Abstract
 Top of page
 Abstract
 1. Introduction
 2. Calculating the A_{h} Index
 3. Centennial Increase and Its Latitudinal Variation
 4. Global A_{h} Indices
 5. Comparison With Ap
 6. Conclusions
 Acknowledgments
 References
 Supporting Information
[1] The K indices have long been a very important way to estimate geomagnetic activity. However, they have some basic and practical problems which restrict their reliability and applicability for longterm (centennial) studies. Here we discuss these problems, modify the K method and construct a new, straightforward, easily verifiable and homogeneous index, the so called A_{h} index, which is based on digital, hourly data and is dedicated for centennial studies. The local A_{h} indices correlate with the local K and ak indices very well and extend them typically by several decennia. A_{h} indices at all studied stations verify that geomagnetic activity has increased during the last century. However, the amount of centennial increase varies greatly with latitude, being largest at high latitudes, smaller at low latitudes and, unexpectedly, smallest at midlatitudes. The centennial increase in the aa index is roughly twice larger than in the A_{h} index at similar midlatitudes. This is due to the erroneous scaling of the aa index in the late 1950s, requiring aa to be revised. The global A_{h} index correlates uniquely well with the Ap index, better than aa or the notK based IHV (InterHourly Variability) index. Thus A_{h} yields the most accurate extension of the Ap index by roughly 30 years.
1. Introduction
 Top of page
 Abstract
 1. Introduction
 2. Calculating the A_{h} Index
 3. Centennial Increase and Its Latitudinal Variation
 4. Global A_{h} Indices
 5. Comparison With Ap
 6. Conclusions
 Acknowledgments
 References
 Supporting Information
[2] Geomagnetic activity is a crucial parameter to study the longterm change in the Sun and nearEarth space. E.g., the aa index was used to suggest that the open solar magnetic field was more than doubled since 1900 [Lockwood et al., 1999]. The increasing trend is supported by cosmogenic isotopes [Usoskin et al., 2003] and solar activity [Solanki et al., 2000]. However, despite this seeming consistency, serious concern has been raised on the centennial increase [Svalgaard et al., 2003, 2004] and the consistency of the aa index [Mursula et al., 2004; Jarvis, 2005; Lockwood et al., 2007; Mursula and Martini, 2006].
[3] Geomagnetic indices aim to estimate irregular variations, excluding regular variations like the solar quiet (S_{q}) daily variation. K index method defines irregular variations as the range (difference) between the upper and lower fitting quiet daily curves during each threehour interval, associating this with an integer (0 to 9) [Bartels et al., 1939; Mayaud, 1980; Menvielle and Berthelier, 1991]. Since K scale is quasilogarithmic, K indices are often linearized to equivalent amplitudes, the ak indices. Kp and Ap indices, based on 13 stations, are perhaps the most reliable longterm measure of global geomagnetic activity but only exist since 1932. The aa index runs since 1868 and was long the only centennial measure of geomagnetic activity.
[4] Despite their merit, K indices have some problems for longterm studies. K index is based on the observer's personal evaluation and, with changing observers, the longterm consistency is hard to guarantee. (Since 1990s K indices are mostly determined by computer methods; see Menvielle et al. [1995].) The K method to “digitize” ranges to 10 values is problematic, forcing the observer to select, often arbitrarily, between two K values. This is particularly difficult for low K levels where the exact form of the S_{q} curve is important. Because of the great number of low K values, the selection has a large effect. Different selection principles may cause, e.g., the different distributions of low K values at different stations. This problem can be avoided by using continuous range values (“amplitudes”) instead of digitized K values. Also, the fixed K = 9 limit is problematic for longterm studies. During increasing activity such a limit may underweight the highest disturbance levels, leading to an erroneously small trend. (Changing the K = 9 limit would compromise homogeneity.) This problem can also be avoided using continuous range values with no artificial limits.
[5] A practical problem is that the early measurements are not in digital format at high sampling. Thus, examining the correctness and homogeneity of K and ak values is difficult. Recent analyses of aa suggest that the calibration was changed by roughly 2 nT in the 1950s [Jarvis, 2005; Lockwood et al., 2007]. Accordingly, the longterm consistency of aa is questionable and the index must be revised. Clearly other, more straightforward and easily verifiable measures of geomagnetic activity are needed for centennial studies. Data availability problem is corrected in the IHV index [Svalgaard et al., 2003, 2004], a recent alternative measure of geomagnetic activity. (IHV is calculated from absolute differences between successive hourly values of the H component during seven night hours in the aim to minimize the effect of the daily curve.) Using hourly digital values available at the World Data Centers (WDC), IHV can be examined in detail [Mursula et al., 2004; Mursula and Martini, 2006]. However, IHV is a measure of hourly variability while the K index is a threehourly range measure. IHV is a daily index including only nighttime activity, while the eight threehourly K indices cover both day and night, which matters since geomagnetic activity has a strong diurnal variation. Thus, IHV and K indices measure somewhat different processes of the nearEarth space.
