for example , storm types have been defined based on the magnitude of the dst index : minor storm ( 30  nt  >  dst  >  50  nt ) , moderate storm ( 50  nt  >  dst  >  100  nt ) , intense storm ( dst  <  100  nt ) , and great storm ( dst  <  250  nt ) [ e.g. , gonzalez et al . , 1999 ] . the dst index is designed to be a measure of the magnetic perturbation near the equator from currents flowing above the ionosphere . as such , it is adjusted for the sq dayside ionospheric current system and for the secular variation due to changes in the internal magnetic field of the earth . the kyoto dst index baseline is corrected for the secular variation of the earth 's internal magnetic field by making a quadratic fit to each of the four dst observatories by using the last 5  years of magnetic data from that observatory . each year 's contribution to the quadratic fit is based on the five quietest days of each month of that year . ( the five quietest days of each month produce sixty values for that year , which are then averaged to produce a single value for that year . an additional point is added whose value is the baseline value at the end of the current year as determined in the first step , and then a second quadratic fit is done using this additional point [ sugiura and kamei , 1991 ] ) . is determined using a different set of years , a discontinuity occurs at the end of each year and because quiet days during solar maximum may not be as quiet as quiet days during solar minimum , the average dst value may underestimate the change in magnetospheric activity between solar maximum and solar minimum . the main point of this report is that this is the case : the kyoto dst index underestimates the solar cycle variation of magnetic activity . we have previously developed a model of the kyoto dst index based solely on the solar wind [ temerin and li , 2002 , 2006 ] . this model does a good job of duplicating the kyoto dst index for the years 19952002 using the solar wind magnetic field , velocity , and density as input . the model also had a baseline correction with a single discontinuity at the end of 1999 as we were not then aware that there was in fact a discontinuity at the end of each year in the kyoto dst index . we have now extended the model to years 19952009 using omni solar wind data ( instead of using solely wind and ace satellite data ) , added effects based on the f 
 10.7 index and effects using all three components of the solar wind velocity instead of just the vx component . we report on the effect of changing the baseline correction to the model . to find the baseline correction in the model we have made a quadratic fit to each year separately . the coefficients of each year 's quadratic fit are found by minimizing the rms error between the model and the final kyoto dst index . the resulting baseline correction in our model the solar cycle has a minimum based on the sunspot number and the f 
 10.7 index in 1996 and again in 2008 and 2009 and a maximum in 2000 and 2001 . geomagnetic activity has a double peak in 2000 and an even larger peak during the declining phase of the solar cycle in 2003 . the three coefficients in each quadratic expression are found by minimizing the rms difference between the model and kyoto dst index . figure 1 shows the baseline correction added to the model to minimize the rms difference between the model and the kyoto dst index . in particular , conversely , the values in figure 1 can be regarded as the values that need to be subtracted from the kyoto dst index to make it agree with the model . figure 2 shows that the model with the baseline correction agrees well with the kyoto dst index . a comparison of the model output with the kyoto dst index for 3.5  months around the end of the year 2002 . the point of the figure is to show the good agreement between the model and the kyoto dst index . figure 3 ( top ) shows the model error without the baseline correction for the same time period . figure 3 ( bottom ) shows the model error after the baseline correction is applied . ( the kyoto dst index itself changes from 16  nt from the last hour of 2002 to 4  nt for the first hour of 2003 . ) ( top ) the difference ( i.e. , the error ) between the model and the kyoto dst index when the baseline correction is not applied to the model for the period shown in figure 2 . the point of the figure is to demonstrate that the kyoto dst index can have significant discontinuities . figure 4 ( top ) shows the 27  day running average of the kyoto dst index and of the model if no baseline correction is applied . note that there is less solar cycle variation in the averaged kyoto dst index than in the modeled dst index . there is substantially more solar cycle variation in the modeled dst index when no baseline correction is applied . since the kyoto dst index is corrected using quiet days and since quiet days during solar maximum are likely to be less quiet than during solar minimum , the baseline correction we apply to our model to make it agree with the kyoto dst index removes much of the solar cycle variation in the averaged data . the modeled dst with no baseline correction , however , does not remove the solar cycle variation in the process of removing the secular variation . ( top ) a comparison of the 27  day running average of the kyoto dst index with