Introduction

Long-range communications using high frequency (HF) radio waves (3 - 30 MHz) depend on reflection of the signals in the ionosphere. Radio waves are typically reflected near the peak of the F2 layer (~300 km altitude), but along the path to the F2 peak and back the radio wave signal suffers attenuation due to absorption by the intervening ionosphere.

Absorption is the process by which the energy of radio waves is converted into heat and electromagnetic (EM) noise through interactions between the radio wave, ionospheric electrons, and the neutral atmosphere (for a more extensive description of the absorption process see Davies, 1990). Most of the absorption occurs in the ionospheric D region (50–90 km altitude) where the product of the electron density and the electron-neutral collision frequency attains a maximum. Within this region the neutral density is relatively constant over time, so variations in the local electron density drive the total amount of absorption. The electron density is a function of many parameters and normally varies with local time, latitude, season, and over the solar cycle. These "natural" changes are predictable, and affect absorption only moderately at the lowest HF frequencies. Much more significant changes to the absorption strength are seen as a result of sudden increases of electron density in the D region (the classic short wave fade) due to, for example, solar X-ray flares on the dayside or solar proton precipitation in the polar regions.

Solar X-ray flares have significant emission in the 0.1-0.8 nm [1-8 Å] wavelength range. This is important because these wavelengths ionize the D region, dramatically increasing local electron density, and hence the total EM absorption. The flares, which can last from a few minutes to several hours, are rated C, M, or X according to the 0.1-0.8 nm flux as measured by instruments on the GOES satellites. To qualify as a C-class flare the flux, F, must fall within the range 10^-6 ≤ F < 10^-5 W·m^-2, for M-class 10^-5 ≤ F < 10^-4 W·m^-2, and X-class F ≥ 10^-4 W·m^-2. In standard notation the letters act as multipliers, for example C3.2 equates to a flux of 3.2 x 10^-6 W·m^-2. The C, M, and X classification is based on the full-disk X-ray emission from the sun. During periods of high solar activity, such as solar maximum, the background flux may increase to C-class levels for days at a time, even without flare activity. The D region electron density is directly driven by the total X-ray flux regardless of the source, so these periods of high background flux are equally important to radio absorption. Due to geometric effects, D region ionization by solar X-rays is greatest at the sub-solar point, where the sun is directly overhead. The amount of ionization and absorption falls with distance away from the sub-solar point, reaching zero at the day/night terminator. The night-side of the Earth is unaffected.

The precipitation of protons (as well as other ions) into the earth’s atmosphere during the Solar Energetic Particle (SEP) events can also create significant enhancements of ionospheric electron densities in the D region. Solar protons with energies between 1 to 200 MeV are primarily responsible for most of ionization of the D region and, consequently, for the ionospheric absorption of HF radio waves. Because of shielding of the earth by its magnetic field SEPs find easy access to the atmosphere only in high latitude regions around the earth’s geomagnetic poles. Such occurrences are therefore termed Polar Cap Absorption (PCA) events. The latitudinal extent of the polar cap in turn is determined by the disturbance level of the geomagnetic field, which is typically characterized by geomagnetic indices such as Kp. Determination of the rate of ion-pair production due to the propagation of energetic particles through the atmosphere requires the input particle spectrum, which is best provided by direct satellite observations, as well as a realistic model of the atmospheric density. Determination of the effective recombination coefficients which determine the resulting electron density profiles is less certain. These parameters depend upon a complex atmospheric chemistry and so upon altitude, time of day, season, and solar illumination. As a consequence of these dependencies, the day-time and night-time recombination and detachment rates are significantly different and therefore result in quite different levels of absorption for same incident energetic particle spectrum.

Product

The D Region Absorption Product addresses the operational impact of the solar X-ray flux and SEP events on HF radio communication. 

