The spatial uniformity of polar cap absorption events has been exploited to test the performance of riometer systems. In an imaging riometer the use of a fixed conversion factor for obtaining the equivalent zenithal absorption from that measured with an oblique beam is verified for most of the beams, and revised factors are suggested. The readings from the corner beams are found to be unreliable, however. Factors for converting the readings from a wide-beam antenna to true zenithal values are derived. The significance of antenna sidelobes is pointed out, and the upper limits to the absorption measurement due to the temperature of the mesosphere and to uncertainty of riometer calibration at the lowest signal levels are demonstrated.
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 The technique of measuring the absorption of radio waves in the ionosphere by receiving the cosmic radio noise is well established, having been first used over 40 years ago [Mitra and Shain, 1953; Little, 1954]. Its principal application has been to the high-latitude region where the lower ionosphere (notably the D region) is ionized by incoming energetic particles, both electrons and protons. The absorption per unit length of path depends on the product of electron density and electron-neutral collision frequency in the absorbing region, but the absorption indicated by the receiver, which is usually, but not necessarily, a riometer [Little and Leinbach, 1959], depends also on the length of path traversed by the signal and, therefore, on the obliquity of the rays passing through the ionosphere. The measurement is therefore affected by the pointing of the antenna with respect to the zenith and by its polar diagram.
 If the antenna is pointed at angle χ to the zenith, the observed absorption may be multiplied by cos χ to give the “equivalent zenithal” value. This procedure would give the correct answer if the beam were very narrow, but otherwise, the signals are being received over a range of angles, and the correction is not precise. Even an antenna pointed to the zenith is affected by obliquity because of off-axis contributions. These effects might not be important in some applications, but for precise measurement of the “zenithal absorption,” which we define as the absorption measured by an ideal pencil beam antenna pointed to the zenith, they should be taken into account.
 To take an example, computations indicate that for a typical wide-beam riometer antenna, typical of those used at most riometer installations, the “apparent absorption” (meaning the value actually measured) is about 1.4 times the true zenithal value [Ecklund and Hargreaves, 1968]. Most lists of published absorption data, however, do not include a correction or indicate the likely effect of the antenna.
 Over the last few years there has been increasing use of “imaging riometer” systems, which use a larger array to form a number of narrower beams. These have increased the potential accuracy of riometer data because they indicate the spatial distribution of the absorption as well as its magnitude. The effect of beam width will now be less than in a wide-beam system, but it does not vanish entirely. An earlier comparative study of imaging and broad-beam riometer measurements was performed for several auroral absorption events of varying intensity and localization by Rosenberg et al. . The results confirmed the dependence of measured absorption on the spatial uniformity of electron precipitation over the beam field of view.
 This paper addresses the question of correction from apparent to zenithal absorption, making use of measurements on polar cap absorption (PCA) events, which are generally considered to be relatively uniform over distances of several hundred kilometers. We shall estimate corrections for various beams of an imaging riometer and for a wide-beam instrument and compare them with values derived computationally. The results include the effect of sidelobes, which is another aspect of riometry that is often conveniently forgotten.
2. The Maryland Imaging Riometer
 The imaging riometer at Kilpisjärvi, Finland [Browne et al., 1995], is technically similar to that developed by Detrick and Rosenberg  for use at the South Pole. It consists of a broadside array of 64 crossed dipoles over a ground plane, operating at 38.2 MHz. Butler matrices are used to form 49 independent beams simultaneously, one being zenithal and the others being at zenith angles between 14° and 67°. The projections of the beams at the 90 km level are shown in Figure 1. The Kilpisjärvi antenna is aligned accurately north-south, and the beam pattern is symmetrical about north-south and east-west lines and also about the diagonals.
 Because of the symmetries, just 10 different types of beam are involved. For the present purpose these are labeled A to J. There is one beam of type A, four each of types B to G, and eight each of types H to J. Figure 2 indicates the type of each beam and its designation in the sequential and the column-row systems of beam numbering. Table 1 gives for each type the zenith angle of the beam center, the angular width of the beam in zenith angle, and the equivalent radial distances from overhead at 90 km altitude. We note that the beams extend over distances from 20 to 128 km, but if the outer 12 beams are excluded, giving almost circular coverage of about 100 km radius, individual beams extend over no more than 55 km. Over the central region (beams A, B, C, E, and H) the definition is 20–30 km.