the model with no baseline correction applied . ( bottom ) the good agreement between the 27  day running averages when the baseline correction is applied to the model . it is important to note that our point is that the model without the baseline correction is a far more accurate representation of the effects of magnetospheric currents that affect the magnetic field at dst observatories than the kyoto dst index . figure 4 ( bottom ) compares the 27  day moving averages once the baseline correction is applied to the model . now the agreement between the model and the kyoto dst index is very good ( correlation coefficient  =  0.981 ) . ( except for the baseline coefficients , the coefficients of the model were optimized using only data from the years 19952002 . ) in addition , we have looked at all the year end final kyoto dst data between 1957 and 2009 and found that the average change at the end of the year ( 5.9  nt ) is more than twice as large as in each of the 2  h before and after ( 2.5  nt ) the end of the year , implying an average discontinuity in the kyoto dst index of between 5 and 6  nt at the end of each year . the largest discontinuity appears to have occurred at the end of 1982 when the kyoto dst index decreased by 20  nt for no apparent reason . for any individual year it is not possible to determine the discontinuity by the change at year 's end since some of the change can be physical . but by comparing the model with the dst index as in figure 3 , it can be estimated well . we conclude that the process of removing the secular variation from the kyoto dst index inadvertently removes some of the solar cycle variation . thus , the average value of the kyoto dst index underestimates the modulation effects of the solar cycle on magnetospheric activity and in particular on the ring current . conversely , if one uses the kyoto dst index to remove the magnetospheric current contribution to the magnetic field to determine the secular variation of the magnetic field , one will also get an incorrect result for the secular variation . to find the baseline correction in the model we have made a quadratic fit to each year separately . the coefficients of each year 's quadratic fit are found by minimizing the rms error between the model and the final kyoto dst index . the resulting baseline correction in our model the solar cycle has a minimum based on the sunspot number and the f 
 10.7 index in 1996 and again in 2008 and 2009 and a maximum in 2000 and 2001 . geomagnetic activity has a double peak in 2000 and an even larger peak during the declining phase of the solar cycle in 2003 . the three coefficients in each quadratic expression are found by minimizing the rms difference between the model and kyoto dst index . figure 1 shows the baseline correction added to the model to minimize the rms difference between the model and the kyoto dst index . in particular , conversely , the values in figure 1 can be regarded as the values that need to be subtracted from the kyoto dst index to make it agree with the model . figure 2 shows that the model with the baseline correction agrees well with the kyoto dst index . a comparison of the model output with the kyoto dst index for 3.5  months around the end of the year 2002 . the point of the figure is to show the good agreement between the model and the kyoto dst index . figure 3 ( top ) shows the model error without the baseline correction for the same time period . figure 3 ( bottom ) shows the model error after the baseline correction is applied . ( the kyoto dst index itself changes from 16  nt from the last hour of 2002 to 4  nt for the first hour of 2003 . ) ( top ) the difference ( i.e. , the error ) between the model and the kyoto dst index when the baseline correction is not applied to the model for the period shown in figure 2 . the point of the figure is to demonstrate that the kyoto dst index can have significant discontinuities . figure 4 ( top ) shows the 27  day running average of the kyoto dst index and of the model if no baseline correction is applied . note that there is less solar cycle variation in the averaged kyoto dst index than in the modeled dst index . there is substantially more solar cycle variation in the modeled dst index when no baseline correction is applied . since the kyoto dst index is corrected using quiet days and since quiet days during solar maximum are likely to be less quiet than during solar minimum , the baseline correction we apply to our model to make it agree with the kyoto dst index removes much of the solar cycle variation in the averaged data . the modeled dst with no baseline correction , however , does not remove the solar cycle variation in the process of removing the secular variation . ( top ) a comparison of the 27  day running average of the kyoto dst index with the model with no baseline correction applied . ( bottom ) the good agreement between the 27  day running averages when the baseline correction is applied to the model . it is important to note that our point is that the model without the baseline correction is a far more accurate representation of the effects of magnetospheric currents that affect the magnetic field at dst observatories than the kyoto dst index . figure 4 ( bottom ) compares the 27  day moving averages once the baseline correction is applied to