procedure of ionospheric characteristics

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1 Radio Science, Volume 36, Number 5, Pages , September/October 2001 Generation of instantaneous. maps of ionospheric characteristics I. Stanistawska, G. Juchnikowski, and Z. Zbyszyfiski Space Research Centre, Polish Academy of Sciences, Warsaw, Poland Abstract. A way of producing limited-area instantaneous maps of ionospheric characteristics shown. An interpolation technique is applied for construction of the mapping model. The model combines monthly median maps of ionospheric characteristics and a set of measurements for a single moment of time that are exactly replicated during the mapping procedure. The accuracy of the mapping results is discussed, and samples of maps for different geophysical conditions for fof2, fofl,foe and M(3000)F 2 are presented. 1. Introduction where the number of observational data points can be adjusted to provide a near-exact solution to any specific Although monthly median maps of ionospheric required accuracy. When there are large areas in the characteristics can be a suitable representation of the ionosphere not covered by measurements, instantaneous average ionosphere, they are inadequate.for describing maps can be more accurately reproduced when the pure hourly or higher-frequency ionospherichanges. The interpolation method is augmented with synthesized values availability of instantaneous maps offof 2 or M(3000)F 2 is from a monthly median model. This enables us to construct of particular importance for HF point-to-point and Eartha map with higher precision [Edwards et al., 1975; space ionospheric propagation assessments. For this Stanislawska and Juchnikowski, 1997], as the monthly purpose, models more true to observations are required for median model itself contains physical information about map construction [Bradley, 1995]. Different empirical models have been developed [Bradley, 1995, and the expected gradients. There are various ways of using monthly median data in an instantaneous mapping references therein; Mikhailov et al., 1995; Stanistawska et procedure. Some of the techniques do not use monthly al., 1996a]. median models at all. Such an approach is represented by There are two different instantaneous mapping methodsuch as geostatistical kriging [Samardjiev et al., approaches to the use of observations. An exact fitting 1993; Stanistawska et al., 1996a, 1996b], the technique reproduces precisely the same measured values multiquadratic method [Hardy, 1971 ], and the method of used for map construction. There is a price to pay for this adjusted cap harmonic analysis [De Franceschi et al., feature, i.e., high gradients that appear when two close 1994]. Some proceduresupplement the input data set with observations yield significantly different values. The goal artificial point data whose values are taken from a monthly of another approach is to minimize these gradients, but at median model at sites geographically far distant from the the expense of not reproducing the measured values. This observations [Bradley, 1995; Mikhailov et al., 1995]. is the price paid for the smoothness of the.map. Other methods use the median model as a background. The It is well known that the weak point of every mapping interpolation procedure takes as input not measurements procedure of ionospheric characteristics generally the but the differences: "measurement minus monthly model". small number and/or uneven distribution of measurement As output the result of the interpolation is added to the locations. In ionospheric mapping, all possible available monthly median map. In this group are the methods of data have to be used, as opposed to geological prospecting, Rush and Edwards [ 1976], Juchnikowski and Zbyszytiski [ 1991 ], and Stanistawsk and Juchnikowski [ 1997]. The Copyright 2001 by the American Geophysical Union. methods of this group differ not only with respecto the interpolation method applied but also in the approach to Paper number 1999RS the use of observations. The first method minimizes only /01/1999RS the gradients, while the two others also reproduce the 1073