Table 1. Zenith Angles and Distances for the Beam Types at Kilpisjärvi
Zenith Angle, deg
Radial Distance From Zenith at 90 km Height, km
Of Width to 3 dB
To Beam Center
Between 3 dB Points
2.2. Effect of Sidelobes
 Like all antennas, this array has sidelobes as well as a main beam. The sidelobes are more significant in riometry than they would be in some other applications because the cosmic noise source covers the whole sky and therefore the unwanted signal is collected over a large solid angle. The narrower the main beam, the larger is the solid angle over which the sidelobes can make mischief.
 By way of illustration, Figures 3 and 4 show the patterns of main beam and sidelobes associated with beam types A and G. The largest sidelobes are 17 dB and 9 dB down from the main lobe in the two cases, respectively. However, this is not the point. What matters in riometry is how much power enters the sidelobes in total. Table 2 gives the fraction of the total received power coming from main beam and from major and minor sidelobes, assuming a uniform radio sky. The major sidelobes, seen clearly in Figures 3 and 4, are those corresponding to the same row or column as the main beam. They account for less than 8% of the power in the beams of types A, B, C, E, and F, but for 14–16% in types I and D. The figure rises to 35% for the corner beams of type G. Although the minor sidelobes are more numerous, they account for only a tiny fraction (≤0.3%, except for type G) of the received power. In the best case, 93% of the power is collected in the main beam; in the worst case it is only 64%. When contemplating absorption measurements by imaging riometer, consideration needs to be given as to whether they may be affected by antenna sidelobes.
Table 2. Distribution of Received Power Among Main Beams and Sidelobes According to Beam Type
 The PCA event is caused by an influx of energetic protons from the Sun, which enter the geomagnetic field without further energization but are deflected (by the Lorentz force), so that they may reach the Earth's atmosphere over the polar caps but not at low latitude. The influx is reasonably uniform over the polar caps down to a “cutoff latitude” depending on the energy spectrum. In the absence of local acceleration the structuring which affects auroral electron precipitation does not arise. The property of spatial uniformity is what we shall exploit in this investigation.
 PCA events giving significant radiowave absorption occur from zero to about a dozen times a year, with a strong dependence on the solar cycle. Substantial events occurred on 20–23 April 1998 (days 110–113) and 14–17 July 2000 (days 196–199). Figure 5 shows the 38.2 MHz absorption during these events, as measured by the vertical beam (0, 0) of the Kilpisjärvi imaging riometer. At that site the vertical absorption reached 4.2 dB in the first event and 14 dB in the second. There is an overall rise and fall (as well as some smaller increases and decreases) due to the general growth and decay (and some minor variations) in the proton flux reaching Earth. The major reduction every night is, however, due to chemical change in the mesosphere, which increases the effective recombination coefficient and so reduces the electron density for given proton flux. A spatial gradient in the absorption is therefore expected at sunrise and sunset, but not at other times. In some cases, where the proton spectrum is soft, a latitudinal variation could exist due to the proximity of the cutoff latitude. A systematic north-south gradient over the field of view of an imaging riometer is easily tested for and appears not to have been present in the events considered here.
3.2. Antenna Calibration: Theoretical
 It has been the practice to correct the absorption measured with an oblique antenna to an equivalent vertical value by applying a factor cos χ, χ being the zenith angle of the beam center (Table 3). However, this may be refined by a computation which sums the received signal over all angles, using a theoretical representation of the antenna pattern and making the assumption of a uniform absorption slab. The program takes into account the sidelobes as well as the theoretical shape of the main beam. The radio sky is assumed uniform.
Table 3. Equivalent Zenithal Absorption, Calculated Using the Standard Correction Factors, for Different Levels of True Zenithal Absorption
Equivalent Zenithal Absorption, Given True Zenithal Absorption
 Columns 3 to 11 of Table 3 give the equivalent vertical absorption for beams A to J at various levels of zenithal absorption, the correction having been made using the correction factor in column 2. Note that for the one vertical beam (type A) the reading is about 3% larger than the true zenithal value. In general, the error is less than 10%, the exception being for beams G (the extreme corner beams), where the results fall well below the correct values at large absorption. Figure 6 presents, as a function of the zenithal absorption, the ratio between the corrected zenithal value and the absorption calculated for beam (0, 0). It is clear that beams A, B, C, E, and H are correct to a few percent. All these beams are centered on zenith angles less than 40°. The corrected absorption values from more oblique beams are too large at low absorption and too small at high absorption. The errors become worse as the obliquity increases. We shall compare the results of the PCA event calibration with these results based on theoretical beam patterns.
