stations are the points of a magnetic network where the
three-component magnetic field is periodically measured at
intervals of some years (e.g. Newitt et al., 1996). The region
under investigation is however not uniformly covered by
ground magnetic measurements. The complete Italian terri-
tory on the other hand is comprehensively covered by mag-
netic repeat station measurements whereas the Albanian
territory has always been poorly surveyed. Thanks to the
short distance between these two countries, during the last
20 years there have been continuous collaboration between
the “Istituto Nazionale di Geofisica e Vulcanologia” (INGV;
Copyright c
The Society of Geomagnetism and Earth, Planetary and Space Sci-
ences (SGEPSS); The Seismological Society of Japan; The Volcanological Society
of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sci-
ences; TERRAPUB.
doi:10.5047/eps.xxxx.xx.xxx
“Istituto Nazionale di Geofisica”, ING till 2001), which is
the Italian Institution responsible of the magnetic monitor-
ing in Italy, and the Academy of Science of Albania, Centre
of Geochemistry and Geophysics (CGG) and Physics De-
partment of Tirana University (PDTU), i.e. the Albanian
Institutions that usually perform magnetic measurements in
Albania. This collaboration has leaded to coordinate spe-
cific campaigns of geomagnetic surveys over a designed re-
peat station network in Albania. As mentioned in a previ-
ous paper (Duka et al., 2004), INGV provided some per-
sonnel and instruments during the performance of measure-
ment campaigns and afterwards with the competence in the
modelling procedure.
In order to develop our regional reference field model, in
this paper we make extensive use of the datasets of magnetic
measurements in Albania from 1990 till present, together
with recent results from the Italian repeat station network
and from the Ørsted and CHAMP satellite missions. First
we compute a regional model by means of SCHA (Haines,
1985) with polynomial time dependency. Then, we present
a new technique (RS-SCHA) which is a simplification of the
former in the radial variation function. Both the techniques
provide an optimal representation of the geomagnetic field
over the area of investigation, which is an improvement on
1
EPS2874IGRF11 galley proofs

2 E. QAMILI et al.: XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX
a) b) c)
Fig. 1. (a) Location of Italian and Albanian ground magnetic data with 18 vector and scalar magnetic field data points (red stars) and 28 scalar magnetic
field data points (green squares) from 1990 to 2010; 19 synthetic vector data points from IGRF-11 (blue circles) at 5-year intervals from 1990 to
2005: (b) and (c) are the location of Ørsted (red circles) and CHAMP (green circles) satellite data used for the SCHA, respectively, from 1999.4 to
2009.4.
the International Geomagnetic Reference Field (IGRF-11).
Since most of the recent analysed data were not used to
form IGRF-11, this work represents also an independent
test of the global model.
2. Data
The data used in this study have been collected dur-
ing different Italian (vector and scalar measurements from
1990.5 to 2010.0) and Albanian (vector and scalar measure-
ments from 1990.0 to 2009.7) magnetic repeat station sur-
veys (Duka et al., 2004). In particular, 12 stations of the
Albanian network have been taken into account in addition
to 6 stations located in southern Italy. Because of the poor
coverage of this area with geomagnetic data, especially at
the borders of this cap, we calculated from IGRF-11 field
model the corresponding synthetic Cartesian X,Y,Zcom-
ponents at sea level in 19 fixed points of this area, at years
1990, 1995, 2000 and 2005 (blue circles in Fig. 1(a)). Loca-
tions of all ground geomagnetic measurements and selected
Ørsted and CHAMP satellite data are shown in Fig. 1(a),
1(b) and 1(c), respectively.
The older dataset of magnetic measurements used here
is the total intensity Fmeasured by means of a proton
magnetometer around 1990.0 by the former Geophysical
Enterprise of Tirana and covers all Albanian territory with
an array of 28 sites (Duka and Bushati, 1991). In September
1994 (epoch 1994.75), in the framework of a joint project
between the CGG, PDTU and the former ING a new vector
magnetic survey measuring F, inclination Iand declination
D(Chiappini et al., 1997, 1999) covered the Albanian terri-
tory. The measurements were taken by using a Geometrics
proton magnetometer and a Bartington fluxgate theodo-
lite, together with a gyro-theodolite for the absolute de-
termination of the geographical azimuth. In August 2003
(epoch 2003.6; Duka et al., 2004) another scalar field cam-
paign was conducted for the total intensity Fonly using an
Overhauser effect magnetometer, repeating the scalar mea-
surements at 10 of the 28 sites of the previous Fsurvey. At
each site data were recorded for 1–2 hours in order to obtain
a satisfactory accumulation of total intensity data.
Another three component survey in the Albanian territory
was made in September 2004 when a total of 12 (with
the addition of Berat station) vector measurements were
undertaken. In order to remove the effect of the diurnal
variation, for the full duration of the campaign, a temporary
station with a fluxgate variometer (30 sec. sampling) was
installed not far from Tirana for the full duration of the
campaign to reduce all values to the closest night time.
During September 2009 (epoch 2009.7) INGV carried
out the last campaign of absolute measurements at all
the 2004 points, measuring F,Iand Dmagnetic ele-
ments. These data were reduced using data from L’Aquila
Observatory because of some malfunctions in an installed
temporary station in Tirana (Albania).
To derive a more representative and accurate model, we
analyse together with the measurements in Albania, also
those in Italian territory, in particular we considered 6 lo-
cations from the Italian magnetic repeat stations network
placed in South-East Italy (Dominici et al., 2007). For a
better temporal behaviour of the model and to improve the
stability of the inversion, we have synthesized X,Yand Z
components at the limits of the considered temporal inter-
val, i.e. 1990.0 and 2010.0, for the 12 Albanian stations re-
ducing the real vector measurements available for 1994.75
and 2009.7 to the closest extreme epoch. The corresponding
temporal reduction was made applying the secular variation
predicted by an updated version of the Italian geomagnetic
reference field model (ITGRF; De Santis et al., 2003), a
model that has been demonstrated to predict the temporal
change of the magnetic field in this area better than global
models, such as the IGRF-11 field model. With the aim of
temporal stability, we added also L’Aquila observatory an-
nual means from 1990.5 to 2010.0.
To overcome the non-uniform distribution of the data
in this region (especially for the sea area), and since our
models will take into account the proper altitude variation