2 1074 STANISLAWSKA ET AL.' IONOSPHERIC INSTANTANEOUS MAPS observations exactly. Moreover, statistically, for the fof2 As a result of combining a median model with parameter both give betteresults than the first one does experimental data a function f*(½,/l) has to be obtained. [Juchnikowski and Zbyszytiski, 1991 ]. The following formula is proposed for f*: The aim of this paper is to show a practical application N of Juchnikowski and Zbyszyhski' s [ 1991 ] fitting method. Fitting can be thought of as a spreading of the point f* _ f + (gi _ fi)w i, i=1 measurements over a background surface: the monthly where median map. This method statistically gives betteresults (1) for fof2 than smoothed versions. Therefore it has been i i applied to different ionospheric characteristics. The largest Wi ßmW i N S ' S i W "I-E i ' spatial and temporal changes occur in the F2-1ayer [Rush et al., 1974]. By comparison, the E and F l layers behave s j 1 - w + œ much more regularly in space and time [Bradley, 1995], j=l but still the difference between the quiet and disturbed and g is a small number, e.g., conditions may exceed _+15% of the median. For some The variable s i is a measure similar to w, but in the applications it may be useful to consider more accurate range (0, + oo). The use of g reduces the problem of infinite maps than the median maps; hence alsof, E andfof l have s when w = 1 or all w = 0; it needs to be sufficiently been taken into account. The accuracy of the mapping small to avoid distorting the mapped values at the results is discussed, and the samples of maps for different measured locations but not so small that s i becomes too geophysical conditions are presented. large for w = 1. The weight %*, like w i, is a measure of 2. Mathematical Method of Fitting the influence of the data at the point ((p,2 i) on the model at (½,i) with the screening effect of all other data points The symbols used in this section have the following considered. The use of %* instead of % in (1) differentiates the method t¾om that of Rush and Edwards [1976]. meaning' In the simplest approach, the weighting function ½,J. coordinates of the point on a sphere where the median model is improved; depends only on the distance between the observation and the querying point. However, this dependence is f median model before improvement anisotropic. This assumes that the locus of points distant equal tof(½,j.); from a given measurement location and having the same f* improved model equal tof*(½,j.); correlation coefficient is elliptical in geographical latitude (pi, j.i coordinate.s of the ith point and longitude. The anisotropy expressed as CRX, CRY where fof 2 is measured; (correlation radius measured between points collocated g i experimental values equal to g ((pi, J. ); longitudinally (CRX) and latitudinally (CRY). The N number of data points; correlation radius is the distance between two points for fi value of the median model which the correlation of the ionospheri characteristic at an experimental point equal to f((d,j. ); equal to 0.5. The tbllowing weighting function was used in w factor of influence of a data point practical calculatiohs: on the model equal to w Input to the method proposed consists of the following W = exp [-(dx/crx) 2- (dy/cry)2], (2) quantities' (1)f(rp, J.), which represents the monthly median where dx and dy are the longitudinal and latitudinal model of an ionosphericharacteristic, such as fof2, for distances between the point of measurement and the instance, (2) a set of N measured values g, and (3) queried point. weighting functions w, which are a measure of statistical dependence offof 2 between points (½,J.) and ((pi, j. ). The 3. Results weight w = 1 when ((p,j. ) = (rp, J.), and 0 < w < 1 when points do not coincide. In a simple case, w is a function of distance between the two points. A more detailed study of To analyze the instantaneous maps created for different solar-geophysical conditions, data from different stations the weighting factors forfof 2 was conducted by Rush and within Europe have been used. This database has been Edwards [ 1976]. collected and made available on CD-ROM for European