3.3. Antenna Calibration: PCA
 Comparisons between the measured values of equivalent vertical absorption from beams of different type agree reasonably well in general. We take the vertical beam (type A, beam 0, 0) as the common reference, and the correlation between the absorption in other beams and in beam A is high in most cases (Figure 7). The left-hand plots in Figure 7 are for the PCA event of April 1998, in which the vertical absorption did not exceed 4.5 dB. Except for beams of type G the correlation coefficients (assuming a linear relationship) are at least 0.99. By way of illustration, Figure 7 shows all four beams each of types B, D, and G. The first two clearly follow a linear relationship up to 4 dB, whereas the third shows the nonlinearity predicted by Figure 6. There is some variation between beams of the same type, however, which requires further investigation.
 The PCA event of July 2000 gives similar results up to 5 dB, but there are deviations at larger absorption in the more oblique beams. We consider this point below.
 The gradients of the plots of corrected oblique reading to vertical reading have been estimated by linear regression analysis and are shown in Figure 8 against the zenith angle of the beam center. The results from the two PCA events are given separately. In each case the slope tends to be slightly above unity up to zenith angle 50° but to fall to lower values at greater obliquity. The consistency between the results from the two events gives some confidence that we are seeing a property of the system rather than some peculiarity of a given event. The behavior is consistent with the results of Figures 6 and 7 and is probably due to (1) the greater values of sec χ involved in the more oblique beams and (2) the greater fraction of the total power contributed by sidelobes. In Table 4 the average slope for each beam type is used to obtain a revised correction factor from oblique to equivalent zenithal absorption. The results suggest that care should be taken with measurements using beams J and that beams G are better not used at all. Otherwise, the present analysis vindicates the use of a constant correction factor (preferably the revised one) for the other beams.
Table 4. Observed Slope of Corrected Oblique Reading to Vertical Reading, and Revised Correction Factor, for Each Beam Typea
 In Figure 7 the plots of the four beams of type G diverge seriously above about 6 dB of vertical absorption. Those turning up are beams (3, −3) and (−3, −3), and those turning down are (3, 3) and (−3, 3). This gives a clue to the cause, supported by the fact that the beam turning up in the plots of beam D is (0, −3). In fact, the turning up is seen to some degree in all the beams of column −3. In the Kilpisjärvi imaging riometer for ionospheric studies (IRIS) the signals are received into seven riometers, each of which is switched rapidly between the beams in a single north-south column. The effect we have noted appears to be due to the riometers separately servicing columns 3 and −3, and the cause would appear to be a nonlinearity in the riometers concerned.
 However, it also brings us to the question of a fundamental limit to the measurement. At 38.2 MHz the temperature of the radio sky Tsky visible from Kilpisjärvi is generally between 10,000 and 20,000 K. When the absorption is very large, the received signal increasingly represents not the radio sky but the temperature of the absorbing region of the mesosphere Tmesosphere, about 200 K. The absorption measurement is limited to 10 log (Tsky/Tmesosphere) decibels, in our case of the order of 17 to 20 dB. If the zenithal absorption is 6 dB, beam G should measure 15 dB. If the zenithal value is 14 dB (the maximum in the event of July 2000), the oblique value in beam G is 36 dB. This is clearly too large to be measured accurately with this system. The deviations observed in oblique beams at high absorption occur because in that event the system is approaching its limit.
3.5. Small-Scale Irregularity
 If the PCA event is not uniform over the field of view of the imaging riometer, differences will be seen between the readings from beams of the same type. Figure 7, which plots sets of four beams in each panel, indicates such differences, which must be due either to real differences of absorption or to instrumental differences or to both. To examine this point further, Figure 9 plots readings from pairs of like beams, one against the other. The pairs of beams are of types D and F, diametrically separated by 160 to 180 km in the D region (Table 1). The data are for days 111 and 112 of the PCA event of 1998. The line of unit slope and lines marking 10% difference are superimposed.
 In the event that the trend of the plot deviates from unit slope an instrumental cause might be suspected. If the whole plot is displaced uniformly to one side of the unit line, an error in the quiet day curve would be suspected. Irregular variations away from a straight line could well be due to spatial variation of absorption over 160–180 km. The indications are that such variations do not exceed 10% in general.