The main product consists of following four dynamic components: a global map of the highest frequency affected by absorption of 1 dB due to either solar X-ray flux or SEP events or a combination of both, an attenuation bar graph, status messages, and an estimated recovery clock. Each of these components is described below. All of the components update continuously, driven by one-minute GOES X-ray flux data and by five-minute GOES proton flux data.

To complement the global frequency map, polar projection maps of the highest frequency affected by absorption of 10 dB due to primarily to SEP events are also available by clicking on the North Pole and South Pole links. The Tabular Values link displays numeric values of the frequency map in 5 degree latitude and 15 degree longitude increments.

Frequency Maps

The global and polar frequency maps graphically illustrate the Highest Affected Frequency (HAF) as a function of latitude and longitude. For the global map we define HAF as the frequency which suffers a loss of 1 dB during vertical propagation from the ground, through the ionosphere, and back to ground. Radio frequencies lower than the HAF suffer an even greater loss as described in the Attenuation Bar Graph section. Since the ionization rates and absorption during SEP events are generally larger, for the polar maps we define HAF as the frequency which suffers a loss of 10 dB during vertical propagation to the ionosphere and back to the ground.  

X-ray absorption

The X-ray HAF is calculated at the sub-solar point based on the current X-ray flux value. This calculation is made using an empirical formula derived from the following relationships between solar X-ray flux at 0.1-0.8 nm and degraded frequency (Space Environmental Forecaster Operations Manual):

M1.0 -> 15 MHz

M5.0 -> 20 MHz

X1.0 -> 25 MHz

X5.0 -> 30 MHz

A fit of these empirically derived relationships results in the following equation for the sub-solar highest affected frequency:

HAF = 10·log[flux (W·m^-2)] + 65 MHz

At other geographic locations the HAF becomes lower, based on the solar zenith angle χ dependence. The degraded frequencies taper off from the maximum as (cosχ)^0.75. For example, an M5.0 flare shows a HAF of 20 MHz at the sub-solar point decreasing to zero at the day/night terminator.

SEP Absorption

Absorption in the polar regions due to SEP events is calculated following the algorithm described in detail by Sauer and Wilkinson (2008). Daytime and nighttime polar cap absorption, A_d and A_n, at the standard frequency 30 MHz is calculated first depending on the integral proton fluxes J above certain energy E thresholds:

A_d = 0.115 [J(E>5.2 MeV)]^1/2 dB

A_n = 0.020 [J(E>2.2 MeV)]^1/2 dB

These values are assumed to be effective for the solar elevation angle greater than 10^o or smaller than -10^o, respectively. In the twilight zone between the two limits a bilinear interpolation in the solar elevation angle is adopted. The geographic extent of the affected polar region is derived from a numerical model of the proton cutoff energy as a function of invariant latitude and geomagnetic activity index K_p (Sauer and Wilkinson, 2008). The cutoff energy then replaces the energy thresholds in the above expressions for A_d and A_n in order to include only protons able to reach the altitude of 50 km.

Combined Absorption

Absorption at any given frequency f (in MHz) due to either ionization mechanism may be determined from absorption calculated at any other frequency f₀ using the well-established empirical relation (Davies, 1990; Stonehocker, 1970; Sauer and Wilkinson, 2008):

                           A(f) = (f₀/f)^1.5A(f₀) dB,

where f₀ may equal the HAF for solar X-rays or the standard frequency of 30 MHz for SEP absorption. Using this equation we can determine the absorption due to both mechanisms at the same control frequency, say, f_c = 10 MHz. The combined absorption at this frequency A_c = A(f_c) is then calculated as a sum of the absorption due to solar X-rays and the absorption due to solar proton precipitation:

                           A_c = A_X + A_P dB

Using the above power-law dependence of absorption on frequency, the frequency f₁ at which the combined absorption equals 1 dB may be easily calculated for the global map:

                           f₁ = f_c(A_c/A₁)^2/3 MHz,

where A₁ = 1 dB. For the polar projection map, the frequency f₁₀ attenuated by 10 dB is calculated using the same equation but with A₁replaced by A₁₀ = 10 dB. 