the model . now the agreement between the model and the kyoto dst index is very good ( correlation coefficient  =  0.981 ) . ( except for the baseline coefficients , the coefficients of the model were optimized using only data from the years 19952002 . ) in addition , we have looked at all the year end final kyoto dst data between 1957 and 2009 and found that the average change at the end of the year ( 5.9  nt ) is more than twice as large as in each of the 2  h before and after ( 2.5  nt ) the end of the year , implying an average discontinuity in the kyoto dst index of between 5 and 6  nt at the end of each year . the largest discontinuity appears to have occurred at the end of 1982 when the kyoto dst index decreased by 20  nt for no apparent reason . for any individual year it is not possible to determine the discontinuity by the change at year 's end since some of the change can be physical . but by comparing the model with the dst index as in figure 3 , it can be estimated well . we conclude that the process of removing the secular variation from the kyoto dst index inadvertently removes some of the solar cycle variation . thus , the average value of the kyoto dst index underestimates the modulation effects of the solar cycle on magnetospheric activity and in particular on the ring current . conversely , if one uses the kyoto dst index to remove the magnetospheric current contribution to the magnetic field to determine the secular variation of the magnetic field , one will also get an incorrect result for the secular variation . it is our claim that the baseline as determined by the standard procedure used to remove the secular variation from the kyoto dst index results in significant offsets ( errors ) so that the kyoto dst index and especially its longerterm average do not accurately represent the magnetic effects near the equator of the earth of currents flowing above the ionosphere and that the offsets determined by our model are more accurate . there are discontinuities in the kyoto dst index at the end of each year , which are typically larger during solar maximum and which , it is important to note , affect the level of the kyoto dst index for the rest of the year with respect to the previous year . in addition to the discontinuity at the end of each year , a different quadratic function determines the kyoto dst index baseline during that year . the second part of our claim , that our model provides a better baseline offset , is maybe less clear . it is based on the fact that the model ( without its own offset term ) has no discontinuities at year 's end and generally accurately reproduces the kyoto dst index based on the solar wind and now also on the f 
 10.7 index . it is however possible that if there are additional differences , not captured by the model , in the response of the magnetosphere between solar minimum and solar maximum , that some of the baseline correction determined by the model are corrections to the model 's own incorrect response to the solar wind and the f 
 10.7 index . however , we can think of no reason this should be a large effect . laying aside the above concern we can say that the average value of the kyoto dst index should be approximately 13  nt more negative for the active year 2003 compared to quiet years 2006 and 2009 ( since the values in figure 1 should be subtracted from the dst index to make it agree with model ) and by implication , although we have not modeled other solar cycles , it is likely that the kyoto dst index more generally underestimates the solar cycle modulation of the surface magnetic field due to currents flowing above the ionosphere . the model also suggests that in addition to underestimating the solar cycle variation , the solar minimumquiet baseline of the kyoto dst index should be around 15  nt as is clear from figure 1 while the baseline during solar maximum can vary between about 20  nt and more than 30  nt . that is to say during solar minimum when the kyoto dst index reads 0  nt , currents flowing above the ionosphere produce a negative depression of the surface equatorial magnetic field of about 15  nt while during solar maximum when the kyoto dst index reads 0  nt such currents produce a negative depression of the surface equatorial magnetic field between 20 and 30  nt . we care more about the relative change in the baseline offset between solar minimum and solar maximum than we do about its average value . the relative change is much less sensitive to changes in the model parameters than the average value . nevertheless , we note that our baseline offset has an average value of 21.2  nt ( 23.0  nt if only the first 11  years are used to avoid two solar minima ) . this is very similar to the 20  nt constant in the burton equation [ burton et al . , 1975 ] , which is based on a much simpler model of the response of dst to the solar wind . jorgensen et al . , using crres satellite magnetometer data , also conclude that  there is an offset in the dst index so that dst  =  0 actually corresponds to a ring current that would create a 20  nt depression .  thus , our average baseline offset corresponds well to the effect of the quiet time ring current as determined by others . our results have significant implications for statistical studies of geomagnetic storms . in such studies , thresholds are often set ; such that , for instance , a dst value of less than 30  nt is considered an indication of a geomagnetic storm [ e.g. , gonzalez et al . , 1999 ] and that a period when dst remains above 30  nt is regarded as nonstorm [ e.g. , schiller et al . , 2014 ] . since dst can differ by over 10  nt from nonphysical baseline corrections , threshold values should be carefully considered . we get a correlation coefficient of 0.965 between our model and the kyoto dst index for the years 19952002 using only the solar wind and the f 