3 STANISLAWSKA ET AL.: IONOSPHERIC INSTANTANEOUS MAPS 1075 Table 1. Stations That Contribute Data to the Mapping Procedure, Their Geographical Coordinates and Codes Station Country Coordinates Code Amdenna Arkhangelsk Ashkhabad Turkmenistan Athens Greece Bekescsaba Hungary Belgrade (Grocka) Yugoslavia De Bilt Netherlands Dourbes Belgium E! Arenosi!!o Spain Freiburg Germany Garchy France Gibilmanna Italy Gorky Juliusruh-Rugen Germany Kaliningrad Kiev Kiruna Sweden Lannion France Lindau Germany Lisbon Portugal Loparskaya Lycksele Sweden Miedzeszyn-Warsaw Poland Moscow Murmansk 69.5øN, 61.4øE AM øN, 40.5øE AZI øN, 58.3øE AS øN, 23.6øE ATI øN, 21.2øE BHI øN, 20.5øE BEI øn, 5.2øE DT øn, 4.6øE DB øN, 353.3øE EA øn, 7.6øE FR øN, 3.1øE GY øN, 14.0øE GM øN, 44.3øE GKI øN, 13.4øE JR øN, 20.6øE KLI øN, 30.5øE KVI øN, 20.4øE KI øN, 356.7øE LN øN, 10.1øE LI øN, 350:7øE LE øN, 33.0øE MMI øN, 18.8øE LYI øN, 21.2øE MZI øN, 37.3øE MO øN, 33.0øE MMI68 Kazakhstan 45.5øN, 62.1øE NK246 Finland 60.5øN, 24.6øE NUI59 France 48.1 øn, 2.3øE SC047 France 46.6øN, 0.3øE PT046 Czech Republic 50.0øN, 14.6øE PQ052 Novokazalinsk Nurmijarvi Paris-Saclay Poitiers Pruhonice Reykjavik Iceland 64.1øN, 338.2øE RKA64 Rome Italy 41.8øN, 12.5øE RO041 Rostov 47.2øN, 39.7øE RVI49 St. Petersburg 60.0øN, 30.7øE LDI60 Salekhard 66.5øN, 66.5øE SD266 Slough Ehgland, 51.5øN, 359.4øE SL051 United Kingdom Sodankyla Finland 67.4øN, 26.6øE SO166 Sofia Bulgaria 42.7øN, 23.4øE SQ143 South Uist Scotland, 57.4øN, 352.7øE UI057 United Kingdom Sverdlovsk 56.4øN, 58.6øE SV256 Tashkent Uzbekistan 41.3øN, 69.6øE TQ241 Tbilisi Georgia 41.7øN, 44:8øE TBI42 Tortosa (Ebre) Spain 40.8øN, 0.5øE EB040 Uppsala Sweden 59.8øN, 17.6øE UPI58 Cooperation in the Field of Scientific and Technical Research (COST) Action 251 [Hanbaba, 1999] by Rutherford Appleton Laboratory, England, United Kingdom. Table 1 shows the location of vertical incidence ionosondes contributing data to the analysis. Four ionosphericharacteristics from the years have been considered: fof2, M(3000)F 2, fofl, and fo E. In a given application all available measurements are used as input data, with no required minimum number for the mapping to proceed. All characteristics for 2 days of 1993, June 4 and 16, have been taken to show the behavior of the ionosphere during quiet (June 16) and disturbed (June 4) conditions. Hence plusigns in Figures 1-4'show locations of measurements that exist for particular map constructions. Fitting the long-term maps with the data points is done for the correlation distances according to Stanistawska et al. [1996a, 1998a], for similar solargeophysical conditions and seasons at middle latitudes from Europe. During years, the 0.5 correlation distance varies with season and ionospheric activity from 700 to 1500!an N-S and is considerably greater, from 1000 to 1900 kin, E-W. In particular, in the cases of June 4 and 16, 1993, the distances are 1600 and 1200 km E-W and 1400 and 900 km N-S., respectively. These distances are consistent with mean spatial. correlation distances [Gibson andbradley, 1991 ]. The International Telecommunications Union Radiocommunications Sector (ITU-R) long-term prediction model [International Telecommunications Union Radiocommunications Sector, 1997] was used as the monthly median background model. Graphical maps for figure presentation were constructed by creating the values in uniformly spaced grid points (36 x 36, 1" for latitude and 2 ø for longitude), while for tests only the value in the testing point was created. Figure 1 presents a M(3000)F 2 map for quiet (June 16, 1993, 0600 UT) conditions. Figure 2 present samples of maps of the fo E parameter for quiet (June 16, 1993, 1300 UT, lower panel) and disturbed (June 4, 1993, 1300 UT, upper panel) conditions created with the use of fitting. As can be seen from the measurements,foe changes in a quite wide range between quiet and disturbed days, which exceeded _+5% decile ranges, expected earlier by Rush et al. [ 1974] for this parameter. The influence of the number of measurements i /shown on a sample of instantaneous f,f 2 maps. Figure 3 presents four maps obtained for June 4, 1993, 1900 UT (upper panels), and for June 16, 1993, 1900 UT (lower panels), when a different number of data are used. The maps in the right panels have been constructed with the use of only four data points (Askhabad, E1 Arenosillo, Uppsala, and'warsaw). The maps on the left use all available data: 16 measurements for disturbed (June 4, 1993) conditions and 20 for quiet (June 16, 1993) conditions. A sample fofl map for disturbed conditions (June 4, 1993, 0700 UT) is shown in Figure 4. This mapping method-fitting enables us to show the area where fofl layer is not observed. Fitting has been tested against a large database of vertical incidence ionospheric soundings for the years