E. QAMILI et al.: XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX 3
Table 1. Model coefficients gm
k,q
and hm
k,q
in nT/yearq
of the Albanian-Italian Geomagnetic Reference Model developed by SCHA. Final model values
are obtained adding the IGRF-11 field values at 2000.0.
km n
k(m)gm
k,0hm
k,0gm
k,1hm
k,1gm
k,2hm
k,2gm
k,3
0 0 0 109.525 −375.209 −69.876 49.579
1 0 8.1068 −20.418 13.921 9.367
1 1 6.1481 −0.902 −21.239 14.851 −140.221 11.438 −10.827
2 0 13.2304 3.474 −7.619
2 1 13.2304 0.172 8.193 −0.226 32.542
2 2 10.5214 −7.947 −4.328 −7.25 −6.688
of the field, together with the ground data we also included
a set of total intensity magnetic field measurements from
Ørsted and CHAMP satellite missions, selected between
1999.4 and 2009.4 during low external magnetic activity
characterized by Kp≤3 and |Dst |≤10 nT magnetic
indices.
The different datasets were weighted according to the
reciprocal of the variance of the total error associated with
the measurements (Duka et al., 2004). Each variance was
computed as the sum of the error σmintrinsically involved
in the measurement process (instrumental errors, etc.) and
that related to the lithospheric field, σl. We assumed that the
ground data have σl=50 nT and σm=10 nT, whereas no
lithospheric contribution was assigned to satellite data, and
their σmwas set equal to that of ground data.
In the next section we will apply our regional tech-
niques to the data set obtained from the original ob-
servations after removing the main field predicted by
IGRF-10 (Macmillan and Maus, 2005) and IGRF-11
(http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html) up to
degree 13 at the central epoch (2000.0).
3. Spherical Cap Harmonic Analysis Model and a
Radially Simplified Version
Modelling the geomagnetic field over the whole terres-
trial sphere is usually approached using spherical harmonic
analysis (SHA). When we are interested only in details
of a certain area with typical lengths shorter than a given
size (say, one thousand km, like the area under investiga-
tion), we must resort to a local analysis. The first regional
model we propose is based on the Spherical Cap Harmonic
Analysis (SCHA; Haines, 1985). The SCHA is a power-
ful analytical tool for modelling Laplacian potential and the
corresponding field components over a spherical cap, over-
coming most of the problems (e.g., non-orthogonality and
huge number of model coefficients) that arise when global
spherical harmonic models are applied to restricted areas.
Introduced for the first time in 1985 by Haines, SCHA
has evolved progressively during the recent years (e.g. De
Santis et al., 1991, 1992) finally arriving to the Revised
SCHA (R-SCHA; Th´
ebault et al., 2004, 2006).
The solution of Laplace’s equation in spherical coordi-
nates (r,θ,φ) for the magnetic potential due to internal
sources (thus the subscript “int” for K) over a spherical cap
can be written as an expansion of non integer-degree spher-
ical harmonics:
V=a
Kint