4. Calibration of a Wide-Beam Riometer
4.1. Computed Performance
 Most observations of high-latitude radio absorption have been, and still are, made using riometers with a simple antenna which forms a single wide beam that is usually 60° or more between half-power points. Even when it is pointed vertically, most of the signal received at such an antenna has passed through the absorbing region obliquely, and thus the apparent absorption (the value directly measured) must exceed the zenithal absorption. A wide-beam riometer is operated at Kilpisjärvi for general monitoring and for quick-look purposes. The antenna is a single crossed dipole over a ground plane, a unit of the same design as the elements of the imaging riometer, and its polar diagram is shown in Figure 10. The beam is 94° between half-power points and is almost the same at all azimuths. Figure 11 shows the relation between apparent absorption and zenithal absorption for this antenna derived by the computational method described in section 3.2. The ratio of apparent to zenithal absorption is 1.55 at low absorption (0.5 dB), reducing to 1.40 at 4 dB and to 1.24 at 20 dB. These ratios (regarded as effective values of sec χ) correspond to zenith angles 50°, 44°, and 36° respectively, indicating a narrowing of the effective beam as the absorption increases.
4.2. Calibration Using PCA Events
 The measurements with the wide-beam riometer have been compared with those using the vertical beam (0, 0) of the imaging riometer at Kilpisjärvi during the PCA events of April 1998 and July 2000. For the first event (Figure 12a) the values of observed absorption agree well with those computed. The agreement is slightly less close in the second event (Figure 12b), and there is significant deviation at the highest absorption values.
 The effect of the mesospheric temperature at high absorption, discussed in section 3.4, will apply also to the wide-beam antenna. No matter how intense the absorption, the apparent sky temperature cannot fall below the temperature of the mesosphere, and this will affect the rays reaching the antenna progressively, starting with the most oblique. We should therefore expect the absorption read from the wide-beam antenna to be smaller than predicted at high absorption. The lower line in Figure 12b assumes a mesospheric temperature that is smaller than the sky temperature by a factor of 100 (i.e., 200 K against 20,000 K), and this appears to explain the trend of the data. The effect amounts to 3 dB at the 15 dB level.
5. Conclusions and Discussion
 The spatial uniformity of a polar cap absorption event may be exploited to verify or to correct the conversion of an oblique absorption measurement to an equivalent zenithal value in an imaging riometer and to find the appropriate correction factor for a wide-beam installation. In the case of the imaging riometer operating at Kilpisjärvi the use of a constant correction factor for most of the beams is vindicated, though the results raise a doubt about the utility of the outermost beams. A study of this kind, aided by a computational assessment (sections 3.2 and 4.1), would be expected to reveal any major antenna problems that may have arisen during construction or because of weather damage. There is no suggestion of any such problem in the present case.
 The study has highlighted some topics that are too easily overlooked in riometer studies. The significance of antenna sidelobes was brought out by the computational study and verified by the observed poor performance of the beams of type G. Second, the maximum absorption that may be measured accurately is determined by the temperature of the mesosphere in relation to the temperature of the radio sky. The oblique beams are affected the most, but the effect potentially limits measurements using all beams, and it should be kept in mind when considering the significance of riometer data. Very high absorption may occur (though over limited times and distances) in auroral absorption as well as in PCA, and such events may well come to light in greater numbers as systems achieve finer resolution in space and time. The calibration of the riometers may be less accurate at the lowest signal levels.
 Spatial uniformity has been a tenet of PCA studies since the earliest observations. Those studies used data from wide-beam riometers, incapable of seeing detail at the level of tens of kilometers. The present work extends the tenet to a finer scale, having found no great degree of spatial irregularity within the (approximately) 200 km field of view of the imaging riometer at Kilpisjärvi. Such variations as there are seem to be no more than about 10% in general.
 That being so, it would appear that at most sites an imaging riometer will not advance PCA studies much beyond the potential of a wide-beam instrument. Indeed, if PCA is the main concern, the best use of limited resources would be to construct a network of wide-beam riometers (as has been done in the past) rather than a single imaging riometer. However, the proper correction from apparent to zenithal absorption then needs to be applied. The present study has defined the correction factors for one design of wide-beam riometer antenna. The same technique would be equally applicable to others.
 The riometers at Kilpisjärvi are operated as a joint project between the University of Lancaster and the Geophysical Institute, Sodankylä. We are grateful to S. Marple (Lancaster) for system operation and data work and to T. J. Rosenberg (Maryland) for suggestions and comments on the paper. The work at Maryland is partially supported by NSF grant 0PP9732662.