Attenuation Bar Graph

A bar graph on the right-hand side of the graphic displays the expected attenuation in decibels as a function of frequency for vertical radio wave propagation at the point of maximum absorption Amax on the globe. This graph is only valid at this point, although users can re-create it for any location using the tabular data. The displayed values can also be scaled to approximately account for oblique radio wave propagation using the 1/sin(α) dependence, where α is the elevation angle of the propagation path.

Status Messages

Text messages appear at the bottom of the frequency map based on the following criteria:

Where "Background" refers to the previous day's background x-ray flux. It is estimated by using the lower of two values, either (a) the average of 1-minute data between 0800 UT and 1600 UT, or (b) the average of the 0000 UT to 0800 UT and the 1600 UT to 2400 UT data.

Estimated Recovery Clock

X-rays

After an X-ray event (defined as flux greater than M1 levels) peaks and the flux begins to decrease, an estimated recovery time to normal background conditions is calculated. The estimate is based on the following empirically derived values relating the magnitude of a flare to the statistical average of the flare duration:

             M1.0 ->  25 minutes 

             M5.0 ->  40 minutes 

             X1.0 ->  60 minutes 

             X5.0 -> 120 minutes

(Space Environmental Forecaster Operations Manual, 1997)

The above values are fit using the following set of equations, where k = log[2 × background flux]. In order to determine which equation to use, the algorithm sequentially tests the current x-ray flux against the listed criteria.

log[flux] ≤ -5.7  
   or 
≤ k

0

-5.7 < log[flux] <  -5.0
   or
k < log[flux] <  -5.0

25×(k - log[flux])/(k + 5)

-5.0 ≤ log[flux] ≤ -3.3

32.19×(log[flux])^2 + 

323.45×(log[flux]) + 837.2     

log[flux] > -3.3

100×(log[flux]) + 450

SEP

An empirical relationship for a recovery time after SEP events has been developed from the analysis of 30 largest events over the 7-year period from 1997 to 2003 (Sauer and Wilkinson, 2008). It relates the minimum time to event end, Dur, to the integral flux of protons with energy greater than 10 MeV:

                           Dur = 24.235 log₁₀(flux/15) hr

where flux is measured in protons per cm²·s·sr.

Combined

In the case of overlapping X-ray and SEP events, the estimated recovery time clock displays the longest of the two recovery times.

The program uses the current X-ray and proton flux data to re-calculate the estimated recovery time every minute. It is therefore possible that the clock will not countdown sequentially as it updates. For example, if the duration of an X-ray flare is extremely short, the clock might read 25 min, 20 min, 15 min, 5 min after each update. Conversely, if the duration is especially long, the clock might read 25 min, 25 min, 25 min, 24 min, ect. as it updates. Likewise, during the rising phase of SEP events, the estimated time to recovery may be substantially underestimated until the peak flux value is reached.

When the flux is increasing or no event is in progress, the dialog box displays "No Estimate".

References

1. Davies, K., Ionospheric Radio. Peregrinus Ltd., London, UK. 1990.
2. Sauer, H. H., and D. C. Wilkinson, A Global Space Weather Model of Ionospheric HF/VHF Radio-Wave Absorption due to Solar Energetic Protons,Space Weather, submitted, 2008.
3. Space Environmental Forecaster Operations Manual, page 4.3.1, 55th Space Weather Squadron, Falcon AFB, USAF, 21 October 1997.
4. Stonehocker, G. H., Advanced Telecommunication Forecasting Technique, in Ionospheric Forecasting, AGARD CONF. Proc. No. 49, Advisory Group for Aerospace Research and Development, NATO; Agy, V. (Ed), p27-1, 1970.

Please send questions and comments to Mihail.Codrescu@noaa.gov.

Updated: May 11, 2010