[6] Here we aim to combine the simplicity and easy verifiability of IHV with the basic principles of the K method by introducing a new index of geomagnetic activity, the A_{h} index (A for amplitude, analogue of the equivalent amplitude ak; h for hourly data), which is tailored for longterm studies.
2. Calculating the A_{h} Index
 Top of page
 Abstract
 1. Introduction
 2. Calculating the A_{h} Index
 3. Centennial Increase and Its Latitudinal Variation
 4. Global A_{h} Indices
 5. Comparison With Ap
 6. Conclusions
 Acknowledgments
 References
 Supporting Information
[7] We use six longoperating stations (Sodankylä SOD, Sitka SIT, Niemegk NGK, Cheltenham/Fredericksburg CLH/FRD, Honolulu HON, Tucson TUC) that have the longest and most uniform records of magnetic observations from early 1900s onwards (for more information, see Mursula and Martini [2006, Table 1]). They include two highlatitude (SOD, SIT), two midlatitude (NGK, CLH/FRD) and two lowlatitude (HON, TUC) observatories, allowing to study latitudinal differences in centennial evolution.
[8] We use hourly data available at WDC. Note that the very early hourly values (at most stations until 1915) were hourly spot values, not hourly means [Mursula and Martini, 2006]. Since spot values include more variability than means, the early A_{h} indices would, without due correction, remain too large and their centennial increases too small. We have corrected the A_{h} indices for this effect in a similar way as the IHV indices [Mursula and Martini, 2006] using highsampling data for the more recent years. While the sampling correction of the A_{h} indices is presented in detail elsewhere (see D. Martini and K. Mursula, Centennial geomagnetic activity studied by a new, reliable longterm index, submitted to Journal of Atmospheric and SolarTerrestrial Physics, 2007), note that the reduction needed for A_{h}, roughly 20%, is smaller than the 30% reduction typically required for IHV [Mursula and Martini, 2006].
[9] To derive the A_{h} index we first calculate the quiet daily variation. We use local IHV indices [Mursula et al., 2004; Mursula and Martini, 2006] to find the five quietest days in each month at each observatory. Using local rather than global quiet days gives a better account of local conditions. Also, the official global quiet days exist only since 1932. The S_{q} curve is the average daily curve of the H component in the five quietest days of each month. This takes into account the seasonal variation of the quiet daily curve even more accurately than the seasonal model curves typically used by observers. Also, the quiet daily variation is no longer subjective and can be easily reproduced and examined.
[10] As for the K index, the quiet daily curve is fit to the data in each threehour interval as an upper and lower limiting envelope curve. The difference (range) between the two envelope curves is the A_{h} index of the respective threehourly interval. No digitization of the range value is made, contrary to the K method. Accordingly, the continuous range (or amplitude; analogue to ak) is the fundamental, linear parameter. Thus, the A_{h} index solves the above mentioned problems of the K method in longterm studies.
3. Centennial Increase and Its Latitudinal Variation
 Top of page
 Abstract
 1. Introduction
 2. Calculating the A_{h} Index
 3. Centennial Increase and Its Latitudinal Variation
 4. Global A_{h} Indices
 5. Comparison With Ap
 6. Conclusions
 Acknowledgments
 References
 Supporting Information
[11] We have depicted the yearly A_{h} indices for the six stations in Figure 1. Despite large differences in absolute level, all six A_{h} series depict the same qualitative longterm pattern [Mursula et al., 2004; Mursula and Martini, 2006]: on top of solar cycle variation, there is an increase from the beginning of the century until about 1960, then a dramatic dropout in early 1960s, and a weaker increase thereafter. (A twoline fit emphasizes this behavior.) A qualitatively similar behavior is also found, e.g., for Ap, aa, and IHV indices [Mursula et al., 2004; Mursula and Martini, 2006]. However, the various indices differ significantly in quantitative details, e.g., the centennial trend.