4 1076 STANISLAWSKA ET AL.: IONOSPHERIC INSTANTANEOUS MAPS 70 ø 60 ø - 50 ø- 40 ø - 0 ø 0 ø 10 ø 20 ø 30 ø 40 ø 50 ø 60 ø Figure 1. M(3000)F 2 map of Europe for quiet (June 16, 1993, 0600 UT) conditions. Plus signshow locations of measurements. 70 ø c 0 o 0 o 10 ø 20 ø 30 ø 40 ø 50 ø 60 ø o ø 50 ø 60 ø Figure 2. Samples of maps of Europe of foe parameter for disturbed (June 4, 1993, 1300 UT) and quiet (June 16, 1993, 1300 UT) conditions created with the use of fitting. Plus signs show locations of measurements.

5 STANISLAWSKA ET AL.: IONOSPHERIC INSTANTANEOUS MAPS o m 50 c,-i o 0 ø 10 o 20 o 30 o 40 o 50 o 60 o -10 ø 0 ø 10 ø 20 o 30 o 40 o 50 o m 50,_ ø 0 ø 10 ø Figure 3. Four f,f 2 maps of the Europe obtained tbr June 4, 1993, 1900 UT (upper panels), and for June 16, 1993, 1900 UT (lower panels), when a different number of data are used. The maps in the right panels have been constructed with the use of only tour data points (Askhabad, El Arenosillo, Uppsala, and Warsaw). The left maps use all available data: 16 measurements for disturbed (June 4, 1993) conditions and 20 for quiet (June 16, 1993) conditions. Plus signs show locations of measurements. Values are in megahertz. 0 I I I 60 ø : 50 c ø 0 ø 0 ø 10 ø ø Figure 4. Samplef,,F map of the Europe for disturbed conditions (June 4, 1993, 0700 UT). Plus signshow locations of measurements. The bottom letl area with "no F 1 layer" is created by the influence of the monthly median model. Values are in megahertz. 6O ø

6 1078 STANISLAWSKA ET AL.: IONOSPHERIC INSTANTANEOUS MAPS Table 2. RMS Errors forfof 2, M(3000)F2,foF I, and foe for the Presented Fitting Technique and for the Monthly Medi'an Model.f,F 2, MHz M(3000)F 2 j,f l, MHz j,e, MHz Fitting ITU-R , 1967, 1973, 1978, and Testing is conducted by means of a cyclic rotation technique in which maps are generated for given measurement data sets in turn, with a different measurement omitted each time for testing. This means that each time an observation is compared with the resultant model, this observation was not used for production of the map. For comparison the errors of the monthly median model against the measurements are presented. The accuracy of both monthly median and instantaneous mapping procedures has been discussed in terms of average percentage deviation (PERCE} 0 and rootmean-squar error (RMS): PERCER - x100%, K i=i xi RMS - i-1 Yi 2 (3) --X i, (4) where K is the total number of samples, Yi is the value predicted by the model (instantaneous mapping model or monthly median model) for sample i, and xi is the measured value for sample i. Table 2 presents the RMS errors for different' ionospheric characteristics. Figure 5 presents the percentage deviation offof 2 and M(3000)F 2 values created by the mapping technique and measurements for the years that are obtained by the presented mapping technique. The statistics obtained forfof 2 values within Europe under the COST Action 251 European project [Hanbaba, 1999] for' instantaneous mapping model PLES (PL, Poland; ES, Spain) [Stanislawska et al., 1998b], which also implements this mapping technique, show a RMS error of MHz, while for M(3000)F 2 it is [Levy et al., 1998]. 4. Discussion Every map presented replicates the measurements exactly. This requirement sometimes creates unphysical features: "bubbles" around the observation points. Figures 1-4 reflecthis fact. However, it has to be pointed out that the isolines in Figures 1-4 are more dense than the usual accuracy of the measurements, which allows recognition of the bubbles and potentially eliminates wrong measurements (probable errors). Figures 1-4 confirm that smoothness of the maps even in extreme geophysical conditions is higher than might be expected. A useful advantage of the fitting technique is also the fact that the gradients in the map are controlled by the model of the weighting function, which is an external 25 2O 15 <1: YEARS Figure 5. Yearly average of the percentage deviation offof 2 (dotted line) and M(3000)F 2 (solid line).

