K-index

The K-index quantifies disturbances in the horizontal component of Earth's magnetic field with an integer in the range 0–9 with 1 being calm and 5 or more indicating a geomagnetic storm. It is derived from the maximum fluctuations of horizontal components observed on a magnetometer during a three-hour interval. The label K comes from the German word Kennziffer[1] meaning "characteristic digit". The K-index was introduced by Julius Bartels in 1939.[2][1]

Calculation of K-index

The K-scale is quasi-logarithmic. The conversion table from maximum fluctuation R (in units of nano teslas, nT) to K-index, varies from observatory to observatory in such a way that the historical rate of occurrence of certain levels of K are about the same at all observatories. In practice this means that observatories at higher geomagnetic latitude require higher levels of fluctuation for a given K-index. For example, at Godhavn, Greenland, a value of K = 9 is derived with R = 1500 nT, while in Honolulu, Hawaii, a fluctuation of only 300 nT is recorded as K = 9. In Kiel, Germany, K = 9 corresponds to R = 500 nT or greater.[3] The real-time K-index is determined after the end of prescribed intervals of 3 hours each: 00:00–03:00, 03:00–06:00, ..., 21:00–24:00. The maximum positive and negative deviations during the 3 hour period are added together to determine the total maximum fluctuation. These maximum deviations may occur any time during the 3 hour period.

The K_p-index and estimated K_p-index

The official planetary K_p-index is derived by calculating a weighted average of K-indices from a network of 13 geomagnetic observatories at mid-latitude locations. Since these observatories do not report their data in real-time, various operations centers around the globe estimate the index based on data available from their local network of observatories. The K_p-index was introduced by Bartels in 1939.[2]

The relationship between K and A

Plot of a-index vs. K-index

The A-index provides a daily average level for geomagnetic activity. Because of the non-linear relationship of the K-scale to magnetometer fluctuations, it is not meaningful to take the average of a set of K-indices. What is done instead is to convert each K back into a linear scale called the "equivalent three hourly range" a-index (note the lower case "a"), according to the following table:[3][4][5]

Equivalent range a for given K
K	0	0+	1−	1	1+	2−	2	2+	3−	3	3+	4−	4	4+
a	0	2	3	4	5	6	7	9	12	15	18	22	27	32
K	5−	5	5+	6−	6	6+	7−	7	7+	8−	8	8+	9−	9
a	39	48	56	67	80	94	111	132	154	179	207	236	300	400

The daily A-index is merely the average of eight a-indices.

Thus, for example, if the K-indices for the day were 3, 4, 6, 5, 3, 2, 2 and 1, the daily A-index is the average of the equivalent amplitudes:

A=(15+27+80+48+15+7+7+4)/8=25.375

The A_p-index is averaged planetary A-index based on data from a set of specific K_p stations.[4]

G-scale

This is a description of the relationship between the NOAA G-scale and K_p. The K_p-scale is a scientific way to summarize the global level of geomagnetic activity, but it has not always been easy for those affected by the space environment to understand its significance. The NOAA G-scale[6] was designed to correspond, in a straightforward way, to the significance of effects of geomagnetic storms.

Scale and effects of geomagnetic storms
Scale	Level	Effect			K_p equivalent	Average frequency (1 cycle = 11 years)	Days during solar cycle 24[7]
Scale	Level	Power system	Spacecraft operations	Other systems	K_p equivalent	Average frequency (1 cycle = 11 years)	Days during solar cycle 24[7]
G1	Minor	Weak power grid fluctuations can occur.	Minor impact on satellite operations possible.	Migratory animals are affected at this and higher levels; aurora is commonly visible at high latitudes (northern Michigan and Maine).	5	1700 per cycle (900 days per cycle)	256
G2	Moderate	High-latitude power systems may experience voltage alarms, long-duration storms may cause transformer damage.	Corrective actions to orientation may be required by ground control; possible changes in drag affect orbit predictions.	HF radio propagation can fade at higher latitudes, and aurora has been seen as low as New York and Idaho (typically 55° geomagnetic lat.).	6	600 per cycle (360 days per cycle)	86
G3	Strong	Voltage corrections may be required, false alarms triggered on some protection devices.	Surface charging may occur on satellite components, drag may increase on low-Earth-orbit satellites, and corrections may be needed for orientation problems.	Intermittent satellite navigation and low-frequency radio navigation problems may occur, HF radio may be intermittent, and aurora has been seen as low as Illinois and Oregon (typically 50° geomagnetic lat.).	7	200 per cycle (130 days per cycle)	18
G4	Severe	Possible widespread voltage control problems and some protective systems will mistakenly trip out key assets from the grid.	May experience surface charging and tracking problems, corrections may be needed for orientation problems.	Induced pipeline currents affect preventive measures, HF radio propagation sporadic, satellite navigation degraded for hours, low-frequency radio navigation disrupted, and aurora has been seen as low as Alabama and northern California (typically 45° geomagnetic lat.).	8-9	100 per cycle (60 days per cycle)	9
G5	Extreme	Widespread voltage control problems and protective system problems can occur, some grid systems may experience complete collapse or blackouts. Transformers may experience damage.	May experience extensive surface charging, problems with orientation, uplink/downlink and tracking satellites.	Pipeline currents can reach hundreds of amps, HF (high frequency) radio propagation may be impossible in many areas for one to two days, satellite navigation may be degraded for days, low-frequency radio navigation can be out for hours, and aurora has been seen as low as Florida and southern Texas (typically 40° geomagnetic lat.).	9	4 per cycle (4 days per cycle)	0