k=0
k

m=0a
rnk(m)+1
Pm
nk(m)(cos θ)
·
Q

q=0gm
k,qcos(mφ) +hm
k,qsin(mφ)·tq(1)
where the polynomial time dependency is included: this al-
lows to easily extrapolate the model forward in time (we
propose here a prediction up to 2012); gm
k,qand hm
k,qare
the spherical cap harmonic coefficients that determine the
model; Pm
nk(m)(cos θ) are the associated Legendre functions
that satisfy appropriate boundary conditions (null potential
or co-latitudinal derivative at the border of the cap) and have
integer order mand generally non-integer degree nk(m);k
is an integer index selected to arrange, in increasing order,
the different roots nfor a given min the boundary condi-
tions. The number of coefficients depends on the maximum
spatial and temporal indices of the expansion, Kint and Q,
respectively.
The geomagnetic components X,Yand Zare obtained as
appropriate spatial derivatives of Eq. (1) in spherical coor-
dinates, since the potential is non-observable. To overcome
the non linearity problem that arises when combining vector
measurements with total field measurements, we used a first
order Taylor expansion of the total magnetic field intensity,
as a square root function of the X,Yand Zcomponents
(Haines and Newitt, 1997).
After many tests, the model parameters that best repre-
sent the input data in the period between 1990 and 2010
were found to be Kint =2 and Q=3. The gm
k,qand hm
k,q
coefficients were obtained through a least squares regres-
sion procedure.
The model so defined was chosen with basis functions
defined over a cap with a semi-angle of 16◦, in order to
represent the main field and its secular variation, includ-
ing the most significant harmonics of the regional geomag-
netic field (the minimum and maximum degrees are approx-
imately equal to 6.1 and 13.2, respectively). In order to
reduce the typical problems in SV modelling over small re-
gions (e.g., Torta et al., 2006), we chose to use a larger cap
than that actually containing the data. Of course this choice
is made at expenses of losing the orthogonality of the ba-
sis functions over the data interval, since the real data are
mostly concentrated within the central 4◦half-angle. How-
ever we still have the advantage of reducing significantly
the number of model coefficients and improving the quality
of the model. The coefficients of the Albanian-Italian Ge-
omagnetic Reference Model developed by SCHA for this
region are shown in the Table 1. The final model values are
obtained with the addition of IGRF-11 values at 2000.0.
After this SCHA model, here we present also another

4 E. QAMILI et al.: XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX
Table 2. Model coefficients gm
k,q
and hm
k,q
in nT/yearq
of the Albanian Geomagnetic Reference Model developed by RS-SCHA. Final model values are
obtained adding the IGRF-11 field values at 2000.0.
km n
k(m)gm
k,0hm
k,0gm
k,1hm
k,1gm
k,2hm
k,2gm
k,3
00 0 −20.636 −322.601 −1.308 50.145
1 0 8.1068 9.336 −22.656 8.562
1 1 6.1481 2.224 −28.61 −18.668 −113.745 10.712 −11.294
2 0 13.2304 −8.31 6.178
2 1 13.2304 −1.462 12.034 16.725 19.064
2 2 10.5214 −6.824 −4.676 −8.258 −7.37
Table 3. Root mean square fits of SCHA, RS-SCHA, IGRF-10 and IGRF-11 models to the analysed ground data and satellite data for magnetic field
(nT) (for the first four lines) and the secular variation (nT/yr) (for the second four lines). Underlined bold values are the best RMS values among the
models.
Ground Satellite
Model RMS XRMS YRMS ZRMS FRMS F
IGRF-10 44.0 73.0 53.1 60.5 28.4
IGRF-11 43.3 72.1 44.8 56.5 6.7
SCHA 39.4 62.0 42.7 50.6 4.6
RS-SCHA 35.6 61.8 38.4 45.6 4.6
SV-IGRF-10 6.3 4.2 6.4 6.5
SV-IGRF-11 6.1 6.1 5.5 5.3
SV-SCHA 6.2 6.0 5.7 5.3
SV-RS-SCHA 6.2 5.9 5.6 5.3
a) b) c)
Fig. 2. Maps (in nT) for X(top left), Y(top right), Z(bottom left), and F(bottom right) elements for epoch 2012.0 at sea level obtained from SCHA
(a), RS-SCHA (b) and IGRF-11 (c) models developed on an 16◦half-angle cap.
regional model that we consider a good compromise be-
tween the SHA and SCHA techniques. It takes advantage
of both the original concepts of the SCHA and those typ-
ical of the most recent R-SCHA. We call this new sim-
ple method “Radially Simplified Spherical Cap Harmonic
Analysis” (RS-SCHA). It consists in simplifying the ex-
pression in radial distance rof the geomagnetic potential V
in Eq. (1) “emulating” the radial behaviour of the conven-
tional spherical harmonics analysis (SHA) as follows:
V=a
Kint