7 STANISLAWSKA ET AL.' IONOSPHERIC INSTANTANEOUS MAPS c 6õ c. 66q.5o q 45 c. 40 c. 3 i o 0 o _, o 0, o 1'0 o 1'5 o 2'00 2'50 3 3o 3' Figure 6. Distribution of the singular point deviations over the surface when using "fitting". parameter. The weighting function depends on the correlation distances. This is the crucial point of this technique. The most simple model of the weighting function has been adopted, but it also enables us to introduce different correlation distances depending on the actual solar-geophysical conditions and in geographical locations, as well as more complicated function according to knowledge about the behavior of the ionospheric parameters. Figure 6 shows. how a singular point deviation is distributed over the surface when using the fitting interpolation method. The method itself does not impose the tbrm of the ellipsoidal shape structure. This shape, i.e. its width in longitudinal and latitudinal directions, is q 600 _,,,, o,,<> 01 o -1 o 40 Figure 7. Distribution of the deviations created by two close points when using fitting.

8 1080 STANISLAWSKA ET AL.: IONOSPHERIC INSTANTANEOUS MAPS controlled by the adopted model of the weighting function. the Eur. Communities, Eur. Coal and Steel Community - Eur. Hence it can be changed according to knowledge abouthe Econ. Community - Eur. At. Energy Community, Brussels, ionosphere at different latitudes and in different geomagnetic and ionosphericonditions; longitudinal and De Franceschi, G., A. De Santis, and S. Pau, Ionospheric latitudinal correlations distances can be thought of as an mapping by regional spherical harmonic analysis: New developments, Adv. Space Res., 14(12), 61-64, external parameter of the mapping procedure. Figure 7 Edwards, W. R. Jr., C. M. Rush, and D. M. Miller, Studies on the shows an example of "fitting" when two close point Development of an Automated Objective Ionospheric measurements return significantly different values. In this Mapping Technique, Air Force Surv. Geophys., Vol.302, Air method the surface is altered so that it passes exactly Force Cambridge Res. Cent., Bedford, Mass., through both data points, which sometimes generates big Gibson, A. J., and P. A. Bradley, Additional vertical-incidence gradients. Unfortunately, the ionosphere is subject to ionosondes/'or PRIME, in Proceedings of the PRIME COST marked temporal and spatial variability. Hourly data from 238 Workshop, vol. 529, pp , Ist. Naz. di Geofis., the ionosondes sometimes ignore within-an-hour Rome, variability; therefore the resulting soundings might be Hanbaba, R., COST 251 Final Report, SRC Print. Off., Warsaw, representative of the whole hour. In such a case the Hardy, R. L., Multiquadratic equations of topography and other generated big gradients might be an important irregular surfaces, J. Geophys. Res., 76, , disadvantage of the presented mapping technique. International Telecommunications Union Rhdibc'ommunicatio s Sector, Reference ionosphericharacteristics, Rec. ITU-R P. 5. Conclusions 1239, Geneva, Juchnikowski, G., and Z. Zbyszyfiski, A mod.ification of fof2 All figures show that many structures in ionospheric statistical model using vertical sounding data, in Proceedings layers are represented quite accurately by the fitting of the PRIME COST 238 Workshop, vol. 529, pp , presented. Moreover, the statistical results given are Ist. Naz. di Geofis., Rome, significantly better than the monthly median ITU-R model Levy, M., M. I. Dick, P. Spalla, C. Scotto, I. Kutiev, and P. for every characteristiconsidered. Most