[12] We have quantified the centennial increase in A_{h} in two ways. First, we calculated the average values of A_{h} during the last (1979–2000) and first (1901–1922) 22 years of the last century. (Note that the stations cover slightly different fractions of the first 22 years.) Thereby one can quantify the centennial increase between the beginning and end of the last century, neglecting everything (e.g., the local peak around 1960) in between these time intervals. This method is independent of the normalization of indices. We have depicted the average levels and the percentage changes (relative centennial increases) in Table 1. All six A_{h} series depict clearly larger values at the end of the century. The centennial increases at the six stations depict the same latitudinal ordering as the IHV indices [Mursula and Martini, 2006]. Although the increases can not be simply compared because of different start years, it is clear that the largest increases are found at high latitudes (SOD, SIT), smaller increases at low latitudes (TUC, HON) and, surprisingly, the smallest increases at midlatitudes (NGK, CLH/FRD). This latitudinal ordering of the centennial increases is systematic and even more clear than in IHV.
Table 1. Mean Values of A_{h} Indices for Six Stations at the Beginning and End of the Last Century, Their Relative Increase, and the Slope of the BestFit Line for the Mean Normalized Values in 1914–2000^{a}Station or Index  A_{h} Start  A_{h} End  Relative Increase  1000 * Slope 


SOD  33.35  46.85  40.5%  3.87 
SIT  13.46  23.14  71.9%  3.22 
NGK  8.17  10.01  22.5%  0.65 
CLH/FRD  7.61  9.13  20.0%  0.65 
TUC  7.61  9.66  26.9%  1.89 
HON  5.94  7.49  26.1%  1.58 
A_{h6}  0.9186  1.0436  13.6%  1.64 
aa1914  17.90  24.63  37.6%  4.48 
A_{h3}  0.8055  1.1023  36.8%  3.57 
aa1902  15.20  24.63  62.0%  5.88 
[13] Second, we calculated the slopes of the best fit lines in 1914–2000 (see Table 1). For that, we normalized A_{h} indices by their means in 1914–2000. One can see that the latitudinal ordering is clearly valid also for slopes. Midlatitude stations depict quite a small slope while slopes at low (resp., high) latitudes are more than twice (five times) larger.
4. Global A_{h} Indices
 Top of page
 Abstract
 1. Introduction
 2. Calculating the A_{h} Index
 3. Centennial Increase and Its Latitudinal Variation
 4. Global A_{h} Indices
 5. Comparison With Ap
 6. Conclusions
 Acknowledgments
 References
 Supporting Information
[14] We have taken the latitude variation of trends into account by including stations from different latitudes in our estimates of global Ah indices. We have constructed two versions of global A_{h} indices. First, each local A_{h} index was normalized by its mean in 1914–2000 and then averaged, yielding a sixstation global index A_{h6}. In order to extend to earlier years, we constructed similarly the A_{h3} index for 1902–2000 using one station from high (SIT), mid (NGK) and low (HON) latitudes.
[15] Table 1 shows the relative increases and slopes for A_{h6} and A_{h3}. A_{h6} depicts an increase of 13.6% and a slope of 1.64 · 10^{−3} in 1914–2000, to be compared with 37.6% increase and 4.48 · 10^{−3} slope for aa (aa1914 in Table 1). Similarly, A_{h3} shows a 36.8% increase and a slope of 3.57 · 10^{−3} in 1902–2000 to be compared with 62.0% and 5.88 · 10^{−3} for aa (aa1902 in Table 1). Thus, the centennial increase in global A_{h} indices is clearly lower than in aa. Also, the centennial increase in A_{h} at midlatitudes is about 21%, i.e., much smaller than the 62% increase in aa, also based on midlatitude stations. Clearly, aa greatly exaggerates the centennial increase. However, because the qualitative similarity of centennial change, A_{h3} and aa are fairly well correlated (cc = 0.946).
5. Comparison With Ap
 Top of page
 Abstract
 1. Introduction
 2. Calculating the A_{h} Index
 3. Centennial Increase and Its Latitudinal Variation
 4. Global A_{h} Indices
 5. Comparison With Ap
 6. Conclusions
 Acknowledgments
 References
 Supporting Information
[16] Annual Ap correlates well with aa (cc = 0.95), but even better with A_{h3} (0.97) and A_{h6} (0.98). We have depicted in Figure 2 the yearly Ap and the (correlated) A_{h3} and aa together with the best fit lines in 1932–2000 and in 1902–2000. The lines for Ap and A_{h3} in 1932–2000 are so close that they can hardly be distinguished (slopes 0.0116 and 0.0065) but the aa line shows a larger increase (slope 0.0536). The difference between A_{h3} and aa becomes even more clear in the early years (A_{h3} slope is 0.0606, aa slope is 0.0965).