k=0a
rk+1k

m=0
Pm
nk(m)(cos θ)
·
Q

q=0gm
k,qcos(mφ) +hm
k,qsin(mφ)·tq(2)
Please note that although this form of geomagnetic field po-
tential is not usual, nevertheless it satisfies Laplace’s equa-
tion separately for each spherical coordinate: indeed, for the
radial variation it is the typical solution in the global case,
while for the angular coordinates it is the typical SCHA so-
lution. Given the differences in the radial function only with
respect with the typical SCHA, we can affirm that our model
satisfies the Laplace’s equation at Earth’s surface (r=a).
When we consider satellite altitude we actually multiply all
surface spherical cap functions by a given constant that it
is taken into account in the final estimated model coeffi-
cients. Also here, the model is still solution of Laplace’s
equation at the ground or satellite altitudes. We admit that
there is a mixture of eigen-values m,nwhich is not cor-
rect. However this is analogous with what is normally done

E. QAMILI et al.: XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX 5
Fig. 3. Maps (in nT) for Ycomponent for epochs 1995.0 (top left), 2000.0 (top right), 2005.0 (bottom left) and 2010.0 (bottom right) at sea level
obtained from SCHA model. It is clear a fast westward drift of 0.4◦–0.5◦/year.
a) b) c)
Fig. 4. Maps (in nT/year) for the secular variation of X(top left), Y(top right), Z(bottom left), and F(bottom right) magnetic elements centred at
2005 (deduced from differences from 2004 to 2006) at sea level obtained from the SCHA (a), RS-SCHA (b) and IGRF-11 (c) models.
a) b) c)
Fig. 5. Maps (in nT/year) for the secular variation of X(top left), Y(top right), Z(bottom left), and F(bottom right) magnetic elements centred at
2010 (deduced from differences from 2009 to 2011) at sea level obtained from the SCHA (a), RS-SCHA (b) and IGRF-11 (c) models.

6 E. QAMILI et al.: XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX
Fig. 6. Comparison between observed (stars), SCHA, RS-SCHA and IGRF-11 X,Yand Zcomponents and total intensity Ffor sites of Tirana (Albania)
and Masseria Maserino (Italy).
when removing a SHA model (typically IGRF) from obser-
vations and then applying SCHA inversion (and vice-versa
when we synthesise the model values): the final potential is
the sum of two different potentials, a global and a regional
one, with two different n,msets; the former is characterised
by integer nvalues (SHA) while the latter is expressed with
non-integer nkvalues (SCHA or even R-SCHA). Our pro-
posal is such to say that SHA radial functions works better
than SCHA radial functions, at least for the area and the
period of interest.
To check the validity of this technique, we applied
the RS-SCHA to the region under investigation (Albania,

E. QAMILI et al.: XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX 7
Fig. 7. Comparison between observed (stars), SCHA, RS-SCHA and IGRF-11 values of the secular variation of the X,Yand Zcomponents and total
intensity Ffor sites of Tirana (Albania) and Masseria Maserino (Italy).
Southern part of Italy and surrounding seas) using the same
parameters as above (SCHA model). The final RS-SCHA
coefficients of the Albanian-Italian Geomagnetic Reference
Model are shown in Table 2. As in the previous case, the fi-
nal model values are obtained with the addition of IGRF-11
values at 2000.0.