other mapping Muhtarov, Results of COST 251 testing of mappings and methods extend the measurements to the area where, for models, Tech. Doc. COST 251, (98)021, Eur. Coop. in the instance, F 1 layer is not observed, while fitting avoids this. Field of Sci. and Tech. Res., EUR-OP Off. ofpubl., Adv. Inf. It has to be noted that for more accurate applications, Databases, Inc., Eastpointe, Mich., when soundings used present exact observations, the Mikhailov, A. V., V. V. Mikhailov, and M. G. Skoblin, A above-mentioned problem of gradients becomes the method forfof 2 and M(3000)F 2 instantaneous mapping over Europe (MQMF2-INST model), in Proceedings of the COST substantial advantage of the method; gradients obtained 238 Workshop on "Development and Testing of an Electronare created for physical reasons, and the constructed maps Density Height Profile Model for PRIME", El Arenosillo, might be a useful tool in studies of these reasons. The use September 1994, pp , Univ. de Huelva, Huelva, of the maps constructed by this model is particularly Spain, advocated for rapid sequence soundings, for instance. An Rush, C. M., and W. R. Edwards Jr., An automated mapping additional gain of this technique is the. fact that this technique for representing the hourly behavior of the procedure can be applied to the whole globe, so that any ionosphere, Radio Sci., 11 (11), , problem of the buffer zone that appears in limited-area Rush, C. M., D. Miller, and J. Gibbs, The relative daily variation models can be avoided. of fof2 and hmf 2 and their implications for HF radio propagation, Radio Sci., 9(8-9), , Acknowledgments. The authors would like to express their Samardjiev, T., P. A. Bradley, L. R. Cander, and M. I. Dick, appreciation to A. W. Wernik tbr valuable help during Ionospheric mapping by computer contouring techniques, preparation of this manuscript. His comments and suggestions Electron. Lett., 29(20) , improved a lot the final version of the paper. This research was Stanistawska, I., and G. Juchnikowski, A note on use of screen partly supported by Polish Committee of Scientific Research points in regional ionospheric mapping, Acta Geophys. Pol., grant 2 P03C XLV(4), , References Stanistawska, I., G. Juchnikowski, and L. R. Cander, The kriging Bradley, P. A., PRIME (Prediction and Retrospective Ionospheric Modelling over Europe), final report, Comm. of method of ionospheric parameterfof 2 instantaneous mapping, Ann. Geophys., 39(4), , 1996a. Stanislawska, I., G. Juchnikowski, and L. R. Cander, Kriging

9 STANISLAWSKA ET AL.: IONOSPHERIC INSTANTANEOUS MAPS 1081 method lbr instantaneous mapping at low and equatorial latitudes, Adv. Space Rex., 18(6), , 1996b. Stanistawska, I., T. L. Gulyaeva, and G. Juchnikowski, Correlation distances based on ionospheric and magnetic catalogues, in Solar-Terrestrial Predictions, V, Proceedings of a Workshop, edited by G. Heckman et al., pp , RWC Tokyo, Hiraiso Sol. Res. Cent., Commun. Res. Lab., Hitachinaka, Ibaraki, Japan, 1998a. Stanistawska, I., G. Juchnikowski, Z. Zbyszyfiski, and G. Sole, Instantaneous mapping offof 2 and M(3000)F 2 with use of fitting algorithm, Tech. Doc. COST 251, (98)012, Eur. Coop. in the Field of Sci. and Tech. Res., EUR-OP Off. of Publ., Adv. Inf. Databases, Inc., Eastpointe, Mich.,1998b. G. Juchnikowski, I. Stanistawska, and Z. Zbyszyfiski, Space Research Centre, Polish Academy of Sciences, ul. Bartycka 18a, Warsaw, Poland. (stanis@cbk. waw.pl) (Received November 8, 1999; revised September 26, 2000; accepted September 29, 2000.)