 10.7 index ( a good but not perfect [ e.g. , chen et al . , 2011 ] proxy for the solar euv flux and thus for the ionization of the ionosphere ) as input to our model . such a good correlation would not be possible if the kyoto dst index had large random components . still , no index is perfect , and others have also tried to remove its defects , both real and imaginary . the index is created in the same manner as the kyoto dst but extends back to 1932 and corrects a few technical issues with the kyoto dst index . since the secular variation in the dxt index is removed in the same manner as in the kyoto dst index , the problem that we have identified here remains in the dxt index . karinen and mursula   then use annual averages of the dxt index to study the longterm and solar cycle variations of the dxt index . given that the correction for the secular variation can introduce both random and systematic variations in the annual average of dst and dxt , the results of such studies should be accepted with care . mursula and karinen   and karinen and mursula   have also created another index that they call dcx , which they say removes the excessive semiannual variation in the dst index related to the semiannual , nonstorm time behavior of the dst index . we have not noticed an  excessive  semiannual variation in kyoto dst index and suggest that in the same manner that quiet days during solar maximum are on average less quiet than quiet days during solar minimum , quiet days around the equinoxes are less quiet than quiet days around the solstices . this index removes much of residual sq current system variation that remains in the kyoto dst index . the residual sq current system variation is indeed a problem with the kyoto dst index and can dominate the error in our model during quiet times [ temerin and li , 2006 ] . ( much of the highfrequency error seen in figure 3 is probably due to this . ) however , dst 
  also removes other regular variations including the excessive semiannual variation and even perhaps some of the solar cycle variation . also , the magnetosphere has a real diurnal variation since the reconnection rate can depend on the angle between the dipole axis and the solar wind velocity that can also be removed when effects of the sq current system are removed . svalgaard   has suggested using another index ( dsv ) that depends only on nighttime observations to avoid problems with the sq current system that mostly affects daytime observations . the creation of both the dcx and dst 
  indices seems motivated by a desire to remove the nonstorm component of the dst index . we think that making a hard distinction between storm and nonstorm or quiet times in the dst index is not useful . the dst index and the magnetospheric currents that it reflects are constantly changing in response to the changing solar wind . level in the 3.5  months of data shown in figure 2 , and the number of magnetic storms during this interval depends on ones arbitrary threshold for determining storms : there are number of excursions of the dst index below 50  nt and even more below 30  nt . we have shown that the average value of the kyoto dst index should be approximately 13  nt more negative for the active year 2003 compared to quiet years 2006 and 2009 and that discontinuities in the kyoto dst index at the end of each year have an average value of about 5  nt but may be as large as 20  nt . this implies that the kyoto dst index underestimates the solar cycle variation of currents above the ionosphere that affect the surface equatorial magnetic field . our study also implies that quiet time currents above the ionosphere produce a negative depression of the surface equatorial magnetic field of at least 15  nt even during solar minimum and as much as 30  nt during solar maximum .
abstractit is known that the correction of the kyoto dst index for the secular variation of the earth 's internal field produces a discontinuity in the kyoto dst index at the end of each year . 
 we show that this secular correction also introduces a significant baseline error to the kyoto dst index that leads to an underestimate of the solar cycle variation of geomagnetic activity and of the strength of the ring current as measured by the kyoto dst index . 
 thus , the average value of the kyoto dst index would be approximately 13  nt more negative for the active year 2003 compared to quiet years 2006 and 2009 if the kyoto dst index properly measured the effects of the ring current and other currents that influence the dst observatories . 
 discontinuities in the kyoto dst index at the end of each year have an average value of about 5  nt , but the discontinuity at the end of year 2002 was approximately 12  nt , and the discontinuity at the end of year 1982 may have been as large as 20  nt .