8 E. QAMILI et al.: XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX
4. Results
Regional models usually represent the spatial and tempo-
ral variations in a particular region in more detail and accu-
racy compared to global geomagnetic models (e.g. IGRF-10
and IGRF-11). This is confirmed also by our analysis. Ta-
ble 3 shows the root mean square (RMS) fits of SCHA,
RS-SCHA, IGRF-10 and IGRF-11 models to the analysed
ground and satellite data for the magnetic field (in nT) and
its secular variation (in nT/yr). From a statistical analysis
in terms of RMS we see that both SCHA and RS-SCHA
techniques provide better results for the field in compari-
son with both IGRFs. In particular the RS-SCHA model
improves the fit of all ground and satellite components bet-
ter then IGRF-s and better than SCHA. Moreover, we see
that IGRF most recent version, IGRF-11, has better perfor-
mances than the previous version, especially for F satellite
data.
Figure 2 shows the regional X,Y,Zcharts for the anal-
ysed area for the epoch 2012.0 at sea level obtained from
SCHA, RS-SCHA and IGRF-11. The evaluation in time
from 1995 to 2010 of the geomagnetic field, especially of
the Ycomponent (Fig. 3), shows a clear fast westward drift
of the geomagnetic field (e.g. Barraclough et al., 1999) of
0.4◦–0.5◦/year.
To estimate the SV at some epoch we used the differ-
ences between two close epochs, one year before and one
year after; however the numerical results would have been
the same by performing numerical derivation of the poly-
nomial part of the regional models. All SV models (SCHA,
RS-SCHA and IGRF-11) show practically the same RMS
for all the components (Table 3) and confirm that the region
under study presents low SV values for this period (see,
Figs. 4 and 5), with less than 50 nT/year for all compo-
nents (e.g. Gubbins, 1990). We notice that the larger dif-
ferences in both the field and SV between IGRF-11 and
our regional models are in Albania. To better visualise this
fact, in Fig. 6 we show the differences between observed
data, SCHA, RS-SCHA and IGRF-11 values in X,Yand Z
components for the sites of Tirana (Albania) and Masseria
Maserino (Italy). As it can see, the IGRF-11 does not fit the
observations in the Albanian station as well as in the Italian
station. This could be probably ascribed to some crustal
bias present in the Albanian station but absent in Italian sta-
tions, details that only a regional model is able to grasp in
comparison with those provided by a global model. This is
confirmed by both SCHA and RS-SCHA models, especially
in Y- and Z-components when compared with IGRF-11.
The SV differences between observed data, SCHA, RS-
SCHA and IGRF-11 values in X,Yand Zand Ffor the
sites of Tirana (Albania) and Masseria Maserino (Italy) are
shown in Fig. 7. We notice that both regional models pro-
vide a better polynomial interpolation among the observed
SV components in the two repeat stations than the abrupt
IGRF-11 SV changes at each 5-year interval.
5. Conclusions
In this paper, we present two regional models for South-
East Italy, Albania and surrounding sea area, both based
on a spherical cap harmonic expansion of the potential but
with different radial functions. The introduction of a ra-
dially simplified version of SCHA, i.e. RS-SCHA, charac-
terised by a SHA-like radial variation of the field, allows us
to model both ground and satellite data better than SCHA.
The validity in time of both regional models is in the period
1990–2010 with prediction to 2012. One of our objectives
was also to show how IGRF-11 works in this area of the
world. The comparison between RMS fits of the regional
models to real data and those of IGRF allows us to con-
firm that both SCHA and RS-SCHA models represent an
improvement with respect to the global model when repre-
senting the field and its secular variation, probably because
some of the most recent data were not used to construct
IGRF-11 model. Thus in conclusion, the regional mod-
els can be used to estimate the values of the geomagnetic
field (and its secular variation) all over the region consid-
ered (South-East Italy and Albania, seas included). They
can be utilized as well for reducing magnetic survey data
taken in the area of interest in the period of validity of the
model.
Acknowledgments. We thank J. Miquel Torta and Peter Kotz`
e
for their comments that improved the paper. Financial supports
given by the Italian Foreign Ministry for the visits to Albania by
two co-authors (ADS and EQ) is gratefully acknowledged. INGV
supported the visit of Bejo Duka to Italy and two Magnetic Re-
peat Station Campaigns of the Italian group to Albania. Draw-
ings were made using the Generic Mapping Tools (GMT) (Wessel
1991). Part of this work was performed in the frame of the Italian-
Albanian bilateral project E-MAG,
References
Barraclough, D. R. and S. R. C. Malin, A fast moving feature of westword
drift, Ann. Geofis.,42(1), 21–26, 1999.
Chiappini, M., O. Battelli, S. Bushati, G. Dominici, B. Duka, and A.
Meloni, The Albanian geomagnetic repeat station network at 1994.75,
J. Geomag. Geoelectr.,49, 701–708, 1997.
Chiappini, M., A. De Santis, G. Dominici, and M. Torta, A normal refer-
ence field for the Ionian Sea area, Phys. Chem. Earth A,24(5), 433–438,
1999.
De Santis, A., Translated origin spherical cap harmonic analysis, Geophys.
J. Int.,106, 253–263, 1991.
De Santis, A., Conventional spherical harmonic analysis for regional mod-
elling of the geomagnetic field, Geophys. Res. Lett.,19, 1065–1067,
1992.
De Santis, A., L. R. Gaya-Piqu´
e, G. Dominici, A. Meloni, J. M. Torta,
and R. Tozzi, Italian Geomagnetic Reference Field (ITGRF): update
for 2000 and secular variation model up to 2005 by autoregressive
forecasting, Ann. Geophys.,46(3), 491–500, 2003.
Dominici, G., A. Meloni, M. Miconi, M. Pierozzi, and M. Sperti, Italian
Magnetic Network and Geomagnetic Field Maps of Italy at year 2005.0,
Boll. Geod. Sci. Affini,1, 1–47, 2007.
Duka, B. and S. Bushati, The normal geomagnetic field and the IGRF over
Albania, Boll. Geofis. Teor. Appl.,XXXIII(130/131), 129–134, 1991.
Duka, B., L. R. Gaya-Piqu´
e, A. De Santis, S. Bushati, M. Chiappini, and G.
Dominici, A geomagnetic reference model for Albania, Southern Italy
and the Ionian Sea from 1990 to 2005, Ann. Geophys.,47(5), 1609–
1615, 2004.
Duka, B., A. De Santis, and L. R. Gaya-Piqu´e, On the modelling of the
geomagnetic reference field over Balkan region, in Geomagnetics for
Aeronautical Safety: A Case Study in and around the Balkans, edited
by Rasson J. L. and T. Delipetrov, 83–95, Nato Advanced Study Series,
2006.
Gubbins, D., Geomagnetism: the next Millenium, Palaeogeogr.
Palaeoecol., Global Planet, Change Sec., 89, 255–262, 1990.
Haines, G. V., Spherical cap harmonic analysis, J. Geophys. Res.,90(B3),
2583–2591, 1985.
Haines, G. V. and L. R. Newitt, The Canadian geomagnetic reference field
1995, J. Geomag. Geoelectr.,49, 317–336, 1997.
Macmillan, S. and S. Maus, Modelling the Earth’s magnetic field: the 10th