[17] We have depicted ApA_{h3} and Apaa differences in 1932–2000 in Figure 3. Despite fluctuations, Apaa is systematically above zero until about 1960 and below zero thereafter. This is in a good agreement with recent studies [Lockwood et al., 2007; Jarvis, 2005; Clilverd et al., 1998], concluding that the calibration of aa fails in late 1950s because of the change of the northern aa station from Abinger to Hartland. The average value of Apaa difference in 1932–1960 is 1.1 nT and −0.80 nT in 1965–2000, yielding a step of about 2 nT, in a good agreement with earlier estimates. On the other hand, ApA_{h3} shows no systematic trend off zero, in agreement with the result that Ap and A_{h} indices are more consistent and better correlated than Ap and aa.
[18] We have also calculated the correlation between Ap and local A_{h}′s (see Table 2). The highest correlations are found for the two midlatitude stations. This is understandable since most Kp stations are at midlatitudes. Note that most correlations between Ap and local A_{h} indices are better than between Ap and aa. (For lowlatitude stations correlations are smallest: for HON it is slightly smaller and for TUC equal to that with aa.) The agreement between Ap and all A_{h} indices is due to the fairly similar basic definitions and the fact that both indices include geomagnetic activity from all local time sectors. Since Ap correlates with the midlatitude A_{h} indices better than with aa, these similarities must be more important than the differences (e.g., different sampling frequency).
Table 2. Correlation Coefficients Between Ap and the Local A_{h} Indices and Ap and the Local IHV Indices at Six StationsStation Index  Correlation Coefficient 

ApA_{h}(SOD)  0.97 
ApA_{h}(SIT)  0.96 
ApA_{h}(NGK)  0.98 
ApA_{h}(CLH/FRD)  0.98 
ApA_{h}(TUC)  0.95 
ApA_{h}(HON)  0.94 
ApIHV(SOD)  0.91 
ApIHV(SIT)  0.92 
ApIHV(NGK)  0.92 
ApIHV(CLH/FRD)  0.93 
ApIHV(TUC)  0.90 
ApIHV(HON)  0.94 
[19] We have included in Table 2 the correlation of Ap with local IHV indices. These correlations are also fair but remain clearly below those between Ap and local A_{h}. (For HON they are equal.) Contrary to correlations between Ap and local A_{h}, the correlations between Ap and local IHV are, in all cases, below the correlation between Ap and aa. This is because IHV differs from the main principles of the K method. Thus, A_{h} rather than IHV, should be used to extend the Kp and Ap to earlier times.
[20] We have calculated the average values of SOD ak indices in 1914–2000 in the eight threehourly UT (or LT; SOD LT = UT + 2.5 h) sectors separately, depicting a strong diurnal variation with activity maximum in the night (Figure 4). The same threehourly averages calculated for the SOD A_{h} index depict a very similar diurnal distribution as SOD ak (see Figure 4). The correlation coefficient between the curves is 0.981, implying a probability better than 99.992%. (Note the different absolute scales because of different normalization.) This extremely good correlation yields compelling evidence for the detailed success of the A_{h} index. Note also that the strong diurnal variation of activity denies a detailed comparison between the K based indices (which include local activity from all LT sectors) and IHV (which includes night sector only). This is a fundamental difference between the K (including A_{h}) indices, and the IHV index, and suggests A_{h} rather than IHV to be used as a longterm proxy or extension of local and global K indices.
6. Conclusions
 Top of page
 Abstract
 1. Introduction
 2. Calculating the A_{h} Index
 3. Centennial Increase and Its Latitudinal Variation
 4. Global A_{h} Indices
 5. Comparison With Ap
 6. Conclusions
 Acknowledgments
 References
 Supporting Information
[21] We have discussed here the K index method of geomagnetic activity and its problems for longterm studies. We have modified the K method so that these problems can be avoided and hourly magnetic data can be used to calculate a new, verifiable and homogeneous index, the A_{h} index, which is dedicated for centennial studies. The A_{h} indices at six stations studied verify that geomagnetic activity has increased during the last century. However, the amount of centennial increase varies greatly with latitude so that the increase is largest at high latitudes, smaller at low latitudes and, unexpectedly, smallest at midlatitudes [Mursula and Martini, 2006].
[22] While the centennial increase in the aa index is roughly twice larger than in midlatitude A_{h} index, comparison with the Ap index verifies that the scaling of the aa index was changed by a few nT in late 1950s, and that the index must be revised [Lockwood et al., 2007; Jarvis, 2005]. Local and global A_{h} indices correlate extremely well with the Ap index, better than aa or the IHV index. A_{h} indices depict a closely similar trend with Ap since 1932, while aa shows a clearly larger trend. Local A_{h} indices depict a very similar diurnal variation as local K indices, yielding compelling evidence that the new method preserves the essential properties of the original K indices. Local A_{h} indices can be used to extend the local K and ak indices by several decennia, and the global A_{h} index gives the most reliable extension of the Ap index by roughly 30 years.