Use in radio propagation studies

The K_p-index is used for the study and prediction of ionospheric propagation of high frequency radio signals. Geomagnetic storms, indicated by a K_p = 5 or higher, have no direct effect on propagation. However they disturb the F-layer of the ionosphere, especially at middle and high geographical latitudes, causing a so-called ionospheric storm which degrades radio propagation. The degradation mainly consists of a reduction of the maximum usable frequency (MUF) by as much as 50%.[8] Sometimes the E-layer may be affected as well. In contrast with sudden ionospheric disturbances (SID), which affect high frequency radio paths mostly at mid and low latitudes, the effects of ionospheric storms are more intense at high latitudes and the polar regions.

References

Bartels, J.; Heck, N. H.; Johnston, H. F. (1939). "The three‐hour‐range index measuring geomagnetic activity". Journal of Geophysical Research. 44 (4): 411–454. doi:10.1029/TE044i004p00411.
Fleming, J. A.; Harradon, H. D.; Joyce, J. W. (1939). "Seventh General Assembly of the Association of Terrestrial Magnetism and Electricity at Washington, D.C., September 4–15, 1939". Terrestrial Magnetism and Atmospheric Electricity. 44 (4). pp. 477–478, Resolution 2. doi:10.1029/TE044i004p00471.
Davies, Kenneth (1990). Ionospheric Radio. IEE Electromagnetic Waves Series #31. London, UK: Peter Peregrinus Ltd/The Institution of Electrical Engineers. p. 50. ISBN 0-86341-186-X.
"Help on SPIDR Data – Geomagnetic And Solar Indices Data Description". NOAA Space Physics Interactive Data Resource (SPIDR). Archived from the original on 2013-02-20. Retrieved 2012-09-12.
"Geomagnetic kp and ap Indices". NOAA National Centers for Environmental Information (NESDIS). Retrieved 2016-08-21.
NOAA/SWPC Space Weather Scales which are used to communicate to the public current and future space weather conditions and their possible effects
"The aurora and solar activity archive". Space Weather Live. Retrieved 3 March 2022.
George Jacobs and Theodore J. Cohen (1997). The New Shortwave Propagation Handbook. Hicksville, New York: CQ Publishing. p. 1.14. ISBN 0-943016-11-8.

External links

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[Bartels1939-1] Bartels, J.; Heck, N. H.; Johnston, H. F. (1939). "The three‐hour‐range index measuring geomagnetic activity". Journal of Geophysical Research. 44 (4): 411–454. doi:10.1029/TE044i004p00411.

[resolution2-2] Fleming, J. A.; Harradon, H. D.; Joyce, J. W. (1939). "Seventh General Assembly of the Association of Terrestrial Magnetism and Electricity at Washington, D.C., September 4–15, 1939". Terrestrial Magnetism and Atmospheric Electricity. 44 (4). pp. 477–478, Resolution 2. doi:10.1029/TE044i004p00471.

[Davis-3] Davies, Kenneth (1990). Ionospheric Radio. IEE Electromagnetic Waves Series #31. London, UK: Peter Peregrinus Ltd/The Institution of Electrical Engineers. p. 50. ISBN 0-86341-186-X.

[SPIDR-4] "Help on SPIDR Data – Geomagnetic And Solar Indices Data Description". NOAA Space Physics Interactive Data Resource (SPIDR). Archived from the original on 2013-02-20. Retrieved 2012-09-12.

[5] "Geomagnetic kp and ap Indices". NOAA National Centers for Environmental Information (NESDIS). Retrieved 2016-08-21.

[6] NOAA/SWPC Space Weather Scales which are used to communicate to the public current and future space weather conditions and their possible effects

[7] "The aurora and solar activity archive". Space Weather Live. Retrieved 3 March 2022.

[8] George Jacobs and Theodore J. Cohen (1997). The New Shortwave Propagation Handbook. Hicksville, New York: CQ Publishing. p. 1.14. ISBN 0-943016-11-8.