E. QAMILI et al.: XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX 9
generation IGRF, Earth Planets Space,57(12), 1133–1133, 2005.
Newitt, L. R., C. E. Barton, and J. Bitterly, Guide for Magnetic Repeat
Station Surveys, International Association of Geomagnetism and Aeron-
omy, Boulder, Colorado, 1996.
Th´
ebault, E., J. J. Schott, M. Mandea, and J. P. Hoffbeck, A new proposal
for Spherical Cap Harmonic Analysis, Geophys. J. Int.,159, 83–105,
2004.
Th´
ebault, E., J. J. Schott, and M. Mandea, Revised spherical cap harmonic
analysis (R-SCHA): validation and properties, J. Geophys. Res.,11,
B01102, doi: 10.1029/2005JB003836, 2006.
Torta, J. M., L. R. Gaya-Piqu´
e, and A. De Santis, Spherical cap harmonic
analysis of the Geomagnetic Field with application for aeronautical
mapping, in Geomagnetics for Aeronautical Safety: A Case Study in and
around the Balkans, edited by Rasson, J. L. and T. Delipetrov, NATO
Security through science series, 291–307, 2006.
Wessel, P. and W. H. F. Smith, Free software helps map and display data,
Eos. Trans. AGU,72(41), 441, 445–446, 1991.
E. Qamili (e-mail: enkelejda.qamili@ingv.it), A. De Santis, G.
Cianchini, B. Duka, L. R. Gaya-Piqu´
e, G. Dominici, and N. Hyka